Reduced flow model and transmissibility upscaling in multi-layered faulted reservoirs

Abstract

We construct a new three-scale model for single phase incompressible flow in faulted rocks containing multiple damage zones. At the finer scale (O(1m)), flow is influenced by the high-contrast layered heterogeneities inherent to the core and adjacent damage zones, which are populated by geological anomalies, such as compaction bands, debris, and fine sediments and joints. In the first stage of the reiterated homogenization procedure, we construct a lower-dimensional reduced model, where the discontinuity is envisioned as (n−1)-dimensional manifold (n=2,3), topologically attached to multiple layered structures, with flow patterns characterized by various jumps in pressure and velocity fields. Subsequently, by aligning the fault with the interface between adjacent simulation cells of a coarse grid, the upscaling of the reduced flow model gives rise to transmissibility multipliers, whose constitutive response stems naturally from the local flow patterns, exhibiting improved accuracy compared to the traditional harmonic mean, inherent to the two-point flux approximation. Computational simulations obtained with the finite element method with localized discontinuous spaces illustrate the ability of the three-scale model to provide further insight into the behavior of the transmissibility multipliers, which capture the effects of fault zone texture upon the flow discretization. The methodology proposed herein shows enormous potential for the development of more accurate transmissibility preprocessors at relatively low computational costs, consequently overcoming the shortcomings of a direct application of the local high-fidelity approach.