RESEARCH ON ANALYTICAL AND NUMERICAL SOLUTIONS OF A MOVING BOUNDARY MODEL OF SEEPAGE FLOWIN LOW- PERMEABLE POROUS MEDIA

The modes of non-Darcy seepage flow in low- permeable porous media with threshold pressure gradient belong to the moving boundary problems with strong nonlinearity. In this paper, a moving boundary model of one- dimensional non-Darcy seepage flow in low- permeable porous media with threshold pressure gradient is studied for the case of a variable pressure at the inner boundary. A similarity transformation method and a spatial coordinate transformation based finite difference method are applied to obtain the exact analytical solution and numerical solution of the moving boundary model, respectively. Research results show that the moving boundary model has a unique exact analytical solution, which also strictly verifies the accuracy of the numerical solution; and when the value of threshold pressure gradient tends to zero, the exact analytical solution of the moving boundary model of non-Darcy seepage flow can reduce to the one corresponding to Darcy's seepage flow. The formation pressure distribution curves with non- zero dimensionless threshold pressure gradient from these solutions exhibit the characteristics of compact support, which is obviously different from those corresponding to Darcy's flow model. Therefore, the study on the unsteady seepage flow problem in low- permeable porous media should take into account the effect of moving boundary condition. The presented research improves the theory of non-Darcy seepage flow in low- permeable porous media, and also builds theoretical foundation for the technologies of well testing interpretation and reservoir numerical simulation involved in the development of low- permeable oil and gas reservoirs.