The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics
Abstract This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two gove...
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| Autor*in: |
Zhang, Miao [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
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2022 |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature B.V. 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Transport in porous media - Springer Netherlands, 1986, 142(2022), 3 vom: 18. März, Seite 531-557 |
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| Übergeordnetes Werk: |
volume:142 ; year:2022 ; number:3 ; day:18 ; month:03 ; pages:531-557 |
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10.1007/s11242-022-01757-9 |
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| 520 | |a Abstract This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator. | ||
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10.1007/s11242-022-01757-9 doi (DE-627)OLC2078873756 (DE-He213)s11242-022-01757-9-p DE-627 ger DE-627 rakwb eng 530 VZ Zhang, Miao verfasserin aut The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator. Boundary element method Shale gas Diffusion Ayala, Luis F. aut Enthalten in Transport in porous media Springer Netherlands, 1986 142(2022), 3 vom: 18. März, Seite 531-557 (DE-627)129206105 (DE-600)54858-3 (DE-576)014457431 0169-3913 nnns volume:142 year:2022 number:3 day:18 month:03 pages:531-557 https://doi.org/10.1007/s11242-022-01757-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY AR 142 2022 3 18 03 531-557 |
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10.1007/s11242-022-01757-9 doi (DE-627)OLC2078873756 (DE-He213)s11242-022-01757-9-p DE-627 ger DE-627 rakwb eng 530 VZ Zhang, Miao verfasserin aut The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator. Boundary element method Shale gas Diffusion Ayala, Luis F. aut Enthalten in Transport in porous media Springer Netherlands, 1986 142(2022), 3 vom: 18. März, Seite 531-557 (DE-627)129206105 (DE-600)54858-3 (DE-576)014457431 0169-3913 nnns volume:142 year:2022 number:3 day:18 month:03 pages:531-557 https://doi.org/10.1007/s11242-022-01757-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY AR 142 2022 3 18 03 531-557 |
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10.1007/s11242-022-01757-9 doi (DE-627)OLC2078873756 (DE-He213)s11242-022-01757-9-p DE-627 ger DE-627 rakwb eng 530 VZ Zhang, Miao verfasserin aut The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator. Boundary element method Shale gas Diffusion Ayala, Luis F. aut Enthalten in Transport in porous media Springer Netherlands, 1986 142(2022), 3 vom: 18. März, Seite 531-557 (DE-627)129206105 (DE-600)54858-3 (DE-576)014457431 0169-3913 nnns volume:142 year:2022 number:3 day:18 month:03 pages:531-557 https://doi.org/10.1007/s11242-022-01757-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY AR 142 2022 3 18 03 531-557 |
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10.1007/s11242-022-01757-9 doi (DE-627)OLC2078873756 (DE-He213)s11242-022-01757-9-p DE-627 ger DE-627 rakwb eng 530 VZ Zhang, Miao verfasserin aut The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator. Boundary element method Shale gas Diffusion Ayala, Luis F. aut Enthalten in Transport in porous media Springer Netherlands, 1986 142(2022), 3 vom: 18. März, Seite 531-557 (DE-627)129206105 (DE-600)54858-3 (DE-576)014457431 0169-3913 nnns volume:142 year:2022 number:3 day:18 month:03 pages:531-557 https://doi.org/10.1007/s11242-022-01757-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY AR 142 2022 3 18 03 531-557 |
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10.1007/s11242-022-01757-9 doi (DE-627)OLC2078873756 (DE-He213)s11242-022-01757-9-p DE-627 ger DE-627 rakwb eng 530 VZ Zhang, Miao verfasserin aut The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator. Boundary element method Shale gas Diffusion Ayala, Luis F. aut Enthalten in Transport in porous media Springer Netherlands, 1986 142(2022), 3 vom: 18. März, Seite 531-557 (DE-627)129206105 (DE-600)54858-3 (DE-576)014457431 0169-3913 nnns volume:142 year:2022 number:3 day:18 month:03 pages:531-557 https://doi.org/10.1007/s11242-022-01757-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY AR 142 2022 3 18 03 531-557 |
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Abstract This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator. © The Author(s), under exclusive licence to Springer Nature B.V. 2022 |
| abstractGer |
Abstract This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator. © The Author(s), under exclusive licence to Springer Nature B.V. 2022 |
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Abstract This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator. © The Author(s), under exclusive licence to Springer Nature B.V. 2022 |
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The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics |
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