Profile side-pore diffusion transport model

Laboratory column experiments were used to identify potential rate-controlling mechanisms that could affect transport of molybdate in a natural-gradient tracer test conducted at Cape Cod, Mass. Column-breakthrough curves for molybdate were simulated by using a one-dimensional solute-transport model modified to include four different rate mechanisms equilibrium sorption, rate-controlled sorption, and two side-pore diffusion models. The equilibrium sorption model failed to simulate the experimental data, which indicated the presence of a ratecontrolling mechanism. The rate-controlled sorption model simulated results from one column reasonably well, but could not be applied to five other columns that had different input concentrations of molybdate without changing the reaction-rate constant. One side-pore diffusion model was based on an average side-pore concentration of molybdate (mixed side-pore diffusion) the other on a concentration profile for the overall side-pore depth (profile side-pore diffusion). 

The fourth model (profile side-pore diffusion) is similar to the third but the assumption is made that a concentration profile exists throughout the thickness of the immobile-water phase. Molecular diffusion of solute is the major transport mechanism in the immobile-water phase. The transfer rate of solute from the flowing- to the immobile-water phase is assumed to be the dif-fusional flux at the interface between these phases. Therefore, Equations 7 and 9 are replaced by ... 

Transferability of the results from this study to the Cape Cod natural gradient tracer test will provide information about the validity of laboratory experiments in providing information about onsite processes. Although actual values for some of the physical parameters determined in the laboratory may not apply to an aquifer because of scale differences between laboratory and field, conceptually realistic models such as the profile side-pore diffusion model may be able to simulate onsite transport conditions more accurately. 

The concentration profile in the immobile-water phase is controlled by a diffusional-transport mechanism. The transfer rate from the immobile-water phase to the flowing-water phase is the diffusive flux, which depends on the concentration gradient in the immobile-water phase at the interface. Parameters V, 6, A, and Lg in the profile side-pore model are estimated from the shape of the breakthrough curve for a nonreactive tracer. Parameters Pbf and pbs are estimated from the shape of the breakthrough curve for a reactive solute. The effective molecular diffusivity Dm is estimated from values published in the literature. 

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