Abstract
Equations of motion of a slurry in a narrow slot, such as a hydraulic fracture, are presented and solved numerically to obtain an estimate of the amount of gravity-driven vertical motion of proppantthat can occur within a fracture during placement.Two types of gravity-driven motion are studied: settling of heavy-proppant particles; and convective proppant transport, which refers to the motion driven by large-scale density differences between regions of different proppant concentration.Computer simulations are performed using realistic parameter values. In particular, the vertical motion of proppant in a slurry in which proppant particles are uniformly distributed across the fracture width (referred to as homogeneous flow) is compared with that in a slurry in which some unspecified, but rapid, process has caused all proppant to migrate across the fracture width into a close-packed sheet at the fracture center (referred to as sheet flow).In addition to considering a constant channel width, we also investigate the effects of an elliptic-fracture cross section on proppant placement. This fracture shape is predicted by idealized fracture propagation models such as the Perkins-Kerns-Nordgren (PKN) model. Main conclusions are that during placement: Proppant settling and convection can occur under practical conditions;Convection rates are slightly greater in sheet flow than in homogeneous flow, and settling is greatly enhanced in sheet flow. Overall, settling in sheet flow gives the worst vertical motion of proppant. Settling and convection in homogeneous flow cause no problems under conditions considered in this paper;In elliptic fractures, heavy, proppant-laden slurry can override earlier-pumped lighter pad (zero solids) under most fracturing conditions