kourosh khadivi - department of chemical and petroleum eng.
mohammad soltanieh

This article considers the application of finite element method (FEM) for numerical analysis of pressure transients under conditions where no reliable analytical solution is available . Analysisof pressure transients from well tests is normally based on various analytical solutions of the linear one -dimensional diffusion equation under restrictive assumptions about the formation and its boundaries. for example the formation is either assumed isotropic or a restrictive a priori assumption is made about its heterogeneity. well bore storage effect is also often considered without regard to the possibility of phase redistribution. in this article we present a numerical solution of the nonlinear diffusion equation based on the finite lement method FEM that can be used without any restrictive a priori assumptions. through the use of the weak formulation of the FEM, the solution can be obtained for heterogeneous media with discontinuous properties. the weak formulaiton also enables the handling of time dependent boundary conditions and hence problems involving well bore storage with significant phase redistribution. the speed ans accuracy of the numerical technique is first confirmed by comparison with simple test cases thay admit an analytical solution . the practical utility of the proposed method is then demonstrated for a number of test cases thatinvolve discontinuous formation properties and / or well bore storage with phase redistribution. in particular the potential errors caused by unjustified linearization of inherently nonlinear phenomena in well test analysis are clearly highlighted.