Numerical study of proppant embedment under proppant-coal seam interaction

Abstract

Experimental studies on proppant embedment in coal seams often overlook factors like pulverized coal shedding, leading to inaccuracies. This study developed a numerical model for proppant embedment in coal seams using elastoplastic theory and the material point method (MPM). This approach addresses the underestimation of embedment depth under high closure stress due to ignored pulverized coal shedding in experiments and overcomes challenges in the traditional numerical simulation of large coal deformation and contact issues. We validated the model through two fundamental numerical cases. Proppant-coal interactions were analyzed under five closure stresses, along with the effects of proppant size and coal strength. Results revealed that proppant embedment occurs in two distinct stages: an initial linear increase attributed to shear damage, followed by a nonlinear rise driven by shear-tensile damage. Traditional experiments underestimated the embedment depth, which was consistent with numerical simulations during the damage stage; however, simulations indicated that embedment depths were doubled at high stress levels. Smaller proppants or higher coal strength raised the critical stress for coal failure. Notably, 1.5 mm proppants embedded ten times deeper than 0.3 mm proppants, with a quadrupled coal damage area. Low-rank coal demonstrated 1.5 times deeper embedment and double the damage area compared to high-rank coal. This study provides a theoretical basis for optimizing proppant selection in hydraulic fracturing.