Non-Darcian flow of shear-thinning fluids through packed beads: Experiments and predictions using Forchheimer's law and Ergun's equation

Abstract

The flow of shear-thinning fluids through unconsolidated porous media is present in a number of important industrial applications such as soil depollution, Enhanced Oil Recovery or filtration of polymeric liquids. Therefore, predicting the pressure drop-flow rate relationship in model porous media has been the scope of major research efforts during the last decades. Although the flow of Newtonian fluids through packs of spherical particles is well understood in most cases, much less is known regarding the flow of shear-thinning fluids as high molecular weight polymer aqueous solutions. In particular, the experimental data for the non-Darcian flow of shear-thinning fluids are scarce and so are the current approaches for their prediction. Given the relevance of non-Darcian shear-thinning flow, the scope of this work is to perform an experimental study to systematically evaluate the effects of fluid shear rheology on the flow rate-pressure drop relationships for the non-Darcian flow through different packs of glass spheres. To do so, xanthan gum aqueous solutions with different polymer concentrations are injected through four packs of glass spheres with uniform size under Darcian and inertial flow regimes. A total of 1560 experimental data are then compared with predictions coming from different methods based on the extension of widely used Ergun's equation and Forchheimer's law to the case of shear thinning fluids, determining the accuracy of these predictions. The use of a proper definition for Reynolds number and a realistic model to represent the rheology of the injected fluids results in the porous media are shown to be key aspects to successfully predict pressure drop-flow rate relationships for the inertial shear-thinning flow in packed beads.

Non-Darcy Flow Experiments of Water Seepage through Rough-Walled Rock Fractures

“…Typical characteristics of natural rock fractures include rough walls and asperity contact [2,3], and non-Darcy flow may occur as a result of nonnegligible inertial losses. Previous experimental work demonstrated that Darcy's law fails to predict pressure drops in fractures when inertial effects are relevant before the fully developed turbulence [4][5][6][7]. In the post-Darcy regimes where inertial effects are significant, two equations are invariably used to describe pressure drop as a function of average velocity: Forchheimer and Ergun equation [7,8].…”

Flow of yield stress and Carreau fluids through rough‐walled rock fractures: Prediction and experiments

“…This flow equation was expressed in the form of a full cubic law: where β and d are the inertial coefficients which may be positive or negative, depending on the channel geometry. and d were shown to be independent of the shear rheology of the injected fluid in previous numerical [ Firdaouss et al ., ; Yazdchi and Luding , ; Tosco et al ., ] and experimental works [ Rodríguez de Castro and Radilla , , ]. In this full cubic law, the quadratic term describes the pure inertia effect caused by an irreversible loss of kinetic energy due to flow acceleration and the cubic term corresponds to a cross viscous‐inertia effect caused by the streamline deformation due to inertia forces.…”

“…This macroscopic flow equation is valid not only in the Darcian flow regime but also, to some limited extent, for the non‐Darcian flow regimes. β and d can be obtained either through fitting to experimental data [ Dukhan et al ., ; Rodríguez de Castro and Radilla , , ] or through theoretical predictions obtained from porosity, permeability, and roughness of the porous medium [ Cornell and Katz , ; Geertsma , ; Neasham , ; Noman and Archer , ; López , ; Agnaou et al ., ].…”

“…Previous experimental works demonstrated that Darcy's law fails to predict pressure drops in fractures when inertial effects are relevant [ Zimmerman et al ., ; Radilla et al ., ; Javadi et al ., ; Rodríguez de Castro and Radilla , , ]. Zimmerman et al .…”

“…Another interesting prospect consisted in extending this prediction method to the case of shear‐thinning fluids with yield stress. The same authors also proposed a simple method to predict non‐Darcian flow of Carreau fluids through packed beads [ Rodríguez de Castro and Radilla , ]. However, the flow of yield stress fluids was not tackled in these works and no estimate of the shift parameter relating the apparent viscosity of the fluid in the porous medium to its bulk viscosity was provided either.…”