Mathematical Model for Describing the Growth of Mini-Fractures in a Fractured Medium

The main feature of fractured porous reservoirs, such as carbonates, is the presence of cracks of all scales, from the micro level to the main cracks that can cross the whole field. In connection with this feature, and beacause of the influence of formation perturbations on the geometric parameters of cracks, the interpretation of minifrac is a difficult task, since leak-off depends in a complex way on pressure. In this regard, the actual task of building a mathematical and numerical model that could be able to take into account the many processes that affect the anomalous dynamics of the bottomhole pressure. As a resul, a physico-mathematical model, which describes the opening of pre-specified cracks in the three-dimensional case, as well as the generation of new cracks on the basis of the fracture criterion was constructed. Filtration in the matrix and the cracks on a small scale was considered in in obedience to the double porosity model – double permeability. The features of multiphase filtration of a power-law fluid were taken into account. The calculation of geomechanical equilibrium was carried out according to the model associated with the method of calculating frames and trusses.