STEADY INCOMPRESSIBLE LAMINAR-FLOW IN POROUS-MEDIA

Steady incompressible laminar flow in porous media is studied. The volume averaging technique is revisited resulting in a new averaging approach to the pressure gradient term. The difference between the traditionally obtained volume averaged equation for very small flow rate and Brinkman's equation is resolved. The Kozeny-Carman theory is modified. By including a two-dimensionally modelled tortuosity and curvature ratio as well as pore cross-sectional area variation, a new semi-empirical equation for the pressure drop for flow through porous media is obtained. The pressure drop dependence on the porosity epsilon for Darcy's flow region is established as epsilon(-11/13)(1 - epsilon)(2) as opposed to epsilon(-3)(1 -,)2 in the original Kozeny-Carman's theory. A modified Reynolds number is also defined. The regions of Darcy's flow and Forchheimer's flow are unified. The wall effects are incorporated into the unified pressure drop equation. The final form of the normalized pressure drop equation for a one-dimensional medium is given by -Delta p'/L d'(2)(s) epsilon(11/3)/mu U(1 - epsilon)(2) = f(v) = 85.2[1 + pi d(s)/6(1 - epsilon)](2) + 0.69[1 - pi(2)d(s)/24(1-0.5d(s))]Re-m Re-m(2)/16(2) + Re-m(2) for d(s) = d'(s)/D < 0.75. Here f(v) is the normalized pressure drop factor, -Delta p' is the pressure across a fixed thickness L of the porous bed, epsilon is the porosity, d: is the equivalent spherical particle diameter, D is the bed diameter, U is the superficial velocity or fluid discharge rate, mu is the dynamic viscosity of the fluid and Re-m is the modified Reynolds number. The one-dimensional pressure drop equation is also modified to give a shear factor for use with the volume averaged Navier-Stokes equation and it is given as F = (1 - epsilon)(2)/4 epsilon(11/3)d(s)(2){85.2[1 + pi d(s)/6(1 - epsilon)](2) + 0.69[1 - pi(2)d(s)/24(1 - 0.5d(s))]Re-v Re-v(2)/16(2) + Re-v(2)} where F is the shear factor and Re-v is the local modified Reynolds number. The semi-theoretical model was tested with available acid new experimental pressure drop data for packed beds. Further comparison was made with experimental pressure drop data for flow in a fibrous mat. The model was found to correlate well for the whole range of Reynolds number, wall effects and porosity studied.