Reactive Transport with Wellbore Storages in a Single-Well Push-Pull Test
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Abstract. Using the single-well push-pull (SWPP) test to determine the in situ biogeochemical reaction kinetics, a chase phase and a rest phase were recommended to increase the duration of reaction, besides the injection and extraction phases. In this study, we presented multi-species reactive models of the four-phase SWPP test considering the wellbore storages for both groundwater flow and solute transport and a finite aquifer hydraulic diffusivity, including three isotherm-based models (Freundlich, Langmuir and linear sorption models), one-site kinetic sorption model, two-site sorption model, which were also capable of describing the biogeochemical reactive transport processes, e.g. Monod or Michaelis-Menten kinetics. The models of the wellbore storage for solute transport were derived based on the mass balance, and the results showed that ignoring it could produce great errors in the SWPP test. In the injection and chase phases, the influence of the wellbore storage increased with the decreasing aquifer hydraulic diffusivity. The peak values of the breakthrough curves (BTCs) increased with the increasing aquifer hydraulic diffusivity in the extraction phase, and the arrival time of the peak value became shorter with a greater aquifer hydraulic diffusivity. Meanwhile, the Robin condition performed well at the rest phase only when the chase concentration was zero and the solute in the injection phase was completely flushed out of the borehole into the aquifer. The Danckwerts condition was better than the Robin condition even when the chase concentration was not zero. The reaction parameters could be determined by directly best fitting the observed data when the non-linear reactions were described by piece-wise linear functions, while such an approach might not work if one attempted to use non-linear functions to describe such non-linear reactions. The field application demonstrated that the new model of this study performed well in interpreting BTCs of a SWPP test.
