Control-Volume Finite-Element Two-Phase Flow Experiments with Fractured Rock Represented by Unstructured 3D Hybrid Meshes
Authors: Matthäi S.K. , Mezentsev A. , Belayneh M. 
Published: December 2007

Abstract
Fractured reservoir permeability, water-breakthrough and hydrocarbon recovery cannot be extrapolated from experimental data obtained on cores. Instead computer simulations allow these processes to be studied in discrete-fracture models at an intermediate scale. We represent intersecting natural and stochastically generated fractures in massive or layered porous rocks accurately with novel unstructured hybrid finite-element meshes. This high-resolution discretization allows us to compute two-phase flow with an original implicit-pressure implicit-saturation formulation. Computations incorporate unique relative permeability-saturation relationships and capillary pressure curves for individual material domains.
The steady-state flow velocity varies over many orders of magnitude. Velocity spectra have multiple characteristic peaks and show significant overlaps between fracture and matrix domains. In models with well interconnected fractures, residual saturations greatly exceed those initially assigned to the rock matrix. Total mobility is extremely sensitive to small saturation changes. Hence, grid-block averaged relative permeabilities offer little predictability and a new formalism is needed to upscale from core to grid-block scale.
Fracture matrix counter-current imbibition is surprisingly inefficient as it occurs only over a small fraction of the total fracture-matrix interfaces and only where fracture flow velocities are high enough to remove the drained oil. There is also a strong time dependence of the flow. Water breakthrough in transient models occurs earlier than in steady state ones.

Introduction
Oil is difficult to recover from fractured reservoirs but about 60% of the worlds remaining resources reside in such heterogeneously deformed formations1. 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 recovery2.
Qualitatively, the main production obstacle is simple to conceptualize3: while the oil resides in the pores of the rock matrix, production-induced flow will occur predominantly in the fractures. They, however, constitute only a few per mil of the total fluid-saturated void space and are rapidly swept by the injected fluid. Once short-circuited by the injectant, the injection - production stream only entrains oil that enters the fractures as a consequence of counter-current imbibition4. The efficiency of this process is relatively well constrained by experimental work5 and reproduced accurately by transfer functions4. Rate predictions for fractured reservoirs further require an estimate of the area of the fracture matrix interface captured by a shape factor6. However, in cases where this measure is relatively well-constrained, predicted transfer rates appear to greatly exceed actual values (J. Gilman, pers. commun. 2004). This observation suggests that, at any one time in the production history, transfer occurs only over 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 production7–8. This is confirmed by field data-based numerical flow models9–10, 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 useful for the prediction of the behavior of fractured reservoirs?