Improved algorithms for generalized finite element simulations of three‐dimensional hydraulic fracture propagation
Summary This paper reports improvements to algorithms for the simulation of 3‐D hydraulic fracturing with the Generalized Finite Element Method (GFEM). Three optimizations are presented and analyzed. First, an improved initial guess based on solving a 3‐D elastic problem with the pressure from the p...
Saved in:
| Published in | International journal for numerical and analytical methods in geomechanics Vol. 43; no. 18; pp. 2707 - 2742 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Bognor Regis
Wiley Subscription Services, Inc
25.12.2019
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0363-9061 1096-9853 |
| DOI | 10.1002/nag.2977 |
Cover
| Abstract | Summary
This paper reports improvements to algorithms for the simulation of 3‐D hydraulic fracturing with the Generalized Finite Element Method (GFEM). Three optimizations are presented and analyzed. First, an improved initial guess based on solving a 3‐D elastic problem with the pressure from the previous step is shown to decrease the number of Newton iterations and increase robustness. Second, an improved methodology to find the time step that leads to fracture propagation is proposed and shown to decrease significantly the number of iterations. Third, reduced computational cost is observed by properly recycling the linear part of the coupled stiffness matrix. Two representative examples are used to analyze these improvements. Additionally, a methodology to include the leak‐off term is presented and verified against asymptotic analytical solutions. Conservation of mass is shown to be well satisfied in all examples. |
|---|---|
| AbstractList | Summary
This paper reports improvements to algorithms for the simulation of 3‐D hydraulic fracturing with the Generalized Finite Element Method (GFEM). Three optimizations are presented and analyzed. First, an improved initial guess based on solving a 3‐D elastic problem with the pressure from the previous step is shown to decrease the number of Newton iterations and increase robustness. Second, an improved methodology to find the time step that leads to fracture propagation is proposed and shown to decrease significantly the number of iterations. Third, reduced computational cost is observed by properly recycling the linear part of the coupled stiffness matrix. Two representative examples are used to analyze these improvements. Additionally, a methodology to include the leak‐off term is presented and verified against asymptotic analytical solutions. Conservation of mass is shown to be well satisfied in all examples. This paper reports improvements to algorithms for the simulation of 3‐D hydraulic fracturing with the Generalized Finite Element Method (GFEM). Three optimizations are presented and analyzed. First, an improved initial guess based on solving a 3‐D elastic problem with the pressure from the previous step is shown to decrease the number of Newton iterations and increase robustness. Second, an improved methodology to find the time step that leads to fracture propagation is proposed and shown to decrease significantly the number of iterations. Third, reduced computational cost is observed by properly recycling the linear part of the coupled stiffness matrix. Two representative examples are used to analyze these improvements. Additionally, a methodology to include the leak‐off term is presented and verified against asymptotic analytical solutions. Conservation of mass is shown to be well satisfied in all examples. |
| Author | Duarte, Carlos Armando Shauer, Nathan |
| Author_xml | – sequence: 1 givenname: Nathan orcidid: 0000-0002-4703-9928 surname: Shauer fullname: Shauer, Nathan organization: University of Illinois at Urbana‐Champaign – sequence: 2 givenname: Carlos Armando orcidid: 0000-0002-0048-0679 surname: Duarte fullname: Duarte, Carlos Armando email: caduarte@illinois.edu organization: University of Illinois at Urbana‐Champaign |
| BookMark | eNp1kM1KAzEUhYNUsK2CjxBw42ZqMpmfZFmK1kLRja6HNL1pUzIzNckodeUj-Iw-iWnrSnR14Z7v3Hs4A9Rr2gYQuqRkRAlJbxq5GqWiLE9QnxJRJILnrIf6hBUsEaSgZ2jg_YYQkke1j8Ks3rr2FZZY2lXrTFjXHuvW4RU04KQ171HSpjEBMFiooQnYm7qzMpi28bjVOKwdwNfH59JE1cettHi9WzrZWaOwdlKFzgGOb7ZydbCdo1MtrYeLnzlEz3e3T5P7ZP44nU3G80QyWpQJcJ2WilNNFdWFoixlMstUWcapi1JQJQhTDATlWpA0EwsuGXDJRXQvUsmG6Op4N_5-6cCHatN2LubzVcponvOcZ2mkRkdKudZ7B7pSJhxyBieNrSip9s1Wsdlq32w0XP8ybJ2ppdv9hSZH9M1Y2P3LVQ_j6YH_BggHjN8 |
| CitedBy_id | crossref_primary_10_1002_nme_6945 crossref_primary_10_1016_j_engfracmech_2020_107098 crossref_primary_10_1016_j_petsci_2023_03_015 crossref_primary_10_1016_j_cma_2021_114154 crossref_primary_10_1016_j_engfracmech_2022_108783 crossref_primary_10_1016_j_engfracmech_2022_108360 crossref_primary_10_1007_s40948_022_00460_9 crossref_primary_10_1007_s11440_021_01184_y crossref_primary_10_1002_nag_3378 crossref_primary_10_1016_j_compgeo_2024_106267 crossref_primary_10_1007_s11440_022_01557_x crossref_primary_10_1002_nme_6852 crossref_primary_10_1002_nme_6935 crossref_primary_10_1016_j_cma_2024_116940 crossref_primary_10_1016_j_tafmec_2024_104747 crossref_primary_10_1016_j_engfracmech_2022_108874 crossref_primary_10_3390_su162411087 crossref_primary_10_1007_s40430_019_1945_y crossref_primary_10_1155_2020_8881901 crossref_primary_10_1007_s10704_022_00623_5 crossref_primary_10_1002_fld_5129 crossref_primary_10_1002_nag_3383 crossref_primary_10_1016_j_cma_2022_114639 crossref_primary_10_1016_j_tafmec_2024_104382 crossref_primary_10_1007_s00603_022_02989_3 crossref_primary_10_1016_j_cma_2021_114136 crossref_primary_10_1007_s10704_021_00535_w crossref_primary_10_1002_nag_3603 crossref_primary_10_1016_j_cma_2020_113606 |
| Cites_doi | 10.1007/BF01201264 10.1002/nag.581 10.1016/j.engfracmech.2014.08.002 10.1002/nag.2305 10.1016/j.cma.2013.07.010 10.1002/nag.2557 10.1115/1.3656897 10.1016/0142-1123(88)90061-8 10.1016/S0045-7825(96)01087-0 10.1016/S0045-7825(96)01085-7 10.1137/S1064827597323373 10.1016/j.jmps.2015.05.010 10.1002/nme.2419 10.2118/144326-MS 10.1002/(SICI)1098-2426(199611)12:6<673::AID-NUM3>3.0.CO;2-P 10.1002/nag.2719 10.1016/j.cma.2010.11.013 10.1142/S0219876204000083 10.1002/2017JB014740 10.1016/j.jmps.2016.07.019 10.1016/S0045-7825(97)00039-X 10.1137/0731051 10.1002/nag.2485 10.1016/j.jngse.2017.10.012 10.1016/j.cma.2015.09.021 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J 10.1002/2016JB013183 10.1016/j.jmps.2015.04.006 10.1016/j.ijrmms.2006.11.006 10.1007/BF00033829 10.1016/j.cma.2016.02.037 10.2118/166259-MS 10.1023/A:1020980311611 10.1016/j.engfracmech.2017.03.035 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N 10.1016/S0045-7825(00)00233-4 10.1016/j.cma.2014.08.024 10.1016/j.chemer.2010.05.016 10.1007/978-3-319-39022-2_6 10.2118/84-35-28 10.1007/s10704-005-0154-0 10.1007/s10704-018-0302-y 10.2118/96968-MS 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S 10.1016/S0020-7683(02)00492-4 10.1016/j.ijrmms.2016.07.020 10.1098/rsta.2015.0423 10.1016/j.cma.2008.01.013 10.1002/nag.2565 10.2118/173363-MS 10.1007/s00466-010-0491-3 |
| ContentType | Journal Article |
| Copyright | 2019 John Wiley & Sons, Ltd. |
| Copyright_xml | – notice: 2019 John Wiley & Sons, Ltd. |
| DBID | AAYXX CITATION 7SC 7UA 8FD C1K F1W FR3 H96 JQ2 KR7 L.G L7M L~C L~D |
| DOI | 10.1002/nag.2977 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Water Resources Abstracts Technology Research Database Environmental Sciences and Pollution Management ASFA: Aquatic Sciences and Fisheries Abstracts Engineering Research Database Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources ProQuest Computer Science Collection Civil Engineering Abstracts Aquatic Science & Fisheries Abstracts (ASFA) Professional Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Aquatic Science & Fisheries Abstracts (ASFA) Professional Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest Computer Science Collection Computer and Information Systems Abstracts Water Resources Abstracts Environmental Sciences and Pollution Management Computer and Information Systems Abstracts Professional Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources ASFA: Aquatic Sciences and Fisheries Abstracts Engineering Research Database Advanced Technologies Database with Aerospace |
| DatabaseTitleList | CrossRef Civil Engineering Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1096-9853 |
| EndPage | 2742 |
| ExternalDocumentID | 10_1002_nag_2977 NAG2977 |
| Genre | article |
| GrantInformation_xml | – fundername: Corporate Strategic Research, ExxonMobil Research and Engineering Company funderid: EM09099.A3 |
| GroupedDBID | -~X .3N .GA 05W 0R~ 10A 1L6 1OB 1OC 1ZS 33P 3SF 3WU 4.4 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5GY 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHHS AAHQN AAMNL AANLZ AAONW AASGY AAXRX AAYCA AAZKR ABCQN ABCUV ABIJN ABJNI ACAHQ ACCFJ ACCZN ACGFS ACIWK ACPOU ACXBN ACXQS ADBBV ADEOM ADIZJ ADKYN ADMGS ADOZA ADXAS ADZMN ADZOD AEEZP AEIGN AEIMD AENEX AEQDE AEUQT AEUYR AFBPY AFFPM AFGKR AFPWT AFRAH AFWVQ AHBTC AITYG AIURR AIWBW AJBDE AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN ALVPJ AMBMR AMYDB ATUGU AUFTA AZBYB AZVAB BAFTC BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BY8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS F00 F01 F04 G-S G.N GNP GODZA H.T H.X HBH HGLYW HHY HZ~ IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LYRES MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 N9A NF~ NNB O66 O9- OIG P2P P2W P2X P4D Q.N Q11 QB0 QRW R.K ROL RWI RWS RX1 RYL SUPJJ TN5 UB1 V2E W8V W99 WBKPD WIB WIH WIK WLBEL WOHZO WQJ WRC WXSBR WYISQ XG1 XPP XV2 ZZTAW ~02 ~IA ~WT AAMMB AAYXX AEFGJ AEYWJ AGHNM AGXDD AGYGG AIDQK AIDYY CITATION 7SC 7UA 8FD C1K F1W FR3 H96 JQ2 KR7 L.G L7M L~C L~D |
| ID | FETCH-LOGICAL-a3167-e8f27c81f1c1f6c1323a44c7723af6791c903c3e918f90249b8a3e8a89167b2a3 |
| IEDL.DBID | DR2 |
| ISSN | 0363-9061 |
| IngestDate | Sun Jul 13 04:38:21 EDT 2025 Wed Oct 01 03:41:38 EDT 2025 Thu Apr 24 22:56:10 EDT 2025 Wed Jan 22 16:39:07 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 18 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a3167-e8f27c81f1c1f6c1323a44c7723af6791c903c3e918f90249b8a3e8a89167b2a3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-4703-9928 0000-0002-0048-0679 |
| PQID | 2315585842 |
| PQPubID | 996377 |
| PageCount | 36 |
| ParticipantIDs | proquest_journals_2315585842 crossref_citationtrail_10_1002_nag_2977 crossref_primary_10_1002_nag_2977 wiley_primary_10_1002_nag_2977_NAG2977 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 25 December 2019 |
| PublicationDateYYYYMMDD | 2019-12-25 |
| PublicationDate_xml | – month: 12 year: 2019 text: 25 December 2019 day: 25 |
| PublicationDecade | 2010 |
| PublicationPlace | Bognor Regis |
| PublicationPlace_xml | – name: Bognor Regis |
| PublicationTitle | International journal for numerical and analytical methods in geomechanics |
| PublicationYear | 2019 |
| Publisher | Wiley Subscription Services, Inc |
| Publisher_xml | – name: Wiley Subscription Services, Inc |
| References | 1995; 74 1987; 2 2017; 41 1997; 40 2005; 134 2016; 305 1963; 85 2018; 123 1999; 46 2002; 117 1999; 45 2016; 304 2004; 1 2007; 31 2018; 42 2014; 131 2018; 49 1998; 153 2015; 82 2000 2018; 213 2016; 41 1984 2016; 40 1981 2010; 70 2017; 122 2008; 197 2011; 200 1996; 139 2016; 88 1994; 31 2015; 283 2002; 39 2011 2000; 22 1988; 10 2013; 266 2016; 96 2005 2017; 179 1957 1996; 12 1999 2009; 77 2010; 46 2001; 190 2014; 38 2018 2017 2016; 374 2016 2015 2013 2007; 44 e_1_2_12_4_1 e_1_2_12_19_1 e_1_2_12_2_1 e_1_2_12_17_1 Lecampion ABB (e_1_2_12_6_1) 2017 e_1_2_12_20_1 e_1_2_12_41_1 e_1_2_12_22_1 e_1_2_12_24_1 e_1_2_12_45_1 e_1_2_12_26_1 Zaman M (e_1_2_12_42_1) 2000 e_1_2_12_47_1 e_1_2_12_62_1 e_1_2_12_60_1 e_1_2_12_28_1 Howard GC (e_1_2_12_38_1) 1957 e_1_2_12_31_1 e_1_2_12_52_1 e_1_2_12_33_1 e_1_2_12_54_1 e_1_2_12_35_1 e_1_2_12_56_1 e_1_2_12_37_1 e_1_2_12_58_1 e_1_2_12_14_1 e_1_2_12_12_1 e_1_2_12_8_1 e_1_2_12_10_1 e_1_2_12_3_1 e_1_2_12_5_1 e_1_2_12_18_1 e_1_2_12_16_1 e_1_2_12_39_1 e_1_2_12_21_1 e_1_2_12_44_1 e_1_2_12_63_1 e_1_2_12_23_1 e_1_2_12_46_1 e_1_2_12_25_1 e_1_2_12_48_1 Huang Z (e_1_2_12_43_1) 2018 e_1_2_12_61_1 e_1_2_12_40_1 e_1_2_12_27_1 e_1_2_12_29_1 e_1_2_12_30_1 e_1_2_12_53_1 e_1_2_12_32_1 Carter R (e_1_2_12_49_1) 1957 e_1_2_12_55_1 e_1_2_12_34_1 e_1_2_12_57_1 e_1_2_12_36_1 e_1_2_12_59_1 e_1_2_12_15_1 e_1_2_12_13_1 Zienkiewicz O (e_1_2_12_50_1) 1981 e_1_2_12_11_1 e_1_2_12_7_1 e_1_2_12_51_1 e_1_2_12_9_1 |
| References_xml | – volume: 82 start-page: 235 year: 2015 end-page: 258 article-title: Simultaneous initiation and growth of multiple radial hydraulic fractures from a horizontal wellbore publication-title: J Mech Phys Solids – year: 1981 – volume: 31 start-page: 945 issue: 4 year: 1994 end-page: 981 article-title: special finite element methods for a class of second order elliptic problems with rough coefficients publication-title: SIAM J Numer Anal – year: 2005 – volume: 96 start-page: 264 year: 2016 end-page: 290 article-title: Phase‐field modeling of hydraulic fracture publication-title: J Mech Phys Solids – volume: 305 start-page: 111 year: 2016 end-page: 132 article-title: Pressure and fluid‐driven fracture propagation in porous media using an adaptive finite element phase field model publication-title: Comput Meth Appl Mech – volume: 179 start-page: 120 year: 2017 end-page: 153 article-title: Accuracy and robustness of stress intensity factor extraction methods for the generalized/eXtended Finite Element Method publication-title: Eng Fract Mech – volume: 139 start-page: 237 year: 1996 end-page: 262 article-title: An hp adaptive method using clouds publication-title: Comput Meth Appl Mech Eng – volume: 46 start-page: 431 issue: 3 year: 2010 end-page: 453 article-title: Three‐dimensional crack growth with hp‐generalized finite element and face offsetting methods publication-title: Comput Mech – volume: 41 year: 2017 article-title: A stabilized extended finite element framework for hydraulic fracturing simulations publication-title: Int J Numer Anal Methods Geomech – volume: 41 start-page: 627 year: 2016 end-page: 653 article-title: A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3‐dimensions publication-title: Int J Numer Anal Methods Geomech – volume: 85 start-page: 519 year: 1963 end-page: 525 article-title: On the crack extension in plates under plane loading and transverse shear publication-title: J Basic Eng – year: 2018 – volume: 40 start-page: 1402 issue: 10 year: 2016 end-page: 1437 article-title: Coupled formulation and algorithms for the simulation of non‐planar three‐dimensional hydraulic fractures using the generalized finite element method publication-title: Int J Numer Anal Methods Geomech – volume: 190 start-page: 2227 issue: 15‐17 year: 2001 end-page: 2262 article-title: Generalized finite element method for the simulation of three‐ dimensional dynamic crack propagation publication-title: Comput Methods Appl Mech Eng – volume: 77 start-page: 601 issue: 5 year: 2009 end-page: 633 article-title: hp‐Generalized FEM and crack surface representation for non‐planar 3‐D cracks publication-title: Int J Numer Methods Eng – volume: 1 start-page: 67 issue: 1 year: 2004 end-page: 103 article-title: Generalized finite element methods‐ main ideas, results and perspective international publication-title: Int J Comput Methods – volume: 45 start-page: 601 year: 1999 end-page: 620 article-title: Elastic crack growth in finite elements with minimal remeshing publication-title: Int J Numer Methods Eng – volume: 12 start-page: 673 year: 1996 end-page: 705 article-title: Hp clouds‐an hp meshless method publication-title: Numer Methods Partial Differential Equations – volume: 197 start-page: 33 year: 2008 end-page: 40 article-title: An implicit level set method for modeling hydraulically driven fractures publication-title: Comput Meth Appl Mech – volume: 46 start-page: 131 year: 1999 end-page: 150 article-title: A finite element method for crack growth without remeshing publication-title: Int J Numer Methods Eng – volume: 40 start-page: 727 year: 1997 end-page: 758 article-title: The partition of unity method publication-title: Int J Numer Methods Eng – year: 2015 – volume: 123 start-page: 2127 year: 2018 end-page: 2155 article-title: Phase field model of hydraulic fracturing in poroelastic media: fracture propagation, arrest, and branching under fluid injection and extraction publication-title: J Geophys Res Solid Earth – volume: 38 start-page: 1397 year: 2014 end-page: 1430 article-title: Simulation of non‐planar three‐dimensional hydraulic fracture propagation publication-title: Int J Numer Anal Methods Geomech – volume: 22 start-page: 431 issue: 2 year: 2000 end-page: 448 article-title: Locally adapted tetrahedral meshes using bisection publication-title: SIAM J Sci Comput – volume: 134 start-page: 175 year: 2005 end-page: 190 article-title: Toughness‐dominated hydraulic fracture with leak‐off publication-title: Int J Fract – volume: 49 start-page: 66 year: 2018 end-page: 83 article-title: Numerical methods for hydraulic fracture propagation: a review of recent trends publication-title: J Nat Gas Sci Eng – volume: 31 start-page: 331 year: 2007 end-page: 345 article-title: Mesh adaptation and transfer schemes for discrete fracture propagation in porous materials publication-title: Int J Numer Anal Meth Geomech – volume: 44 start-page: 739 year: 2007 end-page: 757 article-title: Computer simulation of hydraulic fractures publication-title: Int J Rock Mech Min Sci Geomech Abstr – volume: 213 start-page: 1 year: 2018 end-page: 16 article-title: The configurational‐forces view of the nucleation and propagation of fracture and healing in elastomers as a phase transitions publication-title: Int J Fract – volume: 139 start-page: 289 year: 1996 end-page: 314 article-title: The partition of unity finite element method: basic theory and applications publication-title: Comput Meth Appl Mech Eng – volume: 42 start-page: 143 issue: 1 year: 2018 end-page: 180 article-title: Coupled hydromechanical‐fracture simulations of nonplanar three‐dimensional hydraulic fracture propagation publication-title: Int J Numer Anal Methods Geomech – start-page: 297 year: 1999 – year: 2000 – start-page: 261 year: 1957 end-page: 270 article-title: Optimum fluid characteristics for fracture extension publication-title: Drilling and Prod Prac (API) – volume: 374 issue: 2078 year: 2016 article-title: Implicit level set algorithms for modelling hydraulic fracture propagation publication-title: Philos Trans R Soc Lond A Math Phys Eng Sci – start-page: 14 year: 2011 end-page: 16 – start-page: 261 year: 1957 end-page: 270 article-title: Derivation of the general equation for estimating the extent of the fractured area, Appendix to optimum fluid charecteristics for fracture extension publication-title: Drilling and Production Practices – year: 2016 – volume: 82 start-page: 186 year: 2015 end-page: 217 article-title: Minimization principles for the coupled problem of Darcy‐Biot‐type fluid transport in porous media linked to phase field modeling of fracture publication-title: J Mech Phys Solids – volume: 10 start-page: 187 year: 1988 end-page: 192 article-title: Three‐dimensional fatigue crack propagation analysis using the boundary element method publication-title: Int J Fatigue – volume: 74 start-page: 219 year: 1995 end-page: 251 article-title: boundary element method for two dimensional linear elastic fracture analysis publication-title: Int J Fract – year: 1984 – volume: 153 start-page: 117 year: 1998 end-page: 126 article-title: A new cloud‐based hp finite element method publication-title: Comput Meth Appl Mech Eng – volume: 131 start-page: 269 year: 2014 end-page: 281 article-title: A coupled finite element method for the numerical simulation of hydraulic fracturing with a condensation technique publication-title: Eng Fract Mech – volume: 39 start-page: 6311 issue: 26 year: 2002 end-page: 6337 article-title: Propagation of a penny‐shaped fluid‐driven fracture in an impermeable rock: asymptotic solutions publication-title: Int J Solids Struct – volume: 70 start-page: 107 year: 2010 end-page: 117 article-title: Hydraulic fracturing stimulation techniques and formation damage mechanisms—implications from laboratory testing of tight sandstone proppant systems publication-title: Chemie der Erde ‐ Geochemistry – volume: 283 start-page: 881 year: 2015 end-page: 908 article-title: Modeling multi‐scale processes in hydraulic fracture propagation using the implicit level set algorithm publication-title: Comput Methods Appl Mech Eng – volume: 122 year: 2017 article-title: Experiments versus theory for the initiation and propagation of radial hydraulic fractures in low permeability materials publication-title: J Geophys Res Solid Earth – volume: 88 start-page: 137 year: 2016 end-page: 150 article-title: A variational hydraulic fracturing model coupled to a reservoir simulator publication-title: Int J mRock Mech Min Sci – year: 2017 – volume: 117 start-page: 129 issue: 2 year: 2002 end-page: 141 article-title: A new criterion for the prediction of crack development in multiaxially loaded structures publication-title: Int J Fract – volume: 266 start-page: 23 year: 2013 end-page: 39 article-title: A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics publication-title: Comput Meth Appl Mech Eng – volume: 2 start-page: 167 year: 1987 end-page: 183 article-title: Boundary element modeling of crack propagation in three dimensions publication-title: Engng Comput – volume: 304 start-page: 619 year: 2016 end-page: 655 article-title: Phase field modeling of fracture in multi‐physics problems. Part III. crack driving forces in hydro‐poroelasticity and hydraulic fracturing of fluid‐saturated porous media publication-title: Comput Meth Appl Mech – volume: 200 start-page: 953 issue: 9‐12 year: 2011 end-page: 966 article-title: Numerical simulation of multiple 3D fracture propagation using arbitrary meshes publication-title: Comput Methods Appl Mech Eng – year: 2013 – ident: e_1_2_12_14_1 doi: 10.1007/BF01201264 – ident: e_1_2_12_10_1 doi: 10.1002/nag.581 – volume-title: Rock Mechanics and Engineering year: 2017 ident: e_1_2_12_6_1 – ident: e_1_2_12_41_1 doi: 10.1016/j.engfracmech.2014.08.002 – ident: e_1_2_12_47_1 doi: 10.1002/nag.2305 – ident: e_1_2_12_56_1 doi: 10.1016/j.cma.2013.07.010 – ident: e_1_2_12_40_1 doi: 10.1002/nag.2557 – start-page: 261 year: 1957 ident: e_1_2_12_49_1 article-title: Derivation of the general equation for estimating the extent of the fractured area, Appendix to optimum fluid charecteristics for fracture extension publication-title: Drilling and Production Practices – ident: e_1_2_12_52_1 doi: 10.1115/1.3656897 – ident: e_1_2_12_13_1 doi: 10.1016/0142-1123(88)90061-8 – ident: e_1_2_12_30_1 doi: 10.1016/S0045-7825(96)01087-0 – ident: e_1_2_12_31_1 doi: 10.1016/S0045-7825(96)01085-7 – volume-title: Modeling in Geomechanics year: 2000 ident: e_1_2_12_42_1 – ident: e_1_2_12_55_1 doi: 10.1137/S1064827597323373 – ident: e_1_2_12_3_1 doi: 10.1016/j.jmps.2015.05.010 – ident: e_1_2_12_35_1 doi: 10.1002/nme.2419 – ident: e_1_2_12_4_1 doi: 10.2118/144326-MS – ident: e_1_2_12_32_1 doi: 10.1002/(SICI)1098-2426(199611)12:6<673::AID-NUM3>3.0.CO;2-P – ident: e_1_2_12_37_1 doi: 10.1002/nag.2719 – ident: e_1_2_12_11_1 doi: 10.1016/j.cma.2010.11.013 – ident: e_1_2_12_34_1 doi: 10.1142/S0219876204000083 – volume-title: Hydraulic Fracture Modeling year: 2018 ident: e_1_2_12_43_1 – ident: e_1_2_12_18_1 doi: 10.1002/2017JB014740 – ident: e_1_2_12_21_1 doi: 10.1016/j.jmps.2016.07.019 – ident: e_1_2_12_33_1 doi: 10.1016/S0045-7825(97)00039-X – ident: e_1_2_12_28_1 doi: 10.1137/0731051 – ident: e_1_2_12_53_1 – ident: e_1_2_12_48_1 doi: 10.1002/nag.2485 – ident: e_1_2_12_61_1 – ident: e_1_2_12_7_1 – ident: e_1_2_12_9_1 doi: 10.1016/j.jngse.2017.10.012 – volume-title: The Finite Element Method year: 1981 ident: e_1_2_12_50_1 – ident: e_1_2_12_20_1 doi: 10.1016/j.cma.2015.09.021 – ident: e_1_2_12_46_1 doi: 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J – ident: e_1_2_12_24_1 doi: 10.1002/2016JB013183 – ident: e_1_2_12_19_1 doi: 10.1016/j.jmps.2015.04.006 – ident: e_1_2_12_8_1 doi: 10.1016/j.ijrmms.2006.11.006 – ident: e_1_2_12_15_1 doi: 10.1007/BF00033829 – ident: e_1_2_12_22_1 doi: 10.1016/j.cma.2016.02.037 – ident: e_1_2_12_16_1 doi: 10.2118/166259-MS – ident: e_1_2_12_51_1 doi: 10.1023/A:1020980311611 – ident: e_1_2_12_57_1 doi: 10.1016/j.engfracmech.2017.03.035 – ident: e_1_2_12_29_1 doi: 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N – start-page: 261 year: 1957 ident: e_1_2_12_38_1 article-title: Optimum fluid characteristics for fracture extension publication-title: Drilling and Prod Prac (API) – ident: e_1_2_12_54_1 doi: 10.1016/S0045-7825(00)00233-4 – ident: e_1_2_12_62_1 – ident: e_1_2_12_27_1 doi: 10.1016/j.cma.2014.08.024 – ident: e_1_2_12_2_1 doi: 10.1016/j.chemer.2010.05.016 – ident: e_1_2_12_12_1 doi: 10.1007/978-3-319-39022-2_6 – ident: e_1_2_12_39_1 doi: 10.2118/84-35-28 – ident: e_1_2_12_44_1 doi: 10.1007/s10704-005-0154-0 – ident: e_1_2_12_17_1 doi: 10.1007/s10704-018-0302-y – ident: e_1_2_12_63_1 doi: 10.2118/96968-MS – ident: e_1_2_12_45_1 doi: 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S – ident: e_1_2_12_58_1 doi: 10.1016/S0020-7683(02)00492-4 – ident: e_1_2_12_23_1 doi: 10.1016/j.ijrmms.2016.07.020 – ident: e_1_2_12_26_1 doi: 10.1098/rsta.2015.0423 – ident: e_1_2_12_25_1 doi: 10.1016/j.cma.2008.01.013 – ident: e_1_2_12_59_1 doi: 10.1002/nag.2565 – ident: e_1_2_12_60_1 – ident: e_1_2_12_5_1 doi: 10.2118/173363-MS – ident: e_1_2_12_36_1 doi: 10.1007/s00466-010-0491-3 |
| SSID | ssj0005096 |
| Score | 2.4207401 |
| Snippet | Summary
This paper reports improvements to algorithms for the simulation of 3‐D hydraulic fracturing with the Generalized Finite Element Method (GFEM). Three... This paper reports improvements to algorithms for the simulation of 3‐D hydraulic fracturing with the Generalized Finite Element Method (GFEM). Three... |
| SourceID | proquest crossref wiley |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 2707 |
| SubjectTerms | Algorithms Aquatic reptiles Computer applications Computer simulation Conservation of mass Crack propagation Exact solutions Finite element method finite element method (FEM) Fracture mechanics generalized finite element method (GFEM) high‐performance computing Hydraulic fracturing Matrix methods Stiffness matrix |
| Title | Improved algorithms for generalized finite element simulations of three‐dimensional hydraulic fracture propagation |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fnag.2977 https://www.proquest.com/docview/2315585842 |
| Volume | 43 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVWIB databaseName: Wiley Online Library - Core collection (SURFmarket) issn: 0363-9061 databaseCode: DR2 dateStart: 19960101 customDbUrl: isFulltext: true eissn: 1096-9853 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0005096 providerName: Wiley-Blackwell |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV07T8MwELYQEwy8EYWCjIRgSlvHSZqMFaJUSHRAVKrEENmO3Ub0gZJ0oBM_gd_IL-EcJ21BICGmDPHF8ePuPp_t7xC60KiTKt6wItujlsOlZ3GHMwuckw-qpQKShy7uu16n59z13X5xqlLfhTH8EIuAm9aM3F5rBWc8ra-QhrJBzQb0AuaXUDffoX1YMkdpVpNymzIAn1Xyzjbsein41RMt4eUqSM29THsbPZX_Zw6XPNdmGa-J-Tfqxv81YAdtFeATt8xs2UVrcrKHNlcoCfdRZqIMMsJsNJgmcTYcpxiALR4Yfup4Dq9UrJEqluboOU7jcZEELMVThTOYHvLj7T3SiQMM6QcevkYJm41igZW-ljVLJIZqwJjlYgeo1755vO5YRWYGi-mb85b0ld0UPlFEEOUJWNFS5jgCkDplymsGRAQNKqgMiK8CTUrIfUalz3wAo01uM3qI1ifTiTxCWMelpQufI6rp6OxkJAATQQLFQTwidgVdlaMUioK2XGfPGIWGcNkOoR9D3Y8VdL4o-WKoOn4oUy0HOiyUNQ0B4rqwavIdqOwyH7Ff5cNu61Y_j_9a8ARtAMTKM07YbhWtZ8lMngKMyfhZPmE_AYk48Y8 |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT-MwEB7xOACHXWAXUZaHkRB7SqmTNE20J7Q8yqsHBBKHlSLbsduI0qI2PSyn_Qn8Rn7JzsRJW9CuhDjlEE8cezyez2P7G4A9Qp2ekTUncQPP8aUOHOlL4aBzCtG0TMTz0MVVK2je-ud39bsZ-FHehbH8EOOAG1lGPl-TgVNA-mCKNVS0qy7Cl1mYp-05ssqj6wl3FPGalBuVEXqtknm25h6Ukq990QRgTsPU3M-cfIZf5R_a4yX31VEmq-rpDXnjB5uwDJ8K_MkO7YBZgRndW4WlKVbCL5DZQINOmOi2-4M06zwMGWJb1rYU1ekTvjIpgVWm7elzNkwfijxgQ9Y3LMMRol_-PCeUO8DyfrDO72QgRt1UMUM3s0YDzbAanM9ysa9we3J887PpFMkZHEGX5x0dGrehQm644iZQuKj1hO8rBOueMEEj4iqqecrTEQ9NRLyEMhSeDkWIeLQhXeGtwVyv39PrwCg0rev4OW4aPiUo4xHOEjwyEsUT7lbge6mmWBXM5ZRAoxtbzmU3xn6MqR8rsDsu-WjZOv5RZrPUdFzY6zBGlFvHhVPoY2X7ucr-Kx-3Dk_pufHegjuw0Ly5uowvz1oX32AREVeegMKtb8JcNhjpLUQ1mdzOR-9fk1r1qw |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3JTsMwELWgSAgO7IhCASMhOKWtkzRNjhVQylYhRCUkDpHt2G1EN7XpgZ74BL6RL2EcJ21BICFOOcQTJ54Zz_PEfoPQsUKdlmRFIzAdy7CZcAxmM2pAcHLBtaRH4tTFXd2pNezrp9JTsqtSnYXR_BCThJvyjHi-Vg7eD2RhhjSUNvMmoJd5tGA7sLhSgOhhSh2laE3S_5QeBK2UeLZoFlLJr6Foii9nUWocZqqr6Dl9Qb275CU_iliej79xN_7vC9bQSoI-cUWbyzqaE90NtDzDSbiJIp1mEAGm7WZvEEatzhADssVNTVAdjuGWDBVUxULvPcfDsJNUARvinsQR2If4eHsPVOUAzfqBW6_BgI7aIcdSncsaDQSGbmA2i8W2UKN68XhWM5LSDAZVR-cN4UqzzF0iCSfS4bCktahtc4DqFpVO2SPcK1rcEh5xpadYCZlLLeFSF9BomZnU2kaZbq8rdhBWiWlRgscRWbZVeTLiwRxBPMlAPCBmFp2mWvJ5wluuyme0fc24bPowjr4axyw6mrTsa66OH9rkUkX7ibcOfcC4JVg2uTZ0dhJr7Fd5v165VNfdvzY8RIv351X_9qp-s4eWAG7F1SfMUg5losFI7AOkidhBbLufyr_0Wg |
| 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=Improved+algorithms+for+generalized+finite+element+simulations+of+three%E2%80%90dimensional+hydraulic+fracture+propagation&rft.jtitle=International+journal+for+numerical+and+analytical+methods+in+geomechanics&rft.au=Shauer%2C+Nathan&rft.au=Duarte%2C+Carlos+Armando&rft.date=2019-12-25&rft.issn=0363-9061&rft.eissn=1096-9853&rft.volume=43&rft.issue=18&rft.spage=2707&rft.epage=2742&rft_id=info:doi/10.1002%2Fnag.2977&rft.externalDBID=10.1002%252Fnag.2977&rft.externalDocID=NAG2977 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0363-9061&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0363-9061&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0363-9061&client=summon |