csh_lecture10_noneq - CWR 6537 Subsurface Contaminant...

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CWR 6537 - Subsurface Contaminant Hydrology 1 Advective-Dispersive Transport of Reactive Solutes: Non-Equilibrium Sorption Models A. Lecture Goal: To investigate advective-dispersive transport of reactive solutes under the assumption that a contaminant will undergo non-equilibrium sorption-desorption. B. Non-equilibrium Sorption Models: In order to use the aforementioned equilibrium sorption models, we had implicitly assumed that point-wise equilibrium existed between the solution- and sorbed-phases. This approach is of course satisfactory only when sorption-desorption processes are instantaneous; that is, the rates of the sorption-desorption processes are so rapid that it is practically (or measurably) instantaneous. The rates of sorption can usually be described with the aid of standard chemical kinetics or using mass transfer theories based on diffusion-controlled processes. During water flow through soils, the average pore-water velocity determines the mean solute residence time (e.g., 1/ v is the time of residence per unit length; L / v is the time of residence in a column of length L ). It should be evident that with increasing v , the residence time decreases. Thus, depending upon the rates of sorption-desorption processes the short residence times at high average velocities might not be sufficient to guarantee equilibrium conditions for sorption. Similarly, since the advective transport is actually characterized by a velocity distribution, some regions of the media (with high velocities) might experience non- equilibrium sorption velocity even though some other regions (with lower velocity) experience near-equilibrium sorption. Recall from earlier notes that, for steady water flow: x C v - x C D = t S + t C w 2 w 2 w w θ ρ ( 1 ) We need mathematical expressions for describing the time rate of change of amount sorbed (i.e., S/
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2 Stagnant-film Diffusion Mobile-Immobile Zones Aggregated/Structured Soils Fractured Media NON-EQUILIBRIUM SORPTION MODELS Physical Processes Controlling Sorption (e.g., diffusion-controlled access to sites) Chemical Processes Controlling Sorption (e.g., chemical kinetics) One-Site or Two-Site or Multi-Site Kinetics Linear or Non-linear Kinetics Combination of Physical & Chemical Processes
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csh_lecture10_noneq - CWR 6537 Subsurface Contaminant...

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