| The production of oil and gas from a naturally fractured reservoir requires an understanding of fracture connectivity and fracture pattern geometry. To study fracture connectivity, it is important to know fracture path. Pseudo-three-dimensional numerical simulations in linear elastic materials show that fracture growth geometry is affected by not only the ratio of remote differential stress to driving stress but also by bed thickness and fracture propagation environment. Fractures will propagate straight if either the remote differential stress ratio or fracture spacing to bed thickness ratio is above one. Fractures are more planar if the propagation condition is subcritical.; A cumulative fracture length distribution is derived based on mechanical principles. The mechanical interaction between two mode-I cracks is a function of fracture length, spacing, overlap and bed thickness. Crack propagation is enhanced when the en echelon cracks slightly underlap, but it is impeded when the cracks overlap. If a small crack is close enough to a large crack, it can suppress the large crack's propagation and capture it. The probability of a large crack passing close to a small crack depends on the large crack's length and the density of small cracks. Putting the mechanics together with the probability analysis results in a negative exponential distribution for two-dimensional map view sampling.; A semi-analytical geomechanical model is developed to simulate a single set of parallel fracture network. In this model, only a few cracks are modeled explicitly and other cracks are treated as a continuum through an effective elastic modulus controlled by crack density. The semi-analytical model simulates fracture patterns similar to a more rigorous displacement-discontinuity boundary-element model. Compared to the boundary element numerical model, the semi-analytical model computes faster and can deal with thousands fractures. A sensitivity study of fracture pattern development shows that the initial flaw density, subcritical index, bed thickness and elastic modulus affect fracture length, spacing and the degree of fracture clustering. The systematic relationship between the model inputs (boundary conditions and rock properties) and final fracture geometry indicates that this high-speed semi-analytical model can be used for the further investigation of fracture pattern inversion from observed data. |
