Abstract
AbstractWhen modeling fluid flow in fractured reservoirs, it is common to represent the fractures as lower‐dimensional inclusions embedded in the host medium. Existing discretizations of flow in porous media with thin inclusions assume that the principal directions of the inclusion permeability tensor are aligned with the inclusion orientation. While this modeling assumption works well with tensile fractures, it may fail in the context of faults, where the damage zone surrounding the main slip surface may introduce anisotropy that is not aligned with the main fault orientation. In this article, we introduce a generalized dimensional reduced model which preserves full‐tensor permeability effects also in the out‐of‐plane direction of the inclusion. The governing equations of flow for the lower‐dimensional objects are obtained through vertical averaging. We present a framework for discretization of the resulting mixed‐dimensional problem, aimed at easy adaptation of existing simulation tools. We give numerical examples that show the failure of existing formulations when applied to anisotropic faulted porous media, and go on to show the convergence of our method in both two‐dimensional and three‐dimensional.
Highlights
Modeling and simulation of flow in porous media with faults, fractures, and other thin inclusions representing discontinuities is central to a wide range of subsurface engineering applications, including geothermal energy exploitation,[1] shale gas extraction,[2] carbon sequestration,[3] and energy storage.[4]The inclusions are characterized by a high aspect ratio, and permeability significantly different from that of the host medium; they severely affect flow patterns
We presented an improved framework to modeling and discretizing flow in generally anisotropic porous media with thin inclusions, within the context of mixed-dimensional partial differential equations
Our model considers a full permeability tensor for the inclusions, resulting in additional terms arising in our formulation as compared with existing local discretizations
Summary
Modeling and simulation of flow in porous media with faults, fractures, and other thin inclusions representing discontinuities is central to a wide range of subsurface engineering applications, including geothermal energy exploitation,[1] shale gas extraction,[2] carbon sequestration,[3] and energy storage.[4]. All objects (matrix, inclusions, and intersection points and lines) are represented in the model as independent subdomains separated by interfaces, and discretization models arise naturally, thereby avoiding challenges related to complex flow dynamics in the proximity of the intersections, for example, due to capillary flow or fractures with different permeabilities We refer to this representation of the geometry as mixed-dimensional. The contribution of this article is twofold: First, we present a generalized dimensional reduced model that can preserve full-tensor permeability effects in the out-of-plane direction of the fault This type of mixed-dimensional problem involving general permeability tensors has only been treated in a recent publication by Gander et al.,[12] who used Fourier analysis to derive coupling conditions between a single fracture and the surrounding rock in a two-dimensional (2D) setting.
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