A residence-time-based transport approach for the groundwater pathway in performance assessment models

This paper presents the theoretical development and numerical implementation of a new modeling approach for representing the groundwater pathway in risk assessment or performance assessment model of a contaminant transport system. The model developed in the present study, called the Residence Time Distribution (RTD) Mixing Model (RTDMM), allows for an arbitrary distribution of fluid travel times to be represented, to capture the effects on the breakthrough curve of flow processes such as channelized flow and fast pathways and complex three-dimensional dispersion. Mathematical methods for constructing the model for a given RTD are derived directly from the theory of residence time distributions in flowing systems. A simple mixing model is presented, along with the basic equations required to enable an arbitrary RTD to be reproduced using the model. The practical advantages of the RTDMM include easy incorporation into a multi-realization probabilistic simulation; computational burden no more onerous than a one-dimensional model with the same number of grid cells; and straightforward implementation into available flow and transport modeling codes, enabling one to then utilize advanced transport features of that code. For example, in this study we incorporated diffusion into the stagnant fluid in the rock matrix away from the flowing fractures, using a generalized dual porosity model formulation. A suite of example calculations presented herein showed the utility of the RTDMM for the case of a radioactive decay chain, dual porosity transport and sorption.