{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T15:48:58Z","timestamp":1777564138663,"version":"3.51.4"},"reference-count":101,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,8]],"date-time":"2021-01-08T00:00:00Z","timestamp":1610064000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51976235"],"award-info":[{"award-number":["51976235"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51606218"],"award-info":[{"award-number":["51606218"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The thermochemical sulfur-iodine cycle is a potential method for hydrogen production, and the hydrogen iodide (HI) decomposition is the key step to determine the efficiency of hydrogen production in the cycle. To further reduce the irreversibility of various transmission processes in the HI decomposition reaction, a one-dimensional plug flow model of HI decomposition tubular reactor is established, and performance optimization with entropy generate rate minimization (EGRM) in the decomposition reaction system as an optimization goal based on finite-time thermodynamics is carried out. The reference reactor is heated counter-currently by high-temperature helium gas, the optimal reactor and the modified reactor are designed based on the reference reactor design parameters. With the EGRM as the optimization goal, the optimal control method is used to solve the optimal configuration of the reactor under the condition that both the reactant inlet state and hydrogen production rate are fixed, and the optimal value of total EGR in the reactor is reduced by 13.3% compared with the reference value. The reference reactor is improved on the basis of the total EGR in the optimal reactor, two modified reactors with increased length are designed under the condition of changing the helium inlet state. The total EGR of the two modified reactors are the same as that of the optimal reactor, which are realized by decreasing the helium inlet temperature and helium inlet flow rate, respectively. The results show that the EGR of heat transfer accounts for a large proportion, and the decrease of total EGR is mainly caused by reducing heat transfer irreversibility. The local total EGR of the optimal reactor distribution is more uniform, which approximately confirms the principle of equipartition of entropy production. The EGR distributions of the modified reactors are similar to that of the reference reactor, but the reactor length increases significantly, bringing a relatively large pressure drop. The research results have certain guiding significance to the optimum design of HI decomposition reactors.<\/jats:p>","DOI":"10.3390\/e23010082","type":"journal-article","created":{"date-parts":[[2021,1,8]],"date-time":"2021-01-08T08:58:34Z","timestamp":1610096314000},"page":"82","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Minimization of Entropy Generation Rate in Hydrogen Iodide Decomposition Reactor Heated by High-Temperature Helium"],"prefix":"10.3390","volume":"23","author":[{"given":"Rui","family":"Kong","sequence":"first","affiliation":[{"name":"College of Power Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9012-6736","authenticated-orcid":false,"given":"Lingen","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"School of Mechanical &amp; Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaojun","family":"Xia","sequence":"additional","affiliation":[{"name":"College of Power Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Penglei","family":"Li","sequence":"additional","affiliation":[{"name":"College of Power Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanlin","family":"Ge","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"School of Mechanical &amp; Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4048","DOI":"10.1021\/cr050188a","article-title":"Thermochemical cycles for high-temperature solar hydrogen production","volume":"107","author":"Kodama","year":"2007","journal-title":"Chem. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2210","DOI":"10.1016\/j.ijhydene.2011.10.053","article-title":"Dynamic model of a solar thermochemical water-splitting reactor with integrated energy collection and storage","volume":"37","author":"Xu","year":"2012","journal-title":"Int. J. Hydrog. Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1016\/j.pnucene.2008.11.001","article-title":"Nuclear heat for hydrogen production: Coupling a very high temperature reactor to a hydrogen production plant","volume":"51","author":"Elder","year":"2009","journal-title":"Prog. Nucl. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.ijhydene.2006.05.005","article-title":"Flowsheet study of the thermochemical water-splitting iodine-sulfur process for effective hydrogen generation","volume":"32","author":"Kasahara","year":"2007","journal-title":"Int. J. Hydrog. Energy"},{"key":"ref_5","unstructured":"Russel, J.J., Mccorkle, K.H., Norman, J.H., Porter, J.T., Roemer, T.S., and Schuster, J.R. (1976, January 1\u20133). Water splitting\u2014A progress report. Proceedings of the 1st World Hydrogen Energy Conference, Coral Gables, FL, USA."},{"key":"ref_6","unstructured":"Brown, L.C. (2002, January 10\u201314). High efficiency generation of hydrogen fuels using thermochemical cycle and nuclear power. Proceedings of the AICHE 2002 Spring National Meeting, New Orleans, LA, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"13477","DOI":"10.1016\/j.ijhydene.2017.02.163","article-title":"Current R&D status of thermochemical water splitting iodine-sulfur process in Japan Atomic Energy Agency","volume":"42","author":"Kasahara","year":"2017","journal-title":"Int. J. Hydrog. Energy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/j.nucengdes.2008.11.017","article-title":"Conceptual design of sulfur iodine hydrogen production cycle of Korea Institute of Energy Research","volume":"239","author":"Cho","year":"2009","journal-title":"Nucl. Eng. Des."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1802","DOI":"10.1016\/j.rser.2017.05.275","article-title":"Progress of nuclear hydrogen production through the iodine-sulfur process in China","volume":"81","author":"Zhang","year":"2018","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1021\/ef700579h","article-title":"Catalytic thermal decomposition of hydrogen iodide in sulfur-iodine cycle for hydrogen production","volume":"22","author":"Zhang","year":"2008","journal-title":"Energy Fuels"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.nucengdes.2013.11.010","article-title":"Overview of the development of catalysts for HI decomposition in the iodine\u2013sulfur thermochemical cycle at INET","volume":"271","author":"Wang","year":"2014","journal-title":"Nucl. Eng. Des."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1246\/bcsj.54.742","article-title":"Kinetics of the catalytic decomposition of hydrogen iodide in the magnesium-iodine thermochemical cycle","volume":"54","author":"Oosawa","year":"1981","journal-title":"Bull. Chem. Soc. Jpn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1016\/0360-3199(84)90267-2","article-title":"Kinetics of the catalytic decomposition of hydrogen iodide in the thermochemical hydrogen production","volume":"9","author":"Shindo","year":"1984","journal-title":"Int. J. Hydrog. Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.apcatb.2011.03.032","article-title":"Kinetics of hydrogen iodide decomposition over activated carbon catalysts in pellets","volume":"105","author":"Favuzza","year":"2011","journal-title":"Appl. Catal. B Environ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1016\/j.apenergy.2013.09.041","article-title":"Kinetics and modeling of hydrogen iodide decomposition for a bench-scale sulfur-iodine cycle","volume":"115","author":"Nguyen","year":"2014","journal-title":"Appl. Energy"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"18182","DOI":"10.1016\/j.ijhydene.2014.08.102","article-title":"Numerical simulations of HI decomposition in packed bed membrane reactors","volume":"39","author":"Goswami","year":"2014","journal-title":"Int. J. Hydrog. Energy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"9001","DOI":"10.1016\/j.apm.2016.05.051","article-title":"Numerical simulations of HI decomposition in coated wall membrane reactor and comparison with packed bed configuration","volume":"40","author":"Goswami","year":"2016","journal-title":"Appl. Math. Model."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/S0376-7388(01)00540-3","article-title":"Simulation study on the catalytic decomposition of hydrogen iodide in a membrane reactor with a silica membrane for the thermochemical water-splitting IS process","volume":"194","author":"Hwang","year":"2001","journal-title":"J. Membr. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1021\/ar00104a001","article-title":"Thermodynamics for processes in finite time","volume":"17","author":"Andresen","year":"1984","journal-title":"Acc. Chem. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1063\/1.362674","article-title":"Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes","volume":"79","author":"Bejan","year":"1996","journal-title":"J. Appl. Phys."},{"key":"ref_21","unstructured":"Bejan, A. (1996). Entropy Generation Minimization, CRC Press."},{"key":"ref_22","first-page":"327","article-title":"Finite time thermodynamic optimization or entropy generation minimization of energy systems","volume":"22","author":"Chen","year":"1999","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_23","unstructured":"Berry, R.S., Kazakov, V.A., Sieniutycz, S., Szwast, Z., and Tsirlin, A.M. (1999). Thermodynamic Optimization of Finite Time Processes, Wiley."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2690","DOI":"10.1002\/anie.201001411","article-title":"Current trends in finite-time thermodynamics","volume":"50","author":"Andresen","year":"2011","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1007\/s11431-015-5970-5","article-title":"Thermodynamic analyses and optimizations for thermoelectric devices: The state of the arts","volume":"59","author":"Chen","year":"2016","journal-title":"Sci. China Technol. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1515\/jnet-2018-0008","article-title":"Application of finite-time and control thermodynamics to biological processes at multiple scales","volume":"43","author":"Roach","year":"2018","journal-title":"J. Non-Equilibr. Thermodyn."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Kaushik, S.C., Tyagi, S.K., and Kumar, P. (2018). Finite Time Thermodynamics of Power and Refrigeration Cycles, Springer.","DOI":"10.1007\/978-3-319-62812-7"},{"key":"ref_28","unstructured":"Sieniutycz, S., and Jezowski, J. (2018). Energy Optimization in Process Systems and Fuel Cells, Elsevier. [3rd ed.]."},{"key":"ref_29","unstructured":"Sieniutycz, S., and Szwast, Z. (2018). Optimizing Thermal, Chemical and Environmental Systems, Elsevier."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Patel, V.K., Savsani, V.J., and Tawhid, M.A. (2019). Thermal System Optimization, Springer.","DOI":"10.1007\/978-3-030-10477-1"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Feidt, M., and Costea, M. (2019). Progress in Carnot and Chambadal modeling of thermomechnical engine by considering entropy and heat transfer entropy. Entropy, 21.","DOI":"10.3390\/e21121232"},{"key":"ref_32","unstructured":"Sieniutycz, S. (2020). Complexity and Complex Thermo-Economic Systems, Elsevier."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Berry, R.S., Salamon, P., and Andresen, B. (2020). How it all began. Entropy, 22.","DOI":"10.3390\/e22080908"},{"key":"ref_34","first-page":"311","article-title":"Endoreversible thermodynamics","volume":"22","author":"Hoffmann","year":"1997","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1515\/jnet-2015-0061","article-title":"Endoreversible modeling of a PEM fuel cell","volume":"40","author":"Wagner","year":"2015","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1515\/jnet-2018-0087","article-title":"Concepts of phenominological irreversible quantum thermodynamics I: Closed undecomposed Schottky systems in semi-classical description","volume":"44","author":"Muschik","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1515\/jnet-2018-0009","article-title":"Attainability of maximum work and the reversible efficiency of minimally nonlinear irreversible heat engines","volume":"44","author":"Ponmurugan","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1515\/jnet-2019-0020","article-title":"Performance analysis of Diesel cycle under efficient power density condition with variable specific heat of working fluid","volume":"44","author":"Raman","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1515\/jnet-2019-0063","article-title":"Stochastic Novikov engine with Fourier heat transport","volume":"44","author":"Schwalbe","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Yasunaga, T., and Ikegami, Y. (2020). Finite-time thermodynamic model for evaluating heat engines in ocean thermal energy conversion. Entropy, 22.","DOI":"10.3390\/e22020211"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Feidt, M. (2020). Carnot cycle and heat engine: Fundamentals and applications. Entropy, 22.","DOI":"10.3390\/e22030348"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Feidt, M., and Costea, M. (2020). Effect of machine entropy production on the optimal performance of a refrigerator. Entropy, 22.","DOI":"10.3390\/e22090913"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Ma, Y.H. (2020). Effect of finite-size heat source\u2019s heat capacity on the efficiency of heat engine. Entropy, 22.","DOI":"10.3390\/e22091002"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Rogolino, P., and Cimmelli, V.A. (2020). Thermoelectric efficiency of Silicon\u2013Germanium alloys in finite-time thermodynamics. Entropy, 22.","DOI":"10.3390\/e22101116"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Essex, C., and Das, I. (2020). Radiative transfer and generalized wind. Entropy, 22.","DOI":"10.3390\/e22101153"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Dann, R., Kosloff, R., and Salamon, P. (2020). Quantum finite time thermodynamics: Insight from a single qubit engine. Entropy, 22.","DOI":"10.3390\/e22111255"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"113261","DOI":"10.1016\/j.enconman.2020.113261","article-title":"Maximum energy output chemical pump configuration with an infinite-low- and a finite-high-chemical potential mass reservoirs","volume":"223","author":"Chen","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Chen, L.G., Tang, C.Q., Feng, H.J., and Ge, Y.L. (2020). Power, efficiency, power density and ecological function optimizations for an irreversible modified closed variable-temperature reservoir regenerative Brayton cycle with one isothermal heating process. Energies, 13.","DOI":"10.3390\/en13195133"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1515\/jnet-2019-0088","article-title":"Energetic optimization considering a generalization of the ecological criterion in traditional simple-cycle and combined cycle power plants","volume":"45","year":"2020","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1515\/jnet-2020-0039","article-title":"Endoreversible Otto engines at maximal power","volume":"45","author":"Smith","year":"2020","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1515\/JNETDY.2003.015","article-title":"Optimal process paths for endoreversible systems","volume":"28","author":"Hoffman","year":"2003","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_52","first-page":"981","article-title":"Progresses in generalized thermodynamic dynamic-optimization of irreversible processes","volume":"49","author":"Chen","year":"2019","journal-title":"Sci. China Technol. Sci."},{"key":"ref_53","first-page":"1223","article-title":"Progress in generalized thermodynamic dynamic-optimization of irreversible cycles","volume":"49","author":"Chen","year":"2019","journal-title":"Sci. China Technol. Sci."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1515\/jnet-2018-0007","article-title":"Finite time thermodynamics: Realizability domain of heat to work converters","volume":"44","author":"Zaeva","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Masser, R., and Hoffmann, K.H. (2020). Endoreversible modeling of a hydraulic recuperation system. Entropy, 22.","DOI":"10.3390\/e22040383"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Kushner, A., Lychagin, V., and Roop, M. (2020). Optimal thermodynamic processes for gases. Entropy, 22.","DOI":"10.3390\/e22040448"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"De Vos, A. (2020). Endoreversible models for the thermodynamics of computing. Entropy, 22.","DOI":"10.3390\/e22060660"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Masser, R., Khodja, A., Scheunert, M., Schwalbe, K., Fischer, A., Paul, R., and Hoffmann, K.H. (2020). Optimized piston motion for an alpha-type Stirling engine. Entropy, 22.","DOI":"10.3390\/e22060700"},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Chen, L.G., Ma, K., Ge, Y.L., and Feng, H.J. (2020). Re-optimization of expansion work of a heated working fluid with generalized radiative heat transfer law. Entropy, 22.","DOI":"10.3390\/e22070720"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Tsirlin, A., and Gagarina, L. (2020). Finite-time thermodynamics in economics. Entropy, 22.","DOI":"10.3390\/e22080891"},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Tsirlin, A., and Sukin, I. (2020). Averaged optimization and finite-time thermodynamics. Entropy, 22.","DOI":"10.3390\/e22090912"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Muschik, W., and Hoffmann, K.H. (2020). Modeling, simulation, and reconstruction of 2-reservoir heat-to-power processes in finite-time thermodynamics. Entropy, 22.","DOI":"10.3390\/e22090997"},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Insinga, A.R. (2020). The quantum friction and optimal finite-time performance of the quantum Otto cycle. Entropy, 22.","DOI":"10.3390\/e22091060"},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Sch\u00f6n, J.C. (2020). Optimal control of hydrogen atom-like systems as thermodynamic engines in finite time. Entropy, 22.","DOI":"10.3390\/e22101066"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Andresen, B., and Essex, C. (2020). Thermodynamics at very long time and space scales. Entropy, 22.","DOI":"10.3390\/e22101090"},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Chen, L.G., Ma, K., Feng, H.J., and Ge, Y.L. (2020). Optimal configuration of a gas expansion process in a piston-type cylinder with generalized convective heat transfer law. Energies, 13.","DOI":"10.3390\/en13123229"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Scheunert, M., Masser, R., Khodja, A., Paul, R., Schwalbe, K., Fischer, A., and Hoffmann, K.H. (2020). Power-optimized sinusoidal piston motion and its performance gain for an Alpha-type Stirling engine with limited regeneration. Energies, 13.","DOI":"10.3390\/en13174564"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1515\/jnet-2019-0078","article-title":"Evaluation of irreversibility and optimal organization of an integrated multi-stream heat exchange system","volume":"45","author":"Boikov","year":"2020","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_69","unstructured":"Chen, L.G., Wang, C., Zhang, L., and Xia, S.J. (2021). Progress in thermodynamic analyses and optimizations for key component units in sea-based fuel synthesis system. Sci. Sin. Technol."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1021\/i200032a010","article-title":"Optimal temperature profile for an ammonia reactor","volume":"25","author":"Masson","year":"1986","journal-title":"Ind. Eng. Chem. Process Des. Dev."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"1310","DOI":"10.1016\/j.ijheatmasstransfer.2018.04.036","article-title":"Thermodynamic analysis and optimization of extraction process of CO2 from acid seawater by using hollow fiber membrane contactor","volume":"124","author":"Chen","year":"2018","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.energy.2018.01.050","article-title":"Entropy generation minimization for CO2 hydrogenation to light olefins","volume":"147","author":"Chen","year":"2018","journal-title":"Energy"},{"key":"ref_73","first-page":"20180191","article-title":"Maximum hydrogen production rate optimization for tubular steam methane reforming reactor","volume":"17","author":"Li","year":"2019","journal-title":"Int. J. Chem. React. Eng."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1016\/j.egyr.2020.03.011","article-title":"Energy generation rate minimization for steam reforming reactor heated by molten salt","volume":"6","author":"Li","year":"2020","journal-title":"Energy Rep."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/j.cep.2004.06.005","article-title":"Second law optimization of a tubular steam reformer","volume":"44","author":"Nummedal","year":"2005","journal-title":"Chem. Eng. Process"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.energy.2016.01.040","article-title":"Maximum production rate optimization for sulfuric acid decomposition process in tubular plug-flow reactor","volume":"99","author":"Wang","year":"2016","journal-title":"Energy"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"2403","DOI":"10.1016\/j.energy.2004.03.033","article-title":"Minimum entropy production rate in plug flow reactors: An optimal control problem solved for SO2 oxidation","volume":"29","author":"Johannessen","year":"2004","journal-title":"Energy"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"8500","DOI":"10.1021\/ie801585e","article-title":"Efficient conversion of thermal energy into hydrogen: Comparing two methods to reduce exergy losses in a sulfuric acid decomposition reactor","volume":"48","author":"Gross","year":"2009","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"1112","DOI":"10.1016\/j.ijheatmasstransfer.2019.04.022","article-title":"Entropy generation rate minimization hydrocarbon synthesis reactor from carbon dioxide and hydrogen","volume":"137","author":"Zhang","year":"2019","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_80","doi-asserted-by":"crossref","unstructured":"Li, P.L., Chen, L.G., and Xia, S.J. (2019). Entropy generation rate minimization for methanol synthesis via a CO2 hydrogenation reactor. Entropy, 21.","DOI":"10.3390\/e21020174"},{"key":"ref_81","doi-asserted-by":"crossref","unstructured":"Kong, R., Chen, L.G., Xia, S.J., Zhang, L., Li, P.L., Ge, Y.L., and Feng, H.J. (2020). Minimization of entropy generation rate during hydrogen iodide decomposition reaction process. Sci. Sin. Technol., (In Chinese).","DOI":"10.1360\/SST-2020-0008"},{"key":"ref_82","doi-asserted-by":"crossref","unstructured":"Zhang, L., Chen, L.G., Xia, S.J., Wang, C., and Sun, F.R. (2018). Entropy generation minimization for reverse water gas shift (RWGS) reactors. Entropy, 20.","DOI":"10.3390\/e20060415"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"119025","DOI":"10.1016\/j.ijheatmasstransfer.2019.119025","article-title":"Multi-objective optimization for helium-heated reverse water gas shift reactor by using NSGA-II","volume":"148","author":"Zhang","year":"2020","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1016\/j.ces.2018.09.048","article-title":"Multi-objective optimization method for enhancing chemical reaction process","volume":"195","author":"Cao","year":"2019","journal-title":"Chem. Eng. Sci."},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Sun, M., Xia, S.J., Chen, L.G., Wang, C., and Tang, C.Q. (2020). Minimum entropy generation rate and maximum yield optimization of sulfuric acid decomposition process using NSGA-II. Entropy, 22.","DOI":"10.3390\/e22101065"},{"key":"ref_86","first-page":"106754","article-title":"A Multi-objective reactive distillation optimization model for Fischer-Tropsch synthesis","volume":"135","author":"Zhang","year":"2020","journal-title":"Chem. Eng. Sci."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"115601","DOI":"10.1016\/j.ces.2020.115601","article-title":"Entropy generation minimization in a channel flow: Application to different advection-diffusion processes and boundary conditions","volume":"220","author":"Avellaneda","year":"2020","journal-title":"Chem. Eng. Sci."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.compchemeng.2018.06.002","article-title":"Energy efficient design of membrane processes by use of entropy production minimization","volume":"117","author":"Magnanelli","year":"2018","journal-title":"Comput. Chem. Eng."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"115539","DOI":"10.1016\/j.ces.2020.115539","article-title":"Minimum entropy production in a distillation column for air separation described by a continuous non-equilibrium model","volume":"218","author":"Kingston","year":"2020","journal-title":"Chem. Eng. Sci."},{"key":"ref_90","doi-asserted-by":"crossref","unstructured":"Korpy\u015b, M., Gancarczyk, A., Iwaniszyn, M., Sindera, K., Jod\u0142owski, P.J., and Ko\u0142odziej, A. (2020). Analysis of entropy production in structured chemical reactors: Optimization for catalytic combustion of air pollutants. Entropy, 22.","DOI":"10.3390\/e22091017"},{"key":"ref_91","doi-asserted-by":"crossref","unstructured":"Kizilova, N., Sauermoser, M., Kjelstrup, S., and Pollet, B.G. (2020). Fractal-like flow-fields with minimum entropy production for polymer electrolyte membrane fuel cells. Entropy, 22.","DOI":"10.3390\/e22020176"},{"key":"ref_92","doi-asserted-by":"crossref","unstructured":"Yang, K., Huang, W., Li, X., and Wang, J. (2020). Analytical analysis of heat transfer and entropy generation in a tube filled with double-layer porous media. Entropy, 22.","DOI":"10.3390\/e22111214"},{"key":"ref_93","doi-asserted-by":"crossref","unstructured":"Li, B., Wei, W.N., Wan, Q.C., Peng, K., and Chen, L.L. (2020). Numerical investigation into the development performance of gas hydrate by depressurization based on heat transfer and entropy generation analyses. Entropy, 22.","DOI":"10.3390\/e22111212"},{"key":"ref_94","unstructured":"Yaws, C.L. (1999). Chemical Properties Handbook, McGraw-Hill."},{"key":"ref_95","first-page":"500","article-title":"Pressure drop in packed beds of spheres","volume":"9","author":"Hicks","year":"1970","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_96","doi-asserted-by":"crossref","unstructured":"Smith, R. (2005). Chemical Process Design and Integration, John Wiley.","DOI":"10.1002\/0471238961.chemsmit.a01"},{"key":"ref_97","unstructured":"(1977). JANAF Thermochemical Tables, Dow Chemical Company."},{"key":"ref_98","unstructured":"Groot, S.R., and Mazur, P. (1984). Non-Equilibrium Thermodynamics, Dover."},{"key":"ref_99","doi-asserted-by":"crossref","unstructured":"Kjelstrup, S., Bedeaux, D., Johannessen, E., and Gross, G. (2010). Non-Equilibrium Thermodynamics for Engineers, World Scientific.","DOI":"10.1142\/7869"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"3727","DOI":"10.1016\/j.energy.2010.11.012","article-title":"Two performance indicators for characterization of the entropy production in process unit","volume":"36","author":"Gross","year":"2011","journal-title":"Energy"},{"key":"ref_101","unstructured":"Bryson, A., and Ho, Y. (1975). Applied Optimal Control: Optimization, Estimation and Control, Hemisphere Publishing Corporation."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/1\/82\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:08:29Z","timestamp":1760159309000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/1\/82"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,8]]},"references-count":101,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["e23010082"],"URL":"https:\/\/doi.org\/10.3390\/e23010082","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,8]]}}}