Stochastic analysis of field-scale heat advection in heterogeneous aquifers

摘要

Owing to the analogy between the solute and heattransport processes, it can be expected that the rate of growth of thespatial second moments of the heat flux in a heterogeneous aquifer overrelatively large space scales is greater than that predicted by applying theclassical heat transport model. The motivation of stochastic analysis ofheat transport at the field scale is therefore to quantify the enhancedgrowth of the field-scale second moments caused by the spatially varyingspecific discharge field. Within the framework of stochastic theory, aneffective advection-dispersion equation containing effective parameters(namely, the macrodispersion coefficients) is developed to model the meantemperature field. The rate of growth of the field-scale spatial secondmoments of the mean temperature field in the principal coordinate directionsis described by the macrodispersion coefficient. The variance of thetemperature field is also developed to characterize the reliability to beanticipated in applying the mean heat transport model. It is found that theheterogeneity of the medium and the correlation length of the log hydraulicconductivity are important in enhancing the field-scale heat advection,while the effective thermal conductivity plays the role in reducing thefield-scale heat advection.