Flow Through Porous Media of Packed Spheres Saturated With Water

Abstract

The existing literature on the flow of fluids through porous packed beds gives very limited quantitative information on the criteria employed in marking the applicability of the different flow regimes. It is the objective of this paper to provide experimental evidence for determining the demarcation criteria during the flow of water through a bed of randomly packed spherical beads. Two different sizes of glass beads, 3 mm and 6 mm, were employed as the porous matrix through which water flowed at rates varying from 5.07 × 10−6 m3 /s to 4920 × 10−6 m3 /s. Our dimensionless pressure drop data showed less variation when the characteristic length of the porous medium was taken to be proportional to the square root of the permeability over the porosity and not the bead diameter. Curves of properly nondimensionalized pressure drop (P’K/μv) plotted against the actual flow Reynolds number based on the porous medium permeability (R̂eK ) provided the following information. It was found that Darcy’s law has very limited applicability and is valid for a small range of Reynolds numbers (0.06<R̂eK <0.12). This leads to a pre-Darcy flow that is valid for a much broader range of Reynolds numbers than expected (R̂eK <0.06). Alternatively, the range of validity of the post-Darcy laminar Forchheimer flow is also found to be of much more limited applicability (0.34<R̂eK <2.30) than previous studies (Fand et al., 1987) have indicated (0.57<R̂eK Fand et al. <9.00). Transition to turbulence takes place earlier than expected and turbulent flow prevails from then on (R̂eK >3.40). The dimensionless pressure drop in both the Forchheimer and turbulent flow regimes can be modeled by an appropriately nondimensionalized Ergun’s equation (Carman, 1937), i.e., a first-order inertia term correction is sufficient in both flow regimes. However, the magnitude of the correction coefficients in the Forchheimer regime differs significantly from that in the turbulent flow regime (ÂF =1.00, B̂F =0.70, B̂T =1.90, B̂T =0.22). Again, this differs from previous findings (Fand et al., 1987). The effect of the angle of inclination of the porous medium with respect to the horizontal on the transition mechanisms was also experimentally investigated. No changes other than the correction in the pressure drop due to the static liquid column height were observed.