油藏多相流体渗流流-固耦合数学模拟研究

MATH SIMULATION ON COUPLED FLUID FLOW AND GEOMECHANICS FOR MULTIPLE PHASES RESERVOIR

实践表明,油藏开发将引起应力场的变化、导致岩石发生变形、改变储层的渗储特性,进而影响产量。为反应这一问题,建立了油藏流-固耦合渗流模型,并考虑了以下因素:多相流体,油藏岩石变形,地应力、孔隙度和渗透率变化,流体渗流与岩石应变耦合等。导出的控制方程是基于流体孔隙压力、饱和度以及岩石质点位移的非线性方程。由于互含参变量,不能直接求解,采用有限差分方法将流体渗流和岩石应变方程离散成主对角占优的7对角矩阵,采用隐式迭代方法求解。示例分析说明,本模型可用于研究应力、应变、孔隙度和渗透率的动态变化规律以及可能对生产造成的影响。与其他模型对比结果显示,本模型更接近于实际情况。

Oil production will change the stress field of reservoir and induce the strain of rocks. As a resultwill influence the fluid percolation. A math model of coupled fluid flow and geomechanics is set up. The following factors are considered in this model:constant temperature,two phases of oil and water,deformation of reservoirchanges of stress,porosity and permeability. There are seven variables in the governing equations to comprise the matrix of pore pressure,fluid saturation and displacement. The system of the nonlinear governing partialdifferential equations is discreted using the finite difference method. The finite difference equations are arranged as seven-point stencils. A fully implicit procedure is adopted for maximum numerical stability. Analyzed by an example,it is shown that the parameters of stress,strain,porosity and permeability change with time and space. This model can be used to solve many problems,such as simulating deformation of reservoir,calculating changes of stress and strain,analyzing changes of porosity and permeability in reservoir.