Finite Element-Node-Centered Finite-Volume Two-Phase-Flow Experiments With Fractured Rock Represented by Unstructured Hybrid-Element Meshes

摘要

Fractured-reservoir relative permeability, water breakthrough, and recovery cannot be extrapolated from core samples, but computer simulations allow their quantification through the use of discrete fracture models at an intermediate scale. For this purpose, we represent intersecting naturally and stochastically generated fractures in massive or layered porous rock with an unstructured hybrid finite-element (FE) grid. We compute two-phase flow with an implicit FE/finite volume (FV) method (FE/FVM) to identify the emergent properties of this complex system. The results offer many important insights: Flow velocity varies by three to seven orders of magnitude and velocity spectra are multimodal, with significant overlaps between fracture- and matrix-flow domains. Residual saturations greatly exceed those that were initially assigned to the rock matrix. Total mobility is low over a wide saturation range and is very sensitive to small saturation changes. When fractures dominate the flow, but fracture porosity is low (10~(-3) to 1%), gridblock average relative permeabilities, k_(r,avg) cross over during saturation changes of less than 1%. Such upscaled k_(r,avg) yield a convex, highly dispersive fractional-flow function without a shock. Its shape cannot be matched with any conventional model, and a new formalism based on the fracture/matrix flux ratio is proposed. Spontaneous imbibition during waterflooding occurs only over a small fraction of the total fracture/matrix-interface area because water imbibes only a limited number of fractures. Yet in some of these, flow will be sufficiently fast for this process to enhance recovery significantly. We also observe that a rate dependence of recovery and water breakthrough occurs earlier in transient-state flow than in steady-state flow.