This paper provides an analytical solution for a well near a linear leaky boundary, in otherwise infinite laterally composite systems. The leaky boundary is viewed as an infinitesimal damaged discontinuity (linear skin discontinuity) located at the interface between two adjacent media. The zone thickness may or may not be equal, and the infinitesimal damaged zone width is a restatement to the assumption of low fault conductivity and storativity.

The problem was solved using the two-dimensional diffusion equation with successive integral transformations, and the one dimensional green’s function. Both solutions, uniform and non-uniform diffusivity cases merge exactly at early and late time. Solutions presented in this study have been validated by comparing a number of its simplified forms with those available in the literature. Confirmation of the solution is also demonstrated by investigating three limiting cases: (1) a well near a sealing boundary, (2) well near undamaged linear discontinuity in a composite system, and (3) well near a constant pressure linear boundary.

As shown in this paper, a single leaky fault can give appearance of naturally fractured reservoir on a pressure transient response for a unit-mobility ratio case and a linear flow regime may also develop for a low diffusivity contrast. Further investigation of the correlating skin parameter ‘sa’ representing the product (Sf* ad) proves that Yaxley’s definition addressed to the fault (α) is equivalent to the term (1/Sa) derived in this work. Consequently, computing the discontinuity damage leads to an indirect measurement of the fault conductivity. Pressure and pressure derivative type curves have also been generated showing the effect of all the parameters affecting the wellbore responses. Making the use of the flexibility of the final solution, we have also investigated the pressure response of a linear boundary in an infinite naturally fractured composite reservoir. The step-by-step procedure for calculating reservoir parameters is also developed in this study. The Tiab’s Direct Synthesis (TDS) technique is applied to interpret pressure derivative behavior of a vertical well near a linear leaky boundary in laterally composite systems.

Lastly, for a practical implication, the procedure developed is illustrated with one simulated example and one field case.

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