On some integral equations arising in the pressure analysis of inclined wells in anisotropic formations

In this note we look at the effects of anisotropic permeability on the distribution of pressure around an uncased or cased wellbore. We suggest a useful approximation for the form of the density of point sources distributed around the wellbore in order to simulate its influence on the pressure field. We consider both steady state and transient pressure distributions and perform full numerical calculation of some examples to check the accuracy of the approximation.

► Anisotropic diffusion. ► Integral equations for source distributions. ► Approximations for anisotropic source densities. ► Complete numerical solution for various inclined well angles.