Simulated Breakthrough Research Articles

Evaluation of distribution coefficients for the prediction of strontium and cesium migration in a uniform sand

The validity of using a distribution coefficient (Kd) in the mathematical prediction of strontium and cesium transport through uniform saturated sand was investigated by comparing measured breakthrough curves with curves of simulations using the advection-dispersion and the advection equations. Values for Kd were determined by batch equilibration tests and, indirectly, by fitting the mathematical model to breakthrough data from column experiments. Although the advection-dispersion equation accurately represented the breakthrough curves for two nonreactive solutes (chloride and tritium), neither it nor the advection equation provided close representations of the strontium and cesium curves. The simulated breakthrough curves for strontium and cesium were nearly symmetrical, whereas the data curves were very asymmetrical, with long tails. Column experiments with different pore-water velocities indicated that the shape of the normalized breakthrough curves was not sensitive to velocity. This suggests that the asymmetry of the measured curves was the result of nonlinear partitioning of the cations between the solid and liquid phases, rather than nonequilibrium effects. The results indicate that the distribution coefficient, when used in advection-dispersion models for prediction of the migration of strontium and cesium in field situations, can result in significant error.

Evaluating breakthrough curves with the method of moments for systems obeying the Langmuir isotherm

Using numerical simulation, moments of breakthrough curves for systems obeying the Langmuir isotherm have been calculated. The breakthrough curves were observed to fall into three regions. In relatively short columns there is quasi-kinetic behaviour; as the retention time of the breakthrough curve in the column increases relative to the characteristic diffusion time there is a transition region, whereas for relatively long columns constant-pattern breakthrough curves are observed. Numerical solutions have been compared for accuracy with limiting analytical solutions or with literature approximations, when availavable. Judging from the comparisons made, simulated first moments deviate from the true values by less than one percent, reduced second moments by 20–30% in the short-column region and by 11% in the constant-pattern region, and skews by 10–15% in the short-column region and by 10% in the constant-pattern region. Since the constant-pattern breakthrough curves are more nearly symmetrical than those in short columns, it is logical that the errors involved in truncating the tail of simulated breakthrough curves are larger for the shorter columns. Parameter determination may be performed on the basis of the diagrams presented in this paper, or with eqns (46)–(51) depending on the value of η L .