Fracture networks exert a strong influence on flow patterns in the subsurface. We develop a geomechanics-based finite-element models and generate fracture patterns incrementally while studying their impact on fluid flow at each development stage below and above the fracture percolation threshold for a given observation area. Our model - for the first time - also takes into account flow in the porous rock matrix so that its results are applicable to fractured porous media as opposed to crystalline rocks only. The algorithmic approach is iterative and simulates sub-critical quasi-static crack propagation. Initially, a finite set of randomly oriented flaws with varying size populate the matrix. We assume the matrix to be homogeneous, isotropic, and linear elastic. Fracture propagation is based on a combination of failure criteria including the stress intensity factors at the crack tip and a fracture growth index. The propagation angle is determined by the maximum circumferential stress method. Straight and curved fracture geometries are generated by keeping track of the fracture-matrix interfaces on a progressively refined and coarsened mesh. Fracture aperture is an emergent property of the model. Fracture arrest, closure, coalescence, and intersection are handled geometrically by disallowing displacement over fracture boundaries, and merging of polygonal fracture representations. For selected stages of fracture development we compute the effective permeability of the model taking into account the aperture variations. The parallel plate model is used to compute fracture permeability from aperture. The results we obtain depend on the number of initial flaws and the fracture growth rate exponent which determines the length distribution of the evolving fracture set. For a small number of fractures we observe a gradual increase in the model permeability up to the percolation threshold followed by a one-order of magnitude increase as the model begins to percolate. For a larger number of fractures this step is less pronounced.
The study of fractures is relevant in many fields, such as structural integrity studies, contaminant transport, petroleum geology, hydrogeology, and nuclear waste disposal among others. The presence of fractures in aquifers, hydrothermal systems, and oil and gas reservoirs can significantly improve flow properties of rocks, and influence their effective permeability . Fractures form interconnected networks that act as paths of preferred fluid flow in reservoirs and aquifers. Appropriately determining and modeling these fractures in reservoirs is a key aspect of reservoir characterization. Fracture initiation and propagation are two distinct failure processes in rocks. The initiation of fractures is a local failure process whereby single grains crack and void spaces start to coalesce at the grain scale. Fracture propagation, on the other hand, is a failure process driven by stress concentrations at the tip of pre-existing material flaws . Rocks behave like quasi-brittle solids when they are subjected to the relatively low temperatures and pressures such as those found at shallow depths in the subsurface . Under these conditions rocks develop weak zones, formed by microcracks, voids, and material flaws in a heterogeneous manner. These flaws, which we may consider to be randomly distributed at an initial stage, originate due to a variety of force interactions in the sub-surface.