Pressure-Transient Analysis of Fractal Reservoirs

TLDR

We present a formulation for a fractal fracture network embedded into a Euclidean matrix. Single‑phase flow in the fractal network is modeled by a modified diffusivity equation, and the pressure‑transient response is analyzed both without and with matrix participation. The results extend previous pressure‑transient and well‑testing methods to reservoirs of arbitrary fractal dimensions, providing a unified description for both single‑ and dual‑porosity systems and enabling identification and modeling of naturally fractured reservoirs with multiple scales and fractal properties.

Abstract

Summary We present a formulation for a fractal fracture network embedded into a Euclidean matrix. Single-phase flow in the fractal object is described by an appropriate modification of the diffusivity equation. The system's pressure-transient response is then analyzed in the absence of matrix participation and when both the fracture network and the matrix participate. The results obtained extend previous pressure-transient and well-testing methods to reservoirs of arbitrary (fractal) dimensions and provide a unified description for both single- and dual-porosity systems. Results may be used to identify and model naturally fractured reservoirs with multiple scales and fractal properties.