Flow of a FENE Fluid in Packed Beds or Porous Media

Abstract

V iscoelastic flow in packed beds or porous media finds application in such diverse areas as petroleum crude recovery, flow in soils and in filtration of suspensions in polymer solutions or melts. The formulations describing the flow of viscous fluids do not apply to viscoelastic fluids as a consequence of the discovery (Sadowski and Bird, 1965;Marshall and Metzner, 1967;Dauben and Menzie, 1967;Savins, 1969) that in flows through packed beds or porous media viscoelastic fluids exhibit enhanced potential drops exceeding those predicted on the basis of the viscous flow behaviour. It may be noted that Christopher and Middleman (1965) developed an equation based on the Kozeny-Ergun bed model (Kozicki, 2001) that successfully predicts the flow of high shear-thinning fluids (Kozicki and Tiu, 1988) and provides an improved fit of the data of Sadowski and Bird (1965). The increased flow resistance of viscoelastic fluids has been attributed (James and McLaren, 1975;Bird et al., 1977b;Kulicke and Haas, 1984) to the enhanced normal stresses generated by these fluids when subjected to elongational flow fields. The attempts at analytical characterization have been hampered by the joint complexity of the problems associated with the flow geometry and the rheological behaviour of viscoelastic fluids.In the previous study (Kozicki, 2001), a general analysis of viscoelastic flow in porous media was developed based on a capillary hybrid flow model which incorporates an elongational flow mode in addition to the shear mode. The velocity variation in the axial direction was achieved by utilization of a mass source distribution. The increase in the potential drop attributed to elongational flow was evaluated from the energy dissipation rate associated with the elongational mode. The analysis yielded expressions for the flow rate in packed bed and porous media flows, including Darcy's law, and a general expression for the friction factor in terms of the familiar Reynolds number for viscous flow and an analogous Reynolds number expression containing the mean elongational viscosity characterizing the elongational mode of the flow. Since the analysis was conducted entirely in terms of the elongational viscosity of the fluid, the results apply to any arbitrary rheological fluid model.In the following, the formulation is applied to fluids described by the FENE model derived by kinetic theory (Bird et al., 1977b). The FENE fluid designation refers to a dilute polymer solution comprised of linear macromolecules which are represented by elastic dumbbells. Each dumbbell consists of two beads joined by a finitely extendible nonlinear elastic (FENE) spring, as proposed by Warner (1972). This fluid model is of interest because of the fundamental basis it provides for a systematic representation of flow in packed beds or porous media coupled with the i n s i g h t provided into the role of the molecular properties in characterization of the flow behaviour. A considerable body of knowledge (Durst and Haas, 1981;Haas and Durst, 1982;Kulicke and Haas,...

Creeping Flow of Viscoelastic Fluid through a Packed Bed

“…Excess pressure drop has been observed by various investigators in the case of flow of viscoelastic fluids through porous media, compared to that of purely viscous fluids under similar flow conditions . The increased flow resistance of viscoelastic fluids has been attributed to enhanced normal stresses generated by these fluids when subjected to elongational flow fields, with elongation rates that exceed certain “onset” conditions . The importance of viscoelastic effects in determining excess pressure drop in the case of flow through porous media has been studied by various investigators − using different complex fluids flowing through porous media; however, there is significant discrepancy in the reported critical values of the Deborah number ( De ), from which viscoelastic effects begin to dominate.…”