Nonlocal Diffusion in Fractured Rocks
- R. Raghavan (R. Raghavan, Inc.) | C. Chen (Kappa Engineering) | J. J. DaCunha (Pioneer Natural Resources)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- May 2017
- Document Type
- Journal Paper
- 383 - 393
- 2017.Society of Petroleum Engineers
- Long-range effects, Fractured rocks, Memory effects, Nonlocal Diffusion, Power-law declines
- 1 in the last 30 days
- 363 since 2007
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Correction Notice: Eq. 54 on page 388 has been corrected from an earlier version of the paper. This correction does not affect any other information provided in the paper.
Space–time fractional diffusion in a linear, bounded region is considered. An analytical expression for the pressure distribution in the bounded region is derived in terms of the Mittag-Leffler function and the Laplace transformation. Comparisons with numerical solutions indicate excellent agreement. A convenient expression that incorporates a combination of Dirichlet and Neumann boundary conditions, particularly suitable for rapid computations, has been elusive until now. Responses that may be expected in nanoporous reservoirs that are usually produced through horizontal wells containing multiple hydraulic fractures are deduced. It is shown that the existence of obstacles, discontinuities, and other complex flow paths in fractured reservoirs express themselves in the form of power-law declines, whereas long-range interactions reflective of rapid communication, interestingly, express themselves as exponential declines. An understanding of the simultaneous influences of these two effects is the purpose of this study. The application to the “trilinear” model often used to evaluate well performance in shales is demonstrated.
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