Pressure transient behavior in a multilayer reservoir with formation crossflow

This study proposes a new solution to the pressure transient behavior for a uniform-flux with a fully penetrating vertical well in a multilayer reservoir with formation crossflow. The general problem of pressure transient in multilayer reservoirs, in which any two adjacent layers are crossflowing in the formation, is solved analytically. The solution is presented for an infinite-acting system with no wellbore storage or skin factor effects. This analytical solution is obtained using Laplace transform, double Fourier transform, and Green's functions method. This solution provides an accurate and fast tool to: evaluate a vertical well performance in a multilayer reservoir, and estimate the effects of formation properties on pressure behavior at locations both far away from and around the well. Based on the solution, the pressure of the vertical well, which produces with a constant rate in the multilayer reservoir, can be examined in detail. An expression of dimensionless crossflow coefficient is obtained by solving a symmetric tri-angular matrix equation. Based on the solution, it is verified that the dimensionless crossflow coefficient is not constant but behavies as a function of the time and distance away from the wellbore. When producing time is sufficiently long, crossflow will cease to exist and crossflow coefficients are equal to zero, which means there are no effects of adjacent layers on the pressure drop of each layer. These findings indicate that each layer produces independently.