Field data‐based finite‐element simulations of flow partitioning between fractures and a permeable rock matrix reveal critical fracture aperture values that mark the transition from matrix to fracture dominated flow. For matrix permeabilities of 0.00 1–1 D, the matrix either dominates or contributes significantly to the total flow. The percentage of the flow‐normal cross‐section that is occupied by fractures, Af, strongly influences the fracture‐matrix permeability ratio, above which fractures will dominate flow. This ratio is 102–104 for Af = 10−4–10−3 (mean = 5 × 10−3), but also depends on the proportion of fractures which fully penetrate the representative elementary volume. Fluid‐velocity spectra for the fractured rock have three important characteristics: (1) Darcy velocity is only poorly correlated with permeability, (2) flow velocities have characteristic values, even if fracture‐length frequency relations are self similar, and (3) fracture and matrix velocities overlap.

Realistic simulation of structurally complex reservoirs (SCR) is challenging in at least three ways: (1) geological structures must be represented and discretized accurately on vastly different length scales; (2) extreme ranges and discontinuous variations of material properties have to be associated with the discretized structures and accounted for in the computations; and (3) episodic, highly transient and often localized events such as well shut-in have to be resolved adequately within the overall production history, necessitating a highly adaptive resolution of time. To facilitate numerical experiments that elucidate the emergent properties, typical states and state transitions of SCRs, an application programmer interface (API) called complex systems modelling platform (CSMP þþ) has been engineered in ANSI/ISO C þþ. It implements a geometry and process-based SCR decomposition in space and time, and uses an algebraic multigrid solver (SAMG) for the spatio-temporal integration of the governing partial differential equations. This paper describes a new SCR simulation workflow including a two-phase fluid flow model that is compared with ECLIPSE in a single-fracture flow simulation. Geologically realistic application examples are presented for incompressible 2-phase flow, compressible 3-phase flow, and pressure-diffusion in a sector-scale model of a structurally complex reservoir.

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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 fractionalflow 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.