Exact solution for spherical flow and transient behavior of pressure with consideration of effects of quadratic-GRA- Dient term

摘要

Conventional models for fluid flow in well tests have not been consistent with material balance. According to the slightly compressible fluid assumption, the quadratic gra- dient term in the nonlinear partial differential equation has been usually neglected. This approach is questionable for live oil and low permeability reservoirs. We have already known that linearization by neglecting quadratic gradient terms may lead to errors for large values of well-test time. In this paper, a method that is consistent with material balance was proposed on the spherical flow system. All terms in the nonlinear par- tial equiation were retained.