Polymer Flow Through Porous Media: Numerical Prediction of the Contribution of Slip to the Apparent Viscosity

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 18221 Abstract The flow of polymer solutions in porous media is often described using Darcy's law with an apparent viscosity capturing the observed thinning or thickening effects. While the macroscale form is well accepted, the fundamentals of the pore-scale mechanisms, their link with the apparent viscosity, and their relative influence are still a matter of debate. Besides the complex effects associated with the rheology of the bulk fluid, the flow is also deeply influenced by the mechanisms occurring close to the solid/liquid interface, where polymer molecules can arrange and interact in a complex manner. In this paper, we focus on a repulsive mechanism, where polymer molecules are pushed away from the interface, yielding a so-called depletion layer in the vicinity of the wall. This depletion layer acts as a lubricating film that may be represented by an effective slip boundary condition. Here, our goal is to provide a simple mean to evaluate the contribution of this slip effect to the apparent viscosity. To do so, we solve the pore-scale flow numerically in idealized porous media with a slip length evaluated analytically in a tube. Besides its simplicity, the advantage of our approach is also that it captures relatively well the apparent viscosity obtained from core-flood experiments, using only a limited number of inputs. Therefore, it may be useful in many applications to rapidly estimate the influence of the depletion layer effect over the macroscale flow and its relative contribution compared to other phenomena, such as nonNewtonian effects.

Pore‐Scale Flow Characterization of Polymer Solutions in Microfluidic Porous Media

“…Thus, the fluid motion is excited over a broad range of spatial and temporal scales, similar to high‐Re turbulence; intriguingly, however, this power law decay (with a −3.5 exponent) has a different value than the −5/3 Kolmogorov exponent characteristic of high‐Re turbulence. Simulations are able to recover a similar spectral scaling, supporting the idea that it reflects an elastic instability analogous to turbulence; they also reveal that flow fluctuations are stronger near boundaries, potentially due to a depletion layer effect …”

“…This depletion layer arises from a combination of shear‐induced migration, entropic or steric effects, and electrostatic interactions . Though typically neglected from macroscopic models of flow, the formation of a depletion layer could play a considerable role on transport—for example, possibly suppressing polymer adsorption and leading to viscosity reduction at the pore surfaces . Nanofluidic platforms, which provide a means to test pores of width approaching molecular dimensions, could shed light on these effects.…”

“…Simulations are able to recover a similar spectral scaling, supporting the idea that it reflects an elastic instability analogous to turbulence; 148,149 they also reveal that flow fluctuations are stronger near boundaries, 149 potentially due to a depletion layer effect. 150 Single-molecule imaging of fluorescently-labeled DNA demonstrates that a sharp coilstretch transition occurs in these unstable flows. 112 In this case, the mean elongation for polymers in the 'stretched' state is found to be approximately 0.85 the contour length.…”

On the Deviation of Computed Permeability Induced by Unresolved Morphological Features of the Pore Space

“…While the latter allow a gain in accuracy, the use of collocated grids easily aligns the computational points to the experimental datasets. Optimized grid-based methods may be coupled to other methods dedicated to the flow features to be investigated: transport based on particle methods [54,55], anisotropic diffusion for space-variable medium [56,57], phase-field description of multi-phase flows [58,59] and its upscaling [8,60], complex fluid and rheology [61,57], etc...…”

Upscaling Hydrodynamic Dispersion in Non‐Newtonian Fluid Flow Through Porous Media

“…Morais et al (2009) simulated the flow of shear thinning fluids in 3D disordered porous media with large porosity, and proposed a universal curve for describing the relation between the effective permeability and a suitably-defined Reynolds number. Flow of a ST fluid through an array of cylinders was studied by Zami-Pierre et al (2018), who reported that disorder reduces the effect of the nonlinearity on the average flow. Sahimi (1993) used the critical path analysis to derive an expression for the effective permeability of power law fluids, including ST ones, in a porous medium.…”