A Semi-Analytic Solution for Flow in Finite-Conductivity Vertical Fractures Using Fractal Theory
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abstract
The exploitation of unconventional gas reservoirs goes hand in hand with the practice of hydraulic fracturing. With a projected increase in energy demand in the coming years, this practice is set to experience significant growth. Sophisticated numerical and analytical models are needed to accurately describe fluid flow in a hydraulic fracture, and the problem has been approached from different directions in the past 3 decades, starting with the work of Gringarten et al (1974). This topic is still an active area of research and, for the more complicated physical scenarios such as multiple transverse fractures in ultra-tight reservoirs, answers are presently being sought. Fractal theory has been successfully applied to reservoir engineering, albeit with an emphasis on the study of naturally fractured reservoirs. In this paper, we start by re-visiting the fundamentals of fractal theory as applied to fluid flow in porous media by way of a study of the Fractal Diffusivity Equation. Upon completion of this task, we combine this tool with the classic "trilinear flow solution" (Lee and Brockenbrough 1986); our research culminates in the development of a fast and accurate semi-analytical solution for flow in a single vertical fracture, which we name the "Fractal Fracture Solution". This Fractal Fracture Solution allows us to obtain the Cinco-Meng solution (1988) instantaneously while avoiding their tedious and cumbersome method. An additional accomplishment of this exercise is to demonstrate the flexibility of fractal theory, and encourage its use in the development of solutions for other problems. Copyright 2012, Society of Petroleum Engineers.
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SPE Latin America and Caribbean Petroleum Engineering Conference
