An Investigation of the Pseudo-steady State Approach to Modelling Inter-porosity Flow in Fractured Geomaterials

Abstract

This paper examines the assumption of pseudo-steady state inter-porosity mass exchange in dual porosity models of fractured rock. Models of this type rely on the assumption that a pseudo-steady pore pressure distribution prevails in the porous matrix at all times, thereby neglecting transient pressure gradients. The rate of inter-porosity mass exchange is then conveniently expressed as a linear function of the difference between the average pore pressures in the fracture and matrix domains. Whilst providing a relatively simple description of mass exchange, the accuracy of this approach has been debated and it is strictly only valid once the pressure front due to changing conditions in the fracture network reaches the centre of the matrix. The aim of this paper is to compare the pseudo-steady state model of mass exchange with an explicit model of diffusive flow into a rock matrix with parallel-plate geometry. Since the mass exchange coefficient is sometimes described as a function of matrix block geometry and effective diffusivity, an attempt is made to adopt this approach before curve fitting is used. The results indicate that the adopted function underestimates the mass exchange rate compared to the benchmark, although the pseudo-steady state model can provide close agreement if curve fitting is used. It is concluded that the assumption of pseudo-steady state mass exchange may be valid only for cases where calibration of the linear coefficient is possible. Constitutive relationships describing the coefficient should be approached with care, with the possible exception of those considering some level of transiency.