{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:24:36Z","timestamp":1787333076775,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100002923","name":"CONICET","doi-asserted-by":"crossref","award":["112-2011010-0777"],"award-info":[{"award-number":["112-2011010-0777"]}],"id":[{"id":"10.13039\/501100002923","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>The purpose of this work is to present a numerical upscaling procedure to determine a viscoelastic material equivalent to a horizontally fractured fluid-saturated poroelastic---Biot---medium where fractures are modeled as explicit boundary conditions. At long wavelengths compared to the average distance between fractures, the Biot medium behaves as an equivalent (effective) transversely isotropic and viscoelastic (TIV) medium. The stiffness components of the TIV medium are determined using a finite element (FE) technique based on time-harmonic experiments. Each experiment is associated with a boundary value problem (BVP) representing compressibility and shear experiments applied to a sample of the fractured Biot medium. The solutions of these BVP allow us to measure the changes in volume and shape of the sample which in turn determine the stiffness components. Uniqueness of the solution of the continuous and discrete BVP's is demonstrated and a priori $L^2$ and $H^1$ error estimates are derived. The procedure to determine the stiffness components is validated against a theory valid for uniform media, fluid flow perpendicular to the fracture layering, and independent of the loading direction. Finally, an example for the case of patchy gas-brine saturation for which no analytical solution is available is presented.<\/jats:p>","DOI":"10.1137\/15m1040876","type":"journal-article","created":{"date-parts":[[2017,3,9]],"date-time":"2017-03-09T11:03:55Z","timestamp":1489057435000},"page":"B244-B271","source":"Crossref","is-referenced-by-count":1,"title":["Determination of a Transversely Isotropic Medium Equivalent to a Fractured Fluid-Saturated Poroelastic Medium. A Finite Element Approach"],"prefix":"10.1137","volume":"39","author":[{"given":"Juan E.","family":"Santos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robiel Mart\u00ednez","family":"Corredor","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jos\u00e9 M.","family":"Carcione","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,3,9]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jappgeo.2002.11.002"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2478.2009.00785.x"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1121\/1.2747206"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1190\/1.2194512"},{"key":"atypb5","volume-title":"Wave Fields in Real Media. 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Adams,\n                      Sobolev Spaces\n                      , Academic Press, New York, London, 1975."},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2478.1996.tb00136.x"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1029\/JB091iB06p06465"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/15M1040876","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:30:14Z","timestamp":1787329814000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/15M1040876"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/15M1040876"],"URL":"https:\/\/doi.org\/10.1137\/15m1040876","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}