煤层气藏储层形状因子的推导与论证
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摘要
目前广泛使用于双孔隙模型中的形状因子主要是基于常规油气藏储层条件的,并不完全适用于煤层气藏的模拟。文章以双孔隙模型的基础单元为模型,即一个二维或者三维的基质网格被高导流能力裂缝环绕的模型,同时考虑达西渗流、分子扩散运动、气体解吸附效应、滑脱效应等多种渗流机理,推导适合煤层气藏双孔隙模型的形状因子,并且使用精细网格数值模拟的方法对该形状因子进行验证。通过假设在二维/三维矩形网格中的流动近似为柱状径向流和球状球向流流动和通过线性化处理部分系数,求得模型的解析解从而得出二维/三维模型的形状因子分别为18.17/L~2和25.67/L~2。使用精细化网格模拟方法,将本文推导的形状因子对比目前广泛使用的形状因子(Warren and Root,Lim and Aziz,Kazemi et al.),精确度都有了明显的提升。
The double-porosity model,a flow domain is composed of matrix blocks with low permeability,embedded in a network of interconnected fractures,is commonly used to simulate naturally fractured fracture. Global flow and transport in the formation occur only through the fracture system,conceptualized as an effective continuum. An important constant factor called shape factor is applied to simulate the matrix-fracture exchange term. However, most shape factors are borrowed directly from those used in conventional reservoir simulation,which may not be applicable in unconventional gas reservoir simulation. In this paper,geometric shape factors are derived considering the physics of gas slippage and the sorption term with the assumption of Lim and Aziz, getting the results of 18. 17/L2 and 25. 67/L2,and a fine grid discretization of two/three-dimensional system are run to examine the accuracy of the new-derived shape factors.Comparing the results with the most common used shape factors( Warren and Root,Lim and Aziz,Kazemi et al.),the results indicate the shape factors derived in this paper highly increase the accuracy.
The double-porosity model,a flow domain is composed of matrix blocks with low permeability,embedded in a network of interconnected fractures,is commonly used to simulate naturally fractured fracture. Global flow and transport in the formation occur only through the fracture system,conceptualized as an effective continuum. An important constant factor called shape factor is applied to simulate the matrix-fracture exchange term. However, most shape factors are borrowed directly from those used in conventional reservoir simulation,which may not be applicable in unconventional gas reservoir simulation. In this paper,geometric shape factors are derived considering the physics of gas slippage and the sorption term with the assumption of Lim and Aziz, getting the results of 18. 17/L2 and 25. 67/L2,and a fine grid discretization of two/three-dimensional system are run to examine the accuracy of the new-derived shape factors.Comparing the results with the most common used shape factors( Warren and Root,Lim and Aziz,Kazemi et al.),the results indicate the shape factors derived in this paper highly increase the accuracy.
引文
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[6]Wu Y S,Wang C,Li J,et al.Transient Gas Flow in Unconventional Gas Reservoir[M].Society of Petroleum Engineers,2012.
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[14]Kazemi,H.,Merrill,L.S.,Porterfield,K.L.,Zeman,P.R.Numerical Simulation of Water-Oil Flow in Naturally Fractured Reservoirs[J].Society of Petroleum Engineers Journal,1976,16(6):317-326.
[15]COATS K H.Implicit compositional simulation of singleporosity and dual-porosity reservoirs[A]//Proceedings of the SPE Symposium on Reservoir Simulation[C].Texas:Society of Petroleum Engineers,1989.
[16]Jones F.O.,Owens W.W.A Laboratory Study of Low-Permeability Gas Sands[J].Journal of Petroleum Technology,1980,32(9):1631-1640.
[17]Ho C.K.,Webb S.W.Gas Transport Mechanisms[A]//Gas Transport in Porous Media[C].Netherlands:Springer,2006:5-26.
[18]Londono F.,Archer R.A.,Blasingam T.Correlations for Hydrocarbon-Gas Viscosity and Gas Density-Validation and Correlation of Behavior Using a Large-Scale Database[J].SPE Reservoir Evaluation&Engineering 2005,8(6):561-572.
[2]Warren J E,Root P J.The behavior of naturally fractured reservoirs[J].Society of Petroleum Engineering Journal,1963(3):245-255.
[3]范章群,夏致远.煤基质形状因子理论探讨[J].煤田地质与勘探,2009,37(3):15-18.
[4]Wu Y S,Li J F,Ding D,et al.A Generalized Framework Model For The Simulation Of Gas Production In Unconventional Gas Reservoirs[J].SPE Journal,2014,19(5):845-857.
[5]Wu Y S,Fakcharoenphol P.A unified mathematical model for unconventional reservoir simulation[C]//SPE EUROPEC/EAGE Annual Conference and Exhibition.Vienna:Society of Petroleum Engineers,2011.
[6]Wu Y S,Wang C,Li J,et al.Transient Gas Flow in Unconventional Gas Reservoir[M].Society of Petroleum Engineers,2012.
[7]Langmuir L.The Constitution and Fundamental Properties of Solid and Liquids[J].Journal of American Chemical Society,1975,36(2):221-295.
[8]Klinkenberg L J.The Permeability of Porous Media to Liquids and Gases[A]//Drilling and Production Practices[C].New York:American Petroleum Institute,1941.
[9]Fick A V.On liquid diffusion[J].Journal of Membrane Science,1995,100(1):33-38.
[10]LIM K T,AZIZ K.Matrix-fracture transfer shape factors for dual-porosity simulators[J].Journal of Petroleum Science and Engineering,1995(13):169-178.
[11]蔡喜东.低渗透裂缝性砂岩油藏渗吸影响因素数值模拟研究[D].北京:中国石油大学(北京),2010.
[12]何勇明.裂缝性油藏形状因子研究及应用[D].成都:成都理工大学,2007.
[13]Crank J.The Mathematics of Diffusion,2nd Edn[M].London and New York:Oxford University Press(Clarendon),1975.
[14]Kazemi,H.,Merrill,L.S.,Porterfield,K.L.,Zeman,P.R.Numerical Simulation of Water-Oil Flow in Naturally Fractured Reservoirs[J].Society of Petroleum Engineers Journal,1976,16(6):317-326.
[15]COATS K H.Implicit compositional simulation of singleporosity and dual-porosity reservoirs[A]//Proceedings of the SPE Symposium on Reservoir Simulation[C].Texas:Society of Petroleum Engineers,1989.
[16]Jones F.O.,Owens W.W.A Laboratory Study of Low-Permeability Gas Sands[J].Journal of Petroleum Technology,1980,32(9):1631-1640.
[17]Ho C.K.,Webb S.W.Gas Transport Mechanisms[A]//Gas Transport in Porous Media[C].Netherlands:Springer,2006:5-26.
[18]Londono F.,Archer R.A.,Blasingam T.Correlations for Hydrocarbon-Gas Viscosity and Gas Density-Validation and Correlation of Behavior Using a Large-Scale Database[J].SPE Reservoir Evaluation&Engineering 2005,8(6):561-572.