Effects of Electroosmosis on Soil Temperature and Hydraulic Head. II: Numerical Simulation

Abstract

A numerical model to simulate the distributions of the voltage, soil temperature, and hydraulic head during a field test of electroosmosis was developed. The two-dimensional governing equations for the distributions of the voltage, soil temperature, and hydraulic head within a cylindrical domain are derived based on the principles of charge, energy, and mass conservations, Darcy’s law, Ohm’s law, and Fourier’s law of heat conduction. We assumed that the voltage distribution was at steady state, whereas the soil temperature and hydraulic head were at transient states during the test. The simulated domain was segmented with a block-centered finite-difference scheme and the resulting equations were solved numerically with the successive overrelaxation method. The parameters (such as electrical, thermal, hydraulic, and electroosmotic properties of the soil, graphite, and sand) that were required by the model were measured either using core samples or slug tests. The model is able to predict the pattern as well as the magnitude of the voltage profiles observed. The simulated temperatures are similar in pattern and are within 3°C of the values observed in the four casings during 4 weeks of electroosmosis. The changes in the rates of temperature with an increase in energy input predicted by the model are in agreement with the observed changes. The output from the hydraulic head simulations showed that the model could predict patterns of hydraulic head changes in the vicinity of mesh and graphite electrodes. The model, however, underestimated the magnitude of the changes close to the anode. The simulated electroosmotic flow rate of 0.9 L/h is also consistent with the observation of 0.6–0.8 L/h.