Explicit treatment of fractures

The contact surfaces of a fracture are often quite complex, and they are usually described using an effective aperture. Thus, in explicit fracture simulation, fractures are usually treated as low-dimensional objects within the matrix. Even with such a simplified fracture representation, it is quite challenging to model the dynamics of flow in naturally fractured formations due to the complex geometry of the fracture network and the scale discrepancy between the fractures (low-dimensional objects) and the matrix formation they intersect.

Fluid Flow with Fractures

For flow simulation, the so-called dual porosity model (Barenblatt et al., 1960; Warren and Root, 1963), in which the matrix blocks provide fluid storage (large pore volume) and the fracture network provides the conductivity (small pore-volume, large permeability), is widely used. In addition to flow through the fractures, the dual-permeability approach accounts for flow between matrix blocks. In dual-porosity and dual-permeability models, a transfer function is used to characterize the interaction between the matrix and the fracture. However, it is quite challenging to design a single transfer function that captures the wide range of scales, properties, and geometry of naturally fractured formations.

As opposed to a dual-porosity approach, I am interested in employing a Discrete Fracture Modeling (DFM) method (Karimi-Fard et al., 2004; Juanes et al., 2002), in which a single static unstructured grid represents all the fractures as low-dimensional objects (with complex network geometry) embedded within the matrix formation.

The unstructured grid captures the complex geometry of the discrete fracture network by conforming grid elements along the fractures. So, in three dimensions (3D), matrix elements are 3D and fractures are represented as the (2D) interfaces between matrix elements. A Finite-Volume Method (FVM) is used to discretize the flow equations of both the matrix and the fractures. FVM is locally mass conservation and allows for modeling nonlinear multiphase flow with strong gravity or capillarity.

Mechanical Deformation with Fractures

Several strategies exist to model mechanical deformation of fractured media. This includes finite element methods, the smeared crack model, discrete inter-element cracks, discrete cracked element, singular elements, enriched elements, boundary-element schemes, and various meshless methods. The most widely used approach for incorporating fractures in mechanical modeling is the Extended Finite Element Method (XFEM) (Moes et al., 1999; Borja, 2000; Stazi et al., 2003; Borst et al., 2004), which allows to maintain a static mesh