Finite Element-Based Simulation of the Growth of Dense Three-Dimensional Fracture Networks

Paluszny, A. (Imperial College) | Thomas, R. N. (Imperial College) | Zimmerman, R. W. (Imperial College)


ABSTRACT: The growth of fractures within a quasi-brittle rock is computed numerically with the aim of generating high-density geomechanically realistic three-dimensional discrete fracture patterns. Patterns are generated with a finite element-based discrete fracture propagation simulator, in which deformation and flow are numerically computed. These detailed multi-fracture growth simulations study the emergence of patterns as a function of the interaction of fractures and the mechanical effects of pattern evolution on the distribution of apertures in response to in situ stresses.


The growth of multiple interacting fractures is instrumental in understanding how fracture patterns evolve across scales, and how fracture geometry and topology evolves within a group during mixed mode loading. In particular, realistic modeling of hydraulic fracturing is of great interest. However, fracture growth is relevant to a range of other applications, including hydro-geo-mechanical modeling of processes occurring in or near reservoirs, mines, and nuclear waste repositories.

Fracture growth within quasi-brittle rocks involves propagation and interaction across scales. Growth begins from inter-granular and intra-granular micro-fractures, which have been observed to self-organize in a process whereby ‘initially isolated fractures grow and progressively interact, with preferential growth of a subset of fractures developing at the expense of growth of the rest’ (Hooker et al., 2017). Hooker et al. examine over sixty sandstone samples from five different sites, and conclude that the location of fracture clusters is not random but rather controlled by the interaction mechanics of growing fractures. Thus, the authors suggest that initial micro-fracturing in rocks is not random (e.g. Tang et al. 2018) but rather self-organized, leading to scale-dependent mechanisms for selforganization of fractures at larger scales. The formation of dense fractures systems across scales, outside of layer-restricted systems, is briefly investigated in this work.

Modeling the growth of dense fracture networks is challenging, and in general, fracture density is bound to the observation scale, and it must be assumed that a large number of both smaller and larger scale fractures are also present. A range of numerical methods have been applied to model fractures and fracture growth. These including the finite element method (FEM), the extended finite element method (XFEM), the discrete element method (DEM), combinations of FEM and DEM, discontinuous deformation analysis (DDA), the perturbation method, mesh-less, phase-field. These model the growth of multiple fractures both in 2D and 3D, with or without flow. A partial review of these methods can be found in (Lisjak & Grasselli, 2014).