Uncertainty analysis of multi-rate kinetics of uranium desorption from sediments

• Statistical approach is used to assess the uncertainties of multi-rate models.
• Lognormal is an effective assumption for the rate constants in the multi-rate model.
• The smallest rate constants in the multi-rate model contain largest uncertainties.
• Experimental duration is a major factor controlling the rate constant uncertainty.
• Uncertainties in the parameters and conceptual model affect multi-rate model extrapolation.

Multi-rate surface complexation models have been proposed to describe the kinetics of uranyl (U(VI)) surface complexation reactions (SCR) rate-limited by diffusive mass transfer to and from intragranular sorption sites in subsurface sediments. In this study, a Bayesian-based, Differential Evolution Markov Chain method was used to assess the uncertainty and to identify factors controlling the uncertainties of the multi-rate SCR model. The rate constants in the multi-rate SCR were estimated with and without assumption of a specified lognormal distribution to test the lognormal assumption typically used to minimize the number of the rate constants in the multi-rate model. U(VI) desorption under variable chemical conditions from a contaminated sediment at US Hanford 300 Area, Washington was used as an example. The results indicated that the estimated rate constants without a specified lognormal assumption approximately followed a lognormal distribution, indicating that the lognormal is an effective assumption for the rate constants in the multi-rate SCR model. However, those rate constants with their corresponding half-lives longer than the experimental durations for model characterization had larger uncertainties and could not be reliably estimated. The uncertainty analysis revealed that the time-scale of the experiments for calibrating the multi-rate SCR model, the assumption for the rate constant distribution, the geochemical conditions involved in predicting U(VI) desorption, and equilibrium U(VI) speciation reaction constants were the major factors contributing to the extrapolation uncertainties of the multi-rate SCR model. Overall, the results from this study demonstrated that the multi-rate SCR model with a lognormal distribution of its rate constants is an effective approach for describing rate-limited U(VI) desorption; however, the model contains uncertainties, especially for those smaller rate constants, that require careful consideration for predicting U(VI) sorption and desorption.