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Therefore, the criterion for the success of a manager in emergency crisis management is effectiveness as an absolute measure of the presence or absence of a result—it either exists or does not exist.","isbn":"978-1-83880-982-9","printIsbn":"978-1-83880-981-2","pdfIsbn":"978-1-83880-983-6","doi":"10.5772\u002Fintechopen.77623","price":119,"priceEur":129,"priceUsd":155,"priceCbs":null,"slug":"public-sector-crisis-management","numberOfPages":174,"isOpenForSubmission":false,"isInWos":null,"isInBkci":false,"hash":"84a998820880e0f006a5e9eac40d83e7","bookSignature":"Alexander Rozanov, Alexander Barannikov, Olga Belyaeva and Mikhail Smirnov","publishedDate":"October 28th 2020","coverURL":"https:\u002F\u002Fcdn.intechopen.com\u002Fbooks\u002Fimages_new\u002F7806.jpg","cdnWebCoverURL":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F7806\u002F1718277203-1101653481\u002Fweb-cover.jpg","cdnWebCoverURL300":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F7806\u002F1718277203-1101653481\u002Fweb-cover-300.jpg","numberOfDownloads":9964,"numberOfViews":null,"numberOfWosCitations":0,"numberOfCrossrefCitations":16,"numberOfCrossrefCitationsByBook":0,"numberOfDimensionsCitations":21,"numberOfDimensionsCitationsByBook":0,"hasAltmetrics":1,"totalAltmetricsMentions":4,"numberOfTotalCitations":37,"isAvailableForWebshopOrdering":true,"dateEndFirstStepPublish":"June 3rd 2019","dateEndSecondStepPublish":"December 25th 2019","dateEndThirdStepPublish":"February 23rd 2020","dateEndFourthStepPublish":"May 13th 2020","dateEndFifthStepPublish":"July 12th 2020","currentStepOfPublishingProcess":5,"indexedIn":"1,2,3,4,5,6","editedByType":"Edited by","kuFlag":false,"sdgRelated":null,"featuredMarkup":null,"isPublished":true,"isPublisherCbs":false,"cbsWebsiteURL":null,"noAds":0,"editors":[{"id":"233092","title":"Dr.","name":"Alexander","middleName":null,"surname":"Rozanov","slug":"alexander-rozanov","fullName":"Alexander Rozanov","cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F233092\u002F1604448294\u002Fprofile\u002Fimage1.jpg","biography":"Dr. Alexander S. Rozanov is a specialist in Global Security and a graduate of Lomonosov Moscow State University (Russia). He is the author of more than 60 scientific publications. After graduating, Dr. Rozanov worked in the Russian Ministry of Foreign Affairs and the Russian Government. In 2014 he received his Ph.D. in Politics from Lomonosov Moscow State University. From 2014 to 2017, Dr. Rozanov was invited as a guest lecturer in several well-known universities – University of California, Santa Barbara (USA), Paris-Sorbonne (France), and Wroclaw University (Poland). Dr. Rozanov specializes in the analysis of global and regional conflicts, as well as the global dynamics of world development. He is a member of the European International Studies Association (Great Britain). 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From 2012 to 2014, he was an independent expert of the Commission of the Federal Agency for the supply of weapons, military, special equipment and materiel on compliance with the requirements for official behavior of Federal civil servants of the Central Office of the Federal Agency. His list of scientific works includes more than 87 scientific works, including 39 inventions. Dr. Barannikov is a Professor at the Russian Academy of National Economy and Public Administration.","institutionString":"NUST MISIS, Russian Federation","position":null,"outsideEditionCount":null,"totalCites":0,"totalAuthoredChapters":"1","totalChapterViews":"0","totalEditedBooks":"1","institution":null,"countryString":"Russia"},"coeditorTwo":{"id":"303097","title":"Prof.","name":"Olga","middleName":null,"surname":"Belyaeva","slug":"olga-belyaeva","fullName":"Olga Belyaeva","cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F303097\u002F1685533101\u002Fprofile\u002Fimage1.jpg","biography":"Dr. Olga Belyaeva is an Associate Professor at the Russian Academy of National Economy and Public Administration at the Department of Regional Management of the Faculty of International Regional Studies and Regional Management. She has a PhD in Regional Economy. Dr. Belyaeva has 2 specialties – a professional lawyer and an economist. Dr. Belyaeva has published more than 80 scientific publications. She has been providing lectures since 2006. From 2003 to 2006 she worked in the field of audits of small and medium-sized businesses.","institutionString":null,"position":null,"outsideEditionCount":null,"totalCites":0,"totalAuthoredChapters":"0","totalChapterViews":"0","totalEditedBooks":"1","institution":null,"countryString":"Russia"},"coeditorThree":{"id":"308591","title":"Dr.","name":"Mikhail","middleName":null,"surname":"Smirnov","slug":"mikhail-smirnov","fullName":"Mikhail Smirnov","cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F308591\u002F1604448294\u002Fprofile\u002Fimage1.jpg","biography":"Michael Smirnov is a Professor at the Russian Academy of National Economy and Public Administration. He has a PhD in Law. For more than 15 years, Dr. Smirnov worked as a practical lawyer in international banks and consulting companies, at the same time providing lectures at Lomonosov MSU and Russian Academy of National Economy and Public Administration. He is the author of more than 60 scientific publications. Dr. Smirnov is currently the head of the Academic Program ‘Legal Support of Financial Technologies’.","institutionString":"Russian Academy of National Economy and Public Administration","position":null,"outsideEditionCount":0,"totalCites":0,"totalAuthoredChapters":"0","totalChapterViews":"0","totalEditedBooks":"1","institution":null,"countryString":"Russia"},"coeditorFour":null,"coeditorFive":null,"topics":[{"id":"272","title":"Management","slug":"management"}],"productType":{"id":"1","title":"Edited Volume","chapterContentType":"chapter","authoredCaption":"Edited by"},"series":null,"subseries":null,"tags":null,"_preview":0,"chapters":[{"id":"72017","title":"Crisis Management and Communication Strategies: RUSAL’s Case","doi":"10.5772\u002Fintechopen.91644","slug":"crisis-management-and-communication-strategies-rusal-s-case","totalDownloads":969,"totalCrossrefCites":0,"totalDimensionsCites":0,"hasAltmetrics":0,"orderNumber":1,"abstract":"No company is immune to crisis situations, an affirmation which, despite its triviality, is undeniably true. However, from the early 2014, such statement may have become even more true to Russian corporations, as the annexation of the Crimean Peninsula gave start to rounds of economic sanctions that are still perpetrated today. Such measures, which were initiated in response to the Kremlin’s political maneuvers, have hit a number of Russian companies, and increased the degree of uncertainty in which they have to operate, as they see economic restriction’s impact not only on the business activity tangible factors—i.e., economic rewards, service, and performance—but also on intangible factors—i.e., image and reputation—as well. Crises are integral parts of all world systems, unfortunately. While they are a theoretically well-understood issue, in practice, crises are perceived as a very painful phenomenon. A crisis can be compared to riding a roller coaster. First, as we gain speed and climb up the tracks we are filled with a sense of joy and delight. These feelings are quickly replaced with anticipation, panic, and fear as the roller coaster plunges into the “abyss.”","signatures":"Alexander Rozanov, Maria Ivanchenko, Alexandra Baranova, Mikhail Smirnov, Olga Belyaeva, Alexander Barannikov, Mikhail Ilichev, Ludmila Ilicheva, Biyaslan Tambiev, Maria Krotovskaya, Vladimir Chilingaryan, Tatiana Grabovich, Zaru Dulatkyzy, Alla Nikolaeva, Svetlana Ivanova, Kwame Boateng, Mattia Masolletti, Marina Danilina, Dmitry Medvedev and Natalya Ogneva","downloadPdfUrl":"\u002Fchapter\u002Fpdf-download\u002F72017","previewPdfUrl":"\u002Fchapter\u002Fpdf-preview\u002F72017","isPublished":true,"isOnlineFirst":false,"isDeactivated":0,"authors":[{"id":"233092","title":"Dr.","name":"Alexander","surname":"Rozanov","slug":"alexander-rozanov","fullName":"Alexander Rozanov"},{"id":"303094","title":null,"name":"Alexander","surname":"Barannikov","slug":"alexander-barannikov","fullName":"Alexander Barannikov"},{"id":"312160","title":null,"name":"Olga","surname":"Belyaeva","slug":"olga-belyaeva","fullName":"Olga Belyaeva"},{"id":"312161","title":null,"name":"Mikhail","surname":"Smirnov","slug":"mikhail-smirnov","fullName":"Mikhail Smirnov"},{"id":"312162","title":null,"name":"Alexandra","surname":"Baranova","slug":"alexandra-baranova","fullName":"Alexandra Baranova"},{"id":"312163","title":null,"name":"Natalya","surname":"Ogneva","slug":"natalya-ogneva","fullName":"Natalya Ogneva"},{"id":"312164","title":null,"name":"Dmitry","surname":"Medvedev","slug":"dmitry-medvedev","fullName":"Dmitry Medvedev"},{"id":"312165","title":null,"name":"Marina","surname":"Danilina","slug":"marina-danilina","fullName":"Marina Danilina"},{"id":"312197","title":"Ms.","name":"Maria","surname":"Ivanchenko","slug":"maria-ivanchenko","fullName":"Maria Ivanchenko"},{"id":"316770","title":"Dr.","name":"Mattia","surname":"Masolletti","slug":"mattia-masolletti","fullName":"Mattia Masolletti"},{"id":"316771","title":"Dr.","name":"Kwame","surname":"Boateng","slug":"kwame-boateng","fullName":"Kwame Boateng"},{"id":"317588","title":"Dr.","name":"Svetlana","surname":"Ivanova","slug":"svetlana-ivanova","fullName":"Svetlana Ivanova"},{"id":"317589","title":"Dr.","name":"Alla A.","surname":"Nikolaeva","slug":"alla-a.-nikolaeva","fullName":"Alla A. Nikolaeva"},{"id":"317590","title":"Dr.","name":"Zaru","surname":"Dulatkyzy","slug":"zaru-dulatkyzy","fullName":"Zaru Dulatkyzy"},{"id":"317773","title":null,"name":"Tatiana","surname":"Grabovich","slug":"tatiana-grabovich","fullName":"Tatiana Grabovich"},{"id":"317774","title":null,"name":"Vladimir","surname":"Chilingaryan","slug":"vladimir-chilingaryan","fullName":"Vladimir Chilingaryan"},{"id":"318393","title":null,"name":"Maria","surname":"Krotovskaya","slug":"maria-krotovskaya","fullName":"Maria Krotovskaya"},{"id":"318394","title":null,"name":"Biyaslan","surname":"Tambiev","slug":"biyaslan-tambiev","fullName":"Biyaslan Tambiev"}],"corrections":null,"_preview":0},{"id":"72314","title":"The Political Economy of Crisis Recovery","doi":"10.5772\u002Fintechopen.92586","slug":"the-political-economy-of-crisis-recovery","totalDownloads":849,"totalCrossrefCites":0,"totalDimensionsCites":0,"hasAltmetrics":0,"orderNumber":2,"abstract":"The aftermath of the global financial crisis marked another stress test for welfare states and varieties of capitalism. More than ever before, governments were forced to consider substantial reforms to welfare provision and enact flexibility-enhancing measures in order to improve financial solvency and economic performance. The crash, however, was not only a regionally uneven process in its origins but also led to makeshift or uneven policy responses. As a result, the socio-economic effects of the downturn and political reactions to it varied considerably among countries. Nevertheless, there have been some common trends in outcome measures. These have served to blur the dividing lines between different welfare states and production systems, so vividly captured in the mainstream political economy literature.","signatures":"Mohammad Ferdosi","downloadPdfUrl":"\u002Fchapter\u002Fpdf-download\u002F72314","previewPdfUrl":"\u002Fchapter\u002Fpdf-preview\u002F72314","isPublished":true,"isOnlineFirst":false,"isDeactivated":0,"authors":[{"id":"316998","title":"Dr.","name":"Mohammad","surname":"Ferdosi","slug":"mohammad-ferdosi","fullName":"Mohammad Ferdosi"}],"corrections":null,"_preview":0},{"id":"72395","title":"Contagion, Exchange Rate, and Financial Volatility: Indonesian Case in Global Financial Turbulence","doi":"10.5772\u002Fintechopen.92275","slug":"contagion-exchange-rate-and-financial-volatility-indonesian-case-in-global-financial-turbulence","totalDownloads":904,"totalCrossrefCites":1,"totalDimensionsCites":1,"hasAltmetrics":0,"orderNumber":3,"abstract":"Global turbulence after the financial crisis has hit Indonesia and almost all emerging countries. Quantitative Easing (QE) normalization (tapering of) has caused the capital outflows from emerging countries. Trade war and increasing geopolitical tension together raise the pressure. Argentina and Turkey have been experiencing economic shock. Indonesia should identify the contagion possibility and refer to Thai baht contagion experience in 1997. This paper assesses the contagion, exchange rate, and financial volatility triggered by global turbulence and Argentina-Turkey crisis in 2018. We use vector autoregression (VAR), simple correlation, dynamic conditional correlation (DCC), and regression method. We will investigate the potential contagion both in stock and exchange rate markets and in the rupiah exchange rate determination from both contagion and fundamental factors regarding the balance of payment (BOP) condition. The empirical result shows the potential contagion from Argentina and Turkey’s financial crisis to the Indonesian economy, especially to the stock market and exchange rate. The regression and correlation result also shows that Turkey has a higher financial contagion effect than Argentina to Indonesian financial market. Balance of payment condition also has the significant effect to explain rupiah exchange rate depreciation.","signatures":"Telisa Falianty and Arif Budimanta","downloadPdfUrl":"\u002Fchapter\u002Fpdf-download\u002F72395","previewPdfUrl":"\u002Fchapter\u002Fpdf-preview\u002F72395","isPublished":true,"isOnlineFirst":false,"isDeactivated":0,"authors":[{"id":"317414","title":"Dr.","name":"Telisa","surname":"Falianty","slug":"telisa-falianty","fullName":"Telisa Falianty"},{"id":"317419","title":"Dr.","name":"Arif","surname":"Budimanta","slug":"arif-budimanta","fullName":"Arif Budimanta"}],"corrections":null,"_preview":0},{"id":"73192","title":"State Capitalism in Belarus: Behind Economic Anemia","doi":"10.5772\u002Fintechopen.93606","slug":"state-capitalism-in-belarus-behind-economic-anemia","totalDownloads":1215,"totalCrossrefCites":4,"totalDimensionsCites":6,"hasAltmetrics":1,"orderNumber":4,"abstract":"Belarus’ economic model looked rather successful in the late 1990s and in the 2000s with its economic growth above 7% per year. But during the last decade, Belarusian annual economic growth has fallen at the average level around 1% per year. This chapter reveals the rarely known case of state capitalism in this post-Soviet country with its specific indicators, and instruments behind economic anemia. It also outlines several traps on the way of Belarusian economic growth: “debt trap,” “middle-income trap,” “social burden trap,” “resource curse trap,” “conflict neighbors trap,” and “forceful pressure trap.” These pitfalls lead to the long-term economic slowdown in the Republic of Belarus. 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It is recommended, in this study, to provide training opportunities for all people who have a role in the management of tourism crisis especially in the communication sector, the massive presence of police in the tourism site, hotels, and all the tourism places under the condition of not being seen, and to provide the qualified policemen with modern defensive weapons.","signatures":"Omar Jawabreh","downloadPdfUrl":"\u002Fchapter\u002Fpdf-download\u002F71352","previewPdfUrl":"\u002Fchapter\u002Fpdf-preview\u002F71352","isPublished":true,"isOnlineFirst":false,"isDeactivated":0,"authors":[{"id":"311791","title":"Dr.","name":"Omar","surname":"Jawabreh","slug":"omar-jawabreh","fullName":"Omar Jawabreh"}],"corrections":null,"_preview":0},{"id":"70464","title":"Exploring the Three-Way Destination Safety Solution to Crisis Management in Tourist Destinations in Rural Nigeria","doi":"10.5772\u002Fintechopen.89727","slug":"exploring-the-three-way-destination-safety-solution-to-crisis-management-in-tourist-destinations-in-","totalDownloads":861,"totalCrossrefCites":1,"totalDimensionsCites":1,"hasAltmetrics":0,"orderNumber":8,"abstract":"Development of tourist destinations is among topical issues in national discourse for economic growth and sustainability. The past two decades have witnessed massive development and investment in tourist destinations in rural areas. This is owing to the fact that rural tourism has been identified as among the development options for rural communities in most developing nations. Of recent, crisis and other safety issues have been among the militating factors against tourist destinations hence the cry for destination safety. These are said to emanate from the activities of the three major principals in the management of tourist destinations (hosts, tourism resources, and tourists\u002Fvisitors). Incidentally, destination safety discourse is source of worry for these principal factors in tourist destination management. This has left many tourist destinations devastated, abandoned and abused. However, this chapter proposal would seek to identify the way out of this predicament. It tends to explore the meaning and application of the three-way destination safety (TWaDeSS) model in the management of crisis at tourist destinations in rural Nigeria. This will not only promote harmony among the three major principals in tourist destination but also enhance the rate of investment as a result of quality crisis control in these destinations.","signatures":"Elochukwu A. 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This study is predicated on the fact that crisis management is essentially embedded in humanity. Additionally, the study was informed by the established and widely held view by scholars, that social groups by their nature and context, are in fact characterised by conflicts. Consequently, the study established that the public sector in every society is not immune against conflict or crisis, and this will naturally arise as long as there is interaction between and among human elements in the two sectors. The author used the terms—crisis and conflict—interchangeably in the study, and pointed out that the methodology adopted was a descriptive and analytical approach. This is informed by the sources of information accessed which are essentially secondary. The study concluded by asserting that given the humanity-linked nature of conflict, its management in the public sector, particularly in Nigeria, will continue to be an unavoidable responsibility of the government. 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This is offered in the form of a draft requirement for a transport means – a multifunctional special vehicle, intended specifically to intervene in situations against demonstrators, extremists, and football hooligans. 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Introduction\u003C\u002Fh2\u003E\u003Cp id=\"p2\"\u003EChemical engineering processes are frequently composed of multiple complex phenomena. These systems can be represented by a set of several equations, such as \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ez\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E = \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ef\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E(\u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ed\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E; \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ex\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E; \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ep\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E), where \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ez\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E is the vector state of the system. The system of equations is referred to as the mathematical model of the process. The performance of the process is predicted by the model from the assigned data of several “input” variables, \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ed\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E and \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ex\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E, and a group of parameters, \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ep\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E. Among the input variables, some, referred as \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ex\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E, can be changed and are known as design variables, while others, referred as \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ed\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E, are predetermined. The performance of the process can be evaluated through a set of output variables, \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ey = g\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E (\u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ez\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E), referred as the function of state of the system. Optimization in chemical engineering utilizes specialized techniques to determine the values of the decision variables, \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ex\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E, at which the performance of the process, measured as the objective function(s), \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EI\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E(\u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ex\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E), is minimum or maximum. The profitability of the process improves remarkably as a result of this selection of input\u002Foperating\u002Fdecision variables. This benefit has encouraged the broad application of optimization for important industrial challenges. However, many problems in chemical engineering processes are hard to find the optimum using gradient-based algorithms. For example, the cases when the objective functions of the processes are multimodal, discontinuous, or implicit. Genetic algorithms (GAs) are a kind of metaheuristic searching optimization methods, which are inspired by nature, the mechanics of natural evolution, and genetics [\u003Ca href=\"#B1\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E1\u003C\u002Fa\u003E]. Genetic algorithms have received significant attention due to their remarkable advantages over classical algorithms. Compared with traditional optimization approaches, GAs are straightforward, robust, capable of handling the non-differentiable, discontinuous, or multimodal problems. GAs have been effectively employed in a wide range of various engineering, manufacturing, and management applications [\u003Ca href=\"#B2\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E2\u003C\u002Fa\u003E]. The purpose of this chapter is to give several case studies using genetic algorithms in chemical engineering optimization problems. The case studies include the optimization of an autothermal ammonia synthesis reactor, a separation module using membrane technology, and data-driven modeling optimizations of solid oxide fuel cells.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_2\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E2. Optimization of an autothermal ammonia synthesis reactor\u003C\u002Fh2\u003E\u003Cp id=\"p3\"\u003EIn the chemical process industries, ammonia is one of the most widely manufactured inorganic compounds [\u003Ca href=\"#B3\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E3\u003C\u002Fa\u003E]. The majority of ammonia produced commercially is consumed in fertilizers, with the rest going into plastics, synthetic fibers and resins, pharmaceuticals, explosives, papers, and refrigeration [\u003Ca href=\"#B4\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E4\u003C\u002Fa\u003E]. As a result, modeling and optimization of ammonia synthesis process have received a significant attention from both the academia and industry. Ammonia is produced predominantly from the combination of elements such as nitrogen and hydrogen in a catalytic process using a promoted iron catalyst firstly established by Haber and Bosch as the \u003Ca href=\"#E4\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003Ereaction [4]\u003C\u002Fa\u003E:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E1\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m1\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mspace width=\"0.36em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mn\u003E3\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EH\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mspace width=\"0.36em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mo\u003E⇌\u003C\u002Fmml:mo\u003E\u003Cmml:mspace width=\"0.36em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003ENH\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E3\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE1\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p4\"\u003EThe reaction is reversible and exothermic, releasing a significant amount of heat. In order to achieve a high conversion, the heat of the reaction should be removed. Therefore, the process is typically carried out in an autothermal synthesis reactor, in which the heat of reaction is utilized to preheat the feed gas and ensure the suitable temperature inside. The production of ammonia depends on several factors such as the reactor length, the operating pressure, temperature of the feed and reacted gas, the flow rate, and composition of the gas mixture. The optimization problem of the process is to maximize the economic return. Many studies discussing the modeling, simulation, and optimization of an autothermal ammonia synthesis reactor can be found in literature. Some of them can be mentioned here as in Babu et al. [\u003Ca href=\"#B5\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E5\u003C\u002Fa\u003E], Babu and Angira [\u003Ca href=\"#B6\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E6\u003C\u002Fa\u003E], Carvalho et al. [\u003Ca href=\"#B7\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E7\u003C\u002Fa\u003E], Edgar et al. [\u003Ca href=\"#B8\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E8\u003C\u002Fa\u003E], Ksasy et al. [\u003Ca href=\"#B9\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E9\u003C\u002Fa\u003E], Murase et al. [\u003Ca href=\"#B10\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E10\u003C\u002Fa\u003E], Upreti and Deb [\u003Ca href=\"#B11\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E11\u003C\u002Fa\u003E], Yusup et al. [\u003Ca href=\"#B12\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E12\u003C\u002Fa\u003E]. However, the model discussed in the studies of Edgar et al. [\u003Ca href=\"#B8\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E8\u003C\u002Fa\u003E], Murase et al. [\u003Ca href=\"#B10\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E10\u003C\u002Fa\u003E] has some minor errors and has been corrected in Upreti and Deb [\u003Ca href=\"#B11\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E11\u003C\u002Fa\u003E]. Moreover, the studies primarily focus on optimizing reactor length for a specific reactor top temperature, usually 694 K [\u003Ca href=\"#B6\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E6\u003C\u002Fa\u003E, \u003Ca href=\"#B7\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E7\u003C\u002Fa\u003E, \u003Ca href=\"#B12\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E12\u003C\u002Fa\u003E], or for a limited set of temperatures [\u003Ca href=\"#B9\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E9\u003C\u002Fa\u003E, \u003Ca href=\"#B11\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E11\u003C\u002Fa\u003E]. However, as reported in some studies [\u003Ca href=\"#B11\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E11\u003C\u002Fa\u003E, \u003Ca href=\"#B12\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E12\u003C\u002Fa\u003E], the economic return is determined by the top temperature and also the reactor length (the temperature of feed gas entering to the reaction zone). As a result, rather than a single variable problem of reactor length, the optimization problem should be viewed as a multivariable problem.\u003C\u002Fp\u003E\u003Cp id=\"p5\"\u003EIn the study [\u003Ca href=\"#B13\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E13\u003C\u002Fa\u003E], both the reactor length and the reactor top temperature are considered in the design variables for maximizing the profit return of the process. In order to solve the multivariate optimization problem, the cyclic coordinate search technique was employed. This method alters the value of one decision variable at a time, and for each coordinate direction, the golden section search was utilized to solve the single variable optimum problem. However, this traditional searching approach is prone to get caught in local optima. Therefore, the genetic algorithm has higher chance to obtain the global optimum profit of the process.\u003C\u002Fp\u003E\u003Cdiv class=\"section\" id=\"sec_2_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E2.1 Problem formulation of ammonia synthesis reactor\u003C\u002Fh3\u003E\u003Cp id=\"p6\"\u003EThe system discussed here is an autothermal synthesis reactor, which is described in [\u003Ca href=\"#B10\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E10\u003C\u002Fa\u003E] and contains the correction of the objective function reported in [\u003Ca href=\"#B6\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E6\u003C\u002Fa\u003E, \u003Ca href=\"#B11\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E11\u003C\u002Fa\u003E]. The feed gas contains 21.75 mole% nitrogen, 65.25 mole% hydrogen, 5.0 mole% ammonia, 4.0 mole% methane, and 4.0 mole% argon. In an autothermal reactor, the feed gas mixture enters from the bottom of the reactor, flows upward, enters the catalyst zone from the top, and moves downward. In the catalyst zone, the reaction takes place at around 500°C and 200 atm of pressure. The heat generated by the reaction is utilized to preheat the feed gas mixture in counter current flow. \u003Ca href=\"#F1\" class=\"ref-link\" data-ref-style=\"fig\"\u003EFigure 1\u003C\u002Fa\u003E shows the schematic diagram of an autothermal ammonia synthesis reactor. The considered factors affecting the synthesis process are the temperature of feed gas at the entrance of the reaction zone (top temperature) and the reactor length. The goal of the optimal design is to determine the conditions that will give the highest economic return from the reactor operation.\u003C\u002Fp\u003E\u003Cfigure class=\"media-panel\" id=\"F1\"\u003E\u003Cdiv class=\"media\"\u003E\u003Cimg src=\"\u002F\u002Fcdnintech.com\u002Fmedia\u002Fchapter\u002F81877\u002F1512345123\u002Fmedia\u002FF1.png\" class=\"figure-link\" alt=\"\"\u003E\u003C\u002Fdiv\u003E\u003Cfigcaption class=\"caption\"\u003E\u003Ch4\u003EFigure 1.\u003C\u002Fh4\u003E\u003Cp\u003E\u003Cp xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\" id=\"p7\"\u003ESchematic diagram of an autothermal ammonia reactor [\u003Cxref rid=\"B10\" ref-type=\"bibr\"\u003E10\u003C\u002Fxref\u003E].\u003C\u002Fp\u003E\u003C\u002Fp\u003E\u003C\u002Ffigcaption\u003E\u003C\u002Ffigure\u003E\u003Cdiv class=\"section\" id=\"sec_2_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E2.1.1 Objective function\u003C\u002Fh4\u003E\u003Cp id=\"p8\"\u003EThe return of the process, which is calculated from the value of the product gas (heating value and ammonia value), subtract the cost of feed gas (as a source of heat only) and minus the amortization of reactor capital expenses, is the objective function for maximization (\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EF\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E). Other operating costs are not considered [\u003Ca href=\"#B11\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E11\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cdiv id=\"df_E2\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m2\" specific-use=\"web-only\"\u003E\u003Cmml:mtable columnalign=\"left\" displaystyle=\"true\"\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E1.3356\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mn\u003E7\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E1.708\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mn\u003E4\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E704.09\u003C\u002Fmml:mn\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eg\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E699.27\u003C\u002Fmml:mn\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mspace width=\"9.599993em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E3.4566\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mn\u003E7\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E1.9837\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mn\u003E9\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mi\u003EL\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mfrac\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:msup\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003C\u002Fmml:mtable\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE2\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p9\"\u003Ein which,\u003C\u002Fp\u003E\u003Cp id=\"p10\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003Csub\u003Ef\u003C\u002Fsub\u003E\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the temperature of the feed gas.\u003C\u002Fp\u003E\u003Cp id=\"p11\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003Csub\u003Eg\u003C\u002Fsub\u003E\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the temperature of the reacting gas (the gas in the catalyst zone).\u003C\u002Fp\u003E\u003Cp id=\"p12\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E0\u003C\u002Fsub\u003E is the top temperature or temperature at the inlet of the catalyst zone.\u003C\u002Fp\u003E\u003Cp id=\"p13\"\u003E\u003Cspan class=\"inline-formula\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m3\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:math\u003E\u003C\u002Fspan\u003E is the flow rate of nitrogen.\u003C\u002Fp\u003E\u003Cp id=\"p14\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EL\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the length of the reactor.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_3_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E2.1.2 Equality constraints\u003C\u002Fh4\u003E\u003Cp id=\"p15\"\u003EThe heat balance for the feed gas and the reacting gas and the mass balance for the nitrogen flow along the catalyst zone, respectively, give the mathematical model for the system:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E3\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m4\" specific-use=\"web-only\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EdT\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Edx\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EUS\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EWC\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Epf\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eg\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE3\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"df_E4\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m5\" specific-use=\"web-only\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EdT\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eg\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Edx\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EUS\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EWC\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Epg\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eg\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mi mathvariant=\"normal\"\u003EΔ\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EH\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ES\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EWC\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Epg\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EdN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Edx\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE4\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"df_E5\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m6\" specific-use=\"web-only\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EdN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Edx\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ek\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EH\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mn\u003E1.5\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003ENH\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E3\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ek\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003ENH\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E3\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EH\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mn\u003E1.5\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE5\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p16\"\u003Ein which\u003C\u002Fp\u003E\u003Cdiv id=\"df_E6\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m7\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ek\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E1.78954\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mn\u003E4\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mo\u003Eexp\u003C\u002Fmml:mo\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E20800\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003ERT\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eg\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE6\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"df_E7\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m8\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ek\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2.5714\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mn\u003E16\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mo\u003Eexp\u003C\u002Fmml:mo\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E47400\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003ERT\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eg\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE7\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"df_E8\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m9\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EH\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E3\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE8\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"df_E9\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m10\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E286\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E2.598\u003C\u002Fmml:mn\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE9\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"df_E10\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m11\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003ENH\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E3\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E286\u003C\u002Fmml:mn\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E2.23\u003C\u002Fmml:mn\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E2.598\u003C\u002Fmml:mn\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE10\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p17\"\u003EThe differential equations are valid in the interval [0, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EL\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E], in which L is the reactor length (or the length of the catalyst zone).\u003C\u002Fp\u003E\u003Cp id=\"p18\"\u003EThe notations \u003Cspan class=\"inline-formula\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m12\"\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003C\u002Fmml:math\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"inline-formula\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m13\"\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eg\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003C\u002Fmml:math\u003E\u003C\u002Fspan\u003E, and \u003Cspan class=\"inline-formula\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m14\"\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003C\u002Fmml:math\u003E\u003C\u002Fspan\u003E denote the initial value at \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ex\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 0 (at the inlet of the catalyst zone) for \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003Csub\u003Ef\u003C\u002Fsub\u003E\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003Csub\u003Eg\u003C\u002Fsub\u003E\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, and \u003Cspan class=\"inline-formula\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m15\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:math\u003E\u003C\u002Fspan\u003E, respectively, and are given by\u003C\u002Fp\u003E\u003Cdiv id=\"df_E11\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m16\" specific-use=\"web-only\"\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eg\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mspace width=\"0.48em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E701.2\u003C\u002Fmml:mn\u003E\u003Cmml:mspace width=\"0.12em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mtext\u003Ekmol\u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Ehm\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE11\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p19\"\u003EOther notations of the system are summarized in \u003Ca href=\"#tab1\" class=\"ref-link\" data-ref-style=\"table\"\u003ETable 1\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\u003Cdiv class=\"table-wrap\" id=\"tab1\"\u003E\u003Cdiv class=\"table-content\"\u003E\u003Ctable frame=\"hsides\" rules=\"groups\"\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Cthead\u003E\u003Ctr\u003E\u003Cth\u003ENotation\u003C\u002Fth\u003E\u003Cth\u003E\u003C\u002Fth\u003E\u003C\u002Ftr\u003E\u003C\u002Fthead\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EC\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Epf\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EHeat capacity of the feed gas\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EC\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Epg\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EHeat capacity of the reacting gas\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ef\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003ECatalyst activity\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003EΔ\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EH\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EHeat of reaction\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EN\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EMass flow of component designed by subscript\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ek\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EReaction rate constant\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ep\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EPartial pressure of component designated by subscript\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ER\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EUniversal gas constant\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ES\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003ESurface area of catalyst tubes per unit length of reactor\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ES\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003ECross-sectional area of catalyst zone\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EU\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EOverall heat transfer coefficient\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EW\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003ETotal mass transfer flow rate\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003C\u002Ftbody\u003E\u003C\u002Ftable\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"table-caption\"\u003E\u003Ch3 class=\"heading\"\u003ETable 1.\u003C\u002Fh3\u003E\u003Cdiv class=\"text\"\u003E\u003Cp id=\"p20\"\u003ENotation of the synthesis system.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"text\"\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_4_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E2.1.3 Box constraints\u003C\u002Fh4\u003E\u003Cp id=\"p21\"\u003EThe variables are subjected to the following physical constraints, as is typical in industries [\u003Ca href=\"#B10\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E10\u003C\u002Fa\u003E]:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E12\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m17\" specific-use=\"web-only\"\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E<\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EL\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mspace width=\"0.48em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mn\u003E400\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E800\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mspace width=\"0.48em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E3220\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE12\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p22\"\u003EThe length of the reactor and the top temperature are chosen as the design variables. The remaining variables (\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003Csub\u003Ef\u003C\u002Fsub\u003E\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003Csub\u003Eg\u003C\u002Fsub\u003E\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, and \u003Cspan class=\"inline-formula\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m18\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:math\u003E\u003C\u002Fspan\u003E) can be calculated from the model by three differential \u003Ca href=\"#E3\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEqs. (3)\u003C\u002Fa\u003E, \u003Ca href=\"#E4\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003E(4)\u003C\u002Fa\u003E, and \u003Ca href=\"#E5\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003E(5)\u003C\u002Fa\u003E. Then, the objective function is determined by \u003Ca href=\"#E2\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEq. (2)\u003C\u002Fa\u003E. Due to the constraints of temperatures, the variable \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E0\u003C\u002Fsub\u003E is also set to be within 400 and 800.\u003C\u002Fp\u003E\u003Cp id=\"p23\"\u003EThe optimal design problem is summarized as follows:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E13\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m19\" specific-use=\"web-only\"\u003E\u003Cmml:mtable columnalign=\"left\" displaystyle=\"true\"\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mspace width=\"0.12em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mo\u003Emaximize\u003C\u002Fmml:mo\u003E\u003Cmml:mspace width=\"0.24em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\" separators=\",\"\u003E\u003Cmml:mi\u003Ex\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mi\u003Es\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E.\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E.\u003C\u002Fmml:mo\u003E\u003Cmml:mspace width=\"0.36em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mfenced open=\"{\" close=\"\"\u003E\u003Cmml:mtable columnalign=\"left\"\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EdT\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Edx\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EUS\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EWC\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Epf\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eg\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EdT\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Edx\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EUS\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EWC\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Epg\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eg\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mi mathvariant=\"normal\"\u003EΔ\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EH\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ES\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EWC\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Epg\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EdN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Edx\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EdN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Edx\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ek\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EH\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mn\u003E1.5\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003ENH\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E3\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ek\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003ENH\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E3\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003Ep\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EH\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mn\u003E1.5\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eg\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mspace width=\"0.48em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:msubsup\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E701.2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mn\u003E400\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E800\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mspace width=\"0.48em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E3220\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E<\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EL\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mspace width=\"0.36em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mn\u003E400\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E800\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003C\u002Fmml:mtable\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003C\u002Fmml:mtable\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE13\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_6_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E2.2 Optimization strategy\u003C\u002Fh3\u003E\u003Cp id=\"p24\"\u003EThe system of ordinary differential \u003Ca href=\"#E3\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEqs. (3)\u003C\u002Fa\u003E, \u003Ca href=\"#E4\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003E(4)\u003C\u002Fa\u003E, and \u003Ca href=\"#E5\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003E(5)\u003C\u002Fa\u003E with initial \u003Ca href=\"#E11\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003Econditions (11)\u003C\u002Fa\u003E was solved by Runge–Kutta fourth-order method. The system is well defined when the top temperature (\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E0\u003C\u002Fsub\u003E) and the interval of integration (the reactor length \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EL\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E) are assigned. After that, the economic return is clearly evaluated, and it can be considered as two-variable function of the top temperature and reactor length. The genetic algorithm is employed to find the optimal solution. In order to handle the constraints, a penalty or barrier is defined to the objective function whenever any of variable limits is violated. The proposed strategy is detailed as follows.\u003C\u002Fp\u003E\u003Cdiv class=\"section\" id=\"sec_6_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E2.2.1 Genetic algorithm for optimization problem\u003C\u002Fh4\u003E\u003Cp id=\"p25\"\u003EThe range of the design variables is \u003Cspan class=\"inline-formula\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m20\"\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E<\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Ex\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mspace width=\"0.36em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mn\u003E400\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E800\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:math\u003E\u003C\u002Fspan\u003E. The parameters of GA such as population size, crossover probability, mutation probability values were set to be 50, 1.0, and 0.30, respectively. The selection was chosen as roulette wheel selection with elitism. The number of generations was set to be 500.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_7_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E2.2.2 Barrier method for constrained optimization\u003C\u002Fh4\u003E\u003Cp id=\"p26\"\u003EIn barrier or penalty methods, the objective function will receive an undesired value when one of the constraints is violated. Therefore, the solution will be kept in the feasible region. The objective function has been modified as\u003C\u002Fp\u003E\u003Cdiv id=\"df_E14\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m21\" specific-use=\"web-only\"\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfenced open=\"{\" close=\"\"\u003E\u003Cmml:mtable columnalign=\"left\"\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mspace width=\"0.24em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mtext\u003Eif\u003C\u002Fmml:mtext\u003E\u003Cmml:mspace width=\"0.24em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mn\u003E400\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E800\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mspace width=\"0.48em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E3220\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003Cmml:mspace width=\"0.24em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mtext\u003Eotherwise\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003C\u002Fmml:mtable\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE14\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_8_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E2.2.3 Parameters\u003C\u002Fh4\u003E\u003Cp id=\"p27\"\u003EThe parameters were obtained from the literature [\u003Ca href=\"#B7\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E7\u003C\u002Fa\u003E, \u003Ca href=\"#B10\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E10\u003C\u002Fa\u003E] and summarized in \u003Ca href=\"#tab2\" class=\"ref-link\" data-ref-style=\"table\"\u003ETable 2\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\u003Cdiv class=\"table-wrap\" id=\"tab2\"\u003E\u003Cdiv class=\"table-content\"\u003E\u003Ctable frame=\"hsides\" rules=\"groups\"\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Cthead\u003E\u003Ctr\u003E\u003Cth\u003EParameter\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003EValue\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003EUnit\u003C\u002Fth\u003E\u003C\u002Ftr\u003E\u003C\u002Fthead\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EC\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Epf\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.707\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003Ekcal\u002Fkg K\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EC\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Epg\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.719\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003Ekcal\u002Fkg K\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ef\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E1.0\u003C\u002Ftd\u003E\u003Ctd\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003EΔ\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EH\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E−26,000\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003Ekcal\u002Fkmol\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ER\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E1.987\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003Ekcal\u002Fkmol K\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ES\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E10\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003EM\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ES\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.78\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003Em\u003Csup\u003E2\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EU\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E500\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003Ekcal\u002Fh m\u003Csup\u003E2\u003C\u002Fsup\u003E K\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EW\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E26,400\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003Ekg\u002Fh\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003C\u002Ftbody\u003E\u003C\u002Ftable\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"table-caption\"\u003E\u003Ch3 class=\"heading\"\u003ETable 2.\u003C\u002Fh3\u003E\u003Cdiv class=\"text\"\u003E\u003Cp id=\"p28\"\u003EModel parameters [\u003Ca href=\"#B7\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E7\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"text\"\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_10_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E2.3 Optimization results\u003C\u002Fh3\u003E\u003Cp id=\"p29\"\u003E\u003Ca href=\"#F2\" class=\"ref-link\" data-ref-style=\"fig\"\u003EFigure 2\u003C\u002Fa\u003E shows the fitness values as a function of generation. As can be observed, the fitness function value achieved the highest after roughly 20 generations and then stayed unchanged. After 100 generations, it was obtained that the reactor length should be 6.772 m, and the top temperature should be 707.09 K. The process produces a profit of 5.018× 10\u003Csup\u003E6\u003C\u002Fsup\u003E $ per year. The other parameters of the process are summarized in \u003Ca href=\"#tab3\" class=\"ref-link\" data-ref-style=\"table\"\u003ETable 3\u003C\u002Fa\u003E and compared with the findings of a cyclic coordinate search [\u003Ca href=\"#B13\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E13\u003C\u002Fa\u003E]. The profit value is slightly higher than those reported in the literature, which focused solely on reactor length optimization. From the results, the temperature at the entrance of the catalyst zone should be slightly higher, and that the reactor length should also be slightly longer than previously reported.\u003C\u002Fp\u003E\u003Cfigure class=\"media-panel\" id=\"F2\"\u003E\u003Cdiv class=\"media\"\u003E\u003Cimg src=\"\u002F\u002Fcdnintech.com\u002Fmedia\u002Fchapter\u002F81877\u002F1512345123\u002Fmedia\u002FF2.png\" class=\"figure-link\" alt=\"\"\u003E\u003C\u002Fdiv\u003E\u003Cfigcaption class=\"caption\"\u003E\u003Ch4\u003EFigure 2.\u003C\u002Fh4\u003E\u003Cp\u003E\u003Cp xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\" id=\"p30\"\u003EFitness value versus generations.\u003C\u002Fp\u003E\u003C\u002Fp\u003E\u003C\u002Ffigcaption\u003E\u003C\u002Ffigure\u003E\u003Cdiv class=\"table-wrap\" id=\"tab3\"\u003E\u003Cdiv class=\"table-content\"\u003E\u003Ctable frame=\"hsides\" rules=\"groups\"\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Cthead\u003E\u003Ctr\u003E\u003Cth\u003EVariables\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003EInterval\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003ECyclic coordinate [\u003Ca href=\"#B13\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E13\u003C\u002Fa\u003E]\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003EGenetic algorithm\u003C\u002Fth\u003E\u003C\u002Ftr\u003E\u003C\u002Fthead\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ex\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E (m)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E[0,10]\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E6.724\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E6.772\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E0\u003C\u002Fsub\u003E (K)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E[600,800]\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E700.27\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E707.09\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003Csub\u003Ef\u003C\u002Fsub\u003E\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E (K)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E[400,800]\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E400.00\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E401.09\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003Csub\u003Eg\u003C\u002Fsub\u003E\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E (K)\u003C\u002Ftd\u003E\u003Ctd\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E629.94\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E631.12\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EN\u003Csub\u003EN2\u003C\u002Fsub\u003E\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E[0,3220]\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E490.68\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E490.68\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EF\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E (10\u003Csup\u003E6\u003C\u002Fsup\u003E$\u002Fyear)\u003C\u002Ftd\u003E\u003Ctd\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E5.018\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E5.018\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003C\u002Ftbody\u003E\u003C\u002Ftable\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"table-caption\"\u003E\u003Ch3 class=\"heading\"\u003ETable 3.\u003C\u002Fh3\u003E\u003Cdiv class=\"text\"\u003E\u003Cp id=\"p31\"\u003EMaximization results.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"text\"\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_12\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E3. Economic optimization of membrane module for ultrafiltration of protein solution\u003C\u002Fh2\u003E\u003Cp id=\"p32\"\u003EThe behavior of permeate flux has a significant impact on the performance of cross-flow ultrafiltration. Many factors cause flux declination, such as solution properties, membrane properties, and operation conditions. The majority of current research has centered on increasing membrane performance in terms of permeability and selectivity [\u003Ca href=\"#B14\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E14\u003C\u002Fa\u003E, \u003Ca href=\"#B15\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E15\u003C\u002Fa\u003E]. Just a few studies have paid attention to the configuration and operation of the membrane module [\u003Ca href=\"#B16\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E16\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p33\"\u003EVarious factors determine the decision of membrane module geometry for a given application, including fabrication method, power consumption, and fouling potential [\u003Ca href=\"#B17\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E17\u003C\u002Fa\u003E]. Manufacturers frequently recommend the membrane module design from the fabrication standpoint [\u003Ca href=\"#B17\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E17\u003C\u002Fa\u003E]. There is virtually no evidence that their approach prioritizes the energy efficiency. Currently, with a growing in energy concern and a falling in membrane cost, the membrane module design should place a higher attention on energy efficiency. As a result, it is necessary to propose a module design methodology that takes into account the energy factor.\u003C\u002Fp\u003E\u003Cp id=\"p34\"\u003EFurthermore, membrane operating conditions are usually decided by user experience, a handbook, or a manual from the membrane supplier. However, the permeate flux equation governing the performance of the membrane system varies greatly between different situations. In this aspect, for any specific application, a general methodology for the design and operation conditions should be studied.\u003C\u002Fp\u003E\u003Cp id=\"p35\"\u003EIn cross-flow ultrafiltration of protein solution, Nguyen et al. [\u003Ca href=\"#B18\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E18\u003C\u002Fa\u003E] proposed a simple combined model, which simultaneously considers pore blockage and cake filtration, to describe the flux declination. Then, in the study [\u003Ca href=\"#B19\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E19\u003C\u002Fa\u003E], the correlation between the steady-state permeate flux and operation parameters was reported. From the steady-state operation equation, optimal design and operation conditions for each particular application could be established.\u003C\u002Fp\u003E\u003Cp id=\"p36\"\u003EHowever, just a few reports on the optimization of membrane processes and cost estimation have been published, or the cost estimation is too general. For example, Wiley et al. [\u003Ca href=\"#B17\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E17\u003C\u002Fa\u003E] optimized the membrane module configurations for brackish water desalination. However, the operation mode is single-pass and only the membrane cost and energy cost were taken into account. Sethi and Wiesner [\u003Ca href=\"#B20\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E20\u003C\u002Fa\u003E] developed the cost model for the removal of natural organic matter, but the study has not conducted the optimization. In membrane technology, the feed and bleed operation mode, which combines the batch and the single-pass configurations, is commonly utilized for continuous full-scale filtration [\u003Ca href=\"#B21\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E21\u003C\u002Fa\u003E, \u003Ca href=\"#B22\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E22\u003C\u002Fa\u003E]. Therefore, the optimization of a membrane module operated in feed and bleed mode for protein ultrafiltration is considered. The membrane geometry dimensions and operating conditions are design variables in the problem. The system is represented by a set of ordinary differential equations. The objective function is the annual cost, which consists of various types of capital investments and an operating expense. The capital investments are classified into several categories, which are individually correlated to plant scale, particularly the membrane area. The operating expense is the power consumption.\u003C\u002Fp\u003E\u003Cdiv class=\"section\" id=\"sec_12_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E3.1 Process configuration and model calculation\u003C\u002Fh3\u003E\u003Cdiv class=\"section\" id=\"sec_12_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E3.1.1 Membrane plant configuration\u003C\u002Fh4\u003E\u003Cp id=\"p37\"\u003EThe configuration of filtration system is continuous feed and bleed, which is shown schematically in \u003Ca href=\"#F3\" class=\"ref-link\" data-ref-style=\"fig\"\u003EFigure 3\u003C\u002Fa\u003E. The notations are summarized in \u003Ca href=\"#tab4\" class=\"ref-link\" data-ref-style=\"table\"\u003ETable 4\u003C\u002Fa\u003E. There are two main pumps in this operation: the feed pump provides the necessary trans-membrane pressure, while the recirculation pump maintains the cross-flow rate through the modules. The concentrate is continually withdrawn from the system at a flow rate (\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ER\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E).\u003C\u002Fp\u003E\u003Cfigure class=\"media-panel\" id=\"F3\"\u003E\u003Cdiv class=\"media\"\u003E\u003Cimg src=\"\u002F\u002Fcdnintech.com\u002Fmedia\u002Fchapter\u002F81877\u002F1512345123\u002Fmedia\u002FF3.png\" class=\"figure-link\" alt=\"\"\u003E\u003C\u002Fdiv\u003E\u003Cfigcaption class=\"caption\"\u003E\u003Ch4\u003EFigure 3.\u003C\u002Fh4\u003E\u003Cp\u003E\u003Cp xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\" id=\"p38\"\u003ESchematic configuration of feed-and-bleed mode membrane system.\u003C\u002Fp\u003E\u003C\u002Fp\u003E\u003C\u002Ffigcaption\u003E\u003C\u002Ffigure\u003E\u003Cdiv class=\"table-wrap\" id=\"tab4\"\u003E\u003Cdiv class=\"table-content\"\u003E\u003Ctable frame=\"hsides\" rules=\"groups\"\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Cthead\u003E\u003Ctr\u003E\u003Cth\u003ENotation\u003C\u002Fth\u003E\u003Cth\u003EName and units\u003C\u002Fth\u003E\u003C\u002Ftr\u003E\u003C\u002Fthead\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EF\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EFeed flow rate [m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fhr]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ER\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003ERetentate (concentrate) flow rate [m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fhr]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EQ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003ERecirculation flow rate [m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fhr]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EFlow\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EFlow rate in membrane module [m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fhr]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EPermeation flow rate [m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fhr]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EF\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EPressure at outlet of feed pump [kPa]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ei\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EPressure at the inlet of membrane module [kPa]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Eo\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EPressure at the inlet of membrane module [kPa]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EE\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EP\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EEnergy consumed by the feed pump [kW]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EE\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EQ\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EEnergy consumed by the recirculation pump [kW]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eϕ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E0\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EInitial concentration of protein solution [m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fm\u003Csup\u003E3\u003C\u002Fsup\u003E]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eϕ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ei\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EInlet concentration of protein solution [m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fm\u003Csup\u003E3\u003C\u002Fsup\u003E]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eϕ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ef\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EFinal concentration of protein solution [m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fm\u003Csup\u003E3\u003C\u002Fsup\u003E]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eϕ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EP\u003C\u002Fsub\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EConcentration of protein in permeate flux [m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fm\u003Csup\u003E3\u003C\u002Fsup\u003E]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eu\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EFluid flow velocity [m\u002Fs]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eρ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EFluid density [kg\u002Fm\u003Csup\u003E3\u003C\u002Fsup\u003E]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eμ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EFluid viscosity [kg\u002F(m·s)]\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ew, h, L, d\u003Csub\u003Eh\u003C\u002Fsub\u003E\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Ftd\u003E\u003Ctd\u003EWidth, height, length, hydraulic diameter of the membrane module\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003C\u002Ftbody\u003E\u003C\u002Ftable\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"table-caption\"\u003E\u003Ch3 class=\"heading\"\u003ETable 4.\u003C\u002Fh3\u003E\u003Cdiv class=\"text\"\u003E\u003Cp id=\"p39\"\u003ESummary of system configuration notations.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"text\"\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_13_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E3.1.2 Modeling of membrane modules\u003C\u002Fh4\u003E\u003Cp id=\"p40\"\u003EThe material balance for total mass and protein give:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E15\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m22\" specific-use=\"web-only\"\u003E\u003Cmml:mtable columnalign=\"left\" displaystyle=\"true\" rowspacing=\"1\"\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003ER\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003ER\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Ep\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EQ\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EQ\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Ei\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003C\u002Fmml:mtable\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE15\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p41\"\u003EThe viscosity and density of protein solution correlate to its concentration [\u003Ca href=\"#B23\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E23\u003C\u002Fa\u003E]:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E16\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m23\" specific-use=\"web-only\"\u003E\u003Cmml:mtable columnalign=\"left\" displaystyle=\"true\" rowspacing=\"1\"\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eμ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E8.94\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E4\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mo\u003Eexp\u003C\u002Fmml:mo\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E13.5482\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eρ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E1000\u003C\u002Fmml:mn\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E1360\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003C\u002Fmml:mtable\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE16\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p42\"\u003Ein which, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eμ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Em\u003C\u002Fsub\u003E, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eϕ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Em\u003C\u002Fsub\u003E are the viscosity and concentration of the mixture (solution), respectively. \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eρ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Em\u003C\u002Fsub\u003E is the density of protein solution, 1000 kg\u002Fm\u003Csup\u003E3\u003C\u002Fsup\u003E is the density of water, and 1360 kg\u002Fm\u003Csup\u003E3\u003C\u002Fsup\u003E is the density of dry protein powder.\u003C\u002Fp\u003E\u003Cp id=\"p43\"\u003EThe permeate flux through the membrane is [\u003Ca href=\"#B19\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E19\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cdiv id=\"df_E17\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m24\" specific-use=\"web-only\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi\u003EJ\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E3.66\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E7\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eρ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.27\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eρ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Eud\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Eh\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eμ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.52\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE17\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p44\"\u003Ein which \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the trans-membrane pressure, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eu\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the cross-flow velocity, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ed\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Eh\u003C\u002Fsub\u003E is the hydraulic diameter of the flow channel.\u003C\u002Fp\u003E\u003Cp id=\"p45\"\u003EThe equation for permeate flux can be rewritten as:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E18\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m25\" specific-use=\"web-only\"\u003E\u003Cmml:mi\u003EJ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E5.124\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E9\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eρ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.27\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eρ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Eud\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Eh\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eμ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.52\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ed\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Eh\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE18\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p46\"\u003Eor in terms of shear rate \u003Cspan class=\"inline-formula\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m26\"\u003E\u003Cmml:mover accent=\"true\"\u003E\u003Cmml:mi\u003Eγ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003Ė\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mover\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E6\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mi\u003Eh\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E12\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ed\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Eh\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:math\u003E\u003C\u002Fspan\u003E, where \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eh\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the channel height:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E19\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m27\" specific-use=\"web-only\"\u003E\u003Cmml:mi\u003EJ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E4.27\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eρ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.27\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eρ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Eud\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Eh\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eμ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.52\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mover accent=\"true\"\u003E\u003Cmml:mi\u003Eγ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003Ė\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mover\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE19\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p47\"\u003EThe flow rate\u002Fvelocity drop and channel length change are calculated from the total mass balance and component balance within the control volume \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Edz\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E across the channel. Protein is assumed to be fully rejected by the membrane:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E20\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m28\" specific-use=\"web-only\"\u003E\u003Cmml:mi\u003Ed\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003EFlow\u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE20\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"df_E21\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m29\" specific-use=\"web-only\"\u003E\u003Cmml:mi\u003Ed\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003EFlow\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EJ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Ed\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Ewz\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EJ\u003C\u002Fmml:mi\u003E\u003Cmml:mspace width=\"0.12em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mi\u003Ew\u003C\u002Fmml:mi\u003E\u003Cmml:mspace width=\"0.12em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Edz\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE21\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p48\"\u003EThe pressure loss is estimated by the Darcy-Weisbach Equation [\u003Ca href=\"#B24\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E24\u003C\u002Fa\u003E, \u003Ca href=\"#B25\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E25\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cdiv id=\"df_E22\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m30\" specific-use=\"web-only\"\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EdP\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E4\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eρ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Edz\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ed\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Eh\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mfrac\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE22\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p49\"\u003Ein which \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ef\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the friction factor.\u003C\u002Fp\u003E\u003Cp id=\"p50\"\u003EThe set of ordinary equations that describes the membrane module system was established as follows [\u003Ca href=\"#B26\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E26\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cdiv id=\"df_E23\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m31\" specific-use=\"web-only\"\u003E\u003Cmml:mfenced open=\"{\" close=\"\"\u003E\u003Cmml:mtable columnalign=\"left\" rowspacing=\"1\"\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Ed\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003EFlow\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Ed\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003EFlow\u003C\u002Fmml:mtext\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Edz\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Ed\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003EFlow\u003C\u002Fmml:mtext\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mspace width=\"0.12em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mi\u003Ew\u003C\u002Fmml:mi\u003E\u003Cmml:mspace width=\"0.12em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mi\u003EJ\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi mathvariant=\"italic\"\u003EdP\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Ed\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E4\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eρ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mfrac\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ed\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Eh\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mfrac\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mfrac\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003EFlow\u003C\u002Fmml:mtext\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mfrac\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Ew\u003C\u002Fmml:mi\u003E\u003Cmml:mspace width=\"0.12em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mi\u003EJ\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eμ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E8.94\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E4\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mo\u003Eexp\u003C\u002Fmml:mo\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E13.5482\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eρ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E1000\u003C\u002Fmml:mn\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E1360\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mi\u003EJ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E5.124\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E9\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eρ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.27\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eρ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"italic\"\u003Eud\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Eh\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eμ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Em\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.52\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ed\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Eh\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003EFlow\u003C\u002Fmml:mtext\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Eh\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Ew\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:mn\u003E24\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003ERe\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mspace width=\"0.36em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mtext\u003Eif\u003C\u002Fmml:mtext\u003E\u003Cmml:mspace width=\"0.36em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mo\u003ERe\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E<\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2000\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:mn\u003E0.079\u003C\u002Fmml:mn\u003E\u003Cmml:msup\u003E\u003Cmml:mo\u003ERe\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E0.25\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mspace width=\"0.36em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mtext\u003Eif\u003C\u002Fmml:mtext\u003E\u003Cmml:mspace width=\"0.24em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mo\u003ERe\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E>\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2000\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003C\u002Fmml:mtable\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE23\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p51\"\u003Ein the range of concentration [\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eϕ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ei\u003C\u002Fsub\u003E, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eϕ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ef\u003C\u002Fsub\u003E] and the initial condition\u003C\u002Fp\u003E\u003Cdiv id=\"df_E24\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m32\" specific-use=\"web-only\"\u003E\u003Cmml:mfenced open=\"{\" close=\"\"\u003E\u003Cmml:mtable columnalign=\"left\"\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003EFlow\u003C\u002Fmml:mtext\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Ei\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EQ\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mi\u003Ez\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Ei\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eϕ\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Ei\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Ei\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003C\u002Fmml:mtable\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE24\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p52\"\u003EThe system of the ordinary equations can be solved numerically by Runge–Kutta fourth-order method [\u003Ca href=\"#B27\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E27\u003C\u002Fa\u003E] to obtain the flow rate, the length, and the pressure. From that, the two important factors determining the total cost, membrane area, and total energy were calculated:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E25\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m33\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EA\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Emembrane\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Ew\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EL\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE25\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"df_E26\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m34\" specific-use=\"web-only\"\u003E\u003Cmml:mtable columnalign=\"left\" displaystyle=\"true\"\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EE\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Epumps\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EE\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003EP\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EE\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003EQ\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mspace width=\"1.56em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ei\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EQ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mi mathvariant=\"normal\"\u003EΔ\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Edrop\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003C\u002Fmml:mtable\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE26\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p53\"\u003EIn this equation,\u003C\u002Fp\u003E\u003Cp id=\"p54\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EE\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EP\u003C\u002Fsub\u003E, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EE\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EQ\u003C\u002Fsub\u003E are the power supplied by the feed pump and recirculation pump, respectively.\u003C\u002Fp\u003E\u003Cp id=\"p55\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EF\u003C\u002Fsub\u003E, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ei\u003C\u002Fsub\u003E, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Eo\u003C\u002Fsub\u003E are the pressure at the outlet of the feed pump, at the inlet and outlet of the membrane module, respectively.\u003C\u002Fp\u003E\u003Cp id=\"p56\"\u003EΔ\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Edrop\u003C\u002Fsub\u003E is the pressure drop in the membrane module.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_14_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E3.1.3 Cost estimation\u003C\u002Fh4\u003E\u003Cdiv class=\"section\" id=\"sec_14_4\" data-lvl=\"4\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E3.1.3.1 Operating cost\u003C\u002Fh4\u003E\u003Cp id=\"p57\"\u003EThe operating cost consists of power consumption of the pumps and membrane replacement. The annual energy expense of the pumps is calculated as\u003C\u002Fp\u003E\u003Cdiv id=\"df_E27\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m35\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Eenergy\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EE\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Epumps\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mi\u003Eη\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E8000\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mfrac\u003E\u003Cmml:mn\u003E3600\u003C\u002Fmml:mn\u003E\u003Cmml:mn\u003E1000\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003Eelectricity price\u003C\u002Fmml:mtext\u003E\u003Cmml:mspace width=\"5em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mfenced open=\"[\" close=\"]\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mtext\u003E$\u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003Eyear\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE27\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p58\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EE\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Epumps\u003C\u002Fsub\u003E is from \u003Ca href=\"#E26\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEq. (26)\u003C\u002Fa\u003E. The system is assumed to work 8000 hr.\u002Fyear (24 hr.\u002Fday and 333 days\u002Fyear). \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eη\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the efficiency of the pumps, which is set to be 0.7. The electricity price is supposed to be 0.08 $\u002FkWh, which is the price for the industrial sector in the United States [\u003Ca href=\"#B28\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E28\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p59\"\u003EThe membrane replacement cost is calculated as\u003C\u002Fp\u003E\u003Cdiv id=\"df_E28\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m36\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Emembrane\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EA\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Emembrane\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ec\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Emembrane\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi\u003EA\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mspace width=\"4.799997em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mfenced open=\"[\" close=\"]\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mtext\u003E$\u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003Eyear\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE28\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p60\"\u003Ewhere \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EC\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Emembrane\u003C\u002Fsub\u003E [$\u002Fm\u003Csup\u003E2\u003C\u002Fsup\u003E\u002Fyear] is the membrane replacement cost calculated per year.\u003C\u002Fp\u003E\u003Cp id=\"p61\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ec\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Emembrane\u003C\u002Fsub\u003E [$] is the membrane price per unit area,\u003C\u002Fp\u003E\u003Cp id=\"p62\"\u003E\u003Cspan class=\"inline-formula\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m37\"\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi\u003EA\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003C\u002Fspan\u003E is the amortization factor, which presents the time value of money [\u003Ca href=\"#B29\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E29\u003C\u002Fa\u003E] and is calculated as a function of interest rate \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ei\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E and the membrane life.\u003C\u002Fp\u003E\u003Cp id=\"p63\"\u003EThe membrane price is usually about 200 $\u002Fm\u003Csup\u003E2\u003C\u002Fsup\u003E [\u003Ca href=\"#B9\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E9\u003C\u002Fa\u003E], and membrane life is 12–18 months. Therefore, the membrane replacement cost per year is roughly estimated as 200 $\u002Fm\u003Csup\u003E2\u003C\u002Fsup\u003E\u002Fyear for the interest of \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ei\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 8%.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_15_4\" data-lvl=\"4\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E3.1.3.2 Capital cost\u003C\u002Fh4\u003E\u003Cp id=\"p64\"\u003EIt is widely observed that capital costs are correlated to the size in the power-law form [\u003Ca href=\"#B30\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E30\u003C\u002Fa\u003E]:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E29\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m38\" specific-use=\"web-only\"\u003E\u003Cmml:mtext\u003Ecost\u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Ek\u003C\u002Fmml:mi\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mtext\u003Esize\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mi\u003En\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msup\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE29\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p65\"\u003EIn order to achieve higher accuracy, rather than simply predicting the whole capital cost of the membrane plant to capacity, Sethi and Wiesner [\u003Ca href=\"#B20\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E20\u003C\u002Fa\u003E] divided the capital investment into several major categories, which was correlated to the size independently. The major categories include pumps and other manufactured equipment.\u003Col style=\"list-style-type: alpha-lower;\"\u003E\u003Cli\u003E\u003Cp id=\"p66\"\u003EPump capital cost\u003C\u002Fp\u003E\u003Cp id=\"p67\"\u003EThe pumps capital cost can be estimated as (Perry et al. [\u003Ca href=\"#B31\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E31\u003C\u002Fa\u003E]):\u003Cdiv id=\"df_E30\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m39\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E&lowast;\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mtext\u003Epump\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EI\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EL\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E81.27\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003EQ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.4\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE30\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003Cp id=\"p68\"\u003Ein which.\u003C\u002Fp\u003E\u003Cp id=\"p69\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EI\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E: a cost index ratio for updating the cost to the recent year.\u003C\u002Fp\u003E\u003Cp id=\"p70\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ef\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E: an adjust factor for pump construction material.\u003C\u002Fp\u003E\u003Cp id=\"p71\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ef\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E: an adjust factor for suction pressure range.\u003C\u002Fp\u003E\u003Cp id=\"p72\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EC\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EL\u003C\u002Fsub\u003E: a factor used to incorporate labor costs.\u003C\u002Fp\u003E\u003Cp id=\"p73\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EQ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E: flow capacity of the pump [m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fh].\u003C\u002Fp\u003E\u003Cp id=\"p74\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E: pressure outlet of the pump [kPa].\u003C\u002Fp\u003E\u003Cp id=\"p75\"\u003EThe cost index, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EI\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E in \u003Ca href=\"#E30\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEq. (30)\u003C\u002Fa\u003E, can be referred to as the chemical engineering (CE) index to update the cost. It can be obtained from [\u003Ca href=\"#B32\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E32\u003C\u002Fa\u003E], and the value of 2.4 is used. \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EC\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EL\u003C\u002Fsub\u003E = 1.4 with the assumption that 40% of the cost is required to install the equipment [\u003Ca href=\"#B33\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E33\u003C\u002Fa\u003E]. The factors \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ef\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E and \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ef\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E can be found in [\u003Ca href=\"#B31\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E31\u003C\u002Fa\u003E]. \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ef\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E = 1.5 when the material is stainless steel. \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ef\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E = 1.0 when the pump pressure is below 10 bar (1 MPa).\u003C\u002Fp\u003E\u003Cp id=\"p77\"\u003EThe pump size (\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EQ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E × \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E in \u003Ca href=\"#E30\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEq. (30)\u003C\u002Fa\u003E) of the two pumps (feed and recirculation pump) is\u003Cdiv id=\"df_E31\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m40\" specific-use=\"web-only\"\u003E\u003Cmml:mtext\u003Epump size\u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EQ\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:mi mathvariant=\"normal\"\u003Ei\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE31\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003Cli\u003E\u003Cp id=\"p79\"\u003ECapital cost of other equipment\u003C\u002Fp\u003E\u003Cp id=\"p80\"\u003EIn membrane application, the membrane area is the key parameter, which determines the plant capacity [\u003Ca href=\"#B34\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E34\u003C\u002Fa\u003E]. Thus, the membrane area is chosen as the basic for the estimation of various components in the capital costs.\u003C\u002Fp\u003E\u003Cp id=\"p81\"\u003ENon-membrane equipment and facilities, excluding the pumps, were grouped into four main categories: (1) pipes and valves; (2) instruments and controls; (3) tanks and frames; and (4) miscellaneous. The capital cost of each is correlated to the membrane area as follows (Sethi and Wiesner [\u003Ca href=\"#B20\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E20\u003C\u002Fa\u003E])\u003Col style=\"list-style-type: order;\"\u003E\u003Cli\u003E\u003Cp id=\"p82\"\u003EPipes and valves\u003Cdiv id=\"df_E32\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m41\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E&lowast;\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mi\u003EPV\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E6000\u003C\u002Fmml:mn\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EA\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Emembrane\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.42\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mspace width=\"2.999999em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mfenced open=\"[\" close=\"]\"\u003E\u003Cmml:mtext\u003E$\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE32\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003Cli\u003E\u003Cp id=\"p84\"\u003EInstruments and controls\u003Cdiv id=\"df_E33\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m42\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E&lowast;\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mi\u003EIC\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E1500\u003C\u002Fmml:mn\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EA\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Emembrane\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.66\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mspace width=\"3.239999em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mfenced open=\"[\" close=\"]\"\u003E\u003Cmml:mtext\u003E$\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE33\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003Cli\u003E\u003Cp id=\"p86\"\u003ETanks and frames\u003Cdiv id=\"df_E34\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m43\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E&lowast;\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mi\u003ETF\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E3100\u003C\u002Fmml:mn\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EA\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Emembrane\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.53\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mspace width=\"3.119999em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mfenced open=\"[\" close=\"]\"\u003E\u003Cmml:mtext\u003E$\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE34\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003Cli\u003E\u003Cp id=\"p88\"\u003EMiscellaneous\u003Cdiv id=\"df_E35\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m44\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E&lowast;\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mi\u003EMI\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E8000\u003C\u002Fmml:mn\u003E\u003Cmml:msup\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EA\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Emembrane\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mn\u003E0.57\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mspace width=\"3.119999em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mfenced open=\"[\" close=\"]\"\u003E\u003Cmml:mtext\u003E$\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE35\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003C\u002Fol\u003E\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003Cli\u003E\u003Cp id=\"p90\"\u003EAnnual capital cost\u003C\u002Fp\u003E\u003Cp id=\"p91\"\u003EThe capital cost can be annualized using the amortization factor as\u003Cdiv id=\"df_E36\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m45\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003Ecapital cost\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E&lowast;\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mtext\u003Ecapital\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mfrac\u003E\u003Cmml:mi\u003EA\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mspace width=\"4.319998em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mfenced open=\"[\" close=\"]\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mtext\u003E$\u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003Eyear\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE36\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003Cp id=\"p92\"\u003EFor the plant design year of 20 years and the interest rate 8%, the amortization factor will be about 0.1.\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003C\u002Fol\u003E\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_18_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E3.2 Formulizations of the problem\u003C\u002Fh3\u003E\u003Cdiv class=\"section\" id=\"sec_18_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E3.2.1 Fix parameters and design variables\u003C\u002Fh4\u003E\u003Cp id=\"p93\"\u003EIn the problem, some variables, called input variables, are fixed due to the requirement of the design. In membrane design, these are feed flow \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EF\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, inlet concentration \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eϕ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E0\u003C\u002Fsub\u003E, and outlet concentration \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eϕ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ef\u003C\u002Fsub\u003E. The protein is assumed to be entirely rejected by the membrane (\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eϕ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ep\u003C\u002Fsub\u003E = 0).\u003C\u002Fp\u003E\u003Cp id=\"p94\"\u003EThe design variables were: channel geometry (width × length × height), the inlet pressure (\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ei\u003C\u002Fsub\u003E), and recirculation flow rate (\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EQ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E).\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_19_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E3.2.2 Objective function\u003C\u002Fh4\u003E\u003Cp id=\"p95\"\u003EThe objective function is the sum of capital cost and operating cost, which were annualized:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E37\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m46\" specific-use=\"web-only\"\u003E\u003Cmml:mtable columnalign=\"left\" displaystyle=\"true\"\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mtext\u003Eminimum\u003C\u002Fmml:mtext\u003E\u003Cmml:mspace width=\"0.25em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mi mathvariant=\"bold\"\u003Ex\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003Eannual total cost\u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003Eannual capital cost\u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003Eannual operating cost\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mspace width=\"7.2em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003Eenergy\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003Emembrane\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003Ecapital\u003C\u002Fmml:mtext\u003E\u003Cmml:mspace width=\"0.12em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003Epumps\u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mtext mathvariant=\"italic\"\u003Eother\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003C\u002Fmml:mtable\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE37\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_20_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E3.2.3 Constraints\u003C\u002Fh4\u003E\u003Cp id=\"p96\"\u003EThe pressure at the outlet point should be positive. This constraint is satisfied by assigning a high value to the objective function if the outlet pressure is negative.\u003C\u002Fp\u003E\u003Cp id=\"p97\"\u003EThe decision variables are frequently limited on a finite range\u003C\u002Fp\u003E\u003Cdiv id=\"df_E38\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m47\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"bold\"\u003Ex\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003El\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mi mathvariant=\"bold\"\u003Ex\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi mathvariant=\"bold\"\u003Ex\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eu\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE38\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p98\"\u003Ein which \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ex\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E is the vector of decision variables \u003Cstrong\u003E\u003Cbold xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ex\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E = (\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ei\u003C\u002Fsub\u003E,\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EQ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E,\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ew\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E,\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eh\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E), subscripts \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003El\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E and \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eu\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E indicate the lower and upper bound.\u003C\u002Fp\u003E\u003Cp id=\"p99\"\u003EThe system parameters and variables are summarized in \u003Ca href=\"#tab5\" class=\"ref-link\" data-ref-style=\"table\"\u003ETable 5\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\u003Cdiv class=\"table-wrap\" id=\"tab5\"\u003E\u003Cdiv class=\"table-content\"\u003E\u003Ctable frame=\"hsides\" rules=\"groups\"\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Cthead\u003E\u003Ctr\u003E\u003Cth\u003EParameters\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003EValue\u003C\u002Fth\u003E\u003C\u002Ftr\u003E\u003C\u002Fthead\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd\u003EFeed flow rate (m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fhr)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.02–200\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003EInlet pressure (kPa)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E200–1000\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003ERecirculation flow rate (m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fhr)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0–50\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003EInitial solid fraction (m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fm\u003Csup\u003E3\u003C\u002Fsup\u003E)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.1\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003EFinal solid fraction (m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fm\u003Csup\u003E3\u003C\u002Fsup\u003E)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.4\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003EPlant design year (year)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E20\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003EInterest rate (%)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E8\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003EEnergy price ($\u002FkWh)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.08\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003EEfficiency of pumps (%)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E70\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003EOperating temperature (°C)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E25\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003EModule height (mm)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0–100\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003EModule width (m)\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0–30\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003C\u002Ftbody\u003E\u003C\u002Ftable\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"table-caption\"\u003E\u003Ch3 class=\"heading\"\u003ETable 5.\u003C\u002Fh3\u003E\u003Cdiv class=\"text\"\u003E\u003Cp id=\"p100\"\u003ESystem parameters and variables.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"text\"\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_21_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E3.2.4 Optimization by genetic algorithm\u003C\u002Fh4\u003E\u003Cp id=\"p101\"\u003EThe parameters of GA such as population size, crossover probability, mutation probability values were set to be, 100, 1.0, and 0.30, respectively. The selection was based on roulette wheel with elitism, which means the most fit individual is guaranteed a place in the next generation. The number of generations was assigned to be 500. Because the problem is to minimize the cost, the fitness function was defined as:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E39\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m48\" specific-use=\"web-only\"\u003E\u003Cmml:mtext\u003Efitness\u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mfenced open=\"{\" close=\"\"\u003E\u003Cmml:mtable columnalign=\"left\"\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003Cmml:mspace width=\"6.87em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mtext\u003Eif\u003C\u002Fmml:mtext\u003E\u003Cmml:mspace width=\"0.5em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mi\u003Ex\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E>\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E5\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mn\u003E5\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003Cmml:mtr\u003E\u003Cmml:mtd\u003E\u003Cmml:mn\u003E5\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mn\u003E10\u003C\u002Fmml:mn\u003E\u003Cmml:mn\u003E5\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mi\u003Ex\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mspace width=\"1.44em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mtext\u003Eotherwise\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mtd\u003E\u003C\u002Fmml:mtr\u003E\u003C\u002Fmml:mtable\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE39\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_23_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E3.3 Optimum design\u003C\u002Fh3\u003E\u003Cp id=\"p102\"\u003EFor the demonstration of this method, optimum designs of several feed flow rates have been carried out. The lower limit of the membrane width is 0.1 m, the lower limit for the module height is 0.5 mm. The designs are shown in \u003Ca href=\"#tab6\" class=\"ref-link\" data-ref-style=\"table\"\u003ETable 6\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\u003Cdiv class=\"table-wrap\" id=\"tab6\"\u003E\u003Cdiv class=\"table-content\"\u003E\u003Ctable frame=\"hsides\" rules=\"groups\"\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Ccol\u003E\u003Cthead\u003E\u003Ctr\u003E\u003Cth\u003EFeed [m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fhr]\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eϕ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E0\u003C\u002Fsub\u003E [−]\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003E\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eϕ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ef\u003C\u002Fsub\u003E [−]\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003EPressure [kPa]\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003ERecirculation [m\u003Csup\u003E3\u003C\u002Fsup\u003E\u002Fhr]\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003Ewidth [m]\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003Eheight [mm]\u003C\u002Fth\u003E\u003Cth align=\"center\"\u003Etotal cost [$\u002Fyr]\u003C\u002Fth\u003E\u003C\u002Ftr\u003E\u003C\u002Fthead\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd\u003E0.02\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.1\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.4\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E523\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E2.8\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.1\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E5.0\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E1.29 × 10\u003Csup\u003E3\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E0.2\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.1\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.4\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E1000\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E4.9\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.1\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E8.9\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E4.30 × 10\u003Csup\u003E3\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E2\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.1\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.4\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E1000\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.2\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.1\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E6.9\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E1.18 × 10\u003Csup\u003E4\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E20\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.1\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.4\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E987\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.2\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E1.3\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E5.0\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E5.60 × 10\u003Csup\u003E4\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd\u003E200\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.1\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.4\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E1000\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E0.8\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E11.1\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E5.0\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E3.65 × 10\u003Csup\u003E5\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003C\u002Ftbody\u003E\u003C\u002Ftable\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"table-caption\"\u003E\u003Ch3 class=\"heading\"\u003ETable 6.\u003C\u002Fh3\u003E\u003Cdiv class=\"text\"\u003E\u003Cp id=\"p103\"\u003EOptimum designs of membrane module.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"text\"\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p104\"\u003E\u003Ca href=\"#F4\" class=\"ref-link\" data-ref-style=\"fig\"\u003EFigure 4\u003C\u002Fa\u003E presents the optimum total cost per unit of feed flow. The cost per unit of feed flow decreases with an increase in plant capacity. It reflects the economies of scale.\u003C\u002Fp\u003E\u003Cfigure class=\"media-panel\" id=\"F4\"\u003E\u003Cdiv class=\"media\"\u003E\u003Cimg src=\"\u002F\u002Fcdnintech.com\u002Fmedia\u002Fchapter\u002F81877\u002F1512345123\u002Fmedia\u002FF4.png\" class=\"figure-link\" alt=\"\"\u003E\u003C\u002Fdiv\u003E\u003Cfigcaption class=\"caption\"\u003E\u003Ch4\u003EFigure 4.\u003C\u002Fh4\u003E\u003Cp\u003E\u003Cp xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\" id=\"p105\"\u003EThe behavior of cost per unit flow rate design in optimum condition with plant capacity.\u003C\u002Fp\u003E\u003C\u002Fp\u003E\u003C\u002Ffigcaption\u003E\u003C\u002Ffigure\u003E\u003Cp id=\"p106\"\u003EThe results also suggest that the membrane module dimensions and operation condition will change greatly depending on the process requirements, such as the required feed capacity. It is challenging to predict the direction. It might be concluded that the permeate flux also greatly affects the geometric design and operation strategy in membrane separation processes. It is difficult to find a general rule for the design, for each specific system, the correlation between the permeate flux and operating conditions and membrane geometry should be investigated.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_25\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E4. Modeling and optimization of the BSCF-based single-chamber solid oxide fuel cell by artificial neural network and genetic algorithm\u003C\u002Fh2\u003E\u003Cp id=\"p107\"\u003EFuel cells that are highly effective and green technology for converting chemical energy stored in fuel to useable power are currently regarded as one of the most promising approaches for future energy requirements [\u003Ca href=\"#B35\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E35\u003C\u002Fa\u003E]. The solid oxide fuel cell (SOFC) has demonstrated an exceptional integration of advantages, such as high efficiency, fuel flexibility, wide contamination acceptance, and low pollution [\u003Ca href=\"#B36\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E36\u003C\u002Fa\u003E, \u003Ca href=\"#B37\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E37\u003C\u002Fa\u003E]. Modeling and simulation are valuable tools for determining the impact of various design factors and operating conditions on cell performance, as well as for improving fuel cells [\u003Ca href=\"#B38\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E38\u003C\u002Fa\u003E, \u003Ca href=\"#B39\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E39\u003C\u002Fa\u003E, \u003Ca href=\"#B40\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E40\u003C\u002Fa\u003E]. Plenty of models have been reported to add to the understanding of fuel cells. Modeling approaches can be categorized into two types: theoretical and empirical one [\u003Ca href=\"#B39\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E39\u003C\u002Fa\u003E, \u003Ca href=\"#B41\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E41\u003C\u002Fa\u003E, \u003Ca href=\"#B42\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E42\u003C\u002Fa\u003E]. In the theoretical approach, the spatial dimensions of the models range from simple 0 (0-D) [\u003Ca href=\"#B43\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E43\u003C\u002Fa\u003E, \u003Ca href=\"#B44\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E44\u003C\u002Fa\u003E] and 1 (1-D) [\u003Ca href=\"#B42\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E42\u003C\u002Fa\u003E, \u003Ca href=\"#B45\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E45\u003C\u002Fa\u003E, \u003Ca href=\"#B46\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E46\u003C\u002Fa\u003E, \u003Ca href=\"#B47\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E47\u003C\u002Fa\u003E], to more complicated 2 (2-D) [\u003Ca href=\"#B48\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E48\u003C\u002Fa\u003E, \u003Ca href=\"#B49\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E49\u003C\u002Fa\u003E, \u003Ca href=\"#B50\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E50\u003C\u002Fa\u003E, \u003Ca href=\"#B51\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E51\u003C\u002Fa\u003E] and 3 (3-D) [\u003Ca href=\"#B52\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E52\u003C\u002Fa\u003E, \u003Ca href=\"#B53\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E53\u003C\u002Fa\u003E, \u003Ca href=\"#B54\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E54\u003C\u002Fa\u003E], all with various characteristics and directed at different objectives. The mathematical models, which are based on conservation principles, require a lot of data on parameters and properties of fuel cell, as well as complicated equations and time-consuming calculation.\u003C\u002Fp\u003E\u003Cp id=\"p108\"\u003EEmpirical or data-driven approach may be more feasible for fuel cell users since the behavior can be quickly and simply deduced without a comprehensive understanding of the internal components, just based on the experimental data [\u003Ca href=\"#B39\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E39\u003C\u002Fa\u003E, \u003Ca href=\"#B41\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E41\u003C\u002Fa\u003E]. Least squares support vector machine (LS-SVM) [\u003Ca href=\"#B55\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E55\u003C\u002Fa\u003E], Hammerstein model [\u003Ca href=\"#B56\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E56\u003C\u002Fa\u003E, \u003Ca href=\"#B57\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E57\u003C\u002Fa\u003E] are examples of these approaches. In this approach, artificial neural network (ANN) shows several advantages, including high nonlinearity, rapid computation, a low degree of error in matching experimental data. Using ANNs to model SOFCs appears to be a very promising method.\u003C\u002Fp\u003E\u003Cp id=\"p109\"\u003EIn this section, an ANN was used to model the performance of the BSCF\u002FGDC-based cathode SOFC. The cell voltage was predicted from cathode sintering temperature, cell operating temperature, and cell current. Several network architectures were examined to find the best structure, and the network was trained using back-propagation methods. The data for training, validation, and testing were taken from our study [\u003Ca href=\"#B58\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E58\u003C\u002Fa\u003E]. The genetic algorithm and the developed ANN were then used to find the best conditions for achieving maximum power.\u003C\u002Fp\u003E\u003Cdiv class=\"section\" id=\"sec_25_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E4.1 Artificial neural network models\u003C\u002Fh3\u003E\u003Cp id=\"p110\"\u003EArtificial neural networks (ANNs), which were analogous to biological nervous systems, consist of interconnected nodes known as neurons to receive and transfer data [\u003Ca href=\"#B59\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E59\u003C\u002Fa\u003E]. The most basic form, feed-forward architecture, is made up of an input layer, one hidden layers, and an output layer. The input and output layers have the same number of neurons as the number of inputs and outputs in the system to be modeled. Weighted connections connect each neuron to every other neuron in the next layer. In any layer except the input, the weighted sum of data from the previous layer is the input of a neuron. The neuron then activates the data using a function and transfers the response to all neurons in the next layer. The size of the hidden layers is a significant factor that affects the estimation precision because it can make the network become insufficient or overfitting [\u003Ca href=\"#B60\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E60\u003C\u002Fa\u003E]. The number of neurons in hidden layer is generally determined through trials. \u003Ca href=\"#F5\" class=\"ref-link\" data-ref-style=\"fig\"\u003EFigure 5\u003C\u002Fa\u003E illustrates a 3–5-1 feed forward artificial neural network with operating temperature, sintering temperature, and current as inputs.\u003C\u002Fp\u003E\u003Cfigure class=\"media-panel\" id=\"F5\"\u003E\u003Cdiv class=\"media\"\u003E\u003Cimg src=\"\u002F\u002Fcdnintech.com\u002Fmedia\u002Fchapter\u002F81877\u002F1512345123\u002Fmedia\u002FF5.png\" class=\"figure-link\" alt=\"\"\u003E\u003C\u002Fdiv\u003E\u003Cfigcaption class=\"caption\"\u003E\u003Ch4\u003EFigure 5.\u003C\u002Fh4\u003E\u003Cp\u003E\u003Cp xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\" id=\"p111\"\u003EArtificial neural network (3–5-1) structure.\u003C\u002Fp\u003E\u003C\u002Fp\u003E\u003C\u002Ffigcaption\u003E\u003C\u002Ffigure\u003E\u003Cp id=\"p112\"\u003EThe activation function employed in this model is the logistic sigmoid\u003Cspan class=\"inline-formula\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m49\"\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mi\u003Ex\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Ee\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Ex\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msup\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003C\u002Fmml:math\u003E\u003C\u002Fspan\u003E.\u003C\u002Fp\u003E\u003Cp id=\"p113\"\u003EThe input data (\u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ex\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ei\u003C\u002Fsub\u003E) are scaled to normalized value (x\u003Csub\u003Enorm\u003C\u002Fsub\u003E) to enhance the performance of the network:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E40\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m50\" specific-use=\"web-only\"\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ex\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Enorm\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E0.8\u003C\u002Fmml:mn\u003E\u003Cmml:mspace width=\"0.25em\"\u003E\u003C\u002Fmml:mspace\u003E\u003Cmml:mfrac\u003E\u003Cmml:mfenced open=\"(\" close=\")\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Ex\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ex\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Emin\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mspace width=\"0.25em\"\u003E\u003C\u002Fmml:mspace\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfenced\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ex\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Emax\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Ex\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Emin\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E0.1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE40\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p114\"\u003Ein which x\u003Csub\u003Emax\u003C\u002Fsub\u003E and x\u003Csub\u003Emin\u003C\u002Fsub\u003E are the bounded interval of the experimental data.\u003C\u002Fp\u003E\u003Cp id=\"p115\"\u003ETo assess the performance of ANN, the mean squared error (MSE) and coefficient of determination (R\u003Csup\u003E2\u003C\u002Fsup\u003E) are usually used [\u003Ca href=\"#B61\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E61\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p116\"\u003EVarious factors affect the performance of fuel cells such as cathode and anode structure, electrolyte material and thickness, cell temperature, inlet and outlet gas compositions. Two important factors, cathode sintered temperature and cell operating temperature, were considered in this model. The sintered temperature is from 1000–1050°C, whereas the operating temperature ranges from 625–700°C. The sintered temperature affects the structure of the obtained cathode as reported in [\u003Ca href=\"#B58\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E58\u003C\u002Fa\u003E]. The explanation of the range for the investigated parameters can be found in [\u003Ca href=\"#B62\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E62\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p117\"\u003EAn ANN with one input layer, one hidden layer, and one single output layer was proposed. Current density, sintered temperature of the cathode, and cell operating temperature are the inputs. Back-propagation algorithm [\u003Ca href=\"#B63\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E63\u003C\u002Fa\u003E] was used to train the network. The maximum number of iteration and minimum performance gradient were set to 400 and 10\u003Csup\u003E−5\u003C\u002Fsup\u003E, respectively, to stop the training. The proper network structure is determined through a series of trial tests. The data were split into three subsets at random: training, validation, and test, each containing 70, 20, 10% of the total samples, respectively. The validation and test sets are necessary for evaluating the validation and power of the networks.\u003C\u002Fp\u003E\u003Cp id=\"p118\"\u003EThe parameters of the neural network were saved and utilized in the next stage to optimize the power density using genetic algorithms.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_26_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E4.2 Optimization by genetic algorithm\u003C\u002Fh3\u003E\u003Cp id=\"p119\"\u003EThe objective function is the power density of the fuel cell\u003C\u002Fp\u003E\u003Cdiv id=\"df_E41\" class=\"formula panel\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"m51\" specific-use=\"web-only\"\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EI\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EV\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:math\u003E\u003Cspan class=\"equ\"\u003EE41\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"p120\"\u003Ewhere \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the power density (mW.cm\u003Csup\u003E−2\u003C\u002Fsup\u003E), \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EI\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the current density (mA.cm\u003Csup\u003E−2\u003C\u002Fsup\u003E) and is the input to the ANN model, and V is the cell voltage (V), which is calculated from the model.\u003C\u002Fp\u003E\u003Cp id=\"p121\"\u003EThe design variables and their corresponding ranges are summarized as follows:\u003Cul\u003E\u003Cli\u003E\u003Cp id=\"p122\"\u003Esintered temperature of the cathode, [1000–1050] (°C).\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003Cli\u003E\u003Cp id=\"p123\"\u003Eoperating temperature of the cell, [625–700] (°C).\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003Cli\u003E\u003Cp id=\"p124\"\u003Eelectric current of the cell, [0–1500] (mA.cm\u003Csup\u003E−2\u003C\u002Fsup\u003E)\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003C\u002Ful\u003E\u003C\u002Fp\u003E\u003Cp id=\"p125\"\u003EThe parameters of GA as population size, mutation probability values were set to be 100 and 0.10, respectively. The survival of the individuals was decided by roulette wheel with elitism. The number of generations was 500.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_27_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E4.3 Optimization results\u003C\u002Fh3\u003E\u003Cp id=\"p126\"\u003E\u003Ca href=\"#F6\" class=\"ref-link\" data-ref-style=\"fig\"\u003EFigure 6\u003C\u002Fa\u003E depicts the fitness values (maximum and mean) of the population versus generation. As indicated in the figure, after about 20 generations, the value of fitness function attained to a maximum value and then remained unchanged. After 100 generations, the maximum fuel cell power density of 451.64 mW\u002Fcm\u003Csup\u003E2\u003C\u002Fsup\u003E could be achieved at the sintered temperature of 1005°C, operating temperature of 668°C, and current density of 777 mA\u002Fcm\u003Csup\u003E2\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cfigure class=\"media-panel\" id=\"F6\"\u003E\u003Cdiv class=\"media\"\u003E\u003Cimg src=\"\u002F\u002Fcdnintech.com\u002Fmedia\u002Fchapter\u002F81877\u002F1512345123\u002Fmedia\u002FF6.png\" class=\"figure-link\" alt=\"\"\u003E\u003C\u002Fdiv\u003E\u003Cfigcaption class=\"caption\"\u003E\u003Ch4\u003EFigure 6.\u003C\u002Fh4\u003E\u003Cp\u003E\u003Cp xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\" id=\"p127\"\u003EThe fitness values versus generation.\u003C\u002Fp\u003E\u003C\u002Fp\u003E\u003C\u002Ffigcaption\u003E\u003C\u002Ffigure\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_29\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E5. Conclusions\u003C\u002Fh2\u003E\u003Cp id=\"p128\"\u003EThe application of genetic algorithm in chemical engineering processes has been illustrated by three case studies. The results suggest that the optimum conditions of complex chemical problems can be easily obtained using genetic algorithm. The successes of genetic algorithm for the challenging problems reported herein, the development of many faster and flexible versions of GA, the improvement of computing ability all suggest the continually increasing impact of metaheuristic methods in chemical engineering systems.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\n","keywords":"optimization, genetic algorithm, chemical engineering, modeling","chapterPDFUrl":"https:\u002F\u002Fcdn.intechopen.com\u002Fpdfs\u002F81877.pdf","chapterXML":"https:\u002F\u002Fmts.intechopen.com\u002Fsource\u002Fxml\u002F81877.xml","webChapterXML":"s3:\u002F\u002Fintech-chapter-xmls\u002Fxmls-chapter\u002F81877\u002F1672149221\u002F","downloadPdfUrl":"\u002Fchapter\u002Fpdf-download\u002F81877","previewPdfUrl":"\u002Fchapter\u002Fpdf-preview\u002F81877","cdnMediaBaseUrl":"s3:\u002F\u002Fintech-cdn\u002Fmedia\u002Fchapter\u002F81877\u002F1512345123\u002F","totalDownloads":359,"totalViews":1100,"totalCrossrefCites":0,"totalDimensionsCites":1,"dateSubmitted":"December 20th 2021","dateReviewed":"April 11th 2022","datePrePublished":"May 19th 2022","datePublished":"October 12th 2022","dateFinished":"May 19th 2022","readingETA":"0","abstract":"Chemical engineering processes are frequently composed of multiple complex phenomena. These systems can be represented by a set of several equations, which are referred to as mathematical model of the process. Optimization in chemical engineering utilizes specialized techniques to determine the values of the decision variables at which the performance of the process, measured as the objective function(s), is minimum or maximum. The profitability of the process improves remarkably as a result of this selection. This benefit has encouraged the broad application of optimization for important industrial challenges. However, many problems in chemical engineering processes are hard to find the optimum using gradient-based algorithms. For example, the cases when the objective functions of the processes are multimodal, discontinuous, or implicit. Genetic algorithms (GAs) are a kind of metaheuristic searching optimization methods, which are inspired by nature, the mechanics of natural evolution and genetics. Genetic algorithms have received significant attention due to their remarkable advantages over classical algorithms. Compared with traditional optimization approaches, GAs are straightforward, robust, capable of handling the non-differentiable, discontinuous, or multimodal problems. The purpose of this paper is to give several case studies using genetic algorithms in chemical engineering optimization problems.","reviewType":"peer-reviewed","bibtexUrl":"\u002Fchapter\u002Fbibtex\u002F81877","risUrl":"\u002Fchapter\u002Fris\u002F81877","signatures":"Thi Anh-Nga Nguyen and Tuan-Anh Nguyen","isPublished":true,"isOnlineFirst":false,"isDeactivated":0,"noAds":0,"subseries":null,"book":{"id":"10694","type":"book","title":"Genetic Algorithms","subtitle":null,"fullTitle":"Genetic Algorithms","slug":"genetic-algorithms","isPublished":true,"publishedDate":"October 12th 2022","bookSignature":"Sebastián Ventura, José María Luna and José María Moyano","coverURL":"https:\u002F\u002Fcdn.intechopen.com\u002Fbooks\u002Fimages_new\u002F10694.jpg","cdnCoverURL":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F10694\u002F1713444989-960888035\u002Fcover.jpg","cdnCoverURL300":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F10694\u002F1713444989-960888035\u002Fcover-300.jpg","cdnWebCoverURL":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F10694\u002F1718280416-1935065913\u002Fweb-cover.jpg","cdnWebCoverURL300":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F10694\u002F1718280416-1935065913\u002Fweb-cover-300.jpg","cdnCoverWithTextURL":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F10694\u002F1718118054-70160891\u002Fcover-text.jpg","cdnCoverWithTextURL300":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F10694\u002F1718118054-70160891\u002Fcover-text-300.jpg","licenceType":"CC BY 3.0","editedByType":"Edited by","isbn":"978-1-80355-178-4","printIsbn":"978-1-80355-177-7","pdfIsbn":"978-1-80355-179-1","isAvailableForWebshopOrdering":true,"isDeactivated":false,"kuFlag":false,"noAdsSub":0,"editors":[{"id":"136112","title":"Dr.","name":"Sebastian","middleName":null,"surname":"Ventura","slug":"sebastian-ventura","fullName":"Sebastian Ventura"}],"productType":{"id":"1","title":"Edited Volume","chapterContentType":"chapter","authoredCaption":"Edited by"}},"authors":[{"id":"437310","title":"Associate Prof.","name":"Tuan-Anh","middleName":null,"surname":"Nguyen","fullName":"Tuan-Anh Nguyen","slug":"tuan-anh-nguyen","email":"anh.nguyen@hcmut.edu.vn","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F46.025\u002Fauthor.svg","institution":{"name":"Ho Chi Minh City University of Technology","institutionURL":null,"country":{"name":"Vietnam"}}},{"id":"450522","title":"Dr.","name":"Thi Anh-Nga","middleName":null,"surname":"Nguyen","fullName":"Thi Anh-Nga Nguyen","slug":"thi-anh-nga-nguyen","email":"chemist2001@gmail.com","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F46.025\u002Fauthor.svg","institution":{"name":"Ton Duc Thang University","institutionURL":null,"country":{"name":"Vietnam"}}}],"sections":[{"id":"sec_1","title":"1. Introduction","level":"1"},{"id":"sec_2","title":"2. Optimization of an autothermal ammonia synthesis reactor","level":"1"},{"id":"sec_2_2","title":"2.1 Problem formulation of ammonia synthesis reactor","level":"2"},{"id":"sec_2_3","title":"2.1.1 Objective function","level":"3"},{"id":"sec_3_3","title":"Table 1.","level":"3"},{"id":"sec_4_3","title":"2.1.3 Box constraints","level":"3"},{"id":"sec_6_2","title":"2.2 Optimization strategy","level":"2"},{"id":"sec_6_3","title":"2.2.1 Genetic algorithm for optimization problem","level":"3"},{"id":"sec_7_3","title":"2.2.2 Barrier method for constrained optimization","level":"3"},{"id":"sec_8_3","title":"Table 2.","level":"3"},{"id":"sec_10_2","title":"2.3 Optimization results","level":"2"},{"id":"sec_12","title":"3. Economic optimization of membrane module for ultrafiltration of protein solution","level":"1"},{"id":"sec_12_2","title":"3.1 Process configuration and model calculation","level":"2"},{"id":"sec_12_3","title":"Table 4.","level":"3"},{"id":"sec_13_3","title":"3.1.2 Modeling of membrane modules","level":"3"},{"id":"sec_14_3","title":"3.1.3 Cost estimation","level":"3"},{"id":"sec_14_4","title":"3.1.3.1 Operating cost","level":"4"},{"id":"sec_15_4","title":"3.1.3.2 Capital cost","level":"4"},{"id":"sec_18_2","title":"3.2 Formulizations of the problem","level":"2"},{"id":"sec_18_3","title":"3.2.1 Fix parameters and design variables","level":"3"},{"id":"sec_19_3","title":"3.2.2 Objective function","level":"3"},{"id":"sec_20_3","title":"Table 5.","level":"3"},{"id":"sec_21_3","title":"3.2.4 Optimization by genetic algorithm","level":"3"},{"id":"sec_23_2","title":"3.3 Optimum design","level":"2"},{"id":"sec_25","title":"4. Modeling and optimization of the BSCF-based single-chamber solid oxide fuel cell by artificial neural network and genetic algorithm","level":"1"},{"id":"sec_25_2","title":"4.1 Artificial neural network models","level":"2"},{"id":"sec_26_2","title":"4.2 Optimization by genetic algorithm","level":"2"},{"id":"sec_27_2","title":"4.3 Optimization results","level":"2"},{"id":"sec_29","title":"5. Conclusions","level":"1"}],"chapterReferences":[{"id":"B1","body":"\u003Cref id=\"B1\"\u003E\u003Cmixed-citation publication-type=\"book\"\u003EGoldberg DE. Genetic Algorithms in Search, Optimization, and Machine Learning. Boston, MA, United States: Addison-Wesley; 1989\u003C\u002Fmixed-citation\u003E\u003C\u002Fref\u003E"},{"id":"B2","body":"\u003Cref id=\"B2\"\u003E\u003Cmixed-citation publication-type=\"book\"\u003EDeb K. Introduction to genetic algorithms for engineering optimization. In: Onwubolu GC, Babu BV, editors. New Optimization Techniques in Engineering. Berlin, Heidelberg: Springer Berlin Heidelberg; 2004. pp. 13-51\u003C\u002Fmixed-citation\u003E\u003C\u002Fref\u003E"},{"id":"B3","body":"\u003Cref id=\"B3\"\u003E\u003Cmixed-citation publication-type=\"book\"\u003ENielsen A, Aika K, Christiansen LJ, Dybkjaer I, Hansen JB, Nielsen PEH, et al. Ammonia: Catalysis and Manufacture. Berlin Heidelberg: Springer; 1995\u003C\u002Fmixed-citation\u003E\u003C\u002Fref\u003E"},{"id":"B4","body":"\u003Cref id=\"B4\"\u003E\u003Cmixed-citation publication-type=\"book\"\u003EAmmonia AM. Priciples & Industrial Practice. Weinheim, Germany: Wiley; 1999\u003C\u002Fmixed-citation\u003E\u003C\u002Fref\u003E"},{"id":"B5","body":"\u003Cref id=\"B5\"\u003E\u003Cmixed-citation publication-type=\"book\"\u003EBabu B, Angira R, Nilekar A. Optimal design of an auto-thermal ammonia synthesis reactor using differential evolution. In: Proceedings of the Eighth World Multi-Conference on Systemics, Cybernetics and Informatics (SCI-2004). 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High education and expert work is the best way to share and improve professional knowledge, expand area of professional activity involving and tutoring yang qualified colleagues. In this sense working in the Transport University is the great opportunity to improve GNSS\u002FDGNSS technologies as a key factor of industrial growing. One of the most important applications for GNSS is railroads. Space Weather impact on the GNSS-based traffic control systems is a great challenge for the research and engineering community. Finally, Vladislav Demyanov got more than 15 years of experience in the technical writing, reviewing and editing in the area of Earth and Environmental Sciences and Engineering. It provides him an opportunity to collaborate with high-impact journals (Advances in Space Research, Ann. Geophys., GPS Solutions, J. of Geophys. 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The male reproductive system is particularly sensitive to a broad variety of reproductive and developmental toxicants, including many environmental pollutants and recent studies suggest that human semen is an early and sensitive environmental and health marker. A set of semen biomarkers is described for reproductive health effects in relation to environmental exposure, where human semen seems to be an early and sensitive source of biomarkers than blood to monitor high environmental pressure on human health. Environmental health should consider reproductive health and development, from intrauterine life to childhood and puberty: these are both vulnerable targets and high-value protection goals, inasmuch as they represent the future of our societies. Hence, biomarkers of reproductive health should be exploited as early signals of environmental pressure and increased risk of adverse chronic health effects so that the use of “human seminal model” might be the main objective to be considered in the agenda of public prevention policies for early detection and innovative programs of health surveillance in environmental risk areas.","isPublished":true,"isOnlineFirst":false,"book":{"id":"6079","slug":"spermatozoa-facts-and-perspectives","title":"Spermatozoa","fullTitle":"Spermatozoa - Facts and Perspectives","isOpenForSubmission":false,"isPublished":true},"signatures":"Luigi Montano, Paolo Bergamo, Maria Grazia Andreassi and\nStefano Lorenzetti","authors":[{"id":"206180","title":"Dr.","name":"Luigi","middleName":null,"surname":"Montano","slug":"luigi-montano","fullName":"Luigi Montano"},{"id":"222782","title":"Dr.","name":"Paolo","middleName":null,"surname":"Bergamo","slug":"paolo-bergamo","fullName":"Paolo Bergamo"},{"id":"222783","title":"Dr.","name":"Maria Grazia","middleName":null,"surname":"Andreassi","slug":"maria-grazia-andreassi","fullName":"Maria Grazia Andreassi"},{"id":"222784","title":"Dr.","name":"Stefano","middleName":null,"surname":"Lorenzetti","slug":"stefano-lorenzetti","fullName":"Stefano Lorenzetti"}]}],"mostDownloadedChaptersLast30Days":[{"id":"47460","title":"The Role of the Dialysate Flow Rate in Haemodialysis","slug":"the-role-of-the-dialysate-flow-rate-in-haemodialysis","totalDownloads":4999,"totalCrossrefCites":4,"totalDimensionsCites":5,"abstract":null,"isPublished":true,"isOnlineFirst":false,"book":{"id":"4547","slug":"updates-in-hemodialysis","title":"Updates in Hemodialysis","fullTitle":"Updates in Hemodialysis","isOpenForSubmission":false,"isPublished":true},"signatures":"Peter Ahrenholz, Roland E. 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As a result of this heterogeneity of the ejaculate, sperm selection has become a necessary step to carry out prior to in vitro fertilization. Furthermore, the choice of sperm cell selection techniques depend on sperm concentration and sperm biology and the recovery of highly functional sperm cell population depend on the combination of more than one technique in some cases. The regular sperm cell selection methods in ART laboratory are swim up, density gradient, simple wash and other advanced and emerging sperm selection techniques which include hyaluronic acid mediated sperm binding, Zeta potential, hypoosmotic swelling test, magnetic activated cell sorting and microfluidic separation of sperm cells. The various methods have its own advantages and disadvantages which may be applicable to the individual need of infertile men and its effect on ART outcome.","isPublished":true,"isOnlineFirst":false,"book":{"id":"10724","slug":"male-reproductive-anatomy","title":"Male Reproductive Anatomy","fullTitle":"Male Reproductive Anatomy","isOpenForSubmission":false,"isPublished":true},"signatures":"Abimibola Nanna","authors":[{"id":"349382","title":"M.Sc.","name":"Abimibola","middleName":null,"surname":"Nanna","slug":"abimibola-nanna","fullName":"Abimibola Nanna"}]},{"id":"79287","title":"Endocrine Functions of the Testes","slug":"endocrine-functions-of-the-testes","totalDownloads":1550,"totalCrossrefCites":4,"totalDimensionsCites":5,"abstract":"The testes, also known as the male gonads are found in the scrotal sacs. In addition to their spermatogenic functions, they also secrete steroids and protein hormones. The steroid hormones are the androgens, testosterone and dihydrotestosterone as well as estrogen, while the protein hormones are inhibins, activins, and anti-Mullerian hormone (AMH). This chapter therefore discusses the role of the testis in the production and functions of the testicular androgens as well as testicular protein hormones.","isPublished":true,"isOnlineFirst":false,"book":{"id":"10724","slug":"male-reproductive-anatomy","title":"Male Reproductive Anatomy","fullTitle":"Male Reproductive Anatomy","isOpenForSubmission":false,"isPublished":true},"signatures":"Emojevwe Victor, Igiehon Osarugue, Oyovwi Mega Obukohwo, Nwangwa Eze Kingsley and Naiho Alexander Obidike","authors":[{"id":"349696","title":"Dr.","name":"Emojevwe","middleName":null,"surname":"Victor","slug":"emojevwe-victor","fullName":"Emojevwe Victor"},{"id":"420885","title":"Ms.","name":"Osarugue","middleName":null,"surname":"Igiehon","slug":"osarugue-igiehon","fullName":"Osarugue Igiehon"}]},{"id":"40903","title":"Vascular Access for Hemodialysis - Overview and Emphasis on Complications","slug":"vascular-access-for-hemodialysis-overview-and-emphasis-on-complications","totalDownloads":4858,"totalCrossrefCites":1,"totalDimensionsCites":2,"abstract":null,"isPublished":true,"isOnlineFirst":false,"book":{"id":"3267","slug":"hemodialysis","title":"Hemodialysis","fullTitle":"Hemodialysis","isOpenForSubmission":false,"isPublished":true},"signatures":"Octavio J. 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Insecticides damage the male reproductive system but can be rescued via the use of medicinal fruit extracts (MFEs). A number of experimental studies have shown that MFEs ameliorate testicular histopathologies induced by environmental (toxin) exposure in albino mice. MFEs show good capacity for testicular rehabilitation because of the presence of phytochemicals, especially phytosterols and natural antioxidants. Additionally, we have recently reported better survival rates and fertilizability of cryopreserved spermatozoa on the fortification of semen extenders with MFEs. On the basis of these findings, it is concluded that chemicals and insecticides are potential disruptors of spermatogenic activity and testicular microarchitecture \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ein vivo,\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E whereas the MFEs have shown excellent rehabilitative potentials in these contexts. Moreover, MFEs have also been shown to contribute to the post -hawed semen quality parameters.\u003C\u002Fp\u003E\n","isPublished":false,"isOnlineFirst":true,"book":{"id":"1004225","title":"Andrology Insights - Understanding Male Reproductive Health and Diseases","coverURL":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa04Tc000004ioDZIAY\u002F0016129_TrikoderCover%20%282024-03-13%2010%3A22%3A15%29.jpg","isOpenForSubmission":false,"isPublished":false},"signatures":"Syeda Nadia Ahmad and Khawaja Raees Ahmad"},{"id":"1198694","title":"A Comparative Analysis of Gradient Centrifugation and Microfluidic Chips for Sperm Selection","slug":null,"totalDownloads":19,"totalDimensionsCites":0,"doi":"10.5772\u002Fintechopen.1008736","abstract":"\u003Cp id=\"p1\"\u003EA variety of techniques have been employed in the field of sperm selection, including methods based on sperm density, morphological characteristics, motility characteristics, membrane integrity, and surface charge. Among these techniques, the density gradient centrifugation (DGC) method stands out as the most prevalent and widely utilized today. However, this technique involves centrifugation steps that have been linked to oxidative stress and subsequent cellular damage. Consequently, alternatives to DGC are being continuously developed. The recently developed microfluidic chip method has also been implemented for sperm selection in intracytoplasmic sperm injection (ICSI). However, the microfluidic chip method also presents certain disadvantages that must be addressed. This chapter evaluates the advantages and disadvantages of sperm selection methods from the past to the present, with a particular focus on DGC and microfluidic devices.\u003C\u002Fp\u003E\n","isPublished":false,"isOnlineFirst":true,"book":{"id":"1004225","title":"Andrology Insights - Understanding Male Reproductive Health and Diseases","coverURL":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa04Tc000004ioDZIAY\u002F0016129_TrikoderCover%20%282024-03-13%2010%3A22%3A15%29.jpg","isOpenForSubmission":false,"isPublished":false},"signatures":"Hale Bayram and Yaprak Donmez Cakil"},{"id":"1192624","title":"Complement Activation in Kidney Transplantation","slug":null,"totalDownloads":14,"totalDimensionsCites":0,"doi":"10.5772\u002Fintechopen.1007083","abstract":"\u003Cp id=\"p1\"\u003EKidney transplantation is a life-saving procedure for individuals with end-stage renal disease, yet the process of transplantation can trigger the activation of the complement system, a critical component of the body’s immune response. This activation can lead to adverse outcomes, including acute and chronic rejection of the graft, thereby complicating patient management and graft survival. Furthermore, the interplay between complement activation and immunosuppressive therapies remains a key area of research, as prolonged immunosuppression may enhance the risk of complications while failing to adequately control the immune response against the transplanted organ, necessitating a balance between these factors to optimize transplant outcomes. In recent years, advances in understanding the mechanisms of complement activation have led to the exploration of novel therapeutic strategies aimed at minimizing damage to the graft and enhancing its long-term functionality, emphasizing the need for tailored immunosuppressive regimens to mitigate the associated risks and improve the overall success of kidney transplantation.\u003C\u002Fp\u003E\n","isPublished":false,"isOnlineFirst":true,"book":{"id":"1004016","title":"Advances in Kidney Transplantation","coverURL":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa043Y000011YN3vQAG\u002F0015920_TrikoderCover%20%282023-10-29%2016%3A53%3A59%29.jpg","isOpenForSubmission":true,"isPublished":false},"signatures":"Pande Made Wisnu Tirtayasa, Gerhard Reinaldi Situmorang, Gede Wirya Kusuma Duarsa, Arry Rodjani and Nur Rasyid"},{"id":"1193826","title":"Spermatogenesis","slug":null,"totalDownloads":24,"totalDimensionsCites":0,"doi":"10.5772\u002Fintechopen.1007771","abstract":"\u003Cp id=\"p1\"\u003ESpermatogenesis is a complex process involving stages of spermatocytogenesis, spermatidogenesis and spermiogenesis. It is defined as the process of producing haploid sperm cells from primordial diploid germ cells in the seminiferous tubules of the testis. Hormonal role at each stage of spermatogenesis and signaling or regulatory pathways that is associated with the process has been discussed in this chapter. The factors that alters spermatogenesis which spans through hormones, medication, temperature, toxins etc., are further explained. Diagrams showing the stages of spermatogenesis and tables, which explains various alterations in genetic materials resulting in disorders of spermatogenesis, are also explained. The various stages and phases in each processes of spermatogenesis have been explained in detail. Also, chromosomal changes and cellular divisions that constitute spermatogenesis are further discussed. Finally, the role of calcium in spermatogenesis is discussed.\u003C\u002Fp\u003E\n","isPublished":false,"isOnlineFirst":true,"book":{"id":"1004225","title":"Andrology Insights - Understanding Male Reproductive Health and Diseases","coverURL":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa04Tc000004ioDZIAY\u002F0016129_TrikoderCover%20%282024-03-13%2010%3A22%3A15%29.jpg","isOpenForSubmission":false,"isPublished":false},"signatures":"Ekementeabasi Aniebo Umoh"},{"id":"1199718","title":"Peritoneal Dialysis in Children","slug":null,"totalDownloads":38,"totalDimensionsCites":0,"doi":"10.5772\u002Fintechopen.1007128","abstract":"\u003Cp id=\"p1\"\u003EFor children undergoing chronic dialysis, peritoneal dialysis (PD) is still the most popular method, especially for younger patients and those living in lower- and middle-income nations (LMICs). When compared to extracorporeal therapy, PD for acute kidney injury (AKI) in children has a lengthy history of success. It is still widely utilized, particularly in Europe, in both high- and low-resource environments. The use of PD for AKI in low birthweight and post-cardiac surgery neonates is of special interest in these areas. There are few high-quality randomized trials conducted on children, and most of the data used in clinical practice today are either taken from observational cohort studies on children or extrapolated from studies conducted on adults. Guidelines for starting dialysis, choosing a modality, clearing tiny solutes, maintaining kidney function, and removing fluid from children receiving post-natal dialysis are provided by the International Society for Peritoneal Dialysis (ISPD). The evidence for PD in children is still quite weak, The recommendation’s strength and level of evidence are GRADE-ed. Although every patient should still aim for optimal dialysis, it is crucial to have a thorough conversation about expectations for dialysis with caregivers and patients who are fully informed.\u003C\u002Fp\u003E\n","isPublished":false,"isOnlineFirst":true,"book":{"id":"1004014","title":"Peritoneal Dialysis in the Modern Era","coverURL":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa043Y000011YN3tQAG\u002F0015918_TrikoderCover%20%282023-10-29%2016%3A53%3A59%29.jpg","isOpenForSubmission":false,"isPublished":false},"signatures":"Souad Chelghoum, Salah-eddine Benfarhi and Atmane Seba"},{"id":"1201032","title":"Peritoneal Dialysis-Related Complications: A Comprehensive Review","slug":null,"totalDownloads":28,"totalDimensionsCites":0,"doi":"10.5772\u002Fintechopen.1007873","abstract":"\u003Cp id=\"p1\"\u003EPeritoneal dialysis is considered a less invasive, flexible, independent, easy, and financially more accessible technique for patients who require renal replacement therapy. Based on a purification technique using the peritoneum as a filter, it offers the comfort of internal filtration and does not require the complex machinery of traditional hemodialysis. Since its first use many decades ago, progress has been made over the last years to improve the technique and understand the pathophysiological processes regarding the peritoneal membrane. However, peritoneal dialysis remains associated with complications that can be mechanical or more serious and life-threatening, such as peritonitis. Peritoneal dialysis complications are classified as short- or long-term. It is essential to address them, as they are related to increased morbidity, technique failure, transition to hemodialysis, and death but could be preventable. Through this chapter, we will explore these complications, focusing on the most common in terms of incidence and long-term prognosis.\u003C\u002Fp\u003E\n","isPublished":false,"isOnlineFirst":true,"book":{"id":"1004014","title":"Peritoneal Dialysis in the Modern Era","coverURL":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa043Y000011YN3tQAG\u002F0015918_TrikoderCover%20%282023-10-29%2016%3A53%3A59%29.jpg","isOpenForSubmission":false,"isPublished":false},"signatures":"Axler Jean Paul and Abigael Francis"}],"onlineFirstChaptersTotal":16},"preDownload":{"success":null,"errors":{}},"subscriptionForm":{"success":null,"errors":{}},"aboutIntechopen":{},"privacyPolicy":{},"cookiePolicy":{},"recruitmentPrivacyNotice":{},"peerReviewing":{},"howOpenAccessPublishingWithIntechopenWorks":{},"sponsorshipBooks":{"sponsorshipBooks":[],"offset":0,"limit":8,"total":null},"allSeries":{"pteSeriesList":[],"lsSeriesList":[],"hsSeriesList":[],"sshSeriesList":[],"testimonialsList":[]},"series":{"item":{"id":"1003807","title":"Oncology","doi":"10.5772\u002Fintechopen.1003112","issn":"3049-8864","scope":"\u003Cp\u003EThe field of oncology has undergone extraordinary change and progress over the past several decades. Today, information is evolving at a rapid rate, with standards of management far different than standards of care applied during the training of most practicing oncologists. Oncology practitioners in all disciplines must remain current to optimize patient care. Basic and translational science remain critical in developing process improvements for patient care. The closer we understand the mechanism, the more we can improve targeted therapies and apply them to patient care. The pace of information is moving faster than at any previous time in history, and all oncology disciplines must remain current to provide excellent service to patients. The modern oncologist must be fluent in using big data and the volume of information generated in clinical trials. 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They will represent an excellent initial grouping of published works on these critical topics. \u003C\u002Fspan\u003E\u003C\u002Fp\u003E","coverUrl":"https:\u002F\u002Fcdn.intechopen.com\u002Fseries\u002Fcovers\u002F25.jpg","latestPublicationDate":"February 13th, 2025","hasOnlineFirst":true,"numberOfPublishedBooks":23,"editor":{"id":"197485","title":"Dr.","name":"J. Kevin","middleName":null,"surname":"Summers","slug":"j.-kevin-summers","fullName":"J. Kevin Summers","cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F197485\u002F1604448294\u002Fprofile\u002Fimage1.jpg","biography":"J. Kevin Summers is a Senior Research Ecologist at the Environmental Protection Agency’s (EPA) Gulf Ecosystem Measurement and Modeling Division. He is currently working with colleagues in the Sustainable and Healthy Communities Program to develop an index of community resilience to natural hazards, an index of human well-being that can be linked to changes in the ecosystem, social and economic services, and a community sustainability tool for communities with populations under 40,000. He leads research efforts for indicator and indices development. Dr. Summers is a systems ecologist and began his career at the EPA in 1989 and has worked in various programs and capacities. This includes leading the National Coastal Assessment in collaboration with the Office of Water which culminated in the award-winning National Coastal Condition Report series (four volumes between 2001 and 2012), and which integrates water quality, sediment quality, habitat, and biological data to assess the ecosystem condition of the United States estuaries. He was acting National Program Director for Ecology for the EPA between 2004 and 2006. 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