Proppant Transport in a Newtonian Fluid Under Laminar Flow

Abstract

Summary Model proppant transport experiments are conducted at the laboratory scale using a Newtonian carrier fluid in a long tube of rectangular cross section. Under the particular flow conditions studied, we observe the buildup of a dense but flowing sediment, which rapidly reaches a steady-state height. The existence of this steady-state flowing sediment implies that the proppant flux leaving the channel equals that entering the channel; that is, “efficient” proppant transport occurs. As soon as the suspension flow is stopped, the fluidized sediment ceases flowing and quickly becomes more compact. This collapse implies that the particle sediment is maintained in an expanded state while under flow, with an average volume fraction considerably lower than that under static conditions. The relevant mechanism of sediment transport is identified as viscous resuspension because the flow is at a low Reynolds number (Re at approximately 0.1). We estimate the average volume fraction of the resuspended sediment from experimental measurements of the “expanded” flowing sediment height, with the assumption that the corresponding compact sediment volume fraction is ϕ0=0.61, the volume fraction at which the suspension viscosity diverges. Predictions of the resuspended sediment heights are made with a simple approach based on the diffusive flux model by Leighton and Acrivos (1986) using the average shear stress across the channel width. A good agreement is found between the predicted and experimental values, indicating that 2D effects remain weak. Microscopic observations show that the sediment is fully fluidized while under flow for all the flow rates studied in our channel, and one does not observe the buildup of static sediment banks that are observed in larger-scale tests during the suspension flow (Kern et al. 1959; Babcock et al. 1967; Schols and Visser 1974; Sievert et al. 1981). This apparent difference is explained in the context of the viscous resuspension model.

Finite volume simulations of particle-laden viscoelastic fluid flows: application to hydraulic fracture processes

“…is as close as possible to the desired packing fraction, where n s is the number of spheres enclosed in the square duct (whose volume is LH 2 ) and a is the sphere radius. For the purpose of simulating the proppant transport phenomena that occur during hydraulic fracturing operations, we consider in this work moderately dense suspensions where the particle volume fraction range is 0 < φ ≤ 0.2 [5,43,56]. Following Hill et al [20] we note that the system to be studied must include a sufficient number of spheres, n s , to minimize artifacts and statistical oscillations coming from the finite size of the computational domain.…”

“…In the first case, we study proppant transport and sedimentation in a long conduit of rectangular cross section, a typical geometry to study flow in hydraulic fracturing [43]. In the second case, we study the segregation phenomena which occurs in cement casing for horizontal wells.…”

“…Proppant particles must be carried over large distances to ensure successful placement, which requires a spatially homogeneous distribution of particles [6]. However, flows of non-Brownian particles, such as proppant, often result in non-homogeneous patterns, in which particle sedimentation is commonly observed [43]. The proppant particles that will be modeled in this section are glass microspheres of diameter 73 µm and of density 2.54 g/cm 3 , in order to simulate the experiments conducted by Meeker et al [43].…”

“…Additionally, we note that fully-resolved particle-laden viscoelastic solvers [40,41] are presently only able to directly resolve O(10 3 ) particles [42], which limits their application to large industrial case studies [43]. To overcome this limitation we implement an Eulerian-Lagrangian viscoelastic solver (DP M viscoelastic), which employs the closure drag model that we develop here for moderately dense suspensions with a viscoelastic matrix fluid to quantify the momentum exchange between the two constituent phases (a moderate volume fraction of rigid spherical particles and a non-shear thinning viscoelastic matrix fluid).…”

Finite volume simulations of particle-laden viscoelastic fluid flows: application to hydraulic fracture processes

“…and define appropriate characteristic values for ¯ f to quantify h and h 0 . For particular flow conditions of a non-Brownian suspension flowing at Q = 100 cm 3 /h, Meeker et al [43] observed the buildup of a dense but flowing sediment that rapidly reaches a steady-state height h. The existence of this steady-state flowing sediment implies that the proppant flux leaving the channel equals that entering the channel, and thus, an "efficient" proppant transport occurs. Knowing this fact, we define the criteria to compute h as ¯ f = 1 − φ i (see Fig.…”