ON NON-NEWTONIAN FLUID-FLOW IN DUCTS AND POROUS-MEDIA

In this communication a three-shape-factor approach is developed to ch aracterize both the flow of non-Newtonian fluids, in particular genera lized Newtonian fluids, in an arbitrarily shaped duct and the flow ove r an isolated sphere. The flow of Herschel-Bulkley fluid and Meter flu id is studied. While the detailed solution for a Herschel-Bulkley flui d can be used to deduce the values of the shape factors, the simplifie d solution for a Meter fluid is also provided to enable for easy appli cation. The interaction of macromolecules with fine capillary duct wal ls, i.e. the discontinuity in flow, is modeled using the Meter fluid m odel. At the low shear limit (dr very low flow rate), the solutions of Chauveteau (1982, J. Rheol. 26, 111-142) and Kozicki et at. (1987, Ch em. Engng Commun. 59, 137-160) are recovered. For a high flow rate, th e present study predicts an increased pressure drop for surface-adhesi ve capillary and a pressure drop reduction for a wall macromolecule de pleted/aligned system. The success in modeling flow in arbitrary shape d ducts and flow over isolated spheres using the same approach suggest s that the present approach is also applicable to flow in porous media . When a volume averaging technique is employed to arrive at the conti nuum governing equations for flow of a generalized Newtonian fluid in porous media, the macroscopic viscosity is obtained. The macroscopic v iscosity is the single quantity in the governing equations that must b e determined for a non-Newtonian fluid flow in addition to the paramet ers already known for a Newtonian fluid flow. In the Newtonian limit, the macroscopic viscosity becomes identical to the Newtonian viscosity . Otherwise, the macroscopic viscosity is the apparent viscosity of th e Suid under the average microscopic shear conditions in porous media. The expressions for the macroscopic viscosity for various fluids: nam ely, Herschel-Bulkley fluid, Meter fluid and Cross fluid, are derived in this communication. Porous medium matrix-macromolecule interactions due to flow discontinuity are studied using two phenomenological mode ls: macromolecule retention and macromolecule alignment/depletion. In particular, the Meter fluid model is used to derive the effects of the porous medium matrix-macromolecule interactions. Predictions based on this study agree well with experimental data for flow of non-Newtonia n fluids in packed beds and consolidated sandstones. (C) 1998 Elsevier Science Ltd. All rights reserved.