Sampling-based stochastic analysis of the PKN model for hydraulic fracturing
Hydraulic fracturing processes are surrounded by uncertainty, as available data is typically scant. In this work, we present a sampling-based stochastic analysis of the hydraulic fracturing process by considering various system parameters to be random. Our analysis is based on the Perkins-Kern-Nordg...
Saved in:
| Published in: | Computational geosciences Vol. 23; no. 1; pp. 81 - 105 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article Publication |
| Language: | English |
| Published: |
Cham
Springer International Publishing
01.02.2019
Springer Nature B.V |
| Subjects: | |
| ISSN: | 1420-0597, 1573-1499 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Hydraulic fracturing processes are surrounded by uncertainty, as available data is typically scant. In this work, we present a sampling-based stochastic analysis of the hydraulic fracturing process by considering various system parameters to be random. Our analysis is based on the Perkins-Kern-Nordgren (PKN) model for hydraulic fracturing. This baseline model enables computation of high fidelity solutions, which avoids pollution of our stochastic results by inaccuracies in the deterministic solution procedure. In order to obtain the desired degree of accuracy of the computed solution, we supplement the employed time-dependent moving-mesh finite element method with two new enhancements: (i) global conservation of volume is enforced through a Lagrange multiplier; (ii) the weakly singular behavior of the solution at the fracture tip is resolved by supplementing the solution space with a tip enrichment function. This tip enrichment function enables the computation of the tip speed directly from its associated solution coefficient. A novel incremental-iterative solution procedure based on a backward-Euler time-integrator with sub-iterations is employed to solve the PKN model. Direct Monte-Carlo sampling is performed based on random variable and random field input parameters. The presented stochastic results quantify the dependence of the fracture evolution process—in particular the fracture length and fracture opening—on variations in the elastic properties and leak-off coefficient of the formation, and the height of the fracture. |
|---|---|
| AbstractList | Hydraulic fracturing processes are surrounded by uncertainty, as available data is typically scant. In this work, we present a sampling-based stochastic analysis of the hydraulic fracturing process by considering various system parameters to be random. Our analysis is based on the Perkins-Kern-Nordgren (PKN) model for hydraulic fracturing. This baseline model enables computation of high fidelity solutions, which avoids pollution of our stochastic results by inaccuracies in the deterministic solution procedure. In order to obtain the desired degree of accuracy of the computed solution, we supplement the employed time-dependent moving-mesh finite element method with two new enhancements: (i) global conservation of volume is enforced through a Lagrange multiplier; (ii) the weakly singular behavior of the solution at the fracture tip is resolved by supplementing the solution space with a tip enrichment function. This tip enrichment function enables the computation of the tip speed directly from its associated solution coefficient. A novel incremental-iterative solution procedure based on a backward-Euler time-integrator with sub-iterations is employed to solve the PKN model. Direct Monte-Carlo sampling is performed based on random variable and random field input parameters. The presented stochastic results quantify the dependence of the fracture evolution process—in particular the fracture length and fracture opening—on variations in the elastic properties and leak-off coefficient of the formation, and the height of the fracture. The final publication is available at Springer via http://dx.doi.org/10.1007/s10596-018-9784-y Hydraulic fracturing processes are surrounded by uncertainty, as available data is typically scant. In this work, we present a sampling-based stochastic analysis of the hydraulic fracturing process by considering various system parameters to be random. Our analysis is based on the Perkins-Kern-Nordgren (PKN) model for hydraulic fracturing. This baseline model enables computation of high fidelity solutions, which avoids pollution of our stochastic results by inaccuracies in the deterministic solution procedure. In order to obtain the desired degree of accuracy of the computed solution, we supplement the employed time-dependent moving-mesh finite element method with two new enhancements: (i) global conservation of volume is enforced through a Lagrange multiplier; (ii) the weakly singular behavior of the solution at the fracture tip is resolved by supplementing the solution space with a tip enrichment function. This tip enrichment function enables the computation of the tip speed directly from its associated solution coefficient. A novel incremental-iterative solution procedure based on a backward-Euler time-integrator with sub-iterations is employed to solve the PKN model. Direct Monte-Carlo sampling is performed based on random variable and random field input parameters. The presented stochastic results quantify the dependence of the fracture evolution process—in particular the fracture length and fracture opening—on variations in the elastic properties and leak-off coefficient of the formation, and the height of the fracture. Peer Reviewed |
| Author | Zlotnik, Sergio van Brummelen, E. Harald Díez, Pedro Verhoosel, Clemens V. Garikapati, Hasini |
| Author_xml | – sequence: 1 givenname: Hasini surname: Garikapati fullname: Garikapati, Hasini email: h.garikapati@tue.nl organization: Eindhoven University of Technology, Universitat Politècnica de Catalunya – sequence: 2 givenname: Clemens V. surname: Verhoosel fullname: Verhoosel, Clemens V. organization: Eindhoven University of Technology – sequence: 3 givenname: E. Harald surname: van Brummelen fullname: van Brummelen, E. Harald organization: Eindhoven University of Technology – sequence: 4 givenname: Sergio surname: Zlotnik fullname: Zlotnik, Sergio organization: Universitat Politècnica de Catalunya – sequence: 5 givenname: Pedro surname: Díez fullname: Díez, Pedro organization: Universitat Politècnica de Catalunya |
| BookMark | eNp9kF1LwzAUhoNMcFN_gHcFr6MnSdu0lzL8wqGCeh3O0sR1dM1M0ov-ezOm6I1ehOTA-7ycPDMy6V1vCDljcMEA5GVgUNQlBVbRWlY5HQ_IlBVSUJbX9SS9cw40ReQRmYWwBoBaCjYlixfcbLu2f6dLDKbJQnR6hSG2OsMeuzG0IXM2iyuTPT88ZhvXmC6zzmersfE4dClnPeo4-NRxQg4tdsGcft3H5O3m-nV-RxdPt_fzqwXFnOeRlmgMlE1ViZJX0Ghe2MICl41GsLYEFFynCWQhlqXOa2wQQAuGdQlSlI04Jmzfq8OglTfaeI1ROWx_ht3hILkSQuYyT8z5ntl69zGYENXaDT59MSjORFGxGiqeUvKr2bsQvLFKtxFj6_rose0UA7XTrfa6VdKtdrrV-Gunb3Lr2w368V-G75mw3ekz_menv6FPZhWUeQ |
| CitedBy_id | crossref_primary_10_1016_j_compgeo_2023_105709 crossref_primary_10_3390_su162411087 crossref_primary_10_1016_j_engfracmech_2020_107475 crossref_primary_10_1016_j_jmps_2022_105082 crossref_primary_10_3389_feart_2022_906923 crossref_primary_10_3390_en15165811 crossref_primary_10_1016_j_jngse_2021_104158 |
| Cites_doi | 10.1007/s10659-007-9122-4 10.1115/1.321162 10.1108/02644409510799532 10.1016/j.ijrmms.2006.11.006 10.2118/2458-PA 10.1017/S0305004100004175 10.1016/j.petrol.2017.12.048 10.1007/s10596-015-9532-5 10.1016/j.petrol.2011.04.001 10.1002/nag.213 10.1016/j.cma.2015.09.021 10.2118/6089-PA 10.1017/S0013091500011457 10.1016/j.jmps.2016.07.019 10.1007/s10596-017-9702-8 10.1007/s11242-009-9403-4 10.1088/0305-4470/22/9/026 10.2118/10505-PA 10.1098/rspa.1946.0077 10.1016/j.petrol.2010.03.032 10.1016/j.cma.2013.12.005 10.1017/S0305004100037099 10.1016/S0045-7825(96)01087-0 10.1016/j.cma.2014.12.025 10.1061/(ASCE)0733-9399(1989)115:5(1035) 10.1016/j.cma.2012.08.017 10.1007/s10596-013-9396-5 10.2118/8942-PA 10.1061/(ASCE)0733-9399(1986)112:1(85) 10.1098/rsta.1937.0005 10.1139/t99-049 10.1002/cnm.1111 10.1029/GM122p0213 10.2118/3009-PA 10.2172/10176839 10.1017/CBO9780511800955 10.2118/89-PA 10.1146/annurev-fluid-010814-014736 10.2118/8941-PA 10.2118/18959-PA |
| ContentType | Journal Article Publication |
| Contributor | Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
| Contributor_xml | – sequence: 1 fullname: Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental – sequence: 2 fullname: Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
| Copyright | The Author(s) 2018 Computational Geosciences is a copyright of Springer, (2018). All Rights Reserved. © 2018. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. info:eu-repo/semantics/openAccess |
| Copyright_xml | – notice: The Author(s) 2018 – notice: Computational Geosciences is a copyright of Springer, (2018). All Rights Reserved. © 2018. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. – notice: info:eu-repo/semantics/openAccess |
| DBID | C6C AAYXX CITATION 3V. 7SC 7UA 7XB 88I 8AL 8FD 8FE 8FG 8FK ABUWG AEUYN AFKRA ARAPS AZQEC BENPR BGLVJ BHPHI BKSAR C1K CCPQU DWQXO F1W GNUQQ H8D H96 HCIFZ JQ2 K7- L.G L7M L~C L~D M0N M2P P5Z P62 PCBAR PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS Q9U XX2 |
| DOI | 10.1007/s10596-018-9784-y |
| DatabaseName | Springer Nature OA Free Journals CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Water Resources Abstracts ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) Computing Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ProQuest Central (Alumni) ProQuest One Sustainability ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Technology collection Natural Science Collection (ProQuest) Earth, Atmospheric & Aquatic Science Collection Environmental Sciences and Pollution Management ProQuest One Community College ProQuest Central ASFA: Aquatic Sciences and Fisheries Abstracts ProQuest Central Student Aerospace Database Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database Aquatic Science & Fisheries Abstracts (ASFA) Professional Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Science Database AAdvanced Technologies & Aerospace Database (subscription) ProQuest Advanced Technologies & Aerospace Collection Earth, Atmospheric & Aquatic Science Database ProQuest Central Premium ProQuest One Academic ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China ProQuest Central Basic Recercat |
| DatabaseTitle | CrossRef Aquatic Science & Fisheries Abstracts (ASFA) Professional Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China Water Resources Abstracts Environmental Sciences and Pollution Management ProQuest Central Earth, Atmospheric & Aquatic Science Collection ProQuest One Applied & Life Sciences Aerospace Database ProQuest One Sustainability Natural Science Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Advanced Technologies & Aerospace Collection ProQuest Computing ProQuest Science Journals (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition Earth, Atmospheric & Aquatic Science Database ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources ProQuest One Academic UKI Edition ASFA: Aquatic Sciences and Fisheries Abstracts ProQuest One Academic ProQuest Central (Alumni) ProQuest One Academic (New) |
| DatabaseTitleList | Aquatic Science & Fisheries Abstracts (ASFA) Professional |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Geology |
| EISSN | 1573-1499 |
| EndPage | 105 |
| ExternalDocumentID | oai_recercat_cat_2072_337474 10_1007_s10596_018_9784_y |
| GrantInformation_xml | – fundername: Education, Audiovisual and Culture Executive Agency funderid: https://doi.org/10.13039/501100000785 – fundername: Generalitat de Catalunya grantid: 2017-SGR-1278 funderid: https://doi.org/10.13039/501100002809 |
| GroupedDBID | -5D -5G -BR -EM -Y2 -~C .86 .VR 06D 0R~ 0VY 199 1N0 1SB 203 29F 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5VS 67Z 6NX 88I 8FE 8FG 8FH 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEUYN AEVLU AEXYK AFBBN AFGCZ AFKRA AFLOW AFQWF AFRAH AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. BA0 BAPOH BDATZ BENPR BGLVJ BGNMA BHPHI BKSAR BPHCQ BSONS C6C CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 DWQXO EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I-F I09 IHE IJ- IKXTQ ITM IWAJR IXC IXE IZIGR IZQ I~X I~Z J-C J0Z J9A JBSCW JCJTX JZLTJ K6V K7- KDC KOV LAK LK5 LLZTM M0N M2P M4Y M7R MA- N2Q N9A NPVJJ NQJWS NU0 O9- O93 O9J OAM OVD P62 P9R PCBAR PF0 PQQKQ PROAC PT4 PT5 Q2X QOS R89 R9I RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S27 S3B SAP SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TEORI TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z5O Z7R Z7Y Z81 ZMTXR ~02 ~A9 AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 7SC 7UA 7XB 8AL 8FD 8FK C1K F1W H8D H96 JQ2 L.G L7M L~C L~D PKEHL PQEST PQUKI PRINS Q9U XX2 |
| ID | FETCH-LOGICAL-a424t-6aee06d8836280dc25f5f027dca0ff60a32c27d0753b6c49ada00c31a960736d3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 7 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000459423400005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1420-0597 |
| IngestDate | Fri Nov 07 13:46:29 EST 2025 Tue Nov 04 23:06:30 EST 2025 Tue Nov 18 21:57:07 EST 2025 Sat Nov 29 06:12:22 EST 2025 Fri Feb 21 02:36:41 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Finite element method Stochastic analysis Random fields Sensitivity analysis Moving-boundary problem Perkins-Kern-Nordgren model Monte-Carlo method Hydraulic fracturing |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a424t-6aee06d8836280dc25f5f027dca0ff60a32c27d0753b6c49ada00c31a960736d3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://link.springer.com/10.1007/s10596-018-9784-y |
| PQID | 2135819082 |
| PQPubID | 55381 |
| PageCount | 25 |
| ParticipantIDs | csuc_recercat_oai_recercat_cat_2072_337474 proquest_journals_2135819082 crossref_citationtrail_10_1007_s10596_018_9784_y crossref_primary_10_1007_s10596_018_9784_y springer_journals_10_1007_s10596_018_9784_y |
| PublicationCentury | 2000 |
| PublicationDate | 20190200 2019-2-00 20190201 2019-02 |
| PublicationDateYYYYMMDD | 2019-02-01 |
| PublicationDate_xml | – month: 2 year: 2019 text: 20190200 |
| PublicationDecade | 2010 |
| PublicationPlace | Cham |
| PublicationPlace_xml | – name: Cham – name: Dordrecht |
| PublicationSubtitle | Modeling, Simulation and Data Analysis |
| PublicationTitle | Computational geosciences |
| PublicationTitleAbbrev | Comput Geosci |
| PublicationYear | 2019 |
| Publisher | Springer International Publishing Springer Nature B.V |
| Publisher_xml | – name: Springer International Publishing – name: Springer Nature B.V |
| References | Spanos, Ghanem (CR38) 1989; 115 England, Green (CR8) 1963; 59 Adachi, Siebrits, Peirce, Desroches (CR2) 2007; 44 CR39 CR16 Wheeler, Wick, Wollner (CR42) 2014; 271 Adachi, Peirce (CR3) 2008; 90 Gutiérrez, Krenk (CR13) 2017 Miehe, Mauthe (CR24) 2016; 304 CR31 Sneddon (CR37) 1965; 61 CR30 Ganis, Mear, Sakhaee-Pour, Wheeler, Wick (CR9) 2014; 18 Lowengrub (CR21) 1966; 15 Zhao, Li, Zhu, Ru (CR46) 2018; 162 Kenney (CR17) 2013 Garagash, Detournay (CR10) 2000; 67 Lecampion (CR20) 2009; 25 Simonson, Abou-Sayed, Clifton (CR35) 1978; 18 Kovalyshen, Detournay (CR19) 2010; 81 Howard, Fast (CR15) 1957 Remij, Remmers, Huyghe, Smeulders (CR32) 2015; 286 CR4 Settari, Cleary (CR34) 1986; 1 CR6 Melenk, Babuška (CR23) 1996; 139 Sneddon (CR36) 1946; 187 Wilson, Landis (CR43) 2016; 96 CR7 Kiureghian, Liu (CR18) 1986; 112 CR29 Mikeliċ, Wheeler, Wick (CR25) 2015; 19 Gordeliy, Peirce (CR12) 2013; 253 CR48 CR47 Meakin, Li, Sander, Louis, Guinea (CR22) 1989; 22 CR44 Remij, Remmers, Huyghe, Smeulders (CR33) 2018; 22 Wangen (CR40) 2011; 77 CR41 Adachi, Detournay (CR1) 2002; 26 Ng, Small (CR28) 1999; 36 Hanson, Shaffer, Anderson (CR14) 1981; 21 Geertsma, De Klerk (CR11) 1969; 21 Zhang, Liu, Zhang, Wu, Wang (CR45) 2010; 72 Neyman (CR27) 1937; 236 Barker, Barker, Burr, Polk, Smid (CR5) 2012; 800 Munjiza, Owen, Bicanic (CR26) 1995; 12 M Lowengrub (9784_CR21) 1966; 15 A Munjiza (9784_CR26) 1995; 12 9784_CR30 9784_CR31 JI Adachi (9784_CR3) 2008; 90 E Barker (9784_CR5) 2012; 800 B Ganis (9784_CR9) 2014; 18 JM Melenk (9784_CR23) 1996; 139 E Simonson (9784_CR35) 1978; 18 P Meakin (9784_CR22) 1989; 22 H Zhao (9784_CR46) 2018; 162 J Adachi (9784_CR2) 2007; 44 9784_CR16 9784_CR39 A Settari (9784_CR34) 1986; 1 AK Ng (9784_CR28) 1999; 36 J Neyman (9784_CR27) 1937; 236 MF Wheeler (9784_CR42) 2014; 271 AD Kiureghian (9784_CR18) 1986; 112 Y Kovalyshen (9784_CR19) 2010; 81 J Geertsma (9784_CR11) 1969; 21 GC Howard (9784_CR15) 1957 M Wangen (9784_CR40) 2011; 77 A Mikeliċ (9784_CR25) 2015; 19 J Adachi (9784_CR1) 2002; 26 E Gordeliy (9784_CR12) 2013; 253 C Miehe (9784_CR24) 2016; 304 PD Spanos (9784_CR38) 1989; 115 EW Remij (9784_CR33) 2018; 22 9784_CR41 9784_CR44 ZA Wilson (9784_CR43) 2016; 96 9784_CR47 9784_CR48 JF Kenney (9784_CR17) 2013 9784_CR29 G Zhang (9784_CR45) 2010; 72 IN Sneddon (9784_CR37) 1965; 61 9784_CR6 9784_CR7 9784_CR4 ME Hanson (9784_CR14) 1981; 21 AH England (9784_CR8) 1963; 59 D Garagash (9784_CR10) 2000; 67 IN Sneddon (9784_CR36) 1946; 187 M Gutiérrez (9784_CR13) 2017 B Lecampion (9784_CR20) 2009; 25 EW Remij (9784_CR32) 2015; 286 |
| References_xml | – volume: 90 start-page: 43 issue: 1 year: 2008 end-page: 69 ident: CR3 article-title: Asymptotic analysis of an elasticity equation for a finger-like hydraulic fracture publication-title: J. Elast. doi: 10.1007/s10659-007-9122-4 – year: 1957 ident: CR15 publication-title: API-57-261, chap. Optimum Fluid Characteristics for Fracture Extension – volume: 67 start-page: 183 issue: 1 year: 2000 end-page: 192 ident: CR10 article-title: The tip region of a fluid-driven fracture in an elastic medium publication-title: Trans.-Amer. Soc. Mech. Eng. J. Appl. Mech. doi: 10.1115/1.321162 – volume: 12 start-page: 145 issue: 2 year: 1995 end-page: 174 ident: CR26 article-title: A combined finite-discrete element method in transient dynamics of fracturing solids publication-title: Eng. Comput. doi: 10.1108/02644409510799532 – ident: CR47 – volume: 44 start-page: 739 issue: 5 year: 2007 end-page: 757 ident: CR2 article-title: Computer simulation of hydraulic fractures publication-title: Int. J. Rock Mech. Mining Sci. doi: 10.1016/j.ijrmms.2006.11.006 – volume: 21 start-page: 1 issue: 12 year: 1969 end-page: 571 ident: CR11 article-title: A rapid method of predicting width and extent of hydraulically induced fractures publication-title: J. Petrol. Tech. doi: 10.2118/2458-PA – ident: CR4 – volume: 800 start-page: 1 issue: 57 year: 2012 end-page: 147 ident: CR5 article-title: Recommendation for key management part 1: General (revision 3) publication-title: NIST Spec. Publ. – ident: CR39 – ident: CR16 – volume: 61 start-page: 609 issue: 2 year: 1965 end-page: 611 ident: CR37 article-title: A note on the problem of the penny-shaped crack publication-title: Math. Proc. Camb. Philos. Soc. doi: 10.1017/S0305004100004175 – ident: CR30 – volume: 162 start-page: 150 year: 2018 end-page: 157 ident: CR46 article-title: Reliability analysis models for hydraulic fracturing publication-title: J. Pet. Sci. Eng. doi: 10.1016/j.petrol.2017.12.048 – volume: 19 start-page: 1171 issue: 6 year: 2015 end-page: 1195 ident: CR25 article-title: Phase-field modeling of a fluid-driven fracture in a poroelastic medium publication-title: Comput. Geosci. doi: 10.1007/s10596-015-9532-5 – volume: 77 start-page: 274 issue: 3 year: 2011 end-page: 285 ident: CR40 article-title: Finite element modeling of hydraulic fracturing on a reservoir scale in 2d publication-title: J. Pet. Sci. Eng. doi: 10.1016/j.petrol.2011.04.001 – volume: 26 start-page: 579 issue: 6 year: 2002 end-page: 604 ident: CR1 article-title: Self-similar solution of a plane-strain fracture driven by a power-law fluid publication-title: Int. J. Numer. Anal. Methods Geomech. doi: 10.1002/nag.213 – volume: 304 start-page: 619 year: 2016 end-page: 655 ident: CR24 article-title: Phase field modeling of fracture in multi-physics problems. Part III. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2015.09.021 – ident: CR6 – ident: CR29 – volume: 18 start-page: 27 issue: 01 year: 1978 end-page: 32 ident: CR35 article-title: Containment of massive hydraulic fractures publication-title: Soc. Pet. Eng. J. doi: 10.2118/6089-PA – volume: 15 start-page: 131 issue: 2 year: 1966 end-page: 134 ident: CR21 article-title: A note on Griffith cracks publication-title: Proc. Edinb. Math. Soc. doi: 10.1017/S0013091500011457 – volume: 96 start-page: 264 year: 2016 end-page: 290 ident: CR43 article-title: Phase-field modeling of hydraulic fracture publication-title: J. Mech. Phys. Solids doi: 10.1016/j.jmps.2016.07.019 – volume: 22 start-page: 423 issue: 1 year: 2018 end-page: 437 ident: CR33 article-title: On the numerical simulation of crack interaction in hydraulic fracturing publication-title: Comput. Geosci. doi: 10.1007/s10596-017-9702-8 – start-page: 1 year: 2017 end-page: 25 ident: CR13 publication-title: Stochastic Finite Element Methods, chap. 20 – year: 2013 ident: CR17 publication-title: Mathematics of Statistics – volume: 81 start-page: 317 year: 2010 end-page: 339 ident: CR19 article-title: A reexamination of the classical PKN model of hydraulic fracture publication-title: Transp. Porous Media doi: 10.1007/s11242-009-9403-4 – volume: 22 start-page: 1393 issue: 9 year: 1989 ident: CR22 article-title: A simple two-dimensional model for crack propagation publication-title: J. Phys. A Math. Gen. doi: 10.1088/0305-4470/22/9/026 – volume: 1 start-page: 449 issue: 06 year: 1986 end-page: 466 ident: CR34 article-title: Development and testing of a pseudo-three-dimensional model of hydraulic fracture geometry publication-title: SPE Prod. Eng. doi: 10.2118/10505-PA – ident: CR44 – volume: 187 start-page: 229 issue: 1009 year: 1946 end-page: 260 ident: CR36 article-title: The distribution of stress in the neighbourhood of a crack in an elastic solid publication-title: Proc. R. Soc. London A: Math. Phys. Eng. Sci. doi: 10.1098/rspa.1946.0077 – volume: 72 start-page: 310 issue: 3 year: 2010 end-page: 317 ident: CR45 article-title: Three-dimensional finite element simulation and parametric study for horizontal well hydraulic fracture publication-title: J. Pet. Sci. Eng. doi: 10.1016/j.petrol.2010.03.032 – volume: 271 start-page: 69 year: 2014 end-page: 85 ident: CR42 article-title: An augmented-Lagrangian method for the phase-field approach for pressurized fractures publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2013.12.005 – ident: CR48 – volume: 59 start-page: 489 issue: 2 year: 1963 end-page: 500 ident: CR8 article-title: Some two-dimensional punch and crack problems in classical elasticity publication-title: Math. Proc. Camb. Philos. Soc. doi: 10.1017/S0305004100037099 – volume: 139 start-page: 289 issue: 1-4 year: 1996 end-page: 314 ident: CR23 article-title: The partition of unity finite element method: basic theory and applications publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/S0045-7825(96)01087-0 – volume: 286 start-page: 293 year: 2015 end-page: 312 ident: CR32 article-title: The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2014.12.025 – volume: 115 start-page: 1035 issue: 5 year: 1989 end-page: 1053 ident: CR38 article-title: Stochastic finite element expansion for random media publication-title: J. Eng. Mech. doi: 10.1061/(ASCE)0733-9399(1989)115:5(1035) – ident: CR31 – volume: 253 start-page: 305 year: 2013 end-page: 322 ident: CR12 article-title: Coupling schemes for modeling hydraulic fracture propagation using the xfem publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2012.08.017 – volume: 18 start-page: 613 issue: 5 year: 2014 end-page: 624 ident: CR9 article-title: Modeling fluid injection in fractures with a reservoir simulator coupled to a boundary element method publication-title: Comput. Geosci. doi: 10.1007/s10596-013-9396-5 – volume: 21 start-page: 435 issue: 04 year: 1981 end-page: 443 ident: CR14 article-title: Effects of various parameters on hydraulic fracturing geometry publication-title: Soc. Pet. Eng. J. doi: 10.2118/8942-PA – volume: 112 start-page: 85 issue: 1 year: 1986 end-page: 104 ident: CR18 article-title: Structural reliability under incomplete probability information publication-title: J. Eng. Mech. doi: 10.1061/(ASCE)0733-9399(1986)112:1(85) – ident: CR7 – volume: 236 start-page: 333 issue: 767 year: 1937 end-page: 380 ident: CR27 article-title: Outline of a theory of statistical estimation based on the classical theory of probability publication-title: Philos. Trans. R. Soc. London. Series A Math. Phys. Sci. doi: 10.1098/rsta.1937.0005 – ident: CR41 – volume: 36 start-page: 861 issue: 5 year: 1999 end-page: 875 ident: CR28 article-title: A case study of hydraulic fracturing using finite element methods publication-title: Can. Geotech. J. doi: 10.1139/t99-049 – volume: 25 start-page: 121 issue: 2 year: 2009 end-page: 133 ident: CR20 article-title: An extended finite element method for hydraulic fracture problems publication-title: Commun. Numer. Methods Eng. doi: 10.1002/cnm.1111 – ident: 9784_CR48 doi: 10.1029/GM122p0213 – volume: 36 start-page: 861 issue: 5 year: 1999 ident: 9784_CR28 publication-title: Can. Geotech. J. doi: 10.1139/t99-049 – volume: 115 start-page: 1035 issue: 5 year: 1989 ident: 9784_CR38 publication-title: J. Eng. Mech. doi: 10.1061/(ASCE)0733-9399(1989)115:5(1035) – ident: 9784_CR29 doi: 10.2118/3009-PA – ident: 9784_CR41 doi: 10.2172/10176839 – volume: 304 start-page: 619 year: 2016 ident: 9784_CR24 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2015.09.021 – volume: 67 start-page: 183 issue: 1 year: 2000 ident: 9784_CR10 publication-title: Trans.-Amer. Soc. Mech. Eng. J. Appl. Mech. doi: 10.1115/1.321162 – volume: 12 start-page: 145 issue: 2 year: 1995 ident: 9784_CR26 publication-title: Eng. Comput. doi: 10.1108/02644409510799532 – ident: 9784_CR6 doi: 10.1017/CBO9780511800955 – ident: 9784_CR39 – volume: 72 start-page: 310 issue: 3 year: 2010 ident: 9784_CR45 publication-title: J. Pet. Sci. Eng. doi: 10.1016/j.petrol.2010.03.032 – volume: 271 start-page: 69 year: 2014 ident: 9784_CR42 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2013.12.005 – volume: 21 start-page: 1 issue: 12 year: 1969 ident: 9784_CR11 publication-title: J. Petrol. Tech. doi: 10.2118/2458-PA – ident: 9784_CR31 doi: 10.2118/89-PA – ident: 9784_CR30 – volume: 253 start-page: 305 year: 2013 ident: 9784_CR12 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2012.08.017 – volume: 112 start-page: 85 issue: 1 year: 1986 ident: 9784_CR18 publication-title: J. Eng. Mech. doi: 10.1061/(ASCE)0733-9399(1986)112:1(85) – volume: 286 start-page: 293 year: 2015 ident: 9784_CR32 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2014.12.025 – volume: 236 start-page: 333 issue: 767 year: 1937 ident: 9784_CR27 publication-title: Philos. Trans. R. Soc. London. Series A Math. Phys. Sci. doi: 10.1098/rsta.1937.0005 – volume: 18 start-page: 27 issue: 01 year: 1978 ident: 9784_CR35 publication-title: Soc. Pet. Eng. J. doi: 10.2118/6089-PA – volume-title: Mathematics of Statistics year: 2013 ident: 9784_CR17 – volume: 162 start-page: 150 year: 2018 ident: 9784_CR46 publication-title: J. Pet. Sci. Eng. doi: 10.1016/j.petrol.2017.12.048 – volume: 139 start-page: 289 issue: 1-4 year: 1996 ident: 9784_CR23 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/S0045-7825(96)01087-0 – volume: 22 start-page: 423 issue: 1 year: 2018 ident: 9784_CR33 publication-title: Comput. Geosci. doi: 10.1007/s10596-017-9702-8 – volume: 61 start-page: 609 issue: 2 year: 1965 ident: 9784_CR37 publication-title: Math. Proc. Camb. Philos. Soc. doi: 10.1017/S0305004100004175 – volume: 15 start-page: 131 issue: 2 year: 1966 ident: 9784_CR21 publication-title: Proc. Edinb. Math. Soc. doi: 10.1017/S0013091500011457 – volume: 77 start-page: 274 issue: 3 year: 2011 ident: 9784_CR40 publication-title: J. Pet. Sci. Eng. doi: 10.1016/j.petrol.2011.04.001 – volume: 25 start-page: 121 issue: 2 year: 2009 ident: 9784_CR20 publication-title: Commun. Numer. Methods Eng. doi: 10.1002/cnm.1111 – ident: 9784_CR44 – volume: 800 start-page: 1 issue: 57 year: 2012 ident: 9784_CR5 publication-title: NIST Spec. Publ. – ident: 9784_CR7 doi: 10.1146/annurev-fluid-010814-014736 – volume: 96 start-page: 264 year: 2016 ident: 9784_CR43 publication-title: J. Mech. Phys. Solids doi: 10.1016/j.jmps.2016.07.019 – volume-title: API-57-261, chap. Optimum Fluid Characteristics for Fracture Extension year: 1957 ident: 9784_CR15 – volume: 44 start-page: 739 issue: 5 year: 2007 ident: 9784_CR2 publication-title: Int. J. Rock Mech. Mining Sci. doi: 10.1016/j.ijrmms.2006.11.006 – volume: 21 start-page: 435 issue: 04 year: 1981 ident: 9784_CR14 publication-title: Soc. Pet. Eng. J. doi: 10.2118/8942-PA – start-page: 1 volume-title: Stochastic Finite Element Methods, chap. 20 year: 2017 ident: 9784_CR13 – volume: 26 start-page: 579 issue: 6 year: 2002 ident: 9784_CR1 publication-title: Int. J. Numer. Anal. Methods Geomech. doi: 10.1002/nag.213 – volume: 19 start-page: 1171 issue: 6 year: 2015 ident: 9784_CR25 publication-title: Comput. Geosci. doi: 10.1007/s10596-015-9532-5 – ident: 9784_CR4 doi: 10.2118/8941-PA – volume: 90 start-page: 43 issue: 1 year: 2008 ident: 9784_CR3 publication-title: J. Elast. doi: 10.1007/s10659-007-9122-4 – volume: 59 start-page: 489 issue: 2 year: 1963 ident: 9784_CR8 publication-title: Math. Proc. Camb. Philos. Soc. doi: 10.1017/S0305004100037099 – volume: 22 start-page: 1393 issue: 9 year: 1989 ident: 9784_CR22 publication-title: J. Phys. A Math. Gen. doi: 10.1088/0305-4470/22/9/026 – volume: 187 start-page: 229 issue: 1009 year: 1946 ident: 9784_CR36 publication-title: Proc. R. Soc. London A: Math. Phys. Eng. Sci. doi: 10.1098/rspa.1946.0077 – volume: 1 start-page: 449 issue: 06 year: 1986 ident: 9784_CR34 publication-title: SPE Prod. Eng. doi: 10.2118/10505-PA – ident: 9784_CR16 doi: 10.2118/18959-PA – volume: 81 start-page: 317 year: 2010 ident: 9784_CR19 publication-title: Transp. Porous Media doi: 10.1007/s11242-009-9403-4 – volume: 18 start-page: 613 issue: 5 year: 2014 ident: 9784_CR9 publication-title: Comput. Geosci. doi: 10.1007/s10596-013-9396-5 – ident: 9784_CR47 |
| SSID | ssj0009731 |
| Score | 2.216678 |
| Snippet | Hydraulic fracturing processes are surrounded by uncertainty, as available data is typically scant. In this work, we present a sampling-based stochastic... The final publication is available at Springer via http://dx.doi.org/10.1007/s10596-018-9784-y Hydraulic fracturing processes are surrounded by uncertainty, as... |
| SourceID | csuc proquest crossref springer |
| SourceType | Open Access Repository Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 81 |
| SubjectTerms | 49 Calculus of variations and optimal control; optimization 49Q Manifolds 58 Global analysis, analysis on manifolds 58J Partial differential equations on manifolds; differential operators 60 Probability theory and stochastic processes 60H Stochastic analysis Analysis Anàlisi estocàstica Classificació AMS Computation Computer simulation Differential equations, Partial Earth and Environmental Science Earth Sciences Elastic properties Equacions diferencials parcials Equation of continuity Finite element method Geometria Geotechnical Engineering & Applied Earth Sciences Hydraulic fracturing Hydrogeology Investigació operativa Iterative methods Iterative solution Lagrange multiplier Manifolds (Mathematics) Matemàtiques i estadística Mathematical Modeling and Industrial Mathematics Mathematical models Monte Carlo simulation Monte-Carlo method Moving-boundary problem Optimització Original Paper Parameters Perkins-Kern-Nordgren model Pollution Probabilitat Random fields Random variables Sampling Sensitivity analysis Soil Science & Conservation Solution space Solutions Stochastic analysis Stochastic processes Time dependence Tip speed Varietats (Matematiques) Àrees temàtiques de la UPC |
| SummonAdditionalLinks | – databaseName: Science Database dbid: M2P link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lb9QwEB7BAhIXylMsFOQDJ1CE7TivE0KoBQlYrQRIvVmTsU0rVbtlH5X233cmm3TVSu2FQw5WHCfKZ3tm7PH3AbxrTE5Ju8AIYOQApWiztsUiM8EknQJiWWInNlFNJvXRUTPtF9yWfVrlMCd2E3WYk6yRf7RGmLpEoPvT2b9MVKNkd7WX0LgL99izMZLS9dNOd6S7VadHaJyVDd-mGnY1t0fnCkm_NTzcq9plmyt2aUTLNV3xOa9tk3bW53Dvf7_7MTzq_U71edtRnsCdOHsKD752ur6bZ_DjF0pq-exvJmYtKHYJ6RiFw1lhT1ui5kmxt6im3yeq089R7O-q401Y4PqU6yU5b9UdenwOfw4Pfn_5lvVCCxk661ZZiTHqMtQ1W7NaB7JFKhLHq4FQp1RqzC1xib2LvC3JNRhQa8oNcvhT5WXIX8BoNp_Fl6AoUVGX3FKVjIumqoljThut1RRdq5sx6OE3e-pZyEUM49Tv-JMFGc_IeEHGb8bw_vKRsy0Fx-2VGTvP5iIuCFde6LMvC3JZXVmf5xxGuTHsD5j5fugu_Q6wMXwYUN_dvvHNr25v7DU8ZF-r2SZ878NotVjHN3Cfzlcny8Xbrt9eAOeC8q0 priority: 102 providerName: ProQuest |
| Title | Sampling-based stochastic analysis of the PKN model for hydraulic fracturing |
| URI | https://link.springer.com/article/10.1007/s10596-018-9784-y https://www.proquest.com/docview/2135819082 https://recercat.cat/handle/2072/337474 |
| Volume | 23 |
| WOSCitedRecordID | wos000459423400005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: AAdvanced Technologies & Aerospace Database (subscription) customDbUrl: eissn: 1573-1499 dateEnd: 20241213 omitProxy: false ssIdentifier: ssj0009731 issn: 1420-0597 databaseCode: P5Z dateStart: 19970101 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1573-1499 dateEnd: 20241213 omitProxy: false ssIdentifier: ssj0009731 issn: 1420-0597 databaseCode: K7- dateStart: 19970101 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Earth, Atmospheric & Aquatic Science Database customDbUrl: eissn: 1573-1499 dateEnd: 20241213 omitProxy: false ssIdentifier: ssj0009731 issn: 1420-0597 databaseCode: PCBAR dateStart: 19970101 isFulltext: true titleUrlDefault: https://search.proquest.com/eaasdb providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1573-1499 dateEnd: 20241213 omitProxy: false ssIdentifier: ssj0009731 issn: 1420-0597 databaseCode: BENPR dateStart: 19970101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1573-1499 dateEnd: 20241213 omitProxy: false ssIdentifier: ssj0009731 issn: 1420-0597 databaseCode: M2P dateStart: 19970101 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1573-1499 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009731 issn: 1420-0597 databaseCode: RSV dateStart: 19970401 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dS9xAEB_0tNCXam1Lr9VjH_pUCexuNtnksS3agvYI2or0ZZnsRy3IWe5DuP_e2VziqaigD1lYstmEmd3MDDvz-wF8KkVqA1eONICeApSsTuoas0Q4EXhwiHmODdmEHg6L09Oyauu4J122e3ck2fypbxS7ZTFhVtAG1YVK5quwRtauiHwNR8cnS6Rd3ZAQCiXjKW-pu6PM-6a4ZYx6djKztxzNO2ejjcnZ33jWx27Cq9bDZF8WS-I1rPjRFrz43jD4zt_A4THGJPLR3yQaMMfI-bNnGNGaGbYAJewiMPILWXUwZA1TDiPPlp3N3Rhn5zQuxMqqprzxLfze3_v17UfSUiokqKSaJjl6z3NXFGS3Cu6szEIWKDJ1FnkIOcdUWuqRH5HWuVUlOuTcpgIp0NFp7tJ30BtdjPx7YDbYrMhpJh2E8kIXlqJL6aXk1qual33gnWyNbfHGI-3FuVkiJUchGRKSiUIy8z58vn7k_wJs4_HBpDBDhsGPLU5NBMq-7sRLci1NmlLApPqw3anVtJt0YqSI4G-R870Pu50al7cffPOHJ43-CC_JySoXmd7b0JuOZ34H1u3l9N9kPIC1r3vD6mgAqwc6ofanrKitsj-DZlVfAbBO7YI |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Jb9QwFH4qA1W5sLWIoQV8gAsoqu0426FCVaG0mmE0EkXqzTheaKVqpswCyp_iN_Jelo6KRG89cMjBiuMo8Ze3xM_fB_C6ELENXDmcAeMxQUnKqCxNEgknAg_OmDQ1tdhENhrlp6fFeA1-d3thqKyys4m1oXZTS__Id6Ugpi4S6H5_-SMi1ShaXe0kNBpYDHz1C1O2-d7xB5zfN1Iefjw5OIpaVYHIKKkWUWq856nLczTdOXdWJiEJmJw5a3gIKTextNhCVxqXqVWFcYZzGwuDsX4Wpy7Gce_AXUXMYlQqKMcrkt-s1j8UStICc5F1q6jNVr2Eyn0FmpcsV1F1zQ_27Hxpr8W4fy3L1t7u8OH_9p4ewYM2rmb7zYfwGNb85Amsf6p1i6tNGH4xVDo_-R6R23YMQ157ZoijmpmWloVNA8NomI0HI1brAzGM59lZ5WZmeYH9Au0nqzd1bsHXW3mUp9CbTCf-GTAbbJKnOFIWhPIiyy3m1NJLya1XJS_6wLtp1bZlWSexjwu94ocmJGhEgiYk6KoPb68uuWwoRm7ujFjR6A79zJqFJnrwqwYdEnGp4xjTRNWHnQ4jujVNc70CSB_edShbnf7nnZ_fPNgr2Dg6-TzUw-PRYBvuY1xZNMXtO9BbzJb-BdyzPxfn89nL-pth8O22wfcH2y9PBQ |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Jb9QwFH4qwyIu7KgDBXyACyiq7ThxckAIUQaqqUYjAVLFxTheaKVqpswCyl_j1_Felo6KRG89cMjBiuMo8Ze35C0fwPNSpC5y5XEHbEAHJauSqrJZIryIPHpr89w2ZBN6MikOD8vpFvzua2EorbKXiY2g9nNH_8h3paBOXUTQvRu7tIjp3ujN6Y-EGKQo0trTabQQGYf6F7pvy9f7e7jXL6Qcvf_87mPSMQwkVkm1SnIbAs99UaAYL7h3MotZREfNO8tjzLlNpcMRqtW0yp0qrbecu1RYtPt1mvsU170CVzX6mJROOM2-bhr-6oYLUShJweZS9xHVtmwvo9RfgaJGFyqpz-nEgVuu3Tl7968QbaP5Rrf_53d2B2519jZ7234gd2ErzO7B9Q8Nn3F9Hw4-WUqpn31PSJ17hqawO7LUu5rZrl0Lm0eGVjKbjies4Q1iaOezo9ov7PoE50WqM2uKPR_Al0t5lIcwmM1nYRuYiy4rclxJR6GC0IVDX1sGKbkLquLlEHi_xcZ13deJBOTEbPpGEyoMosIQKkw9hJdnl5y2rUcunoy4Magmw8LZlaG24WcDOiTX0qQpuo9qCDs9XkwnspZmA5YhvOoRtzn9zzs_unixZ3ADMWcO9ifjx3ATzc2yzXnfgcFqsQ5P4Jr7uTpeLp42nw-Db5eNvT9YYFfx |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Sampling-based+stochastic+analysis+of+the+PKN+model+for+hydraulic+fracturing&rft.jtitle=Computational+geosciences&rft.au=Garikapati%2C+Hasini&rft.au=Verhoosel%2C+Clemens+V.&rft.au=van+Brummelen%2C+E.+Harald&rft.au=Zlotnik%2C+Sergio&rft.date=2019-02-01&rft.issn=1420-0597&rft.eissn=1573-1499&rft.volume=23&rft.issue=1&rft.spage=81&rft.epage=105&rft_id=info:doi/10.1007%2Fs10596-018-9784-y&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10596_018_9784_y |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1420-0597&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1420-0597&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1420-0597&client=summon |