Pressure Transient Analysis of Vertical Fault Leakage to a High Permeability Zone

Mojtaba Mosaheb, Craft and Hawkins Department of Petroleum Engineering, Louisiana State University, Baton Rouge, LA, 70803: mmosah1@lsu.edu
Mehdi Zeidouni, Craft and Hawkins Department of Petroleum Engineering, Louisiana State University, Baton Rouge, LA, 70803: zeidouni@lsu.edu

In this study, an analytical solution to evaluate the pressure transient corresponding to injection near a leaky fault is presented. The leaky fault can generally act as a conduit for both lateral and vertical flows. Therefore, the injection zone may be in hydraulic communication with the overlying layer by the leaky fault. The leakage to multiple overlying layers is simplified as a leakage to a single overlying layer with infinite transmissivity. Hence, it is assumed that pressure of the overlying layer does not change during the injection. The permeability and formation thickness of the injection zone in two sides of the fault may not be identical. This assumption may be correct because of vertical displacement of sedimentary layers through the fault plane. The governing diffusivity equation is written for the injection zone. The injection zone is divided into two regions on two sides of the fault. The system of partial differential equations is solved based on Fourier and Laplace transforms applied respectively on space and time. The analytical solution is validated by numerical simulation and can be used in well testing packages as a module for leaky fault characterization. Moreover, type curves are presented to implement the inverse solution and introduce a method to estimate vertical and horizontal conductivities of the fault and transmissivity of the region on the other side of the fault.

Key words: Fault leakage, Analytical solution, Pressure transient, Conductivity

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