Formulation of the flow problem in anisotropic porous media using different coordinate transformations

To solve an anisotropic flow problem, we transform the problem into an equivalent isotropic problem. We expect that an anisotropic solution can be readily obtained from the equivalent isotropic solution. However, sometimes it is not the case. In this paper we use the drawdown equation of a fully-penetrated vertical well test, and the drawdown and buildup equations for a probe test to discuss when we can and when we cannot directly obtain an anisotropic solution from an isotropic solution in this paper. Due to the fact that transformation causes the changes in flow geometry and the shape of the wellbore or probe, we have to modify the equivalent isotropic solution to obtain the anisotropic solution. Finally, we present a case that the horizontal well productivity was incorrectly derived in a published paper, due to the misuse of the concept of anisotropy.