The effects of the viscous pressure drop on the growth of a cluster of activated fractures

Convective transport in low permeable rocks can be enhanced by injection of a pressurized fluid to activate pre-existing weak planes (fractures). These fractures are initially closed, but fluid-pressure-induced slippage creates void space that allows fluid flow. Mohr’s criterion yields a critical pressure required to open each of the fractures. The activation process of a discrete well-connected network in a highly heterogeneous rock was simulated to analyze the process at a meso-scale that is larger than the average fractures’ length, λ, but smaller than the radius of a cluster of activated fractures, R . We show that depending on the ratio, F_N , between the variability in the critical pressures and the viscous pressure drop, the activation process at large length scales can be described using continuum models. When F_N << 1, the cluster is well connected, and a linear diffusion equation can be used to describe the cluster’s growth. When F_N >> R/λ, a fractal network is formed by an invasion percolation process. In the intermediate regime, 1 << F_N << R/λ, percolation theory relates the porosity and permeability of the network to the local pressure and a continuum diffusion model with pressure-dependent properties describes the cluster growth on length scales much larger than λF_N.