关键词: 水平井; 低渗透油藏, 启动压力梯度, 二次梯度项, 有限元方法, 压力动态

Abstract:

In view of the threshold pressure gradient(TPG) phenomenon that the seepage flow in low permeability reservoirs must overcome, an unsteady flow mathematical model for the horizontal well in box-shaped reservoirs was established with the nonlinear quadratic gradient term remaining in differential equations. Firstly, nonlinear differential equations were linearized through logarithmic transformation, then model controlling equations were derived using the Galerkin finite element method(FEM) and solved by the direct iteration method. After the substitution of the inverse transformation, the numerical solution of bottom pressure was finally obtained and verified by comparison with the classic Odeh solution. Calculation results of bottom hole pressure for the horizontal wells demonstrated that both pressure and pressure derivative curves showed an upwarping tendency as the TPG was considered, the bigger the TPG was, the more distinct the curves upwarped, i.e. the greater the downhole pressure difference was required. With the presence of fluid compressibility, the downhole pressure difference was less than that derived from the model that ignored the nonlinear quadratic gradient term, and the error between them increased nonlinearly with the increase of the fluid compressibility factor.

Key words: horizontal well, low permeability reservoir, threshold pressure gradient, quadratic gradient term, finite element method, pressure behavior