Simulation of Proppant Transport in Fractures with DNS-Derived Drag Correlations

Multiphase flow simulations of proppant transport, a particulate flow process encountered in hydraulic fracturing of oil and gas reservoirs, need problem-relevant drag correlations. In this study, DNS was employed to study the influences of several dimensionless numbers, namely the Reynolds number of cross flows, the Archimedes number, the density of particles relative to that of the carrying fluid, particle volume fraction, and the ratio of fracture width over particle size on the settling velocity. DNS results show that fracture width significantly impedes the settling velocity. Cross flow and particle-fluid density ratio (provided that the Archimedes number is held as a constant) on the other hand do not have significant effects.

The aim of DNS is not only to understand the influence of the dimensionless numbers, but also to obtain data for developing the needed drag correlation. A drag correlation developed from DNS data using quadratic polynomials and interpolations was incorporated into MFIX. MFIX simulations of particle transport in narrow fractures predicted slower formation of particle sediment layers at the bottom of the fracture compared to default drag laws, because particle-fluid drag is enhanced by the width of fractures. Simulations using the DNS-derived drag correlation can better match experimentally determined sediment layer thickness, compared to those using other drag laws.