Supercritical flow during extraction through a point sink in a porous medium

Supercritical flow during extraction through a point sink in a porous medium | 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 Supercritical flow during extraction through a point sink in a porous medium Jyothi Jose, Graeme Hocking, Duncan Farrow This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8293624/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Fluid withdrawal through porous media plays a critical role in numerous applications, including oil recovery from underground reservoirs, extraction of fresh water from aquifers, and mineral leaching in mining operations. In many instances, these fluids exhibit density stratification due to differences in intrinsic properties (e.g., oil-water), salt content (freshwater-saltwater), or temperature. Supercritical flows into a point sink, where both fluid layers are entrained into the sink, are examined. These present a complex challenge due to the unknown interface shape and the singularity at the sink. By employing a spectral method, we can remove the singularity and obtain numerical solutions, including two exact solutions: one where the sink is positioned at the initial interface height, and another in the limit of large flow rates. For all other flow rates, numerical solutions are obtained. Our results show that as the sink moves away from the initial height of the interface, the critical flow rate required to induce coning and supercritical flow increases significantly, aligning with the behaviour observed in single-layer flow dynamics. Porous media axisymmetric flow nonlinear density stratification spectral method sharp interface supercritical solutions exact solutions oil recovery aquifers point sink coning critical flow rate two-layer density Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 19 Jan, 2026 Reviews received at journal 18 Jan, 2026 Reviews received at journal 14 Jan, 2026 Reviews received at journal 04 Jan, 2026 Reviewers agreed at journal 17 Dec, 2025 Reviewers agreed at journal 17 Dec, 2025 Reviewers agreed at journal 17 Dec, 2025 Reviewers invited by journal 11 Dec, 2025 Editor assigned by journal 07 Dec, 2025 Submission checks completed at journal 07 Dec, 2025 First submitted to journal 06 Dec, 2025 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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