Rate-controlled sorption 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 second transport model (rate-controlled sorption) is based on the assumption that the sorption mechanism does not have time to reach equilibrium at each point along the column. Mansell et al. (16) used this model to simulate phosphorus transport through sandy soils. Therefore, Equation 1 is replaced by the sorption rate expression ... 

Finite-difference techniques were used to compute numerical solutions as column-breakthrough curves because of the nonlinear Freundlich isotherm in each transport model. Along the column, 100 nodes were used, and 10 nodes were used in the side-pore direction for the profile model. A predictor-corrector calculation was used at each time step to account for nonlinearity. An iterative solver was used for the profile model whereas, a direct solution was used for the mixed side-pore and the rate-controlled sorption models. 

Transport models employing the bicontinuum-sorption formulation, with one domain equilibrium controlled, were presented by Selim et al. (1976) and Cameron and Klute (1977), while Selim et al. (1976) also presented a model where both domains were rate limited. The one-site model mentioned previously is a special case of the two-site model, where all sorption sites are assumed to be of the time-dependent class (Selim et al., 1976 van Genuchten, 1981). The bicontinuum-based model has generally been able to represent nonequilibrium data much better than has the one-site model. 

Many one-dimensional solute-transport models have been developed and used to analyze column data. For a recent review, see Grove and Stollenwerk (13). Four different models were used in the study discussed in this article to simulate the shape of the column-breakthrough curves. All four models contain a one-dimensional solute-transport equation and use the Freundlich equation to describe sorption. They differ in the rate mechanism that is assumed to control transport of Mo(VI) from flowing phase to solid surface. The essential features of each model are summarized in Table III. 

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