The Mass Transfer Index (MTI): A semi-empirical approach for quantifying transport of solutes in variably saturated porous media.

The processes impacting solute transport through unsaturated porous media have been receiving renewed attention due to their relevance to the transport of emerging contaminants. A set of well-monitored and highly controlled experiments in sand columns were conducted to determine the effect of partial saturation on conservative solute breakthrough in porous media. The results suggest traditional transport parameter estimation methods inadequately account for the pore-scale processes of mass transfer to the immobile zones and the effects of partial saturation on advective transport, even for conservative tracers. Accurate estimation of these basic transport parameters is critical to evaluate the multi-phase partitioning of nonconservative solutes, as any errors in these parameters would bias the estimates of multi-phase partitioning parameters. Herein, we introduced the Mass Transfer Index (MTI), a semi-empirical approach for quantifying the impact of non-Fickian elements of pore-scale unsaturated solute transport (i.e. immobile water, tortuous flow paths, and non-uniform solute distribution), which become increasingly important as the wetting fluid saturation decreases. Importantly, this MTI was determined independently of chemically driven phase partitioning and is supported by experimental data. Based on this conceptualization, the 1-D equilibrium advection dispersion equation was modified to incorporate the MTI as a lumped parameter which quantifies resistance to (MTI > 1) or promotion of (MTI < 1) of advective solute flux. Analytical solutions to the modified advection-dispersion-reaction equation for pulse and step inputs were developed. Conservative tracer experiments were conducted in variably saturated sand columns to validate both the MTI conceptualization and the inversion method used to estimate the MTI. These experiments involved the use of X-ray absorption spectroscopy integrated with sensor-based measurements of soil moisture, temperature, and electrical conductivity for tracer breakthrough. The mathematical model developed herein adapts traditional macroscopic models of solute transport to account for the non-Fickian pore-scale transport behaviors observed in unsaturated porous media with significant advective flux.