Viscoelastic flow simulations in random porous media

S De,J.A.M Kuipers,E.A.J.F Peters,J.T Padding

doi:10.1016/j.jnnfm.2017.08.010

Abstract

We investigate creeping flow of a viscoelastic fluid through a three dimensional random porous medium using computational fluid dynamics. The simulations are performed using a finite volume methodology with a staggered grid. The no slip boundary condition on the fluid-solid interface is implemented using a second order finite volume immersed boundary (FVM-IBM) methodology [1]. The viscoelastic fluid is modeled using a FENE-P type model. The simulations reveal a transition from a laminar regime to a nonstationary regime with increasing viscoelasticity. We find an increased flow resistance with increase in Deborah number even though shear rheology is shear thinning nature of the fluid. By choosing a length scale based on the permeability of the porous media, a Deborah number can be defined, such that a universal curve for the flow transition is obtained. A study of the flow topology shows how in such disordered porous media shear, extensional and rotational contributions to the flow evolve with increased viscoelasticity. We correlate the flow topology with the dissipation function distribution across the porous domain, and find that most of the mechanical energy is dissipated in shear dominated regimes instead, even at high viscoelasticity.

Highlights

The flow of complex fluids through porous media is a field of considerable interest due to its wide range of practical applications including enhanced oil recovery, blood flow, polymer processing, catalytic polymerization, bioprocessing, geology and many others [2,3,4]
We have employed a finite volume - immersed boundary methodology to study the flow of viscoelastic fluids through an array of randomly arranged equal-sized spheres representing a three dimensional disordered porous medium, for a range of solid fractions
Irrespective of the solid fraction, we found a strong increase in flow resistance after a critical De number is reached

Summary

Introduction

The flow of complex fluids through porous media is a field of considerable interest due to its wide range of practical applications including enhanced oil recovery, blood flow, polymer processing, catalytic polymerization, bioprocessing, geology and many others [2,3,4]. Flow through disordered porous media of viscoelastic fluids, i.e. non-Newtonian fluids displaying elasticity, is far from being understood [5,7,8] This is due to the complex interplay between the nonlinear fluid rheology and the porous geometry. Morais et al [18] applied direct numerical simulations to investigate the flow of power-law fluids through a disordered porous medium and found that pore geometry and fluid rheology are responsible for an increase in hydraulic conductance at moderate Reynolds numbers. We will show how the distribution of mechanical energy dissipation in the porous medium changes with increasing viscoelasticity and correlate this with the flow topology This analysis will help us to understand the interplay of pore structure and fluid rheology in three dimensional random porous media

Constitutive equations

Problem description

Apparent relative viscosity

Flow topology

Dissipation function

Conclusion