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I received my BS in Environment Engineering from Henan Polytechnic University, and then received MS in Geographyic Infromation Science from China University of Mining and Technology (Being) . In 2011, I received Doctor degree in Tectonic Geology from Peking University.","image":"https://0.academia-photos.com/17238727/5176201/89171765/s200_yi.jin.jpg","thumbnailUrl":"https://0.academia-photos.com/17238727/5176201/89171765/s65_yi.jin.jpg","primaryImageOfPage":{"@type":"ImageObject","url":"https://0.academia-photos.com/17238727/5176201/89171765/s200_yi.jin.jpg","width":200},"sameAs":["http://rei.hpu.edu.cn/TeacherShow.aspx?id=83"],"relatedLink":"https://www.academia.edu/100863232/Morphology_differences_between_fractional_Brownian_motion_and_the_Weierstrass_Mandelbrot_function_and_corresponding_Hurst_evaluation"}</script><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/heading-95367dc03b794f6737f30123738a886cf53b7a65cdef98a922a98591d60063e3.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/button-8c9ae4b5c8a2531640c354d92a1f3579c8ff103277ef74913e34c8a76d4e6c00.css" /><link rel="stylesheet" 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I received my BS in Environment Engineering from Henan Polytechnic University, and then received MS in Geographyic Infromation Science from China University of Mining and Technology (Being) . In 2011, I received Doctor degree in Tectonic Geology from Peking University.<br /><b>Address: </b>Jiaozuo, Henan, China<br /><div class="js-profile-less-about u-linkUnstyled u-tcGrayDarker u-textDecorationUnderline u-displayNone">less</div></div></div><div class="suggested-academics-container"><div class="suggested-academics--header"><h3 class="ds2-5-heading-sans-serif-xs">Related Authors</h3></div><ul class="suggested-user-card-list" data-nosnippet="true"><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a data-nosnippet="" href="https://independent.academia.edu/NicolaPastore"><img class="profile-avatar u-positionAbsolute" alt="Nicola Pastore related author profile picture" border="0" src="//a.academia-assets.com/images/s200_no_pic.png" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" 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href="https://www.academia.edu/100863232/Morphology_differences_between_fractional_Brownian_motion_and_the_Weierstrass_Mandelbrot_function_and_corresponding_Hurst_evaluation"><img alt="Research paper thumbnail of Morphology differences between fractional Brownian motion and the Weierstrass-Mandelbrot function and corresponding Hurst evaluation" class="work-thumbnail" src="https://attachments.academia-assets.com/101564205/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100863232/Morphology_differences_between_fractional_Brownian_motion_and_the_Weierstrass_Mandelbrot_function_and_corresponding_Hurst_evaluation">Morphology differences between fractional Brownian motion and the Weierstrass-Mandelbrot function and corresponding Hurst evaluation</a></div><div class="wp-workCard_item"><span>Geomechanics and Geophysics for Geo-Energy and Geo-Resources</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Fractional Brownian motion (FBM) and the Weierstrass-Mandelbrot (W-M) function are two important ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Fractional Brownian motion (FBM) and the Weierstrass-Mandelbrot (W-M) function are two important methods for constructing self-affine objects. Accurately characterizing their features, such as the morphology and fractal geometry, is fundamental for their follow-up applications. However, due to the differences between self-similar and self-affine properties, the fractal dimension evaluation is difficult and sometimes unconvincing. In addition, the sampling length and diversity of calculation methods both lead to the non-uniqueness of the fractal dimension. This study compared the morphology differences between FBM and the W-M function and then analyzed the effects of each parameter on their morphology. Comparisons indicated that FBM has fewer control parameters than the W-M function. Finally, from basic fractal geometric properties, we derived the relationship between the measurement scale r and profile lengths L(r) for self-affine profiles and found that it is a complicated form rat...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="a5d44ffdac9a75f047ace48731b54ee8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101564205,"asset_id":100863232,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101564205/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100863232"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100863232"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100863232; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=100863232]").text(description); $(".js-view-count[data-work-id=100863232]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 100863232; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='100863232']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "a5d44ffdac9a75f047ace48731b54ee8" } } $('.js-work-strip[data-work-id=100863232]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":100863232,"title":"Morphology differences between fractional Brownian motion and the Weierstrass-Mandelbrot function and corresponding Hurst evaluation","translated_title":"","metadata":{"abstract":"Fractional Brownian motion (FBM) and the Weierstrass-Mandelbrot (W-M) function are two important methods for constructing self-affine objects. Accurately characterizing their features, such as the morphology and fractal geometry, is fundamental for their follow-up applications. However, due to the differences between self-similar and self-affine properties, the fractal dimension evaluation is difficult and sometimes unconvincing. In addition, the sampling length and diversity of calculation methods both lead to the non-uniqueness of the fractal dimension. This study compared the morphology differences between FBM and the W-M function and then analyzed the effects of each parameter on their morphology. Comparisons indicated that FBM has fewer control parameters than the W-M function. Finally, from basic fractal geometric properties, we derived the relationship between the measurement scale r and profile lengths L(r) for self-affine profiles and found that it is a complicated form rat...","publisher":"Springer Science and Business Media LLC","ai_title_tag":"FBM vs W-M Function: Morphology and Hurst Analysis","publication_name":"Geomechanics and Geophysics for Geo-Energy and Geo-Resources"},"translated_abstract":"Fractional Brownian motion (FBM) and the Weierstrass-Mandelbrot (W-M) function are two important methods for constructing self-affine objects. Accurately characterizing their features, such as the morphology and fractal geometry, is fundamental for their follow-up applications. However, due to the differences between self-similar and self-affine properties, the fractal dimension evaluation is difficult and sometimes unconvincing. In addition, the sampling length and diversity of calculation methods both lead to the non-uniqueness of the fractal dimension. This study compared the morphology differences between FBM and the W-M function and then analyzed the effects of each parameter on their morphology. Comparisons indicated that FBM has fewer control parameters than the W-M function. Finally, from basic fractal geometric properties, we derived the relationship between the measurement scale r and profile lengths L(r) for self-affine profiles and found that it is a complicated form rat...","internal_url":"https://www.academia.edu/100863232/Morphology_differences_between_fractional_Brownian_motion_and_the_Weierstrass_Mandelbrot_function_and_corresponding_Hurst_evaluation","translated_internal_url":"","created_at":"2023-04-27T08:09:52.848-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":101564205,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/101564205/thumbnails/1.jpg","file_name":"s40948-023-00532-4.pdf","download_url":"https://www.academia.edu/attachments/101564205/download_file","bulk_download_file_name":"Morphology_differences_between_fractiona.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/101564205/s40948-023-00532-4-libre.pdf?1682609922=\u0026response-content-disposition=attachment%3B+filename%3DMorphology_differences_between_fractiona.pdf\u0026Expires=1743389187\u0026Signature=YCkNqmI2JsINgwIJdnA1bEBrzwD2dVDeA6gKgyExIue~NLe8g8bthwF~~hRVN3FEs~nH6YfK1fGkkA7fVgvvE-YJ-FpsM~uQXgmpmfk8BSiXHds1II1w09lTSP4aP-b-rksjffpvn2fv1-QGX5oIFUZPyh3~a-za6rFERe11aVcQ8iXb4cvG-I~8YJ~v05ccwPvEA60~UAUmxabuv5nq6HddcQTupfbi0weM4UmoU5jDSUAS6fjdmaVny-HM6GPebMV1Et5S1PknfsM1v60wI32J6KKhg-q4Lnu4DYwa0kxiFUlQLVquNhBoI3dkBGpqeDUd604l4c32~gOTs~d3ZQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Morphology_differences_between_fractional_Brownian_motion_and_the_Weierstrass_Mandelbrot_function_and_corresponding_Hurst_evaluation","translated_slug":"","page_count":15,"language":"en","content_type":"Work","summary":"Fractional Brownian motion (FBM) and the Weierstrass-Mandelbrot (W-M) function are two important methods for constructing self-affine objects. Accurately characterizing their features, such as the morphology and fractal geometry, is fundamental for their follow-up applications. However, due to the differences between self-similar and self-affine properties, the fractal dimension evaluation is difficult and sometimes unconvincing. In addition, the sampling length and diversity of calculation methods both lead to the non-uniqueness of the fractal dimension. This study compared the morphology differences between FBM and the W-M function and then analyzed the effects of each parameter on their morphology. Comparisons indicated that FBM has fewer control parameters than the W-M function. Finally, from basic fractal geometric properties, we derived the relationship between the measurement scale r and profile lengths L(r) for self-affine profiles and found that it is a complicated form rat...","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":101564205,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/101564205/thumbnails/1.jpg","file_name":"s40948-023-00532-4.pdf","download_url":"https://www.academia.edu/attachments/101564205/download_file","bulk_download_file_name":"Morphology_differences_between_fractiona.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/101564205/s40948-023-00532-4-libre.pdf?1682609922=\u0026response-content-disposition=attachment%3B+filename%3DMorphology_differences_between_fractiona.pdf\u0026Expires=1743389187\u0026Signature=YCkNqmI2JsINgwIJdnA1bEBrzwD2dVDeA6gKgyExIue~NLe8g8bthwF~~hRVN3FEs~nH6YfK1fGkkA7fVgvvE-YJ-FpsM~uQXgmpmfk8BSiXHds1II1w09lTSP4aP-b-rksjffpvn2fv1-QGX5oIFUZPyh3~a-za6rFERe11aVcQ8iXb4cvG-I~8YJ~v05ccwPvEA60~UAUmxabuv5nq6HddcQTupfbi0weM4UmoU5jDSUAS6fjdmaVny-HM6GPebMV1Et5S1PknfsM1v60wI32J6KKhg-q4Lnu4DYwa0kxiFUlQLVquNhBoI3dkBGpqeDUd604l4c32~gOTs~d3ZQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":30970925,"url":"https://link.springer.com/content/pdf/10.1007/s40948-023-00532-4.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-100863232-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="91334815"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/91334815/Seepage_Characteristics_Study_of_Single_Rough_Fracture_Based_on_Numerical_Simulation"><img alt="Research paper thumbnail of Seepage Characteristics Study of Single Rough Fracture Based on Numerical Simulation" class="work-thumbnail" src="https://attachments.academia-assets.com/94651489/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/91334815/Seepage_Characteristics_Study_of_Single_Rough_Fracture_Based_on_Numerical_Simulation">Seepage Characteristics Study of Single Rough Fracture Based on Numerical Simulation</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A single fracture is the basic unit of fracture medium, and the roughness of fracture wall surfac...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A single fracture is the basic unit of fracture medium, and the roughness of fracture wall surface is an important factor influencing hydraulic characteristics of the ﬂow in bedrock fracture. However, effects of the shape and density of roughness elements (various bulges/pits on rough fracture wall surfaces) on water ﬂow in a single rough fracture have not been thoroughly discovered. Thus the water ﬂow in single fracture with different shapes and densities of roughness elements was simulated by using Fluent software in this study. The results show that in wider fractures the flow rate mainly depends on fracture aperture, while in narrow and close fracture medium the surface roughness of fracture wall is the main factor of head loss of seepage; there is a negative power exponential relation between the hydraulic gradient index and the average fracture aperture, i.e. with the increase of fracture aperture, the relative roughness of fracture and the influence weight of hydraulic gradie...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d64c83bdf313fe0064afc6c1a2c53ebf" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":94651489,"asset_id":91334815,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/94651489/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91334815"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91334815"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91334815; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=91334815]").text(description); $(".js-view-count[data-work-id=91334815]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 91334815; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='91334815']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "d64c83bdf313fe0064afc6c1a2c53ebf" } } $('.js-work-strip[data-work-id=91334815]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":91334815,"title":"Seepage Characteristics Study of Single Rough Fracture Based on Numerical Simulation","translated_title":"","metadata":{"abstract":"A single fracture is the basic unit of fracture medium, and the roughness of fracture wall surface is an important factor influencing hydraulic characteristics of the ﬂow in bedrock fracture. However, effects of the shape and density of roughness elements (various bulges/pits on rough fracture wall surfaces) on water ﬂow in a single rough fracture have not been thoroughly discovered. Thus the water ﬂow in single fracture with different shapes and densities of roughness elements was simulated by using Fluent software in this study. The results show that in wider fractures the flow rate mainly depends on fracture aperture, while in narrow and close fracture medium the surface roughness of fracture wall is the main factor of head loss of seepage; there is a negative power exponential relation between the hydraulic gradient index and the average fracture aperture, i.e. with the increase of fracture aperture, the relative roughness of fracture and the influence weight of hydraulic gradie...","publisher":"MDPI AG"},"translated_abstract":"A single fracture is the basic unit of fracture medium, and the roughness of fracture wall surface is an important factor influencing hydraulic characteristics of the ﬂow in bedrock fracture. However, effects of the shape and density of roughness elements (various bulges/pits on rough fracture wall surfaces) on water ﬂow in a single rough fracture have not been thoroughly discovered. Thus the water ﬂow in single fracture with different shapes and densities of roughness elements was simulated by using Fluent software in this study. The results show that in wider fractures the flow rate mainly depends on fracture aperture, while in narrow and close fracture medium the surface roughness of fracture wall is the main factor of head loss of seepage; there is a negative power exponential relation between the hydraulic gradient index and the average fracture aperture, i.e. with the increase of fracture aperture, the relative roughness of fracture and the influence weight of hydraulic gradie...","internal_url":"https://www.academia.edu/91334815/Seepage_Characteristics_Study_of_Single_Rough_Fracture_Based_on_Numerical_Simulation","translated_internal_url":"","created_at":"2022-11-21T22:41:41.666-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":94651489,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/94651489/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/94651489/download_file","bulk_download_file_name":"Seepage_Characteristics_Study_of_Single.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/94651489/pdf-libre.pdf?1669100565=\u0026response-content-disposition=attachment%3B+filename%3DSeepage_Characteristics_Study_of_Single.pdf\u0026Expires=1743389187\u0026Signature=RP4SRBov~yGMn-Qdcm0Os97ZgiZ1CX8~tErJzR0A1r-Uk9VIqUTNjOLde1tuo~QVVC1sEKxNOxJmFNBStuqY9vRRQYJq7BmaPqy1G1nok0IL9EUf00FdqtG5GSwPNLZvbC5vHVuGzo1CGjyqYYJT5h7cVACN7LRl0j9O~oef5GdaGGDOjEHup2~tK~w1GF2Gk1SzbhJHiQfAt0ucLzPtd7EG8xLz5TSFHHyJVQ0DIfaccorEpwxwUSrZJ6fcN3HLr0qXBJIwONbEYdkPpPlJQ3ROi9H~GWLExtGtcmTnYHNH3UaaILyv56pu7bLjGEoDXvHSUiiRp12ThHZFAhvSLA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Seepage_Characteristics_Study_of_Single_Rough_Fracture_Based_on_Numerical_Simulation","translated_slug":"","page_count":16,"language":"en","content_type":"Work","summary":"A single fracture is the basic unit of fracture medium, and the roughness of fracture wall surface is an important factor influencing hydraulic characteristics of the ﬂow in bedrock fracture. However, effects of the shape and density of roughness elements (various bulges/pits on rough fracture wall surfaces) on water ﬂow in a single rough fracture have not been thoroughly discovered. Thus the water ﬂow in single fracture with different shapes and densities of roughness elements was simulated by using Fluent software in this study. The results show that in wider fractures the flow rate mainly depends on fracture aperture, while in narrow and close fracture medium the surface roughness of fracture wall is the main factor of head loss of seepage; there is a negative power exponential relation between the hydraulic gradient index and the average fracture aperture, i.e. with the increase of fracture aperture, the relative roughness of fracture and the influence weight of hydraulic gradie...","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":94651489,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/94651489/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/94651489/download_file","bulk_download_file_name":"Seepage_Characteristics_Study_of_Single.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/94651489/pdf-libre.pdf?1669100565=\u0026response-content-disposition=attachment%3B+filename%3DSeepage_Characteristics_Study_of_Single.pdf\u0026Expires=1743389187\u0026Signature=RP4SRBov~yGMn-Qdcm0Os97ZgiZ1CX8~tErJzR0A1r-Uk9VIqUTNjOLde1tuo~QVVC1sEKxNOxJmFNBStuqY9vRRQYJq7BmaPqy1G1nok0IL9EUf00FdqtG5GSwPNLZvbC5vHVuGzo1CGjyqYYJT5h7cVACN7LRl0j9O~oef5GdaGGDOjEHup2~tK~w1GF2Gk1SzbhJHiQfAt0ucLzPtd7EG8xLz5TSFHHyJVQ0DIfaccorEpwxwUSrZJ6fcN3HLr0qXBJIwONbEYdkPpPlJQ3ROi9H~GWLExtGtcmTnYHNH3UaaILyv56pu7bLjGEoDXvHSUiiRp12ThHZFAhvSLA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":3717,"name":"Geotechnical Engineering","url":"https://www.academia.edu/Documents/in/Geotechnical_Engineering"},{"id":33296,"name":"Surface Roughness","url":"https://www.academia.edu/Documents/in/Surface_Roughness"},{"id":159232,"name":"Applied Sciences","url":"https://www.academia.edu/Documents/in/Applied_Sciences"},{"id":236358,"name":"Hydraulic Roughness","url":"https://www.academia.edu/Documents/in/Hydraulic_Roughness"},{"id":1342788,"name":"Surface Finish","url":"https://www.academia.edu/Documents/in/Surface_Finish"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-91334815-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="91334812"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/91334812/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures"><img alt="Research paper thumbnail of Validity of triple-effect model for fluid flow in mismatched, self-affine fractures" class="work-thumbnail" src="https://attachments.academia-assets.com/94651493/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/91334812/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures">Validity of triple-effect model for fluid flow in mismatched, self-affine fractures</a></div><div class="wp-workCard_item"><span>Advances in Water Resources</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="347e320d4ca948e82250edd9a234d274" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":94651493,"asset_id":91334812,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/94651493/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91334812"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91334812"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91334812; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=91334812]").text(description); $(".js-view-count[data-work-id=91334812]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 91334812; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='91334812']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "347e320d4ca948e82250edd9a234d274" } } $('.js-work-strip[data-work-id=91334812]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":91334812,"title":"Validity of triple-effect model for fluid flow in mismatched, self-affine fractures","translated_title":"","metadata":{"publisher":"Elsevier BV","grobid_abstract":"This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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However, the c...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hu...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="26a49c359b4cfd250eb2ccd900ae8420" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":94651226,"asset_id":91334527,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/94651226/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91334527"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91334527"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91334527; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=91334527]").text(description); $(".js-view-count[data-work-id=91334527]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 91334527; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='91334527']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "26a49c359b4cfd250eb2ccd900ae8420" } } $('.js-work-strip[data-work-id=91334527]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":91334527,"title":"Definition of fractal topography to essential understanding of scale-invariance","translated_title":"","metadata":{"abstract":"Fractal behavior is scale-invariant and widely characterized by fractal dimension. 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In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstructures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity, including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framewo...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="82355316"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="82355316"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 82355316; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=82355316]").text(description); $(".js-view-count[data-work-id=82355316]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 82355316; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='82355316']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=82355316]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":82355316,"title":"Systematic Definition of Complexity Assembly in Fractal Porous Media","translated_title":"","metadata":{"abstract":"Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. 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The results indicate that our framewo...","internal_url":"https://www.academia.edu/82355316/Systematic_Definition_of_Complexity_Assembly_in_Fractal_Porous_Media","translated_internal_url":"","created_at":"2022-06-29T09:43:51.871-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Systematic_Definition_of_Complexity_Assembly_in_Fractal_Porous_Media","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstructures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity, including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framewo...","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[],"research_interests":[{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics"},{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics"},{"id":511,"name":"Materials Science","url":"https://www.academia.edu/Documents/in/Materials_Science"},{"id":24831,"name":"Fractals","url":"https://www.academia.edu/Documents/in/Fractals"},{"id":172625,"name":"Fractal","url":"https://www.academia.edu/Documents/in/Fractal"},{"id":890611,"name":"Fractal Dimension","url":"https://www.academia.edu/Documents/in/Fractal_Dimension"},{"id":2689528,"name":"self-affinity","url":"https://www.academia.edu/Documents/in/self-affinity"},{"id":3797714,"name":"Behavioral complexity","url":"https://www.academia.edu/Documents/in/Behavioral_complexity"}],"urls":[{"id":21807890,"url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218348X20500796"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-82355316-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="44531334"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/44531334/Characterizing_the_complexity_assembly_of_pore_structure_in_a_coal_matrix_principle_methodology_and_modeling_application"><img alt="Research paper thumbnail of Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title">Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application</div><div class="wp-workCard_item"><span>Journal of Geophysical Research: Solid Earth</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The pore structure in a coal matrix is a dual‐porosity system where fractures and pores coexist a...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The pore structure in a coal matrix is a dual‐porosity system where fractures and pores coexist and feature scale‐invariance properties, that would affect the occurrence and migration of coalbed methane (CBM) significantly. Therefore, it is of fundamental importance to well define complexity types and effectively characterize their assembly mechanism of pore structure in a coal matrix. Here we identify the pore structure in a coal matrix as a dual‐complexity system consisting of original complexity and behavioral complexity independent to each other, where the former determines the scaling types of single‐ or dual‐porosity structure, while the latter dominates the scale‐invariance properties of self‐similarity, self‐affinity, and multifractality. Next we clarify the essentials of scale‐invariance properties and unify the definition of behavioral complexity. By employing Voronoi diagrams, we develop a dual‐porosity coupling algorithm to describe the original complexity, and set up a mathematical framework to characterize the complexity assembly in fractal dual‐porosity media. For modeling demonstration, we select some typical coal samples from different reservoirs in China, extract the scale‐invariance parameters and establish fractal topography based on mercury intrusion porosimetry (MIP) and N2 adsorption data. Using experimental tests, mathematical derivation and numerical simulations in combination, we reveal the principle and methodology for the characterization of the complexity assembly in a coal matrix.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="44531334"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="44531334"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 44531334; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=44531334]").text(description); $(".js-view-count[data-work-id=44531334]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 44531334; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='44531334']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=44531334]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":44531334,"title":"Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application","translated_title":"","metadata":{"doi":"10.1029/2020JB020110","abstract":"The pore structure in a coal matrix is a dual‐porosity system where fractures and pores coexist and feature scale‐invariance properties, that would affect the occurrence and migration of coalbed methane (CBM) significantly. Therefore, it is of fundamental importance to well define complexity types and effectively characterize their assembly mechanism of pore structure in a coal matrix. Here we identify the pore structure in a coal matrix as a dual‐complexity system consisting of original complexity and behavioral complexity independent to each other, where the former determines the scaling types of single‐ or dual‐porosity structure, while the latter dominates the scale‐invariance properties of self‐similarity, self‐affinity, and multifractality. Next we clarify the essentials of scale‐invariance properties and unify the definition of behavioral complexity. By employing Voronoi diagrams, we develop a dual‐porosity coupling algorithm to describe the original complexity, and set up a mathematical framework to characterize the complexity assembly in fractal dual‐porosity media. For modeling demonstration, we select some typical coal samples from different reservoirs in China, extract the scale‐invariance parameters and establish fractal topography based on mercury intrusion porosimetry (MIP) and N2 adsorption data. Using experimental tests, mathematical derivation and numerical simulations in combination, we reveal the principle and methodology for the characterization of the complexity assembly in a coal matrix.","publication_date":{"day":null,"month":null,"year":2020,"errors":{}},"publication_name":"Journal of Geophysical Research: Solid Earth"},"translated_abstract":"The pore structure in a coal matrix is a dual‐porosity system where fractures and pores coexist and feature scale‐invariance properties, that would affect the occurrence and migration of coalbed methane (CBM) significantly. Therefore, it is of fundamental importance to well define complexity types and effectively characterize their assembly mechanism of pore structure in a coal matrix. Here we identify the pore structure in a coal matrix as a dual‐complexity system consisting of original complexity and behavioral complexity independent to each other, where the former determines the scaling types of single‐ or dual‐porosity structure, while the latter dominates the scale‐invariance properties of self‐similarity, self‐affinity, and multifractality. Next we clarify the essentials of scale‐invariance properties and unify the definition of behavioral complexity. By employing Voronoi diagrams, we develop a dual‐porosity coupling algorithm to describe the original complexity, and set up a mathematical framework to characterize the complexity assembly in fractal dual‐porosity media. For modeling demonstration, we select some typical coal samples from different reservoirs in China, extract the scale‐invariance parameters and establish fractal topography based on mercury intrusion porosimetry (MIP) and N2 adsorption data. Using experimental tests, mathematical derivation and numerical simulations in combination, we reveal the principle and methodology for the characterization of the complexity assembly in a coal matrix.","internal_url":"https://www.academia.edu/44531334/Characterizing_the_complexity_assembly_of_pore_structure_in_a_coal_matrix_principle_methodology_and_modeling_application","translated_internal_url":"","created_at":"2020-11-18T22:48:58.127-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":35964000,"work_id":44531334,"tagging_user_id":17238727,"tagged_user_id":42433086,"co_author_invite_id":null,"email":"c***i@yeah.net","display_order":0,"name":"Mengyu Zhao","title":"Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application"},{"id":35964001,"work_id":44531334,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832185,"email":"z***g@163.com","display_order":4194304,"name":"Junling Zheng","title":"Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application"},{"id":35964002,"work_id":44531334,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6910670,"email":"l***x@hpu.edu.cn","display_order":6291456,"name":"Shunxi Liu","title":"Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application"}],"downloadable_attachments":[],"slug":"Characterizing_the_complexity_assembly_of_pore_structure_in_a_coal_matrix_principle_methodology_and_modeling_application","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"The pore structure in a coal matrix is a dual‐porosity system where fractures and pores coexist and feature scale‐invariance properties, that would affect the occurrence and migration of coalbed methane (CBM) significantly. Therefore, it is of fundamental importance to well define complexity types and effectively characterize their assembly mechanism of pore structure in a coal matrix. Here we identify the pore structure in a coal matrix as a dual‐complexity system consisting of original complexity and behavioral complexity independent to each other, where the former determines the scaling types of single‐ or dual‐porosity structure, while the latter dominates the scale‐invariance properties of self‐similarity, self‐affinity, and multifractality. Next we clarify the essentials of scale‐invariance properties and unify the definition of behavioral complexity. By employing Voronoi diagrams, we develop a dual‐porosity coupling algorithm to describe the original complexity, and set up a mathematical framework to characterize the complexity assembly in fractal dual‐porosity media. For modeling demonstration, we select some typical coal samples from different reservoirs in China, extract the scale‐invariance parameters and establish fractal topography based on mercury intrusion porosimetry (MIP) and N2 adsorption data. Using experimental tests, mathematical derivation and numerical simulations in combination, we reveal the principle and methodology for the characterization of the complexity assembly in a coal matrix.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[],"research_interests":[{"id":2657126,"name":"fractal topography","url":"https://www.academia.edu/Documents/in/fractal_topography"},{"id":3797714,"name":"Behavioral complexity","url":"https://www.academia.edu/Documents/in/Behavioral_complexity"}],"urls":[{"id":9144948,"url":"https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020JB020110"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-44531334-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="44416906"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/44416906/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures"><img alt="Research paper thumbnail of Validity of triple-effect model for fluid flow in mismatched, self-affine fractures" class="work-thumbnail" src="https://attachments.academia-assets.com/64829797/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/44416906/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures">Validity of triple-effect model for fluid flow in mismatched, self-affine fractures</a></div><div class="wp-workCard_item"><span>Advances in Water Resources</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted br...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted broad attention because of its fundamental importance for complex hydrodynamic problems. Although it is natural to assume that permeability value depends on aperture size, it is hard to determine which is the appropriate relationship between them because of the large number of parameters related to the multi-scale geometries and mismatched behaviors in internal surfaces. Moreover, those parameters are hard to obtain by field observation or laboratory tests. For these, we focused on synthesising mismatched composite topography of natural fractures and numerical simulation of fluid flow through them at pore scale. Firstly, the control mechanism of self-affine property was clarified, and a novel Weierstrass-Mandelbrot (W-M) function was proposed to model self-affine profile as per fractal topography theory. Afterwards, a weighting algorithm was developed to construct the composite topography of fractures accounting for the mismatched behavior. Finally, the effects of mismatched behavior, hydraulic and surface tortuosities on fracture flow were systematically analyzed by numerical simulations using Lattice Boltzmann methods (LBM) at pore scale. Our investigation indicates that the aperture distribution is dominated by the mismatched range between internal surfaces, however the hydraulic and surface tortuosity effects are approximately scaled by 2(− 1) (H is the Hurst exponent) with the mean aperture despite of its distribution. Moreover, it was found that the local surface roughness factor, accounting for effects from surface geometries with size smaller than the value of mean aperture, is stationary at long range and inversely proportional to fracture permeability. Based on above discussions, the validity of triple-effect model for permeability prediction of mismatched self-affine fractures was established.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="174bc37c457580dfbd8841c45b0d4111" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":64829797,"asset_id":44416906,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/64829797/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="44416906"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="44416906"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 44416906; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=44416906]").text(description); $(".js-view-count[data-work-id=44416906]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 44416906; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='44416906']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "174bc37c457580dfbd8841c45b0d4111" } } $('.js-work-strip[data-work-id=44416906]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":44416906,"title":"Validity of triple-effect model for fluid flow in mismatched, self-affine fractures","translated_title":"","metadata":{"doi":"10.1016/j.advwatres.2020.103585","abstract":"Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted broad attention because of its fundamental importance for complex hydrodynamic problems. Although it is natural to assume that permeability value depends on aperture size, it is hard to determine which is the appropriate relationship between them because of the large number of parameters related to the multi-scale geometries and mismatched behaviors in internal surfaces. Moreover, those parameters are hard to obtain by field observation or laboratory tests. For these, we focused on synthesising mismatched composite topography of natural fractures and numerical simulation of fluid flow through them at pore scale. Firstly, the control mechanism of self-affine property was clarified, and a novel Weierstrass-Mandelbrot (W-M) function was proposed to model self-affine profile as per fractal topography theory. Afterwards, a weighting algorithm was developed to construct the composite topography of fractures accounting for the mismatched behavior. Finally, the effects of mismatched behavior, hydraulic and surface tortuosities on fracture flow were systematically analyzed by numerical simulations using Lattice Boltzmann methods (LBM) at pore scale. Our investigation indicates that the aperture distribution is dominated by the mismatched range between internal surfaces, however the hydraulic and surface tortuosity effects are approximately scaled by 2(− 1) (H is the Hurst exponent) with the mean aperture despite of its distribution. Moreover, it was found that the local surface roughness factor, accounting for effects from surface geometries with size smaller than the value of mean aperture, is stationary at long range and inversely proportional to fracture permeability. Based on above discussions, the validity of triple-effect model for permeability prediction of mismatched self-affine fractures was established.","ai_title_tag":"Triple-Effect Model for Self-Affine Fractures","publication_date":{"day":null,"month":null,"year":2020,"errors":{}},"publication_name":"Advances in Water Resources"},"translated_abstract":"Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted broad attention because of its fundamental importance for complex hydrodynamic problems. Although it is natural to assume that permeability value depends on aperture size, it is hard to determine which is the appropriate relationship between them because of the large number of parameters related to the multi-scale geometries and mismatched behaviors in internal surfaces. Moreover, those parameters are hard to obtain by field observation or laboratory tests. For these, we focused on synthesising mismatched composite topography of natural fractures and numerical simulation of fluid flow through them at pore scale. Firstly, the control mechanism of self-affine property was clarified, and a novel Weierstrass-Mandelbrot (W-M) function was proposed to model self-affine profile as per fractal topography theory. Afterwards, a weighting algorithm was developed to construct the composite topography of fractures accounting for the mismatched behavior. Finally, the effects of mismatched behavior, hydraulic and surface tortuosities on fracture flow were systematically analyzed by numerical simulations using Lattice Boltzmann methods (LBM) at pore scale. Our investigation indicates that the aperture distribution is dominated by the mismatched range between internal surfaces, however the hydraulic and surface tortuosity effects are approximately scaled by 2(− 1) (H is the Hurst exponent) with the mean aperture despite of its distribution. Moreover, it was found that the local surface roughness factor, accounting for effects from surface geometries with size smaller than the value of mean aperture, is stationary at long range and inversely proportional to fracture permeability. Based on above discussions, the validity of triple-effect model for permeability prediction of mismatched self-affine fractures was established.","internal_url":"https://www.academia.edu/44416906/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures","translated_internal_url":"","created_at":"2020-11-02T00:46:33.986-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":35901189,"work_id":44416906,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832185,"email":"z***g@163.com","display_order":1,"name":"Junling Zheng","title":"Validity of triple-effect model for fluid flow in mismatched, self-affine fractures"},{"id":35901190,"work_id":44416906,"tagging_user_id":17238727,"tagged_user_id":178383415,"co_author_invite_id":7135913,"email":"5***1@qq.com","display_order":2,"name":"Cheng Wang","title":"Validity of triple-effect model for fluid flow in mismatched, self-affine fractures"},{"id":35901191,"work_id":44416906,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":7135915,"email":"a***5@qq.com","display_order":3,"name":"Xiaokun Liu","title":"Validity of triple-effect model for fluid flow in mismatched, self-affine fractures"}],"downloadable_attachments":[{"id":64829797,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/64829797/thumbnails/1.jpg","file_name":"Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures.pdf","download_url":"https://www.academia.edu/attachments/64829797/download_file","bulk_download_file_name":"Validity_of_triple_effect_model_for_flui.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/64829797/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures-libre.pdf?1604312100=\u0026response-content-disposition=attachment%3B+filename%3DValidity_of_triple_effect_model_for_flui.pdf\u0026Expires=1743389187\u0026Signature=Af6R~JUNxAoLbCYCdlnqsiojxtXXXCv7VbJAwuukvjkWt0HJsNgjNM38Ka0kJX1LdoZzHIPvOvTmedwf5sONpZcPEp78eOSjgBK8OveqApvQhnsS~bqAiXUqEWSCoCsFTIe54cD5NmKkkkHb2utXBcd17b7PinZkkeE1dX-b-dFiw7omTnHU3MakS2RD1JCWVcgl8fEGskZ635Dy9LvBYZus~nXEqoRyX9gOoFl8gnBYWpkQ2fVoJ67yy2zxaNjizf2b16XqmrWDWC5zkf8Nw-j5KXgvWuH4gYhQx1Q0O3qFY17k4jHnFzKp84GeDVqClXy5TWc5bTiEzmnKF9tYfg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures","translated_slug":"","page_count":10,"language":"en","content_type":"Work","summary":"Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted broad attention because of its fundamental importance for complex hydrodynamic problems. Although it is natural to assume that permeability value depends on aperture size, it is hard to determine which is the appropriate relationship between them because of the large number of parameters related to the multi-scale geometries and mismatched behaviors in internal surfaces. Moreover, those parameters are hard to obtain by field observation or laboratory tests. For these, we focused on synthesising mismatched composite topography of natural fractures and numerical simulation of fluid flow through them at pore scale. Firstly, the control mechanism of self-affine property was clarified, and a novel Weierstrass-Mandelbrot (W-M) function was proposed to model self-affine profile as per fractal topography theory. Afterwards, a weighting algorithm was developed to construct the composite topography of fractures accounting for the mismatched behavior. Finally, the effects of mismatched behavior, hydraulic and surface tortuosities on fracture flow were systematically analyzed by numerical simulations using Lattice Boltzmann methods (LBM) at pore scale. Our investigation indicates that the aperture distribution is dominated by the mismatched range between internal surfaces, however the hydraulic and surface tortuosity effects are approximately scaled by 2(− 1) (H is the Hurst exponent) with the mean aperture despite of its distribution. Moreover, it was found that the local surface roughness factor, accounting for effects from surface geometries with size smaller than the value of mean aperture, is stationary at long range and inversely proportional to fracture permeability. Based on above discussions, the validity of triple-effect model for permeability prediction of mismatched self-affine fractures was established.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":64829797,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/64829797/thumbnails/1.jpg","file_name":"Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures.pdf","download_url":"https://www.academia.edu/attachments/64829797/download_file","bulk_download_file_name":"Validity_of_triple_effect_model_for_flui.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/64829797/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures-libre.pdf?1604312100=\u0026response-content-disposition=attachment%3B+filename%3DValidity_of_triple_effect_model_for_flui.pdf\u0026Expires=1743389187\u0026Signature=Af6R~JUNxAoLbCYCdlnqsiojxtXXXCv7VbJAwuukvjkWt0HJsNgjNM38Ka0kJX1LdoZzHIPvOvTmedwf5sONpZcPEp78eOSjgBK8OveqApvQhnsS~bqAiXUqEWSCoCsFTIe54cD5NmKkkkHb2utXBcd17b7PinZkkeE1dX-b-dFiw7omTnHU3MakS2RD1JCWVcgl8fEGskZ635Dy9LvBYZus~nXEqoRyX9gOoFl8gnBYWpkQ2fVoJ67yy2zxaNjizf2b16XqmrWDWC5zkf8Nw-j5KXgvWuH4gYhQx1Q0O3qFY17k4jHnFzKp84GeDVqClXy5TWc5bTiEzmnKF9tYfg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":215076,"name":"Fluid flow","url":"https://www.academia.edu/Documents/in/Fluid_flow"},{"id":890611,"name":"Fractal Dimension","url":"https://www.academia.edu/Documents/in/Fractal_Dimension"},{"id":1447726,"name":"Hurst Exponent","url":"https://www.academia.edu/Documents/in/Hurst_Exponent"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-44416906-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="44416814"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/44416814/SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA"><img alt="Research paper thumbnail of SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA" class="work-thumbnail" src="https://attachments.academia-assets.com/64829670/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/44416814/SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA">SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://henanpu.academia.edu/yiJin">yi Jin</a>, <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/ChengWang92">Cheng Wang</a>, and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/WeizheQuan">Weizhe Quan</a></span></div><div class="wp-workCard_item"><span>Fractals</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Microstructures dominate the physical properties of fractal porous media, which means the clarifi...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstruc-tures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity , including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framework is open to arbitrary original and behavioral complexities, and eases the modeling of multi-scale microstructures and the property estimation significantly.</span></div><div class="wp-workCard_item"><div class="carousel-container carousel-container--sm" id="profile-work-44416814-figures"><div class="prev-slide-container js-prev-button-container"><button aria-label="Previous" class="carousel-navigation-button js-profile-work-44416814-figures-prev"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">arrow_back_ios</span></button></div><div class="slides-container js-slides-container"><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278786/figure-11-self-affine-porous-media-with-different-fractal"><img alt="Fig. 11 Self-affine porous media with different fractal topography. (a), (e), and (i) with the increasing of Py; (b), (f), and (j) with the increasing of Py; (c), (g), and (k): with the increasing of F. (d), (h), and (1) have the same D but the fractal topography parameters are different. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_011.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278659/figure-1-the-simple-of-qsgs-where-lists-eight-growth"><img alt="Fig. 1 The simple scheme of QSGS,*! where (a) lists eight growth directions in the QSGS algorithm and (b) represents a modeling result. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_001.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278675/figure-2-generation-processes-of-multi-phase-fractals-where"><img alt="Fig. 2 Generation processes of multi-phase fractals, where @ and others represent modeling process following by or not following by PSF model, respectively. In these three pro- cesses, (a) is the fractal generator which define the original complexity shared by processes @, @, and @, (b) denotes the definition of fractal behavior, and (c) represents frac- tal iteration based on the definitions of original complexity and fractal behaviors. In (a), the original complexity is com- posed of determined phases of pore (p) and solid (s), while the behavioral complexity is enclosed in fractal phase (f). The area ratio tp = 4/9, vs = 2/9, xp = 3/9, and the struc- ture parameter n = 3. In process @, (b) defines the fractal behavior following PSF model with scaling factor taking the value of n. While in process @, (b) defines self-similar behav- ior not following PSF model with scaling factor of 2n. As for process @, (b) defines self-affine behavior with scaling fac- tors in xz- and y-direction, respectively, to be n and 2n. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_002.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278685/figure-3-variant-of-sierpinski-carpet-and-its-fractal"><img alt="Fig. 3 Variant of Sierpinski carpet and its fractal topogra- phy modified after that in Ref. 13. In this fractal structure P = (Pr, Py) = (3,4) and the expectation of F is equal tc 3. Black, white, and yellow denote the three different deter- mined phases, while gray denotes the fractal phase. In the scaling object, vs = 1/9, zy = 2/9 with xy representing the area ratio of yellow phase, rp = 5/12, and af = 1/4 respectively. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_003.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278702/figure-4-comparison-of-qsgs-and-fractal-topography-the-model"><img alt="Fig. 4 Comparison of QSGS and fractal topography. The model on the left-hand side was constructed by QSGS with the ratio of the growth probabilities set to be pa, : Pdz,, = 2 to represent anisotropy, and the fractal models on the right-hand side share the same fractal topography of Q((Pr, Py), F) = 2((2,4), 2) with Hyx = 2 to reflect self-affine properties. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_004.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278712/figure-5-generation-of-self-affine-fractal-model-parameters"><img alt="Fig. 5 Generation of self-affine fractal model. Parameters are Py = 3, Py = 2, and (F’) = 4. Red, blue, and yellow represent three different phases. Red and blue are growing phases with opposite-colored seeds. For convenience, fractal porous media were denoted by F3.(Q,G,L) following our previous denotation,!? with Q being the shortened version of Q(P,F), G representing the multi-type scaling object that is generated by QSGS, and L being the scaling range. As shown in Fig. 5, the scaling object " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_005.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278732/figure-6-fractal-porous-media-generated-by-fqsgs-and-are-the"><img alt="Fig. 6 Fractal porous media generated by FQSGS. (a), (b), and (c) are the self-similarities with fractal topographies of (2,2), 2(2.5,4), and (4,2), respectively. (d), (e), and (f) are the self-affinities with the respective parameters of ((1.2,3), 2), Q((3, 1.5), 2), and Q((2,3),2). (g) and (h) with (3,3) and (2,1) are multi-phase models, in which the proportions of yellow and white phases are (0.15, 0.15) and (0.2, 0.1), respectively. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_006.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278737/figure-8-verification-of-porosity-calculation-for-self"><img alt="Fig. 8 Verification of porosity calculation for (a) self-similar model and (b) self-affine model. Fig. 7 Verification of the behavioral complexity by fractal dimension, where (a) and (b) are the relationships of self-similaz and self-affine porous media, respectively. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_007.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278752/figure-8-systematic-definition-of-complexity-assembly-in"><img alt="" class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_008.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278762/figure-9-fractal-porous-models-with-different-hzy-values"><img alt="Fig. 9 Fractal porous models with different Hzy values. White and black denote the solid and pore phases, respectively. (F) = 2 for all models in this figure. The Hzy values of (a)—(c) are 1.58, 1.63, and 2.58, respectively; and the P values of (d)-(f) are 2, 3, and 6 with Hzy = 1, respectively. The Hzy values of (g)—(i) are 0.63, 0.61, and 0.38, respectively. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_009.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278774/figure-10-self-similar-porous-media-where-the-expectation-of"><img alt="Fig. 10 Self-similar porous media, where the expectation of F increases from the top to the bottom and P increases fror left to right. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_010.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278795/figure-12-models-of-different-original-complexities-models"><img alt="Fig. 12 Models of different original complexities. Models (a)—(d) are self-similar with Q(P, F’) = (2,2). While models (e)— (h) are self-affine with P, = 2, Py = 6, and (F’) = 2. The pore phase is black, whereas the two determined phases are white and yellow. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_012.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278807/figure-13-complexity-assembly-and-control-system-in-fractal"><img alt="Fig. 13 Complexity assembly and control system in fractal porous media. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_013.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278820/table-2-scaling-parameters-sl-and-sc-and-fractal-dimension"><img alt="Table 2 Scaling Parameters, SL and SC, and Fractal Dimension D (by Eq. (10)) of Self-Similar Porous Media in Fig. 10. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/table_001.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278829/table-3-scaling-parameters-sl-and-sc-and-fractal-dimension"><img alt="Table 3 Scaling Parameters, SL and SC, and Fractal Dimension D (by Eq. (10)) of Self-Affine Porous Media in Fig. 11. As P, increases, a compression of the particles in the y-direction increases gradually. While the increase of P, leads to an increasing degree of parti- cle compression in the x-direction, as shown by the porous media in the second column of Fig. 11. This result is consistent with that in Sec. 4.2. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/table_002.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278847/table-4-parameters-of-single-and-multi-phase-models-zs-white"><img alt="Table 4 Parameters of Single- and Multi-Phase Models. 2zs,: ‘“White” Phase, %s,: “Yellow” Phase. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/table_003.jpg" /></a></figure></div><div class="next-slide-container js-next-button-container"><button aria-label="Next" class="carousel-navigation-button js-profile-work-44416814-figures-next"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">arrow_forward_ios</span></button></div></div></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e2de5b0ab8bc4a1f48fe455d40f5b587" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":64829670,"asset_id":44416814,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/64829670/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="44416814"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="44416814"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 44416814; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=44416814]").text(description); $(".js-view-count[data-work-id=44416814]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 44416814; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='44416814']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "e2de5b0ab8bc4a1f48fe455d40f5b587" } } $('.js-work-strip[data-work-id=44416814]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":44416814,"title":"SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA","translated_title":"","metadata":{"doi":"10.1142/S0218348X20500796","abstract":"Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstruc-tures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity , including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framework is open to arbitrary original and behavioral complexities, and eases the modeling of multi-scale microstructures and the property estimation significantly.","ai_title_tag":"Defining Complexity Assembly in Fractal Porous Media","publication_date":{"day":null,"month":null,"year":2020,"errors":{}},"publication_name":"Fractals"},"translated_abstract":"Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstruc-tures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity , including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framework is open to arbitrary original and behavioral complexities, and eases the modeling of multi-scale microstructures and the property estimation significantly.","internal_url":"https://www.academia.edu/44416814/SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA","translated_internal_url":"","created_at":"2020-11-02T00:32:19.294-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":35901152,"work_id":44416814,"tagging_user_id":17238727,"tagged_user_id":178383415,"co_author_invite_id":7135913,"email":"5***1@qq.com","display_order":1,"name":"Cheng Wang","title":"SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA"},{"id":35901153,"work_id":44416814,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6910670,"email":"l***x@hpu.edu.cn","display_order":2,"name":"Shunxi Liu","title":"SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA"},{"id":35901154,"work_id":44416814,"tagging_user_id":17238727,"tagged_user_id":178374458,"co_author_invite_id":7135914,"email":"7***1@qq.com","display_order":3,"name":"Weizhe Quan","title":"SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA"},{"id":35901155,"work_id":44416814,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":7135915,"email":"a***5@qq.com","display_order":4,"name":"Xiaokun Liu","title":"SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA"}],"downloadable_attachments":[{"id":64829670,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/64829670/thumbnails/1.jpg","file_name":"SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA.pdf","download_url":"https://www.academia.edu/attachments/64829670/download_file","bulk_download_file_name":"SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSE.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/64829670/SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA-libre.pdf?1604306113=\u0026response-content-disposition=attachment%3B+filename%3DSYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSE.pdf\u0026Expires=1743389187\u0026Signature=ZukVJZhG1QOadCKSeV7jMhm5N~3d36L5pJUpJE0PXaAzW7jJLofxyTvNp6sAgptqTpkV-dznS4w8Z5dcmiq6gtb3rdU1pqKkSOC8FLu-ahLBPbrMhRBulOa7UEX4YZ-ilWGaFXn8yN366rojtUppWeb4zTtolvVGV4qPsgaebWyaJET8E5hU8b53tAZIk0HP3ODmoFU86LtYOQH9JnOswu8QJ--BJPC49-drSyAPePSJu~vbqgv~P~c1A~RlvIdg1VfjHnUdQIIG2mmm2-kKEIJ8bzw7we0rCFJxfQ62l7MmdlecxAYE0sOql5W8580tGbW3Ek2iaF5vLyJ00sOPCw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA","translated_slug":"","page_count":16,"language":"en","content_type":"Work","summary":"Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstruc-tures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity , including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framework is open to arbitrary original and behavioral complexities, and eases the modeling of multi-scale microstructures and the property estimation significantly.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":64829670,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/64829670/thumbnails/1.jpg","file_name":"SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA.pdf","download_url":"https://www.academia.edu/attachments/64829670/download_file","bulk_download_file_name":"SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSE.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/64829670/SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA-libre.pdf?1604306113=\u0026response-content-disposition=attachment%3B+filename%3DSYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSE.pdf\u0026Expires=1743389187\u0026Signature=ZukVJZhG1QOadCKSeV7jMhm5N~3d36L5pJUpJE0PXaAzW7jJLofxyTvNp6sAgptqTpkV-dznS4w8Z5dcmiq6gtb3rdU1pqKkSOC8FLu-ahLBPbrMhRBulOa7UEX4YZ-ilWGaFXn8yN366rojtUppWeb4zTtolvVGV4qPsgaebWyaJET8E5hU8b53tAZIk0HP3ODmoFU86LtYOQH9JnOswu8QJ--BJPC49-drSyAPePSJu~vbqgv~P~c1A~RlvIdg1VfjHnUdQIIG2mmm2-kKEIJ8bzw7we0rCFJxfQ62l7MmdlecxAYE0sOql5W8580tGbW3Ek2iaF5vLyJ00sOPCw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":24831,"name":"Fractals","url":"https://www.academia.edu/Documents/in/Fractals"},{"id":2689528,"name":"self-affinity","url":"https://www.academia.edu/Documents/in/self-affinity"},{"id":3797714,"name":"Behavioral complexity","url":"https://www.academia.edu/Documents/in/Behavioral_complexity"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (true) { Aedu.setUpFigureCarousel('profile-work-44416814-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="40495697"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/40495697/Control_mechanisms_of_self_affine_rough_cleat_networks_on_flow_dynamics_in_coal_reservoir"><img alt="Research paper thumbnail of Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir" class="work-thumbnail" src="https://attachments.academia-assets.com/60764690/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/40495697/Control_mechanisms_of_self_affine_rough_cleat_networks_on_flow_dynamics_in_coal_reservoir">Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir</a></div><div class="wp-workCard_item"><span>Energy</span><span>, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Cleat networks dominate the migration of coalbed methane (CBM), which is assembled by cleats of d...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Cleat networks dominate the migration of coalbed methane (CBM), which is assembled by cleats of different type following special configuration and possessing rough, self-affine surfaces. Nowadays, configuration implications, scale-invariant properties, fractal control mechanisms, and their relations to flow dynamics have not yet been fully clarified. Herein we explore these issues numerically using effective modeling of cleat networks and pore-scale simulations of fluid flow through them. Firstly, the control mechanics of fractal dynamics was clarified by fractal topography theory, a new definition of Weierstrass-Mandelbrot (W-M) function was proposed to characterize the self-affine surface geometries, an algorithm was developed to effectively construct cleat networks similar in coal, and Lattice Boltzmann method (LBM) was used to reproduce the fluid flow in numerical cleat networks at the pore scale. Af-terwards, the implications of spatial configuration of cleats and fractal control mechanisms of surface geometries on the permeability were systematically analyzed and quantified. Finally, an empirical model was established to predict the permeability of self-affine, rough cleat networks, rather than a rough estimation by a power-law proportionality in previous research. The performance of the proposed model was fully verified by comparative analysis and numerical simulations. Theoretical analysis denotes that our model can generalize several traditional and newly developed models from the literature.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1f7e46e6a8d058b347cbb89590d7c6e8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":60764690,"asset_id":40495697,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/60764690/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="40495697"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="40495697"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 40495697; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=40495697]").text(description); $(".js-view-count[data-work-id=40495697]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 40495697; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='40495697']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1f7e46e6a8d058b347cbb89590d7c6e8" } } $('.js-work-strip[data-work-id=40495697]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":40495697,"title":"Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir","translated_title":"","metadata":{"doi":"10.1016/j.energy.2019.116146","abstract":"Cleat networks dominate the migration of coalbed methane (CBM), which is assembled by cleats of different type following special configuration and possessing rough, self-affine surfaces. Nowadays, configuration implications, scale-invariant properties, fractal control mechanisms, and their relations to flow dynamics have not yet been fully clarified. Herein we explore these issues numerically using effective modeling of cleat networks and pore-scale simulations of fluid flow through them. Firstly, the control mechanics of fractal dynamics was clarified by fractal topography theory, a new definition of Weierstrass-Mandelbrot (W-M) function was proposed to characterize the self-affine surface geometries, an algorithm was developed to effectively construct cleat networks similar in coal, and Lattice Boltzmann method (LBM) was used to reproduce the fluid flow in numerical cleat networks at the pore scale. Af-terwards, the implications of spatial configuration of cleats and fractal control mechanisms of surface geometries on the permeability were systematically analyzed and quantified. Finally, an empirical model was established to predict the permeability of self-affine, rough cleat networks, rather than a rough estimation by a power-law proportionality in previous research. The performance of the proposed model was fully verified by comparative analysis and numerical simulations. Theoretical analysis denotes that our model can generalize several traditional and newly developed models from the literature.","publication_date":{"day":null,"month":null,"year":2019,"errors":{}},"publication_name":"Energy"},"translated_abstract":"Cleat networks dominate the migration of coalbed methane (CBM), which is assembled by cleats of different type following special configuration and possessing rough, self-affine surfaces. Nowadays, configuration implications, scale-invariant properties, fractal control mechanisms, and their relations to flow dynamics have not yet been fully clarified. Herein we explore these issues numerically using effective modeling of cleat networks and pore-scale simulations of fluid flow through them. Firstly, the control mechanics of fractal dynamics was clarified by fractal topography theory, a new definition of Weierstrass-Mandelbrot (W-M) function was proposed to characterize the self-affine surface geometries, an algorithm was developed to effectively construct cleat networks similar in coal, and Lattice Boltzmann method (LBM) was used to reproduce the fluid flow in numerical cleat networks at the pore scale. Af-terwards, the implications of spatial configuration of cleats and fractal control mechanisms of surface geometries on the permeability were systematically analyzed and quantified. Finally, an empirical model was established to predict the permeability of self-affine, rough cleat networks, rather than a rough estimation by a power-law proportionality in previous research. The performance of the proposed model was fully verified by comparative analysis and numerical simulations. Theoretical analysis denotes that our model can generalize several traditional and newly developed models from the literature.","internal_url":"https://www.academia.edu/40495697/Control_mechanisms_of_self_affine_rough_cleat_networks_on_flow_dynamics_in_coal_reservoir","translated_internal_url":"","created_at":"2019-10-01T19:35:53.317-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":33090662,"work_id":40495697,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832185,"email":"z***g@163.com","display_order":1,"name":"Junling Zheng","title":"Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir"},{"id":33090663,"work_id":40495697,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832183,"email":"1***6@qq.com","display_order":2,"name":"Xianhe Liu","title":"Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir"},{"id":33090664,"work_id":40495697,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832186,"email":"j***n@hpu.edu.cn","display_order":3,"name":"Jienan Pan","title":"Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir"},{"id":33090665,"work_id":40495697,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6910670,"email":"l***x@hpu.edu.cn","display_order":4,"name":"Shunxi Liu","title":"Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir"}],"downloadable_attachments":[{"id":60764690,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/60764690/thumbnails/1.jpg","file_name":"Control_mechanisms_of_self-affine__rough_cleat_networks_on_flow_dynamics_in_coal_reservoir20191001-87851-m97kjq.pdf","download_url":"https://www.academia.edu/attachments/60764690/download_file","bulk_download_file_name":"Control_mechanisms_of_self_affine_rough.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/60764690/Control_mechanisms_of_self-affine__rough_cleat_networks_on_flow_dynamics_in_coal_reservoir20191001-87851-m97kjq-libre.pdf?1569984406=\u0026response-content-disposition=attachment%3B+filename%3DControl_mechanisms_of_self_affine_rough.pdf\u0026Expires=1743389187\u0026Signature=B0jblwQvHGEXpH5JV1Nc4WcgWsbLili~BN1rEqwLfBJdEFQxuMteLvdO3EbD~UX6oBa4r9xKnjHPNcCga7yhcHHBiE~Zj7iiWWSVQEn3K-48F9kfhzvBLfG~8ix-J0WAWOhER7sVFlDaxqDwApNsvHvyVySFiWB2mfsJYWCUTxWraQaZtcxHA8BPYBuMyg0UxMw3pjvgIhJk64eLPrBC455xh3rOuhIZuf72LUSM-BjQQNwqmYQ96dV5OdhFdhcgVcgOh602lh62O88hg578Txnrl37nkrQAkA8ik4wMF4dylJQAHA4h46t4MALWJccYmF6uo2D7YZOXOGezCeuJLQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Control_mechanisms_of_self_affine_rough_cleat_networks_on_flow_dynamics_in_coal_reservoir","translated_slug":"","page_count":10,"language":"en","content_type":"Work","summary":"Cleat networks dominate the migration of coalbed methane (CBM), which is assembled by cleats of different type following special configuration and possessing rough, self-affine surfaces. Nowadays, configuration implications, scale-invariant properties, fractal control mechanisms, and their relations to flow dynamics have not yet been fully clarified. Herein we explore these issues numerically using effective modeling of cleat networks and pore-scale simulations of fluid flow through them. Firstly, the control mechanics of fractal dynamics was clarified by fractal topography theory, a new definition of Weierstrass-Mandelbrot (W-M) function was proposed to characterize the self-affine surface geometries, an algorithm was developed to effectively construct cleat networks similar in coal, and Lattice Boltzmann method (LBM) was used to reproduce the fluid flow in numerical cleat networks at the pore scale. Af-terwards, the implications of spatial configuration of cleats and fractal control mechanisms of surface geometries on the permeability were systematically analyzed and quantified. Finally, an empirical model was established to predict the permeability of self-affine, rough cleat networks, rather than a rough estimation by a power-law proportionality in previous research. The performance of the proposed model was fully verified by comparative analysis and numerical simulations. Theoretical analysis denotes that our model can generalize several traditional and newly developed models from the literature.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":60764690,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/60764690/thumbnails/1.jpg","file_name":"Control_mechanisms_of_self-affine__rough_cleat_networks_on_flow_dynamics_in_coal_reservoir20191001-87851-m97kjq.pdf","download_url":"https://www.academia.edu/attachments/60764690/download_file","bulk_download_file_name":"Control_mechanisms_of_self_affine_rough.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/60764690/Control_mechanisms_of_self-affine__rough_cleat_networks_on_flow_dynamics_in_coal_reservoir20191001-87851-m97kjq-libre.pdf?1569984406=\u0026response-content-disposition=attachment%3B+filename%3DControl_mechanisms_of_self_affine_rough.pdf\u0026Expires=1743389187\u0026Signature=B0jblwQvHGEXpH5JV1Nc4WcgWsbLili~BN1rEqwLfBJdEFQxuMteLvdO3EbD~UX6oBa4r9xKnjHPNcCga7yhcHHBiE~Zj7iiWWSVQEn3K-48F9kfhzvBLfG~8ix-J0WAWOhER7sVFlDaxqDwApNsvHvyVySFiWB2mfsJYWCUTxWraQaZtcxHA8BPYBuMyg0UxMw3pjvgIhJk64eLPrBC455xh3rOuhIZuf72LUSM-BjQQNwqmYQ96dV5OdhFdhcgVcgOh602lh62O88hg578Txnrl37nkrQAkA8ik4wMF4dylJQAHA4h46t4MALWJccYmF6uo2D7YZOXOGezCeuJLQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":11997,"name":"Fluid flow in porous media","url":"https://www.academia.edu/Documents/in/Fluid_flow_in_porous_media"},{"id":24831,"name":"Fractals","url":"https://www.academia.edu/Documents/in/Fractals"},{"id":83972,"name":"Permeability","url":"https://www.academia.edu/Documents/in/Permeability"},{"id":216924,"name":"LBM","url":"https://www.academia.edu/Documents/in/LBM"},{"id":2657126,"name":"fractal topography","url":"https://www.academia.edu/Documents/in/fractal_topography"},{"id":3396360,"name":"Cleats","url":"https://www.academia.edu/Documents/in/Cleats"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-40495697-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="38878011"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/38878011/General_fractal_topography_an_open_mathematical_framework_to_characterize_and_model_mono_scale_invariances"><img alt="Research paper thumbnail of General fractal topography: an open mathematical framework to characterize and model mono-scale-invariances" class="work-thumbnail" src="https://attachments.academia-assets.com/58974856/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/38878011/General_fractal_topography_an_open_mathematical_framework_to_characterize_and_model_mono_scale_invariances">General fractal topography: an open mathematical framework to characterize and model mono-scale-invariances</a></div><div class="wp-workCard_item"><span>Nonlinear Dynamics</span><span>, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this work, we reported there are two kinds of independent complexities in mono-scale-invarianc...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this work, we reported there are two kinds of independent complexities in mono-scale-invariance, namely to be behavioral complexity determined by fractal behavior and original one wrapped in scaling object. Quantitative characterization of the complexities is fundamentally important for mechanism exploration and essential understanding of nonlinear systems. Recently, a new concept of fractal topography (Ω) was emerged to define the fractal behavior in self-similarities by scaling lacunarity (P) and scaling coverage (F) as Ω(P, F). It is, however, a “special fractal topography” because fractals are rarely deterministic and always appear stochastic, heterogeneous, and even anisotropic. For that, we reviewed a novel concept of “general fractal topography”, Ω(P, F). In Ω, P is generalized to a set accounting for directiondependent scaling behaviors of the scaling object G, while F is extended to consider stochastic and heterogeneous effects. And then, we decomposed G into G(G+, G−) to ease type controlling and measurement quantification, with G+ wrapping the original complexity while G− enclosing behavioral complexity. Together with Ω and G, a mathematical model F3S (Ω,G) was then established to unify the definition of deterministic or statistical, self-similar or selfaffine, single- or multi-phase properties. For demonstration, algorithms are developed to model natural scale-invariances. Our investigations indicated that the general fractal topography is an open mathematic framework which can admit most complex scaling objects and fractal behaviors.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="f7354bcf603d50f3824924bb09715fa0" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":58974856,"asset_id":38878011,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/58974856/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="38878011"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="38878011"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 38878011; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=38878011]").text(description); $(".js-view-count[data-work-id=38878011]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 38878011; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='38878011']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "f7354bcf603d50f3824924bb09715fa0" } } $('.js-work-strip[data-work-id=38878011]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":38878011,"title":"General fractal topography: an open mathematical framework to characterize and model mono-scale-invariances","translated_title":"","metadata":{"doi":"10.1007/s11071-019-04931-9","abstract":"In this work, we reported there are two kinds of independent complexities in mono-scale-invariance, namely to be behavioral complexity determined by fractal behavior and original one wrapped in scaling object. Quantitative characterization of the complexities is fundamentally important for mechanism exploration and essential understanding of nonlinear systems. Recently, a new concept of fractal topography (Ω) was emerged to define the fractal behavior in self-similarities by scaling lacunarity (P) and scaling coverage (F) as Ω(P, F). It is, however, a “special fractal topography” because fractals are rarely deterministic and always appear stochastic, heterogeneous, and even anisotropic. For that, we reviewed a novel concept of “general fractal topography”, Ω(P, F). In Ω, P is generalized to a set accounting for directiondependent scaling behaviors of the scaling object G, while F is extended to consider stochastic and heterogeneous effects. And then, we decomposed G into G(G+, G−) to ease type controlling and measurement quantification, with G+ wrapping the original complexity while G− enclosing behavioral complexity. Together with Ω and G, a mathematical model F3S (Ω,G) was then established to unify the definition of deterministic or statistical, self-similar or selfaffine, single- or multi-phase properties. For demonstration, algorithms are developed to model natural scale-invariances. Our investigations indicated that the general fractal topography is an open mathematic framework which can admit most complex scaling objects and fractal behaviors.","publication_date":{"day":null,"month":null,"year":2019,"errors":{}},"publication_name":"Nonlinear Dynamics"},"translated_abstract":"In this work, we reported there are two kinds of independent complexities in mono-scale-invariance, namely to be behavioral complexity determined by fractal behavior and original one wrapped in scaling object. Quantitative characterization of the complexities is fundamentally important for mechanism exploration and essential understanding of nonlinear systems. Recently, a new concept of fractal topography (Ω) was emerged to define the fractal behavior in self-similarities by scaling lacunarity (P) and scaling coverage (F) as Ω(P, F). It is, however, a “special fractal topography” because fractals are rarely deterministic and always appear stochastic, heterogeneous, and even anisotropic. For that, we reviewed a novel concept of “general fractal topography”, Ω(P, F). In Ω, P is generalized to a set accounting for directiondependent scaling behaviors of the scaling object G, while F is extended to consider stochastic and heterogeneous effects. And then, we decomposed G into G(G+, G−) to ease type controlling and measurement quantification, with G+ wrapping the original complexity while G− enclosing behavioral complexity. Together with Ω and G, a mathematical model F3S (Ω,G) was then established to unify the definition of deterministic or statistical, self-similar or selfaffine, single- or multi-phase properties. For demonstration, algorithms are developed to model natural scale-invariances. Our investigations indicated that the general fractal topography is an open mathematic framework which can admit most complex scaling objects and fractal behaviors.","internal_url":"https://www.academia.edu/38878011/General_fractal_topography_an_open_mathematical_framework_to_characterize_and_model_mono_scale_invariances","translated_internal_url":"","created_at":"2019-04-20T20:34:17.194-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":32467380,"work_id":38878011,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832183,"email":"1***6@qq.com","display_order":0,"name":"Xianhe Liu","title":"General fractal topography: an open mathematical framework to characterize and model mono-scale-invariances"},{"id":32467381,"work_id":38878011,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832184,"email":"s***5@hpu.edu.cn","display_order":4194304,"name":"Huibo Song","title":"General fractal topography: an open mathematical framework to characterize and model mono-scale-invariances"},{"id":32467382,"work_id":38878011,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832185,"email":"z***g@163.com","display_order":6291456,"name":"Junling Zheng","title":"General fractal topography: an open mathematical framework to characterize and model mono-scale-invariances"},{"id":32467383,"work_id":38878011,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832186,"email":"j***n@hpu.edu.cn","display_order":7340032,"name":"Jienan Pan","title":"General fractal topography: an open mathematical framework to characterize and model mono-scale-invariances"}],"downloadable_attachments":[{"id":58974856,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/58974856/thumbnails/1.jpg","file_name":"General_Fractal_Topography.pdf","download_url":"https://www.academia.edu/attachments/58974856/download_file","bulk_download_file_name":"General_fractal_topography_an_open_mathe.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/58974856/General_Fractal_Topography-libre.pdf?1556310296=\u0026response-content-disposition=attachment%3B+filename%3DGeneral_fractal_topography_an_open_mathe.pdf\u0026Expires=1743389187\u0026Signature=PLfW~4dApYadyGFYgmcQsPB-cedQDEbl1ThDWly7eXUnZJhlRS9DcBn3h36s4GZ5ZFchMQaGkHP1wGXGkYiADCDjsEVy4P5vr41WJBrg6VgaAWLPDmyPQs6CH36FanSZaGj7DCnmknUWnt~nDE3~rWTE7WL~0Hd4E-w7~zkAXvnaub3txXoir2eSlDCjMydGigivrVOXUTRDKwYCjrvRYozXuDCtuROd5mCs4k2Fe6qWGV0axoAasW1Tnk3jCe~1UPjMWpl~-oJmKQ-3mGUmlgD~14SHZcEcBGV2yD~ss0Ew8ZKO0cB7vLgBhhkx2NUlxsNbH2GSDFMCcYwxvoPJ0w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"General_fractal_topography_an_open_mathematical_framework_to_characterize_and_model_mono_scale_invariances","translated_slug":"","page_count":26,"language":"en","content_type":"Work","summary":"In this work, we reported there are two kinds of independent complexities in mono-scale-invariance, namely to be behavioral complexity determined by fractal behavior and original one wrapped in scaling object. Quantitative characterization of the complexities is fundamentally important for mechanism exploration and essential understanding of nonlinear systems. Recently, a new concept of fractal topography (Ω) was emerged to define the fractal behavior in self-similarities by scaling lacunarity (P) and scaling coverage (F) as Ω(P, F). It is, however, a “special fractal topography” because fractals are rarely deterministic and always appear stochastic, heterogeneous, and even anisotropic. For that, we reviewed a novel concept of “general fractal topography”, Ω(P, F). In Ω, P is generalized to a set accounting for directiondependent scaling behaviors of the scaling object G, while F is extended to consider stochastic and heterogeneous effects. And then, we decomposed G into G(G+, G−) to ease type controlling and measurement quantification, with G+ wrapping the original complexity while G− enclosing behavioral complexity. Together with Ω and G, a mathematical model F3S (Ω,G) was then established to unify the definition of deterministic or statistical, self-similar or selfaffine, single- or multi-phase properties. For demonstration, algorithms are developed to model natural scale-invariances. Our investigations indicated that the general fractal topography is an open mathematic framework which can admit most complex scaling objects and fractal behaviors.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":58974856,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/58974856/thumbnails/1.jpg","file_name":"General_Fractal_Topography.pdf","download_url":"https://www.academia.edu/attachments/58974856/download_file","bulk_download_file_name":"General_fractal_topography_an_open_mathe.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/58974856/General_Fractal_Topography-libre.pdf?1556310296=\u0026response-content-disposition=attachment%3B+filename%3DGeneral_fractal_topography_an_open_mathe.pdf\u0026Expires=1743389187\u0026Signature=PLfW~4dApYadyGFYgmcQsPB-cedQDEbl1ThDWly7eXUnZJhlRS9DcBn3h36s4GZ5ZFchMQaGkHP1wGXGkYiADCDjsEVy4P5vr41WJBrg6VgaAWLPDmyPQs6CH36FanSZaGj7DCnmknUWnt~nDE3~rWTE7WL~0Hd4E-w7~zkAXvnaub3txXoir2eSlDCjMydGigivrVOXUTRDKwYCjrvRYozXuDCtuROd5mCs4k2Fe6qWGV0axoAasW1Tnk3jCe~1UPjMWpl~-oJmKQ-3mGUmlgD~14SHZcEcBGV2yD~ss0Ew8ZKO0cB7vLgBhhkx2NUlxsNbH2GSDFMCcYwxvoPJ0w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":6637,"name":"Fracture","url":"https://www.academia.edu/Documents/in/Fracture"},{"id":24831,"name":"Fractals","url":"https://www.academia.edu/Documents/in/Fractals"},{"id":90637,"name":"Porous Media","url":"https://www.academia.edu/Documents/in/Porous_Media"},{"id":154484,"name":"Self-similarity","url":"https://www.academia.edu/Documents/in/Self-similarity"},{"id":890611,"name":"Fractal Dimension","url":"https://www.academia.edu/Documents/in/Fractal_Dimension"},{"id":1432574,"name":"Scale Invariance","url":"https://www.academia.edu/Documents/in/Scale_Invariance"},{"id":1447726,"name":"Hurst Exponent","url":"https://www.academia.edu/Documents/in/Hurst_Exponent"},{"id":1566663,"name":"Weierstrass Mandelbrot functions","url":"https://www.academia.edu/Documents/in/Weierstrass_Mandelbrot_functions"},{"id":2657126,"name":"fractal topography","url":"https://www.academia.edu/Documents/in/fractal_topography"},{"id":2689528,"name":"self-affinity","url":"https://www.academia.edu/Documents/in/self-affinity"}],"urls":[{"id":8747524,"url":"https://doi.org/10.1007/s11071-019-04931-9"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-38878011-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="32678415"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32678415/Definition_of_fractal_topography_to_essential_understanding_of_scale_invariance"><img alt="Research paper thumbnail of Definition of fractal topography to essential understanding of scale- invariance" class="work-thumbnail" src="https://attachments.academia-assets.com/52844510/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32678415/Definition_of_fractal_topography_to_essential_understanding_of_scale_invariance">Definition of fractal topography to essential understanding of scale- invariance</a></div><div class="wp-workCard_item"><span>Scientific Reports</span><span>, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the c...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the correspondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter H xy , a general Hurst exponent, which is analytically expressed by H xy = log P x /log P y where P x and P y are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which D H d F P = ∑ (/)log /log i d xi x =1. Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.</span></div><div class="wp-workCard_item"><div class="carousel-container carousel-container--sm" id="profile-work-32678415-figures"><div class="prev-slide-container js-prev-button-container"><button aria-label="Previous" class="carousel-navigation-button js-profile-work-32678415-figures-prev"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">arrow_back_ios</span></button></div><div class="slides-container js-slides-container"><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/39787931/figure-1-fractals-constructed-by-different-fractal"><img alt="Figure 1. Fractals constructed by different fractal generators with the same fractal behaviors or by the same fractal generators with different fractal behaviors. From left to right in each row, the subfigures demonstrate the construction of fractals with greater detail. Left: the fractal generator is scaled to the characteristic dimension of a fractal object J). Center: following a fractal behavior, a simple fractal is constructed. Right: based on the fractal generator and following the fractal behavior, a more complex fractal is obtained in a scale- invariant manner. " class="figure-slide-image" src="https://figures.academia-assets.com/52844510/figure_001.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/39787933/figure-2-fractal-and-its-topography-for-variant-of-the"><img alt="Figure 2. A fractal and its topography for a variant of the Sierpinski gasket. " class="figure-slide-image" src="https://figures.academia-assets.com/52844510/figure_002.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/39787938/figure-3-fractals-to-demonstrate-the-validity-of-eq-ac-are"><img alt="Figure 3. Fractals to demonstrate the validity of Eq. (9). (a—c) are the initiators of scaling objects of the Koch curve, Sierpinski carpet, and Sierpinski gasket, respectively. For convenience, we denote them as fractal generators. At the next step, each potential subpart is replaced by a reduced replicate of the generator and the fractals are obtained. " class="figure-slide-image" src="https://figures.academia-assets.com/52844510/figure_003.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/39787995/figure-4-fractals-sharing-the-same-fractal-generator-but"><img alt="Figure 4. Fractals sharing the same fractal generator but different fractal topographies Q(F, P). The scaling lacunarities of (a)-(d) are 3, 3, 6, and 6, respectively, while the scaling coverages are 5, 8, 17, and 32. According to Eq. (9), the fractal dimensions of (a-d) are log5/log3, log8/log3, log17/log6, and log32/log6, respectively. " class="figure-slide-image" src="https://figures.academia-assets.com/52844510/figure_004.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/39787998/figure-5-construction-of-self-same-self-similar-and-self"><img alt="Figure 5. Construction of self-same, self-similar, and self-affine objects following different fractal topographies. All the fractals generated from the same generator but with different scaling lacunarities P and scaling coverages F. When P,= P, = 1, the generated objects are self-same; while P,= P,~ 1, the generated objects are self-similar; else the generated objects are self-affines. The scaling coverages F in (a)-(d) are 1-4, respectively. In each subfigure, as P,/P, deviates further from 1, the anisotropy of the fractal increases. " class="figure-slide-image" src="https://figures.academia-assets.com/52844510/figure_005.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/39788001/table-1-definition-of-fractal-topography-to-essential"><img alt="" class="figure-slide-image" src="https://figures.academia-assets.com/52844510/table_001.jpg" /></a></figure></div><div class="next-slide-container js-next-button-container"><button aria-label="Next" class="carousel-navigation-button js-profile-work-32678415-figures-next"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">arrow_forward_ios</span></button></div></div></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="95bf40bd80d6edbe78b93bbaf05b486a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52844510,"asset_id":32678415,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52844510/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32678415"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32678415"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32678415; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32678415]").text(description); $(".js-view-count[data-work-id=32678415]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32678415; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32678415']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "95bf40bd80d6edbe78b93bbaf05b486a" } } $('.js-work-strip[data-work-id=32678415]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32678415,"title":"Definition of fractal topography to essential understanding of scale- invariance","translated_title":"","metadata":{"doi":"10.1038/srep46672","abstract":"Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the correspondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter H xy , a general Hurst exponent, which is analytically expressed by H xy = log P x /log P y where P x and P y are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which D H d F P = ∑ (/)log /log i d xi x =1. Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.","ai_title_tag":"Fractal Topography: Scale-Invariance and Fractal Dimension","publication_date":{"day":null,"month":null,"year":2017,"errors":{}},"publication_name":"Scientific Reports"},"translated_abstract":"Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the correspondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter H xy , a general Hurst exponent, which is analytically expressed by H xy = log P x /log P y where P x and P y are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which D H d F P = ∑ (/)log /log i d xi x =1. Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.","internal_url":"https://www.academia.edu/32678415/Definition_of_fractal_topography_to_essential_understanding_of_scale_invariance","translated_internal_url":"","created_at":"2017-04-27T00:19:28.288-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":52844510,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52844510/thumbnails/1.jpg","file_name":"Definition_of_fractal_topography_to_essential_understanding_of_scale-invariance.pdf","download_url":"https://www.academia.edu/attachments/52844510/download_file","bulk_download_file_name":"Definition_of_fractal_topography_to_esse.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52844510/Definition_of_fractal_topography_to_essential_understanding_of_scale-invariance-libre.pdf?1493277666=\u0026response-content-disposition=attachment%3B+filename%3DDefinition_of_fractal_topography_to_esse.pdf\u0026Expires=1743389187\u0026Signature=IuwMqrc8KqfKRrspX2qwEoA1bR6qxhNDyoZqhEpURP8Ms~F5-eB1g4UqLYrupdIR8akyeENrEEQStpOYzwPCWgYp8GKiCj6ZxxBz93X56DJ5nEU1MV2w5AVj6HpxawoRG1fU7z696g946XSlLYSE74s~NJ4gv2YhsHA7KuhbYvJKdxLlBW~cD3XNsdb-VEZ0bbjERuzSMKK3q8l3K0jC5Soz6K7F2T0YGNib6TaNSg997DyISv2PM~tTRYt5GMoa78p36sN4UawbLMAghJ~ynikt3prm28FRR~JJjV-ZKpJErZD~BUPaMY0v6lD6YMf49gsAypl1nU~Rxep~AC~BXg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Definition_of_fractal_topography_to_essential_understanding_of_scale_invariance","translated_slug":"","page_count":8,"language":"en","content_type":"Work","summary":"Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the correspondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter H xy , a general Hurst exponent, which is analytically expressed by H xy = log P x /log P y where P x and P y are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which D H d F P = ∑ (/)log /log i d xi x =1. Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":52844510,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52844510/thumbnails/1.jpg","file_name":"Definition_of_fractal_topography_to_essential_understanding_of_scale-invariance.pdf","download_url":"https://www.academia.edu/attachments/52844510/download_file","bulk_download_file_name":"Definition_of_fractal_topography_to_esse.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52844510/Definition_of_fractal_topography_to_essential_understanding_of_scale-invariance-libre.pdf?1493277666=\u0026response-content-disposition=attachment%3B+filename%3DDefinition_of_fractal_topography_to_esse.pdf\u0026Expires=1743389187\u0026Signature=IuwMqrc8KqfKRrspX2qwEoA1bR6qxhNDyoZqhEpURP8Ms~F5-eB1g4UqLYrupdIR8akyeENrEEQStpOYzwPCWgYp8GKiCj6ZxxBz93X56DJ5nEU1MV2w5AVj6HpxawoRG1fU7z696g946XSlLYSE74s~NJ4gv2YhsHA7KuhbYvJKdxLlBW~cD3XNsdb-VEZ0bbjERuzSMKK3q8l3K0jC5Soz6K7F2T0YGNib6TaNSg997DyISv2PM~tTRYt5GMoa78p36sN4UawbLMAghJ~ynikt3prm28FRR~JJjV-ZKpJErZD~BUPaMY0v6lD6YMf49gsAypl1nU~Rxep~AC~BXg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":154484,"name":"Self-similarity","url":"https://www.academia.edu/Documents/in/Self-similarity"},{"id":890611,"name":"Fractal Dimension","url":"https://www.academia.edu/Documents/in/Fractal_Dimension"},{"id":1447726,"name":"Hurst Exponent","url":"https://www.academia.edu/Documents/in/Hurst_Exponent"},{"id":2657126,"name":"fractal topography","url":"https://www.academia.edu/Documents/in/fractal_topography"},{"id":2689528,"name":"self-affinity","url":"https://www.academia.edu/Documents/in/self-affinity"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (true) { Aedu.setUpFigureCarousel('profile-work-32678415-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="31824813"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/31824813/A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions"><img alt="Research paper thumbnail of A mathematical model of fluid flow in tight porous media based on fractal assumptions" class="work-thumbnail" src="https://attachments.academia-assets.com/52119646/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/31824813/A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions">A mathematical model of fluid flow in tight porous media based on fractal assumptions</a></div><div class="wp-workCard_item"><span>International Journal of Heat and Mass Transfer</span><span>, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Natural tight reservoirs are networks with high connectivity but low porosity, in which fractal b...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Natural tight reservoirs are networks with high connectivity but low porosity, in which fractal behaviors have been widely observed and proven to affect the transport property significantly. The objective of this study is to establish a mathematical model to describe fluid flow in fractal tight porous media. To address this problem, four fractal dimensions were used: the pore size fractal dimension D f , geometrical and hydraulic tortuosity fractal dimensions D sg and D s , and the fractal dimension D k characterizing the hydraulic diameter-number distribution. The relationship among these fractal dimensions was analyzed and D f was found equal to D k þ D sg. Then a unified model connecting the porosity and D f is deduced for arbitrary fractal tight porous media. Based on the scaling-invariant behaviors assumed, a fractal mathematical model is developed for the permeability estimation, which is fabricated only by fundamental and well-defined physical properties of D f ; D s , the scaling lacunarity P k , the range of the pore sizes, and the porosity of the fractal generator u 0. To validate the permeability model, we developed an algorithm to model fractal tight porous media according to the scaling-invariant topography of fractal objects based on Voronoi tessellations, and to simulate fluid flow in these complex networks by Lattice Boltzmann method (LBM) at pore scale. Numerical experiments indicate that the hydraulic tortuosity fractal dimension D s is approximately equal to 1.1. Consequently, the fractal mathematical model was quantitatively determined and its performance was verified by the LBM simulations. Finally, the fractal mathematical model was rearranged into a permeability-porosity form for practical applications.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9786310b63b033f7c8589f37b128f764" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52119646,"asset_id":31824813,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52119646/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="31824813"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="31824813"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 31824813; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=31824813]").text(description); $(".js-view-count[data-work-id=31824813]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 31824813; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='31824813']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "9786310b63b033f7c8589f37b128f764" } } $('.js-work-strip[data-work-id=31824813]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":31824813,"title":"A mathematical model of fluid flow in tight porous media based on fractal assumptions","translated_title":"","metadata":{"doi":"10.1016/j.ijheatmasstransfer.2016.12.096","volume":"108","abstract":"Natural tight reservoirs are networks with high connectivity but low porosity, in which fractal behaviors have been widely observed and proven to affect the transport property significantly. The objective of this study is to establish a mathematical model to describe fluid flow in fractal tight porous media. To address this problem, four fractal dimensions were used: the pore size fractal dimension D f , geometrical and hydraulic tortuosity fractal dimensions D sg and D s , and the fractal dimension D k characterizing the hydraulic diameter-number distribution. The relationship among these fractal dimensions was analyzed and D f was found equal to D k þ D sg. Then a unified model connecting the porosity and D f is deduced for arbitrary fractal tight porous media. Based on the scaling-invariant behaviors assumed, a fractal mathematical model is developed for the permeability estimation, which is fabricated only by fundamental and well-defined physical properties of D f ; D s , the scaling lacunarity P k , the range of the pore sizes, and the porosity of the fractal generator u 0. To validate the permeability model, we developed an algorithm to model fractal tight porous media according to the scaling-invariant topography of fractal objects based on Voronoi tessellations, and to simulate fluid flow in these complex networks by Lattice Boltzmann method (LBM) at pore scale. Numerical experiments indicate that the hydraulic tortuosity fractal dimension D s is approximately equal to 1.1. Consequently, the fractal mathematical model was quantitatively determined and its performance was verified by the LBM simulations. Finally, the fractal mathematical model was rearranged into a permeability-porosity form for practical applications.","page_numbers":"1078-1088","publication_date":{"day":null,"month":null,"year":2017,"errors":{}},"publication_name":"International Journal of Heat and Mass Transfer"},"translated_abstract":"Natural tight reservoirs are networks with high connectivity but low porosity, in which fractal behaviors have been widely observed and proven to affect the transport property significantly. The objective of this study is to establish a mathematical model to describe fluid flow in fractal tight porous media. To address this problem, four fractal dimensions were used: the pore size fractal dimension D f , geometrical and hydraulic tortuosity fractal dimensions D sg and D s , and the fractal dimension D k characterizing the hydraulic diameter-number distribution. The relationship among these fractal dimensions was analyzed and D f was found equal to D k þ D sg. Then a unified model connecting the porosity and D f is deduced for arbitrary fractal tight porous media. Based on the scaling-invariant behaviors assumed, a fractal mathematical model is developed for the permeability estimation, which is fabricated only by fundamental and well-defined physical properties of D f ; D s , the scaling lacunarity P k , the range of the pore sizes, and the porosity of the fractal generator u 0. To validate the permeability model, we developed an algorithm to model fractal tight porous media according to the scaling-invariant topography of fractal objects based on Voronoi tessellations, and to simulate fluid flow in these complex networks by Lattice Boltzmann method (LBM) at pore scale. Numerical experiments indicate that the hydraulic tortuosity fractal dimension D s is approximately equal to 1.1. Consequently, the fractal mathematical model was quantitatively determined and its performance was verified by the LBM simulations. Finally, the fractal mathematical model was rearranged into a permeability-porosity form for practical applications.","internal_url":"https://www.academia.edu/31824813/A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions","translated_internal_url":"","created_at":"2017-03-11T20:25:55.512-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":52119646,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52119646/thumbnails/1.jpg","file_name":"A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions.pdf","download_url":"https://www.academia.edu/attachments/52119646/download_file","bulk_download_file_name":"A_mathematical_model_of_fluid_flow_in_ti.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52119646/A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions-libre.pdf?1489293115=\u0026response-content-disposition=attachment%3B+filename%3DA_mathematical_model_of_fluid_flow_in_ti.pdf\u0026Expires=1743389187\u0026Signature=XiXCGZ7dfQufJkEvmAUUCpCfFbeJhtJRAfOQBnt3n6FqYU1OT8LMZNGg15walIuwQxvLd4USO~gEFMyEU-1VMnImwilptiU4OChXPnbRXXrvryKGI59LYaRbDVIpmwetTf35FxpwhPYTArbRFYdwqyvexMZsOy7yYx7cdvBz2bByWzjYxL8y7DhK5KNMLjTnNDy6PQLUyw0-m3-iAGB6gstznB7pvvILBIrYgFy1lJ4ssFmFB4rsCJuqvIAGWhiEiynmYQSyGIe~ACSrOPFjRP68toOh9MhJDNa71kg0KH-oWnxSuIp4ASgaxOjuGk-v9rsy5Aieix-S-YgHqBG2pw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions","translated_slug":"","page_count":11,"language":"en","content_type":"Work","summary":"Natural tight reservoirs are networks with high connectivity but low porosity, in which fractal behaviors have been widely observed and proven to affect the transport property significantly. The objective of this study is to establish a mathematical model to describe fluid flow in fractal tight porous media. To address this problem, four fractal dimensions were used: the pore size fractal dimension D f , geometrical and hydraulic tortuosity fractal dimensions D sg and D s , and the fractal dimension D k characterizing the hydraulic diameter-number distribution. The relationship among these fractal dimensions was analyzed and D f was found equal to D k þ D sg. Then a unified model connecting the porosity and D f is deduced for arbitrary fractal tight porous media. Based on the scaling-invariant behaviors assumed, a fractal mathematical model is developed for the permeability estimation, which is fabricated only by fundamental and well-defined physical properties of D f ; D s , the scaling lacunarity P k , the range of the pore sizes, and the porosity of the fractal generator u 0. To validate the permeability model, we developed an algorithm to model fractal tight porous media according to the scaling-invariant topography of fractal objects based on Voronoi tessellations, and to simulate fluid flow in these complex networks by Lattice Boltzmann method (LBM) at pore scale. Numerical experiments indicate that the hydraulic tortuosity fractal dimension D s is approximately equal to 1.1. Consequently, the fractal mathematical model was quantitatively determined and its performance was verified by the LBM simulations. Finally, the fractal mathematical model was rearranged into a permeability-porosity form for practical applications.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":52119646,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52119646/thumbnails/1.jpg","file_name":"A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions.pdf","download_url":"https://www.academia.edu/attachments/52119646/download_file","bulk_download_file_name":"A_mathematical_model_of_fluid_flow_in_ti.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52119646/A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions-libre.pdf?1489293115=\u0026response-content-disposition=attachment%3B+filename%3DA_mathematical_model_of_fluid_flow_in_ti.pdf\u0026Expires=1743389187\u0026Signature=XiXCGZ7dfQufJkEvmAUUCpCfFbeJhtJRAfOQBnt3n6FqYU1OT8LMZNGg15walIuwQxvLd4USO~gEFMyEU-1VMnImwilptiU4OChXPnbRXXrvryKGI59LYaRbDVIpmwetTf35FxpwhPYTArbRFYdwqyvexMZsOy7yYx7cdvBz2bByWzjYxL8y7DhK5KNMLjTnNDy6PQLUyw0-m3-iAGB6gstznB7pvvILBIrYgFy1lJ4ssFmFB4rsCJuqvIAGWhiEiynmYQSyGIe~ACSrOPFjRP68toOh9MhJDNa71kg0KH-oWnxSuIp4ASgaxOjuGk-v9rsy5Aieix-S-YgHqBG2pw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":160248,"name":"Fractal Analysis","url":"https://www.academia.edu/Documents/in/Fractal_Analysis"},{"id":231216,"name":"Tight Gas Reserviors","url":"https://www.academia.edu/Documents/in/Tight_Gas_Reserviors"},{"id":1580515,"name":"3D porosity and mineralogy characterization in tight gas sandstones","url":"https://www.academia.edu/Documents/in/3D_porosity_and_mineralogy_characterization_in_tight_gas_sandstones"},{"id":2657126,"name":"fractal topography","url":"https://www.academia.edu/Documents/in/fractal_topography"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-31824813-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="31824783"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/31824783/Scale_and_size_effects_on_fluid_flow_through_self_affine_rough_fractures"><img alt="Research paper thumbnail of Scale and size effects on fluid flow through self-affine rough fractures" class="work-thumbnail" src="https://attachments.academia-assets.com/52119610/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/31824783/Scale_and_size_effects_on_fluid_flow_through_self_affine_rough_fractures">Scale and size effects on fluid flow through self-affine rough fractures</a></div><div class="wp-workCard_item"><span>International Journal of Heat and Mass Transfer</span><span>, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A permeability estimation of a single rough fracture remains challenging and has attracted broad ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A permeability estimation of a single rough fracture remains challenging and has attracted broad attention because of its fundamental importance. This study examines the effects of surface roughness on fracture flow and proposes a new, triple-effect permeability estimation model that takes surface and hydraulic tortuosity other than surface roughness factor (SRF) into account according to the functioning patterns. Due to the scale effect on hydraulic and surface tortuosities, it can also be reformulated into a scaling aperture-permeability equation for a self-affine fracture. Results indicate that tortuosity effects are scaled by 4(H-1) (H is the Hurst exponent) with the mean aperture and that the local SRF, as expected, is stationary at the measurement scale of the mean aperture. In addition, based on the scaling equation and the size effect of self-affine objects, flow regimes are examined and three flow regimes are then identified. Consequently, different permeability models for these regimes are established by fabricating fundamental and well-defined physical properties. The estimation results from these models are in excellent agreement with results from lattice Boltzmann simulations.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c23e05e42b3d990d643301daa5573c20" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52119610,"asset_id":31824783,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52119610/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="31824783"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="31824783"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 31824783; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=31824783]").text(description); $(".js-view-count[data-work-id=31824783]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 31824783; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='31824783']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "c23e05e42b3d990d643301daa5573c20" } } $('.js-work-strip[data-work-id=31824783]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":31824783,"title":"Scale and size effects on fluid flow through self-affine rough fractures","translated_title":"","metadata":{"doi":"10.1016/j.ijheatmasstransfer.2016.10.010","volume":"105","abstract":"A permeability estimation of a single rough fracture remains challenging and has attracted broad attention because of its fundamental importance. 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The estimation results from these models are in excellent agreement with results from lattice Boltzmann simulations.","publication_date":{"day":null,"month":null,"year":2017,"errors":{}},"publication_name":"International Journal of Heat and Mass Transfer"},"translated_abstract":"A permeability estimation of a single rough fracture remains challenging and has attracted broad attention because of its fundamental importance. This study examines the effects of surface roughness on fracture flow and proposes a new, triple-effect permeability estimation model that takes surface and hydraulic tortuosity other than surface roughness factor (SRF) into account according to the functioning patterns. Due to the scale effect on hydraulic and surface tortuosities, it can also be reformulated into a scaling aperture-permeability equation for a self-affine fracture. 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The link must be accompanied by the following text: \"The final publication is available at link.springer.com\".","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":38125520,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/38125520/thumbnails/1.jpg","file_name":"scaling_invariant_effect_on_permeability.pdf","download_url":"https://www.academia.edu/attachments/38125520/download_file","bulk_download_file_name":"Scaling_Invariant_Effects_on_the_Permeab.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/38125520/scaling_invariant_effect_on_permeability-libre.pdf?1436329130=\u0026response-content-disposition=attachment%3B+filename%3DScaling_Invariant_Effects_on_the_Permeab.pdf\u0026Expires=1743389188\u0026Signature=VJCyCj4-OgP39lbELgINYMbFZMt9CNy14pORvXys4oTL7Zk9k6aPGyRlIctsdo22jfARfr5RqpBuWdproMhIyxA2Hahoz-vGppxlP6AvHHh4uRLMu751zUrlSY1YHPe-DNsYATJl~hmahYpmtneRyEsDveswxW2mtEdUUghPGZIpSyayjkdBvhAtXYCBKhQi7V02rGcwUhTd8sTkorYuw-XCE5bH3AJzeEK1XSsn2ffufzjpmi38K2CvvlN-B17~O427TH224Ekhn3aY8G3Ek99TaW6LV8iz~j3yIs9rOvjiQZfK7Yl9M1AfoU-v~CpeEE9B5Osq2TalxkTsXzCMLg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":317,"name":"Fractal Geometry","url":"https://www.academia.edu/Documents/in/Fractal_Geometry"},{"id":2298,"name":"Computational Fluid Dynamics","url":"https://www.academia.edu/Documents/in/Computational_Fluid_Dynamics"},{"id":11997,"name":"Fluid flow in porous media","url":"https://www.academia.edu/Documents/in/Fluid_flow_in_porous_media"},{"id":61709,"name":"Computational Fluid Dynamics (CFD) modelling and simulation","url":"https://www.academia.edu/Documents/in/Computational_Fluid_Dynamics_CFD_modelling_and_simulation"},{"id":62537,"name":"Porosity and Permeability in Reservoirs","url":"https://www.academia.edu/Documents/in/Porosity_and_Permeability_in_Reservoirs"},{"id":148589,"name":"Coal bed methane","url":"https://www.academia.edu/Documents/in/Coal_bed_methane"},{"id":169172,"name":"Numerical modeling and simulation , fluid flow through porous media, Enhanced oil recoveryy","url":"https://www.academia.edu/Documents/in/Numerical_modeling_and_simulation_fluid_flow_through_porous_media_Enhanced_oil_recoveryy"},{"id":726355,"name":"Porosity-Permeability Correlation","url":"https://www.academia.edu/Documents/in/Porosity-Permeability_Correlation"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-13778347-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="8744175"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/8744175/Lattice_Boltzmann_simulation_of_fluid_flow_through_coal_reservoir_s_fractal_pore_structure"><img alt="Research paper thumbnail of Lattice Boltzmann simulation of fluid flow through coal reservoir’s fractal pore structure" class="work-thumbnail" src="https://attachments.academia-assets.com/35097240/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/8744175/Lattice_Boltzmann_simulation_of_fluid_flow_through_coal_reservoir_s_fractal_pore_structure">Lattice Boltzmann simulation of fluid flow through coal reservoir’s fractal pore structure</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The influences of fractal pore structure in coal reservoir on coalbed methane (CBM) migration wer...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The influences of fractal pore structure in coal reservoir on coalbed methane (CBM) migration were analyzed in detail by coupling theoretical models and numerical methods. Different types of fractals were generated based on the construction thought of the standard Menger Sponge to model the 3D nonlinear coal pore structures. Then a correlation model between the permeability of fractal porous medium and its pore-size-distribution characteristics was derived using the parallel and serial modes and verified by Lattice Boltzmann Method (LBM). Based on the coupled method, porosity (), fractal dimension of pore structure (D b ), pore size range (r min, r max ) and other parameters were systematically analyzed for their influences on the permeability () of fractal porous medium. The results indicate that: ① the channels connected by pores with the maximum size (r max ) dominate the permeability  , approximating in the quadratic law; ② the greater the ratio of r max and r min is, the higher  is; ③ the relationship between D b and  follows a negative power law model, and breaks into two segments at the position where D b ≌2.5. Based on the results above, a predicting model of fractal porous medium permeability was proposed, formulated as max n Cfr  , where C and n (approximately equal to 2) are constants and f is an expression only containing parameters of fractal pore structure. In addition, the equivalence of the new proposed model for porous medium and the Kozeny-Carman model =Cr n was verified at D b =2.0. fractal pore structure, porous media, lattice Boltzmann model, coalbed methane (CBM) Citation: Jin Y, Song H B, Hu B, et al. Lattice Boltzmann simulation of fluid flow through coal reservoir's fractal pore structure.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="dfe5fca420f4828fee3066421744b03d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":35097240,"asset_id":8744175,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/35097240/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="8744175"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="8744175"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 8744175; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=8744175]").text(description); $(".js-view-count[data-work-id=8744175]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 8744175; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='8744175']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "dfe5fca420f4828fee3066421744b03d" } } $('.js-work-strip[data-work-id=8744175]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":8744175,"title":"Lattice Boltzmann simulation of fluid flow through coal reservoir’s fractal pore structure","translated_title":"","metadata":{"ai_title_tag":"Fractal Flow Dynamics in Coal Reservoirs","grobid_abstract":"The influences of fractal pore structure in coal reservoir on coalbed methane (CBM) migration were analyzed in detail by coupling theoretical models and numerical methods. Different types of fractals were generated based on the construction thought of the standard Menger Sponge to model the 3D nonlinear coal pore structures. Then a correlation model between the permeability of fractal porous medium and its pore-size-distribution characteristics was derived using the parallel and serial modes and verified by Lattice Boltzmann Method (LBM). Based on the coupled method, porosity (), fractal dimension of pore structure (D b ), pore size range (r min, r max ) and other parameters were systematically analyzed for their influences on the permeability () of fractal porous medium. The results indicate that: ① the channels connected by pores with the maximum size (r max ) dominate the permeability  , approximating in the quadratic law; ② the greater the ratio of r max and r min is, the higher  is; ③ the relationship between D b and  follows a negative power law model, and breaks into two segments at the position where D b ≌2.5. Based on the results above, a predicting model of fractal porous medium permeability was proposed, formulated as max n Cfr  , where C and n (approximately equal to 2) are constants and f is an expression only containing parameters of fractal pore structure. In addition, the equivalence of the new proposed model for porous medium and the Kozeny-Carman model =Cr n was verified at D b =2.0. fractal pore structure, porous media, lattice Boltzmann model, coalbed methane (CBM) Citation: Jin Y, Song H B, Hu B, et al. Lattice Boltzmann simulation of fluid flow through coal reservoir's fractal pore structure.","grobid_abstract_attachment_id":35097240},"translated_abstract":null,"internal_url":"https://www.academia.edu/8744175/Lattice_Boltzmann_simulation_of_fluid_flow_through_coal_reservoir_s_fractal_pore_structure","translated_internal_url":"","created_at":"2014-10-12T10:31:45.930-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":35097240,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/35097240/thumbnails/1.jpg","file_name":"082012-203-130079.pdf","download_url":"https://www.academia.edu/attachments/35097240/download_file","bulk_download_file_name":"Lattice_Boltzmann_simulation_of_fluid_fl.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/35097240/082012-203-130079-libre.pdf?1413134986=\u0026response-content-disposition=attachment%3B+filename%3DLattice_Boltzmann_simulation_of_fluid_fl.pdf\u0026Expires=1743389188\u0026Signature=LjxynNwQ1gSGk9YOOH9PYVQH-FvbWX5kEosNeI3trrl0ixylZoC8l3PHqLI8tubBBXzcjtl47Wf7sgobHOON-CY4WV9EYP~ZECt0bHz8VugNQ2yDSWFrvoc7iEy7e0OtvRlexjSUQEIZy6egYgWlcvpzCusT1cGrQQ~yjnLcCdMrUgSJHV4Y8orx9MaFziFThMRWBPQns079158nXzbm~F2mwu8e2chKg9yxu2dK9SAsM-kJOlunsbOblHFNFoFR3j2t1hnY9JwCwNK-q~FxijuxlnQLY5pSvzktZjJy7DlhUzD0eVtApSRtgjpX3wnZNhXBBpcYm4zjW0Vyo64PvA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Lattice_Boltzmann_simulation_of_fluid_flow_through_coal_reservoir_s_fractal_pore_structure","translated_slug":"","page_count":12,"language":"en","content_type":"Work","summary":"The influences of fractal pore structure in coal reservoir on coalbed methane (CBM) migration were analyzed in detail by coupling theoretical models and numerical methods. Different types of fractals were generated based on the construction thought of the standard Menger Sponge to model the 3D nonlinear coal pore structures. Then a correlation model between the permeability of fractal porous medium and its pore-size-distribution characteristics was derived using the parallel and serial modes and verified by Lattice Boltzmann Method (LBM). Based on the coupled method, porosity (), fractal dimension of pore structure (D b ), pore size range (r min, r max ) and other parameters were systematically analyzed for their influences on the permeability () of fractal porous medium. The results indicate that: ① the channels connected by pores with the maximum size (r max ) dominate the permeability  , approximating in the quadratic law; ② the greater the ratio of r max and r min is, the higher  is; ③ the relationship between D b and  follows a negative power law model, and breaks into two segments at the position where D b ≌2.5. Based on the results above, a predicting model of fractal porous medium permeability was proposed, formulated as max n Cfr  , where C and n (approximately equal to 2) are constants and f is an expression only containing parameters of fractal pore structure. In addition, the equivalence of the new proposed model for porous medium and the Kozeny-Carman model =Cr n was verified at D b =2.0. fractal pore structure, porous media, lattice Boltzmann model, coalbed methane (CBM) Citation: Jin Y, Song H B, Hu B, et al. Lattice Boltzmann simulation of fluid flow through coal reservoir's fractal pore structure.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":35097240,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/35097240/thumbnails/1.jpg","file_name":"082012-203-130079.pdf","download_url":"https://www.academia.edu/attachments/35097240/download_file","bulk_download_file_name":"Lattice_Boltzmann_simulation_of_fluid_fl.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/35097240/082012-203-130079-libre.pdf?1413134986=\u0026response-content-disposition=attachment%3B+filename%3DLattice_Boltzmann_simulation_of_fluid_fl.pdf\u0026Expires=1743389188\u0026Signature=LjxynNwQ1gSGk9YOOH9PYVQH-FvbWX5kEosNeI3trrl0ixylZoC8l3PHqLI8tubBBXzcjtl47Wf7sgobHOON-CY4WV9EYP~ZECt0bHz8VugNQ2yDSWFrvoc7iEy7e0OtvRlexjSUQEIZy6egYgWlcvpzCusT1cGrQQ~yjnLcCdMrUgSJHV4Y8orx9MaFziFThMRWBPQns079158nXzbm~F2mwu8e2chKg9yxu2dK9SAsM-kJOlunsbOblHFNFoFR3j2t1hnY9JwCwNK-q~FxijuxlnQLY5pSvzktZjJy7DlhUzD0eVtApSRtgjpX3wnZNhXBBpcYm4zjW0Vyo64PvA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":11997,"name":"Fluid flow in porous media","url":"https://www.academia.edu/Documents/in/Fluid_flow_in_porous_media"},{"id":24831,"name":"Fractals","url":"https://www.academia.edu/Documents/in/Fractals"},{"id":142354,"name":"Lattice Boltzmann method for fluid dynamics","url":"https://www.academia.edu/Documents/in/Lattice_Boltzmann_method_for_fluid_dynamics"},{"id":726355,"name":"Porosity-Permeability Correlation","url":"https://www.academia.edu/Documents/in/Porosity-Permeability_Correlation"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-8744175-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="8467703"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/8467703/Derivation_of_permeability_pore_relationship_for_fractal_porous_reservoirs_using_series_parallel_flow_resistance_model_and_lattice_Boltzmann_method"><img alt="Research paper thumbnail of Derivation of permeability-pore relationship for fractal porous reservoirs using series-parallel flow resistance model and lattice Boltzmann method" class="work-thumbnail" src="https://attachments.academia-assets.com/34852638/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/8467703/Derivation_of_permeability_pore_relationship_for_fractal_porous_reservoirs_using_series_parallel_flow_resistance_model_and_lattice_Boltzmann_method">Derivation of permeability-pore relationship for fractal porous reservoirs using series-parallel flow resistance model and lattice Boltzmann method</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Permeability of porous reservoirs plays a significant role in engineering and scientific applicat...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Permeability of porous reservoirs plays a significant role in engineering and scientific applications. In this study, we investigated the relationship between pore size fractal dimension (D f ) § Corresponding author. 1440005-1 Fractals 2014.22. Downloaded from <a href="http://www.worldscientific.com" rel="nofollow">www.worldscientific.com</a> by Dr. Jianchao Cai on 09/04/14. For personal use only. B. Wang et al.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1e21f3a75fcf9241f0ef1a27db5af4c1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":34852638,"asset_id":8467703,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/34852638/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="8467703"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="8467703"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 8467703; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=8467703]").text(description); $(".js-view-count[data-work-id=8467703]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 8467703; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='8467703']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1e21f3a75fcf9241f0ef1a27db5af4c1" } } $('.js-work-strip[data-work-id=8467703]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":8467703,"title":"Derivation of permeability-pore relationship for fractal porous reservoirs using series-parallel flow resistance model and lattice Boltzmann method","translated_title":"","metadata":{"grobid_abstract":"Permeability of porous reservoirs plays a significant role in engineering and scientific applications. In this study, we investigated the relationship between pore size fractal dimension (D f ) § Corresponding author. 1440005-1 Fractals 2014.22. Downloaded from www.worldscientific.com by Dr. Jianchao Cai on 09/04/14. For personal use only. B. Wang et al.","grobid_abstract_attachment_id":34852638},"translated_abstract":null,"internal_url":"https://www.academia.edu/8467703/Derivation_of_permeability_pore_relationship_for_fractal_porous_reservoirs_using_series_parallel_flow_resistance_model_and_lattice_Boltzmann_method","translated_internal_url":"","created_at":"2014-09-23T22:29:59.341-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":26974903,"work_id":8467703,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":481262,"email":"z***l@sdu.edu.cn","display_order":0,"name":"Xiaoyang Zhang","title":"Derivation of permeability-pore relationship for fractal porous reservoirs using series-parallel flow resistance model and lattice Boltzmann method"},{"id":32497531,"work_id":8467703,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6835110,"email":"c***8@gmail.com","display_order":4194304,"name":"Qin Chen","title":"Derivation of permeability-pore relationship for fractal porous reservoirs using series-parallel flow resistance model and lattice Boltzmann method"}],"downloadable_attachments":[{"id":34852638,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/34852638/thumbnails/1.jpg","file_name":"FLOW_RESISTANCE_MODEL_AND_LATTICE_BOLTZMANN_METHOD.pdf","download_url":"https://www.academia.edu/attachments/34852638/download_file","bulk_download_file_name":"Derivation_of_permeability_pore_relation.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/34852638/FLOW_RESISTANCE_MODEL_AND_LATTICE_BOLTZMANN_METHOD-libre.pdf?1411556835=\u0026response-content-disposition=attachment%3B+filename%3DDerivation_of_permeability_pore_relation.pdf\u0026Expires=1743389188\u0026Signature=IuTEdF4U7VyoZSKS73tZioRFwkHPjdsFXiq85FV4Y~~Oc-jGjleOKeOLSuy~z-7qp8zK9gNuPlkEEJJfpVxtPn4Z7QffaSzdFb2X3BCz3A230oP9mqqxxSp-ThBCPJYy8z~cYbcNrUZELctjiwcdrWeMgb7VClgeI5DCEgQ0m0KO8DXWgoZQjIqRQR6oiVLUrn99yUx6Bu3YteU3Hgf-R4wOn0LtbtfXoc3pOS-3dOoiUPf3X21VLBrs3BBgWvzVbvI1la5KEdereqh8dJp58Byt03Aui~WmewH9F9dgZDnzSZm0MOayWBu2jD48kWo65uBelPW8pcKnqEjU7Kv3Gw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Derivation_of_permeability_pore_relationship_for_fractal_porous_reservoirs_using_series_parallel_flow_resistance_model_and_lattice_Boltzmann_method","translated_slug":"","page_count":15,"language":"en","content_type":"Work","summary":"Permeability of porous reservoirs plays a significant role in engineering and scientific applications. In this study, we investigated the relationship between pore size fractal dimension (D f ) § Corresponding author. 1440005-1 Fractals 2014.22. Downloaded from www.worldscientific.com by Dr. Jianchao Cai on 09/04/14. For personal use only. B. Wang et al.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":34852638,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/34852638/thumbnails/1.jpg","file_name":"FLOW_RESISTANCE_MODEL_AND_LATTICE_BOLTZMANN_METHOD.pdf","download_url":"https://www.academia.edu/attachments/34852638/download_file","bulk_download_file_name":"Derivation_of_permeability_pore_relation.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/34852638/FLOW_RESISTANCE_MODEL_AND_LATTICE_BOLTZMANN_METHOD-libre.pdf?1411556835=\u0026response-content-disposition=attachment%3B+filename%3DDerivation_of_permeability_pore_relation.pdf\u0026Expires=1743389188\u0026Signature=IuTEdF4U7VyoZSKS73tZioRFwkHPjdsFXiq85FV4Y~~Oc-jGjleOKeOLSuy~z-7qp8zK9gNuPlkEEJJfpVxtPn4Z7QffaSzdFb2X3BCz3A230oP9mqqxxSp-ThBCPJYy8z~cYbcNrUZELctjiwcdrWeMgb7VClgeI5DCEgQ0m0KO8DXWgoZQjIqRQR6oiVLUrn99yUx6Bu3YteU3Hgf-R4wOn0LtbtfXoc3pOS-3dOoiUPf3X21VLBrs3BBgWvzVbvI1la5KEdereqh8dJp58Byt03Aui~WmewH9F9dgZDnzSZm0MOayWBu2jD48kWo65uBelPW8pcKnqEjU7Kv3Gw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":317,"name":"Fractal Geometry","url":"https://www.academia.edu/Documents/in/Fractal_Geometry"},{"id":62537,"name":"Porosity and Permeability in Reservoirs","url":"https://www.academia.edu/Documents/in/Porosity_and_Permeability_in_Reservoirs"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-8467703-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="8467704"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/8467704/Kinematical_measurement_of_hydraulic_tortuosity_of_fluid_flow_in_porous_media"><img alt="Research paper thumbnail of Kinematical measurement of hydraulic tortuosity of fluid flow in porous media" class="work-thumbnail" src="https://attachments.academia-assets.com/34852664/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/8467704/Kinematical_measurement_of_hydraulic_tortuosity_of_fluid_flow_in_porous_media">Kinematical measurement of hydraulic tortuosity of fluid flow in porous media</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">It is hard to experimentally or analytically derive the hydraulic tortuosity () of porous media°o...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">It is hard to experimentally or analytically derive the hydraulic tortuosity () of porous media°ow because of their complex microstructures. In this work, we propose a kinematical measurement method for by introducing the concept of local tortuosity, which is de¯ned as the ratio of°uid particle velocity to its component along the macro°ow. And then, the calculation model of is analytically deduced in terms of that is the mean value of the local tortuosity. To avoid the impact from the singularity of local tortuosity, the velocity is normalized, and is then approximated by the ratio of the mean normalized velocity to the average value of its component along the macro-°ow direction. The new estimation method is veri¯ed by°ow through di®erent types of porous media via the lattice Boltzmann method, and the relationships between permeabilities and tortuosities obtained by di®erent methods are examined. The numerical results show that tortuosity by the novel approach is in good agreement with the existing theory, and the kinematic de¯nition of hydraulic tortuosity is also proven.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="78933c13a3ca0810b73efde901d55093" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":34852664,"asset_id":8467704,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/34852664/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="8467704"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="8467704"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 8467704; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=8467704]").text(description); $(".js-view-count[data-work-id=8467704]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 8467704; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='8467704']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "78933c13a3ca0810b73efde901d55093" } } $('.js-work-strip[data-work-id=8467704]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":8467704,"title":"Kinematical measurement of hydraulic tortuosity of fluid flow in porous media","translated_title":"","metadata":{"grobid_abstract":"It is hard to experimentally or analytically derive the hydraulic tortuosity () of porous media°ow because of their complex microstructures. In this work, we propose a kinematical measurement method for by introducing the concept of local tortuosity, which is de¯ned as the ratio of°uid particle velocity to its component along the macro°ow. And then, the calculation model of is analytically deduced in terms of that is the mean value of the local tortuosity. To avoid the impact from the singularity of local tortuosity, the velocity is normalized, and is then approximated by the ratio of the mean normalized velocity to the average value of its component along the macro-°ow direction. The new estimation method is veri¯ed by°ow through di®erent types of porous media via the lattice Boltzmann method, and the relationships between permeabilities and tortuosities obtained by di®erent methods are examined. The numerical results show that tortuosity by the novel approach is in good agreement with the existing theory, and the kinematic de¯nition of hydraulic tortuosity is also proven.","grobid_abstract_attachment_id":34852664},"translated_abstract":null,"internal_url":"https://www.academia.edu/8467704/Kinematical_measurement_of_hydraulic_tortuosity_of_fluid_flow_in_porous_media","translated_internal_url":"","created_at":"2014-09-23T22:29:59.353-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":34852664,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/34852664/thumbnails/1.jpg","file_name":"s0129183115500175.pdf","download_url":"https://www.academia.edu/attachments/34852664/download_file","bulk_download_file_name":"Kinematical_measurement_of_hydraulic_tor.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/34852664/s0129183115500175-libre.pdf?1411557773=\u0026response-content-disposition=attachment%3B+filename%3DKinematical_measurement_of_hydraulic_tor.pdf\u0026Expires=1743389188\u0026Signature=WuPvNloGETDBAMp~95nI7CNYqXOUGYposjhrhAGrJ2Hc0ljNeyZF5UVlBbelAIAUbUwH-fLss~Atnj7rM2AhGhJSTKiBZdd5uRC6M3RAXPNY6yTVePzyFX9mUrs-ricUXmPpwTw57yb~Ghz7mhmknBmn5FFGnUl5en8GR9yrGeOinOjRzge11zbmjRr9xuDNGywFOV9LC-djR22vM2lz0OGUzDg9spVTS8mjZkiO9SLhh3zQs6smJi6bBEb7aqY~FtC5U8ktAudEDzjnZjsm1P3lkj24ybTB-5QGN2gPJa-a02CSIVJUZx1Xgkruk9zKtw92TF0cwLY3y8KUuyWRyw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Kinematical_measurement_of_hydraulic_tortuosity_of_fluid_flow_in_porous_media","translated_slug":"","page_count":21,"language":"en","content_type":"Work","summary":"It is hard to experimentally or analytically derive the hydraulic tortuosity () of porous media°ow because of their complex microstructures. In this work, we propose a kinematical measurement method for by introducing the concept of local tortuosity, which is de¯ned as the ratio of°uid particle velocity to its component along the macro°ow. And then, the calculation model of is analytically deduced in terms of that is the mean value of the local tortuosity. To avoid the impact from the singularity of local tortuosity, the velocity is normalized, and is then approximated by the ratio of the mean normalized velocity to the average value of its component along the macro-°ow direction. The new estimation method is veri¯ed by°ow through di®erent types of porous media via the lattice Boltzmann method, and the relationships between permeabilities and tortuosities obtained by di®erent methods are examined. The numerical results show that tortuosity by the novel approach is in good agreement with the existing theory, and the kinematic de¯nition of hydraulic tortuosity is also proven.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":34852664,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/34852664/thumbnails/1.jpg","file_name":"s0129183115500175.pdf","download_url":"https://www.academia.edu/attachments/34852664/download_file","bulk_download_file_name":"Kinematical_measurement_of_hydraulic_tor.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/34852664/s0129183115500175-libre.pdf?1411557773=\u0026response-content-disposition=attachment%3B+filename%3DKinematical_measurement_of_hydraulic_tor.pdf\u0026Expires=1743389188\u0026Signature=WuPvNloGETDBAMp~95nI7CNYqXOUGYposjhrhAGrJ2Hc0ljNeyZF5UVlBbelAIAUbUwH-fLss~Atnj7rM2AhGhJSTKiBZdd5uRC6M3RAXPNY6yTVePzyFX9mUrs-ricUXmPpwTw57yb~Ghz7mhmknBmn5FFGnUl5en8GR9yrGeOinOjRzge11zbmjRr9xuDNGywFOV9LC-djR22vM2lz0OGUzDg9spVTS8mjZkiO9SLhh3zQs6smJi6bBEb7aqY~FtC5U8ktAudEDzjnZjsm1P3lkj24ybTB-5QGN2gPJa-a02CSIVJUZx1Xgkruk9zKtw92TF0cwLY3y8KUuyWRyw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":11997,"name":"Fluid flow in porous media","url":"https://www.academia.edu/Documents/in/Fluid_flow_in_porous_media"},{"id":57085,"name":"Transport Phenomena in Porous Media","url":"https://www.academia.edu/Documents/in/Transport_Phenomena_in_Porous_Media"},{"id":142354,"name":"Lattice Boltzmann method for fluid dynamics","url":"https://www.academia.edu/Documents/in/Lattice_Boltzmann_method_for_fluid_dynamics"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-8467704-figures'); } }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="1868909" id="papers"><div class="js-work-strip profile--work_container" data-work-id="100863232"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100863232/Morphology_differences_between_fractional_Brownian_motion_and_the_Weierstrass_Mandelbrot_function_and_corresponding_Hurst_evaluation"><img alt="Research paper thumbnail of Morphology differences between fractional Brownian motion and the Weierstrass-Mandelbrot function and corresponding Hurst evaluation" class="work-thumbnail" src="https://attachments.academia-assets.com/101564205/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100863232/Morphology_differences_between_fractional_Brownian_motion_and_the_Weierstrass_Mandelbrot_function_and_corresponding_Hurst_evaluation">Morphology differences between fractional Brownian motion and the Weierstrass-Mandelbrot function and corresponding Hurst evaluation</a></div><div class="wp-workCard_item"><span>Geomechanics and Geophysics for Geo-Energy and Geo-Resources</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Fractional Brownian motion (FBM) and the Weierstrass-Mandelbrot (W-M) function are two important ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Fractional Brownian motion (FBM) and the Weierstrass-Mandelbrot (W-M) function are two important methods for constructing self-affine objects. Accurately characterizing their features, such as the morphology and fractal geometry, is fundamental for their follow-up applications. However, due to the differences between self-similar and self-affine properties, the fractal dimension evaluation is difficult and sometimes unconvincing. In addition, the sampling length and diversity of calculation methods both lead to the non-uniqueness of the fractal dimension. This study compared the morphology differences between FBM and the W-M function and then analyzed the effects of each parameter on their morphology. Comparisons indicated that FBM has fewer control parameters than the W-M function. Finally, from basic fractal geometric properties, we derived the relationship between the measurement scale r and profile lengths L(r) for self-affine profiles and found that it is a complicated form rat...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="a5d44ffdac9a75f047ace48731b54ee8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":101564205,"asset_id":100863232,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/101564205/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="100863232"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="100863232"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 100863232; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=100863232]").text(description); $(".js-view-count[data-work-id=100863232]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 100863232; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='100863232']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "a5d44ffdac9a75f047ace48731b54ee8" } } $('.js-work-strip[data-work-id=100863232]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":100863232,"title":"Morphology differences between fractional Brownian motion and the Weierstrass-Mandelbrot function and corresponding Hurst evaluation","translated_title":"","metadata":{"abstract":"Fractional Brownian motion (FBM) and the Weierstrass-Mandelbrot (W-M) function are two important methods for constructing self-affine objects. 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Finally, from basic fractal geometric properties, we derived the relationship between the measurement scale r and profile lengths L(r) for self-affine profiles and found that it is a complicated form rat...","publisher":"Springer Science and Business Media LLC","ai_title_tag":"FBM vs W-M Function: Morphology and Hurst Analysis","publication_name":"Geomechanics and Geophysics for Geo-Energy and Geo-Resources"},"translated_abstract":"Fractional Brownian motion (FBM) and the Weierstrass-Mandelbrot (W-M) function are two important methods for constructing self-affine objects. Accurately characterizing their features, such as the morphology and fractal geometry, is fundamental for their follow-up applications. However, due to the differences between self-similar and self-affine properties, the fractal dimension evaluation is difficult and sometimes unconvincing. In addition, the sampling length and diversity of calculation methods both lead to the non-uniqueness of the fractal dimension. This study compared the morphology differences between FBM and the W-M function and then analyzed the effects of each parameter on their morphology. Comparisons indicated that FBM has fewer control parameters than the W-M function. Finally, from basic fractal geometric properties, we derived the relationship between the measurement scale r and profile lengths L(r) for self-affine profiles and found that it is a complicated form rat...","internal_url":"https://www.academia.edu/100863232/Morphology_differences_between_fractional_Brownian_motion_and_the_Weierstrass_Mandelbrot_function_and_corresponding_Hurst_evaluation","translated_internal_url":"","created_at":"2023-04-27T08:09:52.848-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":101564205,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/101564205/thumbnails/1.jpg","file_name":"s40948-023-00532-4.pdf","download_url":"https://www.academia.edu/attachments/101564205/download_file","bulk_download_file_name":"Morphology_differences_between_fractiona.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/101564205/s40948-023-00532-4-libre.pdf?1682609922=\u0026response-content-disposition=attachment%3B+filename%3DMorphology_differences_between_fractiona.pdf\u0026Expires=1743389187\u0026Signature=YCkNqmI2JsINgwIJdnA1bEBrzwD2dVDeA6gKgyExIue~NLe8g8bthwF~~hRVN3FEs~nH6YfK1fGkkA7fVgvvE-YJ-FpsM~uQXgmpmfk8BSiXHds1II1w09lTSP4aP-b-rksjffpvn2fv1-QGX5oIFUZPyh3~a-za6rFERe11aVcQ8iXb4cvG-I~8YJ~v05ccwPvEA60~UAUmxabuv5nq6HddcQTupfbi0weM4UmoU5jDSUAS6fjdmaVny-HM6GPebMV1Et5S1PknfsM1v60wI32J6KKhg-q4Lnu4DYwa0kxiFUlQLVquNhBoI3dkBGpqeDUd604l4c32~gOTs~d3ZQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Morphology_differences_between_fractional_Brownian_motion_and_the_Weierstrass_Mandelbrot_function_and_corresponding_Hurst_evaluation","translated_slug":"","page_count":15,"language":"en","content_type":"Work","summary":"Fractional Brownian motion (FBM) and the Weierstrass-Mandelbrot (W-M) function are two important methods for constructing self-affine objects. 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Finally, from basic fractal geometric properties, we derived the relationship between the measurement scale r and profile lengths L(r) for self-affine profiles and found that it is a complicated form rat...","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":101564205,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/101564205/thumbnails/1.jpg","file_name":"s40948-023-00532-4.pdf","download_url":"https://www.academia.edu/attachments/101564205/download_file","bulk_download_file_name":"Morphology_differences_between_fractiona.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/101564205/s40948-023-00532-4-libre.pdf?1682609922=\u0026response-content-disposition=attachment%3B+filename%3DMorphology_differences_between_fractiona.pdf\u0026Expires=1743389187\u0026Signature=YCkNqmI2JsINgwIJdnA1bEBrzwD2dVDeA6gKgyExIue~NLe8g8bthwF~~hRVN3FEs~nH6YfK1fGkkA7fVgvvE-YJ-FpsM~uQXgmpmfk8BSiXHds1II1w09lTSP4aP-b-rksjffpvn2fv1-QGX5oIFUZPyh3~a-za6rFERe11aVcQ8iXb4cvG-I~8YJ~v05ccwPvEA60~UAUmxabuv5nq6HddcQTupfbi0weM4UmoU5jDSUAS6fjdmaVny-HM6GPebMV1Et5S1PknfsM1v60wI32J6KKhg-q4Lnu4DYwa0kxiFUlQLVquNhBoI3dkBGpqeDUd604l4c32~gOTs~d3ZQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":30970925,"url":"https://link.springer.com/content/pdf/10.1007/s40948-023-00532-4.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-100863232-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="91334815"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/91334815/Seepage_Characteristics_Study_of_Single_Rough_Fracture_Based_on_Numerical_Simulation"><img alt="Research paper thumbnail of Seepage Characteristics Study of Single Rough Fracture Based on Numerical Simulation" class="work-thumbnail" src="https://attachments.academia-assets.com/94651489/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/91334815/Seepage_Characteristics_Study_of_Single_Rough_Fracture_Based_on_Numerical_Simulation">Seepage Characteristics Study of Single Rough Fracture Based on Numerical Simulation</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A single fracture is the basic unit of fracture medium, and the roughness of fracture wall surfac...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A single fracture is the basic unit of fracture medium, and the roughness of fracture wall surface is an important factor influencing hydraulic characteristics of the ﬂow in bedrock fracture. However, effects of the shape and density of roughness elements (various bulges/pits on rough fracture wall surfaces) on water ﬂow in a single rough fracture have not been thoroughly discovered. Thus the water ﬂow in single fracture with different shapes and densities of roughness elements was simulated by using Fluent software in this study. The results show that in wider fractures the flow rate mainly depends on fracture aperture, while in narrow and close fracture medium the surface roughness of fracture wall is the main factor of head loss of seepage; there is a negative power exponential relation between the hydraulic gradient index and the average fracture aperture, i.e. with the increase of fracture aperture, the relative roughness of fracture and the influence weight of hydraulic gradie...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d64c83bdf313fe0064afc6c1a2c53ebf" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":94651489,"asset_id":91334815,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/94651489/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91334815"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91334815"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91334815; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=91334815]").text(description); $(".js-view-count[data-work-id=91334815]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 91334815; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='91334815']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "d64c83bdf313fe0064afc6c1a2c53ebf" } } $('.js-work-strip[data-work-id=91334815]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":91334815,"title":"Seepage Characteristics Study of Single Rough Fracture Based on Numerical Simulation","translated_title":"","metadata":{"abstract":"A single fracture is the basic unit of fracture medium, and the roughness of fracture wall surface is an important factor influencing hydraulic characteristics of the ﬂow in bedrock fracture. However, effects of the shape and density of roughness elements (various bulges/pits on rough fracture wall surfaces) on water ﬂow in a single rough fracture have not been thoroughly discovered. Thus the water ﬂow in single fracture with different shapes and densities of roughness elements was simulated by using Fluent software in this study. The results show that in wider fractures the flow rate mainly depends on fracture aperture, while in narrow and close fracture medium the surface roughness of fracture wall is the main factor of head loss of seepage; there is a negative power exponential relation between the hydraulic gradient index and the average fracture aperture, i.e. with the increase of fracture aperture, the relative roughness of fracture and the influence weight of hydraulic gradie...","publisher":"MDPI AG"},"translated_abstract":"A single fracture is the basic unit of fracture medium, and the roughness of fracture wall surface is an important factor influencing hydraulic characteristics of the ﬂow in bedrock fracture. However, effects of the shape and density of roughness elements (various bulges/pits on rough fracture wall surfaces) on water ﬂow in a single rough fracture have not been thoroughly discovered. Thus the water ﬂow in single fracture with different shapes and densities of roughness elements was simulated by using Fluent software in this study. The results show that in wider fractures the flow rate mainly depends on fracture aperture, while in narrow and close fracture medium the surface roughness of fracture wall is the main factor of head loss of seepage; there is a negative power exponential relation between the hydraulic gradient index and the average fracture aperture, i.e. with the increase of fracture aperture, the relative roughness of fracture and the influence weight of hydraulic gradie...","internal_url":"https://www.academia.edu/91334815/Seepage_Characteristics_Study_of_Single_Rough_Fracture_Based_on_Numerical_Simulation","translated_internal_url":"","created_at":"2022-11-21T22:41:41.666-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":94651489,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/94651489/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/94651489/download_file","bulk_download_file_name":"Seepage_Characteristics_Study_of_Single.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/94651489/pdf-libre.pdf?1669100565=\u0026response-content-disposition=attachment%3B+filename%3DSeepage_Characteristics_Study_of_Single.pdf\u0026Expires=1743389187\u0026Signature=RP4SRBov~yGMn-Qdcm0Os97ZgiZ1CX8~tErJzR0A1r-Uk9VIqUTNjOLde1tuo~QVVC1sEKxNOxJmFNBStuqY9vRRQYJq7BmaPqy1G1nok0IL9EUf00FdqtG5GSwPNLZvbC5vHVuGzo1CGjyqYYJT5h7cVACN7LRl0j9O~oef5GdaGGDOjEHup2~tK~w1GF2Gk1SzbhJHiQfAt0ucLzPtd7EG8xLz5TSFHHyJVQ0DIfaccorEpwxwUSrZJ6fcN3HLr0qXBJIwONbEYdkPpPlJQ3ROi9H~GWLExtGtcmTnYHNH3UaaILyv56pu7bLjGEoDXvHSUiiRp12ThHZFAhvSLA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Seepage_Characteristics_Study_of_Single_Rough_Fracture_Based_on_Numerical_Simulation","translated_slug":"","page_count":16,"language":"en","content_type":"Work","summary":"A single fracture is the basic unit of fracture medium, and the roughness of fracture wall surface is an important factor influencing hydraulic characteristics of the ﬂow in bedrock fracture. However, effects of the shape and density of roughness elements (various bulges/pits on rough fracture wall surfaces) on water ﬂow in a single rough fracture have not been thoroughly discovered. Thus the water ﬂow in single fracture with different shapes and densities of roughness elements was simulated by using Fluent software in this study. The results show that in wider fractures the flow rate mainly depends on fracture aperture, while in narrow and close fracture medium the surface roughness of fracture wall is the main factor of head loss of seepage; there is a negative power exponential relation between the hydraulic gradient index and the average fracture aperture, i.e. with the increase of fracture aperture, the relative roughness of fracture and the influence weight of hydraulic gradie...","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":94651489,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/94651489/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/94651489/download_file","bulk_download_file_name":"Seepage_Characteristics_Study_of_Single.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/94651489/pdf-libre.pdf?1669100565=\u0026response-content-disposition=attachment%3B+filename%3DSeepage_Characteristics_Study_of_Single.pdf\u0026Expires=1743389187\u0026Signature=RP4SRBov~yGMn-Qdcm0Os97ZgiZ1CX8~tErJzR0A1r-Uk9VIqUTNjOLde1tuo~QVVC1sEKxNOxJmFNBStuqY9vRRQYJq7BmaPqy1G1nok0IL9EUf00FdqtG5GSwPNLZvbC5vHVuGzo1CGjyqYYJT5h7cVACN7LRl0j9O~oef5GdaGGDOjEHup2~tK~w1GF2Gk1SzbhJHiQfAt0ucLzPtd7EG8xLz5TSFHHyJVQ0DIfaccorEpwxwUSrZJ6fcN3HLr0qXBJIwONbEYdkPpPlJQ3ROi9H~GWLExtGtcmTnYHNH3UaaILyv56pu7bLjGEoDXvHSUiiRp12ThHZFAhvSLA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":3717,"name":"Geotechnical Engineering","url":"https://www.academia.edu/Documents/in/Geotechnical_Engineering"},{"id":33296,"name":"Surface Roughness","url":"https://www.academia.edu/Documents/in/Surface_Roughness"},{"id":159232,"name":"Applied Sciences","url":"https://www.academia.edu/Documents/in/Applied_Sciences"},{"id":236358,"name":"Hydraulic Roughness","url":"https://www.academia.edu/Documents/in/Hydraulic_Roughness"},{"id":1342788,"name":"Surface Finish","url":"https://www.academia.edu/Documents/in/Surface_Finish"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-91334815-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="91334812"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/91334812/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures"><img alt="Research paper thumbnail of Validity of triple-effect model for fluid flow in mismatched, self-affine fractures" class="work-thumbnail" src="https://attachments.academia-assets.com/94651493/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/91334812/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures">Validity of triple-effect model for fluid flow in mismatched, self-affine fractures</a></div><div class="wp-workCard_item"><span>Advances in Water Resources</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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However, the c...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hu...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="26a49c359b4cfd250eb2ccd900ae8420" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":94651226,"asset_id":91334527,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/94651226/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91334527"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91334527"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91334527; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=91334527]").text(description); $(".js-view-count[data-work-id=91334527]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 91334527; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='91334527']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "26a49c359b4cfd250eb2ccd900ae8420" } } $('.js-work-strip[data-work-id=91334527]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":91334527,"title":"Definition of fractal topography to essential understanding of scale-invariance","translated_title":"","metadata":{"abstract":"Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hu...","publication_date":{"day":24,"month":1,"year":2017,"errors":{}},"publication_name":"Scientific reports"},"translated_abstract":"Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. 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However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. 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In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstructures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity, including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framewo...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="82355316"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="82355316"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 82355316; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=82355316]").text(description); $(".js-view-count[data-work-id=82355316]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 82355316; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='82355316']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=82355316]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":82355316,"title":"Systematic Definition of Complexity Assembly in Fractal Porous Media","translated_title":"","metadata":{"abstract":"Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstructures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity, including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framewo...","publisher":"World Scientific Pub Co Pte Lt","publication_date":{"day":null,"month":null,"year":2020,"errors":{}},"publication_name":"Fractals"},"translated_abstract":"Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstructures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity, including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framewo...","internal_url":"https://www.academia.edu/82355316/Systematic_Definition_of_Complexity_Assembly_in_Fractal_Porous_Media","translated_internal_url":"","created_at":"2022-06-29T09:43:51.871-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Systematic_Definition_of_Complexity_Assembly_in_Fractal_Porous_Media","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstructures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity, including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framewo...","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[],"research_interests":[{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics"},{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics"},{"id":511,"name":"Materials Science","url":"https://www.academia.edu/Documents/in/Materials_Science"},{"id":24831,"name":"Fractals","url":"https://www.academia.edu/Documents/in/Fractals"},{"id":172625,"name":"Fractal","url":"https://www.academia.edu/Documents/in/Fractal"},{"id":890611,"name":"Fractal Dimension","url":"https://www.academia.edu/Documents/in/Fractal_Dimension"},{"id":2689528,"name":"self-affinity","url":"https://www.academia.edu/Documents/in/self-affinity"},{"id":3797714,"name":"Behavioral complexity","url":"https://www.academia.edu/Documents/in/Behavioral_complexity"}],"urls":[{"id":21807890,"url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218348X20500796"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-82355316-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="44531334"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/44531334/Characterizing_the_complexity_assembly_of_pore_structure_in_a_coal_matrix_principle_methodology_and_modeling_application"><img alt="Research paper thumbnail of Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title">Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application</div><div class="wp-workCard_item"><span>Journal of Geophysical Research: Solid Earth</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The pore structure in a coal matrix is a dual‐porosity system where fractures and pores coexist a...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The pore structure in a coal matrix is a dual‐porosity system where fractures and pores coexist and feature scale‐invariance properties, that would affect the occurrence and migration of coalbed methane (CBM) significantly. Therefore, it is of fundamental importance to well define complexity types and effectively characterize their assembly mechanism of pore structure in a coal matrix. Here we identify the pore structure in a coal matrix as a dual‐complexity system consisting of original complexity and behavioral complexity independent to each other, where the former determines the scaling types of single‐ or dual‐porosity structure, while the latter dominates the scale‐invariance properties of self‐similarity, self‐affinity, and multifractality. Next we clarify the essentials of scale‐invariance properties and unify the definition of behavioral complexity. By employing Voronoi diagrams, we develop a dual‐porosity coupling algorithm to describe the original complexity, and set up a mathematical framework to characterize the complexity assembly in fractal dual‐porosity media. For modeling demonstration, we select some typical coal samples from different reservoirs in China, extract the scale‐invariance parameters and establish fractal topography based on mercury intrusion porosimetry (MIP) and N2 adsorption data. Using experimental tests, mathematical derivation and numerical simulations in combination, we reveal the principle and methodology for the characterization of the complexity assembly in a coal matrix.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="44531334"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="44531334"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 44531334; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=44531334]").text(description); $(".js-view-count[data-work-id=44531334]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 44531334; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='44531334']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=44531334]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":44531334,"title":"Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application","translated_title":"","metadata":{"doi":"10.1029/2020JB020110","abstract":"The pore structure in a coal matrix is a dual‐porosity system where fractures and pores coexist and feature scale‐invariance properties, that would affect the occurrence and migration of coalbed methane (CBM) significantly. Therefore, it is of fundamental importance to well define complexity types and effectively characterize their assembly mechanism of pore structure in a coal matrix. Here we identify the pore structure in a coal matrix as a dual‐complexity system consisting of original complexity and behavioral complexity independent to each other, where the former determines the scaling types of single‐ or dual‐porosity structure, while the latter dominates the scale‐invariance properties of self‐similarity, self‐affinity, and multifractality. Next we clarify the essentials of scale‐invariance properties and unify the definition of behavioral complexity. By employing Voronoi diagrams, we develop a dual‐porosity coupling algorithm to describe the original complexity, and set up a mathematical framework to characterize the complexity assembly in fractal dual‐porosity media. For modeling demonstration, we select some typical coal samples from different reservoirs in China, extract the scale‐invariance parameters and establish fractal topography based on mercury intrusion porosimetry (MIP) and N2 adsorption data. Using experimental tests, mathematical derivation and numerical simulations in combination, we reveal the principle and methodology for the characterization of the complexity assembly in a coal matrix.","publication_date":{"day":null,"month":null,"year":2020,"errors":{}},"publication_name":"Journal of Geophysical Research: Solid Earth"},"translated_abstract":"The pore structure in a coal matrix is a dual‐porosity system where fractures and pores coexist and feature scale‐invariance properties, that would affect the occurrence and migration of coalbed methane (CBM) significantly. Therefore, it is of fundamental importance to well define complexity types and effectively characterize their assembly mechanism of pore structure in a coal matrix. Here we identify the pore structure in a coal matrix as a dual‐complexity system consisting of original complexity and behavioral complexity independent to each other, where the former determines the scaling types of single‐ or dual‐porosity structure, while the latter dominates the scale‐invariance properties of self‐similarity, self‐affinity, and multifractality. Next we clarify the essentials of scale‐invariance properties and unify the definition of behavioral complexity. By employing Voronoi diagrams, we develop a dual‐porosity coupling algorithm to describe the original complexity, and set up a mathematical framework to characterize the complexity assembly in fractal dual‐porosity media. For modeling demonstration, we select some typical coal samples from different reservoirs in China, extract the scale‐invariance parameters and establish fractal topography based on mercury intrusion porosimetry (MIP) and N2 adsorption data. Using experimental tests, mathematical derivation and numerical simulations in combination, we reveal the principle and methodology for the characterization of the complexity assembly in a coal matrix.","internal_url":"https://www.academia.edu/44531334/Characterizing_the_complexity_assembly_of_pore_structure_in_a_coal_matrix_principle_methodology_and_modeling_application","translated_internal_url":"","created_at":"2020-11-18T22:48:58.127-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":35964000,"work_id":44531334,"tagging_user_id":17238727,"tagged_user_id":42433086,"co_author_invite_id":null,"email":"c***i@yeah.net","display_order":0,"name":"Mengyu Zhao","title":"Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application"},{"id":35964001,"work_id":44531334,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832185,"email":"z***g@163.com","display_order":4194304,"name":"Junling Zheng","title":"Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application"},{"id":35964002,"work_id":44531334,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6910670,"email":"l***x@hpu.edu.cn","display_order":6291456,"name":"Shunxi Liu","title":"Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application"}],"downloadable_attachments":[],"slug":"Characterizing_the_complexity_assembly_of_pore_structure_in_a_coal_matrix_principle_methodology_and_modeling_application","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"The pore structure in a coal matrix is a dual‐porosity system where fractures and pores coexist and feature scale‐invariance properties, that would affect the occurrence and migration of coalbed methane (CBM) significantly. Therefore, it is of fundamental importance to well define complexity types and effectively characterize their assembly mechanism of pore structure in a coal matrix. Here we identify the pore structure in a coal matrix as a dual‐complexity system consisting of original complexity and behavioral complexity independent to each other, where the former determines the scaling types of single‐ or dual‐porosity structure, while the latter dominates the scale‐invariance properties of self‐similarity, self‐affinity, and multifractality. Next we clarify the essentials of scale‐invariance properties and unify the definition of behavioral complexity. By employing Voronoi diagrams, we develop a dual‐porosity coupling algorithm to describe the original complexity, and set up a mathematical framework to characterize the complexity assembly in fractal dual‐porosity media. For modeling demonstration, we select some typical coal samples from different reservoirs in China, extract the scale‐invariance parameters and establish fractal topography based on mercury intrusion porosimetry (MIP) and N2 adsorption data. Using experimental tests, mathematical derivation and numerical simulations in combination, we reveal the principle and methodology for the characterization of the complexity assembly in a coal matrix.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[],"research_interests":[{"id":2657126,"name":"fractal topography","url":"https://www.academia.edu/Documents/in/fractal_topography"},{"id":3797714,"name":"Behavioral complexity","url":"https://www.academia.edu/Documents/in/Behavioral_complexity"}],"urls":[{"id":9144948,"url":"https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020JB020110"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-44531334-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="44416906"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/44416906/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures"><img alt="Research paper thumbnail of Validity of triple-effect model for fluid flow in mismatched, self-affine fractures" class="work-thumbnail" src="https://attachments.academia-assets.com/64829797/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/44416906/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures">Validity of triple-effect model for fluid flow in mismatched, self-affine fractures</a></div><div class="wp-workCard_item"><span>Advances in Water Resources</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted br...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted broad attention because of its fundamental importance for complex hydrodynamic problems. Although it is natural to assume that permeability value depends on aperture size, it is hard to determine which is the appropriate relationship between them because of the large number of parameters related to the multi-scale geometries and mismatched behaviors in internal surfaces. Moreover, those parameters are hard to obtain by field observation or laboratory tests. For these, we focused on synthesising mismatched composite topography of natural fractures and numerical simulation of fluid flow through them at pore scale. Firstly, the control mechanism of self-affine property was clarified, and a novel Weierstrass-Mandelbrot (W-M) function was proposed to model self-affine profile as per fractal topography theory. Afterwards, a weighting algorithm was developed to construct the composite topography of fractures accounting for the mismatched behavior. Finally, the effects of mismatched behavior, hydraulic and surface tortuosities on fracture flow were systematically analyzed by numerical simulations using Lattice Boltzmann methods (LBM) at pore scale. Our investigation indicates that the aperture distribution is dominated by the mismatched range between internal surfaces, however the hydraulic and surface tortuosity effects are approximately scaled by 2(− 1) (H is the Hurst exponent) with the mean aperture despite of its distribution. Moreover, it was found that the local surface roughness factor, accounting for effects from surface geometries with size smaller than the value of mean aperture, is stationary at long range and inversely proportional to fracture permeability. Based on above discussions, the validity of triple-effect model for permeability prediction of mismatched self-affine fractures was established.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="174bc37c457580dfbd8841c45b0d4111" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":64829797,"asset_id":44416906,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/64829797/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="44416906"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="44416906"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 44416906; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=44416906]").text(description); $(".js-view-count[data-work-id=44416906]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 44416906; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='44416906']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "174bc37c457580dfbd8841c45b0d4111" } } $('.js-work-strip[data-work-id=44416906]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":44416906,"title":"Validity of triple-effect model for fluid flow in mismatched, self-affine fractures","translated_title":"","metadata":{"doi":"10.1016/j.advwatres.2020.103585","abstract":"Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted broad attention because of its fundamental importance for complex hydrodynamic problems. Although it is natural to assume that permeability value depends on aperture size, it is hard to determine which is the appropriate relationship between them because of the large number of parameters related to the multi-scale geometries and mismatched behaviors in internal surfaces. Moreover, those parameters are hard to obtain by field observation or laboratory tests. For these, we focused on synthesising mismatched composite topography of natural fractures and numerical simulation of fluid flow through them at pore scale. Firstly, the control mechanism of self-affine property was clarified, and a novel Weierstrass-Mandelbrot (W-M) function was proposed to model self-affine profile as per fractal topography theory. Afterwards, a weighting algorithm was developed to construct the composite topography of fractures accounting for the mismatched behavior. Finally, the effects of mismatched behavior, hydraulic and surface tortuosities on fracture flow were systematically analyzed by numerical simulations using Lattice Boltzmann methods (LBM) at pore scale. Our investigation indicates that the aperture distribution is dominated by the mismatched range between internal surfaces, however the hydraulic and surface tortuosity effects are approximately scaled by 2(− 1) (H is the Hurst exponent) with the mean aperture despite of its distribution. Moreover, it was found that the local surface roughness factor, accounting for effects from surface geometries with size smaller than the value of mean aperture, is stationary at long range and inversely proportional to fracture permeability. Based on above discussions, the validity of triple-effect model for permeability prediction of mismatched self-affine fractures was established.","ai_title_tag":"Triple-Effect Model for Self-Affine Fractures","publication_date":{"day":null,"month":null,"year":2020,"errors":{}},"publication_name":"Advances in Water Resources"},"translated_abstract":"Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted broad attention because of its fundamental importance for complex hydrodynamic problems. Although it is natural to assume that permeability value depends on aperture size, it is hard to determine which is the appropriate relationship between them because of the large number of parameters related to the multi-scale geometries and mismatched behaviors in internal surfaces. Moreover, those parameters are hard to obtain by field observation or laboratory tests. For these, we focused on synthesising mismatched composite topography of natural fractures and numerical simulation of fluid flow through them at pore scale. Firstly, the control mechanism of self-affine property was clarified, and a novel Weierstrass-Mandelbrot (W-M) function was proposed to model self-affine profile as per fractal topography theory. Afterwards, a weighting algorithm was developed to construct the composite topography of fractures accounting for the mismatched behavior. Finally, the effects of mismatched behavior, hydraulic and surface tortuosities on fracture flow were systematically analyzed by numerical simulations using Lattice Boltzmann methods (LBM) at pore scale. Our investigation indicates that the aperture distribution is dominated by the mismatched range between internal surfaces, however the hydraulic and surface tortuosity effects are approximately scaled by 2(− 1) (H is the Hurst exponent) with the mean aperture despite of its distribution. Moreover, it was found that the local surface roughness factor, accounting for effects from surface geometries with size smaller than the value of mean aperture, is stationary at long range and inversely proportional to fracture permeability. Based on above discussions, the validity of triple-effect model for permeability prediction of mismatched self-affine fractures was established.","internal_url":"https://www.academia.edu/44416906/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures","translated_internal_url":"","created_at":"2020-11-02T00:46:33.986-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":35901189,"work_id":44416906,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832185,"email":"z***g@163.com","display_order":1,"name":"Junling Zheng","title":"Validity of triple-effect model for fluid flow in mismatched, self-affine fractures"},{"id":35901190,"work_id":44416906,"tagging_user_id":17238727,"tagged_user_id":178383415,"co_author_invite_id":7135913,"email":"5***1@qq.com","display_order":2,"name":"Cheng Wang","title":"Validity of triple-effect model for fluid flow in mismatched, self-affine fractures"},{"id":35901191,"work_id":44416906,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":7135915,"email":"a***5@qq.com","display_order":3,"name":"Xiaokun Liu","title":"Validity of triple-effect model for fluid flow in mismatched, self-affine fractures"}],"downloadable_attachments":[{"id":64829797,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/64829797/thumbnails/1.jpg","file_name":"Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures.pdf","download_url":"https://www.academia.edu/attachments/64829797/download_file","bulk_download_file_name":"Validity_of_triple_effect_model_for_flui.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/64829797/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures-libre.pdf?1604312100=\u0026response-content-disposition=attachment%3B+filename%3DValidity_of_triple_effect_model_for_flui.pdf\u0026Expires=1743389187\u0026Signature=Af6R~JUNxAoLbCYCdlnqsiojxtXXXCv7VbJAwuukvjkWt0HJsNgjNM38Ka0kJX1LdoZzHIPvOvTmedwf5sONpZcPEp78eOSjgBK8OveqApvQhnsS~bqAiXUqEWSCoCsFTIe54cD5NmKkkkHb2utXBcd17b7PinZkkeE1dX-b-dFiw7omTnHU3MakS2RD1JCWVcgl8fEGskZ635Dy9LvBYZus~nXEqoRyX9gOoFl8gnBYWpkQ2fVoJ67yy2zxaNjizf2b16XqmrWDWC5zkf8Nw-j5KXgvWuH4gYhQx1Q0O3qFY17k4jHnFzKp84GeDVqClXy5TWc5bTiEzmnKF9tYfg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures","translated_slug":"","page_count":10,"language":"en","content_type":"Work","summary":"Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted broad attention because of its fundamental importance for complex hydrodynamic problems. Although it is natural to assume that permeability value depends on aperture size, it is hard to determine which is the appropriate relationship between them because of the large number of parameters related to the multi-scale geometries and mismatched behaviors in internal surfaces. Moreover, those parameters are hard to obtain by field observation or laboratory tests. For these, we focused on synthesising mismatched composite topography of natural fractures and numerical simulation of fluid flow through them at pore scale. Firstly, the control mechanism of self-affine property was clarified, and a novel Weierstrass-Mandelbrot (W-M) function was proposed to model self-affine profile as per fractal topography theory. Afterwards, a weighting algorithm was developed to construct the composite topography of fractures accounting for the mismatched behavior. Finally, the effects of mismatched behavior, hydraulic and surface tortuosities on fracture flow were systematically analyzed by numerical simulations using Lattice Boltzmann methods (LBM) at pore scale. Our investigation indicates that the aperture distribution is dominated by the mismatched range between internal surfaces, however the hydraulic and surface tortuosity effects are approximately scaled by 2(− 1) (H is the Hurst exponent) with the mean aperture despite of its distribution. Moreover, it was found that the local surface roughness factor, accounting for effects from surface geometries with size smaller than the value of mean aperture, is stationary at long range and inversely proportional to fracture permeability. Based on above discussions, the validity of triple-effect model for permeability prediction of mismatched self-affine fractures was established.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":64829797,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/64829797/thumbnails/1.jpg","file_name":"Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures.pdf","download_url":"https://www.academia.edu/attachments/64829797/download_file","bulk_download_file_name":"Validity_of_triple_effect_model_for_flui.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/64829797/Validity_of_triple_effect_model_for_fluid_flow_in_mismatched_self_affine_fractures-libre.pdf?1604312100=\u0026response-content-disposition=attachment%3B+filename%3DValidity_of_triple_effect_model_for_flui.pdf\u0026Expires=1743389187\u0026Signature=Af6R~JUNxAoLbCYCdlnqsiojxtXXXCv7VbJAwuukvjkWt0HJsNgjNM38Ka0kJX1LdoZzHIPvOvTmedwf5sONpZcPEp78eOSjgBK8OveqApvQhnsS~bqAiXUqEWSCoCsFTIe54cD5NmKkkkHb2utXBcd17b7PinZkkeE1dX-b-dFiw7omTnHU3MakS2RD1JCWVcgl8fEGskZ635Dy9LvBYZus~nXEqoRyX9gOoFl8gnBYWpkQ2fVoJ67yy2zxaNjizf2b16XqmrWDWC5zkf8Nw-j5KXgvWuH4gYhQx1Q0O3qFY17k4jHnFzKp84GeDVqClXy5TWc5bTiEzmnKF9tYfg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":215076,"name":"Fluid flow","url":"https://www.academia.edu/Documents/in/Fluid_flow"},{"id":890611,"name":"Fractal Dimension","url":"https://www.academia.edu/Documents/in/Fractal_Dimension"},{"id":1447726,"name":"Hurst Exponent","url":"https://www.academia.edu/Documents/in/Hurst_Exponent"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-44416906-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="44416814"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/44416814/SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA"><img alt="Research paper thumbnail of SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA" class="work-thumbnail" src="https://attachments.academia-assets.com/64829670/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/44416814/SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA">SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://henanpu.academia.edu/yiJin">yi Jin</a>, <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/ChengWang92">Cheng Wang</a>, and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/WeizheQuan">Weizhe Quan</a></span></div><div class="wp-workCard_item"><span>Fractals</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Microstructures dominate the physical properties of fractal porous media, which means the clarifi...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstruc-tures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity , including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framework is open to arbitrary original and behavioral complexities, and eases the modeling of multi-scale microstructures and the property estimation significantly.</span></div><div class="wp-workCard_item"><div class="carousel-container carousel-container--sm" id="profile-work-44416814-figures"><div class="prev-slide-container js-prev-button-container"><button aria-label="Previous" class="carousel-navigation-button js-profile-work-44416814-figures-prev"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">arrow_back_ios</span></button></div><div class="slides-container js-slides-container"><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278786/figure-11-self-affine-porous-media-with-different-fractal"><img alt="Fig. 11 Self-affine porous media with different fractal topography. (a), (e), and (i) with the increasing of Py; (b), (f), and (j) with the increasing of Py; (c), (g), and (k): with the increasing of F. (d), (h), and (1) have the same D but the fractal topography parameters are different. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_011.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278659/figure-1-the-simple-of-qsgs-where-lists-eight-growth"><img alt="Fig. 1 The simple scheme of QSGS,*! where (a) lists eight growth directions in the QSGS algorithm and (b) represents a modeling result. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_001.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278675/figure-2-generation-processes-of-multi-phase-fractals-where"><img alt="Fig. 2 Generation processes of multi-phase fractals, where @ and others represent modeling process following by or not following by PSF model, respectively. In these three pro- cesses, (a) is the fractal generator which define the original complexity shared by processes @, @, and @, (b) denotes the definition of fractal behavior, and (c) represents frac- tal iteration based on the definitions of original complexity and fractal behaviors. In (a), the original complexity is com- posed of determined phases of pore (p) and solid (s), while the behavioral complexity is enclosed in fractal phase (f). The area ratio tp = 4/9, vs = 2/9, xp = 3/9, and the struc- ture parameter n = 3. In process @, (b) defines the fractal behavior following PSF model with scaling factor taking the value of n. While in process @, (b) defines self-similar behav- ior not following PSF model with scaling factor of 2n. As for process @, (b) defines self-affine behavior with scaling fac- tors in xz- and y-direction, respectively, to be n and 2n. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_002.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278685/figure-3-variant-of-sierpinski-carpet-and-its-fractal"><img alt="Fig. 3 Variant of Sierpinski carpet and its fractal topogra- phy modified after that in Ref. 13. In this fractal structure P = (Pr, Py) = (3,4) and the expectation of F is equal tc 3. Black, white, and yellow denote the three different deter- mined phases, while gray denotes the fractal phase. In the scaling object, vs = 1/9, zy = 2/9 with xy representing the area ratio of yellow phase, rp = 5/12, and af = 1/4 respectively. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_003.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278702/figure-4-comparison-of-qsgs-and-fractal-topography-the-model"><img alt="Fig. 4 Comparison of QSGS and fractal topography. The model on the left-hand side was constructed by QSGS with the ratio of the growth probabilities set to be pa, : Pdz,, = 2 to represent anisotropy, and the fractal models on the right-hand side share the same fractal topography of Q((Pr, Py), F) = 2((2,4), 2) with Hyx = 2 to reflect self-affine properties. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_004.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278712/figure-5-generation-of-self-affine-fractal-model-parameters"><img alt="Fig. 5 Generation of self-affine fractal model. Parameters are Py = 3, Py = 2, and (F’) = 4. Red, blue, and yellow represent three different phases. Red and blue are growing phases with opposite-colored seeds. For convenience, fractal porous media were denoted by F3.(Q,G,L) following our previous denotation,!? with Q being the shortened version of Q(P,F), G representing the multi-type scaling object that is generated by QSGS, and L being the scaling range. As shown in Fig. 5, the scaling object " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_005.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278732/figure-6-fractal-porous-media-generated-by-fqsgs-and-are-the"><img alt="Fig. 6 Fractal porous media generated by FQSGS. (a), (b), and (c) are the self-similarities with fractal topographies of (2,2), 2(2.5,4), and (4,2), respectively. (d), (e), and (f) are the self-affinities with the respective parameters of ((1.2,3), 2), Q((3, 1.5), 2), and Q((2,3),2). (g) and (h) with (3,3) and (2,1) are multi-phase models, in which the proportions of yellow and white phases are (0.15, 0.15) and (0.2, 0.1), respectively. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_006.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278737/figure-8-verification-of-porosity-calculation-for-self"><img alt="Fig. 8 Verification of porosity calculation for (a) self-similar model and (b) self-affine model. Fig. 7 Verification of the behavioral complexity by fractal dimension, where (a) and (b) are the relationships of self-similaz and self-affine porous media, respectively. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_007.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278752/figure-8-systematic-definition-of-complexity-assembly-in"><img alt="" class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_008.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278762/figure-9-fractal-porous-models-with-different-hzy-values"><img alt="Fig. 9 Fractal porous models with different Hzy values. White and black denote the solid and pore phases, respectively. (F) = 2 for all models in this figure. The Hzy values of (a)—(c) are 1.58, 1.63, and 2.58, respectively; and the P values of (d)-(f) are 2, 3, and 6 with Hzy = 1, respectively. The Hzy values of (g)—(i) are 0.63, 0.61, and 0.38, respectively. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_009.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278774/figure-10-self-similar-porous-media-where-the-expectation-of"><img alt="Fig. 10 Self-similar porous media, where the expectation of F increases from the top to the bottom and P increases fror left to right. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_010.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278795/figure-12-models-of-different-original-complexities-models"><img alt="Fig. 12 Models of different original complexities. Models (a)—(d) are self-similar with Q(P, F’) = (2,2). While models (e)— (h) are self-affine with P, = 2, Py = 6, and (F’) = 2. The pore phase is black, whereas the two determined phases are white and yellow. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_012.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278807/figure-13-complexity-assembly-and-control-system-in-fractal"><img alt="Fig. 13 Complexity assembly and control system in fractal porous media. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/figure_013.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278820/table-2-scaling-parameters-sl-and-sc-and-fractal-dimension"><img alt="Table 2 Scaling Parameters, SL and SC, and Fractal Dimension D (by Eq. (10)) of Self-Similar Porous Media in Fig. 10. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/table_001.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278829/table-3-scaling-parameters-sl-and-sc-and-fractal-dimension"><img alt="Table 3 Scaling Parameters, SL and SC, and Fractal Dimension D (by Eq. (10)) of Self-Affine Porous Media in Fig. 11. As P, increases, a compression of the particles in the y-direction increases gradually. While the increase of P, leads to an increasing degree of parti- cle compression in the x-direction, as shown by the porous media in the second column of Fig. 11. This result is consistent with that in Sec. 4.2. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/table_002.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/46278847/table-4-parameters-of-single-and-multi-phase-models-zs-white"><img alt="Table 4 Parameters of Single- and Multi-Phase Models. 2zs,: ‘“White” Phase, %s,: “Yellow” Phase. " class="figure-slide-image" src="https://figures.academia-assets.com/64829670/table_003.jpg" /></a></figure></div><div class="next-slide-container js-next-button-container"><button aria-label="Next" class="carousel-navigation-button js-profile-work-44416814-figures-next"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">arrow_forward_ios</span></button></div></div></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e2de5b0ab8bc4a1f48fe455d40f5b587" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":64829670,"asset_id":44416814,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/64829670/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="44416814"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="44416814"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 44416814; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=44416814]").text(description); $(".js-view-count[data-work-id=44416814]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 44416814; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='44416814']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "e2de5b0ab8bc4a1f48fe455d40f5b587" } } $('.js-work-strip[data-work-id=44416814]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":44416814,"title":"SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA","translated_title":"","metadata":{"doi":"10.1142/S0218348X20500796","abstract":"Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstruc-tures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity , including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framework is open to arbitrary original and behavioral complexities, and eases the modeling of multi-scale microstructures and the property estimation significantly.","ai_title_tag":"Defining Complexity Assembly in Fractal Porous Media","publication_date":{"day":null,"month":null,"year":2020,"errors":{}},"publication_name":"Fractals"},"translated_abstract":"Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstruc-tures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity , including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framework is open to arbitrary original and behavioral complexities, and eases the modeling of multi-scale microstructures and the property estimation significantly.","internal_url":"https://www.academia.edu/44416814/SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA","translated_internal_url":"","created_at":"2020-11-02T00:32:19.294-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":35901152,"work_id":44416814,"tagging_user_id":17238727,"tagged_user_id":178383415,"co_author_invite_id":7135913,"email":"5***1@qq.com","display_order":1,"name":"Cheng Wang","title":"SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA"},{"id":35901153,"work_id":44416814,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6910670,"email":"l***x@hpu.edu.cn","display_order":2,"name":"Shunxi Liu","title":"SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA"},{"id":35901154,"work_id":44416814,"tagging_user_id":17238727,"tagged_user_id":178374458,"co_author_invite_id":7135914,"email":"7***1@qq.com","display_order":3,"name":"Weizhe Quan","title":"SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA"},{"id":35901155,"work_id":44416814,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":7135915,"email":"a***5@qq.com","display_order":4,"name":"Xiaokun Liu","title":"SYSTEMATIC DEFINITION OF COMPLEXITY ASSEMBLY IN FRACTAL POROUS MEDIA"}],"downloadable_attachments":[{"id":64829670,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/64829670/thumbnails/1.jpg","file_name":"SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA.pdf","download_url":"https://www.academia.edu/attachments/64829670/download_file","bulk_download_file_name":"SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSE.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/64829670/SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA-libre.pdf?1604306113=\u0026response-content-disposition=attachment%3B+filename%3DSYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSE.pdf\u0026Expires=1743389187\u0026Signature=ZukVJZhG1QOadCKSeV7jMhm5N~3d36L5pJUpJE0PXaAzW7jJLofxyTvNp6sAgptqTpkV-dznS4w8Z5dcmiq6gtb3rdU1pqKkSOC8FLu-ahLBPbrMhRBulOa7UEX4YZ-ilWGaFXn8yN366rojtUppWeb4zTtolvVGV4qPsgaebWyaJET8E5hU8b53tAZIk0HP3ODmoFU86LtYOQH9JnOswu8QJ--BJPC49-drSyAPePSJu~vbqgv~P~c1A~RlvIdg1VfjHnUdQIIG2mmm2-kKEIJ8bzw7we0rCFJxfQ62l7MmdlecxAYE0sOql5W8580tGbW3Ek2iaF5vLyJ00sOPCw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA","translated_slug":"","page_count":16,"language":"en","content_type":"Work","summary":"Microstructures dominate the physical properties of fractal porous media, which means the clarification of complexity types and their assembly are of fundamental importance for static or dynamic purposes. In this work, we identified fractal porous media to dual-complexity systems composed of stationary and scale-invariant complexities as per fractal topography theory, and proposed an open mathematical framework to characterize complexity assembly in microstruc-tures, realized the original complexity, such as random, multi-phase, and multi-type features by the quartet structure generation set (QSGS) algorithm, and unified the behavioral complexity , including the self-similar and self-affine properties by fractal topography model. For demonstration, the control mechanisms on the microstructures from different complexities are discussed, with their physical implications and relations to the physical properties of porous media clarified in principle. The results indicate that our framework is open to arbitrary original and behavioral complexities, and eases the modeling of multi-scale microstructures and the property estimation significantly.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":64829670,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/64829670/thumbnails/1.jpg","file_name":"SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA.pdf","download_url":"https://www.academia.edu/attachments/64829670/download_file","bulk_download_file_name":"SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSE.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/64829670/SYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSEMBLY_IN_FRACTAL_POROUS_MEDIA-libre.pdf?1604306113=\u0026response-content-disposition=attachment%3B+filename%3DSYSTEMATIC_DEFINITION_OF_COMPLEXITY_ASSE.pdf\u0026Expires=1743389187\u0026Signature=ZukVJZhG1QOadCKSeV7jMhm5N~3d36L5pJUpJE0PXaAzW7jJLofxyTvNp6sAgptqTpkV-dznS4w8Z5dcmiq6gtb3rdU1pqKkSOC8FLu-ahLBPbrMhRBulOa7UEX4YZ-ilWGaFXn8yN366rojtUppWeb4zTtolvVGV4qPsgaebWyaJET8E5hU8b53tAZIk0HP3ODmoFU86LtYOQH9JnOswu8QJ--BJPC49-drSyAPePSJu~vbqgv~P~c1A~RlvIdg1VfjHnUdQIIG2mmm2-kKEIJ8bzw7we0rCFJxfQ62l7MmdlecxAYE0sOql5W8580tGbW3Ek2iaF5vLyJ00sOPCw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":24831,"name":"Fractals","url":"https://www.academia.edu/Documents/in/Fractals"},{"id":2689528,"name":"self-affinity","url":"https://www.academia.edu/Documents/in/self-affinity"},{"id":3797714,"name":"Behavioral complexity","url":"https://www.academia.edu/Documents/in/Behavioral_complexity"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (true) { Aedu.setUpFigureCarousel('profile-work-44416814-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="40495697"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/40495697/Control_mechanisms_of_self_affine_rough_cleat_networks_on_flow_dynamics_in_coal_reservoir"><img alt="Research paper thumbnail of Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir" class="work-thumbnail" src="https://attachments.academia-assets.com/60764690/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/40495697/Control_mechanisms_of_self_affine_rough_cleat_networks_on_flow_dynamics_in_coal_reservoir">Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir</a></div><div class="wp-workCard_item"><span>Energy</span><span>, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Cleat networks dominate the migration of coalbed methane (CBM), which is assembled by cleats of d...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Cleat networks dominate the migration of coalbed methane (CBM), which is assembled by cleats of different type following special configuration and possessing rough, self-affine surfaces. Nowadays, configuration implications, scale-invariant properties, fractal control mechanisms, and their relations to flow dynamics have not yet been fully clarified. Herein we explore these issues numerically using effective modeling of cleat networks and pore-scale simulations of fluid flow through them. Firstly, the control mechanics of fractal dynamics was clarified by fractal topography theory, a new definition of Weierstrass-Mandelbrot (W-M) function was proposed to characterize the self-affine surface geometries, an algorithm was developed to effectively construct cleat networks similar in coal, and Lattice Boltzmann method (LBM) was used to reproduce the fluid flow in numerical cleat networks at the pore scale. Af-terwards, the implications of spatial configuration of cleats and fractal control mechanisms of surface geometries on the permeability were systematically analyzed and quantified. Finally, an empirical model was established to predict the permeability of self-affine, rough cleat networks, rather than a rough estimation by a power-law proportionality in previous research. The performance of the proposed model was fully verified by comparative analysis and numerical simulations. Theoretical analysis denotes that our model can generalize several traditional and newly developed models from the literature.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1f7e46e6a8d058b347cbb89590d7c6e8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":60764690,"asset_id":40495697,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/60764690/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="40495697"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="40495697"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 40495697; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=40495697]").text(description); $(".js-view-count[data-work-id=40495697]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 40495697; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='40495697']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1f7e46e6a8d058b347cbb89590d7c6e8" } } $('.js-work-strip[data-work-id=40495697]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":40495697,"title":"Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir","translated_title":"","metadata":{"doi":"10.1016/j.energy.2019.116146","abstract":"Cleat networks dominate the migration of coalbed methane (CBM), which is assembled by cleats of different type following special configuration and possessing rough, self-affine surfaces. Nowadays, configuration implications, scale-invariant properties, fractal control mechanisms, and their relations to flow dynamics have not yet been fully clarified. Herein we explore these issues numerically using effective modeling of cleat networks and pore-scale simulations of fluid flow through them. Firstly, the control mechanics of fractal dynamics was clarified by fractal topography theory, a new definition of Weierstrass-Mandelbrot (W-M) function was proposed to characterize the self-affine surface geometries, an algorithm was developed to effectively construct cleat networks similar in coal, and Lattice Boltzmann method (LBM) was used to reproduce the fluid flow in numerical cleat networks at the pore scale. Af-terwards, the implications of spatial configuration of cleats and fractal control mechanisms of surface geometries on the permeability were systematically analyzed and quantified. Finally, an empirical model was established to predict the permeability of self-affine, rough cleat networks, rather than a rough estimation by a power-law proportionality in previous research. The performance of the proposed model was fully verified by comparative analysis and numerical simulations. Theoretical analysis denotes that our model can generalize several traditional and newly developed models from the literature.","publication_date":{"day":null,"month":null,"year":2019,"errors":{}},"publication_name":"Energy"},"translated_abstract":"Cleat networks dominate the migration of coalbed methane (CBM), which is assembled by cleats of different type following special configuration and possessing rough, self-affine surfaces. Nowadays, configuration implications, scale-invariant properties, fractal control mechanisms, and their relations to flow dynamics have not yet been fully clarified. Herein we explore these issues numerically using effective modeling of cleat networks and pore-scale simulations of fluid flow through them. Firstly, the control mechanics of fractal dynamics was clarified by fractal topography theory, a new definition of Weierstrass-Mandelbrot (W-M) function was proposed to characterize the self-affine surface geometries, an algorithm was developed to effectively construct cleat networks similar in coal, and Lattice Boltzmann method (LBM) was used to reproduce the fluid flow in numerical cleat networks at the pore scale. Af-terwards, the implications of spatial configuration of cleats and fractal control mechanisms of surface geometries on the permeability were systematically analyzed and quantified. Finally, an empirical model was established to predict the permeability of self-affine, rough cleat networks, rather than a rough estimation by a power-law proportionality in previous research. The performance of the proposed model was fully verified by comparative analysis and numerical simulations. Theoretical analysis denotes that our model can generalize several traditional and newly developed models from the literature.","internal_url":"https://www.academia.edu/40495697/Control_mechanisms_of_self_affine_rough_cleat_networks_on_flow_dynamics_in_coal_reservoir","translated_internal_url":"","created_at":"2019-10-01T19:35:53.317-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":33090662,"work_id":40495697,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832185,"email":"z***g@163.com","display_order":1,"name":"Junling Zheng","title":"Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir"},{"id":33090663,"work_id":40495697,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832183,"email":"1***6@qq.com","display_order":2,"name":"Xianhe Liu","title":"Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir"},{"id":33090664,"work_id":40495697,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6832186,"email":"j***n@hpu.edu.cn","display_order":3,"name":"Jienan Pan","title":"Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir"},{"id":33090665,"work_id":40495697,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6910670,"email":"l***x@hpu.edu.cn","display_order":4,"name":"Shunxi Liu","title":"Control mechanisms of self-affine, rough cleat networks on flow dynamics in coal reservoir"}],"downloadable_attachments":[{"id":60764690,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/60764690/thumbnails/1.jpg","file_name":"Control_mechanisms_of_self-affine__rough_cleat_networks_on_flow_dynamics_in_coal_reservoir20191001-87851-m97kjq.pdf","download_url":"https://www.academia.edu/attachments/60764690/download_file","bulk_download_file_name":"Control_mechanisms_of_self_affine_rough.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/60764690/Control_mechanisms_of_self-affine__rough_cleat_networks_on_flow_dynamics_in_coal_reservoir20191001-87851-m97kjq-libre.pdf?1569984406=\u0026response-content-disposition=attachment%3B+filename%3DControl_mechanisms_of_self_affine_rough.pdf\u0026Expires=1743389187\u0026Signature=B0jblwQvHGEXpH5JV1Nc4WcgWsbLili~BN1rEqwLfBJdEFQxuMteLvdO3EbD~UX6oBa4r9xKnjHPNcCga7yhcHHBiE~Zj7iiWWSVQEn3K-48F9kfhzvBLfG~8ix-J0WAWOhER7sVFlDaxqDwApNsvHvyVySFiWB2mfsJYWCUTxWraQaZtcxHA8BPYBuMyg0UxMw3pjvgIhJk64eLPrBC455xh3rOuhIZuf72LUSM-BjQQNwqmYQ96dV5OdhFdhcgVcgOh602lh62O88hg578Txnrl37nkrQAkA8ik4wMF4dylJQAHA4h46t4MALWJccYmF6uo2D7YZOXOGezCeuJLQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Control_mechanisms_of_self_affine_rough_cleat_networks_on_flow_dynamics_in_coal_reservoir","translated_slug":"","page_count":10,"language":"en","content_type":"Work","summary":"Cleat networks dominate the migration of coalbed methane (CBM), which is assembled by cleats of different type following special configuration and possessing rough, self-affine surfaces. Nowadays, configuration implications, scale-invariant properties, fractal control mechanisms, and their relations to flow dynamics have not yet been fully clarified. Herein we explore these issues numerically using effective modeling of cleat networks and pore-scale simulations of fluid flow through them. Firstly, the control mechanics of fractal dynamics was clarified by fractal topography theory, a new definition of Weierstrass-Mandelbrot (W-M) function was proposed to characterize the self-affine surface geometries, an algorithm was developed to effectively construct cleat networks similar in coal, and Lattice Boltzmann method (LBM) was used to reproduce the fluid flow in numerical cleat networks at the pore scale. Af-terwards, the implications of spatial configuration of cleats and fractal control mechanisms of surface geometries on the permeability were systematically analyzed and quantified. Finally, an empirical model was established to predict the permeability of self-affine, rough cleat networks, rather than a rough estimation by a power-law proportionality in previous research. The performance of the proposed model was fully verified by comparative analysis and numerical simulations. Theoretical analysis denotes that our model can generalize several traditional and newly developed models from the literature.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":60764690,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/60764690/thumbnails/1.jpg","file_name":"Control_mechanisms_of_self-affine__rough_cleat_networks_on_flow_dynamics_in_coal_reservoir20191001-87851-m97kjq.pdf","download_url":"https://www.academia.edu/attachments/60764690/download_file","bulk_download_file_name":"Control_mechanisms_of_self_affine_rough.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/60764690/Control_mechanisms_of_self-affine__rough_cleat_networks_on_flow_dynamics_in_coal_reservoir20191001-87851-m97kjq-libre.pdf?1569984406=\u0026response-content-disposition=attachment%3B+filename%3DControl_mechanisms_of_self_affine_rough.pdf\u0026Expires=1743389187\u0026Signature=B0jblwQvHGEXpH5JV1Nc4WcgWsbLili~BN1rEqwLfBJdEFQxuMteLvdO3EbD~UX6oBa4r9xKnjHPNcCga7yhcHHBiE~Zj7iiWWSVQEn3K-48F9kfhzvBLfG~8ix-J0WAWOhER7sVFlDaxqDwApNsvHvyVySFiWB2mfsJYWCUTxWraQaZtcxHA8BPYBuMyg0UxMw3pjvgIhJk64eLPrBC455xh3rOuhIZuf72LUSM-BjQQNwqmYQ96dV5OdhFdhcgVcgOh602lh62O88hg578Txnrl37nkrQAkA8ik4wMF4dylJQAHA4h46t4MALWJccYmF6uo2D7YZOXOGezCeuJLQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":11997,"name":"Fluid flow in porous media","url":"https://www.academia.edu/Documents/in/Fluid_flow_in_porous_media"},{"id":24831,"name":"Fractals","url":"https://www.academia.edu/Documents/in/Fractals"},{"id":83972,"name":"Permeability","url":"https://www.academia.edu/Documents/in/Permeability"},{"id":216924,"name":"LBM","url":"https://www.academia.edu/Documents/in/LBM"},{"id":2657126,"name":"fractal topography","url":"https://www.academia.edu/Documents/in/fractal_topography"},{"id":3396360,"name":"Cleats","url":"https://www.academia.edu/Documents/in/Cleats"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-40495697-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="38878011"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/38878011/General_fractal_topography_an_open_mathematical_framework_to_characterize_and_model_mono_scale_invariances"><img alt="Research paper thumbnail of General fractal topography: an open mathematical framework to characterize and model mono-scale-invariances" class="work-thumbnail" src="https://attachments.academia-assets.com/58974856/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/38878011/General_fractal_topography_an_open_mathematical_framework_to_characterize_and_model_mono_scale_invariances">General fractal topography: an open mathematical framework to characterize and model mono-scale-invariances</a></div><div class="wp-workCard_item"><span>Nonlinear Dynamics</span><span>, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this work, we reported there are two kinds of independent complexities in mono-scale-invarianc...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this work, we reported there are two kinds of independent complexities in mono-scale-invariance, namely to be behavioral complexity determined by fractal behavior and original one wrapped in scaling object. Quantitative characterization of the complexities is fundamentally important for mechanism exploration and essential understanding of nonlinear systems. Recently, a new concept of fractal topography (Ω) was emerged to define the fractal behavior in self-similarities by scaling lacunarity (P) and scaling coverage (F) as Ω(P, F). It is, however, a “special fractal topography” because fractals are rarely deterministic and always appear stochastic, heterogeneous, and even anisotropic. For that, we reviewed a novel concept of “general fractal topography”, Ω(P, F). In Ω, P is generalized to a set accounting for directiondependent scaling behaviors of the scaling object G, while F is extended to consider stochastic and heterogeneous effects. And then, we decomposed G into G(G+, G−) to ease type controlling and measurement quantification, with G+ wrapping the original complexity while G− enclosing behavioral complexity. Together with Ω and G, a mathematical model F3S (Ω,G) was then established to unify the definition of deterministic or statistical, self-similar or selfaffine, single- or multi-phase properties. For demonstration, algorithms are developed to model natural scale-invariances. Our investigations indicated that the general fractal topography is an open mathematic framework which can admit most complex scaling objects and fractal behaviors.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="f7354bcf603d50f3824924bb09715fa0" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":58974856,"asset_id":38878011,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/58974856/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="38878011"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="38878011"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 38878011; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=38878011]").text(description); $(".js-view-count[data-work-id=38878011]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 38878011; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='38878011']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "f7354bcf603d50f3824924bb09715fa0" } } $('.js-work-strip[data-work-id=38878011]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":38878011,"title":"General fractal topography: an open mathematical framework to characterize and model mono-scale-invariances","translated_title":"","metadata":{"doi":"10.1007/s11071-019-04931-9","abstract":"In this work, we reported there are two kinds of independent complexities in mono-scale-invariance, namely to be behavioral complexity determined by fractal behavior and original one wrapped in scaling object. 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Together with Ω and G, a mathematical model F3S (Ω,G) was then established to unify the definition of deterministic or statistical, self-similar or selfaffine, single- or multi-phase properties. For demonstration, algorithms are developed to model natural scale-invariances. Our investigations indicated that the general fractal topography is an open mathematic framework which can admit most complex scaling objects and fractal behaviors.","publication_date":{"day":null,"month":null,"year":2019,"errors":{}},"publication_name":"Nonlinear Dynamics"},"translated_abstract":"In this work, we reported there are two kinds of independent complexities in mono-scale-invariance, namely to be behavioral complexity determined by fractal behavior and original one wrapped in scaling object. Quantitative characterization of the complexities is fundamentally important for mechanism exploration and essential understanding of nonlinear systems. 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For demonstration, algorithms are developed to model natural scale-invariances. 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Our investigations indicated that the general fractal topography is an open mathematic framework which can admit most complex scaling objects and fractal behaviors.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":58974856,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/58974856/thumbnails/1.jpg","file_name":"General_Fractal_Topography.pdf","download_url":"https://www.academia.edu/attachments/58974856/download_file","bulk_download_file_name":"General_fractal_topography_an_open_mathe.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/58974856/General_Fractal_Topography-libre.pdf?1556310296=\u0026response-content-disposition=attachment%3B+filename%3DGeneral_fractal_topography_an_open_mathe.pdf\u0026Expires=1743389187\u0026Signature=PLfW~4dApYadyGFYgmcQsPB-cedQDEbl1ThDWly7eXUnZJhlRS9DcBn3h36s4GZ5ZFchMQaGkHP1wGXGkYiADCDjsEVy4P5vr41WJBrg6VgaAWLPDmyPQs6CH36FanSZaGj7DCnmknUWnt~nDE3~rWTE7WL~0Hd4E-w7~zkAXvnaub3txXoir2eSlDCjMydGigivrVOXUTRDKwYCjrvRYozXuDCtuROd5mCs4k2Fe6qWGV0axoAasW1Tnk3jCe~1UPjMWpl~-oJmKQ-3mGUmlgD~14SHZcEcBGV2yD~ss0Ew8ZKO0cB7vLgBhhkx2NUlxsNbH2GSDFMCcYwxvoPJ0w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":6637,"name":"Fracture","url":"https://www.academia.edu/Documents/in/Fracture"},{"id":24831,"name":"Fractals","url":"https://www.academia.edu/Documents/in/Fractals"},{"id":90637,"name":"Porous Media","url":"https://www.academia.edu/Documents/in/Porous_Media"},{"id":154484,"name":"Self-similarity","url":"https://www.academia.edu/Documents/in/Self-similarity"},{"id":890611,"name":"Fractal Dimension","url":"https://www.academia.edu/Documents/in/Fractal_Dimension"},{"id":1432574,"name":"Scale Invariance","url":"https://www.academia.edu/Documents/in/Scale_Invariance"},{"id":1447726,"name":"Hurst Exponent","url":"https://www.academia.edu/Documents/in/Hurst_Exponent"},{"id":1566663,"name":"Weierstrass Mandelbrot functions","url":"https://www.academia.edu/Documents/in/Weierstrass_Mandelbrot_functions"},{"id":2657126,"name":"fractal topography","url":"https://www.academia.edu/Documents/in/fractal_topography"},{"id":2689528,"name":"self-affinity","url":"https://www.academia.edu/Documents/in/self-affinity"}],"urls":[{"id":8747524,"url":"https://doi.org/10.1007/s11071-019-04931-9"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-38878011-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="32678415"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32678415/Definition_of_fractal_topography_to_essential_understanding_of_scale_invariance"><img alt="Research paper thumbnail of Definition of fractal topography to essential understanding of scale- invariance" class="work-thumbnail" src="https://attachments.academia-assets.com/52844510/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32678415/Definition_of_fractal_topography_to_essential_understanding_of_scale_invariance">Definition of fractal topography to essential understanding of scale- invariance</a></div><div class="wp-workCard_item"><span>Scientific Reports</span><span>, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the c...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the correspondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter H xy , a general Hurst exponent, which is analytically expressed by H xy = log P x /log P y where P x and P y are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which D H d F P = ∑ (/)log /log i d xi x =1. Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.</span></div><div class="wp-workCard_item"><div class="carousel-container carousel-container--sm" id="profile-work-32678415-figures"><div class="prev-slide-container js-prev-button-container"><button aria-label="Previous" class="carousel-navigation-button js-profile-work-32678415-figures-prev"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">arrow_back_ios</span></button></div><div class="slides-container js-slides-container"><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/39787931/figure-1-fractals-constructed-by-different-fractal"><img alt="Figure 1. Fractals constructed by different fractal generators with the same fractal behaviors or by the same fractal generators with different fractal behaviors. From left to right in each row, the subfigures demonstrate the construction of fractals with greater detail. Left: the fractal generator is scaled to the characteristic dimension of a fractal object J). Center: following a fractal behavior, a simple fractal is constructed. Right: based on the fractal generator and following the fractal behavior, a more complex fractal is obtained in a scale- invariant manner. " class="figure-slide-image" src="https://figures.academia-assets.com/52844510/figure_001.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/39787933/figure-2-fractal-and-its-topography-for-variant-of-the"><img alt="Figure 2. A fractal and its topography for a variant of the Sierpinski gasket. " class="figure-slide-image" src="https://figures.academia-assets.com/52844510/figure_002.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/39787938/figure-3-fractals-to-demonstrate-the-validity-of-eq-ac-are"><img alt="Figure 3. Fractals to demonstrate the validity of Eq. (9). (a—c) are the initiators of scaling objects of the Koch curve, Sierpinski carpet, and Sierpinski gasket, respectively. For convenience, we denote them as fractal generators. At the next step, each potential subpart is replaced by a reduced replicate of the generator and the fractals are obtained. " class="figure-slide-image" src="https://figures.academia-assets.com/52844510/figure_003.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/39787995/figure-4-fractals-sharing-the-same-fractal-generator-but"><img alt="Figure 4. Fractals sharing the same fractal generator but different fractal topographies Q(F, P). The scaling lacunarities of (a)-(d) are 3, 3, 6, and 6, respectively, while the scaling coverages are 5, 8, 17, and 32. According to Eq. (9), the fractal dimensions of (a-d) are log5/log3, log8/log3, log17/log6, and log32/log6, respectively. " class="figure-slide-image" src="https://figures.academia-assets.com/52844510/figure_004.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/39787998/figure-5-construction-of-self-same-self-similar-and-self"><img alt="Figure 5. Construction of self-same, self-similar, and self-affine objects following different fractal topographies. All the fractals generated from the same generator but with different scaling lacunarities P and scaling coverages F. When P,= P, = 1, the generated objects are self-same; while P,= P,~ 1, the generated objects are self-similar; else the generated objects are self-affines. The scaling coverages F in (a)-(d) are 1-4, respectively. In each subfigure, as P,/P, deviates further from 1, the anisotropy of the fractal increases. " class="figure-slide-image" src="https://figures.academia-assets.com/52844510/figure_005.jpg" /></a></figure><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/39788001/table-1-definition-of-fractal-topography-to-essential"><img alt="" class="figure-slide-image" src="https://figures.academia-assets.com/52844510/table_001.jpg" /></a></figure></div><div class="next-slide-container js-next-button-container"><button aria-label="Next" class="carousel-navigation-button js-profile-work-32678415-figures-next"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">arrow_forward_ios</span></button></div></div></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="95bf40bd80d6edbe78b93bbaf05b486a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52844510,"asset_id":32678415,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52844510/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32678415"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32678415"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32678415; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32678415]").text(description); $(".js-view-count[data-work-id=32678415]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32678415; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32678415']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "95bf40bd80d6edbe78b93bbaf05b486a" } } $('.js-work-strip[data-work-id=32678415]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32678415,"title":"Definition of fractal topography to essential understanding of scale- invariance","translated_title":"","metadata":{"doi":"10.1038/srep46672","abstract":"Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the correspondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter H xy , a general Hurst exponent, which is analytically expressed by H xy = log P x /log P y where P x and P y are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which D H d F P = ∑ (/)log /log i d xi x =1. Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.","ai_title_tag":"Fractal Topography: Scale-Invariance and Fractal Dimension","publication_date":{"day":null,"month":null,"year":2017,"errors":{}},"publication_name":"Scientific Reports"},"translated_abstract":"Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the correspondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter H xy , a general Hurst exponent, which is analytically expressed by H xy = log P x /log P y where P x and P y are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which D H d F P = ∑ (/)log /log i d xi x =1. Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.","internal_url":"https://www.academia.edu/32678415/Definition_of_fractal_topography_to_essential_understanding_of_scale_invariance","translated_internal_url":"","created_at":"2017-04-27T00:19:28.288-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":52844510,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52844510/thumbnails/1.jpg","file_name":"Definition_of_fractal_topography_to_essential_understanding_of_scale-invariance.pdf","download_url":"https://www.academia.edu/attachments/52844510/download_file","bulk_download_file_name":"Definition_of_fractal_topography_to_esse.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52844510/Definition_of_fractal_topography_to_essential_understanding_of_scale-invariance-libre.pdf?1493277666=\u0026response-content-disposition=attachment%3B+filename%3DDefinition_of_fractal_topography_to_esse.pdf\u0026Expires=1743389187\u0026Signature=IuwMqrc8KqfKRrspX2qwEoA1bR6qxhNDyoZqhEpURP8Ms~F5-eB1g4UqLYrupdIR8akyeENrEEQStpOYzwPCWgYp8GKiCj6ZxxBz93X56DJ5nEU1MV2w5AVj6HpxawoRG1fU7z696g946XSlLYSE74s~NJ4gv2YhsHA7KuhbYvJKdxLlBW~cD3XNsdb-VEZ0bbjERuzSMKK3q8l3K0jC5Soz6K7F2T0YGNib6TaNSg997DyISv2PM~tTRYt5GMoa78p36sN4UawbLMAghJ~ynikt3prm28FRR~JJjV-ZKpJErZD~BUPaMY0v6lD6YMf49gsAypl1nU~Rxep~AC~BXg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Definition_of_fractal_topography_to_essential_understanding_of_scale_invariance","translated_slug":"","page_count":8,"language":"en","content_type":"Work","summary":"Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the correspondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter H xy , a general Hurst exponent, which is analytically expressed by H xy = log P x /log P y where P x and P y are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which D H d F P = ∑ (/)log /log i d xi x =1. Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":52844510,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52844510/thumbnails/1.jpg","file_name":"Definition_of_fractal_topography_to_essential_understanding_of_scale-invariance.pdf","download_url":"https://www.academia.edu/attachments/52844510/download_file","bulk_download_file_name":"Definition_of_fractal_topography_to_esse.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52844510/Definition_of_fractal_topography_to_essential_understanding_of_scale-invariance-libre.pdf?1493277666=\u0026response-content-disposition=attachment%3B+filename%3DDefinition_of_fractal_topography_to_esse.pdf\u0026Expires=1743389187\u0026Signature=IuwMqrc8KqfKRrspX2qwEoA1bR6qxhNDyoZqhEpURP8Ms~F5-eB1g4UqLYrupdIR8akyeENrEEQStpOYzwPCWgYp8GKiCj6ZxxBz93X56DJ5nEU1MV2w5AVj6HpxawoRG1fU7z696g946XSlLYSE74s~NJ4gv2YhsHA7KuhbYvJKdxLlBW~cD3XNsdb-VEZ0bbjERuzSMKK3q8l3K0jC5Soz6K7F2T0YGNib6TaNSg997DyISv2PM~tTRYt5GMoa78p36sN4UawbLMAghJ~ynikt3prm28FRR~JJjV-ZKpJErZD~BUPaMY0v6lD6YMf49gsAypl1nU~Rxep~AC~BXg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":154484,"name":"Self-similarity","url":"https://www.academia.edu/Documents/in/Self-similarity"},{"id":890611,"name":"Fractal Dimension","url":"https://www.academia.edu/Documents/in/Fractal_Dimension"},{"id":1447726,"name":"Hurst Exponent","url":"https://www.academia.edu/Documents/in/Hurst_Exponent"},{"id":2657126,"name":"fractal topography","url":"https://www.academia.edu/Documents/in/fractal_topography"},{"id":2689528,"name":"self-affinity","url":"https://www.academia.edu/Documents/in/self-affinity"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (true) { Aedu.setUpFigureCarousel('profile-work-32678415-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="31824813"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/31824813/A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions"><img alt="Research paper thumbnail of A mathematical model of fluid flow in tight porous media based on fractal assumptions" class="work-thumbnail" src="https://attachments.academia-assets.com/52119646/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/31824813/A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions">A mathematical model of fluid flow in tight porous media based on fractal assumptions</a></div><div class="wp-workCard_item"><span>International Journal of Heat and Mass Transfer</span><span>, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Natural tight reservoirs are networks with high connectivity but low porosity, in which fractal b...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Natural tight reservoirs are networks with high connectivity but low porosity, in which fractal behaviors have been widely observed and proven to affect the transport property significantly. The objective of this study is to establish a mathematical model to describe fluid flow in fractal tight porous media. To address this problem, four fractal dimensions were used: the pore size fractal dimension D f , geometrical and hydraulic tortuosity fractal dimensions D sg and D s , and the fractal dimension D k characterizing the hydraulic diameter-number distribution. The relationship among these fractal dimensions was analyzed and D f was found equal to D k þ D sg. Then a unified model connecting the porosity and D f is deduced for arbitrary fractal tight porous media. Based on the scaling-invariant behaviors assumed, a fractal mathematical model is developed for the permeability estimation, which is fabricated only by fundamental and well-defined physical properties of D f ; D s , the scaling lacunarity P k , the range of the pore sizes, and the porosity of the fractal generator u 0. To validate the permeability model, we developed an algorithm to model fractal tight porous media according to the scaling-invariant topography of fractal objects based on Voronoi tessellations, and to simulate fluid flow in these complex networks by Lattice Boltzmann method (LBM) at pore scale. Numerical experiments indicate that the hydraulic tortuosity fractal dimension D s is approximately equal to 1.1. Consequently, the fractal mathematical model was quantitatively determined and its performance was verified by the LBM simulations. Finally, the fractal mathematical model was rearranged into a permeability-porosity form for practical applications.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9786310b63b033f7c8589f37b128f764" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52119646,"asset_id":31824813,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52119646/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="31824813"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="31824813"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 31824813; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=31824813]").text(description); $(".js-view-count[data-work-id=31824813]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 31824813; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='31824813']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "9786310b63b033f7c8589f37b128f764" } } $('.js-work-strip[data-work-id=31824813]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":31824813,"title":"A mathematical model of fluid flow in tight porous media based on fractal assumptions","translated_title":"","metadata":{"doi":"10.1016/j.ijheatmasstransfer.2016.12.096","volume":"108","abstract":"Natural tight reservoirs are networks with high connectivity but low porosity, in which fractal behaviors have been widely observed and proven to affect the transport property significantly. The objective of this study is to establish a mathematical model to describe fluid flow in fractal tight porous media. To address this problem, four fractal dimensions were used: the pore size fractal dimension D f , geometrical and hydraulic tortuosity fractal dimensions D sg and D s , and the fractal dimension D k characterizing the hydraulic diameter-number distribution. The relationship among these fractal dimensions was analyzed and D f was found equal to D k þ D sg. Then a unified model connecting the porosity and D f is deduced for arbitrary fractal tight porous media. Based on the scaling-invariant behaviors assumed, a fractal mathematical model is developed for the permeability estimation, which is fabricated only by fundamental and well-defined physical properties of D f ; D s , the scaling lacunarity P k , the range of the pore sizes, and the porosity of the fractal generator u 0. To validate the permeability model, we developed an algorithm to model fractal tight porous media according to the scaling-invariant topography of fractal objects based on Voronoi tessellations, and to simulate fluid flow in these complex networks by Lattice Boltzmann method (LBM) at pore scale. Numerical experiments indicate that the hydraulic tortuosity fractal dimension D s is approximately equal to 1.1. Consequently, the fractal mathematical model was quantitatively determined and its performance was verified by the LBM simulations. 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Then a unified model connecting the porosity and D f is deduced for arbitrary fractal tight porous media. Based on the scaling-invariant behaviors assumed, a fractal mathematical model is developed for the permeability estimation, which is fabricated only by fundamental and well-defined physical properties of D f ; D s , the scaling lacunarity P k , the range of the pore sizes, and the porosity of the fractal generator u 0. To validate the permeability model, we developed an algorithm to model fractal tight porous media according to the scaling-invariant topography of fractal objects based on Voronoi tessellations, and to simulate fluid flow in these complex networks by Lattice Boltzmann method (LBM) at pore scale. Numerical experiments indicate that the hydraulic tortuosity fractal dimension D s is approximately equal to 1.1. Consequently, the fractal mathematical model was quantitatively determined and its performance was verified by the LBM simulations. Finally, the fractal mathematical model was rearranged into a permeability-porosity form for practical applications.","internal_url":"https://www.academia.edu/31824813/A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions","translated_internal_url":"","created_at":"2017-03-11T20:25:55.512-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":52119646,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52119646/thumbnails/1.jpg","file_name":"A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions.pdf","download_url":"https://www.academia.edu/attachments/52119646/download_file","bulk_download_file_name":"A_mathematical_model_of_fluid_flow_in_ti.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52119646/A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions-libre.pdf?1489293115=\u0026response-content-disposition=attachment%3B+filename%3DA_mathematical_model_of_fluid_flow_in_ti.pdf\u0026Expires=1743389187\u0026Signature=XiXCGZ7dfQufJkEvmAUUCpCfFbeJhtJRAfOQBnt3n6FqYU1OT8LMZNGg15walIuwQxvLd4USO~gEFMyEU-1VMnImwilptiU4OChXPnbRXXrvryKGI59LYaRbDVIpmwetTf35FxpwhPYTArbRFYdwqyvexMZsOy7yYx7cdvBz2bByWzjYxL8y7DhK5KNMLjTnNDy6PQLUyw0-m3-iAGB6gstznB7pvvILBIrYgFy1lJ4ssFmFB4rsCJuqvIAGWhiEiynmYQSyGIe~ACSrOPFjRP68toOh9MhJDNa71kg0KH-oWnxSuIp4ASgaxOjuGk-v9rsy5Aieix-S-YgHqBG2pw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions","translated_slug":"","page_count":11,"language":"en","content_type":"Work","summary":"Natural tight reservoirs are networks with high connectivity but low porosity, in which fractal behaviors have been widely observed and proven to affect the transport property significantly. The objective of this study is to establish a mathematical model to describe fluid flow in fractal tight porous media. To address this problem, four fractal dimensions were used: the pore size fractal dimension D f , geometrical and hydraulic tortuosity fractal dimensions D sg and D s , and the fractal dimension D k characterizing the hydraulic diameter-number distribution. The relationship among these fractal dimensions was analyzed and D f was found equal to D k þ D sg. Then a unified model connecting the porosity and D f is deduced for arbitrary fractal tight porous media. Based on the scaling-invariant behaviors assumed, a fractal mathematical model is developed for the permeability estimation, which is fabricated only by fundamental and well-defined physical properties of D f ; D s , the scaling lacunarity P k , the range of the pore sizes, and the porosity of the fractal generator u 0. To validate the permeability model, we developed an algorithm to model fractal tight porous media according to the scaling-invariant topography of fractal objects based on Voronoi tessellations, and to simulate fluid flow in these complex networks by Lattice Boltzmann method (LBM) at pore scale. Numerical experiments indicate that the hydraulic tortuosity fractal dimension D s is approximately equal to 1.1. Consequently, the fractal mathematical model was quantitatively determined and its performance was verified by the LBM simulations. Finally, the fractal mathematical model was rearranged into a permeability-porosity form for practical applications.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":52119646,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52119646/thumbnails/1.jpg","file_name":"A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions.pdf","download_url":"https://www.academia.edu/attachments/52119646/download_file","bulk_download_file_name":"A_mathematical_model_of_fluid_flow_in_ti.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52119646/A_mathematical_model_of_fluid_flow_in_tight_porous_media_based_on_fractal_assumptions-libre.pdf?1489293115=\u0026response-content-disposition=attachment%3B+filename%3DA_mathematical_model_of_fluid_flow_in_ti.pdf\u0026Expires=1743389187\u0026Signature=XiXCGZ7dfQufJkEvmAUUCpCfFbeJhtJRAfOQBnt3n6FqYU1OT8LMZNGg15walIuwQxvLd4USO~gEFMyEU-1VMnImwilptiU4OChXPnbRXXrvryKGI59LYaRbDVIpmwetTf35FxpwhPYTArbRFYdwqyvexMZsOy7yYx7cdvBz2bByWzjYxL8y7DhK5KNMLjTnNDy6PQLUyw0-m3-iAGB6gstznB7pvvILBIrYgFy1lJ4ssFmFB4rsCJuqvIAGWhiEiynmYQSyGIe~ACSrOPFjRP68toOh9MhJDNa71kg0KH-oWnxSuIp4ASgaxOjuGk-v9rsy5Aieix-S-YgHqBG2pw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":160248,"name":"Fractal Analysis","url":"https://www.academia.edu/Documents/in/Fractal_Analysis"},{"id":231216,"name":"Tight Gas Reserviors","url":"https://www.academia.edu/Documents/in/Tight_Gas_Reserviors"},{"id":1580515,"name":"3D porosity and mineralogy characterization in tight gas sandstones","url":"https://www.academia.edu/Documents/in/3D_porosity_and_mineralogy_characterization_in_tight_gas_sandstones"},{"id":2657126,"name":"fractal topography","url":"https://www.academia.edu/Documents/in/fractal_topography"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-31824813-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="31824783"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/31824783/Scale_and_size_effects_on_fluid_flow_through_self_affine_rough_fractures"><img alt="Research paper thumbnail of Scale and size effects on fluid flow through self-affine rough fractures" class="work-thumbnail" src="https://attachments.academia-assets.com/52119610/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/31824783/Scale_and_size_effects_on_fluid_flow_through_self_affine_rough_fractures">Scale and size effects on fluid flow through self-affine rough fractures</a></div><div class="wp-workCard_item"><span>International Journal of Heat and Mass Transfer</span><span>, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A permeability estimation of a single rough fracture remains challenging and has attracted broad ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A permeability estimation of a single rough fracture remains challenging and has attracted broad attention because of its fundamental importance. This study examines the effects of surface roughness on fracture flow and proposes a new, triple-effect permeability estimation model that takes surface and hydraulic tortuosity other than surface roughness factor (SRF) into account according to the functioning patterns. Due to the scale effect on hydraulic and surface tortuosities, it can also be reformulated into a scaling aperture-permeability equation for a self-affine fracture. Results indicate that tortuosity effects are scaled by 4(H-1) (H is the Hurst exponent) with the mean aperture and that the local SRF, as expected, is stationary at the measurement scale of the mean aperture. In addition, based on the scaling equation and the size effect of self-affine objects, flow regimes are examined and three flow regimes are then identified. Consequently, different permeability models for these regimes are established by fabricating fundamental and well-defined physical properties. The estimation results from these models are in excellent agreement with results from lattice Boltzmann simulations.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c23e05e42b3d990d643301daa5573c20" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52119610,"asset_id":31824783,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52119610/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="31824783"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="31824783"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 31824783; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=31824783]").text(description); $(".js-view-count[data-work-id=31824783]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 31824783; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='31824783']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "c23e05e42b3d990d643301daa5573c20" } } $('.js-work-strip[data-work-id=31824783]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":31824783,"title":"Scale and size effects on fluid flow through self-affine rough fractures","translated_title":"","metadata":{"doi":"10.1016/j.ijheatmasstransfer.2016.10.010","volume":"105","abstract":"A permeability estimation of a single rough fracture remains challenging and has attracted broad attention because of its fundamental importance. This study examines the effects of surface roughness on fracture flow and proposes a new, triple-effect permeability estimation model that takes surface and hydraulic tortuosity other than surface roughness factor (SRF) into account according to the functioning patterns. Due to the scale effect on hydraulic and surface tortuosities, it can also be reformulated into a scaling aperture-permeability equation for a self-affine fracture. Results indicate that tortuosity effects are scaled by 4(H-1) (H is the Hurst exponent) with the mean aperture and that the local SRF, as expected, is stationary at the measurement scale of the mean aperture. In addition, based on the scaling equation and the size effect of self-affine objects, flow regimes are examined and three flow regimes are then identified. Consequently, different permeability models for these regimes are established by fabricating fundamental and well-defined physical properties. The estimation results from these models are in excellent agreement with results from lattice Boltzmann simulations.","publication_date":{"day":null,"month":null,"year":2017,"errors":{}},"publication_name":"International Journal of Heat and Mass Transfer"},"translated_abstract":"A permeability estimation of a single rough fracture remains challenging and has attracted broad attention because of its fundamental importance. This study examines the effects of surface roughness on fracture flow and proposes a new, triple-effect permeability estimation model that takes surface and hydraulic tortuosity other than surface roughness factor (SRF) into account according to the functioning patterns. Due to the scale effect on hydraulic and surface tortuosities, it can also be reformulated into a scaling aperture-permeability equation for a self-affine fracture. Results indicate that tortuosity effects are scaled by 4(H-1) (H is the Hurst exponent) with the mean aperture and that the local SRF, as expected, is stationary at the measurement scale of the mean aperture. In addition, based on the scaling equation and the size effect of self-affine objects, flow regimes are examined and three flow regimes are then identified. Consequently, different permeability models for these regimes are established by fabricating fundamental and well-defined physical properties. The estimation results from these models are in excellent agreement with results from lattice Boltzmann simulations.","internal_url":"https://www.academia.edu/31824783/Scale_and_size_effects_on_fluid_flow_through_self_affine_rough_fractures","translated_internal_url":"","created_at":"2017-03-11T20:17:58.005-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":52119610,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52119610/thumbnails/1.jpg","file_name":"Scale_and_size_effects_on_fluid_flow_through_self-affine_rough_fractures.pdf","download_url":"https://www.academia.edu/attachments/52119610/download_file","bulk_download_file_name":"Scale_and_size_effects_on_fluid_flow_thr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52119610/Scale_and_size_effects_on_fluid_flow_through_self-affine_rough_fractures-libre.pdf?1489292528=\u0026response-content-disposition=attachment%3B+filename%3DScale_and_size_effects_on_fluid_flow_thr.pdf\u0026Expires=1743389187\u0026Signature=G-mWyFdQuHGwTmMnsehiiA9YlNI4J1zcUXN2KCZlKhlEvN1O77lNplOD~QTnwP56X9phApLMXBrhDE~lnL1YVkGKdGXW-OSJLAwM-3gubeInRSqMJyWk0HqJRZN2EngGV343bYLlqy64x9KirJuIAL8WNXA2ViCcC~uLUhLAcWWeB1X-tD7ZEL6tSyObBeREYTkXk51tIewnOQ5tj~jqMjL3uA0ew8ixs7BjGzMy13vh8fpbyy~dxP3lc6jXzyYOzbgcOpyFS~owv2vdrnT7YGTSP8Cdkna0Bgq-xf2EibFH7tEH4rBp-mjtwZt9WInjnIHH0OzTVBpNklBBzTfcSw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Scale_and_size_effects_on_fluid_flow_through_self_affine_rough_fractures","translated_slug":"","page_count":9,"language":"en","content_type":"Work","summary":"A permeability estimation of a single rough fracture remains challenging and has attracted broad attention because of its fundamental importance. This study examines the effects of surface roughness on fracture flow and proposes a new, triple-effect permeability estimation model that takes surface and hydraulic tortuosity other than surface roughness factor (SRF) into account according to the functioning patterns. Due to the scale effect on hydraulic and surface tortuosities, it can also be reformulated into a scaling aperture-permeability equation for a self-affine fracture. Results indicate that tortuosity effects are scaled by 4(H-1) (H is the Hurst exponent) with the mean aperture and that the local SRF, as expected, is stationary at the measurement scale of the mean aperture. In addition, based on the scaling equation and the size effect of self-affine objects, flow regimes are examined and three flow regimes are then identified. Consequently, different permeability models for these regimes are established by fabricating fundamental and well-defined physical properties. The estimation results from these models are in excellent agreement with results from lattice Boltzmann simulations.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":52119610,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52119610/thumbnails/1.jpg","file_name":"Scale_and_size_effects_on_fluid_flow_through_self-affine_rough_fractures.pdf","download_url":"https://www.academia.edu/attachments/52119610/download_file","bulk_download_file_name":"Scale_and_size_effects_on_fluid_flow_thr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52119610/Scale_and_size_effects_on_fluid_flow_through_self-affine_rough_fractures-libre.pdf?1489292528=\u0026response-content-disposition=attachment%3B+filename%3DScale_and_size_effects_on_fluid_flow_thr.pdf\u0026Expires=1743389187\u0026Signature=G-mWyFdQuHGwTmMnsehiiA9YlNI4J1zcUXN2KCZlKhlEvN1O77lNplOD~QTnwP56X9phApLMXBrhDE~lnL1YVkGKdGXW-OSJLAwM-3gubeInRSqMJyWk0HqJRZN2EngGV343bYLlqy64x9KirJuIAL8WNXA2ViCcC~uLUhLAcWWeB1X-tD7ZEL6tSyObBeREYTkXk51tIewnOQ5tj~jqMjL3uA0ew8ixs7BjGzMy13vh8fpbyy~dxP3lc6jXzyYOzbgcOpyFS~owv2vdrnT7YGTSP8Cdkna0Bgq-xf2EibFH7tEH4rBp-mjtwZt9WInjnIHH0OzTVBpNklBBzTfcSw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-31824783-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="13778347"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/13778347/Scaling_Invariant_Effects_on_the_Permeability_of_Fractal_Porous_Media"><img alt="Research paper thumbnail of Scaling Invariant Effects on the Permeability of Fractal Porous Media" class="work-thumbnail" src="https://attachments.academia-assets.com/38125520/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/13778347/Scaling_Invariant_Effects_on_the_Permeability_of_Fractal_Porous_Media">Scaling Invariant Effects on the Permeability of Fractal Porous Media</a></div><div class="wp-workCard_item"><span>Transport in porous media</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Your article is protected by copyright and all rights are held exclusively by Springer Science +B...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media Dordrecht. 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This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: \"The final publication is available at link.springer.com\".","publication_name":"Transport in porous media","grobid_abstract_attachment_id":38125520},"translated_abstract":null,"internal_url":"https://www.academia.edu/13778347/Scaling_Invariant_Effects_on_the_Permeability_of_Fractal_Porous_Media","translated_internal_url":"","created_at":"2015-07-07T21:16:41.440-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":38125520,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/38125520/thumbnails/1.jpg","file_name":"scaling_invariant_effect_on_permeability.pdf","download_url":"https://www.academia.edu/attachments/38125520/download_file","bulk_download_file_name":"Scaling_Invariant_Effects_on_the_Permeab.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/38125520/scaling_invariant_effect_on_permeability-libre.pdf?1436329130=\u0026response-content-disposition=attachment%3B+filename%3DScaling_Invariant_Effects_on_the_Permeab.pdf\u0026Expires=1743389187\u0026Signature=ER6s6xIbLrrk5C3q~eQGIb4g119L50PAxw08rKlPuRlako-ceGTbugtWXno4hkAmmGn4WjFSrwqMXga1mioSLjOe~NO-xfRfmXhIWqDpE5i3P~yqdtyKpxDWV2B8N4T5N-nXu7mcELVjElAUw5Lmfn7rqiLUZBFuwdsk~M7iLlvSeX8i3RUFekxxFH9Klqkt1lVWytoH5S5f6kwab~aU--kzT7WQE7-smNgFzvzBZ55eo1Y~ouBzVSO41tE8B-OIHLcxaqGFuFTxEI-HpE4ex4deWAO56Pwa-QZYD5cL0XGh3zsaZJvJOzkJCWzOgGvOLXOhiw9HioOaDZjCAIpfXg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Scaling_Invariant_Effects_on_the_Permeability_of_Fractal_Porous_Media","translated_slug":"","page_count":23,"language":"en","content_type":"Work","summary":"Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media Dordrecht. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: \"The final publication is available at link.springer.com\".","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":38125520,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/38125520/thumbnails/1.jpg","file_name":"scaling_invariant_effect_on_permeability.pdf","download_url":"https://www.academia.edu/attachments/38125520/download_file","bulk_download_file_name":"Scaling_Invariant_Effects_on_the_Permeab.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/38125520/scaling_invariant_effect_on_permeability-libre.pdf?1436329130=\u0026response-content-disposition=attachment%3B+filename%3DScaling_Invariant_Effects_on_the_Permeab.pdf\u0026Expires=1743389188\u0026Signature=VJCyCj4-OgP39lbELgINYMbFZMt9CNy14pORvXys4oTL7Zk9k6aPGyRlIctsdo22jfARfr5RqpBuWdproMhIyxA2Hahoz-vGppxlP6AvHHh4uRLMu751zUrlSY1YHPe-DNsYATJl~hmahYpmtneRyEsDveswxW2mtEdUUghPGZIpSyayjkdBvhAtXYCBKhQi7V02rGcwUhTd8sTkorYuw-XCE5bH3AJzeEK1XSsn2ffufzjpmi38K2CvvlN-B17~O427TH224Ekhn3aY8G3Ek99TaW6LV8iz~j3yIs9rOvjiQZfK7Yl9M1AfoU-v~CpeEE9B5Osq2TalxkTsXzCMLg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":317,"name":"Fractal Geometry","url":"https://www.academia.edu/Documents/in/Fractal_Geometry"},{"id":2298,"name":"Computational Fluid Dynamics","url":"https://www.academia.edu/Documents/in/Computational_Fluid_Dynamics"},{"id":11997,"name":"Fluid flow in porous media","url":"https://www.academia.edu/Documents/in/Fluid_flow_in_porous_media"},{"id":61709,"name":"Computational Fluid Dynamics (CFD) modelling and simulation","url":"https://www.academia.edu/Documents/in/Computational_Fluid_Dynamics_CFD_modelling_and_simulation"},{"id":62537,"name":"Porosity and Permeability in Reservoirs","url":"https://www.academia.edu/Documents/in/Porosity_and_Permeability_in_Reservoirs"},{"id":148589,"name":"Coal bed methane","url":"https://www.academia.edu/Documents/in/Coal_bed_methane"},{"id":169172,"name":"Numerical modeling and simulation , fluid flow through porous media, Enhanced oil recoveryy","url":"https://www.academia.edu/Documents/in/Numerical_modeling_and_simulation_fluid_flow_through_porous_media_Enhanced_oil_recoveryy"},{"id":726355,"name":"Porosity-Permeability Correlation","url":"https://www.academia.edu/Documents/in/Porosity-Permeability_Correlation"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-13778347-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="8744175"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/8744175/Lattice_Boltzmann_simulation_of_fluid_flow_through_coal_reservoir_s_fractal_pore_structure"><img alt="Research paper thumbnail of Lattice Boltzmann simulation of fluid flow through coal reservoir’s fractal pore structure" class="work-thumbnail" src="https://attachments.academia-assets.com/35097240/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/8744175/Lattice_Boltzmann_simulation_of_fluid_flow_through_coal_reservoir_s_fractal_pore_structure">Lattice Boltzmann simulation of fluid flow through coal reservoir’s fractal pore structure</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The influences of fractal pore structure in coal reservoir on coalbed methane (CBM) migration wer...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The influences of fractal pore structure in coal reservoir on coalbed methane (CBM) migration were analyzed in detail by coupling theoretical models and numerical methods. Different types of fractals were generated based on the construction thought of the standard Menger Sponge to model the 3D nonlinear coal pore structures. Then a correlation model between the permeability of fractal porous medium and its pore-size-distribution characteristics was derived using the parallel and serial modes and verified by Lattice Boltzmann Method (LBM). Based on the coupled method, porosity (), fractal dimension of pore structure (D b ), pore size range (r min, r max ) and other parameters were systematically analyzed for their influences on the permeability () of fractal porous medium. The results indicate that: ① the channels connected by pores with the maximum size (r max ) dominate the permeability  , approximating in the quadratic law; ② the greater the ratio of r max and r min is, the higher  is; ③ the relationship between D b and  follows a negative power law model, and breaks into two segments at the position where D b ≌2.5. Based on the results above, a predicting model of fractal porous medium permeability was proposed, formulated as max n Cfr  , where C and n (approximately equal to 2) are constants and f is an expression only containing parameters of fractal pore structure. In addition, the equivalence of the new proposed model for porous medium and the Kozeny-Carman model =Cr n was verified at D b =2.0. fractal pore structure, porous media, lattice Boltzmann model, coalbed methane (CBM) Citation: Jin Y, Song H B, Hu B, et al. Lattice Boltzmann simulation of fluid flow through coal reservoir's fractal pore structure.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="dfe5fca420f4828fee3066421744b03d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":35097240,"asset_id":8744175,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/35097240/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="8744175"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="8744175"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 8744175; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=8744175]").text(description); $(".js-view-count[data-work-id=8744175]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 8744175; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='8744175']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "dfe5fca420f4828fee3066421744b03d" } } $('.js-work-strip[data-work-id=8744175]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":8744175,"title":"Lattice Boltzmann simulation of fluid flow through coal reservoir’s fractal pore structure","translated_title":"","metadata":{"ai_title_tag":"Fractal Flow Dynamics in Coal Reservoirs","grobid_abstract":"The influences of fractal pore structure in coal reservoir on coalbed methane (CBM) migration were analyzed in detail by coupling theoretical models and numerical methods. Different types of fractals were generated based on the construction thought of the standard Menger Sponge to model the 3D nonlinear coal pore structures. Then a correlation model between the permeability of fractal porous medium and its pore-size-distribution characteristics was derived using the parallel and serial modes and verified by Lattice Boltzmann Method (LBM). Based on the coupled method, porosity (), fractal dimension of pore structure (D b ), pore size range (r min, r max ) and other parameters were systematically analyzed for their influences on the permeability () of fractal porous medium. The results indicate that: ① the channels connected by pores with the maximum size (r max ) dominate the permeability  , approximating in the quadratic law; ② the greater the ratio of r max and r min is, the higher  is; ③ the relationship between D b and  follows a negative power law model, and breaks into two segments at the position where D b ≌2.5. Based on the results above, a predicting model of fractal porous medium permeability was proposed, formulated as max n Cfr  , where C and n (approximately equal to 2) are constants and f is an expression only containing parameters of fractal pore structure. In addition, the equivalence of the new proposed model for porous medium and the Kozeny-Carman model =Cr n was verified at D b =2.0. fractal pore structure, porous media, lattice Boltzmann model, coalbed methane (CBM) Citation: Jin Y, Song H B, Hu B, et al. Lattice Boltzmann simulation of fluid flow through coal reservoir's fractal pore structure.","grobid_abstract_attachment_id":35097240},"translated_abstract":null,"internal_url":"https://www.academia.edu/8744175/Lattice_Boltzmann_simulation_of_fluid_flow_through_coal_reservoir_s_fractal_pore_structure","translated_internal_url":"","created_at":"2014-10-12T10:31:45.930-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":35097240,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/35097240/thumbnails/1.jpg","file_name":"082012-203-130079.pdf","download_url":"https://www.academia.edu/attachments/35097240/download_file","bulk_download_file_name":"Lattice_Boltzmann_simulation_of_fluid_fl.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/35097240/082012-203-130079-libre.pdf?1413134986=\u0026response-content-disposition=attachment%3B+filename%3DLattice_Boltzmann_simulation_of_fluid_fl.pdf\u0026Expires=1743389188\u0026Signature=LjxynNwQ1gSGk9YOOH9PYVQH-FvbWX5kEosNeI3trrl0ixylZoC8l3PHqLI8tubBBXzcjtl47Wf7sgobHOON-CY4WV9EYP~ZECt0bHz8VugNQ2yDSWFrvoc7iEy7e0OtvRlexjSUQEIZy6egYgWlcvpzCusT1cGrQQ~yjnLcCdMrUgSJHV4Y8orx9MaFziFThMRWBPQns079158nXzbm~F2mwu8e2chKg9yxu2dK9SAsM-kJOlunsbOblHFNFoFR3j2t1hnY9JwCwNK-q~FxijuxlnQLY5pSvzktZjJy7DlhUzD0eVtApSRtgjpX3wnZNhXBBpcYm4zjW0Vyo64PvA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Lattice_Boltzmann_simulation_of_fluid_flow_through_coal_reservoir_s_fractal_pore_structure","translated_slug":"","page_count":12,"language":"en","content_type":"Work","summary":"The influences of fractal pore structure in coal reservoir on coalbed methane (CBM) migration were analyzed in detail by coupling theoretical models and numerical methods. Different types of fractals were generated based on the construction thought of the standard Menger Sponge to model the 3D nonlinear coal pore structures. Then a correlation model between the permeability of fractal porous medium and its pore-size-distribution characteristics was derived using the parallel and serial modes and verified by Lattice Boltzmann Method (LBM). Based on the coupled method, porosity (), fractal dimension of pore structure (D b ), pore size range (r min, r max ) and other parameters were systematically analyzed for their influences on the permeability () of fractal porous medium. The results indicate that: ① the channels connected by pores with the maximum size (r max ) dominate the permeability  , approximating in the quadratic law; ② the greater the ratio of r max and r min is, the higher  is; ③ the relationship between D b and  follows a negative power law model, and breaks into two segments at the position where D b ≌2.5. Based on the results above, a predicting model of fractal porous medium permeability was proposed, formulated as max n Cfr  , where C and n (approximately equal to 2) are constants and f is an expression only containing parameters of fractal pore structure. In addition, the equivalence of the new proposed model for porous medium and the Kozeny-Carman model =Cr n was verified at D b =2.0. fractal pore structure, porous media, lattice Boltzmann model, coalbed methane (CBM) Citation: Jin Y, Song H B, Hu B, et al. Lattice Boltzmann simulation of fluid flow through coal reservoir's fractal pore structure.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":35097240,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/35097240/thumbnails/1.jpg","file_name":"082012-203-130079.pdf","download_url":"https://www.academia.edu/attachments/35097240/download_file","bulk_download_file_name":"Lattice_Boltzmann_simulation_of_fluid_fl.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/35097240/082012-203-130079-libre.pdf?1413134986=\u0026response-content-disposition=attachment%3B+filename%3DLattice_Boltzmann_simulation_of_fluid_fl.pdf\u0026Expires=1743389188\u0026Signature=LjxynNwQ1gSGk9YOOH9PYVQH-FvbWX5kEosNeI3trrl0ixylZoC8l3PHqLI8tubBBXzcjtl47Wf7sgobHOON-CY4WV9EYP~ZECt0bHz8VugNQ2yDSWFrvoc7iEy7e0OtvRlexjSUQEIZy6egYgWlcvpzCusT1cGrQQ~yjnLcCdMrUgSJHV4Y8orx9MaFziFThMRWBPQns079158nXzbm~F2mwu8e2chKg9yxu2dK9SAsM-kJOlunsbOblHFNFoFR3j2t1hnY9JwCwNK-q~FxijuxlnQLY5pSvzktZjJy7DlhUzD0eVtApSRtgjpX3wnZNhXBBpcYm4zjW0Vyo64PvA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":11997,"name":"Fluid flow in porous media","url":"https://www.academia.edu/Documents/in/Fluid_flow_in_porous_media"},{"id":24831,"name":"Fractals","url":"https://www.academia.edu/Documents/in/Fractals"},{"id":142354,"name":"Lattice Boltzmann method for fluid dynamics","url":"https://www.academia.edu/Documents/in/Lattice_Boltzmann_method_for_fluid_dynamics"},{"id":726355,"name":"Porosity-Permeability Correlation","url":"https://www.academia.edu/Documents/in/Porosity-Permeability_Correlation"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-8744175-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="8467703"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/8467703/Derivation_of_permeability_pore_relationship_for_fractal_porous_reservoirs_using_series_parallel_flow_resistance_model_and_lattice_Boltzmann_method"><img alt="Research paper thumbnail of Derivation of permeability-pore relationship for fractal porous reservoirs using series-parallel flow resistance model and lattice Boltzmann method" class="work-thumbnail" src="https://attachments.academia-assets.com/34852638/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/8467703/Derivation_of_permeability_pore_relationship_for_fractal_porous_reservoirs_using_series_parallel_flow_resistance_model_and_lattice_Boltzmann_method">Derivation of permeability-pore relationship for fractal porous reservoirs using series-parallel flow resistance model and lattice Boltzmann method</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Permeability of porous reservoirs plays a significant role in engineering and scientific applicat...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Permeability of porous reservoirs plays a significant role in engineering and scientific applications. In this study, we investigated the relationship between pore size fractal dimension (D f ) § Corresponding author. 1440005-1 Fractals 2014.22. Downloaded from <a href="http://www.worldscientific.com" rel="nofollow">www.worldscientific.com</a> by Dr. Jianchao Cai on 09/04/14. For personal use only. B. Wang et al.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1e21f3a75fcf9241f0ef1a27db5af4c1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":34852638,"asset_id":8467703,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/34852638/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="8467703"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="8467703"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 8467703; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=8467703]").text(description); $(".js-view-count[data-work-id=8467703]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 8467703; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='8467703']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1e21f3a75fcf9241f0ef1a27db5af4c1" } } $('.js-work-strip[data-work-id=8467703]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":8467703,"title":"Derivation of permeability-pore relationship for fractal porous reservoirs using series-parallel flow resistance model and lattice Boltzmann method","translated_title":"","metadata":{"grobid_abstract":"Permeability of porous reservoirs plays a significant role in engineering and scientific applications. In this study, we investigated the relationship between pore size fractal dimension (D f ) § Corresponding author. 1440005-1 Fractals 2014.22. Downloaded from www.worldscientific.com by Dr. Jianchao Cai on 09/04/14. For personal use only. B. Wang et al.","grobid_abstract_attachment_id":34852638},"translated_abstract":null,"internal_url":"https://www.academia.edu/8467703/Derivation_of_permeability_pore_relationship_for_fractal_porous_reservoirs_using_series_parallel_flow_resistance_model_and_lattice_Boltzmann_method","translated_internal_url":"","created_at":"2014-09-23T22:29:59.341-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":26974903,"work_id":8467703,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":481262,"email":"z***l@sdu.edu.cn","display_order":0,"name":"Xiaoyang Zhang","title":"Derivation of permeability-pore relationship for fractal porous reservoirs using series-parallel flow resistance model and lattice Boltzmann method"},{"id":32497531,"work_id":8467703,"tagging_user_id":17238727,"tagged_user_id":null,"co_author_invite_id":6835110,"email":"c***8@gmail.com","display_order":4194304,"name":"Qin Chen","title":"Derivation of permeability-pore relationship for fractal porous reservoirs using series-parallel flow resistance model and lattice Boltzmann method"}],"downloadable_attachments":[{"id":34852638,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/34852638/thumbnails/1.jpg","file_name":"FLOW_RESISTANCE_MODEL_AND_LATTICE_BOLTZMANN_METHOD.pdf","download_url":"https://www.academia.edu/attachments/34852638/download_file","bulk_download_file_name":"Derivation_of_permeability_pore_relation.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/34852638/FLOW_RESISTANCE_MODEL_AND_LATTICE_BOLTZMANN_METHOD-libre.pdf?1411556835=\u0026response-content-disposition=attachment%3B+filename%3DDerivation_of_permeability_pore_relation.pdf\u0026Expires=1743389188\u0026Signature=IuTEdF4U7VyoZSKS73tZioRFwkHPjdsFXiq85FV4Y~~Oc-jGjleOKeOLSuy~z-7qp8zK9gNuPlkEEJJfpVxtPn4Z7QffaSzdFb2X3BCz3A230oP9mqqxxSp-ThBCPJYy8z~cYbcNrUZELctjiwcdrWeMgb7VClgeI5DCEgQ0m0KO8DXWgoZQjIqRQR6oiVLUrn99yUx6Bu3YteU3Hgf-R4wOn0LtbtfXoc3pOS-3dOoiUPf3X21VLBrs3BBgWvzVbvI1la5KEdereqh8dJp58Byt03Aui~WmewH9F9dgZDnzSZm0MOayWBu2jD48kWo65uBelPW8pcKnqEjU7Kv3Gw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Derivation_of_permeability_pore_relationship_for_fractal_porous_reservoirs_using_series_parallel_flow_resistance_model_and_lattice_Boltzmann_method","translated_slug":"","page_count":15,"language":"en","content_type":"Work","summary":"Permeability of porous reservoirs plays a significant role in engineering and scientific applications. In this study, we investigated the relationship between pore size fractal dimension (D f ) § Corresponding author. 1440005-1 Fractals 2014.22. Downloaded from www.worldscientific.com by Dr. Jianchao Cai on 09/04/14. For personal use only. B. Wang et al.","owner":{"id":17238727,"first_name":"yi","middle_initials":null,"last_name":"Jin","page_name":"yiJin","domain_name":"henanpu","created_at":"2014-09-23T22:24:34.232-07:00","display_name":"yi Jin","url":"https://henanpu.academia.edu/yiJin"},"attachments":[{"id":34852638,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/34852638/thumbnails/1.jpg","file_name":"FLOW_RESISTANCE_MODEL_AND_LATTICE_BOLTZMANN_METHOD.pdf","download_url":"https://www.academia.edu/attachments/34852638/download_file","bulk_download_file_name":"Derivation_of_permeability_pore_relation.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/34852638/FLOW_RESISTANCE_MODEL_AND_LATTICE_BOLTZMANN_METHOD-libre.pdf?1411556835=\u0026response-content-disposition=attachment%3B+filename%3DDerivation_of_permeability_pore_relation.pdf\u0026Expires=1743389188\u0026Signature=IuTEdF4U7VyoZSKS73tZioRFwkHPjdsFXiq85FV4Y~~Oc-jGjleOKeOLSuy~z-7qp8zK9gNuPlkEEJJfpVxtPn4Z7QffaSzdFb2X3BCz3A230oP9mqqxxSp-ThBCPJYy8z~cYbcNrUZELctjiwcdrWeMgb7VClgeI5DCEgQ0m0KO8DXWgoZQjIqRQR6oiVLUrn99yUx6Bu3YteU3Hgf-R4wOn0LtbtfXoc3pOS-3dOoiUPf3X21VLBrs3BBgWvzVbvI1la5KEdereqh8dJp58Byt03Aui~WmewH9F9dgZDnzSZm0MOayWBu2jD48kWo65uBelPW8pcKnqEjU7Kv3Gw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":317,"name":"Fractal Geometry","url":"https://www.academia.edu/Documents/in/Fractal_Geometry"},{"id":62537,"name":"Porosity and Permeability in Reservoirs","url":"https://www.academia.edu/Documents/in/Porosity_and_Permeability_in_Reservoirs"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-8467703-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="8467704"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/8467704/Kinematical_measurement_of_hydraulic_tortuosity_of_fluid_flow_in_porous_media"><img alt="Research paper thumbnail of Kinematical measurement of hydraulic tortuosity of fluid flow in porous media" class="work-thumbnail" src="https://attachments.academia-assets.com/34852664/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/8467704/Kinematical_measurement_of_hydraulic_tortuosity_of_fluid_flow_in_porous_media">Kinematical measurement of hydraulic tortuosity of fluid flow in porous media</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">It is hard to experimentally or analytically derive the hydraulic tortuosity () of porous media°o...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">It is hard to experimentally or analytically derive the hydraulic tortuosity () of porous media°ow because of their complex microstructures. In this work, we propose a kinematical measurement method for by introducing the concept of local tortuosity, which is de¯ned as the ratio of°uid particle velocity to its component along the macro°ow. And then, the calculation model of is analytically deduced in terms of that is the mean value of the local tortuosity. To avoid the impact from the singularity of local tortuosity, the velocity is normalized, and is then approximated by the ratio of the mean normalized velocity to the average value of its component along the macro-°ow direction. The new estimation method is veri¯ed by°ow through di®erent types of porous media via the lattice Boltzmann method, and the relationships between permeabilities and tortuosities obtained by di®erent methods are examined. The numerical results show that tortuosity by the novel approach is in good agreement with the existing theory, and the kinematic de¯nition of hydraulic tortuosity is also proven.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="78933c13a3ca0810b73efde901d55093" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":34852664,"asset_id":8467704,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/34852664/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="8467704"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="8467704"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 8467704; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=8467704]").text(description); $(".js-view-count[data-work-id=8467704]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 8467704; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='8467704']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "78933c13a3ca0810b73efde901d55093" } } $('.js-work-strip[data-work-id=8467704]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":8467704,"title":"Kinematical measurement of hydraulic tortuosity of fluid flow in porous media","translated_title":"","metadata":{"grobid_abstract":"It is hard to experimentally or analytically derive the hydraulic tortuosity () of porous media°ow because of their complex microstructures. In this work, we propose a kinematical measurement method for by introducing the concept of local tortuosity, which is de¯ned as the ratio of°uid particle velocity to its component along the macro°ow. And then, the calculation model of is analytically deduced in terms of that is the mean value of the local tortuosity. To avoid the impact from the singularity of local tortuosity, the velocity is normalized, and is then approximated by the ratio of the mean normalized velocity to the average value of its component along the macro-°ow direction. The new estimation method is veri¯ed by°ow through di®erent types of porous media via the lattice Boltzmann method, and the relationships between permeabilities and tortuosities obtained by di®erent methods are examined. The numerical results show that tortuosity by the novel approach is in good agreement with the existing theory, and the kinematic de¯nition of hydraulic tortuosity is also proven.","grobid_abstract_attachment_id":34852664},"translated_abstract":null,"internal_url":"https://www.academia.edu/8467704/Kinematical_measurement_of_hydraulic_tortuosity_of_fluid_flow_in_porous_media","translated_internal_url":"","created_at":"2014-09-23T22:29:59.353-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":17238727,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":34852664,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/34852664/thumbnails/1.jpg","file_name":"s0129183115500175.pdf","download_url":"https://www.academia.edu/attachments/34852664/download_file","bulk_download_file_name":"Kinematical_measurement_of_hydraulic_tor.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/34852664/s0129183115500175-libre.pdf?1411557773=\u0026response-content-disposition=attachment%3B+filename%3DKinematical_measurement_of_hydraulic_tor.pdf\u0026Expires=1743389188\u0026Signature=WuPvNloGETDBAMp~95nI7CNYqXOUGYposjhrhAGrJ2Hc0ljNeyZF5UVlBbelAIAUbUwH-fLss~Atnj7rM2AhGhJSTKiBZdd5uRC6M3RAXPNY6yTVePzyFX9mUrs-ricUXmPpwTw57yb~Ghz7mhmknBmn5FFGnUl5en8GR9yrGeOinOjRzge11zbmjRr9xuDNGywFOV9LC-djR22vM2lz0OGUzDg9spVTS8mjZkiO9SLhh3zQs6smJi6bBEb7aqY~FtC5U8ktAudEDzjnZjsm1P3lkj24ybTB-5QGN2gPJa-a02CSIVJUZx1Xgkruk9zKtw92TF0cwLY3y8KUuyWRyw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Kinematical_measurement_of_hydraulic_tortuosity_of_fluid_flow_in_porous_media","translated_slug":"","page_count":21,"language":"en","content_type":"Work","summary":"It is hard to experimentally or analytically derive the hydraulic tortuosity () of porous media°ow because of their complex microstructures. In this work, we propose a kinematical measurement method for by introducing the concept of local tortuosity, which is de¯ned as the ratio of°uid particle velocity to its component along the macro°ow. And then, the calculation model of is analytically deduced in terms of that is the mean value of the local tortuosity. To avoid the impact from the singularity of local tortuosity, the velocity is normalized, and is then approximated by the ratio of the mean normalized velocity to the average value of its component along the macro-°ow direction. The new estimation method is veri¯ed by°ow through di®erent types of porous media via the lattice Boltzmann method, and the relationships between permeabilities and tortuosities obtained by di®erent methods are examined. 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