Analytical model of leakage through fault to overlying formations

A fault is generally composed of a fault core surrounded by damage zones and can accommodate both lateral and vertical flow. In this paper we develop an analytical model to evaluate the leakage rate through a fault and corresponding pressure changes in the injection zone and a shallower permeable interval. The leaky fault connects the upper interval and the target zone, which are otherwise separated by a confining layer. We account for both across-fault and up-fault flow to honor the general architecture of the fault. We extend the two-formation analytical solution to consider multiple overlying formations with alternating confining layers offset by the fault. The solution methodology involves writing and transforming the coupled governing flow equations successively into the Laplace and Fourier domains and solving the resulting ordinary differential equations. The solution is verified through a comparison with existing analytical solutions for bounding cases. Two examples are presented to demonstrate the behavior and potential applications of our analytical model.