Proceedings of 2001 ASME International Mechanical Engineering Congress and Exposition November 11-16,2001, New York, NY FED-Vol. 255 IMECE2001/FED-24903 CFD SIMULATIONS OF FLOW DYNAMICS IN POROUS MEDIA OF VARIABLE PERMEABILITY ARRANGED IN SERIES Sayavur I. Bakhtiyarov Department of Mechanical Engineering 201 Ross Hall, Auburn University, AL 36849-5320 Phone: (334) 844-6198 Fax: (334) 844-5900 'ABSTRACT In this paper we present the results of the CFD simulations of the viscous fluid flow in two porous media of different permeability and same porosity arranged in series. FLOW-3D software package (Flow-Simulations, Inc.) has been used to predict flow velocity distributions and pressure losses when Newtonian fluid flows through the non-homogenous porous medium. The results of simulations are compared to those obtained experimentally earlier. INTRODUCTION The physical understanding of fluid flow in porous media of variable permeability is important to many scientific and engineering problems in such areas as petroleum and chemical engineering, microbiology and soil physics. According to Darcy's law, for a single-phase fluid flow through a porous medium, the superficial velocity (u) is proportional to the pressure gradient k dP U=--- J..l dx, (1) where k is the permeability of the porous medium, Jl is the viscosity of the fluid. The equation (I) is valid for low Reynolds numbers and porous medium with homogenous permeability. At high Reynolds numbers the pressure gradient is non-linearly related to the superficial velocity dP 2 - dx = lq..t u + bp u , (2) where p is the fluid density, b is the empirical constant. A nonlinear relationship (2) between the pressure gradient and the fluid velocity was first suggested by Forchheimer (1901). Dennis A. Siginer College of Engineering, 105 Wallace Hall Wichita State University, KS 67260-0044 Phone: (316) 978-3400 Fax: (316) 978-3853 25 Ergun (1952) obtained the following empirical equation for the fluid flow in the solid matrix: (3) where dp is the particle diameter, <!> is the porosity of the porous matrix, A and B are empirical dimensionless constants. However a fluid flow through heterogeneous porous media is not studied sufficiently. Recently we reported first experimental results concerning the flow of Newtonian, viscoelastic and viscoinelastic liquids in a porous medium with a step change in permeability, that is, two porous media of different permeabilities and same porosity in series (Siginer and Bakhtiyarov, 1996a, 1996b, 2001). It was shown that the energy loss is higher if the polymeric solution flows first through the porous medium with the smaller permeability rather than through the section with the larger permeability. The difference in energy requirements increases with increasing Reynolds number and may be as high as 25-35% for Reynolds numbers of 0(1). This is a novel effect not observed for Newtonian and highly shear thinning inelastic fluids flowing through the same configuration. Energy requirements for the same volume flow rate are much higher than a Newtonian fluid of the same zero shear viscosity as the polymeric solution. Expressions for the fiiction factor and the resistance coefficient as a function of the Reynolds number have been developed for inelastic and viscoelastic fluids based on the Kutateladze-Popov-Khabakhpasheva and eight constant Oldroyd models, respectively. The behavior of the former and the latter is predicted qualitatively except the difference in energy requirements when the flow direction is reversed in the case of the latter. In this paper we report the results of the preliminary numerical simulations concerning the flow of Newtonian liquid in a porous