{"id":"https://openalex.org/W2084065501","doi":"https://doi.org/10.1137/040607654","title":"On a Mathematical Model of the Productivity Index of a Well from Reservoir Engineering","display_name":"On a Mathematical Model of the Productivity Index of a Well from Reservoir Engineering","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2084065501","doi":"https://doi.org/10.1137/040607654","mag":"2084065501"},"language":"en","primary_location":{"id":"doi:10.1137/040607654","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607654","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/A5052690130","display_name":"Akif Ibragimov","orcid":"https://orcid.org/0000-0001-6827-8007"},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Akif Ibragimov","raw_affiliation_strings":["Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042","institution_ids":["https://openalex.org/I12315562"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051271240","display_name":"Dinara Khalmanova","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dinara Khalmanova","raw_affiliation_strings":["Department of Petroleum Engineering, Texas A&M University, College Station, TX 77840","Department of Mathematics, Texas A&M University, MS 3368, College Station, TX 77840"],"affiliations":[{"raw_affiliation_string":"Department of Petroleum Engineering, Texas A&M University, College Station, TX 77840","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, MS 3368, College Station, TX 77840","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008815397","display_name":"Peter P. Valk\u00f3","orcid":"https://orcid.org/0000-0001-9942-2403"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter P. Valko","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023909048","display_name":"Jay R. Walton","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jay R. Walton","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, MS 3368, College Station, TX 77840"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, MS 3368, College Station, TX 77840","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5052690130"],"corresponding_institution_ids":["https://openalex.org/I12315562"],"apc_list":null,"apc_paid":null,"fwci":2.8718,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.89950989,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"65","issue":"6","first_page":"1952","last_page":"1980"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10635","display_name":"Hydraulic Fracturing and Reservoir Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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/T11801","display_name":"Reservoir Engineering and Simulation Methods","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/T10491","display_name":"Enhanced Oil Recovery Techniques","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"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/boundary-value-problem","display_name":"Boundary value problem","score":0.7015045881271362},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6652109026908875},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.6527869701385498},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6191110610961914},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5516180992126465},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.46072128415107727},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4519769847393036},{"id":"https://openalex.org/keywords/mixed-boundary-condition","display_name":"Mixed boundary condition","score":0.43842944502830505},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42749032378196716},{"id":"https://openalex.org/keywords/robin-boundary-condition","display_name":"Robin boundary condition","score":0.4175068736076355},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33622610569000244},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11511805653572083}],"concepts":[{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.7015045881271362},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6652109026908875},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.6527869701385498},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6191110610961914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5516180992126465},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.46072128415107727},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4519769847393036},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.43842944502830505},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42749032378196716},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.4175068736076355},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33622610569000244},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11511805653572083},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/040607654","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607654","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:10.1.1.89.9974","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.9974","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.pe.tamu.edu/valko/CV/ValkoPDF/2005IKVW_SIAM_7-60765.pdf","raw_type":"text"},{"id":"pmh:oai:oaktrust.library.tamu.edu:1969.1/178672","is_oa":false,"landing_page_url":"https://hdl.handle.net/1969.1/178672","pdf_url":null,"source":{"id":"https://openalex.org/S4306400291","display_name":"OakTrust (Texas A&M University Libraries)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91045830","host_organization_name":"Texas A&M University","host_organization_lineage":["https://openalex.org/I91045830"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","score":0.5799999833106995,"display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W619784351","https://openalex.org/W642649008","https://openalex.org/W1602967628","https://openalex.org/W1680579736","https://openalex.org/W1968547568","https://openalex.org/W1969455273","https://openalex.org/W1992381571","https://openalex.org/W1997392114","https://openalex.org/W1999162826","https://openalex.org/W2001682773","https://openalex.org/W2010284321","https://openalex.org/W2019195604","https://openalex.org/W2036471570","https://openalex.org/W2040389183","https://openalex.org/W2041657812","https://openalex.org/W2043639528","https://openalex.org/W2046365335","https://openalex.org/W2051551279","https://openalex.org/W2065613143","https://openalex.org/W2076548969","https://openalex.org/W2084617865","https://openalex.org/W2149115535","https://openalex.org/W2248380161","https://openalex.org/W4229914181"],"related_works":["https://openalex.org/W1514481392","https://openalex.org/W4322770021","https://openalex.org/W2174317416","https://openalex.org/W2020502833","https://openalex.org/W4387165380","https://openalex.org/W2100405323","https://openalex.org/W3203194254","https://openalex.org/W2059354999","https://openalex.org/W2767841216","https://openalex.org/W4300850840"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"the":[2,7,28,56,61,64,103,108,131,136,153,158,173],"reservoir":[3,183],"engineering":[4],"concept":[5],"of":[6,10,55,63,95,105,115,148,152,157,171,176,187],"productivity":[8,113,174],"index":[9,175],"a":[11,21,36,76,96,116,143,177,180,185],"producing":[12],"oil":[13],"well":[14,117,178,188],"in":[15,168,179],"an":[16],"isolated":[17],"reservoir,":[18],"we":[19],"analyze":[20],"time":[22,43,154],"dependent":[23],"functional,":[24],"diffusive":[25,45,58,97,159],"capacity,":[26],"on":[27,60],"solutions":[29],"to":[30,102,129],"initial":[31],"boundary":[32,51,65,71,125],"value":[33],"problems":[34],"for":[35,42,49,83,135,142,184],"parabolic":[37],"equation.":[38],"Sufficient":[39],"conditions":[40],"providing":[41],"independent":[44,155],"capacity":[46,59,98,160],"are":[47,161,166],"given":[48],"different":[50],"conditions.":[52],"The":[53,123,146,163],"dependence":[54],"constant":[57,93,137],"type":[62],"condition":[66,126],"(Dirichlet,":[67],"Neumann,":[68],"or":[69],"third":[70,124],"condition)":[72],"is":[73,99,127],"investigated":[74],"using":[75],"known":[77],"variational":[78],"principle":[79],"and":[80,111,150],"confirmed":[81],"numerically":[82],"various":[84],"geometrical":[85],"settings.":[86],"An":[87],"important":[88],"comparison":[89],"between":[90],"two":[91],"principal":[92],"values":[94,156],"made,":[100],"leading":[101],"establishment":[104],"criteria":[106],"when":[107],"so-called":[109],"pseudo-steady-state":[110],"boundary-dominated":[112],"indices":[114],"significantly":[118],"differ":[119],"from":[120],"each":[121],"other.":[122],"shown":[128],"model":[130],"thin":[132],"skin":[133],"effect":[134],"wellbore":[138],"pressure":[139],"production":[140],"regime":[141],"damaged":[144],"well.":[145],"questions":[147],"stabilization":[149],"uniqueness":[151],"addressed.":[162],"derived":[164],"formulas":[165],"used":[167],"numerical":[169],"study":[170],"evaluating":[172],"general":[181],"three-dimensional":[182],"variety":[186],"configurations.":[189]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}