Implementação de Simulador Bifásico baseado na Equação de Brinkman para Reservatórios Carstificados
DOI:
https://doi.org/10.21712/lajer.2018.v5.n1.p1-24Resumo
Apresenta-se, neste artigo, um estudo sobre a dinâmica do escoamento de fluidos em meios altamente porosos e com baixos números de Reynolds. A validade da equação de Darcy é questionável para estes meios, enquanto a equação de Brinkman, ainda pouco utilizada para escoamento de hidrocarbonetos, é proposta como uma alternativa.
Neste trabalho se desenvolve um simulador de fluxo numérico capaz de representar o escoamento monofásico e bifásico (água - óleo) seguindo os dois equacionamentos distintamente. Para uma variedade de casos representativos os resultados destes equacionamentos são comparados. A aplicação deste estudo é para reservatórios de petróleo carstificados.
Observa-se pequena ou nenhuma influência do termo viscoso de Brinkman em meios porosos convencionais, até que altíssimas permeabilidades sejam atribuídas ao meio de alta porosidade quando pode-se notar diferenças significativas nas velocidades do escoamento, no avanço da frente de água e nos fatores de recuperação.
Downloads
Não há dados estatísticos.
Referências
Wayne M Ahr, David Allen, Austin Boyd, H Nate Bachman, Tony Smithson, EA Clerke, KBM Gzara, JK Hassall, CRK Murty, H Zubari, et al. Confronting the carbonate conundrum. Oilfield Review, 17(1): 18–29, 2005.
Todd Arbogast e Heather L Lehr. Homogenization of a darcy–stokes system modeling vuggy porous media. Computational Geosciences, 10(3):291–302, 2006.
Jean-Louis Auriault. On the domain of validity of brinkman’s equation. Transport in porous media, 79 (2):215–223, 2009.
George Keith Batchelor. An introduction to fluid dynamics. Cambridge university press, 2000.
HC Brinkman. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Applied Scientific Research, 1(1):27–34, 1949a.
HC Brinkman. On the permeability of media consisting of closely packed porous particles. Flow, Turbulence and Combustion, 1(1):81, 1949b.
Rodolfo Camacho-Velazquez, Mario Vasquez-Cruz, Rafael Castrejon-Aivar, Victor Arana-Ortiz, et al. Pressure transient and decline curve behaviors in naturally fractured vuggy carbonate reservoirs. In SPE
Annual Technical Conference and Exhibition. Society of Petroleum Engineers, 2002.
Ricardo Casar-Gonz´alez, Vinicio Suro-P´erez, et al. Stochastic imaging of vuggy formations. In SPE International Petroleum Conference and Exhibition in Mexico. Society of Petroleum Engineers, 2000.
Nikolai Chemetov e Wladimir Neves. On a generalized muskat-brinkman type problem. Interfaces and Free Boundaries, 16(3):339–357, 2014.
KH Coats et al. Impes stability: the cfl limit. In SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, 2001.
Giuseppe M Coclite, Siddhartha Mishra, Nils Henrik Risebro, e Franziska Weber. Analysis and numerical approximation of brinkman regularization of two-phase flows in porous media. Computational Geosciences, 18(5):637–659, 2014.
C Dabbouk, A Liaqat, GWilliams, e G Beattie. Waterflood in vuggy layer of a middle eastern reservoir–displacement physics understood. spe-78530. In 10th ADIPEC Conference, Abu Dhabi, UAE, 2002.
Henry Darcy. Les fontaines publique de la ville de dijon. Dalmont, Paris, 647, 1856.
L Durlofsky e JF Brady. Analysis of the brinkman equation as a model for flow in porous media. The Physics of fluids, 30(11):3329–3341, 1987.
Turgay Ertekin, Jamal H Abou-Kassen, e Gregory R King. Basic Applied Reservoir Simulations. Society of Petroleum Engineers, 2001.
Fabrice Golfier, D Lasseux, e M Quintard. Investigation of the effective permeability of vuggy or fractured porous media from a darcy-brinkman approach. Computational Geosciences, 19(1):63–78, 2015.
Jie He, John E Killough, F Fadlelmula, M Mohamed, Michael Fraim, et al. A unified finite difference model for the simulation of transient flow in naturally fractured carbonate karst reservoirs. In SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, 2015.
ID Howells. Drag due to the motion of a newtonian fluid through a sparse random array of small fixed rigid objects. Journal of Fluid Mechanics, 64(3):449–476, 1974.
Guido Kanschat, Raytcho Lazarov, e Youli Mao. Geometric multigrid for darcy and brinkman models of flows in highly heterogeneous porous media: A numerical study. Journal of Computational and Applied
Mathematics, 310:174–185, 2017.
Irina Evgenievna Khvatova, Antoine Renaud, Elena Golitsina, Galina Malutina, Gergiy Sansiev, Igor Kuzilov, et al. Simulation of complex carbonate field: Double media vs. single media kharyaga field
case (russian). In SPE Russian Oil and Gas Exploration and Production Technical Conference and Exhibition. Society of Petroleum Engineers, 2012.
Joel Koplik, Herbert Levine, e A Zee. Viscosity renormalization in the brinkman equation. The Physics of fluids, 26(10):2864–2870, 1983.
Marcin Krotkiewski, Ingeborg S Ligaarden, Knut-Andreas Lie, e Daniel W Schmid. On the importance of the stokes-brinkman equations for computing effective permeability in karst reservoirs. Communications
in Computational Physics, 10(05):1315–1332, 2011.
N Martys, Dale P Bentz, e Edward J Garboczi. Computer simulation study of the effective viscosity in brinkman’s equation. Physics of Fluids, 6(4):1434–1439, 1994.
DA Nield e AV Kuznetsov. An historical and topical note on convection in porous media. Journal of Heat Transfer, 135(6):061201, 2013.
Mayur Pal. A unified approach to simulation and upscaling of single-phase flow through vuggy carbonates. International Journal for Numerical Methods in Fluids, 69(6):1096–1123, 2012.
Xiaolong Peng, Zhilin Qi, Baosheng Liang, Xueli Liu, et al. A new darcy-stokes flow model for cavityfractured reservoir. In Production and Operations Symposium. Society of Petroleum Engineers, 2007.
Xiaolong Peng, Zhimin Du, Baosheng Liang, Zhilin Qi, et al. Darcy-stokes streamline simulation for the tahe-fractured reservoir with cavities. SPE Journal, 14(03):543–552, 2009.
Peter Popov, Guan Qin, Linfeng Bi, Yalchin Efendiev, Richard E Ewing, Jianglong Li, et al. Multiphysics and multiscale methods for modeling fluid flow through naturally fractured carbonate karst reservoirs.
SPE Reservoir Evaluation & Engineering, 12(02):218–231, 2009.
JW Sheldon, WT Cardwell Jr, et al. One-dimensional, incompressible, noncapillary, two-phase fluid flow in a porous medium. 1959.
Cyprien Soulaine. On the origin of darcy’s law, 2015. URL https://web.stanford.edu/˜csoulain/PORE_SCALE/Chap1_Darcy.pdf.
Shriram Srinivasan e KR Rajagopal. On the flow of fluids through inhomogeneous porous media due to high pressure gradients. International Journal of Non-Linear Mechanics, 78:112–120, 2016.
Yu-Shu Wu, HH Liu, e GS Bodvarsson. A triple-continuum approach for modeling flow and transport processes in fractured rock. Journal of Contaminant Hydrology, 73(1-4):145–179, 2004.
Yu-ShuWu, Christine Ehlig-Economides, Guan Qin, Zhijang Kang,Wangming Zhang, Babatunde Ajayi, e Qingfeng Tao. A triple-continuum pressure-transient model for a naturally fractured vuggy reservoir.
2007.
Jun Yao, Zhaoqin Huang, Yajun Li, Chenchen Wang, Xinrui Lv, et al. Discrete fracture-vug network model for modeling fluid flow in fractured vuggy porous media. In International oil and gas conference and exhibition in China. Society of Petroleum Engineers, 2010.
Todd Arbogast e Heather L Lehr. Homogenization of a darcy–stokes system modeling vuggy porous media. Computational Geosciences, 10(3):291–302, 2006.
Jean-Louis Auriault. On the domain of validity of brinkman’s equation. Transport in porous media, 79 (2):215–223, 2009.
George Keith Batchelor. An introduction to fluid dynamics. Cambridge university press, 2000.
HC Brinkman. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Applied Scientific Research, 1(1):27–34, 1949a.
HC Brinkman. On the permeability of media consisting of closely packed porous particles. Flow, Turbulence and Combustion, 1(1):81, 1949b.
Rodolfo Camacho-Velazquez, Mario Vasquez-Cruz, Rafael Castrejon-Aivar, Victor Arana-Ortiz, et al. Pressure transient and decline curve behaviors in naturally fractured vuggy carbonate reservoirs. In SPE
Annual Technical Conference and Exhibition. Society of Petroleum Engineers, 2002.
Ricardo Casar-Gonz´alez, Vinicio Suro-P´erez, et al. Stochastic imaging of vuggy formations. In SPE International Petroleum Conference and Exhibition in Mexico. Society of Petroleum Engineers, 2000.
Nikolai Chemetov e Wladimir Neves. On a generalized muskat-brinkman type problem. Interfaces and Free Boundaries, 16(3):339–357, 2014.
KH Coats et al. Impes stability: the cfl limit. In SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, 2001.
Giuseppe M Coclite, Siddhartha Mishra, Nils Henrik Risebro, e Franziska Weber. Analysis and numerical approximation of brinkman regularization of two-phase flows in porous media. Computational Geosciences, 18(5):637–659, 2014.
C Dabbouk, A Liaqat, GWilliams, e G Beattie. Waterflood in vuggy layer of a middle eastern reservoir–displacement physics understood. spe-78530. In 10th ADIPEC Conference, Abu Dhabi, UAE, 2002.
Henry Darcy. Les fontaines publique de la ville de dijon. Dalmont, Paris, 647, 1856.
L Durlofsky e JF Brady. Analysis of the brinkman equation as a model for flow in porous media. The Physics of fluids, 30(11):3329–3341, 1987.
Turgay Ertekin, Jamal H Abou-Kassen, e Gregory R King. Basic Applied Reservoir Simulations. Society of Petroleum Engineers, 2001.
Fabrice Golfier, D Lasseux, e M Quintard. Investigation of the effective permeability of vuggy or fractured porous media from a darcy-brinkman approach. Computational Geosciences, 19(1):63–78, 2015.
Jie He, John E Killough, F Fadlelmula, M Mohamed, Michael Fraim, et al. A unified finite difference model for the simulation of transient flow in naturally fractured carbonate karst reservoirs. In SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, 2015.
ID Howells. Drag due to the motion of a newtonian fluid through a sparse random array of small fixed rigid objects. Journal of Fluid Mechanics, 64(3):449–476, 1974.
Guido Kanschat, Raytcho Lazarov, e Youli Mao. Geometric multigrid for darcy and brinkman models of flows in highly heterogeneous porous media: A numerical study. Journal of Computational and Applied
Mathematics, 310:174–185, 2017.
Irina Evgenievna Khvatova, Antoine Renaud, Elena Golitsina, Galina Malutina, Gergiy Sansiev, Igor Kuzilov, et al. Simulation of complex carbonate field: Double media vs. single media kharyaga field
case (russian). In SPE Russian Oil and Gas Exploration and Production Technical Conference and Exhibition. Society of Petroleum Engineers, 2012.
Joel Koplik, Herbert Levine, e A Zee. Viscosity renormalization in the brinkman equation. The Physics of fluids, 26(10):2864–2870, 1983.
Marcin Krotkiewski, Ingeborg S Ligaarden, Knut-Andreas Lie, e Daniel W Schmid. On the importance of the stokes-brinkman equations for computing effective permeability in karst reservoirs. Communications
in Computational Physics, 10(05):1315–1332, 2011.
N Martys, Dale P Bentz, e Edward J Garboczi. Computer simulation study of the effective viscosity in brinkman’s equation. Physics of Fluids, 6(4):1434–1439, 1994.
DA Nield e AV Kuznetsov. An historical and topical note on convection in porous media. Journal of Heat Transfer, 135(6):061201, 2013.
Mayur Pal. A unified approach to simulation and upscaling of single-phase flow through vuggy carbonates. International Journal for Numerical Methods in Fluids, 69(6):1096–1123, 2012.
Xiaolong Peng, Zhilin Qi, Baosheng Liang, Xueli Liu, et al. A new darcy-stokes flow model for cavityfractured reservoir. In Production and Operations Symposium. Society of Petroleum Engineers, 2007.
Xiaolong Peng, Zhimin Du, Baosheng Liang, Zhilin Qi, et al. Darcy-stokes streamline simulation for the tahe-fractured reservoir with cavities. SPE Journal, 14(03):543–552, 2009.
Peter Popov, Guan Qin, Linfeng Bi, Yalchin Efendiev, Richard E Ewing, Jianglong Li, et al. Multiphysics and multiscale methods for modeling fluid flow through naturally fractured carbonate karst reservoirs.
SPE Reservoir Evaluation & Engineering, 12(02):218–231, 2009.
JW Sheldon, WT Cardwell Jr, et al. One-dimensional, incompressible, noncapillary, two-phase fluid flow in a porous medium. 1959.
Cyprien Soulaine. On the origin of darcy’s law, 2015. URL https://web.stanford.edu/˜csoulain/PORE_SCALE/Chap1_Darcy.pdf.
Shriram Srinivasan e KR Rajagopal. On the flow of fluids through inhomogeneous porous media due to high pressure gradients. International Journal of Non-Linear Mechanics, 78:112–120, 2016.
Yu-Shu Wu, HH Liu, e GS Bodvarsson. A triple-continuum approach for modeling flow and transport processes in fractured rock. Journal of Contaminant Hydrology, 73(1-4):145–179, 2004.
Yu-ShuWu, Christine Ehlig-Economides, Guan Qin, Zhijang Kang,Wangming Zhang, Babatunde Ajayi, e Qingfeng Tao. A triple-continuum pressure-transient model for a naturally fractured vuggy reservoir.
2007.
Jun Yao, Zhaoqin Huang, Yajun Li, Chenchen Wang, Xinrui Lv, et al. Discrete fracture-vug network model for modeling fluid flow in fractured vuggy porous media. In International oil and gas conference and exhibition in China. Society of Petroleum Engineers, 2010.
Downloads
Publicado
05-02-2021
Como Citar
Hallack, D. M. C., Cavalcante Filho, J. S. de A., & Couto, P. (2021). Implementação de Simulador Bifásico baseado na Equação de Brinkman para Reservatórios Carstificados. Latin American Journal of Energy Research, 5(1), 1–24. https://doi.org/10.21712/lajer.2018.v5.n1.p1-24
Edição
Seção
Artigos
Licença
Copyright (c) 2018 Latin American Journal of Energy Research
Este trabalho está licenciado sob uma licença Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
O autor, no ato da submissão do artigo, transfere o direito autoral ao periódico.
