An analytical solution for heterogeneous and anisotropic anticline reservoirs under well injection

This study develops a mathematical model for describing the steady-state head response to fluid injection into a fully penetrating well in a heterogeneous and anisotropic anticline reservoir. In the model, the upper boundary of the anticline reservoir is approximated by a form of step change in reservoir thickness and the domain of the reservoir is divided into two regions with different hydraulic conductivities. By virtue of the properties of Fourier series, the method of separation of variables is employed to develop the analytical solution of the model.This new solution can be applied to estimating head distributions or injection rates for various geometrical conditions of the reservoir. If the trap is absent, the solution can be utilized to analyze head distributions in the reservoir system with two concentric transmissivity zones. Moreover, if the upper boundary becomes flat and the reservoir is homogeneous and isotropic, the solution reduces to the Thiem equation.