A monolithic coupled hydraulic fracture model with proppant transport

This article presents the first monolithic coupled numerical model for simulating proppant transport through a non-planar propagating hydraulic fracture. A fracture is propagated through a two-dimensional domain, driven by the flow of a proppant-laden slurry. Modeling of the slurry flow includes the effects of proppant bridging and the subsequent flow of fracturing fluid through the packed proppant. This allows for simulation of a tip screen-out, a phenomenon in which there is a high degree of physical interaction between the rock deformation, fluid flow, and proppant transport and leads to shock formation in the solution. The numerical implementation is verified and the model is used to simulate a tip screen-out in both planar and non-planar fractures. An analysis of the results is performed for three different coupling schemes: monolithic, sequential, and loose coupling. The monolithic scheme is shown to be optimal in terms of computational efficiency, robustness, and accuracy. In addition, a robust and more efficient algorithm for injection-rate controlled hydraulic fracturing simulation based on global mass conservation is presented in this article.