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Coupled 3-D Numerical Simulation of Proppant Transport and Fluid Flow in Hydraulic Fracturing By Bing Kong Hydraulic fracturing is one of the most common and important stimulation techniques used in oil and gas industry to create high conductivity flow paths for hydrocarbons to flow from the reservoir matrix to the wellbore. Hydraulic fracturing is a complex process including different physical and chemical phenomena. It involves rock mechanics for the part of fracture propagation and involves fluid mechanics for the part of slurry injection, fluid flow, fluid leakoff, proppant transport, proppant settling and interaction between fluid and proppant particles. In this study, the focus is on fluid and proppant motion within hydraulic fractures. The effectiveness of hydraulic fracturing treatment is highly dependent on the fracture geometry and conductivity after flow back. Fracture geometry is a function of proppant placement while fracture conductivity is determined by both proppant placement and proppant pack permeability. Advanced understanding of these properties is essential for optimization of hydraulic fracturing treatment. For proppant placement, the proppant jamming principles are considered based on sphere packing theory while for proppant pack permeability, correlations based on published experimental data have been implemented. Navier-Stokes equation describing fluid flow in the fracture is coupled with mass conservation equation governing the proppant transport, and solved using finite difference approach based on staggered grid to avoid checkerboard solution while fracture propagation is simulated using in house 3D hydraulic fracturing simulator (HFWVU, Dr Bao). Slippage between proppant and fracturing fluid induced by gravity and affected by fracture width, particle interaction and non-Newtonian effect are considered in our formulation to obtain precise proppant distribution profile in the hydraulic fracture during the injection. Next, Fracture-Production model simulating fluid flow in a non-uniform-conductivity fracture is established for the evaluation of fracture performance, where the fracture geometry after flow back follows proppant concentration profile considering proppant pack contraction due to effective closure stress. Sensitivity analysis and optimization of parameters such as initial proppant concentration, proppant size and injection rate, fluid viscosity and reservoir permeability has been performed using Plackett-Burman design. This study is a unique approach for the further understanding of the hydraulic fracturing process to allow for possible enhancements of hydraulic fracture performance.

Coupled 3-d numerical simulation of proppant transport and fluid flow in hydraulic fracturing