Tensorial Fracture-Matrix Ensemble Relative Permeabilities in Naturally Fractured Reservoirs: Evidence from Discrete Fracture and Matrix Simulations

Abstract

The prediction of water breakthrough and oil recovery for naturally fractured reservoirs (NFRs) cannot be performed accurately without dynamic upscaled relative permeability functions. Relative permeability is commonly assumed to be a scalar quantity, although a justification for NFRs has yet to be presented. In this study, we show how accurate this assumption is for fracture-matrix ensemble relative permeabilities determined by numeric simulations of unsteady-state core flooding. Numerical determination of relative permeability requires a realistic flow model, a spatially adaptive simulation approach and a sophisticated analysis procedure. To fulfil these requirements, we apply discrete fracture and matrix modelling to well characterised hm-km outcrop analogues. These are parametrized with aperture, permeability, and capillary pressure data. Fracture attributes are allowed to vary from segment to segment, trying to emulate in situ conditions. The finite-element-centered-finite-volume method is used to simulate two-phase flow in the fractured rock, considering different wettability conditions. Our results indicate that the ensemble relative permeability of 2D digital NFR outcrop analog models is a tensor property. The tensors are not necessarily symmetric, and their eigenvalues are not always equal to the diagonal terms. Also, the off-diagonal terms can determine the type, i.e., counter vs co-current imbibition, and the direction of imbibition.