{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T08:34:47Z","timestamp":1775205287359,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,10,29]],"date-time":"2021-10-29T00:00:00Z","timestamp":1635465600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Processes"],"abstract":"<jats:p>This study proposed a hybrid modeling framework for membrane separation processes where lithium from batteries is recovered. This is a pertinent problem nowadays as lithium batteries are popularized in hybrid and electric vehicles. The hybrid model is based on an artificial intelligence (AI) structure to model the mass transfer resistance of several experimental separations found in the literature. It is also based on a phenomenological model to represent the transient system regime. An optimization framework was designed to perform the AI model training and simultaneously solve the Ordinary Differential Equation (ODE) system representing the phenomenological model. The results demonstrate that the hybrid model can better represent the experimental validation sets than the phenomenological model alone. This strategy opens doors for further investigations of this system.<\/jats:p>","DOI":"10.3390\/pr9111939","type":"journal-article","created":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T22:24:22Z","timestamp":1635805462000},"page":"1939","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Hybrid Modeling Framework for Membrane Separation Processes: Application to Lithium-Ion Recovery from Batteries"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2774-8302","authenticated-orcid":false,"given":"Maria Jo\u00e3o","family":"Regufe","sequence":"first","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]},{"given":"Vinicius V.","family":"Santana","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]},{"given":"Alexandre F. P.","family":"Ferreira","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]},{"given":"Ana M.","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6051-6039","authenticated-orcid":false,"given":"Jos\u00e9 M.","family":"Loureiro","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0963-6449","authenticated-orcid":false,"given":"Idelfonso B. R.","family":"Nogueira","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.asoc.2018.03.001","article-title":"A quasi-virtual online analyser based on an artificial neural networks and offline measurements to predict purities of raffinate\/extract in simulated moving bed processes","volume":"67","author":"Nogueira","year":"2018","journal-title":"Appl. Soft Comput. 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