基于ALE方法的油水两相流固耦合模型研究
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摘要
文章应用任意拉格朗日-欧拉方法(ALE)对油水两相流固耦合问题进行了研究;详细推导了ALE描述下的两相渗流与变形多孔介质的耦合数学模型方程,解决了孔隙骨架变形介质与渗流方程的统一描述问题;通过编制相应的ALE有限元程序,分析了注水驱替过程,检验了所提出的模型及相关数值算法。对该模型方程讨论发现,若取ALE网格移动速度为岩层骨架变形速度将简化两相渗流方程,降低数值求解难度。
In this paper,the Arbitrary Lagrangian-Eulerian method(ALE) is applied to the coupled model for oil/water flow in deformed porous media.The ALE frame referred to porous solid and fluid flow is derived and a consistent coordinate frame description for the governing formation is established.When the mesh motion is equal to the velocity of the deformed porous media,a simpler formulation can be presented which reduces the difficulty of numerical solution.In the numerical testing,it is applied to the simulation of water injection in reservoir.Some simulation results,which demonstrate the validity of the ALE formulation,have been obtained.
In this paper,the Arbitrary Lagrangian-Eulerian method(ALE) is applied to the coupled model for oil/water flow in deformed porous media.The ALE frame referred to porous solid and fluid flow is derived and a consistent coordinate frame description for the governing formation is established.When the mesh motion is equal to the velocity of the deformed porous media,a simpler formulation can be presented which reduces the difficulty of numerical solution.In the numerical testing,it is applied to the simulation of water injection in reservoir.Some simulation results,which demonstrate the validity of the ALE formulation,have been obtained.
引文
[1]Bear J.多孔介质流体动力学[M].北京:中国建筑工业出版社,1983:54-57.
[2]Cooper H H.The equation of ground water flow in fixedand deforming coordinates[J].J Geophys Res,1966,71(20):4785-4790.
[3]薛世峰.非混溶饱和两相渗流与变形孔隙介质耦合作用的理论研究及其在石油开发中的应用[D].北京:中国地震地质研究所,2000.
[4]Tran D,Nghiem L,Buchanan L.Iterative coupling be-tween geomechanical deformation and reservoir flow[J].Journal of Petroleum Technology,2006,58(9):102-105.
[5]Fung L S K.A coupled geomechanic-multiphase flow modelfor analysis of in situ recovery in cohesionless oil sands[J].The Journal of Canadian Petroleum Technlogy,1992,31(6):56-67.
[6]冉启全.顾小芸.弹塑性变形油藏中多相渗流的数值模拟[J].计算力学学报,1999,16(1):24-31.
[7]陈波,李宁.多孔介质的变形场-渗流场-温度场耦合有限元分析[J].岩石力学与工程学报.1999,20(4):467-472.
[8]刘晓丽,梁冰,王思敬,等.水气二相渗流与双重介质变形的流固耦合数学模型[J].水利学报,2005,17(4):405-412.
[9]熊伟,田根林,黄立信,等.变形介质多相流动流固耦合数学模型[J].水动力学研究与进展,2002,17(6):770-776.
[10]刘晓旭,胡勇,赵金洲,等.流-固全耦合新模型研究[J].断块油气田,2006,13(3):45-46.
[11]李培超,孔祥言,卢德唐.饱和多孔介质流固耦合渗流的数学模型[J].水动力学研究与进展,2003,18(4):419-426.
[12]Belytschko T,Liu W K,Mron B.Nonlinear finite elementsfor continua and structures[M].北京:清华大学出版社,2005:341-387.
[13]Hughes T J R,Liu W K.Lagrangian-Eulerian finite ele-ment formulation for incompressible viscous flows[J].Computer Methods in Applied Mechanics and Engineer-ing,1981,29:329-349.
[14]Biot M A.Theory of deformation of a porous viscoelasticanisotropic solid[J].J Appl Phys,1956,5(27):459-467.
[15]李传亮.多孔介质的有效应力及其应用研究[D].北京:中国科学技术大学力学和机械工程系,2000.
[2]Cooper H H.The equation of ground water flow in fixedand deforming coordinates[J].J Geophys Res,1966,71(20):4785-4790.
[3]薛世峰.非混溶饱和两相渗流与变形孔隙介质耦合作用的理论研究及其在石油开发中的应用[D].北京:中国地震地质研究所,2000.
[4]Tran D,Nghiem L,Buchanan L.Iterative coupling be-tween geomechanical deformation and reservoir flow[J].Journal of Petroleum Technology,2006,58(9):102-105.
[5]Fung L S K.A coupled geomechanic-multiphase flow modelfor analysis of in situ recovery in cohesionless oil sands[J].The Journal of Canadian Petroleum Technlogy,1992,31(6):56-67.
[6]冉启全.顾小芸.弹塑性变形油藏中多相渗流的数值模拟[J].计算力学学报,1999,16(1):24-31.
[7]陈波,李宁.多孔介质的变形场-渗流场-温度场耦合有限元分析[J].岩石力学与工程学报.1999,20(4):467-472.
[8]刘晓丽,梁冰,王思敬,等.水气二相渗流与双重介质变形的流固耦合数学模型[J].水利学报,2005,17(4):405-412.
[9]熊伟,田根林,黄立信,等.变形介质多相流动流固耦合数学模型[J].水动力学研究与进展,2002,17(6):770-776.
[10]刘晓旭,胡勇,赵金洲,等.流-固全耦合新模型研究[J].断块油气田,2006,13(3):45-46.
[11]李培超,孔祥言,卢德唐.饱和多孔介质流固耦合渗流的数学模型[J].水动力学研究与进展,2003,18(4):419-426.
[12]Belytschko T,Liu W K,Mron B.Nonlinear finite elementsfor continua and structures[M].北京:清华大学出版社,2005:341-387.
[13]Hughes T J R,Liu W K.Lagrangian-Eulerian finite ele-ment formulation for incompressible viscous flows[J].Computer Methods in Applied Mechanics and Engineer-ing,1981,29:329-349.
[14]Biot M A.Theory of deformation of a porous viscoelasticanisotropic solid[J].J Appl Phys,1956,5(27):459-467.
[15]李传亮.多孔介质的有效应力及其应用研究[D].北京:中国科学技术大学力学和机械工程系,2000.
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