On Laminar Flow of Non-Newtonian Fluids in Porous Media

Abstract

Flow of generalized Newtonian fluids in porous media can be modeled as a bundle of capillary tubes or a pore-scale network. In general, both approaches rely on the solution of Hagen-Poiseuille equation using power law to estimate the variations in the fluid viscosity due to the applied shear rate. Despite the effectiveness and simplicity, power law tends to provide unrealistic values for the effective viscosity especially in the limits of zero and infinite shear rates. Here instead of using power law, Carreau model [5] is used to determine the effective viscosity as a function of the shear strain rate. Carreau model can predict accurately variation of the viscosity at all shear rates and provide more accurate solution for the flow physics in a single pore. Using the results for a single pore, normalized Fanning friction coefficient has been calculated and plotted as a function of the newly defined Reynolds number based on pressure gradient. For laminar flow, the variation of the friction coefficient with Reynolds number has been plotted and scaled. It is observed that generalized Newtonian fluid flows show Newtonian nature up to a certain Reynolds number. At high Reynolds number deviation from the Newtonian behavior is observed. The main contribution of this paper is to present a closed form solution for the flow in a single pore using Carreau model, which allows for fast evaluation of the relationship between flux and pressure gradient in an arbitrary pore diameter. In this way we believe that our development will open the perspectives for using Carreau models in pore network simulations at low computational costs to obtain more accurate prediction for generalize Newtonian fluid flows in porous media.

The Effect of Heat Transfer and Polymer Concentration on Non-Newtonian Fluid from Pore-Scale Simulation of Rock X-ray Micro-CT

“…Furthermore, the effect of polymer concentration on the shear thinning behavior of bio-polymers seems to be well-captured by the proposed model equation given in Equation (9). This model (see Figure 1) is in line with experimental measurements of polymer solutions used for EOR [21,24,25].…”

“…The typical values used in Equation (9) are given in Table 1. It is worth noting that even though our model may approximate well some polymers rheology for EOR, generally polymer solutions exhibit a more complex constitutive relation such as in the case of viscoelasticity.…”

“…The high mobility would indicate a better transmissibility of the fluid as opposed to the low mobility. In order to investigate the concentration effect on the mobility, we simulated the fluid flow at pore-scale by varying the concentration at a fixed temperature using the proposed fluid rheology model given in Equation (9). The kinematic viscosity field resulting from the simulation, which spans two orders of magnitude, is shown in Figure 7, highlighting the complexity nature of the concentration-dependent shear-thinning fluid flow within the rock.…”

“…Most of the numerical simulation concerns with the modeling at pore-scale deals with Newtonian fluid or simplified pore network, which significantly alters the porous media geometry, assuming it consists of connected capillary tubes [8,9]. Despite a large body of work, modeling of non-Newtonian is still challenging and remains an active field of research [8,[10][11][12][13].…”

Shear Rate Determination from Pore-Scale Flow Fields

“…A direct link between the bulk viscosity μ = μ(γ ) and Darcy scale μ eff = μ eff (v Darcy ) can be made by using approximate analytical models (Fayed et al 2016) or hydrodynamic simulation of the pore-scale flow field for the non-Newtonian rheology (Balhoff 2000;Afshar-poor et al 2012;Clemens et al 2012;Afsharpoor and Balhoff 2013;Tosco et al 2013). Even though these approaches become more and more available, the most commonly used approach are semi-empirical correlations for the Darcy-scale effective shear rate (Delshad et al 2008).…”