Inferring Stiff CO2-Brine Interface Dynamics: Finite Difference vs Transfer Learning

Inferring Stiff CO2-Brine Interface Dynamics: Finite Difference vs Transfer Learning | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Inferring Stiff CO2-Brine Interface Dynamics: Finite Difference vs Transfer Learning Jose Kevin Pauyac Estrada, Mehdi Zeidouni This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8927595/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In the context of CO2 storage in deep saline aquifers, when CO2 flows through the aquifer, three major regions can be distinguished: i) dry-out region (single-phase CO2), ii) two-phase region (brine and CO2), and iii) brine region (single-phase brine). Assuming fully immiscible fluids and neglecting local capillary pressure, the transition zone between CO2 and brine can be considered a sharp interface. Additionally, due to the density difference between the displacing CO2 and displaced (brine) fluid (CO2 is less dense than the resident brine), gravity plays a significant role. The CO2 displacement is governed by a nonlinear ordinary differential equation (ODE) that presents variations of the CO2-brine interface with respect to time and (radial) space. To numerically solve this highly unstable ODE, this study presents and compares two distinct solutions: finite difference method (FDM), and physics-informed neural networks (PINNs). Although some researchers addressed the governing ODE in question previously, they neither specified the solution methods used nor provided solutions for the entire CO2-brine interface, motivating a deeper exploration of solution approaches. Our findings indicate that the tested finite difference schemes (forward, backward, central) fail to provide accurate and stable solutions within analytically bechmarked cases. In contrast, the proposed PINN framework accurately captures the physics of the governing ODE and closely matches the analytical solution. After validation, the PINN model was optimized through a grid search and a loss-weighting sensitivity analysis to identify the most robust framework. Using this optimized model, transfer learning was performed beyond the analytical regime, revealing that the pretrained PINN model generalizes to moderately stiffer conditions, but fails in strongly stiff regimes. CO2-Brine Sharp Interface Finite Difference Scientifc Transfer Learning Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8927595","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":604689414,"identity":"6ee7abd5-924d-44f6-9777-5e6396ac4562","order_by":0,"name":"Jose Kevin Pauyac Estrada","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvklEQVRIiWNgGAWjYBACxgYwJSHHB6bZiNdiYcxGtBYoqEhsI1oL8+zmZ9I8NRLpbfxnDBg+lB0mwmFzjplJ8xyTyG2TyDFgnHGOGC0zEoBa2EBaeAyYeduI0pL+TZrnn0Q6G9BhzH+J05JjJs3bJpHAxpBjwMxIlJY5Z4ot5/ZJGLZJpBUc7DmXTliL4ez2jTfefKuT5+c/vPHBjzJrIrTMYGBg4oFyDhBWDwTyEkDH/SBK6SgYBaNgFIxYAAABSzOPjJHYvAAAAABJRU5ErkJggg==","orcid":"","institution":"Louisiana State University","correspondingAuthor":true,"prefix":"","firstName":"Jose","middleName":"Kevin Pauyac","lastName":"Estrada","suffix":""},{"id":604689419,"identity":"d50de80d-ac22-45b0-936a-1ebda5768901","order_by":1,"name":"Mehdi Zeidouni","email":"","orcid":"","institution":"Louisiana State University","correspondingAuthor":false,"prefix":"","firstName":"Mehdi","middleName":"","lastName":"Zeidouni","suffix":""}],"badges":[],"createdAt":"2026-02-20 16:09:34","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8927595/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8927595/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104781902,"identity":"68e54a48-0d51-48cd-a9f9-b2cbe2964918","added_by":"auto","created_at":"2026-03-17 07:56:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10154383,"visible":true,"origin":"","legend":"","description":"","filename":"ComputationalGeoscienceJournalfinalv02.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8927595/v1_covered_90ba3707-f2a8-4d11-82fe-7f90d55bdfe2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Inferring Stiff CO2-Brine Interface Dynamics: Finite Difference vs Transfer Learning","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"CO2-Brine Sharp Interface, Finite Difference, Scientifc Transfer Learning","lastPublishedDoi":"10.21203/rs.3.rs-8927595/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8927595/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In the context of CO2 storage in deep saline aquifers, when CO2 flows through the aquifer, three major regions can be distinguished: i) dry-out region (single-phase CO2), ii) two-phase region (brine and CO2), and iii) brine region (single-phase brine). Assuming fully immiscible fluids and neglecting local capillary pressure, the transition zone between CO2 and brine can be considered a sharp interface. Additionally, due to the density difference between the displacing CO2 and displaced (brine) fluid (CO2 is less dense than the resident brine), gravity plays a significant role. The CO2 displacement is governed by a nonlinear ordinary differential equation (ODE) that presents variations of the CO2-brine interface with respect to time and (radial) space. To numerically solve this highly unstable ODE, this study presents and compares two distinct solutions: finite difference method (FDM), and physics-informed neural networks (PINNs). Although some researchers addressed the governing ODE in question previously, they neither specified the solution methods used nor provided solutions for the entire CO2-brine interface, motivating a deeper exploration of solution approaches. Our findings indicate that the tested finite difference schemes (forward, backward, central) fail to provide accurate and stable solutions within analytically bechmarked cases. In contrast, the proposed PINN framework accurately captures the physics of the governing ODE and closely matches the analytical solution. After validation, the PINN model was optimized through a grid search and a loss-weighting sensitivity analysis to identify the most robust framework. 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