Characterization of stochastic uncertainty in the 1996 performance assessment for the Waste Isolation Pilot Plant

The 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) maintains a separation between stochastic (i.e. aleatory) and subjective (i.e. epistemic) uncertainty, with stochastic uncertainty arising from the possible disruptions that could occur at the WIPP over the 10,000-yr regulatory period specified by the US Environmental Protection Agency (40 CFR 191, 40 CFR 194) and subjective uncertainty arising from an inability to uniquely characterize many of the inputs required in the 1996 WIPP PA. The characterization of stochastic uncertainty is discussed, including drilling intrusion time, drilling location, penetration of excavated/nonexcavated areas of the repository, penetration of pressurized brine beneath the repository, borehole plugging patterns, activity level of waste, and occurrence of potash mining. Additional topics discussed include sampling procedures, generation of individual 10,000-yr futures for the WIPP, construction of complementary cumulative distribution functions (CCDFs), mechanistic calculations carried out to support CCDF construction, the Kaplan/Garrick ordered triple representation for risk, and determination of scenarios and scenario probabilities.     

Regulatory basis for the Waste Isolation Pilot Plant performance assessment

The Waste Isolation Pilot Plant (WIPP) is the first operational repository designed for the safe disposal of transuranic (TRU) radioactive waste from the defense programs of the US Department of Energy (DOE). The US Environmental Protection Agency (EPA) is responsible for certifications and regulation of the WIPP facility for the radioactive components of the waste. The EPA has promulgated general radioactive waste disposal standards at 40 CFR Part 191, and WIPP-specific criteria to implement and interpret the generic disposal standards at 40 CFR Part 194. In October 1996, the DOE submitted its Compliance Certification Application (CCA) to the EPA to demonstrate compliance with the disposal standards at Subparts B and C of 40 CFR Part 191. This paper summarizes the development of the overall legal framework for radioactive waste disposal at the WIPP, the parallel development of the WIPP performance assessment (PA), and how the EPA disposal standards and implementing criteria formed the basis for the CCA WIPP PA. The CCA resulted in a certification in May 1998 by the EPA of the WIPP's compliance with the EPA's disposal standard, thus enabling the WIPP to begin radioactive waste disposal.     

Characterization of subjective uncertainty in the 1996 performance assessment for the Waste Isolation Pilot Plant

The 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) maintains a separation between stochastic (i.e. aleatory) and subjective (i.e. epistemic) uncertainty, with stochastic uncertainty arising from the possible disruptions that could occur at the WIPP over the 10,000 yr regulatory period specified by the US Environmental Protection Agency (40 CFR 191, 40 CFR 194) and subjective uncertainty arising from an inability to uniquely characterize many of the inputs required in the 1996 WIPP PA. The characterization of subjective uncertainty is discussed, including assignment of distributions, uncertain variables selected for inclusion in analysis, correlation control, sample size, statistical confidence on mean complementary cumulative distribution functions, generation of Latin hypercube samples, sensitivity analysis techniques, and scenarios involving stochastic and subjective uncertainty.     

Conceptual basis for the definition and calculation of expected dose in performance assessments for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada

A deep geologic repository for high-level radioactive waste is under development by the US Department of Energy (DOE) at Yucca Mountain (YM), Nevada. As mandated in the Energy Policy Act of 1992, the US Environmental Protection Agency has promulgated public health and safety standards (i.e., 40 CFR Part 197) for the YM repository, and the US Nuclear Regulatory Commission has promulgated licensing standards (i.e., 10 CFR Parts 2, 19, 20, etc.) consistent with 40 CFR Part 197 that the DOE must establish are met in order for the YM repository to be licensed for operation. Important requirements in 40 CFR Part 197 and 10 CFR Parts 2, 19, 20, etc. relate to the determination of expected (i.e., mean) dose to a reasonably maximally exposed individual (RMEI) and the incorporation of uncertainty into this determination. This paper is the first part of a two-part presentation and describes how general and typically nonquantitative statements in 40 CFR Part 197 and 10 CFR Parts 2, 19, 20, etc. can be given a formal mathematical structure that facilitates both the calculation of expected dose to the RMEI and the appropriate separation in this calculation of aleatory uncertainty (i.e., randomness in the properties of future occurrences such as igneous and seismic events) and epistemic uncertainty (i.e., lack of knowledge about quantities that are imprecisely known but assumed to have constant values in the calculation of expected dose to the RMEI). The second part of this presentation is contained in the following paper, “Computational Implementation of Sampling-Based Approaches to the Calculation of Expected Dose in Performance Assessments for the Proposed High-Level Radioactive Waste Repository at Yucca Mountain, Nevada,” and both describes and illustrates sampling-based procedures for the estimation of expected dose and the determination of the uncertainty in estimates for expected dose.     

Computational implementation of sampling-based approaches to the calculation of expected dose in performance assessments for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada

A deep geologic repository for high-level radioactive waste is under development by the US Department of Energy (DOE) at Yucca Mountain (YM), Nevada. As mandated in the Energy Policy Act of 1992, the US Environmental Protection has promulgated public health and safety standards (i.e., 40 CFR Part 197) for the YM repository, and the US Nuclear Regulatory Commission has promulgated licensing standards (i.e., 10 CFR Parts 2, 19, 20, etc.) consistent with 40 CFR Part 197 that the DOE must establish are met in order for the YM repository to be licensed for operation. Important requirements in 40 CFR Part 197 and 10 CFR Parts 2, 19, 20, etc. relate to the determination of expected (i.e., mean) dose to a reasonably maximally exposed individual (RMEI) and the incorporation of uncertainty into this determination. This paper is the second part of a two-part presentation on the determination of expected dose to the RMEI in the context of 40 CFR Part 197 and 10 CFR Parts 2, 19, 20, etc. The first part of this presentation is contained in the preceding paper, “Conceptual Basis for the Definition and Calculation of Expected Dose in Performance Assessments for the Proposed High-Level Radioactive Waste Repository at Yucca Mountain, Nevada”, and describes how general and typically nonquantitative statements in 40 CFR Part 197 and 10 CFR Parts 2, 19, 20, etc. can be given a formal mathematical structure that facilitates both the calculation of expected dose to the RMEI and the appropriate separation in this calculation of aleatory uncertainty (i.e., randomness in the properties of future occurrences such as igneous and seismic events) and epistemic uncertainty (i.e., lack of knowledge about quantities that are poorly known but assumed to have constant values in the calculation of expected dose to the RMEI). The present paper describes and illustrates sampling-based procedures for the estimation of expected dose and the determination of the uncertainty in estimates for expected dose.     

Radioactive and nonradioactive waste intended for disposal at the Waste Isolation Pilot Plant

Transuranic (TRU) waste generated by the handling of plutonium during research on or production of U.S. nuclear weapons will be disposed of in the Waste Isolation Pilot Plant (WIPP). This paper describes the physical and radiological properties of the TRU waste that will be deposited in the WIPP. This geologic repository will accommodate up to 175,564 m³ of TRU waste, corresponding to 168,485 m³ of contact-handled (CH-) TRU waste and 7079 m³ of remote-handled (RH-) TRU waste. Approximately 35% of the TRU waste is currently packaged and stored (i.e. legacy) waste, with the remainder of the waste to be packaged or generated and packaged in activities before the year 2033, which is the closure time for the repository. These wastes were produced at 27 U.S. Department of Energy (DOE) sites in the course of generating defense nuclear materials. The radionuclide and nonradionuclide inventories for the TRU wastes described in this paper were used in the 1996 WIPP Compliance Certification Application (CCA) performance assessment calculations by the Sandia National Laboratories/New Mexico (SNL/NM).     

Construction of complementary cumulative distribution functions for comparison with the EPA release limits for radioactive waste disposal

The US Environmental Protection Agency (EPA) has promulgated a standard for the geologic disposal of radioactive waste (40 CFR 191) that requires the construction of a complementary cumulative distribution function (CCDF) that defines the probability of exceeding radionuclide releases of various sizes. Construction of this CCDF involves three interrelated activities: development of scenarios that describe the various disruptions that could occur at a waste disposal site, determination of probabilities for scenarios, and calculation of radionuclide releases for scenarios. The computational procedures being used in the performance assesement for the Waste Isolation Pilot Plant (WIPP) in southeastern New Mexico to bring these three activities together to produce the CCDF in 40 CFR 191 are described and illustrated with results obtained in a recent analysis.     

Assignment of probability distributions for parameters in the 1996 performance assessment for the Waste Isolation Pilot Plant. Part 1: description of process

A managed process was used to consistently and traceably develop probability distributions for parameters representing epistemic uncertainty in four preliminary and the final 1996 performance assessment (PA) for the Waste Isolation Pilot Plant. Between 67 probability density functions (PDFs) in the 1989 PA and 236 PDFs in the 1996 PA were assigned by a parameter development team, using a process described in a companion paper. In the five iterative PAs conducted, the most commonly used distributions were the uniform PDF and piecewise-uniform PDF (also referred to as a piecewise-linear cumulative distribution function (CDF)). Other distributions used included the truncated normal, truncated Student-t, and triangular PDFs. In a few instances, a discrete delta (piecewise-uniform CDF), beta, and exponential PDF were also used. The PDFs produced for the 24 most important parameters observed in the five iterative PAs are presented. As background, the list of 194 parameters documented in the first 1989 PA through the 1471 parameters documented in the 1996 compliance PA are also provided.     

Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems

The following techniques for uncertainty and sensitivity analysis are briefly summarized: Monte Carlo analysis, differential analysis, response surface methodology, Fourier amplitude sensitivity test, Sobol' variance decomposition, and fast probability integration. Desirable features of Monte Carlo analysis in conjunction with Latin hypercube sampling are described in discussions of the following topics: (i) properties of random, stratified and Latin hypercube sampling, (ii) comparisons of random and Latin hypercube sampling, (iii) operations involving Latin hypercube sampling (i.e. correlation control, reweighting of samples to incorporate changed distributions, replicated sampling to test reproducibility of results), (iv) uncertainty analysis (i.e. cumulative distribution functions, complementary cumulative distribution functions, box plots), (v) sensitivity analysis (i.e. scatterplots, regression analysis, correlation analysis, rank transformations, searches for nonrandom patterns), and (vi) analyses involving stochastic (i.e. aleatory) and subjective (i.e. epistemic) uncertainty.     

Quantification of margins and uncertainties: Example analyses from reactor safety and radioactive waste disposal involving the separation of aleatory and epistemic uncertainty

In 2001, the National Nuclear Security Administration (NNSA) of the U.S. Department of Energy (DOE) in conjunction with the national security laboratories (i.e., Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and Sandia National Laboratories) initiated development of a process designated quantification of margins and uncertainties (QMU) for the use of risk assessment methodologies in the certification of the reliability and safety of the nation's nuclear weapons stockpile. A previous presentation, “Quantification of Margins and Uncertainties: Conceptual and Computational Basis,” describes the basic ideas that underlie QMU and illustrates these ideas with two notional examples. The basic ideas and challenges that underlie NNSA's mandate for QMU are present, and have been successfully addressed, in a number of past analyses for complex systems. To provide perspective on the implementation of a requirement for QMU in the analysis of a complex system, three past analyses are presented as examples: (i) the probabilistic risk assessment carried out for the Surry Nuclear Power Station as part of the U.S. Nuclear Regulatory Commission's (NRC's) reassessment of the risk from commercial nuclear power in the United States (i.e., the NUREG-1150 study), (ii) the performance assessment for the Waste Isolation Pilot Plant carried out by the DOE in support of a successful compliance certification application to the U.S. Environmental Agency, and (iii) the performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada, carried out by the DOE in support of a license application to the NRC. Each of the preceding analyses involved a detailed treatment of uncertainty and produced results used to establish compliance with specific numerical requirements on the performance of the system under study. As a result, these studies illustrate the determination of both margins and the uncertainty in margins in real analyses.     

Drilling intrusion probabilities for use in performance assessment for radioactive waste disposal

Product integral techniques are used to derive computational procedures to determine probabilities for scenarios resulting from drilling intrusions at geologic disposal facilities for radioactive waste. For these derivations, the occurence of individual drilling intrusions is assumed to be random in time and space, although the drilling rate is not assumed to be constant or even continuous through time. The use of product integral techniques allows the probability model for drilling intrusions to be initially cast in a very general form involving interval functions and then specialized to nonhomogeneous Poisson processes and ultimately to homogeneous Poisson processes. The resultant computational procedures are illustrated with results for the Waste Isolation Pilot Plant (WIPP) in southeastern New Mexico using the maximum drilling rate specified by the US Environmental Protection Agency (EPA) in its standard for the geologic disposal of radioactive waste (40 CFR 191).     

Quantification of margins and uncertainties: Conceptual and computational basis

In 2001, the National Nuclear Security Administration of the U.S. Department of Energy in conjunction with the national security laboratories (i.e., Los Alamos National Laboratory, Lawrence Livermore National Laboratory and Sandia National Laboratories) initiated development of a process designated Quantification of Margins and Uncertainties (QMU) for the use of risk assessment methodologies in the certification of the reliability and safety of the nation's nuclear weapons stockpile. This presentation discusses and illustrates the conceptual and computational basis of QMU in analyses that use computational models to predict the behavior of complex systems. The following topics are considered: (i) the role of aleatory and epistemic uncertainty in QMU, (ii) the representation of uncertainty with probability, (iii) the probabilistic representation of uncertainty in QMU analyses involving only epistemic uncertainty, and (iv) the probabilistic representation of uncertainty in QMU analyses involving aleatory and epistemic uncertainty.     

The geologic and hydrogeologic setting of the Waste Isolation Pilot Plant

The Waste Isolation Pilot Plant (WIPP) is a mined repository for the permanent disposal of transuranic wastes. It has been constructed by the United States Department of Energy (DOE) in semiarid, sparsely inhabited rangeland in southeastern New Mexico. The disposal area is 655 m below the land surface, in bedded salt of the Late Permian (approximately 255 million-years-old) Salado Formation. The extremely low permeability of the halite and other evaporite rocks provide the primary geologic barrier assuring long-term (10,000-year-plus) isolation of the radioactive waste from the accessible environment. Extensive geologic investigations during site characterization have provided information on the stratigraphy, structure, and natural resources of the region (including hydrocarbons, potash, and groundwater), and have investigated the potential for disruption by processes such as dissolution, salt deformation, tectonic activity, and climate change. Hydrogeologic investigations have documented the physical properties of the evaporite rocks, and have identified the Culebra Dolomite Member of the overlying Rustler Formation as the most transmissive water-bearing unit in the region. If the evaporite barriers are breached by accidental drilling intrusion, the Culebra would provide the most likely pathway for radionuclide transport away from the site. Although water in the Culebra is of poor quality and none is currently used for human consumption, groundwater flow and potential radionuclide transport in the unit have been studied in detail. Results of geologic and hydrogeologic studies of the WIPP region indicate that the geologic and hydrogeologic features of the site will provide effective long-term containment of radionuclides. Geologic and hydrogeologic information is used in the performance assessment that supported the DOE’s compliance certification application to the United States Environmental Protection Agency.     

Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty

Three applications of sampling-based sensitivity analysis in conjunction with evidence theory representations for epistemic uncertainty in model inputs are described: (i) an initial exploratory analysis to assess model behavior and provide insights for additional analysis; (ii) a stepwise analysis showing the incremental effects of uncertain variables on complementary cumulative belief functions and complementary cumulative plausibility functions; and (iii) a summary analysis showing a spectrum of variance-based sensitivity analysis results that derive from probability spaces that are consistent with the evidence space under consideration.