Discrete fracture network model analysis of the effects of fluid transport on the morphology of a cluster of activated fractures.

Convective transport in low-permeability rocks can be enhanced by the injection of a pressurized fluid to activate preexisting weak planes (fractures). These fractures are initially closed, but fluid-pressure-induced slippage creates void space that allows for fluid flow. The Coulomb-Mohr criterion yields a critical pressure required to open each of the fractures. Due to the intrinsic porosity of the rock, the injected fluid can flow from the fractures' surfaces to the rock matrix through a process referred to as leakoff. Following this activation mechanism, the connectivity of the cluster of activated fractures is strongly dependent on the ratio ${F}_{N}$ of the standard deviation of the critical pressures to the viscous pressure drop over a fracture's length. Recently, we proposed a continuum model to predict the effects of fluid transport on the morphology of the cluster of activated fractures formed by this process over a specific intermediate range of values of ${F}_{N}$ [Alhashim and Koch, J. Fluid Mech. 847, 286 (2018)]. In this paper, the activation process of a discrete well-connected network of preexisting fractures embedded in a highly heterogeneous rock is modeled to analyze the effects of fluid transport on the resulting cluster's morphology for a wider range of ${F}_{N}$ and show how the idealized averaged equation solution arises in a discrete system. We derive a length scale ${\ensuremath{\xi}}_{ch}$, which is a function of ${F}_{N}$ above which the viscous pressure drop is important. This length scale, along with the radius of the cluster $R$ and the average separation between the preexisting fractures ${\ensuremath{\xi}}_{0}$, can be used to define distinct growth regimes where different models can be used to describe the growth dynamics and predict the connectivity of the active network. When ${\ensuremath{\xi}}_{0}\ensuremath{\sim}{\ensuremath{\xi}}_{ch}\ensuremath{\ll}R$, the cluster is well connected and a linear pressure diffusion equation can be used to describe the cluster's growth. When ${\ensuremath{\xi}}_{ch}\ensuremath{\gg}R\ensuremath{\gg}{\ensuremath{\xi}}_{0}$, a fractal network is formed by an invasion percolation process. In an intermediate regime ${\ensuremath{\xi}}_{0}\ensuremath{\ll}{\ensuremath{\xi}}_{ch}\ensuremath{\ll}R$, percolation theory relates the porosity and permeability of the network to the local fluid pressure. For this regime, we validate the predictions of the continuum theory we recently developed to describe the cluster growth on length scales larger than ${\ensuremath{\xi}}_{ch}$.