Time-Dependent Matrix-Fracture Shape Factors for Partially and Completely Immersed Fractures

Abstract

Abstract Modeling multiphase flow in fractured porous media relies on the accurate description of matrix to fracture transfer of water. The rate of mass transfer between the rock matrix and fractures is significant, and calculation of this rate, within dual-continuum models, depends on matrix-fracture transfer functions incorporating the shape factor. Typically, matrix-to-fracture transfer functions are obtained by assuming all fractures to be instantaneously immersed in water (instantly-filled), with a uniform fracture pressure distribution under pseudo-steady state conditions. The result is constant, timeindependent, shape factors. Clearly, this is not necessarily true. Partially immersed fractures and other unsteady-state conditions do not lead to constant shape factors. The current formulations for modeling flow in fractured porous media need to be reconsidered. A new time-dependent matrix-fracture transfer shape factor formulation and transfer functions for both filling- and instantly-filled fracture transfer are derived based on dimensional analysis of experimental data. The general shape factor is expressed as the area of the matrix block contacted by the wetting phase divided by the product of the bulk volume of the rock matrix times the distance between the saturation at the fracture and the matrix average saturation. These parameters are readily obtained. The dimensional analysis of full-physics data avoids simplifications that may lead to expressions that do not represent accurately matrix-fracture transfer. The new shape factor carries information of the transient behavior of the water saturation, Sw, and so it leads to more accurate description of the matrix-fracture transfer. Good agreement was found between experimental data, an analytical model, and a proposed modified dual-porosity formulation with the new time-dependent shape factor and transfer function.