Hydrodynamic dispersion and mass transfer in unsaturated flow

Tracer response experiments were carried out using a packed bed of glass beads, where fluid flowed as either a single phase (water) or two phases (water and gas) under steady unsaturated conditions. The results depended on the water saturation and could be divided into two regions at the critical water saturation, that is, the saturation at which the gas phase began to be immobile. To determine the hydrodynamic dispersion coefficients, the experimental responses were compared with the numerical results of a one-dimensional advection-dispersion equation. These results demonstrated that the hydrodynamic dispersion coefficients increased with a decrease in water saturation. Furthermore, the rates of the increase in the dispersion coefficients above the critical saturation were different from those below it. The following mathematical relations between the Peclet number, Pe, and the water saturation, S(w), were obtained from the results of the two unsaturated flow experiments: Pe = 0.8S(w)/^1.2 for single-phase flow and Pe = 0.9S(w)/^3.1 for two-phase flow. When S(w) = 1 in the relation for single-phase flow, the value of Pe is in a range that has been reported previously. The relation for two-phase flow was used to analyze the mass transport of the two-phase tracer (ammonia-water solution) through unsaturated beds.