Applied mechanics in Moving Boundary problems of one-dimensional non-Darcy Flow in Semi-infinite Long Porous Media

摘要

Dimensionless mathematical models of the fluid flow in the semi-infinite long porous media with constant production pressure on the inner boundary conditions are built, which include the effect of threshold pressure gradient (TPG). The analytical solutions of these dimensionless mathematical models are derived through new definitions of dimensionless variables. Comparison curves of the dimensionless moving boundary under different values of dimensionless TPG are plotted from the proposed analytical solutions. For the case of constant production pressure, a maximum moving boundary exists, beyond which the fluid flow will not occur. The value of maximum boundary distance decreases with increasing TPG. However, the velocity of pressure propagation decreases with time. The larger the TPG is, the steeper the curve of pressure depression cone is and the shorter the distance of the pressure propagation is.