Modeling of Fracture Width and Conductivity in Channel Fracturing With Nonlinear Proppant-Pillar Deformation

Channel fracturing acknowledges that there will be local concentrations of proppant that generate high-conductivity channel networks within a hydraulic fracture. These concentrations of proppant form pillars that maintain aperture. The mechanical properties of these proppant pillars and the reservoir rock are important factors affecting conductivity. In this paper, the nonlinear stress/strain relationship of proppant pillars is first determined using experimental results. A predictive model for fracture width and conductivity is developed when unpropped, highly conductive channels are generated during the stimulation. This model considers the combined effects of pillar and fracture-surface deformation, as well as proppant embedment. The influence of the geomechanical parameters related to the formation and the operational parameters of the stimulation are analyzed using the proposed model. The results of this work indicate the following: Proppant pillars clearly exhibit compaction in response to applied closure stress, and the resulting axial and radial deformation should not be ignored in the prediction of fracture conductivity. There is an optimal ratio (approximately 0.6 to 0.7) of pillar diameter to pillar distance that results in a maximum hydraulic conductivity regardless of pillar diameter. The critical ratio of rock modulus to closure stress currently used in the industry to evaluate the applicability of a channel-fracturing technique is quite conservative. The operational parameters of fracturing jobs should also be considered in the evaluation.