Analytical Solution for 2D Inter-Well Porous Flow in a Rectangular Reservoir
Inter-well fluid flows through porous media are commonly encountered in the production of groundwater, oil, and geothermal energy. In this paper, inter-well porous flow inside a rectangular reservoir is solved based on the complex variable function theory combined with the method of mirror images. I...
Gespeichert in:
| Veröffentlicht in: | Applied sciences Jg. 8; H. 4; S. 586 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Basel
MDPI AG
01.04.2018
|
| Schlagworte: | |
| ISSN: | 2076-3417, 2076-3417 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | Inter-well fluid flows through porous media are commonly encountered in the production of groundwater, oil, and geothermal energy. In this paper, inter-well porous flow inside a rectangular reservoir is solved based on the complex variable function theory combined with the method of mirror images. In order to derive the solution analytically, the inter-well flow is modeled as a 2D flow in a homogenous and isotropic porous medium. The resulted exact analytical solution takes the form of an infinite series, but it can be truncated to give high accuracy approximation. In terms of nine cases of inter-well porous flow associated with enhanced geothermal systems, the applications of the obtained analytical solution are demonstrated, and the convergence properties of the truncated series are investigated. It is shown that the convergent rate of the truncated series increases with the symmetric level of well distribution inside the reservoir, and the adoption of Euler transform significantly accelerates the convergence of alternating series cases associated with asymmetric well distribution. In principle, the analytical solution proposed in this paper can be applied to other scientific and engineering fields, as long as the involved problem is governed by 2D Laplace equation in a rectangular domain and subject to similar source/sink and boundary conditions, i.e., isolated point sources/sinks and uniform Dirichlet or homogeneous Neumann boundary conditions. |
|---|---|
| AbstractList | Inter-well fluid flows through porous media are commonly encountered in the production of groundwater, oil, and geothermal energy. In this paper, inter-well porous flow inside a rectangular reservoir is solved based on the complex variable function theory combined with the method of mirror images. In order to derive the solution analytically, the inter-well flow is modeled as a 2D flow in a homogenous and isotropic porous medium. The resulted exact analytical solution takes the form of an infinite series, but it can be truncated to give high accuracy approximation. In terms of nine cases of inter-well porous flow associated with enhanced geothermal systems, the applications of the obtained analytical solution are demonstrated, and the convergence properties of the truncated series are investigated. It is shown that the convergent rate of the truncated series increases with the symmetric level of well distribution inside the reservoir, and the adoption of Euler transform significantly accelerates the convergence of alternating series cases associated with asymmetric well distribution. In principle, the analytical solution proposed in this paper can be applied to other scientific and engineering fields, as long as the involved problem is governed by 2D Laplace equation in a rectangular domain and subject to similar source/sink and boundary conditions, i.e., isolated point sources/sinks and uniform Dirichlet or homogeneous Neumann boundary conditions. [...]an analytical solution provides an ideal tool for quantifying the accuracy of numerical modeling. In a rectangular domain with impermeable boundaries at x=±a and y=±b , the normal gradient of pore pressure on the boundaries vanishes following Darcy’s law, resulting in the following no-penetration boundary conditions: u=−kμ∂p∂x=0, at x=±a, v=−kμ∂p∂y=0, at y=±b. As the injection and production wells have a size much smaller than the inter-well distance, an injection well may be well represented by a point source, while a production well may be represented by a point sink. [...]the steady fluxes associated with the wells may be simulated by a number of isolated point sources or sinks with constant volumetric flow rates Qj=Q(xj,yj)=∮u⋅ds=−kμ∮∇p⋅ds, j=1,2,…,J, constrained by an overall mass conservation for steady porous flow ∑j=1JQj=0. [...]the analytical solutions for the potential function, stream function, pore pressure, and Darcy velocity components can be expressed, respectively, by φ=φ0+∑m=−MM∑n=−NN∑j=1JQj4πln[x−(2na+(−1)n xj)]2+[y−(2mb+(−1)m yj)]2[x0−(2na+(−1)n xj)]2+[y0−(2mb+(−1)m yj)]2, ψ=ψ0+∑m=−MM∑n=−NN∑j=1JQj2π(tan−1y−[2mb+(−1)m yj]x−[2na+(−1)n xj]−tan−1y0−[2mb+(−1)m yj]x0−[2na+(−1)n xj]), p=p0+μ4πk∑m=−MM∑n=−NN∑j=1JQjln[x0−(2na+(−1)n xj)]2+[y0−(2mb+(−1)m yj)]2[x−(2na+(−1)n xj)]2+[y−(2mb+(−1)m yj)]2, u=μ2πk∑m=−MM∑n=−NN∑j=1JQj[x−(2na+(−1)n xj)][x−(2na+(−1)n xj)]2+[y−(2mb+(−1)m yj)]2, v=μ2πk∑m=−MM∑n=−NN∑j=1JQj[y−(2mb+(−1)m yj)][x−(2na+(−1)n xj)]2+[y−(2mb+(−1)m yj)]2. [...]the analytical solution proposed in this paper has sufficient flexibility to deal with different aspect ratios of the rectangular reservoir and different distributions of isolated sources/sinks, as long as the condition of overall mass conservation for steady porous flow, Equation (6), is satisfied. |
| Author | Wang, Shimin Ding, Junfeng |
| Author_xml | – sequence: 1 givenname: Junfeng surname: Ding fullname: Ding, Junfeng – sequence: 2 givenname: Shimin surname: Wang fullname: Wang, Shimin |
| BookMark | eNptkFtLxDAQhYMouK774i8I-CZUk6abpI_idWFB8YKPYZpOli6xWZNW2X9vdUVFnJc5DGfOMN8e2W5Di4QccHYsRMlOYLXSrGBTLbfIKGdKZqLgavuX3iWTlJZsqJILzdmIzE9b8OuuseDpffB914SWuhBpfk5nbYcxe0Lv6W2IoU_00oc32rQU6B3aDtpF7yEOOmF8DU3cJzsOfMLJVx-Tx8uLh7PrbH5zNTs7nWdWSN5lZc1k5XKJMte10jnqUsmaS6xlPgWunQXHhJKqRgaskHVV2VKpSjghCy6tGJPZJrcOsDSr2DxDXJsAjfkchLgwEIefPBrBQQsUjJdYFFa4Cqc2r0G6skTLcDpkHW6yVjG89Jg6swx9HKAkkwteMKWl5IPraOOyMaQU0X1f5cx8wDc_8Acz-2O2TQcfZLsIjf9v5R3QLYev |
| CitedBy_id | crossref_primary_10_1017_jfm_2021_126 crossref_primary_10_1007_s10665_024_10405_8 |
| Cites_doi | 10.1017/CBO9781139626804 10.1021/acs.energyfuels.7b00834 10.1016/S1001-6058(13)60416-3 10.1016/j.jngse.2015.07.043 10.1063/1.366648 10.1007/978-3-540-30274-2 10.1126/science.1235640 10.1016/j.renene.2014.07.056 10.1063/1.4975393 10.1098/rsta.1927.0008 10.1016/j.advwatres.2014.07.002 10.1007/s40314-014-0164-5 10.1088/1751-8113/46/11/115201 10.1017/CBO9780511843877 10.1007/978-1-4614-5541-7 10.1016/S0309-1708(02)00027-1 10.1016/j.energy.2018.08.061 10.1016/j.jcp.2013.03.047 |
| ContentType | Journal Article |
| Copyright | 2018. This work is licensed under https://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. |
| Copyright_xml | – notice: 2018. This work is licensed under https://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. |
| DBID | AAYXX CITATION ABUWG AFKRA AZQEC BENPR CCPQU DWQXO PHGZM PHGZT PIMPY PKEHL PQEST PQQKQ PQUKI PRINS DOA |
| DOI | 10.3390/app8040586 |
| DatabaseName | CrossRef ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central ProQuest One Community College ProQuest Central ProQuest Central Premium ProQuest One Academic (New) Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest Central Essentials ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Academic UKI Edition ProQuest Central Korea ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | CrossRef Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: PIMPY name: ProQuest Publicly Available Content url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Sciences (General) |
| EISSN | 2076-3417 |
| ExternalDocumentID | oai_doaj_org_article_31a83e3019e44c3fbe5c2da6f99ec0e5 10_3390_app8040586 |
| GeographicLocations | United Kingdom--UK New York United States--US |
| GeographicLocations_xml | – name: New York – name: United Kingdom--UK – name: United States--US |
| GroupedDBID | .4S 5VS 7XC 8CJ 8FE 8FG 8FH AADQD AAFWJ AAYXX ADBBV ADMLS AFFHD AFKRA AFPKN AFZYC ALMA_UNASSIGNED_HOLDINGS APEBS ARCSS BCNDV BENPR CCPQU CITATION CZ9 D1I D1J D1K GROUPED_DOAJ IAO IPNFZ K6- K6V KC. KQ8 L6V LK5 LK8 M7R MODMG M~E OK1 P62 PHGZM PHGZT PIMPY PROAC RIG TUS ABUWG AZQEC DWQXO PKEHL PQEST PQQKQ PQUKI PRINS |
| ID | FETCH-LOGICAL-c361t-9d06bf26e628d782e8976d16ed625a18fcaf03767de0a046dbbc977b3f36416c3 |
| IEDL.DBID | PIMPY |
| ISICitedReferencesCount | 3 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000434996400113&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 2076-3417 |
| IngestDate | Tue Oct 14 19:03:14 EDT 2025 Mon Oct 20 02:42:49 EDT 2025 Sat Nov 29 07:11:17 EST 2025 Tue Nov 18 20:56:28 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c361t-9d06bf26e628d782e8976d16ed625a18fcaf03767de0a046dbbc977b3f36416c3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://www.proquest.com/publiccontent/docview/2314078661?pq-origsite=%requestingapplication% |
| PQID | 2314078661 |
| PQPubID | 2032433 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_31a83e3019e44c3fbe5c2da6f99ec0e5 proquest_journals_2314078661 crossref_primary_10_3390_app8040586 crossref_citationtrail_10_3390_app8040586 |
| PublicationCentury | 2000 |
| PublicationDate | 2018-04-01 |
| PublicationDateYYYYMMDD | 2018-04-01 |
| PublicationDate_xml | – month: 04 year: 2018 text: 2018-04-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Basel |
| PublicationPlace_xml | – name: Basel |
| PublicationTitle | Applied sciences |
| PublicationYear | 2018 |
| Publisher | MDPI AG |
| Publisher_xml | – name: MDPI AG |
| References | Ciraolo (ref_25) 2015; 34 Richardson (ref_7) 1927; 226 ref_14 Qi (ref_11) 2015; 27 Luo (ref_12) 2013; 25 Zonta (ref_6) 2017; 29 Moore (ref_16) 2013; 340 ref_19 ref_17 Sondow (ref_20) 1994; 120 ref_15 Ciraolo (ref_24) 2013; 246 Li (ref_10) 2017; 31 Zhang (ref_13) 2002; 25 Kordyuka (ref_9) 1998; 83 ref_23 ref_21 Green (ref_5) 2014; 73 ref_1 ref_3 Bailey (ref_22) 2013; 46 ref_2 ref_8 Chen (ref_18) 2015; 74 ref_4 |
| References_xml | – ident: ref_23 doi: 10.1017/CBO9781139626804 – volume: 31 start-page: 8896 year: 2017 ident: ref_10 article-title: Investigation of intermingled fractal model for organic-rich shale publication-title: Energy Fuels doi: 10.1021/acs.energyfuels.7b00834 – volume: 25 start-page: 710 year: 2013 ident: ref_12 article-title: A streamline approach for identification of the flowing and stagnant zones for five-spot well patterns in low permeability reservoirs publication-title: J. Hydrodyn. doi: 10.1016/S1001-6058(13)60416-3 – volume: 27 start-page: 1340 year: 2015 ident: ref_11 article-title: An approach to calculating snake well productivity under steady-state flow publication-title: J. Nat. Gas Sci. Eng. doi: 10.1016/j.jngse.2015.07.043 – volume: 83 start-page: 610 year: 1998 ident: ref_9 article-title: Magnetic levitation for hard superconductors publication-title: J. Appl. Phys. doi: 10.1063/1.366648 – ident: ref_2 doi: 10.1007/978-3-540-30274-2 – volume: 340 start-page: 933 year: 2013 ident: ref_16 article-title: More power from below publication-title: Science doi: 10.1126/science.1235640 – volume: 74 start-page: 37 year: 2015 ident: ref_18 article-title: Designing multi-well layout for enhanced geothermal system to better exploit hot dry rock geothermal energy publication-title: Renew. Energy doi: 10.1016/j.renene.2014.07.056 – ident: ref_14 – ident: ref_1 – volume: 29 start-page: 026601 year: 2017 ident: ref_6 article-title: Dissolution in anisotropic porous media: Modelling convection regimes from onset to shut down publication-title: Phys. Fluids doi: 10.1063/1.4975393 – ident: ref_21 – volume: 226 start-page: 299 year: 1927 ident: ref_7 article-title: The deferred approach to the limit, Part I, single lattice publication-title: Phil. Trans. R. Soc. Lond. Ser. A doi: 10.1098/rsta.1927.0008 – volume: 73 start-page: 65 year: 2014 ident: ref_5 article-title: Steady dissolution rate due to convective mixing in anisotropic porous media publication-title: Adv. Water Resour. doi: 10.1016/j.advwatres.2014.07.002 – ident: ref_8 – volume: 34 start-page: 1035 year: 2015 ident: ref_25 article-title: A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains publication-title: Comp. Appl. Math. doi: 10.1007/s40314-014-0164-5 – volume: 46 start-page: 115201 year: 2013 ident: ref_22 article-title: Lattice sums arising from the Poisson equation publication-title: J. Phys. A Math. Theor. doi: 10.1088/1751-8113/46/11/115201 – ident: ref_4 – ident: ref_3 doi: 10.1017/CBO9780511843877 – ident: ref_17 doi: 10.1007/978-1-4614-5541-7 – ident: ref_15 – volume: 25 start-page: 601 year: 2002 ident: ref_13 article-title: On boundary conditions in the lattice Boltzmann model for advection and anisotropic dispersion equation publication-title: Adv. Water Resour. doi: 10.1016/S0309-1708(02)00027-1 – ident: ref_19 doi: 10.1016/j.energy.2018.08.061 – volume: 120 start-page: 421 year: 1994 ident: ref_20 article-title: Analytic continuation of Riemann’s Zeta function and values at negative integers via Euler’s transfermation of series publication-title: Proc. Am. Math. Soc. – volume: 246 start-page: 78 year: 2013 ident: ref_24 article-title: A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional publication-title: J. Comp. Phys. doi: 10.1016/j.jcp.2013.03.047 |
| SSID | ssj0000913810 |
| Score | 2.0757303 |
| Snippet | Inter-well fluid flows through porous media are commonly encountered in the production of groundwater, oil, and geothermal energy. In this paper, inter-well... [...]an analytical solution provides an ideal tool for quantifying the accuracy of numerical modeling. In a rectangular domain with impermeable boundaries at... |
| SourceID | doaj proquest crossref |
| SourceType | Open Website Aggregation Database Enrichment Source Index Database |
| StartPage | 586 |
| SubjectTerms | Accuracy analytical solution Boundary conditions Energy Euler transform Fluids Geothermal power Helmholtz equations inter-well porous flow Laplace equation method of mirror images Permeability |
| SummonAdditionalLinks | – databaseName: DOAJ Directory of Open Access Journals dbid: DOA link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3PS8MwFA4iHvQgbipOpwT04A7FpOmy5Oiv4UHGDoq7lTR9gcHYpKvz3_cl7WZBwYvX8qDlvZe873tJv0fIlRiwJAGN3ET4bpXTcWSYFZGTlmWZA8chCcMmBqORmkz0uDHqy98Jq-SBK8fdCG6UAExDDUlihcugb-PcSKc1WAZBvZQNdINMhT1Ycy9dVemRCuT1_jxYYcL2_U_TjQoUhPp_7MOhuAwPyH6NCult9TUtsgXzNtlraAW2SatehUt6XUtF9w7Jc9AUCe1oum5wUYShNH6godcXvcFsRseLAgk-Hc4Wn3Q6p4YiWCx9oxJpLfV374rVYlockdfh48v9U1TPR4iskLyMdM5k5mIJMlY5VnpQiC1yLiFHUmO4ctY45tVacmAGeXCeZRbhXiackIjDrDgm2_PFHE4IdX3Rd0rwBA0SMEybxHI5AJ7FTGlnOqS39llqa_FwP8NiliKJ8P5Nv_3bIZcb2_dKMuNXqzvv-o2Fl7kODzD4aR389K_gd0h3Hbi0XnvLFBGrP5xE4HH6H-84I7sIklR1W6dLtsviA87Jjl2V02VxEdLuC67Q3Mc priority: 102 providerName: Directory of Open Access Journals |
| Title | Analytical Solution for 2D Inter-Well Porous Flow in a Rectangular Reservoir |
| URI | https://www.proquest.com/docview/2314078661 https://doaj.org/article/31a83e3019e44c3fbe5c2da6f99ec0e5 |
| Volume | 8 |
| WOSCitedRecordID | wos000434996400113&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: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2076-3417 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913810 issn: 2076-3417 databaseCode: DOA dateStart: 20110101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2076-3417 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913810 issn: 2076-3417 databaseCode: M~E dateStart: 20110101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 2076-3417 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913810 issn: 2076-3417 databaseCode: BENPR dateStart: 20110101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Publicly Available Content customDbUrl: eissn: 2076-3417 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913810 issn: 2076-3417 databaseCode: PIMPY dateStart: 20110101 isFulltext: true titleUrlDefault: http://search.proquest.com/publiccontent providerName: ProQuest |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3BbtQwEB3BLgc4AC0gtpSVJTjQQ1QnTrz2CVHoCiRYRQhEOUWOM65WWm1Ksm1_n7Hj3VYCceKazCHKeMZvnsdvAF6LGc9z1FSbCM9WOZ0lhluROGl5XTt0KeZh2MRssVBnZ7qM16P72Fa5zYkhUQ9qz75vm5LwcdNaz5gfEyrxB1C0uby9-JX4GVL-rDUO1LgLYy-8xUcwLj99KX_uOBevgalSPqiUCqr2_SmxomVc-KvUt_alIN__R3YOW8780f_92MfwMEJP9m5YK3twB9f78OCWIOE-7MVQ79mbqEd99AQ-B-GSwHmzLYvGCOuy7AMLhGLyA1crVrZde9mz-aq9Zss1M4wQ6cazoVQ7M9_g1121y-4pfJ-ffnv_MYlDGBIrZLpJdMNl7TKJMlMNwQlUBGCaVGJDlZNJlbPGcS8J0yA3VGw3dW0JU9bCCUlgz4pnMFq3a3wOzBWicIp-BhnkaLg2uU3lDNM640o7M4GjrQsqGxXK_aCMVUWVindXdeOuCbza2V4Muhx_tTrxntxZeC3t8KDtzqsYmpVIjRJIiU5jnlvhaixs1hjptEbLsZjA4dbJVQzwvrrx6cG_X7-A-4Sx1NDscwijTXeJL-Gevdos-24K45PTRfl1GqiAaVyvvwHjQflw |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VLRJwKLSAWFrAEiDRQ4QTJ177UFVAWXXV7WoPRZRT6jhjtNJqU5JtK_4Uv5FxPraVQNx64JqMIsV-no9n-w3AGzHgcYyaahPh2Sqno8BwKwInLc8yhy7EuG42MZhM1Ompnq7Br-4ujD9W2fnE2lHnhfUc-XvKQ_yWE4WT_fMfge8a5XdXuxYaDSyO8OcVlWzV3uiA5vdtFA0_n3w6DNquAoEVMlwGOucyc5FEGamc4iMqish5KDGnUsCEylnjuNc4yZEbqh7zLLOUJGXCCUnZixX03TuwHhPYeQ_Wp6Pj6bcVq-NVNlXIGx1UITT3-9CKFkriL2vfiHx1g4A__H8d1IYP_7fheAQbbfrMPjR434Q1XGzBgxuiiluw2bqrir1rNbV3H8O4Fl-peXvWMYGM8nUWHbCaFA2-4nzOpkVZXFRsOC-u2GzBDKOseukZXar_mT-kWF4Ws_IJfLmVf3wKvUWxwGfAXCISp2jwySBGw7WJbSgHGGYRV9qZPux2k5zaVmXdN_uYp1RteUCk14Dow-uV7XmjLfJXq48eKysLrwdePyjK72nrXlIRGiWQnLXGOLbCZZjYKDfSaY2WY9KHnQ5GaeukqvQaQ8___foV3Ds8OR6n49HkaBvuU86omsNLO9Bblhf4Au7ay-WsKl-264HB2W1j7jc2nEhU |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VLUL0UGgBdUsBS4BED1GdOMnahwoBy4pVyyoHEOWUOs4YrRRt2mTbir_Gr2Ocj20lELceuCajSImf5-N58gbglRjxMERFtYlwbJVVgae5EZ6NDc8yi9bHsBk2MZrN5MmJStbgV_8vjGur7H1i46jz0jiO_IDyEHfkROHkwHZtEcl48vbs3HMTpNxJaz9Oo4XIEf68ovKtPpyOaa1fB8Hk45cPn7xuwoBnROwvPZXzOLNBjHEgc4qVKCk6536MOZUF2pfWaMud3kmOXFMlmWeZoYQpE1bElMkYQc-9A-sjN793AOvJ9HPyfcXwOMVN6fNWE1UIxd2ZtKRNE7kft29EwWZYwB-xoAlwkwf_86d5CJtdWs3etftgC9ZwsQ0bN8QWt2Grc2M1e9Npbe8_guNGlKXh81nPEDLK41kwZg1Z6n3DomBJWZUXNZsU5RWbL5hmlG0vHdNb6Iq55sXqspxXj-HrrbzjExgsygXuALORiKykhSCDEDVXOjR-PEI_C7hUVg9hv1_w1HTq624ISJFSFebAkV6DYwgvV7ZnrebIX63eO9ysLJxOeHOhrH6kndtJha-lQHLiCsPQCJthZIJcx1YpNByjIez1kEo751Wn13ja_fftF3CPgJYeT2dHT-E-pZKy7Wnag8GyusBncNdcLud19bzbGgxObxtyvwFdKVEd |
| 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=Analytical+Solution+for+2D+Inter-Well+Porous+Flow+in+a+Rectangular+Reservoir&rft.jtitle=Applied+sciences&rft.au=Ding%2C+Junfeng&rft.au=Wang%2C+Shimin&rft.date=2018-04-01&rft.pub=MDPI+AG&rft.eissn=2076-3417&rft.volume=8&rft.issue=4&rft_id=info:doi/10.3390%2Fapp8040586&rft.externalDBID=HAS_PDF_LINK |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2076-3417&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2076-3417&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2076-3417&client=summon |