One-Dimensional Modeling of Imbibition in Porous Media Using an Approximate Analytical Method

One-Dimensional Modeling of Imbibition in Porous Media Using an Approximate Analytical Method | 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 Article One-Dimensional Modeling of Imbibition in Porous Media Using an Approximate Analytical Method Anuj Raval, Mitesh S. Joshi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6691640/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 This paper is concerned with solving the problem of one-dimensional counter-current imbibition in a homogeneous porous medium. In this research, water and oil are treated as two distinct liquid phases, in which the water is the wetting phase while the oil is the non-wetting phase. This is the common scenario during secondary recovery of oil. During this phase, the fluid behavior is characterized by a nonlinear partial differential equation. To find the solution of this equation, we utilize the Homotopy Analysis Method (HAM), which is a powerful analytical method. Proper boundary conditions are chosen according to the physical phenomenon of the problem. The results are visualized and interpreted with the help of Mathematica 12.0 using graphical plots. Physical sciences/Mathematics and computing Physical sciences/Mathematics and computing/Applied mathematics Counter Current Homogeneous Porous Media Imbibition Phenomena Homotopy Analysis Method (HAM) 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. 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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-6691640","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":458222599,"identity":"3505247b-7bf1-41b2-9d2f-9b5e66e2e9b5","order_by":0,"name":"Anuj Raval","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/UlEQVRIiWNgGAWjYJACAxDBB2ZWADEzcwNxWtgYmIHkGZAWRsJaGOBaGNtATAJa+Gf3GBRX1ByWZ+M/f/Bz5bzaaP52oJYfFdtwapG4c8bA8Myxw4ZtEsnMkme3Hc+dcZixgbHnzG3c1tzIMTBsYEtjbJNgZpBs3HYstwGohZmxDbcWebCWf2n2bfyHmX82zjmWO5+QFgOQlsY2m8Q2hmQ2ycaGmtwNhLQY3kgrMGzss0kG+sXMsuHYgdyNQC0H8flF7kbyNsOGbxK2/fwHH99sqKnLnXf+8MEHPyrweB8YIwZInMNg8gA+9UDA/ACJU0dA8SgYBaNgFIxEAAC2GlkYgIFHjgAAAABJRU5ErkJggg==","orcid":"","institution":"Gujarat Technological University","correspondingAuthor":true,"prefix":"","firstName":"Anuj","middleName":"","lastName":"Raval","suffix":""},{"id":458222600,"identity":"daa63e55-958e-4a32-b2b4-0846c6832bf9","order_by":1,"name":"Mitesh S. 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