Abstract
Abstract This paper presents solutions to the pressure diffusivity equation for fractured porous media including multiple block sizes with a uniform distribution, for both unsteady and pseudo-steady states by means of dimensionless variables, the Laplace transform, and the Stehfest algorithm. The general solution was validated through the classic Warren & Root single-sized block distribution and pseudo-steady state model. It is common that in transient well test analysis, generalized plots of the models’ solutions are used. In this paper plots in time domain: " pwD vs. tD" and " tD [d(pwD)/dtD] vs. tD," as well as in Laplace domain: " spwD¯ vs. 1/s " and " s[d(spwD¯)/ds] vs. 1/s" are presented, showing the influence of the parameters that more strongly influence the behavior of the solutions, such as the matrix storativity ratio (ωm), fracture storativity ratio (ωf), maximum interporosity flow coefficient (λmax), and minimum interporosity flow coefficient (λmin). As is known, the derivative pressure curve is more sensitive to the variation of these parameters, providing very valuable information about the reservoir. Thus, various plots including the derivative of dimensionless pressure in both time and Laplace domains, such as tD [d (pwD)/dtD]min and s[d(spwD¯)/ds]min, and their behavior with respect to reservoir parameters were also analyzed. From these plots, empirical and easy-to-evaluate correlations were obtained. Using these correlations, it is possible to calculate initial values for the parameters that characterize fractured reservoirs:ωm0, ωf0, λmax 0, λmin 0, hmax 0, and hmin 0. These initial values are very close to the real ones; therefore, ωm, ωf, λmax, λmin, hmax, and hmin are rapidly found.
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