Modeling the Nonequilibrium Transport of Linearly Interacting Solutes in Porous Media: A Review

Abstract

The transport of linearly interacting solutes in porous media is investigated with the help of residence time distributions, transfer functions, methods of system dynamics, and time-moment analyses. The classical one-dimensional convection-dispersion equation is extended to two-region (mobile-immobile water) transport by including diffusional mass transfer limitations characteristic of aggregated soils. The two-region model is further revised by incorporating the effects of multiple retention sites (in parallel or in series), multiple porosity levels, and arbitrary but steady flow fields. It is shown that different physical situations can be represented by a relatively small number of transfer functions containing only two types of parameters: distribution coefficients to account for equilibrium properties and characteristic times reflecting kinetic processes. Relevant kinetic processes include convective transport, hydrodynamic dispersion, adsorption-desorption, and physical or chemical mass transfer limitations. In most situations, theoretical breakthrough curves are found to be relatively insensitive to the mathematical structure of the transfer function, irrespective of the physical interpretation of the distribution coefficients and the characteristic times in the model. This means that alternative physical and chemical interpretations of model parameters can lead to nearly identical breakthrough curves. Certain transfer time distributions can lead to quite unusual shapes in the breakthrough curves; these curves strongly depend on the characteristic times and a few operational variables. Results of this study show that the transfer time distribution is an extremely useful tool for explaining some unexpected experimental results in the solute transport literature. t' :ms, and the ability or inability of the transport equations to ratch observed solute distributions versus time or distance. the soil and groundwater literature [Valocchi, 1985, 1989, 1990; Sposito et al., 1986; Go!tz and Roberts, 1987]. At the same time, the study of reactors in chemical engineering led to the development of alternative methods for simulating the transport of reactive solutes during nonideal flow, particularly dispersed plug flow [Himmelblau and Bischoff, 1968; Levenspiel, 1972; Wen and Fan, 1975; Villermaux, 1982; Nauman and Buffham, 1983]. Many researchers applied principles of linear system dynamics and ideal reactors to more efficiently model increasingly complex chemical systems. At present, one of the most powerful tools in chemical reaction engineering is the concept of residence time distribution which permits one to describe the main properties of a transport system with only a few key parameters, especially when the solute interacts linearly with the porous medium. This approach was first introduced in hydrology by Jury and coworkers [Jury, 1982; Jury and Sposito, 1986; White et al., 1986; Sposito et al., 1986; Jury and Roth, 1990].Although the prediction of water flow in a soil requires a detailed physical or mechanic...

Tracing Water Flow and Colloidal Particles Transfer in an Unsaturated Soil

“…This observation is made for all three media being studied. It is a characteristic of heterogeneous, dispersive flows [36]. Mass balance of colloidal particles is between 0.69 and 0.96 (Table 3), attesting to irreversible retention of colloidal particles in porous medium.…”

“…The degree of flow heterogeneity impacts the access of pollutants to adsorption sites [36] [37] [47] and even the access of colloidal particles to trapping and adsorption sites [45] [46]. In unsaturated conditions, the small pores have a large capillary force that pulls out colloidal particles trapped in constrictions.…”

Evaluation of continuous distribution models for rate‐limited solute adsorption to geologic media

“…Rate limitations on sorpfion arise from diffusion across the boundary layer, diffusion into the grains of the porous medium, chemical kinetics, or some combination of these processes [Sparks, 1989]. Whether controlled by diffusion or by chemical kinetics, solute adsorption kinetics are heterogeneous; in other words, solute interactions with subsurface materials occur at multiple rates [Skopp, 1986;Brusseau et al, 1992;Sardin et al, 1991].…”

Quantification of microporosity by nuclear magnetic resonance relaxation of water imbibed in porous media

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