Evaluation of Water Oil Relative Permeability of Fractured Rock under Variable Conditions of Hydrostatic Effective Stress and Capillary Number

摘要

In the study of fractured systems petrophysics, the concept of relative permeability is of primary importance as it integrates into a characteristic curve, the net effect of complex interactions between matrix, fracture and fluids as a function of the state of saturation. In most practical applications, this curve is assumed invariant to the state of stresses and / or to the relative magnitude of viscous and capillary forces, normally represented by the capillary number concept Nc. In coupled simulation schemes, some approaches incorporate geomechanical effects to petrophysical attributes such as absolute permeability, porosity, fracture width and fracture permeability and others; incorporate variable capillary number to the relative permeability functions. In a practical sense, the assumption of invariant Kr with the stress and / or the capillary number actually simplifies computational requirements but can underestimate known physical effects that variable stress regime and variable viscous-capillary forces field induce over multiphase flow and of special relevance in the context of naturally fractured reservoirs subject to fluids injection and production. In this work, results of water-oil relative permeability curves, measured over a single fractured Berea core by the unsteady state JBN method, with variable hydrostatic effective stress and capillary number are shown. The aim of the present study is to advance towards the prediction of complex dynamics in systems were matrix-fracture deformation occur due to stress changes, and variable flow regime exist as a function of relative variations of the field of viscous-capillary forces across the reservoir. The methodology is based on the exploration of the variations of Corey relative permeability parameters with both hydrostatic effective stress and capillary number outlining that literature reports studies about the independent effect of these two variables but not of its combined effect. Results to date indicate that the features of relative permeability curves of fractured rocks (e.g. ranges of mobile saturation, curvature, endpoints) get modified when changes on the effective hydrostatic stress, the capillary number or both are induced. It is herein proposed, that the degree and configuration of the variation of the curves with respect to a reference curve is a function of the level of flow transfer between the matrix and fracture which in turn is determined by the relative incidence of the capillary, viscous and deformation effects over both domains. Further phases of the investigation shall include additional variables such as anisotropic stress regime, other types of fractures and wettability conditions towards the derivation of empirical correlations for Kr prediction.