Numerical Prediction of Relative Permeability in Water-Wet Naturally Fractured Reservoir Rocks

The grid-block scale ensemble relative permeability, kri of fractured porous rock with appreciable matrix permeability is of decisive interest to reservoir simulation and the prediction of production, injector-producer water breakthrough, and ultimate recovery. While the dynamic behaviour of naturally fractured reservoirs (NFR) already provides many clues about (pseudo) kri on the inter-well length scale, such data are difficult to interpret because, in the subsurface, the exact fracture geometry is unknown. Here we present numerical simulation results from discrete fracture and matrix (DFM) unstructured grid hybrid FEM-FVM simulation models, predicting the shape of fracture-matrix kri curves. In contrast to earlier work (Matthai et al. 2007, Nick and Matthai, 2011), we also simulate capillary fracture matrix transfer (CFMT) and without relying the frequently made simplifying assumption that fracture saturation reflects fracture-matrix capillary pressure equilibrium. We also use a novel discretization of saturation which permits jump discontinuities to develop across the fracture-matrix interface. This increased physical realism permits – for the first time - to test the Matthai and Nick (2009) semi-analytical model of the flow rate dependence of relative permeability, ensuing from CFMT. The sensitivity analysis presented here constrains the CMFT-related flow rate dependence of kri and illustrates how it manifests itself in two geometries of layer-restricted well-developed fracture patterns mapped in the field. In a companion paper (Lang et al.), also investigate the dependence of kri on fracture aperture as computed using discrete element analysis for plausible states of in situ stress. Our results indicate that fracture-matrix ensemble relative permeability is matched – for fast flow rates – by the semi-analytic model of Matthai and Nick (2009). For slow rates the strong impact of CFMT leads to significantly different behaviour requiring a more elaborate treatment.