Improved Depleting Sand Fracture Model

An improved depleting sand fracture model was derived in this work using Finite Element Methods, taking into consideration the effect of pore pressure and production on in situ stresses. Sets of governing equations from the commercial finite element simulator COMSOL Multiphysics were used to obtain a model that compares well with the existing fracture model, mainly based on the Mohr–Coulomb failure criterion. The model uniquely couples reservoir depletion-induced stress evolution with fracture initiation and propagation within a unified finite element framework. A constant overburden load was used since its value majorly depends on depth, and the formation is assumed to be fixed at the bottom. The reservoir is assumed to be depleting at a constant rate with no water injection to assist pressure, with an average porosity of 25% and an average permeability of 251 mD at the beginning of production. The reservoir compacted during production, and in turn, porosity and permeability were reduced over the years of observation. Fracturing was observed to be much easier for the depleted reservoir, since horizontal stresses, which might have created friction, are reduced during reservoir production, signifying that for depleted reservoirs, a small fracture pressure is required. Created fractures are observed to propagate in the direction of the maximum horizontal stress and perpendicular to the direction of the minimum horizontal stress.