Residual opening of hydraulic fractures filled with compressible proppant

•The residual opening of hydraulic fractures determines the efficiency and success of hydraulic stimulations.•Lack of relatively simple models capable of predicting residual opening of fractures filled with compressible particles.•Simple semi-analytical model based on the Distributed Dislocation Technique and Terzaghi's consolidation model is developed.•It predicts the residual opening of a single crack filled with granular particles.•The method for calculating the residual openings can be employed to estimate the increase in the production rate of hydraulically stimulated reservoirs.

In hydraulic stimulations of oil and gas wells, injection of proppant (or small particles) is normally needed to avoid the closure of the created fractures under confining stresses. The residual openings of these fractures determine the efficiency and, in general, the success of the hydraulic stimulations. Despite the vast number of papers devoted to fluid driven fractures and hydraulic stimulation procedures, there has not been much research conducted on residual fracture profiles. This problem is characterised by a strong non-linearity and represents a challenge for numerical modelling. In this paper a simple semi-analytical method for calculating the residual openings of fractures partially filled with proppant is developed. It is based on the Distributed Dislocation Technique and Terzaghi's classical consolidation model. One of the results of simulations indicates that the proppant distribution and its mechanical properties have a significant influence on the residual fracture profiles.