Modeling ground water flow and radioactive transport in a fractured aquifer

A semi-discrete finite element method for a class of time-fractional diffusion equations

As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly used in the related mathematical descriptions. These models usually involve long-time-range computation, which is a critical obstacle for their application; improvement of computational efficiency is of great significance. In this paper, a semi-discrete method is presented for solving a class of time-fractional diffusion equations that overcome the critical long-time-range computation problem. In the procedure, the spatial domain is discretized by the finite element method, which reduces the fractional diffusion equations to approximate fractional relaxation equations. As analytical solutions exist for the latter equations, the burden arising from long-time-range computation can effectively be minimized. To illustrate its efficiency and simplicity, four examples are presented. In addition, the method is used to solve the time-fractional advection-diffusion equation characterizing the bromide transport process in a fractured granite aquifer. The prediction closely agrees with the experimental data, and the heavy-tail decay of the anomalous transport process is well represented.

Sensitivity of solute advective travel time to porosities of hydrogeologic units

An integral approach is proposed to quantify uncertainty and sensitivity of advective travel time to the effective porosities of hydrogeologic units (HGUs) along groundwater flow paths. The approach is applicable in situations where a groundwater flow model exists, but a full solute transport model is not available. The approach can be used to: (1) determine HGUs whose porosities are influential to the solute advective travel time; and (2) apportion uncertainties of solute advective travel times to the uncertainty contributions from individual HGU porosities. A simple one-dimensional steady-state flow example is used to illustrate the approach. Advective travel times of solutes are obtained based on the one-dimensional steady-state flow results in conjunction with the HGU porosities. The approach can be easily applicable to more complex multi-dimensional cases where advective solute travel time can be calculated based on simulated flow results from groundwater flow models. This approach is particularly valuable for optimizing limited resources when designing field characterization programs for uncertainty reduction by identifying HGUs that contribute most to the estimation uncertainty of advective travel times of solutes.

Developing a long-term monitoring network under uncertain flowpaths

A long-term monitoring well network is developed using complementary and simple approaches in conjunction with a stochastic ground water flow and transport model. The development is illustrated for a case study of a U.S. nuclear testing site (Shoal) that is undergoing environmental restoration. The network design builds on three different, yet complementary, tools for locating the monitoring wells with a main objective of detection monitoring. The first tool is applied to select potential siting horizons where monitoring wells could be located. The second tool is used to place monitoring wells in locations with high success probability. The success here is defined as the detection of migrating stochastic plumes before a certain mass percentage reaches a compliance boundary. The third tool is used to analyze detection efficiency of multiple combinations of three wells. Seventy-six different three-well networks are selected from 20 candidate locations and are evaluated for detection efficiency. From the 76 networks analyzed, 28 attain detection efficiency close to or above 70%. The results of the different analyses provide multiple alternatives for the locations of the three wells, which will become part of the long-term monitoring network at Shoal. A number of combinations are equally good, and the final choice will depend on practical considerations and future agreements between model sponsor and regulators.

A methodology for validating numerical ground water models

Ground water validation is one of the most challenging issues facing modelers and hydrogeologists. Increased complexity in ground water models has created a gap between model predictions and the ability to validate or build confidence in predictions. Specific procedures and tests that can be easily adapted and applied to determine the validity of site-specific ground water models do not exist. This is true for both deterministic and stochastic models, with stochastic models posing the more difficult validation problem. The objective of this paper is to propose a general validation approach that addresses important issues recognized in previous validation studies, conferences, and symposia. The proposed method links the processes for building, calibrating, evaluating, and validating models in an iterative loop. The approach focuses on using collected validation data to reduce uncertainty in the model and narrow the range of possible outcomes. This method is designed for stochastic numerical models utilizing Monte Carlo simulation approaches, but it can be easily adapted for deterministic models. The proposed methodology relies on the premise that absolute validity is not theoretically possible, nor is it a regulatory requirement. Rather, the proposed methodology highlights the importance of testing various aspects of the model and using diverse statistical tools for rigorous checking and confidence building in the model and its predictions. It is this confidence that will encourage regulators and the public to accept decisions based on the model predictions. This validation approach will be applied to a model, described in this paper, dealing with an underground nuclear test site in rural Nevada.