Budhi Sagar

Testing procedures for spatially distributed flow models

Abstract Methods for testing, verifying, and validating predictive models of variably saturated groundwater flow are discussed. Specific procedures are introduced for measuring model complexity, assessing model consistency, and testing model validity. The discussion addresses numerical formulation, verification of internal consistency, benchmarking, groundtruth testing, performance measures, parameter estimation, hypothesis testing, and probabilistic induction. Verification of models includes tests of internal consistency and accuracy, like mass conservation and sensitivity to mesh size. Verification of codes also involves comparing results from the numerical model to analytical solutions, which are, however, limited in scope, and comparison with other numerical codes or ‘benchmarking’. These aspects are illustrated using available three-dimensional codes developed by the authors. Recognizing the diversity of spatially distributed modeling approaches, we also propose measures of model complexity and of the amount of information inherent in model predictions. One of these measures is the spatial degree of freedom, a function of material and boundary heterogeneities in the model. Another one is the quantity of information or entropy, which depends also on precision. Several aspects of ‘groundtruth’ model validation using data from laboratory and field tests are discussed. Logical inference is used to distinguish model validation from refutation. Recognizing that full validation is not possible in practice, we formulate performance criteria to define the ‘degree of validation’. Concepts and methods based on inductive calculus, Bayesian hypothesis testing, and maximum likelihood, are analyzed in some detail as alternative model validation strategies. Several examples of model testing are also discussed.

Importance measures for nuclear waste repositories

Abstract Several importance measures are identified for possible use in the performance assessment of a high-level nuclear waste repository. These importance measures are based on concepts of importance used in system reliability analysis, but the concepts are modified and adapted to the special characteristics of the repository and similar passive systems. In particular, the importance measures proposed here are based on risk (in comparison to traditional importance measures which are based on frequency of failure) and are intended to be more suitable to systems comprised of components whose behavior is most easily and naturally represented as continuous, rather than binary. These importance measures appear to be able to evaluate systems comprised of both continuous-behavior and binary-behavior components. Three separate examples are provided to illustrate the concepts and behavior of these importance measures. The first example demonstrates various formulations for the importance measures and their implementation for a simple radiation safety system comprised of a radiation source and three shields. The second example demonstrates use of these importance measures for a system comprised of components modeled with binary behavior and components modeled with continuous behavior. The third example investigates the use of these importance measures for a proposed repository system, using a total system model and code currently under development. Currently, these concepts and formulations of importance are undergoing further evaluation for a repository system to determine to what degree they provide useful insights and to determine which formulations are most useful.

Sensitivity and Uncertainty Analyses Applied to One-Dimensional Radionuclide Transport in a Layered Fractured Rock. Part II: Probabilistic Methods Based on the Limit-State Approach

An uncertainty and probabilistic sensitivity study of a hypothetical underground high-level waste (HLW) repository intersected by a vertical fracture or fault and under saturated conditions is presented. Several recently developed probabilistic methods, including the advanced mean value method and the adaptive importance sampling method, are applied to a previously developed one-dimensional analytical model. These probabilistic methods are based on a limit-state formulation and provide an effective means of computing performance probability distribution and probability-based random parameter sensitivities. A numerical example related to the transport of 237 Np in a system of Iayered fractured rock is used to illustrate the application of these probabilistic methods for efficient uncertainty and probabilistic sensitivity and analyses

Role of Component Sensitivity Analysis in the Risk Assessment of a Large and Complex System

This paper presents a sensitivity analysis method that provides a powerful tool for understanding the behavior of large and complex systems. This method produces easy-to-understand results that can explain the performance of a system clearly at the component level rather than parameter by parameter. A system model for the proposed disposal of high-level radioactive waste at a potential geologic repository at Yucca Mountain, Nevada is used as an example to illustrate the use of the method. The component sensitivity analysis, together with parametric sensitivity analysis, can produce a more complete picture of system behavior.

Introduction to the Special Issue of Nuclear Technology on “High-Level Radioactive Waste Management”

This special issue of Nuclear Technology is dedicated to the memory of Gudmundur “Bo” Bodvarsson, the director of the Earth Sciences Division ~ESD! at Lawrence Berkeley National Laboratory ~LBNL!. Bo passed away unexpectedly on November 29, 2006, at age 54, from a pulmonary embolism. A native of Iceland, Bo earned his PhD in hydrogeology from the University of California at Berkeley in 1981 and became internationally known for his research in geothermal reservoir simulation and optimization. Starting in the mid-1980s, Bo became increasingly involved in nuclear waste isolation research. He and his team at LBNL constructed threedimensional models of subsurface flow and transport at Yucca Mountain, Nevada, in order to interpret various field data collected at the site. As the Nuclear Waste Program Lead at LBNL, he initiated and directed various testing programs in the underground Exploratory Studies Facility at Yucca Mountain, including seepage testing at niches, heater tests, and a fracture-matrix interaction test. While holding the ESD directorship at LBNL since 2001, Bo remained deeply committed to the nation’s nuclear waste program. He was appointed to be the Natural Barrier Thrust Lead for the U.S. Department of Energy’s Science and Technology Program, Office of Civilian Radioactive Waste Management, formulating a multiuniversity and multinational lab research program. Bo is sorely missed for his scientific achievement, his dynamic leadership, his enthusiasm, and his longterm vision. His death has deeply saddened all the people who were fortunate enough to know and work with him. The papers included in this special issue were selected from those presented at the 2006 International HighLevel Radioactive Waste Management Conference ~IHLRWM! held in Las Vegas from April 30 to May 4, 2006. These papers were selected based on their archival value as representing a cross section of the state-of-theart at the time of the conference. The papers have been peer reviewed and revised following the usual practice of this journal. For interested readers, the entire set of the original papers presented at the 2006 IHLRWM is available from the American Nuclear Society. The safe management of high-level radioactive waste has matured significantly over the last decade. A few countries, notably the United States and Sweden, are close to developing license applications for building deep underground repositories for high-level radioactive waste, while other countries are at various stages of development varying from conceptual formulations, site selection, and detailed site investigation to sophisticated risk assessment. This variability was reflected in the breadth of the papers in the conference. Also represented at this conference was the broad multidisciplinary nature of the endeavor. In our selection of the papers for this special issue, we have tried to capture this multidisciplinary nature of the subject. All of the papers except one are related to postclosure performance of the repository. These include

Sensitivity and uncertainty analyses applied to one-dimensional radionuclide transport in a layered fractured rock: MULTFRAC --Analytic solutions and local sensitivities; Phase 2, Iterative performance assessment: Volume 1

Exact analytical solutions based on the Laplace transforms are derived for describing the one-dimensional space-time-dependent, advective transport of a decaying species in a layered, saturated rock system intersected by a planar fracture of varying aperture. These solutions, which account for advection in fracture, molecular diffusion into the rock matrix, adsorption in both fracture and matrix, and radioactive decay, predict the concentrations in both fracture and rock matrix and the cumulative mass in the fracture. The solute migration domain in both fracture and rock is assumed to be semi-infinite with non-zero initial conditions. The concentration of each nuclide at the source is allowed to decay either continuously or according to some periodical fluctuations where both are subjected to either a step or band release mode. Two numerical examples related to the transport of Np-237 and Cm-245 in a five-layered system of fractured rock were used to verify these solutions with several well established evaluation methods of Laplace inversion integrals in the real and complex domain. In addition, with respect to the model parameters, a comparison of the analytically derived local sensitivities for the concentration and cumulative mass of Np-237 in the fracture with the ones obtained through a finite-difference method of approximation is also reported.

Effects of Some Common Geological Features on Two-Dimensional Variably Saturated Flow

This paper presents results of unsaturated flow simulations undertaken as an auxiliary analysis for the Iterative Performance Assessment (IPA) project, one of the approaches adopted by the U.S. NRC to develop repository license application review capabilities. The effects on flow of common geological features, such as nonhorizontal stratification and vertical or near-vertical fault zones intersecting the strata, in a two-dimensional (2D) domain are studied. Results indicate that the presence of layers and crosscutting fault zones tend to induce three-dimensional (3D) unstable flows in the unsaturated zone. The instability is manifested in our simulations by an oscillatory behavior of steady state. This numerical instability imposes extremely stringent criteria on the time step used in the simulation. Finally, once stable steady-state solutions are attained, the effect of the crossing point in the matrix-fault unsaturated hydraulic conductivity curve on groundwater flux vectors and moisture content distributions is studied.