The hydrodynamics of trickling flow in packed beds is modeled by representing the porous medium as an array of parallel conduits of circular cross section.

First, a straight tube model is developed and analytical solutions are obtained for the relative permeabilities of the gas and liquid phases. Then a periodically constricted tube model is proposed and the equations of motion are solved numerically to determine the effect that surface tension forces have on the relative permeabilities. The constricted tube model predicts that the relative permeabilities of the phases are appreciably sensitive to surface tension forces, a prediction that seems at odds with experimental observations. This discrepancy may be caused by the assumption of fully wetted surface area of particles employed in the model.

The straight tube model confirms experimental results indicating that the liquid phase relative permeability is, for practical purposes, insensitive to the gas flow rate and to the gas-to-liquid density and viscosity ratios. Both conduit models show that the gas phase relative permeability curves are strong functions of the gas phase Reynolds number when this parameter is small. For large gas Reynolds numbers, a single curve for the relative permeability as a function of saturation is obtained. These trends are observed in previous experimental studies.