变形多孔介质流固耦合非线性渗流模型及解析

Fluid-Solid-Coupling Model and Analytical Solution for Nonlinear Flow in Deformable Porous Media

渗流的流固耦合问题在理论上与实践中都十分重要。考虑可变形多孔介质的渗透系数和孔隙率的变化依赖于压强变化,由渗透系数与渗透率的关系,结合非线性渗流流体质量守恒方程和连续性方程等基本微分方程建立了一维流固耦合非线性渗流问题的数学模型,推导了可变形介质非稳定渗流场微分方程。利用分离变量法推导出孔隙水压随时间和空间的变化关系的解析解,分析了渗流方程中的控制参数对渗流的非线性程度的影响。通过引入物理参数的方法处理渗流随时间的变化,并阐明了非线性渗流机理,最后定性分析了影响流体渗流压强分布的因素。

The fluid-solid-coupling issue is very important both theoretically and practically. The mathematical model on the one-dimension nonlinear fluid-solid-coupling issue is established after taking into account the feature that the seepage coefficient and porosity of deformable porous media depends on the change of pressure, introducing the relationship between permeability coefficient and permeability rate, and combining the mass conservation equation and continuity equation of nonlinear flow. Based on the Dacy law and mass conservation law, the differential equation of unsteady flow is derived, in which the porosity change has been taken into account. Besides, the analytical solution which reveals the relationship between pore water pressure with time and space has been deduced by applying the method of separation of variables and combining with the boundary conditions and initial conditions, and the effect that the control parameter of flow equation on the nonlinear degree of flow is al so analyzed. The change of flow with the time is treated by introducing the physical parameters in the course of analysis and the nonlinear flow mechanism is elucidated. At last, the factors influencing the flow pressure are analyzed qualitatively.