Finite Element - Node-Centered Finite-Volume Two-Phase-Flow Experiments With Fractured Rock Represented by Unstructured Hybrid-Element Meshes
Authors: Matthai Stephan Konrad , Mezentsev Andrey A. , Belayneh Mandefro 
Published: January 2008

Summary
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, kr, avg, cross over during saturation changes of less than 1%. Such upscaled kr, 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.

Introduction
Oil is difficult to recover from fractured reservoirs; however, approximately 60% of the world's remaining oil resources reside in heterogeneously deformed formations (Beydoun 1998). The production dilemma is reflected in complex pressure and production histories, unpredictable couplings of wells independent of their spatial separation, rapidly changing flow rates and the risks of rapid water breakthrough, and low final recovery (Kazemi and Gilman 1993).
Qualitatively, the main production obstacle is simple to conceptualize (Barenblatt et al. 1990): while the oil resides in the pores of the rock matrix, production-induced flow will occur predominantly in the fractures. However, they typically contribute less than 1% to the total fluid-saturated void space and are therefore rapidly invaded by the injected fluid. Once short-circuited by the injectant, the injection/production stream entrains only the oil that enters the fractures as a consequence of countercurrent imbibition (CCI) (Lu et al. 2006). The efficiency of this process is relatively well constrained by experimental work (Morrow and Mason 2001) and reproduced accurately by transfer functions (Lu et al. 2006). Rate predictions for fractured reservoirs require a further estimate of the area of the fracture/matrix interface captured by a shape factor (Kazemi et al. 1992). However, in cases where this measure is relatively well-constrained, predicted transfer rates appear to greatly exceed actual values. This observation suggests that, at any one time in the production history, transfer occurs over only a small part of the fracture/matrix interface. Furthermore, as is indicated by packer tests and temperature logs, only a small number of fractures contribute to the flow during production (Long and Billaux 1987, Barton 1995). This is confirmed by field-data-based numerical flow models (Matthäi and Belayneh 2004, Belayneh et al. 2006), highlighting that viscous flow in the rock matrix is usually significant, even if the fractures are well interconnected. All these findings conflict with the simple conceptual model, even qualitatively. How shall we replace it with something more accurate for the prediction of the behavior of fractured reservoirs?