An Analytical Method for the Non-Darcy Flow in a Single Fracture

An Analytical Method for the Non-Darcy Flow in a Single Fracture | 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 An Analytical Method for the Non-Darcy Flow in a Single Fracture YANG Wenjie, Yong HUANG, MIAO Kehan, ZHANG Jie, FU Zhimin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7993762/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 To investigate the seepage behavior in a single fracture, a nonlinear seepage model based on boundary layer theory was developed. An analytical formula for calculating nonlinear flow in a single fracture was derived, providing a new method for assessing non-Darcy flow in single fractures. The flow in this formula consists of two parts: the viscous layer and the inertial layer. When the undetermined coefficient λ is equal to 0.5, the formula is simplified to the traditional cubic law. Under high hydraulic gradient conditions, the formula can be simplified for practical use. COMSOL software was used to explore the relationships between fracture length, fracture width, hydraulic gradient, and flow rate under high hydraulic gradient conditions. Additionally, a semi-empirical formula for calculating non-Darcy flow in single fracture was derived. The flow rates calculated using the proposed method were compared with those obtained from the Forchheimer equation, the Schrauf model and the cubic law. The results confirmed the accuracy and effectiveness of the proposed analytical formula. non-Darcy flow boundary theory turbulent flow single fracture analytical method 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-7993762","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":545787837,"identity":"4bc1d87f-2e19-4532-bc8e-1c16f393bac1","order_by":0,"name":"YANG Wenjie","email":"","orcid":"","institution":"Hohai University","correspondingAuthor":false,"prefix":"","firstName":"YANG","middleName":"","lastName":"Wenjie","suffix":""},{"id":545787838,"identity":"5d258fb1-65fb-4131-950f-0722503df339","order_by":1,"name":"Yong 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