Simulation of proppant transport in slickwater with DNS-derived drag correlations

Abstract

This dissertation is developed to address a need of multiphase flow models for proppant transport: problem-relevant drag correlations. This dissertation consists of small-scale simulations by direct numerical simulations (DNS) and larger, fracture-scale simulations by MFIX (Multiphase Flow with Interaction eXchange). DNS was employed to study the influences of several dimensionless numbers, namely the Reynolds number of cross flow, 〖Re〗_x, the Archimedes number, Ar, consisting of gravity, density difference, slickwater viscosity, and proppant size, the density of proppants relative to that of the fracturing fluid, ρ_p⁄ρ_f , the ratio of fracture width over proppant dimension, W⁄d_p , and proppant concentration, ϕ_s. Another independent parameter was firstly evaluated in this study is the inclination angle of fracture, θ. DNS results show that W⁄d_p plays a significant role in proppant transport. Narrower fractures impede proppant settling more. Cross flow and proppant density over that of fluid (provided that Ar is held as a constant) were found to have negligible effects on the settling velocity. Ar, ϕ_s, and inclination were found to have significant influences on settling. When factures were placed with a large fracture width, the effect of proppant concentration on settling was found to be reversed from that in vertical fractures. The lower the proppant concentration, the slower proppants settle. The aim of DNS was not only to understand the influence of the dimensionless numbers, but also to obtain data for developing drag correlations. Drag correlations were developed from DNS data using quadratic polynomials and interpolations. These drag correlations were incorporated into MFIX to close the momentum equations of fluid and solid phases. MFIX simulation results include the rate of proppant bank formation and the equilibrium height and transition length of the end proppant distribution. First, DNS-derived drag correlation predicted slower proppant bank formation compared to other default drag laws, because proppant settling speed is slower in narrow fractures, a factor that to date has not been considered in proppant transport simulations. Second, the influences of key parameters, proppant size, proppant density, proppant concentration, fluid viscosity, and inclination, on proppant bank formation and distribution, were found to be mostly consistent with their roles in affecting the settling velocity. Higher settling velocity always leads to more rapid formation of proppant banks and shorter transition length. Equilibrium height of proppant bank generally increases with increasing proppant concentration and decreases with increasing fluid viscosity.