{"id":"https://openalex.org/W2074646290","doi":"https://doi.org/10.1137/04062059x","title":"An Asymptotic Framework for Finite Hydraulic Fractures Including Leak\u2010Off","display_name":"An Asymptotic Framework for Finite Hydraulic Fractures Including Leak\u2010Off","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2074646290","doi":"https://doi.org/10.1137/04062059x","mag":"2074646290"},"language":"en","primary_location":{"id":"doi:10.1137/04062059x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/04062059x","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059969690","display_name":"Sarah Mitchell","orcid":"https://orcid.org/0000-0003-3603-2883"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"S. L. Mitchell","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070081332","display_name":"Rachel Kuske","orcid":"https://orcid.org/0000-0002-7140-0365"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"R. Kuske","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034324891","display_name":"Anthony Peirce","orcid":"https://orcid.org/0000-0002-8437-7889"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"A. P. Peirce","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034324891"],"corresponding_institution_ids":["https://openalex.org/I141945490"],"apc_list":null,"apc_paid":null,"fwci":3.4076,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.91531542,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"67","issue":"2","first_page":"364","last_page":"386"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10635","display_name":"Hydraulic Fracturing and Reservoir Analysis","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10635","display_name":"Hydraulic Fracturing and Reservoir Analysis","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7172544598579407},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6448156833648682},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.5095446705818176},{"id":"https://openalex.org/keywords/fracture","display_name":"Fracture (geology)","score":0.4833826422691345},{"id":"https://openalex.org/keywords/plane-stress","display_name":"Plane stress","score":0.47824564576148987},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.4511890709400177},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4282105267047882},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.41396570205688477},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34147849678993225},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24057123064994812},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.21951031684875488},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1754213571548462},{"id":"https://openalex.org/keywords/geotechnical-engineering","display_name":"Geotechnical engineering","score":0.16975975036621094},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.13347914814949036},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.08922556042671204}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7172544598579407},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6448156833648682},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5095446705818176},{"id":"https://openalex.org/C43369102","wikidata":"https://www.wikidata.org/wiki/Q2307625","display_name":"Fracture (geology)","level":2,"score":0.4833826422691345},{"id":"https://openalex.org/C29320194","wikidata":"https://www.wikidata.org/wiki/Q7201019","display_name":"Plane stress","level":3,"score":0.47824564576148987},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.4511890709400177},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4282105267047882},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.41396570205688477},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34147849678993225},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24057123064994812},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.21951031684875488},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1754213571548462},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.16975975036621094},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.13347914814949036},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.08922556042671204},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/04062059x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/04062059x","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.482.6288","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.482.6288","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ubc.ca/~peirce/AsymptoticFrameworforHFwithLeakoff_Mitchell_Kuske_Peirce_SIAM_JAM_V67_N2_p364_2007.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W142717177","https://openalex.org/W145740987","https://openalex.org/W1510184633","https://openalex.org/W1581959532","https://openalex.org/W1606871564","https://openalex.org/W1968070198","https://openalex.org/W1976240542","https://openalex.org/W1980905255","https://openalex.org/W1982543352","https://openalex.org/W1985790107","https://openalex.org/W1989159851","https://openalex.org/W1989288655","https://openalex.org/W1992441782","https://openalex.org/W1993281947","https://openalex.org/W2004598388","https://openalex.org/W2005447590","https://openalex.org/W2007260247","https://openalex.org/W2009653725","https://openalex.org/W2014097614","https://openalex.org/W2016156820","https://openalex.org/W2029838791","https://openalex.org/W2031949788","https://openalex.org/W2033456925","https://openalex.org/W2037745010","https://openalex.org/W2038496290","https://openalex.org/W2045203472","https://openalex.org/W2046424784","https://openalex.org/W2048067805","https://openalex.org/W2064227476","https://openalex.org/W2072740827","https://openalex.org/W2073426801","https://openalex.org/W2074346825","https://openalex.org/W2083766271","https://openalex.org/W2084223864","https://openalex.org/W2085274805","https://openalex.org/W2120223948","https://openalex.org/W2134924775","https://openalex.org/W2143738823","https://openalex.org/W2161123917","https://openalex.org/W2528615156","https://openalex.org/W2978139399","https://openalex.org/W4206755964"],"related_works":["https://openalex.org/W4378770497","https://openalex.org/W2049584446","https://openalex.org/W2079781215","https://openalex.org/W2064404759","https://openalex.org/W4233917511","https://openalex.org/W2033313728","https://openalex.org/W2490927919","https://openalex.org/W2719276165","https://openalex.org/W4221091971","https://openalex.org/W1862304616"],"abstract_inverted_index":{"The":[0,46,84],"dynamics":[1],"of":[2,9,20,67],"hydraulic":[3,119],"fracture,":[4],"described":[5],"by":[6],"a":[7,21,28,55,102],"system":[8],"nonlinear":[10,51],"integro\u2010differential":[11],"equations,":[12],"is":[13],"studied":[14],"through":[15],"the":[16,35,65,68,74,80,106,148],"development":[17],"and":[18,44,50,125,147],"application":[19],"multiparameter":[22],"singular":[23],"perturbation":[24],"analysis.":[25],"We":[26],"present":[27],"new":[29],"single":[30],"expansion":[31],"framework":[32],"which":[33,53,96],"describes":[34],"interaction":[36],"between":[37],"several":[38],"physical":[39,82],"processes,":[40],"namely":[41],"viscosity,":[42],"toughness,":[43],"leak\u2010off.":[45],"problem":[47],"has":[48],"nonlocal":[49],"effects":[52],"give":[54],"complex":[56],"solution":[57,104],"structure":[58],"involving":[59],"transitions":[60],"on":[61,109,116,121],"small":[62],"scales":[63],"near":[64],"tip":[66,76],"fracture.":[69],"Detailed":[70],"solutions":[71],"obtained":[72],"in":[73],"crack":[75],"region":[77],"vary":[78],"with":[79,133],"dominant":[81],"processes.":[83,112],"parameters":[85],"quantifying":[86],"these":[87],"processes":[88],"can":[89],"be":[90],"identified":[91],"from":[92],"critical":[93],"scaling":[94],"relationships,":[95],"are":[97],"then":[98],"used":[99],"to":[100],"construct":[101],"smooth":[103],"for":[105,130],"fracture":[107],"depending":[108],"all":[110],"three":[111],"Our":[113],"work":[114],"focuses":[115],"plane":[117],"strain":[118],"fractures":[120,146],"long":[122],"time":[123,135],"scales,":[124,136],"this":[126],"methodology":[127],"shows":[128],"promise":[129],"related":[131],"models":[132],"additional":[134],"fluid":[137],"lag,":[138],"or":[139],"different":[140],"geometries,":[141],"such":[142],"as":[143],"radial":[144],"(penny\u2010shaped)":[145],"classical":[149],"Perkins\u2013Kern\u2013Nordgren":[150],"(PKN)":[151],"model.":[152]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}