Comparative analysis of formulations for conservative transport in porous media through sensitivity-based parameter calibration

We apply a general strategy based on Global Sensitivity Analysis (GSA) and model discrimination criteria to (a) calibrate the parameters embedded in competing models employed to interpret laboratory-scale tracer experiments, (b) rank these models, and (c) estimate the relative degree of likelihood of each model through a posterior probability weight. We consider a conservative transport experiment in a uniform porous medium [Gramling et al., 2002]. We apply GSA to three transport models, based on: the classical advection-dispersion equation (ADE), a dual-porosity (DP) formulation with mass transfer between mobile and immobile regions, and the Continuous Time Random Walk (CTRW) approach. GSA is performed through Polynomial Chaos Expansion of the governing equations, treating key model parameters as independent random variables. We show how this approach allows identification of (a) the relative importance of model-dependent parameters, and (b) the space-time locations where the models are most sensitive to these parameters. GSA is then employed to assist parameter estimates within a Maximum Likelihood framework. Finally, formal model identification criteria are employed to (a) rank the alternative models, and (b) associate each model with a posterior probability weight for the specific case study. The GSA-based calibration of each model returns an acceptable approximation (remarkably accurate in the case of the CTRW model) of all available concentration data, with calibration being performed using minimum sets of observations corresponding to the most sensitive (space-time) locations.