Modeling Flow in Naturally Fractured Reservoirs: Effect of Fracture Aperture Distribution on Critical Sub-Network for Flow

Abstract

Fracture network connectivity and aperture (or conductivity) distribution are two crucial features controlling the flow behavior of fractured formations. The effect of connectivity on flow properties is well documented. We focus here on the influence of fracture aperture distribution. We model a two-dimensional fractured reservoir in which the matrix is impermeable and the fractures are well-connected. The fractures obey a power-law length distribution, as observed in natural fracture networks. For the aperture distribution, since the information from subsurface fracture networks is limited, we test a number of cases: narrow and broad log-normal and power-law distributions, and one where aperture correlates with fracture length. We show that even a well-connected fracture network can behave like a network near the percolation threshold in some cases: i.e., most fractures can be eliminated leaving a critical sub-network with nearly the same permeability as the original fracture network. We determine how broad the aperture distribution must be to approach this behavior, and the dependence of the critical sub-network on the parameters of the aperture distribution. We also explore whether one can identify the critical sub-network without doing flow calculations.