Fracture characteristics from well flowrate fluctuations: a statistical physics approach

Fracture characteristics from well flowrate fluctuations: a statistical physics approach | 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 Method Article Fracture characteristics from well flowrate fluctuations: a statistical physics approach Kes Heffer This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9260335/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 Previous studies have indicated that fluctuations in flowrates from or into wells over the detailed production history of a mature oilfield are approximate proxies for geomechanical strain changes. Inter-well temporal correlations in the flowrate fluctuations were found to be statistically significant over long distances between wells, raising the possibility that field structure can be analysed with a process analogous to tomography. This paper expounds a theory for the extraction of fracture characteristics from the inter-well correlations of flowrate "noise". I use the maximum information entropy principle of Jaynes, with a constraint of fixed rate of energy input to the reservoir, balanced with either dissipation by Darcy flow or fluctuation in rock strain energy, to make the case for the reservoir system being in a state of maximum entropy production rate or flux. Fluctuating departures from this state allow a simple relationship between the covariances of flowrate fluctuations across all pairs of wells and a matrix of parameters including non-local stiffness tensors, from which estimates of local stress interactions are derived. Best fit fracture densities and orientations are then extracted at each well using the theoretical orientational distribution of the tensile stress field around a given extensional fracture. The novel method is seen as complementary to more conventional fracture characterisation exercises, providing information at low cost from the all-important inter-well regions. Its several assumptions imply that it can only be verified by comparison of its predictions with multiple sets of independent field data: early results are encouraging. fractures faults strike orientations production or injection flowrates in wells correlations fluctuation theory flux entropy statistical physics stresses strains Interference critical system Full Text Additional Declarations The authors declare potential competing interests as follows: The technique has been provided in a "Software as a Service" app by Reservoir Dynamics Ltd 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. 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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-9260335","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":614101873,"identity":"892d99eb-45b1-4271-969d-07d6b9f9f864","order_by":0,"name":"Kes Heffer","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-9474-4312","institution":"Reservoir Dynamics Ltd","correspondingAuthor":true,"prefix":"","firstName":"Kes","middleName":"","lastName":"Heffer","suffix":""}],"badges":[],"createdAt":"2026-03-29 17:30:45","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":true,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9260335/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9260335/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105798410,"identity":"a0189c7f-7a1d-4ac8-9167-0b111be3889d","added_by":"auto","created_at":"2026-03-31 09:12:16","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":721382,"visible":true,"origin":"","legend":"","description":"","filename":"FracturesfromflowratesHefferMathGeosci.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9260335/v1_covered_6cab6302-0ca7-4679-9f2f-684607b3bbf2.pdf"}],"financialInterests":"The authors declare potential competing interests as follows: The technique has been provided in a \"Software as a Service\" app by Reservoir Dynamics Ltd","formattedTitle":"\u003cp\u003eFracture characteristics from well flowrate fluctuations: a statistical physics approach\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Reservoir Dynamics Ltd","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":"fractures, faults, strike orientations, production or injection flowrates in wells, correlations, fluctuation theory, flux entropy, statistical physics, stresses, strains, Interference, critical system","lastPublishedDoi":"10.21203/rs.3.rs-9260335/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9260335/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePrevious studies have indicated that fluctuations in flowrates from or into wells over the detailed production history of a mature oilfield are approximate proxies for geomechanical strain changes. Inter-well temporal correlations in the flowrate fluctuations were found to be statistically significant over long distances between wells, raising the possibility that field structure can be analysed with a process analogous to tomography. This paper expounds a theory for the extraction of fracture characteristics from the inter-well correlations of flowrate \"noise\". I use the maximum information entropy principle of Jaynes, with a constraint of fixed rate of energy input to the reservoir, balanced with either dissipation by Darcy flow or fluctuation in rock strain energy, to make the case for the reservoir system being in a state of maximum entropy production rate or flux. Fluctuating departures from this state allow a simple relationship between the covariances of flowrate fluctuations across all pairs of wells and a matrix of parameters including non-local stiffness tensors, from which estimates of local stress interactions are derived. 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