Column experimental design requirements for estimating model parameters from temporal moments under nonequilibrium conditions

Abstract

Data truncation is a practical necessity of laboratory column experiments because of both time and detection-limit constraints. In this paper, we study the extent to which data truncation can affect estimates of transport modeling parameters, as derived from temporal moment calculations and in the context of solute transport experiments that are influenced by sorption and nonequilibrium partitioning among mobile and immobile phases. Our results show that, for a given amount of solute used, step changes in input conditions can give more accurate moment-derived parameters than Dirac or square-wave pulses, whereas Dirac and square-wave pulses are essentially identical in terms of accuracy of parameter estimates. By simulating data truncation for a wide range of column input and transport conditions, we provide guidance toward the experimental designs that are needed to keep parameter estimation error within specified bounds, assuming nonequilibrium conditions of transport that result from either first-order or diffusion-based rate processes. More specifically, we investigate the relationships between mass of solute added to the system, minimum solute quantification limits, experiment duration times, and accuracy of parameter estimation, all as a function of experimental conditions.