Interpretation of Transport Experiments in Porous Media: Evaluation of Different Formulations via Sensitivity-Based Parameter Calibration

We illustrate a general strategy to (a) calibrate the parameters embedded in competing mathematical models employed to interpret laboratory scale tracer experiments in porous media, (b) rank these alternative models, and (c) estimate the relative degree of likelihood of each model through a posterior probability weight. As an example of application, we consider the interpretation of the conservative and reactive transport experiments of Gramling et al. [2002]. For the interpretation of the conservative experiment three competitive one-dimensional models, i.e., (i) the advection-dispersion equation, (ii) a double porosity formulation, and (iii) the Continuous Time Random Walk are selected. The reactive transport experiment is analyzed by comparing (i) a formulation of the advection-dispersion reaction equation, and (ii) the Continuous Time Random Walk. The methodological framework is based on the joint use of global sensitivity analysis and model discrimination criteria and is fully consistent with Maximum Likelihood methods which are typically employed for groundwater flow and transport model calibration. Global sensitivity analysis is performed via the Polynomial Chaos Expansion approach, providing a minimum set of observations corresponding to the most sensitive (space-time) locations for each of a suite of selected transport formulations. This is accomplished by considering model calibration parameters as sources of uncertainty and treating them as independent random variables. Quantification of the most sensitive locations has strong implications for experiment design, while global sensitivity analysis allows identification of the relative importance of the parameters involved in model calibration practice. Model quality criteria are then employed to assess the capability of each model to approximate its most sensitive observations. Validation against the entire available dataset allows testing of the predictive performance of each selected model. Contrasting results between the model discrimination and validation steps might imply that the most sensitive observations of a selected model are not exhaustive for the interpretation of the overall physical processes involved. As a consequence, the intrinsic interpretive capability of the model may not be adequate for the specific case study. This is manifest, e.g., in the interpretation of the conservative experiment for which the best predictive power is always associated with the Continuous Time Random Walk, also in cases where the posterior probability weight associated with the other selected models is dominant.