Linear Stability Analysis of Two-phase, Two-Component Flow in Porous Media

Linear Stability Analysis of Two-phase, Two-Component Flow in Porous Media | 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 Linear Stability Analysis of Two-phase, Two-Component Flow in Porous Media Paulo Lee Kung Caetano Chang, Kundan Kumar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8918175/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 Viscous fingering instabilities during fluid displacement in porous media can compromise the efficiency of applications such as enhanced oil recovery, CO$_2$ sequestration, and groundwater remediation. While extensive research exists on linear stability analysis for fully immiscible and fully miscible displacements, the intermediate case of partially miscible flow with limited mass transfer between phases remains largely unexplored. This study extends linear stability analysis to a two-phase, two-component system that accounts for gravity effects, fractional flow, capillary forces, mechanical dispersion, and interphase mass transfer, focusing on the case where a partially miscible gaseous fluid displaces a liquid. We formulate an eigenvalue problem to characterize instability growth rates and cutoff wavenumbers. The resulting ordinary differential equations have discontinuous coefficients at the transition from two-phase to pure-liquid flow, resulting in discontinuous eigenfunction derivatives. We derive jump conditions for the derivatives at this transition, and solve the eigenvalue problem using the matched initial value problem method. Results demonstrate that mass transfer has a predominantly stabilizing effect by reducing viscosity contrast and altering shock properties at the displacement front. This stabilizing influence is particularly pronounced for high viscosity contrasts and dampens gravity-induced instability in upward displacements. Mass transfer most significantly affects the perturbation growth rate, while its effect on the cutoff wavenumber is less pronounced. We identify a critical value for the dimensionless longitudinal dispersion coefficient where both growth rate and cutoff wavenumber are maximized, suggesting complex interactions between capillary forces and mechanical dispersion. Linear Stability Analysis Viscous fingering Flow in porous media Partial miscibility Two-component (binary) systems 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-8918175","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":613911434,"identity":"7e8b8698-9ea4-449e-89f0-69db89914693","order_by":0,"name":"Paulo Lee Kung Caetano Chang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABGElEQVRIie2QvUoDQRCAJyyYZuHagxCfYSCFiBJfZZeFXHNIRBDtrrMJXHti0FcwT+AuC6a5WhZyxaW5KkXsTkjhbiTaXH5Kwf1Ylv2Zb4YZAI/nD3KRQEsC9Jk9t0q3Jet3lFsV92WXcApBYE4hBynKKUfhrwI7lGmOcgnyMni8f7/7rHU37aSS0GEBJ+2kuZdRjCoDeR0W+c2MMt17GGsgFCs4HTVXQohRU5A8MfFgBkzzFyOcogENa1aCxbfybJWr2iqve5VwXUXZ5NEbUFcl3KtUQ5Wh4BMTkw4dRL3MCFRjrCjmW3oJxKRc3vb5k4nmH/X5WTfN+LxcrIpjnDZPbDMEC8Wfu0tPd8RvaJcHBHk8Hs9/5Au//2xmIMqSuAAAAABJRU5ErkJggg==","orcid":"","institution":"University of Bergen","correspondingAuthor":true,"prefix":"","firstName":"Paulo","middleName":"Lee Kung Caetano","lastName":"Chang","suffix":""},{"id":613911436,"identity":"1d268dac-014f-4683-942e-0d81346499e8","order_by":1,"name":"Kundan Kumar","email":"","orcid":"","institution":"University of Bergen","correspondingAuthor":false,"prefix":"","firstName":"Kundan","middleName":"","lastName":"Kumar","suffix":""}],"badges":[],"createdAt":"2026-02-19 15:13:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8918175/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8918175/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105904640,"identity":"1fae066b-3db3-4917-add4-8eba92a46bba","added_by":"auto","created_at":"2026-04-01 10:10:02","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":854244,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript20260304.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8918175/v1_covered_435c080d-586c-4b9c-b41e-f5a407bc154b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Linear Stability Analysis of Two-phase, Two-Component Flow in Porous Media","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":"Linear Stability Analysis, Viscous fingering, Flow in porous media, Partial miscibility, Two-component (binary) systems ","lastPublishedDoi":"10.21203/rs.3.rs-8918175/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8918175/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Viscous fingering instabilities during fluid displacement in porous media can compromise the efficiency of applications such as enhanced oil recovery, CO$_2$ sequestration, and groundwater remediation. 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