Abstract
Abstract. Owing to the analogy between the solute and heat transport processes, it can be expected that the rate of growth of the spatial second moments of the heat flux in a heterogeneous aquifer over relatively large space scales is greater than that predicted by applying the classical heat transport model. The motivation of stochastic analysis of heat transport at the field scale is therefore to quantify the enhanced growth of the field-scale second moments caused by the spatially varying specific discharge field. Within the framework of stochastic theory, an effective advection-dispersion equation containing effective parameters (namely, the macrodispersion coefficients) is developed to model the mean temperature field. The rate of growth of the field-scale spatial second moments of the mean temperature field in the principal coordinate directions is described by the macrodispersion coefficient. The variance of the temperature field is also developed to characterize the reliability to be anticipated in applying the mean heat transport model. It is found that the heterogeneity of the medium and the correlation length of the log hydraulic conductivity are important in enhancing the field-scale heat advection, while the effective thermal conductivity plays the role in reducing the field-scale heat advection.
Highlights
The temperature of the land surface is influenced by seasonal heating and cooling
The spatially varied velocity field creates the degree of spreading of a solute plume in a heterogeneous aquifer that is greater than what would occur by local dispersion alone in the uniform velocity field
A stochastic methodology is devoted to relating this enhanced spreading to the characteristics of the velocity field and to the statistical properties of hydraulic conductivity field based on the representation of natural heterogeneity as a spatial random variable characterized by a limited number of statistical parameters
Summary
The temperature of the land surface is influenced by seasonal heating and cooling. Water seepage near the land atmosphere interface results in a heat transport that modifies the temperature profile and, in turn, affects most reactions occurring in the aquifers. A stochastic methodology is devoted to relating this enhanced spreading to the characteristics of the velocity field and to the statistical properties of hydraulic conductivity field based on the representation of natural heterogeneity as a spatial random variable characterized by a limited number of statistical parameters This leads to a solution in terms of an effective dispersion coefficient (macrodispersion coefficient) for describing the rate of growth of the second moments of the ensemble averaged concentration field. Note that the effective dispersion coefficient is determined by half the rate of change of the particle displacement variance (or the spatial second moment of a concentration distribution) This approach has been applied to analyze the nonreactive solute transport in heterogeneous media in a number of papers It is hoped that our findings will provide a basic framework for understanding and quantifying field-scale heat transport processes and be useful in stimulating further research in this area
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