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Analytical model of leakage through fault to overlying formations
Author(s) -
Zeidouni Mehdi
Publication year - 2012
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2012wr012582
Subject(s) - laplace transform , fault (geology) , bounding overwatch , ordinary differential equation , geology , offset (computer science) , leakage (economics) , mechanics , differential equation , computer science , mathematics , mathematical analysis , physics , seismology , artificial intelligence , programming language , economics , macroeconomics
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.