(57c) Viscoelastic Fluid Suspension Problems in Fracking and Drilling

There are no comprehensive simulation-based tools for engineering the flows of viscoelastic fluid-particle suspensions in fully three-dimensional geometries. On the other hand, the need for such a tool in engineering applications, combined with the associated potential for understanding new physics related to elastic fluid/particulate suspensions is immense. Suspensions of rigid particles in viscoelastic fluids play key roles in many energy applications. For example, in oil drilling the “drilling mud” is a very viscous, viscoelastic fluid designed to shear-thin during drilling, but thicken at stoppage so that the “cuttings” can remain suspended. In a related application known as hydraulic fracturing  suspensions of solids called “proppant” are used to prop open the fracture by pumping them into the well. It is well-known that particle settling in a viscoelastic fluid can be quite different from that which is observed in Newtonian fluids. An issue of importance in this context is that in Newtonian fluids, the presence of an imposed shear flow in the direction perpendicular to gravity (which we term a cross or orthogonal shear flow) has no effect on the settling of a spherical particle in Stokes flow (i.e. at vanishingly small Reynolds number or inertial forces). By contrast, in a non-Newtonian liquid, the complex rheological properties induce a nonlinear coupling between the sedimentation and shear flow. Recent experimental data have shown that this coupling is affected by both the shear thinning and the elasticity of the suspending polymeric solutions thus significantly affect the settling rate of the solids. In the present work, we use (a) simulations of viscoelastic flow past a single, torque-free sphere and (b) immersed boundary simulations of multiparticle suspensions including sedimentation with a cross shear flow to study the effect of carrier fluid elasticity on the drag experienced by a given sphere and thus on its settling rate. In the numerical simulations, we use different rheological models to represent the viscoelastic fluids with both highly shear thinning and non-shear thinning fluids considered. Fluid parameters are obtained by fitting rheological data. For weakly shear thinning fluids, we obtain an increase in drag, i.e. a decrease in settling rate, as shear Weissenberg number is increased in both the numerical simulations and the experiments. The simulations are in quantitative agreement with the experiments at small Weissenberg number (Wi <2) and qualitative agreement at higher Weissenberg number. For strongly shear thinning fluids we find a decrease in the drag for increasing Weissenberg numbers. We present the detailed physical mechanism for this remarkable behavior, and demonstrate that there is an optimum polymer concentration if reduction of particle sedimentation rate is the desired engineering criterion for these fluids.