{"id":"https://openalex.org/W1975358344","doi":"https://doi.org/10.1137/070710044","title":"Scaling Analysis for the Tracer Flow Problem in Self-Similar Permeability Fields","display_name":"Scaling Analysis for the Tracer Flow Problem in Self-Similar Permeability Fields","publication_year":2008,"publication_date":"2008-12-18","ids":{"openalex":"https://openalex.org/W1975358344","doi":"https://doi.org/10.1137/070710044","mag":"1975358344"},"language":"en","primary_location":{"id":"doi:10.1137/070710044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070710044","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/Scaling_Analysis_for_the_Tracer_Flow_Problem_in_Self-Similar_Permeability_Fields/13677856","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039998818","display_name":"Marcio R. Borges","orcid":"https://orcid.org/0000-0002-9566-6731"},"institutions":[{"id":"https://openalex.org/I4210142352","display_name":"Laborat\u00f3rio Nacional de Computa\u00e7\u00e3o Cient\u00edfica","ror":"https://ror.org/0498ekt05","country_code":"BR","type":"government","lineage":["https://openalex.org/I4210142352"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"M. R. Borges","raw_affiliation_strings":["Laborat\u00f3rio Nacional de Computa\u00e7\u00e3o Cient\u00edfica, Av. Get\u00falio Vargas, 333, Quitandinha, Petr\u00f3polis, RJ, 25651-075, Brasil"],"affiliations":[{"raw_affiliation_string":"Laborat\u00f3rio Nacional de Computa\u00e7\u00e3o Cient\u00edfica, Av. Get\u00falio Vargas, 333, Quitandinha, Petr\u00f3polis, RJ, 25651-075, Brasil","institution_ids":["https://openalex.org/I4210142352"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058414444","display_name":"Frederico Furtado","orcid":"https://orcid.org/0000-0002-6433-3264"},"institutions":[{"id":"https://openalex.org/I12834331","display_name":"University of Wyoming","ror":"https://ror.org/01485tq96","country_code":"US","type":"education","lineage":["https://openalex.org/I12834331"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"F. Furtado","raw_affiliation_strings":["Department of Mathematics and School for Energy Resources, University of Wyoming, Laramie, WY 82071-3036","Department of Mathematics, University of Wyoming, Laramie, WY 82071-3036"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and School for Energy Resources, University of Wyoming, Laramie, WY 82071-3036","institution_ids":["https://openalex.org/I12834331"]},{"raw_affiliation_string":"Department of Mathematics, University of Wyoming, Laramie, WY 82071-3036","institution_ids":["https://openalex.org/I12834331"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075433174","display_name":"Felipe Pereira","orcid":"https://orcid.org/0000-0002-0482-8636"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. Pereira","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059223152","display_name":"Helio Pedro Amaral Souto","orcid":"https://orcid.org/0000-0002-4107-6322"},"institutions":[{"id":"https://openalex.org/I40034438","display_name":"Universidade do Estado do Rio de Janeiro","ror":"https://ror.org/0198v2949","country_code":"BR","type":"education","lineage":["https://openalex.org/I40034438"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"H. P. Amaral Souto","raw_affiliation_strings":["Instituto Polit\u00e9cnico, Universidade do Estado do Rio de Janeiro, Rua Alberto Rangel"],"affiliations":[{"raw_affiliation_string":"Instituto Polit\u00e9cnico, Universidade do Estado do Rio de Janeiro, Rua Alberto Rangel","institution_ids":["https://openalex.org/I40034438"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5039998818"],"corresponding_institution_ids":["https://openalex.org/I4210142352"],"apc_list":null,"apc_paid":null,"fwci":0.9718,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.76984905,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"7","issue":"3","first_page":"1130","last_page":"1147"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10894","display_name":"Groundwater flow and contamination studies","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10894","display_name":"Groundwater flow and contamination studies","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10770","display_name":"Soil Geostatistics and Mapping","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10716","display_name":"Soil and Unsaturated Flow","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/scaling","display_name":"Scaling","score":0.8404519557952881},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.5571630001068115},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5325219631195068},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.5035275816917419},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.4717969298362732},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.42759138345718384},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.41440489888191223},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3966260552406311},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2881043553352356},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25969579815864563},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11167818307876587}],"concepts":[{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.8404519557952881},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.5571630001068115},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5325219631195068},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5035275816917419},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.4717969298362732},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.42759138345718384},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.41440489888191223},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3966260552406311},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2881043553352356},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25969579815864563},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11167818307876587}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/070710044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070710044","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:figshare.com:article/13677856","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Scaling_Analysis_for_the_Tracer_Flow_Problem_in_Self-Similar_Permeability_Fields/13677856","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:mountainscholar.org:20.500.11919/1573","is_oa":false,"landing_page_url":"https://hdl.handle.net/20.500.11919/1573","pdf_url":null,"source":{"id":"https://openalex.org/S4306402292","display_name":"Digital Collections of Colorado (Colorado State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I92446798","host_organization_name":"Colorado State University","host_organization_lineage":["https://openalex.org/I92446798"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Faculty Publications","raw_type":"Journal contribution"},{"id":"pmh:oai:repository.uwyo.edu:math_facpub-1004","is_oa":false,"landing_page_url":"https://repository.uwyo.edu/math_facpub/5","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Faculty Publications","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/13677856","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Scaling_Analysis_for_the_Tracer_Flow_Problem_in_Self-Similar_Permeability_Fields/13677856","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W587830888","https://openalex.org/W1575648505","https://openalex.org/W1592093959","https://openalex.org/W1982947800","https://openalex.org/W1983318458","https://openalex.org/W1994446031","https://openalex.org/W2000586803","https://openalex.org/W2008076987","https://openalex.org/W2009188658","https://openalex.org/W2016215294","https://openalex.org/W2019157745","https://openalex.org/W2030520530","https://openalex.org/W2031714820","https://openalex.org/W2040086358","https://openalex.org/W2051831312","https://openalex.org/W2057646856","https://openalex.org/W2064681424","https://openalex.org/W2084554625","https://openalex.org/W2098547667","https://openalex.org/W2112761649","https://openalex.org/W2116465625","https://openalex.org/W2125045131","https://openalex.org/W2143529984","https://openalex.org/W2529594109"],"related_works":["https://openalex.org/W3034924094","https://openalex.org/W1488708774","https://openalex.org/W3094954546","https://openalex.org/W2981906196","https://openalex.org/W4391100477","https://openalex.org/W4327779705","https://openalex.org/W1513698804","https://openalex.org/W4310560702","https://openalex.org/W2029712093","https://openalex.org/W332578827"],"abstract_inverted_index":{"The":[0,53,152,161,252],"spatial":[1],"variations":[2],"in":[3,90,149,242,265],"porous":[4],"media":[5],"(aquifers":[6],"and":[7,22,284],"petroleum":[8],"reservoirs)":[9],"occur":[10],"at":[11],"all":[12],"length":[13,74],"scales":[14,148],"(from":[15],"the":[16,19,26,34,44,56,80,91,105,109,115,119,126,136,141,150,158,171,183,187,204,217,222,227,230,233,237,243,246,269],"pore":[17],"to":[18,61,114,176,186,288],"reservoir":[20],"scale)":[21],"are":[23,157,264,282],"incorporated":[24],"into":[25],"governing":[27],"equations":[28],"for":[29,83,170,213,245,291],"multiphase":[30],"flow":[31,173],"problems":[32],"on":[33,79],"basis":[35],"of":[36,51,55,93,108,118,144,154,163,196,216,229,232,254,259,271],"random":[37,49],"fields":[38],"(geostatistical":[39],"models).":[40],"As":[41],"a":[42,48,62,72,164,193,255],"consequence,":[43],"velocity":[45,57],"field":[46,58],"is":[47,112,135,211,236],"function":[50],"space.":[52],"randomness":[54],"gives":[59],"rise":[60],"mixing":[63,73,110],"region":[64,111],"between":[65],"fluids,":[66],"which":[67,263],"can":[68,285],"be":[69,286],"characterized":[70],"by":[71,101,192,208],"$\\ell=\\ell(t)$.":[75],"Here":[76],"we":[77],"focus":[78],"scale-up":[81],"problem":[82,174],"tracer":[84,172],"flows.":[85],"Under":[86],"very":[87],"general":[88],"conditions,":[89],"limit":[92],"small":[94,188],"heterogeneity":[95,124,190,249],"strengths":[96],"it":[97],"has":[98],"been":[99],"derived":[100,207],"perturbation":[102,209],"theories":[103],"that":[104,139,203,277],"scaling":[106,116,127,137,168,195,205],"behavior":[107],"related":[113],"properties":[117],"self-similar":[120,177],"(or":[121],"fractal)":[122],"geological":[123],"through":[125],"law":[128,206],"$\\ell(t)\\sim":[129],"t^{\\gamma}$,":[130],"where":[131],"$\\gamma=\\max\\{1/2,$":[132],"$1-\\beta/2\\}$;":[133],"$\\beta$":[134],"exponent":[138],"controls":[140],"relative":[142],"importance":[143],"short":[145],"vs.":[146],"large":[147,184,247],"geology.":[151,293],"goals":[153],"this":[155,201,235],"work":[156],"following:":[159],"(i)":[160],"derivation":[162],"new,":[165],"mathematically":[166],"rigorous":[167,239],"analysis":[169,202],"subject":[175],"heterogeneities.":[178],"This":[179,275],"theoretical":[180],"development":[181],"relates":[182],"strength":[185,189,215,248],"regime":[191],"simple":[194],"solutions.":[197],"It":[198],"follows":[199],"from":[200],"theory":[210],"valid":[212],"any":[214],"underlying":[218],"geology,":[219],"thereby":[220],"extending":[221],"current":[223],"available":[224,241],"results.":[225],"To":[226],"best":[228],"knowledge":[231],"authors":[234],"only":[238],"result":[240],"literature":[244],"regime.":[250],"(ii)":[251],"presentation":[253],"Monte":[256,279],"Carlo":[257,280],"study":[258],"highly":[260],"resolved":[261],"simulations,":[262],"excellent":[266],"agreement":[267],"with":[268],"predictions":[270],"our":[272,278],"new":[273],"theory.":[274],"indicates":[276],"results":[281],"accurate":[283],"applied":[287],"other":[289],"models":[290],"stochastic":[292]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
