考虑渗流压力梯度时低渗岩土固结控制方程的解析解

A Solution for Governing Equation of Low Permeability Rock Consolidation Considering Initial Seepage Pressure Gradients

基于波动采油技术背景,对初始状态饱和渗流流体低渗岩土的固结控制方程进行了半解析求解。Laplace变换与迭代消去后的一维或径向模型固结控制方程为包含变参量的四阶常(变)系数非线性偏微分方程。通过流体位移解指数形式假设与微分高阶项消除,转换为关于替换系数的特征方程求解,最终得到关于Laplace变换域内的流体位移通解。Matlab编程与数值算例表明,考虑初始渗流压力梯度项时,弹性波作用下低渗孔隙介质的渗流物性变化幅度明显增大.

Based on the application background of low-frequency vibration stimulation technology, a semi-analytical solution was given for the consolidation governing equation in low permeable rock, which was saturated with seepage fluid at the initial state. After Laplace transform and iteration elimination of the solid displacements, the governing equa- tion in one dimension or in radial dimension was shown as a four-order nonlinear partial differential equation with constant or variable coefficients. The coefficients was also related with variable rock parameters. With assuming an exponential form solution to the fluid displacement and eliminating higher-order partial differential term, the governing equation was converted to the eigenvalue equation of coefficient of assumed exponential function. Then, the general solution of fluid displacement in Laplace transform domain could be ob- tained easily. Through Matlab programming and numerical calculation, the results showed that the variations of the parameters and seepage flow in low permeability porous media had obviously increased under elastic wave, when considering the term about initial seepage pressure gradient in the governing equation.