Melvin G. Marietta

Pilot Point Methodology for Automated Calibration of an Ensemble of conditionally Simulated Transmissivity Fields: 1. Theory and Computational Experiments

A new methodology for solution of the inverse problem in groundwater hydrology is proposed and applied to a site in southeastern New Mexico with extensive hydrogeologic data. The methodology addresses the issue of nonuniqueness of the inverse solutions by generating an ensemble of transmissivity fields considered to be equally likely, each of which is in agreement with the measured transmissivity and pressure data. It consists of generating a selected number of conditionally simulated transmissivity fields and then calibrating each of the fields to match the measured steady state or transient pressures, in a least squares sense. The calibration phase involves an iterative implementation of an automated pilot point approach coupled with conditional simulations. Pilot points are the parameters of calibration. They are synthetic transmissivity data which are added to the transmissivity database to produce a revised conditional simulation during calibration. Coupled kriging and adjoint sensitivity analysis is employed for the optimal location of pilot points, and gradient search methods are used to derive their optimal transmissivities. The pilot point methodology is well suited for characterizing the spatial variability of the transmissivity field in contrast to methods using zonation. Pilot points are located where their potential for minimizing the objective function is the highest. This minimizes the perturbations in the transmissivities which are optimally assigned to the pilot point and results in minimal changes to the covariance structure of the transmissivity field. The calibrated fields honor the transmissivity measurements at their locations, preserve the variogram, and match the measured pressures in a least squares sense. Since there are numerous options in the execution of this methodology, computational experiments have been conducted to identify the most efficient among them. The method has been applied to the Waste Isolation Pilot Plant (WIPP) site, in southeastern New Mexico, where the U.S. Department of Energy is conducting probabilistic system assessment for the permanent disposal of transuranic nuclear waste. The resulting calibrated transmissivity fields are input to a Monte Carlo analysis of the total system performance. The present paper, paper 1 of a two-paper presentation, describes the methodology. Paper 2, a companion paper, presents the methodologys application to the WIPP site.

A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow

This paper describes the first major attempt to compare seven different inverse approaches for identifying aquifer transmissivity. The ultimate objective was to determine which of several geostatistical inverse techniques is better suited for making probabilistic forecasts of the potential transport of solutes in an aquifer where spatial variability and uncertainty in hydrogeologic properties are significant. Seven geostatistical methods (fast Fourier transform (FF), fractal simulation (FS), linearized cokriging (LC), linearized semianalytical )LS), maximum likelihood (ML), pilot point (PP), and sequential self-calibration (SS)) were compared on four synthetic data sets. Each data set had specific features meeting (or not) classical assumptions about stationarity, amenability to a geostatistical description, etc. The comparison of the outcome of the methods is based on the prediction of travel times and travel paths taken by conservative solutes migrating in the aquifer for a distance of 5 km. Four of the methods, LS, ML, PP, and SS, were identified as being approximately equivalent for the specific problems considered. The magnitude of the variance of the transmissivity fields, which went as high as 10 times the generally accepted range for linearized approaches, was not a problem for the linearized methods when applied to stationary fields; that is, their inverse solutions and travel time predictions were as accurate as those of the nonlinear methods. Nonstationarity of the “true” transmissivity field, or the presence of “anomalies” such as high-permeability fracture zones was, however, more of a problem for the linearized methods. The importance of the proper selection of the semivariogram of the log10 (T) field (or the ability of the method to optimize this variogram iteratively) was found to have a significant impact on the accuracy and precision of the travel time predictions. Use of additional transient information from pumping tests did not result in major changes in the outcome. While the methods differ in their underlying theory, and the codes developed to implement the theories were limited to varying degrees, the most important factor for achieving a successful solution was the time and experience devoted by the user of the method.

Uncertainty and sensitivity analysis results obtained in the 1992 performance assessment for the waste isolation pilot plant

Uncertainty and sensitivity analysis results obtained in the 1992 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) are presented. The primary performance measure under study is the complementary cumulative distribution function (CCDF) used in assessing compliance with the U.S. Environmental Protection Agencys (EPAs) standard for the geologic disposal of radioactive waste (40 CFR 191, Subpart B). The analysis considers releases to the accessible environment initiated by exploratory drilling for natural resources and models cuttings removal to the surface due to drilling intrusions, brine and gas flow in the vicinity of the repository and through drilling intrusions away from the repository, radionuclide transport by the flow of brine through intruding boreholes, and brine flow and radionuclide transport in permeable formations overlying the repository (i.e., the Culebra Dolomite). The effects of 49 imprecisely known variables are assessed with techniques based on Latin hypercube sampling and regression analysis. In addition, the effects of several alternative conceptual models for radionuclide transport in the Culebra Dolomite are investigated. Important issues identified in the analysis include (1) the importance of characterizing retardations and solubilities for individual elements, (2) the impact of assumptions involving human activities, including the rate and properties of drilling intrusions, and (3) the need to resolve the question of whether a single-porosity or dual-porosity transport model is appropriate for use in the Culebra Dolomite.

Conceptual structure of the 1996 performance assessment for the Waste Isolation Pilot Plant

The conceptual structure of the 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) is described. This structure involves three basic entities (EN1, EN2, EN3): (1) EN1, a probabilistic characterization of the likelihood of different futures occurring at the WIPP site over the next 10,000 yr, (2) EN2, a procedure for estimating the radionuclide releases to the accessible environment associated with each of the possible futures that could occur at the WIPP site over the next 10,000 yr, and (3) EN3, a probabilistic characterization of the uncertainty in the parameters used in the definition of EN1 and EN2. In the formal development of the 1996 WIPP PA, EN1 is characterized by a probability space (S{sub st}, P{sub st}, p{sub st}) for stochastic (i.e., aleatory) uncertainly; EN2 is characterized by a function {line_integral} that corresponds to the models and associated computer programs used to estimate radionuclide releases; and EN3 is characterized by a probability space (S{sub su}, P{sub su}, p{sub su}) for subjective (i.e., epistemic) uncertainty. A high-level overview of the 1996 WIPP PA and references to additional sources of information are given in the context of (S{sub st}, P{sub st}, p{sub st}), {line_integral} and (S{sub su}, P{sub su}, p{sub su}).

The 1996 performance assessment for the Waste Isolation Pilot Plant

The Waste Isolation Pilot Plant (WIPP) is under development by the US Department of Energy (DOE) for the geologic disposal of transuranic (TRU) waste that has been generated at government defense installations in the United States. The WIPP is located in an area of low population density in southeastern New Mexico. Waste disposal will take place in excavated chambers in a bedded salt formation approximately 655 m below the land surface. This presentation describes a performance assessment (PA) carried out at Sandia National Laboratories (SNL) to support the Compliance Certification Application (CCA) made by the DOE to the US Environmental Protection Agency (EPA) in October, 1996, for the certification of the WIPP for the disposal of TRU waste. Based on the CCA supported by the PA described in this presentation, the EPA has issued a preliminary decision to certify the WIPP for the disposal of TRU waste. At present (April 1998), it appears likely that the WIPP will be in operation by the end of 1998.

Performance Assessment in Support of the 1996 Compliance Certification Application for the Waste Isolation Pilot Plant

The conceptual and computational structure of a performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) is described. Important parts of this structure are (1) maintenance of a separation between stochastic (i.e., aleatory) and subjective (i.e., epistemic) uncertainty, with stochastic uncertainty arising from the many possible disruptions that could occur over the 10,000-year regulatory period that applies to the WIPP, and subjective uncertainty arising from the imprecision with which many of the quantities required in the analysis are known, (2) use of Latin hypercube sampling to incorporate the effects of subjective uncertainty, (3) use of Monte Carlo (i.e., random) sampling to incorporate the effects of stochastic uncertainty, and (4) efficient use of the necessarily limited number of mechanistic calculations that can be performed to support the analysis. The WIPP is under development by the U.S. Department of Energy (DOE) for the geologic (i.e., deep underground) disposal of transuranic (TRU) waste, with the indicated PA supporting a Compliance Certification Application (CCA) by the DOE to the U.S. Environmental Protection Agency (EPA) in October 1996 for the necessary certifications for the WIPP to begin operation. The EPA certified the WIPP for the disposal of TRU waste in May 1998, with the result that the WIPP will be the first operational facility in the United States for the geologic disposal of radioactive waste.

Performance Assessment for the Waste Isolation Pilot Plant: From Regulation to Calculation for 40 CFR 191.13

The Waste Isolation Pilot Plant WIPP is being developed by the U.S. Department of Energy as a disposal facility for transuranic waste and must comply with several environmental regulations, including the U.S. Environmental Protection Agencys standard for geologic disposal of radioactive waste 40 CFR 191. Procedures used in recent performance assessments for the WIPP to translate regulations into a structure that facilitates quantitative analysis are described. Topics considered include 1 development of a clear conceptual representation for problems that are initially ill-defined, 2 conversion of qualitative guidance into numerical calculations. 3 explicit incorporation of different types of uncertainty i.e., aleatory and epistemic into analysis outcomes, 4 requirements for efficient computation and models at different levels of complexity, 5 use of sensitivity analysis to guide additional data collection and future calculations, 6 requirements for results to be presented and explained to audiences with different interests and levels of sophistication, and 7 ambiguity with respect to final uses of the analysis and its outcomes. The need to address similar concepts and problems arises in many analyses.

Summary discussion of the 1996 performance assessment for the Waste Isolation Pilot Plant

Abstract The Waste Isolation Pilot Plant (WIPP) is under development by the US Department of Energy (DOE) for the geologic disposal of transuranic waste. The construction of complementary cumulative distribution functions (CCDFs) for total radionuclide release from the WIPP to the accessible environment is described. The resultant CCDFs (i) combine releases due to cuttings and cavings, spallings, direct brine release, and long-term transport in flowing groundwater; (ii) fall substantially to the left of the boundary line specified by the US Environmental Protection Agencys (EPAs) standard 40 CFR 191 for the geologic disposal of radioactive waste; and (iii) constitute an important component of the DOEs successful Compliance Certification Application to the EPA for the WIPP. Insights and perspectives gained in the performance assessment (PA) that led to these CCDFs are described, including the importance of: (i) an iterative approach to PA; (ii) uncertainty and sensitivity analysis; (iii) a clear conceptual model for the analysis; (iv) the separation of stochastic (i.e. aleatory) and subjective (i.e. epistemic) uncertainty; (v) quality assurance procedures; (vi) early involvement of peer reviewers, regulators, and stakeholders; (vii) avoidance of conservative assumptions; and (viii) adequate documentation.

Computational implementation of a systems prioritization methodology for the Waste Isolation Pilot Plant: a preliminary example

Abstract A systems prioritization methodology (SPM) is under development for the Waste Isolation Pilot Plant (WIPP). The SPM is based on a large numerical integration problem that must be repeatedly evaluated to determine compliance probabilities associated with different experimental programs and design modifications. Due to the complexity and computational cost of the underlying integration problem, the implementation of the SPM must be planned very carefully. This presentation describes a preliminary application of the SPM, designated SPM-l, performed to provide insights to facilitate the development and implementation of the methodology. Topics illustrated by SPM-1 include definition of probability spaces on which the SPM is based, use of Latin hypercube sampling and simple random sampling to integrate over different probability spaces, selection of mechanistic calculations to be performed, efficient use of the limited number of mechanistic calculations that can be performed, and assembly of many individual calculations into a complete analysis.

Particle diffusion in electrostatic precipitators

Abstract A summary is presented of the main work in the transient diffusion of (mainly) passive scalars in tubes and channels with the viewpoint of seeking to apply methods of analysis in these areas to the consideration of the diffusion of particles in turbulent flow in a parallel plate electrostatic precipitator. Our theoretical studies indicate that while there is diffusion of dust particles away from the walls of the precipitator the effect of the applied electric field is such to drive the particles towards the walls. The theory appears to be applicable to two types of precipitator: (1) a uniform electric field applied between the plates and (2) a non-uniform electric field generated from wires placed in the flow field between the plates.