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Xiaoqi Li, Dongxiao Zhang, Xiaolong Yin, 'Investigating Proppant Transport in Slickwater Fractures using Direct Numeriacl Simulations (DNS) and Two-Fluid Models (TFM)', Powder Technology, Volume 446, 120151, 2024 https://doi.org/10.1016/j.powtec.2024.120151. (https://www.sciencedirect.com/science/article/pii/S0032591024007952)

Abstract: Proppant / fracturing fluid two-phase separation always occurs in proppant-slickwater systems, especially in fractures with small width created by low-viscosity slickwater. Forces acting on the proppant include drag from the fluid, body force and force due to inter-particles impede / improve proppant settling. In this paper, lattice Boltzmann method (LBM) using direct numerical simulation (DNS) scheme presented is motivated to resolve lightweight and regular-weight proppant carried by slickwater. DNS simulations have investigated Archimedes number (Ar), proppant volume fraction (ϕ), wall effect (W/dp), horizontal crossflow (Rex) and proppant-slickwater density ratio (ρp/ρf). It is observed that Rex and ρp/ρfhave little effect on proppant settlement as the balance between proppant weight and slickwater viscosity is fixed at a constant Ar. Thus, the proppant carried by slickwater relevant drag correlation series have been derived using small-scale DNS, which is a look-up table that takes fracture aperture, amount of proppant and rheology of fracturing fluid into account. Furthermore, the performances of proppant transport were evaluated by the rate of formation of proppant bank quantitatively and the length and height of proppant bank formed in fractures qualitatively. The drag correlations derived from DNS and Beestra Van der Hoef Kuipers (BVK) were then substituted into MFIX Two Fluid Model (TFM). Proppant bank propagation and equilibrium height in the experiments have validated this DNS derived drag model. Finally, it is to apply DNS-derived drag correlations to characterize proppant settling and transport by slickwater.
Keywords: Drag correlations; Hydraulic fracturing; Proppant transport; DNS-LBM; MFIX-TFM; Proppant bank dimensions