Hydrodynamic dispersion and mass transfer in unsaturated flow

Tracer response experiments were carried out using a packed bed of glass be ads, where fluid flowed as either a single phase (water) or two phases (wat er and gas) under steady unsaturated conditions. The results depended on th e water saturation and could be divided into two regions at the critical wa ter saturation, that is, the saturation at which the gas phase began to be immobile. To determine the hydrodynamic dispersion coefficients, the experi mental responses were compared with the numerical results of a one-dimensio nal advection-dispersion equation. These results demonstrated that the hydr odynamic dispersion coefficients increased with a decrease in water saturat ion. Furthermore, the rates of the increase in the dispersion coefficients above the critical saturation were. different from those below it. The foll owing mathematical relations between the Peclet number, Pe, and the water s aturation; S-w, were obtained from results of the two unsaturated flow expe riments: 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 val ue 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 trac er (ammonia-water solution) through unsaturated beds.