Mass-transfer impact on solute mobility in porous media: A new mobile-immobile model

The theory for modeling non-equilibrium solute transport in porous media is still based on approximations to a model proposed by Lapidus and Amundson in 1952 that has not been updated. This Mobile-Immobile Model (MIM) is based on the definition of a mass-transfer coefficient (α), which has been proven subject to some severe limitations. Measurements at both laboratory and field scales have demonstrated the scale-dependency of α values. This means that the MIM theory fails in real applications, since α is not constant, as defined in the kinetic model theory, but is a time-residence (or distance) dependent coefficient. Multi-rate mass-transfer models have been proposed in recent literature to capture real-world solute transport with a multiple mass transfer. In this study, we propose a novel model, which implements the analytical solution of Fick's second law of diffusion directly in the nonequilibrium advection/dispersion equation of solute transport in porous media. New model solutions properly fitted data collected during tracer tests carried out at the CNR-IRSA Laboratory (Bari, Italy) in a horizontal sandbox, 2 m of length, by using sodium chloride as the conservative tracer. Selected breakthrough curves at specific positions were used to validate the proposed model solution and estimate both conventional and proposed coefficients of mass transfer. Results have shown a decreasing trend of α from 0.09 to 0.04 h^-1 after about 1.2 m of filtration for the investigated sand, whereas new solutions provide two scale-invariant tracer coefficients of rate of tracer mass-transfer (0.004 ± 0.005 h^-1) and of tracer time delay (1.19 ± 0.01). The proposed model performs very well, since it provides a readily solved analytical solution with respect to the conventional MIM. Results of the proposed MIM are very similar to those provided by the conventional MIM. The new model solution can be implemented in particle tracking or random walk software in order to solve two-dimensional nonequilibrium solute transport in groundwater.