Discussion of permeability anisotropy effect in transformation

To solve an anisotropic flow problem, the problem is transformed into an equivalent isotropic problem. It is expected that an anisotropic solution can be readily obtained from the equivalent isotropic solution. However, sometimes that is not the case. Using the drawdown equation of a fully penetrated vertical well test and the drawdown and buildup equations for a probe test, this paper discusses when it is both possible and impossible to directly obtain an anisotropic solution from an isotropic solution. Because of the fact that transformation causes the changes in flow geometry and the shape of the wellbore or probe, the equivalent isotropic solution must be modified to obtain the anisotropic solution. Finally, a case of how horizontal well productivity was incorrectly derived in a published paper - caused by the misuse of the concept of anisotropy - is presented.