Analysis of one‐dimensional solute transport through porous media with spatially variable retardation factor

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Abstract
A closed‐form analytical small‐perturbation (or first‐order) solution to the one‐dimensional advection‐dispersion equation with spatially variable retardation factor is derived to investigate the transport of sorbing but otherwise nonreacting solutes in hydraulically homogeneous but geochemically heterogeneous porous formations. The solution is developed for a third‐ or flux‐type inlet boundary condition, which is applicable when considering resident (volume‐averaged) solute concentrations, and a semi‐infinite porous medium. For mathematical simplicity it is hypothesized that the sorption processes are based on linear equilibrium isotherms and that the local chemical equilibrium assumption is valid. The results from several simulations, compared with predictions based on the classical advection‐dispersion equation with constant coefficients, indicate that at early times, spatially variable retardation affects the transport behavior of sorbing solutes. The zeroth moments corresponding to constant and variable retardation are not necessarily equal. The impact of spatially variable retardation increases with increasing Péclet number. The center of mass appears to move more slowly, and solute spreading is enhanced in the variable retardation case. At late times, when the travel distance is much larger than the correlation scale of the retardation factor, the zeroth moment for the variable retardation case is identical to the case of invariant retardation. The small‐perturbation solution agrees closely with a finite difference numerical approximation.