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

Abstract

Accurately resolving the coupled momentum transfer between the liquid and solid phases of complex fluids is a fundamental problem in multiphase transport processes, such as hydraulic fracture operations. Specifically we need to characterize the dependence of the normalized average fluid-particle force F on the volume fraction of the dispersed solid phase and on the rheology of the complex fluid matrix, parameterized through the Weissenberg number W i measuring the relative magnitude of elastic to viscous stresses in the fluid. Here we use direct numerical simulations (DNS) to study the creeping flow (Re ≪ 1) of viscoelastic fluids through static random arrays of monodisperse spherical particles using a finite volume Navier-Stokes/Cauchy momentum solver. The numerical study consists of N = 150 different systems, in which the normalized average fluid-particle force F is obtained as a function of the volume fraction φ (0 < φ ≤ 0.2) of the dispersed solid phase and the Weissenberg number W i (0 ≤ W i ≤ 4). From these predictions a closure law F (W i, φ) for the drag force is derived for the quasi-linear Oldroyd-B viscoelastic fluid model (with fixed retardation ratio β = 0.5) which is, on average, within 5.7% of the DNS results. Additionally, a flow solver able to couple Eulerian and Lagrangian phases (in which the particulate phase is modeled by the discrete particle method (DPM)) is developed, which incorporates the viscoelastic nature of the continuum phase and the closed-form drag law. Two case studies were simulated using this solver, in order to assess the accuracy and robustness of the newly-developed approach for handling particle-laden viscoelastic flow configurations with O(10 5 − 10 6 ) rigid spheres that are representative of hydraulic fracture operations. Three-dimensional settling processes in a Newtonian fluid and in a quasi-linear Oldroyd-B viscoelastic fluid are both investigated

A Primer on CFD-DEM for Polymer-Filled Suspensions

“…A coupled CFD-DEM approach was used for modeling particle-laden flows [13]. The so-called unresolved approach [13,39,40] was employed in this study because only the bulk behavior of the suspension is of interest. In this formulation, the particle size is smaller than the computational grid size.…”

Numerical Study on the Unstable Flow Dynamics of Wormlike Micellar Solutions past a Sphere in the Creeping Flow Regime

“…The governing equations for the transient, incompressible, and isothermal flow of wormlike micellar solutions include the continuity equation, the momentum equation, and the constitutive equations that define the extra elastic stress contribution, as reported by previous research [ 7 , 22 , 30 , 33 , 37 ].…”

“…Su et al [ 32 ] investigated a sphere’s settling in Giesekus and FENE-P fluids and found that shear thinning weakens the oscillation of the settling velocity of the sphere compared with that in the Oldroyd-B fluids under identical rheological parameters. Fernandes et al [ 33 ] developed a fluid–particle interaction force model through a direct simulation method by considering the volume fraction of the dispersed solid phase in Oldroyd-B fluids, which is applicable to the dense particle-laden flows in viscoelastic fluids. Qin et al [ 34 ] recently developed a fully resolved simulation method based on the immersed boundary–lattice Boltzmann method using the Oldroyd-B and the Giesekus constitutive equations to investigate the particle dynamics in viscoelastic fluids, which shows good prospects for the simulation of flow behaviors of the particle-laden viscoelastic fluids.…”

Numerical Simulation of a Thixotropic-Viscoelastic Model in Contraction Geometries

“…A typical example of a structured fluid is a micellar solution, which consists of a dispersion of micelles in a solvent. When surfactant molecules (which have a hydrophilic group (water-loving) that is chemically bonded to a hydrophobic group (water-hating)) are in the solution, they will self-assemble into aggregates such as spherical and wormlike micelles, bilayers, among others [7][8][9]. The rheological behaviour of micelles makes them highly attractive in the industry, specially in oil-recovery processes and in drilling operations [10][11][12][13].…”