Compositional dual mesh method for single phase flow in heterogeneous porous media—application to CO2 storage

Numerical simulation of fluid flow coupled with chemical reactions has been an active field in the hydrogeology community and many formulations have been programmed into different software. In recent years, this subject has attracted increasing interest in the reservoir simulation community, partly...

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Published in	Computational geosciences Vol. 21; no. 5-6; pp. 949 - 961
Main Authors	Guérillot, Dominique, Bruyelle, Jérémie
Format	Journal Article
Language	English
Published	Cham Springer International Publishing 01.12.2017 Springer Nature B.V
Subjects	Carbon dioxide Carbon sequestration Chemical reactions Communities Computational fluid dynamics Computer simulation Earth and Environmental Science Earth Sciences Finite element method Fluid flow Formulations Geochemistry Geology Geotechnical Engineering & Applied Earth Sciences High resolution Hydrogeology Mathematical Modeling and Industrial Mathematics Mathematical models Modelling Original Paper Porous media Resolution Simulation Soil Science & Conservation Transport 80A32 65M08 storage Finite volume CO Heterogeneity Chemically reacting flows Enhanced Oil Recovery Reservoir simulation Compositional 76S05 65M55 injection
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Abstract	Numerical simulation of fluid flow coupled with chemical reactions has been an active field in the hydrogeology community and many formulations have been programmed into different software. In recent years, this subject has attracted increasing interest in the reservoir simulation community, partly for the application of chemical methods for hydrocarbon extraction but also for research on the geological sequestration of CO 2 . In this paper, an extension to the concept of dual mesh for reactive transport modeling is presented. This approach involves two meshes, a low-resolution mesh to resolve the pressure equation and a high-resolution mesh to transport the species and to calculate the geochemical equilibrium. The main objective is to preserve the fine scale heterogeneities to reach a more accurate field behavior simulation than conventional approach which consist in performing simulations on a coarser mesh. The method is applied to a simulation of CO 2 storage in the SPE10 model that keep a high resolution of the heterogeneities.
AbstractList	Numerical simulation of fluid flow coupled with chemical reactions has been an active field in the hydrogeology community and many formulations have been programmed into different software. In recent years, this subject has attracted increasing interest in the reservoir simulation community, partly for the application of chemical methods for hydrocarbon extraction but also for research on the geological sequestration of CO 2 . In this paper, an extension to the concept of dual mesh for reactive transport modeling is presented. This approach involves two meshes, a low-resolution mesh to resolve the pressure equation and a high-resolution mesh to transport the species and to calculate the geochemical equilibrium. The main objective is to preserve the fine scale heterogeneities to reach a more accurate field behavior simulation than conventional approach which consist in performing simulations on a coarser mesh. The method is applied to a simulation of CO 2 storage in the SPE10 model that keep a high resolution of the heterogeneities. Numerical simulation of fluid flow coupled with chemical reactions has been an active field in the hydrogeology community and many formulations have been programmed into different software. In recent years, this subject has attracted increasing interest in the reservoir simulation community, partly for the application of chemical methods for hydrocarbon extraction but also for research on the geological sequestration of CO2. In this paper, an extension to the concept of dual mesh for reactive transport modeling is presented. This approach involves two meshes, a low-resolution mesh to resolve the pressure equation and a high-resolution mesh to transport the species and to calculate the geochemical equilibrium. The main objective is to preserve the fine scale heterogeneities to reach a more accurate field behavior simulation than conventional approach which consist in performing simulations on a coarser mesh. The method is applied to a simulation of CO2 storage in the SPE10 model that keep a high resolution of the heterogeneities.
Author	Guérillot, Dominique Bruyelle, Jérémie
Author_xml	– sequence: 1 givenname: Dominique surname: Guérillot fullname: Guérillot, Dominique email: dominique.guerillot@qatar.tamu.edu organization: Texas A&M University at Qatar – sequence: 2 givenname: Jérémie surname: Bruyelle fullname: Bruyelle, Jérémie organization: Terra 3E
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Cites_doi	10.2172/926875 10.1515/9781501509797-005 10.1029/WR024i010p01781 10.2172/834237 10.1016/S0022-1694(98)00104-8 10.2118/79681-MS 10.2118/69110-PA 10.1007/s002110050380 10.2118/29148-MS 10.1016/j.petrol.2009.05.010 10.1007/BF01448839 10.1016/j.jhydrol.2011.01.042 10.1016/0020-7225(82)90118-5 10.1029/WR023i010p01851 10.1177/109434209901300202 10.1007/BF02141261 10.2118/66599-MS 10.1029/2001WR000862 10.2118/6893-PA
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References	GuérillotDRBruyelleJA fast and accurate upscaling of transmissivities for field scale reservoir simulation14th European conference on the mathematics of oil recovery2014 MarleCMOn macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous mediaInt. J. Eng. Sci.198220564366210.1016/0020-7225(82)90118-5 KhoozanDFiroozabadiBRashtchianDAshjariMAAnalytical dual mesh method for two-phase flow through highly heterogeneous porous mediaJ. Hydrol.2011400119520510.1016/j.jhydrol.2011.01.042 SaaltinkMWBatlleFAyoraCCarreraJOlivellaSRETRASO, a code for modeling reactive transport in saturated and unsaturated porous mediaGeol. Acta20042235251 FiroozabadiBAshjariMAPerformance of combined vorticity-based gridding and dual mesh method for gravity dominated reservoir flowsJ. Pet. Sci. Eng.200967312713910.1016/j.petrol.2009.05.010 Tebes-StevensCValocchiAJVanBriesenJMRittmannBEMulticomponent transport with coupled geochemical and microbiological reactions: model description and example simulationsJ. Hydrol.199820982610.1016/S0022-1694(98)00104-8 BarnardSTBernardoLMSimonHDAn MPI implementation of the SPAI preconditioner on the T3EInt. J. High Perform. Comput. Appl.199913210712310.1177/109434209901300202 Guérillot, D. R., Verdière, S.: Different pressure grids for reservoir simulation in heterogeneous reservoirs. Society of petroleum engineers SPE 29148-MS (1995) MayerCMFrindEOBlowesDWMulticomponent reactive transport modeling in variably saturated media using a generalized formulation for kinetically controlled reactionsWater Resour. Res.2002389117410.1029/2001WR000862 AzizKSettariAPetroleum reservoir simulation1979LondonApplied Science Publishers Ltd Steefel, C. I., MacQuarrie, K. T. B.: Crunch flow: software for modeling multicomponent reactive flow and transport. User’s Manual (2009) Christie, M. A., Blunt, M. J. :Tenth SPE comparative solution project: a comparison of upscaling techniques. SPE Society of Petroleum Engineers 66599 (2001) PeacemanDWInterpretation of well-block pressures in numerical reservoir simulation (includes associated paper 6988)Soc. Pet. Eng. J.1978180318319410.2118/6893-PA Xu, T., Spycher, N., Pruess, K.: TOUGHREACT User’s guide: a simulation program for non-isothermal multiphase reactive geochemical transport in variably saturated geologic media. Lawrence Berkeley National Laboratory Report LBNL- 55460 (2004) ErtekinTAbou-KassemJHKingGRBasic applied reservoir simulation. SPE Textbook Series. Society of Petroleum Engineers2001TexasRichardson Xu, T., Pruess, K.: Coupled modeling of non-isothermal multiphase flow, solute transport and reactive chemistry in porous and fractured media: 1. Model development and validation. Lawrence Berkeley National Laboratory Report LBNL-42050 (1998) CarmanPCFluid flow through granular bedsTrans. Inst. Chem. Eng. London193715150166 Nitao, J. J.: Reference manual for the NUFT flow and transport code. Version 2.0 UCRL-MA-130651 (1998) VossCISouzaWRVariable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zoneWater Resour. Res.198723101851186610.1029/WR023i010p01851 HerbertAWJacksonCPLeverDACoupled groundwater flow and solute transport with fluid density strongly dependent upon concentrationWater Resour. Res.198824101781179510.1029/WR024i010p01781 Sleijpen, G. L., Van der Vorst, H. A., Fokkema, D. R.: BiCGstab (l) and other hybrid bi-CG methods. Numerical Algorithms 7(1), 75–109 (1994) Steefel, C. I., MacQuarrie, K. T. B.: Approaches to modeling reactive transport in porous media. In: Lichtner, P.C., Steefel, C.I., Oelkers, E.H. (eds.) Reactive transport in porous media. Rev. Mineral., vol. 34, pp 83–125 (1996) BethkeCMGeochemical and biogeochemical reaction modeling2008CambridgeCambridge University Press CourantRFriedrichsKLewyHÜber die partiellen Differenzengleichungen der mathematischen PhysikMath. Ann.19281001327410.1007/BF01448839 Audigane, P., Blunt, M. J.: Dual mesh method in upscaling. Society of Petroleum Engineers SPE 79681-MS (2003) LangeABourbiauxBJBouzianJTracer-test simulation on discrete fracture network models for the characterization of fractured reservoirsSPE Europec/EAGE annual conference. society of petroleum engineers, SPE 943442005 VerdièreSVignalMHNumerical and theoretical study of a dual mesh method using finite volume schemes for two phase flow problems in porous mediaNumer. Math.199880460163910.1007/s002110050380 GuedesSSSchiozerDJAn implicit treatment of upscaling in numerical reservoir simulationSPE J.2001601323810.2118/69110-PA YehGTFangYSunJLiYLiMHSiegelMDNumerical modeling of coupled fluid flow and thermal and reactive biogeochemical transport in porous and fractured mediaComput. Geom.201014147170 VerdièreSGuérillotDRThomasJMDual mesh method for multiphase flows in heterogeneous porous media5th European conference on the mathematics of oil recovery, Leoben, Austria, 3–6 September1996 9645_CR7 DR Guérillot (9645_CR12) 2014 CM Mayer (9645_CR17) 2002; 38 9645_CR2 S Verdière (9645_CR26) 1998; 80 D Khoozan (9645_CR14) 2011; 400 CM Bethke (9645_CR4) 2008 PC Carman (9645_CR5) 1937; 15 DW Peaceman (9645_CR19) 1978; 18 C Tebes-Stevens (9645_CR24) 1998; 209 MW Saaltink (9645_CR20) 2004; 2 9645_CR11 AW Herbert (9645_CR13) 1988; 24 9645_CR18 R Courant (9645_CR6) 1928; 100 A Lange (9645_CR15) 2005 9645_CR21 CM Marle (9645_CR16) 1982; 20 GT Yeh (9645_CR30) 2010; 14 B Firoozabadi (9645_CR9) 2009; 67 CI Voss (9645_CR27) 1987; 23 K Aziz (9645_CR1) 1979 T Ertekin (9645_CR8) 2001 SS Guedes (9645_CR10) 2001; 6 ST Barnard (9645_CR3) 1999; 13 9645_CR23 9645_CR22 9645_CR29 9645_CR28 S Verdière (9645_CR25) 1996
References_xml	– reference: Audigane, P., Blunt, M. J.: Dual mesh method in upscaling. Society of Petroleum Engineers SPE 79681-MS (2003) – reference: MayerCMFrindEOBlowesDWMulticomponent reactive transport modeling in variably saturated media using a generalized formulation for kinetically controlled reactionsWater Resour. Res.2002389117410.1029/2001WR000862 – reference: CourantRFriedrichsKLewyHÜber die partiellen Differenzengleichungen der mathematischen PhysikMath. Ann.19281001327410.1007/BF01448839 – reference: ErtekinTAbou-KassemJHKingGRBasic applied reservoir simulation. SPE Textbook Series. Society of Petroleum Engineers2001TexasRichardson – reference: Xu, T., Pruess, K.: Coupled modeling of non-isothermal multiphase flow, solute transport and reactive chemistry in porous and fractured media: 1. Model development and validation. Lawrence Berkeley National Laboratory Report LBNL-42050 (1998) – reference: Tebes-StevensCValocchiAJVanBriesenJMRittmannBEMulticomponent transport with coupled geochemical and microbiological reactions: model description and example simulationsJ. Hydrol.199820982610.1016/S0022-1694(98)00104-8 – reference: Christie, M. A., Blunt, M. J. :Tenth SPE comparative solution project: a comparison of upscaling techniques. SPE Society of Petroleum Engineers 66599 (2001) – reference: YehGTFangYSunJLiYLiMHSiegelMDNumerical modeling of coupled fluid flow and thermal and reactive biogeochemical transport in porous and fractured mediaComput. Geom.201014147170 – reference: GuérillotDRBruyelleJA fast and accurate upscaling of transmissivities for field scale reservoir simulation14th European conference on the mathematics of oil recovery2014 – reference: Steefel, C. I., MacQuarrie, K. T. B.: Crunch flow: software for modeling multicomponent reactive flow and transport. User’s Manual (2009) – reference: Xu, T., Spycher, N., Pruess, K.: TOUGHREACT User’s guide: a simulation program for non-isothermal multiphase reactive geochemical transport in variably saturated geologic media. Lawrence Berkeley National Laboratory Report LBNL- 55460 (2004) – reference: AzizKSettariAPetroleum reservoir simulation1979LondonApplied Science Publishers Ltd – reference: BethkeCMGeochemical and biogeochemical reaction modeling2008CambridgeCambridge University Press – reference: HerbertAWJacksonCPLeverDACoupled groundwater flow and solute transport with fluid density strongly dependent upon concentrationWater Resour. Res.198824101781179510.1029/WR024i010p01781 – reference: VerdièreSVignalMHNumerical and theoretical study of a dual mesh method using finite volume schemes for two phase flow problems in porous mediaNumer. Math.199880460163910.1007/s002110050380 – reference: Nitao, J. J.: Reference manual for the NUFT flow and transport code. Version 2.0 UCRL-MA-130651 (1998) – reference: KhoozanDFiroozabadiBRashtchianDAshjariMAAnalytical dual mesh method for two-phase flow through highly heterogeneous porous mediaJ. Hydrol.2011400119520510.1016/j.jhydrol.2011.01.042 – reference: LangeABourbiauxBJBouzianJTracer-test simulation on discrete fracture network models for the characterization of fractured reservoirsSPE Europec/EAGE annual conference. society of petroleum engineers, SPE 943442005 – reference: SaaltinkMWBatlleFAyoraCCarreraJOlivellaSRETRASO, a code for modeling reactive transport in saturated and unsaturated porous mediaGeol. Acta20042235251 – reference: GuedesSSSchiozerDJAn implicit treatment of upscaling in numerical reservoir simulationSPE J.2001601323810.2118/69110-PA – reference: BarnardSTBernardoLMSimonHDAn MPI implementation of the SPAI preconditioner on the T3EInt. J. High Perform. Comput. Appl.199913210712310.1177/109434209901300202 – reference: VossCISouzaWRVariable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zoneWater Resour. Res.198723101851186610.1029/WR023i010p01851 – reference: Guérillot, D. R., Verdière, S.: Different pressure grids for reservoir simulation in heterogeneous reservoirs. Society of petroleum engineers SPE 29148-MS (1995) – reference: Sleijpen, G. L., Van der Vorst, H. A., Fokkema, D. R.: BiCGstab (l) and other hybrid bi-CG methods. Numerical Algorithms 7(1), 75–109 (1994) – reference: Steefel, C. I., MacQuarrie, K. T. B.: Approaches to modeling reactive transport in porous media. In: Lichtner, P.C., Steefel, C.I., Oelkers, E.H. (eds.) Reactive transport in porous media. Rev. Mineral., vol. 34, pp 83–125 (1996) – reference: CarmanPCFluid flow through granular bedsTrans. Inst. Chem. Eng. London193715150166 – reference: PeacemanDWInterpretation of well-block pressures in numerical reservoir simulation (includes associated paper 6988)Soc. Pet. Eng. J.1978180318319410.2118/6893-PA – reference: VerdièreSGuérillotDRThomasJMDual mesh method for multiphase flows in heterogeneous porous media5th European conference on the mathematics of oil recovery, Leoben, Austria, 3–6 September1996 – reference: FiroozabadiBAshjariMAPerformance of combined vorticity-based gridding and dual mesh method for gravity dominated reservoir flowsJ. Pet. Sci. Eng.200967312713910.1016/j.petrol.2009.05.010 – reference: MarleCMOn macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous mediaInt. J. Eng. Sci.198220564366210.1016/0020-7225(82)90118-5 – volume-title: Geochemical and biogeochemical reaction modeling year: 2008 ident: 9645_CR4 – volume: 15 start-page: 150 year: 1937 ident: 9645_CR5 publication-title: Trans. Inst. Chem. Eng. London – ident: 9645_CR28 doi: 10.2172/926875 – ident: 9645_CR22 doi: 10.1515/9781501509797-005 – ident: 9645_CR18 – volume-title: Petroleum reservoir simulation year: 1979 ident: 9645_CR1 – volume: 24 start-page: 1781 issue: 10 year: 1988 ident: 9645_CR13 publication-title: Water Resour. Res. doi: 10.1029/WR024i010p01781 – ident: 9645_CR29 doi: 10.2172/834237 – volume: 14 start-page: 147 year: 2010 ident: 9645_CR30 publication-title: Comput. Geom. – volume: 209 start-page: 8 year: 1998 ident: 9645_CR24 publication-title: J. Hydrol. doi: 10.1016/S0022-1694(98)00104-8 – ident: 9645_CR2 doi: 10.2118/79681-MS – volume: 6 start-page: 32 issue: 01 year: 2001 ident: 9645_CR10 publication-title: SPE J. doi: 10.2118/69110-PA – ident: 9645_CR23 – volume: 80 start-page: 601 issue: 4 year: 1998 ident: 9645_CR26 publication-title: Numer. Math. doi: 10.1007/s002110050380 – ident: 9645_CR11 doi: 10.2118/29148-MS – volume: 67 start-page: 127 issue: 3 year: 2009 ident: 9645_CR9 publication-title: J. 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SubjectTerms	Carbon dioxide Carbon sequestration Chemical reactions Communities Computational fluid dynamics Computer simulation Earth and Environmental Science Earth Sciences Finite element method Fluid flow Formulations Geochemistry Geology Geotechnical Engineering & Applied Earth Sciences High resolution Hydrogeology Mathematical Modeling and Industrial Mathematics Mathematical models Modelling Original Paper Porous media Resolution Simulation Soil Science & Conservation Transport
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Title	Compositional dual mesh method for single phase flow in heterogeneous porous media—application to CO2 storage
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