Determination of Fractal Parameters of Fracture Networks Using Pressure-Transient Data

Abstract

Summary The objective of this paper is to investigate the transient pressure behavior of naturally fractured reservoirs with fractal characteristics. This work is based on the findings of previous studies, which have shown that the networks of fractures in some reservoirs are fractals. Thus, using this assumption, an approximate analytical solution for dual-porosity systems is derived in the Laplace space. The approximate solution presented in this work uses a pseudosteady-state matrix-to-fractal fracture transfer function. This solution is compared with a finite-element solution, and good agreement is found. Short- and long-time approximations are used to obtain procedures in time to determine some fractal parameters. These approximations are compared to the appropriate expressions when an unsteady-state matrix-to-fractal fracture transfer function is used. Synthetic and field examples are presented to illustrate the methodology proposed in this work. This paper also presents an analytical solution for the pseudosteady-state flow period and demonstrates the importance of analyzing both transient and pseudosteady-state flow-pressure data for a single-well situation to fully characterize a naturally fractured reservoir with a fractal geometry.