多孔介质非线性渗流问题的摄动解

Perturbation Solution of Non-Linear Seepage Problem in Porous Media

考虑变形多孔介质渗透参数 (渗透率和孔隙度 )与孔隙压力呈负指数变化的特点 ,建立了多孔介质渗流问题的数学模型 ,采用积分变换方法求出了一维非线性渗流问题的摄动解 ,并对常数渗透参数和指数渗透参数的渗流问题进行对比分析 ,计算结果表明 :两者之间的差别较大 ,且渗透参数的变化对于流体渗流中后期过程有着重要的影响 ,但对渗流早期影响不大 。

Considering the relationship of the infiltration parameter (permeability and porosity) of deformation porous media with pore pressure, which obeys a negative exponent approximation, a mathematic model is established about seepage problem in porous media. In this nonlinear numerical model, the integral transform is adopted and the perturbation analytic solution is obtained. Furthermore, the comparison analysis with constant infiltration parameter show that the influence on seepage due to the change of infiltration parameters focuses on the middle stage and he evening stage. It provides a theoretical approach for studying the model parameter of non-linear seepage problem in porous media.