Sensitivity of advective travel time of contaminants to correlated formation porosities

An approach is presented to quantify sensitivity of advective contaminant travel time to porosities of hydrogeologic units (HGUs) along the flowpaths when the porosities of different HGUs are correlated. The approach is an extension of the previous sensitivity analysis technique for independent input porosity cases. It is applicable in situations where a calibrated groundwater flow model exists, but a full contaminant transport model is not available. Three sensitivity indices are introduced based on the decomposition of covariance between the advective contaminant travel time and individual input porosities of HGUs. When the input HGU porosities are correlated, the three sensitivity indices quantify the total, intrinsic and correlated contributions from each individual HGU porosity, which should be considered in order to determine the relative importance to the uncertainty in advective contaminant travel time of the input HGU porosities contributing either independently or correlatedly. Two simple one-dimensional flow examples are presented to illustrate the applications of the approach to scenarios when each HGU has distinct porosity and situations of spatially variable porosity field. The approach is applicable to more complex multi-dimensional cases where advective contaminant travel time can be calculated based on simulated flow results from groundwater flow models.