Abstract
Abstract. Most theoretical work on analyzing plume spreading at the field scale in a partially saturated heterogeneous formation assumes weak stationarity of velocity field. While this assumption is not applicable to the case of a bounded flow domain, the nonstationarity in fluctuations of unsaturated velocity fields is induced through the presence of the boundary conditions in the flow domain. In this work, we attempt to quantify the large-time macrodispersion in nonstationary unsaturated velocity fields caused by the presence of a fixed head boundary condition. Application of the perturbation-based nonstationary spectral approach leads to an analytical expression for the macrodispersion describing the field-scale dispersive solute flux in terms of the statistical moments of two formation parameters: the Gardener's parameter (α) and the saturated hydraulic conductivity (Ks). The results predicted from the expression indicate that the enhanced unsaturated plume spreading can arise from a larger correlation scale of ln Ks or ln α fields. In addition, the α-parameter takes the role in reducing the field-scale plume spreading.
Highlights
The spatial variability in the specific discharge fields, arising from the heterogeneities of the geologic formations, enhances the spreading of nonreactive field-scale plumes in heterogeneous formations
The common theme in analyzing the transport processes of field-scale plumes for various stochastic methods is to relate the statistics of the solute displacement or the solute dispersive flux to the statistics of the specific discharge fields
Most of stochastic analyses of field-scale solute transport processes have been performed under the assumption of weak stationarity of velocity field, which is the consequence of the assumptions of an unbounded flow domain and uniformity of mean flow
Summary
The spatial variability in the specific discharge fields, arising from the heterogeneities of the geologic formations, enhances the spreading of nonreactive field-scale plumes in heterogeneous formations. The macrodispersive flux (Gelhar and Axness, 1983), an outcome of the correlation between the velocity field and concentration fluctuations, is introduced to quantify the spreading of the solute plume at the field scale. It is well known that the correlation between the fluctuations of the velocity and concentration enhances the degree of spreading of solute plumes (field-scale dispersion or macrodispersion) in heterogeneous aquifers that is much greater than what would occur by local dispersion The present investigation of field-scale unsaturated transport processes at large times can be considered as an extended work to the previous study by Chang and Yeh (2009) for bounded unsaturated flow processes in heterogeneous aquifers. This study attempts to analyze the spreading of plumes in field-scale unsaturated formation based on the Eulerian framework and nonstationary spectral approach. The findings presented in this paper may be of interest to researchers in seeking further research
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