Analytical Solutions for Reactive Transport of Multiple Volatile Contaminants in the Vadose Zone

Groundwater contamination usually originates from surface contamination. Contaminants then move downward through the vadose zone and finally reach the groundwater table. To date, however, analytical solutions of multi-species reactive transport are limited to transport only in the saturated zone. The motivation of this work is to utilize analytical solutions, which were previously derived for single-phase transport, to describe the reactive transport of multiple volatile contaminants in the unsaturated zone. A mathematical model is derived for describing transport with phase partitioning of sequentially reactive species in the vadose zone with constant flow velocity. Linear reaction kinetics and linear equilibrium partitioning between vapor, liquid, and solid phases are assumed in this model.     

Modeling reactive transport using exact solutions for first-order reaction networks

Operator splitting is often used for solving advection-dispersion-reaction (ADR) equations. Each operator can be solved separately using an algorithm appropriate to its mathematical behavior. Although a lot of research has been done in operator splitting for solving ADR equations, numerical approaches for the reaction operator are computationally expensive. To meet the convergence criteria of ODE (ordinary differential equation) or DAE (differential algebraic equation) solvers, a transport time step has to be subdivided into a large number of reaction time steps. Additional computation effort is also required to reduce the splitting error. In this paper, we develop exact solutions of various first-order reaction networks for the reaction operator and couple those solutions with numerical solutions of the transport operator. The reactions are treated as local phenomena and simulated using exact solutions that we develop, while advection and dispersion are treated as global processes and simulated numerically. The proposed method avoids the numerical error from the reaction operator and requires a single-step calculation to solve the reaction operator. Compared to conventional operator-splitting methods, the proposed method offers both computational efficiency and simulation accuracy.     

Modeling Thermal-Hydrologic Processes for a Heated Fractured Rock System: Impact of a Capillary-Pressure Maximum

Various thermal-hydrologic models have been developed to simulate thermal-hydrologic conditions in emplacement drifts and surrounding host rock for the proposed high-level nuclear waste repository at Yucca Mountain, Nevada. The modeling involves two-phase (liquid and gas) and two-component (water and air) transport in a fractured-rock system, which is conceptualized as a dual-permeability medium. Simulated hydrologic processes depend upon calibrated system parameters, such as the van Genuchten α and m, which quantify the capillary properties of the fractures and rock matrix. Typically, these parameters are not calibrated for strongly heat-driven conditions, i.e., conditions for which boiling and rock dryout occur. The objective of this study is to modify the relationship between capillary pressure and saturation, P _c(S), for strongly heated conditions that drive saturation below the residual saturation (S → 0). We offer various extensions to the van Genuchten capillary-pressure function and compare results from a thermal-hydrologic model with data collected during the Drift-Scale Test, an in situ thermal test at Yucca Mountain, to investigate the suitability of these various P _c extension methods. The study suggests that the use of extension methods and the imposition of a capillary-pressure cap (or maximum) improve the agreement between Drift-Scale Test data and model results for strongly heat-driven conditions. However, for thermal-hydrologic models of the Yucca Mountain nuclear waste repository, temperature and relative humidity are insensitive to the choice of extension method for the capillary-pressure function. Therefore, the choice of extension method applied to models of drift-scale thermal-hydrologic behavior at Yucca Mountain can be made on the basis of numerical performance.