Analytical and Numerical Analysis of Matrix-Fracture Exchanges through Diffusion Mechanisms in Fractured Reservoirs

To model the behaviour of matrix/fracture exchanges in Naturally Fractured Reservoirs (NFRs) through dual-medium models, analytical transfer functions (TF) have been developed. Amongst those novel TFs, the General Transfer Function (GTF), developed by Lu et al. at Imperial College London in 2007, has been already validated for three main recovery mechanisms (gravity, capillarity and expansion).

Within this paper, the behaviour of its diffusing term, inspired by Zimmerman et al. (1993) approach, was simulated and tested, to improve the accuracy of flow simulator for NFRs. For this validation we first checked the behaviour of an industrial flow simulator, on a fine grid, against an analytical solution for the diffusion process, in simple 1D conditions. This gave us our reference cases.

The comparison study of analytical and numerical approaches, revealed differences between diffusion recovery through the GTF and the reference, with a diffusion speed slightly faster with the GTF at early and middle times. A good match was observed at late times in 1D. Meanwhile, an increase in speed was observed in 2D with the increase of the matrix size. A comparison with a commercial double-porosity simulator showed however that the GTF is worth being used instead of the standard TFs.