Abstract
Abstract The paper examines the problem of advective transport of a chemical, which is introduced at the boundary of a spherical cavity contained in a fluid saturated non-deformable porous medium of infinite extent. The advective Darcy flow is caused by a hydraulic potential, maintained at a constant value at the boundary of the spherical cavity. Analytical results are developed for the time- and position-dependent distribution of the chemical concentration in the porous medium, in the presence of natural attenuation and time-dependent variability in the boundary chemical concentration. The analytical results for advective transport problems related to certain two-dimensional flows associated with an annular region are also presented. The analytical solutions provide valuable benchmarks for calibration of computational codes dealing with the advective transport problem.
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