Improving parameter estimation for column experiments by multi-model evaluation and comparison

The equilibrium convection dispersion equation model is often unable to accurately simulate breakthrough curves from column experiments. While the non-equilibrium convection dispersion equation model may match the data well, uncertainty in parameter estimates is often large. In this work we investigate approaches to improve match for the equilibrium model and reduce parameter estimate uncertainty for the non-equilibrium model. Four column experiment data sets are selected from the literature for the illustration. For the equilibrium convection dispersion equation model, we show that measurement error, presence of immobile water, and other mechanisms can cause mismatch between model predictions and observations because the model is sensitive to water content. The mismatch may be overcome by calibrating the effective water content. For the non-equilibrium convection dispersion equation model, simultaneous fitting of multiple tracers with reduced number of calibration parameters (e.g., assuming the dispersivity and mobile water fraction to be identical for different tracers, the mass transfer coefficient to be proportional to tracer molecular diffusion coefficient) can reduce the uncertainty in parameter estimate and better identify/quantify the non-equilibrium processes. By evaluating and comparing the multiple estimates obtained with different choices of calibration parameters (e.g., fixing or estimating water content), parameterizations and models (e.g., equilibrium or non-equilibrium), the reliability of the data interpretation can be improved by quantifying uncertainty in the experiment, considering alternative transport processes, and following the principle of parsimony.