Steady state heat transport in 3D heterogeneous porous media

Heat is transported in aquifers by advection and conduction. Spatial variability of hydraulic conductivity causes fluctuations in small scale advection, whose effect can be represented by a dispersion term. However, the use of this term is still subject to controversy among modelers. The effect of heterogeneity on the heat plume generated by a groundwater heat exchanger (GHE) in a three-dimensional aquifer under steady state conditions is examined. Transverse dispersion is estimated using a stochastic approach in which a distinction between effective and ensemble dispersion coefficients is made. The former quantifies the typical width of the heat plume and the latter takes into account the uncertainty of the lateral plume position. Simulations show that transverse dispersion is proportional to the variance and correlation length of the log-conductivity field. On the one hand, the ensemble transverse dispersion coefficient, which can be used for risk analysis to find the mean temperature and the potential plume spread, is high near the heat source and then decreases. On the other hand, the effective transverse dispersion coefficient, the one required to simulate actual temperature values and plume width, displays a less marked dependence on the distance from the source. For modeling purposes it can be approximated as αT≈0.02σlnK2Lx, where σlnK2 is the variance of the log-conductivity field and LxLx its correlation length in the mean flow direction. However, a zero dispersion should be used to compute the energy dissipated by the GHE.