Viscoelastic flow simulations in model porous media

Abstract

We investigate the flow of unsteadfy three-dimensional viscoelastic fluid through an array of symmetric and asymmetric sets of cylinders constituting a model porous medium. The simulations are performed using a finite-volume methodology with a staggered grid. The solid-fluid interfaces of the porous structure are modeled using a second-order immersed boundary method [S. De et al., J. Non-Newtonian Fluid Mech. 232, 67 (2016)]. A finitely extensible nonlinear elastic constitutive model with Peterlin closure is used to model the viscoelastic part. By means of periodic boundary conditions, we model the flow behavior for a Newtonian as well as a viscoelastic fluid through successive contractions and expansions. We observe the presence of counterrotating vortices in the dead ends of our geometry. The simulations provide detailed insight into how flow structure, viscoelastic stresses, and viscoelastic work change with increasing Deborah number De. We observe completely different flow structures and different distributions of the viscoelastic work at high De in the symmetric and asymmetric configurations, even though they have the exact same porosity. Moreover, we find that even for the symmetric contraction-expansion flow, most energy dissipation is occurring in shear-dominated regions of the flow domain, not in extensional-flow-dominated regions.

Elastoviscoplastic flows in porous media

“…Equation (9) reduces to a form similar to equation (8) for Bi = 0, but with a different pressure drop than for the Newtonian case (120/Re), due to the elasticity effects. In particular, we find that the permeability in the viscoelastic case is 25% higher than in the Newtonian case, in qualitative agreement with the results in [7]. Assuming a relation between the pressure drop and the flow rate of the same form as in equation (7), we can define an apparent permeability by computing the ratio of the pressure gradients of the Newtonian and non-Newtonian fluids and obtain the following relation Figure 15 shows the apparent permeability as a function of the Bingham number for all the considered Reynolds numbers.…”

“…Most synthetic and natural porous media exhibit inhomogeneity due to the randomness of their structure. However, in literature is a common practice to consider as a first approximation the medium as homogeneous and composed of an array of cylinders and consider only a periodic cell [5,6,7], thus we adopted the same discretisation in this study.…”

“…We consider the incompressible EVP flow through a model porous medium composed by an array of cylinders with porosity ε = 0.38. Here, we focus on a single periodic cell, as sketched in figure 5, following the work by [7]. The numerical domain is a square box of size L = 2.25r, r being the radius of the cylinders centered in each corner of the domain and the length-scale of the problem.…”

“…To investigate the effects of the flow rate, the role of weak inertial effects, and of the yield stress on the flow in the porous medium, we perform a series of simulations with different Reynolds numbers (0.1, 0.4, 0.8, 1.6) and different Bingham numbers (0, 0.1, 1, 10 and 100), the latter defined as Bi = τ 0 r/µU . Whenever not specified, in all our simulations we fix the Weissenberg number, defined as W i = λU/r, to a constant intermediate value W i = 0.5 and the viscosity ratio β = µ f /µ = 0.5, chosen as in De et al in [7]. In this way, the viscoelastic behavior of the flow does not change, and we focus uniquely on the role of the Reynolds or the Bingham number.…”

Flow of viscoelastic surfactants through porous media

“…Most researchers have tried to link the increased flow resistance found in viscoelastic fluid flows through porous media to enhanced extensional effects . However, our recent simulations on viscoelastic fluid flow through symmetric and asymmetric periodic sets of cylinders shows that most viscoelastic energy dissipation occurs in the shear‐dominated regions of the flow domain, not in extensional‐flow‐dominated regions …”