Numerical Simulation Of Nonlinear Seepage Flow In Low-permeable Reservoirs With Moving Boundaries

For the two kinematic equations of pseudo-linear kinematic equation and nonlinear kinematic equation for the seepage flow in low-permeable porous media, the seepage velocity is a multi-sectional function with respect to the formation pressure gradient, and their continuity is bad; and then it is very hard to use functions with good continuity to approximate them validly. Then, when the seepage flow process happens in low-permeable formations, different formation pressure gradient range will correspond to different seepage flow areas; there exist boundaries between these seepage flow areas. Because the seepage flow process is unsteady, the formation pressure gradient changes transiently, and then these boundaries between different seepage flow areas can move with time. In the mathematical modeling, the mathematical equations for expressing these moving boundaries are called moving boundary conditions. In the thesis, with innovation, the moving boundary conditions are incorporated in the mathematical models of seepage flow in low-permeable porous media; and the analytical solution methods and the effective numerical computation methods for solving moving boundary problems in heat conduction theory, and the reservoir numerical simulation mode IMEX of CMG are relied on to study on the numerical simulations of the one-phase or oil, gas and water three-phase nonlinear seepage flow in low-permeable reservoirs based on the pseudo-linear kinematic equation and nonlinear kinematic equation. For the case in consideration of threshold pressure gradient in the seepage kinematic equation, the effect of neglecting the quadratic pressure gradient in the governing equation of one-phase seepage flow on the numerical simulation results is analyzed. In addition, the effects of nonlinear seepage flow parameters such as the threshold pressure gradient, the critical pressure gradient and the pseudo threshold pressure gradient on the numerical simulation results are discussed. The presented research supports theoretical foundations for further improving the accuracy of numerical simulation technologies in developing low-permeable oil & gas reservoirs.