Modeling temperature dependence of trace element concentrations in groundwater using temperature dependent distribution coefficient

In our previous study, we have observed trace element concentrations in groundwater increased when groundwater temperature was increased with constant thermal loading using a 50-m long vertical heat exchanger installed at Saitama University, Japan. During the field experiment, 38 degree C fluid was circulated in the heat exchanger resulting 2.8 kW thermal loading over 295 days. Groundwater samples were collected regularly from 17-m and 40-m deep aquifers at four observation wells located 1, 2, 5, and 10 m, respectively, from the heat exchange well and were analyzed with ICP-MS. As a result, concentrations of some trace elements such as boron increased with temperature especially at the 17-m deep aquifer that is known as marine sediment. It has been also observed that the increased concentrations have decreased after the thermal loading was terminated indicating that this phenomenon may be reversible. Although the mechanism is not fully understood, changes in the liquid phase concentration should be associated with dissolution and/or desorption from the solid phase. We therefore attempt to model this phenomenon by introducing temperature dependence in equilibrium linear adsorption isotherms. We assumed that distribution coefficients decrease with temperature so that the liquid phase concentration of a given element becomes higher as the temperature increases under the condition that the total mass stays constant. A shape function was developed to model the temperature dependence of the distribution coefficient. By solving the mass balance equation between the liquid phase and the solid phase for a given element, a new term describing changes in the concentration was implemented in a source/sink term of a standard convection dispersion equation (CDE). The CDE was then solved under a constant ground water flow using FlexPDE. By calibrating parameters in the newly developed shape function, the changes in element concentrations observed were quite well predicted. The model developed in this study is a novel attempt to simulate changes in groundwater quality during thermal loading to the subsurface. Although more experimental and theoretical studies need to be done, the results of this study at least provide some good insights regarding behavior of trace elements in groundwater when temperature is changing.