{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T21:24:13Z","timestamp":1778793853543,"version":"3.51.4"},"reference-count":78,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,13]],"date-time":"2019-02-13T00:00:00Z","timestamp":1550016000000},"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":["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 methanol synthesis via CO2 hydrogenation (MSCH) reaction is a useful CO2 utilization strategy, and this synthesis path has also been widely applied commercially for many years. In this work the performance of a MSCH reactor with the minimum entropy generation rate (EGR) as the objective function is optimized by using finite time thermodynamic and optimal control theory. The exterior wall temperature (EWR) is taken as the control variable, and the fixed methanol yield and conservation equations are taken as the constraints in the optimization problem. Compared with the reference reactor with a constant EWR, the total EGR of the optimal reactor decreases by 20.5%, and the EGR caused by the heat transfer decreases by 68.8%. In the optimal reactor, the total EGRs mainly distribute in the first 30% reactor length, and the EGRs caused by the chemical reaction accounts for more than 84% of the total EGRs. The selectivity of CH3OH can be enhanced by increasing the inlet molar flow rate of CO, and the CO2 conversion rate can be enhanced by removing H2O from the reaction system. The results obtained herein are in favor of optimal designs of practical tubular MSCH reactors.<\/jats:p>","DOI":"10.3390\/e21020174","type":"journal-article","created":{"date-parts":[[2019,2,14]],"date-time":"2019-02-14T03:21:46Z","timestamp":1550114506000},"page":"174","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Entropy Generation Rate Minimization for Methanol Synthesis via a CO2 Hydrogenation Reactor"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8691-8987","authenticated-orcid":false,"given":"Penglei","family":"Li","sequence":"first","affiliation":[{"name":"College of Power Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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":"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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0420-7837","authenticated-orcid":false,"given":"Lei","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Power Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0920-5861(00)00503-4","article-title":"Methanol synthesis: A short review of technology improvements","volume":"64","author":"Lange","year":"2001","journal-title":"Catal. 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