Radiological Assessment: Predicting the Transport, Bioaccumulation and Uptake by Man of Radionuclides Released to the Environment (N C R P Report 1984)

NCRP Report No. 76

RADIOLOGICAL ASSESSMENT: PREDICTING THE TRANSPORT, BIOACCUMULATION, A N D UPTAKE BY M A N OF RADIONUCLIDES RELEASED TO THE ENVIRONMENT Recommendations of the NATIONAL COUNCIL O N RADIATION PROTECTION AND MEASUREMENTS

Issued March 15, 1984 National Council on Radiation Protection and Measurement 7910 WOODMONT AVENUE

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BETHESDA, MD. 20814

LEGAL NOTICE This report was prepared by the National Council on Radiation Protection and Measurements (NCRP). The Council strives to provide accurate, complete and useful information in its reports. However, neither the NCRP, the members of NCRP, other persons contributing to or assisting in the preparation of this report, nor any person acting on the behalf of any of these parties (a) makes any warranty or representation, express or implied, with respect to the accuracy, completeness or usefulness of the information contained in this report, or that the use of any information, method or process disclosed in this report may not infringe on privately owned rights, or (b) assumes any liability with respect to the use of, or for damages resulting from the use of, any information, method or process disclosed in this report.

Library of Congress Cataloging in Publication Data National Council on Radiation Protection and Measurements. Radiological assessment. (NCRP report, ISSN 0083-209X ; no. 76) "Issued December 1, 1983." Bibliography: p. Includes index. 1. Radioisotopes-Physiological effect. 2. Radioisotopes-Migration. 3. Radioisotopes-Migration-Mathematical models. 4. Ionizing radiation-Measurement-Mathematical models. 5. Radioactive pollution. 6. Environmental health. I. Title. 11. Series. RA1231.R2N26 1983 628.5 84-4773 ISBN 0-913392-66-9

Copyright O National Council on Radiation Protection and Measurements 1984 All rights reserved. This publication is protected by copyright. No part of this publication may be reproduced in any form or by any means, including photocopying, or utilized by any information storage and retrieval system without written permission from the copyright owner, except for brief quotation in critical articles or reviews.

Preface T h e management and treatment of radioactive effluents has resulted in controlling exposure of the public to low levels which can be difficult and expensive to verify by environmental monitoring. Accompanying these lower levels of exposure has been an increased knowledge of environmental processes (especially bioaccumulation) which can result in additional exposure which may be greater than that arising from the intake of the environmental radioactivity in air and water alone. In the case of potential groundwater contamination, the exposure to the radioactivity may not even occur for time periods extending to thousands of years and beyond. As a result, the assessment of the potential consequences of the release of radioactive materials to the environment has required the use of mathematical models. Since the ultimate goal of radiological assessment is t o develop relationships between the source term or input of radionuclides to the environment and potential health effects in man, environmental transport models can be very important in some situations. These mathematical models quantitatively describe the air, water, and ground pathways, including the movement of the radioactivity through food pathways. Mathematical models can be used for a variety of purposes, including evaluation of (1) proposed discharges of radionuclides, (2) the routine operational release of radioactivity, and (3) the accidental release of radioactivity to the environment. The use of environmental transport models for radionuclides has been widely accepted with the result that computerized mathematical models (codes) have proliferated. Considerable variation exists in sophistication among models, the types of parameters needed for the models, and the degree t o which the models have been validated. T h e purpose of this report is to review the current status of the application of radionuclide transport models from the point of discharge to the environment to the point of intake by man. Models are reviewed that describe the transport of radionuclides through the atmosphere, surface and ground waters, deposition on terrestrial surfaces and in sediments, and accumulation in food products. Usage factors are considered that determine the intake of radionuclides by ...

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humans due to dietary habits, physiological parameters, and living customs. Evaluation of the prediction capabilities of the various models is important in determining their limitations in meeting current and future requirements for radiological assessment. This report includes an in-depth analysis of the data base accompanying these models in order to examine potential uncertainties inherent in the choice of model input parameters. Where available, model validation experimental results are included. Although the report is written as a reference document for the more technically sophisticated user of environmental transport models, it should be useful to others because of the information provided on important factors that influence environmental transport. The Council has noted the adoption by the 15th General Conference of Weights and Measures of special names for some units of the SysGme International d'UnitCls (SI) used in the field of ionizing radiation. The gray (symbol Gy) has been adopted as the special name for the SI unit of absorbed dose, absorbed dose index, kerma, and specific energy imparted. The becquerel (symbol Bq) has been adopted as the special name for the SI unit of activity (of a radionuclide). One gray equals one joule per kilogram; and one becquerel is equal to one second to the power of minus one. Since the transition from the special units current employed-rad and curie-to the new special names is expected to take some time, the Council has determined to continue, for the time being, the use of rad and curie. To convert from one set of units to the other, the following relationships pertain: 1 rad = 0.01 J kg-'= 0.01 Gy 1curie = 3.7 x 10'' S-' = 3.7 X 10'' Bq (exactly). The present report was prepared by the Council's Task Group 2 and 3 of Scientific Committee 64. Serving on the Task Group were: William L. Templeton, Chirrnan. Task Cmup 2 Battelle, Pacific Northwest Laboratory Richland, Washington

John E.Till, Chairman, Task Croup 3 Radiological Assessment Corp. Neeses, South Carolina

Members David A. B a k e r Battelle, Pacific Northwest Laboratory Richland, Washington B. Gordon Blayloek Oak Ridge National Laboratory Oak Ridge, Tennessee Richard B. Codell U.S. Nuclear Regulatory Commission Washington, D.C. David N. Edgington University of Wisconsin Center for Great Lakes Studies Milwaukee, Wisconsin F r a n k A. Gifford Atmospheric Environmental Research Oak Ridge, Tennessee F. Owen Hoffman Oak Ridge National Laboratory Oak Ridge, Tennessee

Yook Ng Lawrence Radiation Laboratory Livermore, California William L. Robison Lawrence Livermore Laboratory Livermore, California J a m e s 0. Duguid Battelle Memorial Institute Columbus, Ohio David A. Waite Battelle Memorial Institute Columbus, Ohio J o h n P. Witherspoon Oak Ridge National Laboratory Oak Ridge, Tennessee

Consultants

George G. Killough Oak Ridge National Laboratory Oak Ridge, Tennessee Gunther Scbwarz Brinck System Planning Aechen, Federal Republic of Germany Yasuo Onishi Battelle, Pacific Northwest Laboratory Richland, Washington

J a m e s G. Droppo Battelle, Pacific Northwest Laboratory Richland, Washington Charles W. Miller Oak Ridge National Laboratory Oak Ridge, Tennessee

Serving on the Scientific Committee were: Richard Foster, Chairman (1979-1981) Sunriver, Oregon

Melvin W. Carter, Chairman (1981-present) Georgia Institute of Technology Atlanta, Georgia

Merril Eisenbud

William A. Milla

New York University Tuxedo, New York John W. Healy Los Alamos National Laboratory Los Alamos, New Mexico William E. Kreger Bainbridge Island, Washington

Nuclear Regulatory Commission Washington, D.C. J. Newel1 Stannard University of Calif., San Diego La Jolla, California

McDonald E. Wrenn University of Utah Salt Lake City, Utah

NCRP Secretariat-E. Ivan White

The Council wishes to express its appreciation to the members and consultants for the time and effort devoted to the preparation of this report. Warren K. Sinclair President, NCRP Bethesda, Maryland April 30, 1984

Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Assessment of Radionuclides Released to the Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Atmospheric Transport Models . . . . . . . . . . . . . . . . . . 2.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Theories of Atmospheric Diffusion . . . . . . . . . . . . 2.1.3 Types of Atmospheric Models . . . . . . . . . . . . . . . . 2.1.4 Parameters of Atmospheric Models and Their Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 Variability of Concentration Estimates . . . . . . . . . 2.2 Radionuclide Deposition and Resuspension . . . . . . . . . . . 2.2.1 Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Resuspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Terrestrial Transport and Bioaccumulation in TerrestrialFoodProducts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Transfer to Vegetation . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Transfer to Animal Products . . . . . . . . . . . . . . . . . 2.4 Data Base for Terrestrial Transport Bioaccumulation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Transfer to Vegetation . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Transfer to Animal Products 2.5 Special Case Radionuclides (Tritium. Carbon-14) . . . . . 2.5.1 Tritium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Carbon-14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Assessment of Radionuclides Released to Surface Waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Surface Water Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Model Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Evaluation of Parameters and Data Bases . . . . . . 3.1.4 Distribution Coefficients (KD). . . . . . . . . . . . . . . . 3.1.5 Verification of Models . . . . . . . . . . . . . . . . . . . . . . . 3.1.6 Validation and Data Sets . . . . . . . . . . . . . . . . . . . .

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3.2 Bioaccumulation Factors (BF) . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Bioaccumulation Factors for Cesium. Cobalt. and

Strontium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Factors for Iodine and Ruthenium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Bioaccumulation Factors for Plutonium. Uranium and Radium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Bioaccurnulation Factors for Carbon and Tritium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Factors Influencing the Variability of Reported Bioaccumulation Factors . . . . . . . . . . . . . . . . . . . 3.2.6 Uncertainties Associated with . Bioaccumulation factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Assessment of Radionuclides Released to Groundwater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Types of Groundwater Assessments Needed . . . . 4.2 Types of Groundwater Models . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Groundwater Models for Low-Level Waste . . . . . 4.2.2 Groundwater Models for High-Level Waste Repositories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Performance Assessment for Mill Tailing Waste Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Equations for Groundwater Flow and Radionuclide Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Groundwater Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Mass Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Chain Decay of Radionuclides . . . . . . . . . . . . . . . . 4.3.4 Percolation of Water into the Ground . . . . . . . . . 4.4 Parameters for Transport and Flow Equations . . . . . . . . 4.4.1 Dispersion and Diffusion in Porous Media . . . . . . 4.4.2 Porosity and Effective Porosity . . . . . . . . . . . . . . . 4.4.3 Hydraulic Conductivity for Saturated Flow . . . . . 4.4.4 Adsorption and Retardation Coefficients . . . . . . . 4.5 Methods of Solution for Groundwater Movement and Solute Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Model Validation. Use and Misuse . . . . . . . . . . . . . . . . . . 4.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.3 Examples of Validation . . . . . . . . . . . . . . . . . . . . . . 4.6.4 Use of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Bioaccurnulation

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4.6.5 Misuse of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Usage Factors for Predicting Exposure to Man . . . . . . . 5.1 Dietary Pathway Usage Factors . . . . . . . . . . . . . . . . . . . . . 6.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Generic Usage Factors . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Usage Factors for Terrestrial Foods . . . . . . . . . . . 5.1.4 Usage Factors of Aquatic Foods . . . . . . . . . . . . . . . 5.1.5 Usage Rates for Water and Other Beverages . . . . 5.2 Inhalation Pathway Usage Factors . . . . . . . . . . . . . . . . . . 5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Minute Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Significant Factors Affecting Minute Volumes for Radionuclide Intake via Inhalation . . . . . . . . . . 5.2.4 Average Time Spent at Rest and a t Light to Moderate Activity . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.5 Summary and Discussion . . . . . . . . . . . . . . . . . . . . 6.3 Reduction in External Exposure from Shielding Due to Buildings. Homes. and Vehicles . . . . . . . . . . . . . . . . . . . 6 Identification of Uncertainties Associated with Model Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Sources of Model Uncertainties . . . . . . . . . . . . . . . . . . . . . 6.3 Determination of Model Uncertainties . . . . . . . . . . . . . . . 6.3.1 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Parameter Inprecision Analyses . . . . . . . . . . . . . . . 6.3.3 The Effect of Bias in the Selection of Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Uncertainties Among Various Types of Models . . . . . . . 6.4.1 Atmospheric Transport Models . . . . . . . . . . . . . . . 6.4.2 Terrestrial Food Chain Transport Models . . . . . . 6.4.3 Specific Activity Models for % and I'"C . . . . . . . . 6.4.4 Surface Water Transport Models . . . . . . . . . . . . . 6.4.5 Aquatic Food Chain Transport Models . . . . . . . . . 6.4.6 Groundwater Transport Models . . . . . . . . . . . . . . . 6.4.7 Human Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 The Application of Models for Environmental Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Classes of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Environmental Assessment Models . . . . . . . . . . . . 7.1.2 Research Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Application of Environmental Assessment Models for Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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196 198 198 198 199 200 204 208 208 208 210

214 216 216 217 219 219 220 220 220 221 225 225 227 228 229 230 230 231 231 232 233 233 233 234 235

7.3 Improvement of Radiological Assesment Models . . . . . . 7.3.1 Reduce Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Model Simplification . . . . . . . . . . . . . . . . . . . . . . . . 8 Conclusions and Recommendations . . . . . . . . . . . . . . . . . . 8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . APPENDIX A: Applicability of Models for Routine Releases to the Accident Situation . . . . . . . APPENDIX B: Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The NCRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NCRP Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction The development of nuclear material for national defense, of nuclear energy for the generation of electricity, and the applications of radionuclides in medicine, industry, and consumer products result in the release of radioactive material into the environment. Assessment of the radiological impact or consequences of the release of these materials into air and water, or their disposal in the ground, is a quantitative procedure. Fig. 1.1 shows the major steps in this assessment process and the pathways between the source and released material (source term) and the intake by individuals. T o describe these pathways quantitatively requires the use of mathematical models which incorporate the many factors that cause or affect the movement of radionuclides from one compartment to another. In Fig. 1.1 the arrows indicate the links between compartments where the application of mathematical models is useful. These models predict the transport, bioaccumulation, and intake by humans of radionuclides released to the environment. With this knowledge of the amounts of radioactive material released to the environment and ultimately ingested or inhaled, radiation dose may be calculated directly using conversion factors that relate the quantity of the energy absorbed in human tissues to external or internal sources. The ultimate goal of radiological assessment is to develop relationships between the source term or input of radionuclides t o the environment and resulting health effect upon man. A basic tenet for radiation protection of public health is to maintain exposures as low as reasonably achievable (ALARA), taking economic and social considerations into account, within the overall constraint of dose limits. This philosophy requires that models provide reasonable assurance that routine exposure of the public will be in accordance with regulatory guidelines, and also necessitates the use of models in the development of an optimum cost-benefit design for effluent treatment techniques. Mathematical models can be used to fulfill a variety of objectives. They are used for the preoperational evaluation of discharges of radionuclides to determine dominant pathways of exposure, key radionuclides in the source term, and the critical exposure groups or 1

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1. INTRODUCTION

SURFACE WATER TRANSPORT

DEPOSITION TERRESTRIAL

BIOACCUMULATIO IN FOOD PRODUCT

Fig. 1.1 Major steps considered in evaluating the effects of radionuclides released to the environment. (Crosshatched boxes indicate areas not addressed in this report.)

INTRODUCTION

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individuals. During periods of actual emissions, models are relied upon to guide operation of effluent treatment systems, environmental surveillance, predict concentrations in the biosphere which are below detectable limits, and convert measured values of radionuclide intake and exposure, into estimates of radiological dose. The use of environmental transport models for radionuclides has been widely accepted, and this methodology will be helpful to future understanding of the transport of many non-radioactive substances whose chemical behavior is similar to specific radionuclides. Considerable variation exists in sophistication among models, the availability of parameter values, and the degree to which models have been validated. The purpose of this report is to review the current status of the application of radionuclide transport models from the point of discharge to the environment to the point of intake by man. This process, called radiological assessment, is illustrated in Fig. 1.1and begins by defining the quantity of radionuclides that are released and enter the environment. Uncertainties in the measurements or estimates of the source term are passed on to the assessment calculations. This report does not specifically address the development of source terns; however, it should be borne in mind that important information about source terms must be available in order to determine which radionuclide transport models to use in an assessment. This information should incorporate the proximity of different points of release, the time distribution of release, the quantity and species of radionuclides released, and the chemical and physical form of the radionuclides. In the description of the models that follow, sufficient information is presented to allow the user to determine which of the source term conditions listed above should be considered. Models are reviewed that describe the transport of radionuclides through the atmosphere, surface waters, and ground waters, deposition on terrestrial surfaces and in sediments, and accumulation in food products. Uptake of radionuclides by humans is determined with usage factors that describe dietary habits, physiological parameters, and living customs of the receptors. The final steps in the assessment process are estimating dose and health effects from exposure to the radionuclides. Because these last two areas are under study by other committees of the NCRP, dose rate factors and health effects are not included in this report. Radionuclides may be released under a controlled situation in which the point of release, the quantity of radionuclides, and the duration of release are predetermined and monitored. This is commonly referred to as a routine or chronic release and most models assume that an equilibrium condition exists between the source term and concentra-

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1.

INTRODUCTION

tions in model compartments. On the other hand, radionuclides may also be released in an uncontrolled situation such as during an accident in which a pulse of radioactivity escapes for a brief period. This report focuses on models that deal with routine releases although the applicability of equilibrium models to the accident situation is addressed in Appendix A. The report also focuses on methods for assessing exposure to individuals (i.e., critical groups) rather than the collective exposure to large populations, i.e. the methods provide assessments applicable to critical groups representative of individuals in a specific location having specific dietary habits and not all persons within a large geographical area. The latter would involve summations over large distances and long time periods, factors which greatly increase the uncertainty of the assessment. As previously stated, evaluation of the predictive capabilities of the various models is important in defining the limitations in use of the models in meeting current standards and for guiding future decisions on degree of protection desired and achievable. For the models to be useful, it is essential to know their uncertainties and their potential to over- or under-predict dose. This report includes an in-depth analysis of the data base accompanying these models in order to examine potential uncertainties inherent within the choice of values for selected model parameters. Also, where available, the results of model validation experiments which compare model predictions with field observations are included. For those models and parameters that are dependent on specific elements, the discussion is limited to those of most concern for the uranium fuel cycle; these are cobalt, strontium, ruthenium, iodine, cesium, radium, uranium, and plutonium. The specific radionuclides, tritium and carbon-14, are given individual consideration and treated as tracers in the hydrologic and carbon cycles, respectively. The report is written as a reference document for users having a considerable range of technical knowledge of environmental transport. For example, Sections 2, 3, and 4 contain details of mathematical models for atmospheric, surface water, and groundwater transport which are likely to be fully understood only by those with expertise in these areas. However, others are expected to find these sections useful because they provide information on the important factors that qualitatively influence environmental transport. A glossary of terms is included in Appendix B. The remaining sections are expected to be of equal interest to all who must deal with radiological assessment. Because of the interdisciplinary nature of the study, each section is preceded by a concise summary of the environmental transport processes being discussed and how the information relates to the overall assessment scheme shown in Fig. 1.1.

2. Assessment of Radionuclides Released to the Atmosphere Radionuclides released to air are transported away from the point of release and dispersed through atmospheric mechanisms. The objective of atmospheric transport models is to predict the concentration of radionuclides at specific locations surrounding the source. I n order to do this, one must first know the release rate of each nuclide (Ci s-I), physical characteristics of the source (such as stack height), and meteorological data in the vicinity of the point of release. The concentration i n air (Ci m-3) is the input data used to calculate rate of intake by inhalation; deposition (Ci m-2) on soil and water for external exposure rates; intake rate from consumption of growing crops either as a result of direct deposition or resuspension from soil; rate of intake as a result of accumulation by food crops from soil; and exposure due to immersion in a radioactive cloud. Radionuclides may also enter the soil-crop pathway as a result of irrigation with contaminated water. The ultimate goal of terrestrial transport and bioaccumulation models is to determine the quantity of radionuclides reaching man through the food chain. Once the concentration in food or on land surfaces has been calculated, the radiological exposure to individuals may be estimated with appropriate usage and dose rate factors. Tritium and carbon-14 are two radionuclides treated o n a special case basis because of their ubiquitous nature and because of their association with water and carbon dioxide respectively, in the environment.

2.1 Atmospheric Transport Models 2.1.1 Introduction Radionuclides entering the atmosphere from natural and manmade sources are transported and diluted by atmospheric processes. In this 5

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2. ASSESSMENT OF RADIONUCLIDES

section atmospheric transport and diffusion models that are available to describe this phenomenon are discussed briefly and their properties evaluated. Emphasis, however, is given to the most widely used approach, the Gaussian plume model. Our interest is in models that can be used to simulate plumes of material emitted from point sources such as containment leaks, for time periods of a few tens of minutes or more, and for distances up to approximately 100 km from source, within which it is convenient to distinguish between short-range, localscale (0-10 km) models and longer-range, regional-scale (>lo km) models. Airborne radionuclides, like other atmospheric contaminants, are transported by such large, essentially horizontal and two-dimensional motions of atmospheric wind systems as the weather map's "highs and lows." These transport winds are ordinarily treated as given input quantities, and atmospheric models attempt to account for the effect of turbulent diffusion. Turbulent diffusion in the atmosphere occurs a t widely varying rates. It may proceed a t nearly the slow rate of molecular diffusion on a calm, clear night; but most of the time, atmospheric diffusion is much faster. Consequently, the correct specification of turbulent diffusion is a crucial element of atmospheric models. The motion of large-scale winds over the surface of the earth sets up a turbulent boundary layer, or mixed layer, whose highly variable depth and diffusive properties are controlled by two distinct but interrelated turbulence effects; (1) Intense mechanical mixing is caused by turbulence in the shear zone created by the drag of the ground surface on the lower layers of the atmosphere. This effect is stronger the higher the wind speed is in the free atmosphere over the mixed layer, and the rougher the underlying surface. The length scale of the resulting turbulence is related to the size of the surface roughness elements (grains of dirt, vegetation, buildings, forest cover, water waves, city streets, canyons, etc.). (2) Solar heating of the earth's surface creates buoyant thermals, i.e., large, rising "bubbles" of warm air, which result in an upward heat flux. These thermally-driven eddies are much larger than the mechanically-produced eddies and are more vigorous the more intense the upward heat flux a t ground level. The mixed layer is deep, on the order of a kilometer or more, and diffusion is rapid, when thermal and mechanical turbulence effects are strong. When they are weak, as on a calm, clear night, the boundary layer can be only a few meters thick and turbulent diffusion above it is virtually absent. Fig. 2.1 illustrates the daytime portion of this characteristic diurnal sequence of mixed-layer depth changes, as measured simultaneously by vertically-oriented acoustic radar, and pulsed-laser instruments

2.1 ATMOSPHERIC TRANSPORT MODELS

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2.

ASSESSMENT OF RADIONUCLIDES

(Johnson and Ruff, 1975). The essence of the problem of atmospheric modeling is to incorporate relevant physical details of this highly variable, turbulent-flow process into reasonable computer algorithms capable of simulating atmospheric diffusion. Detailed discussions of the physics of the atmospheric boundary layer can be found in the monograph by Lumley and Panofsky (1964), and in two American Meteorological Society workshop volumes (Haugen, 1973; Wyngaard, 1980).

2.1.2

Theories of Atmospheric Diffusion

The mean value of air concentration, x , of a radionuclide (or any other airborne material) is a function of position and time, x = x (x, y, z, t). The object of an atmospheric transport and diffusion model is to specify x and its frequency distribution a t any point in space. Three principal theoretical approaches are available, the so-called statistical, gradient-transport, and similarity theories. G.I. Taylor's (1921) statistical theory assumes a stationary, homogeneous turbulence field and derives x in terms of the mean square displacement of an air "particle" from its average position. Gradient-transport theory, or K-theory, assumes that the material flux, I",, is proportional to the local concentration gradient in the 4-direction and from this derives a diffusion equation based on mass continuity:

where I", = material flux in the xi direction (g s-'m-' or Ci s-'m-'1, Kij = the (i, j) - th component of the diffusion tensor (m2s-I), i, j = 1, 2, 3, x = concentration (g m-3 or Ci m-3), q = coordinate (m) (in what follows, x, y, and z are sometimes substituted for xl, x2, and x3, respectively).

The nine components of Kij form the eddy diffusivity tensor. It cannot in general be assumed that they are constants. In the simplest case, when the off-diagonal (i # j) terms equal zero and the diagonal terms (i = j) are constant, the classical Fickian form of the diffusion equation results, for which many solutions are known. The eddy diffusivity is very much larger than (lo8 to 10'' times) its molecular counterpart. This situation is obtained in the atmosphere only a t very large scales, approaching the global limit. At the smaller scales of

2.1 ATMOSPHERIC TRANSPORT MODELS

1

9

interest to us, the K's are in general functions of x and z, and the offdiagonal components Kx,and K,, are important because of wind shear. Monin and Yaglom (1971), Yaglom (1975), and Pasquill (1974) have published reviews of the few known analytic solutions of Eq. (2-1) for atmospheric boundary layer flows; these solutions tend to be quite complicated mathematically. Similarity theory attempts to overcome the restriction to turbulence homogeneity of statistical theory, and the great complexity of realistic K-theory solutions except in the simplest asymptotic cases, by analyzing the problem dimensionally. But boundary layer turbulent flow in the atmosphere is governed by a large number of physical variables, in addition to space and time coordinates, including surface heat flux, surface roughness, ambient wind speed, air viscosity, source height, and many other less well-defined factors. Consequently, a large number of characteristic dimensionless groups arise, and similarity solutions have been found only for a few limited problems such as the mean, steady-state, axial concentration distribution x (x, 0, 0) in the near-surface layer, which is roughly the lowest 10% of the boundary layer. For more detailed understanding, summaries of all three of these theories from the standpoint of atmospheric pollution applications can be found in Pasquill (1974, 1975) and Gifford (1968, 1975). A fourth class of diffusion theory, called second- or, more generally, higher-order closure theory has recently been applied to atmospheric diffusion modeling, although applications to turbulent flows were first made more than 40 years ago. This theory is based on the principle that knowledge of all the moments of the distribution of a quantity is fully equivalent to knowing its distribution. Expressions for the moments, i.e. the mean, variance, skewness, and so on, of the turbulent velocity field can be obtained from the equations of motion, and similarly for the related field of concentration. However, it develops that the resulting hierarchy of moment equations is infinite; moments of any order turn out to depend on those of the next higher order. Gradient-transport theory can be viewed from this perspective as a first-order truncation of the equation system, in which the flow is characterized in terms of the gradient of the mean concentration. Second-order closure methodology bounds the system by means of assumptions relating higher-order moments to the second-order moment. Atmospheric modeling applications are mathematically complicated and require significant amounts of large-computer time (Donaldson, 1973; Lewallen and Teske, 1976). The best use of this methodology appears to be as a powerful research tool for simulating boundary-layer diffusion in typical, representative situations, rather than as a means of attacking particular operational problems.

10

2.1.3

/

2. ASSESSMENT OF RADIONUCLIDES

Types of Atmospheric Models

The above few interrelated theories of atmospheric diffusion have been applied to the problem of estimating concentration patterns of airborne radionuclides, in order to satisfy various regulatory requirements, in a much larger number of atmospheric diffusion models. The literature describing these applications is vast and growing and has produced a number of critical surveys and reviews, aimed a t the needs of various classes of users. The following recent reviews of this heterogeneous and rapidly expanding body of applications are especially relevant to this report: Barr and Clements (1983); Hanna, et al. (1982); Drake, et al. (1979); Johnson, et al. (1976); Liu (1980); USEPA (1978); Turner (1979); Eliassen (1980); Hoffman, et al. (1977); Crawford (1978); and Hanna (1983). There is a t the moment no particularly standardized scheme for classifying diffusion model types. Models have been grouped in the above reviews in terms of the diffusion theories involved, according to the complexity of the numerical modeling required, by source configuration, by the distance of material transport, and by their relation to particular regulatory requirements. Table 2.1 is a summary of atmospheric model types and characteristics, condensed from tables given by Drake et al. (1979) and Hosker (1983). The classification is a composite in that it reflects regulatory requirements, source types, numerical aspects, and distance scales; but its description of model characteristics is widely understood and accepted by the modeling profession. For present purposes, it provides a useful, operational classification of models. The following brief description of these models, mostly abstracted from Hosker's (1983) review, conveys only their essential features in qualitative terms. The reader requiring details of mathematical structure and input parameter requirements of models should consult the survey by Liu (1980), who has outlined the details of a large number of atmospheric models of various types in convenient tabular form. Gaussian plume and puff models The most widely used model of diffusion is the continuous pointsource Gaussian plume formula: x ( x , Y, z ) / Q = (2*a,aZu)-' exp(-3/2d) (2-2) [exp(-(z - he)'/2a,2) + exp(-(z + h#/2d)]

TABLE 2.1-Characteristics of tranmort and dis~ersionmodels" Model Type

GeorC8p:ical

Steady-State

or Time-Dependent

Frame of Reference

Reaction Mechanisms

Removal Mechanisms

Treatment of Turbulence

Topography Treated

Gaussian plume and puff

Local

Steady-state or Timedependent

Eulerian or Lagrangian

Nonreactive or reactive

Dry and wet

Diffusion coefficients

Homogeneous to simple terrain

Regional trajectory

Regional or National

Time-dependent

Lagrangian, or mixed Lagrangian and Eulerian

Nonreactive or reactive

Dry and wet

Difhion coefficients or eddy diffusivities

Nonhomogeneous to complex terrain

Box and multi-box

Local or Regional

Steady-state or Timedependent

Eulerian or Lagrangian

Nonreactive, reactive, or gas-to-particle

Dry and wet

Well-mixed, or eddy diffusivities

Homogeneous to simple terrain

Grid

Local or Regional

Steady-state or Timedependent

Eulerian

Nonreactive, reactive, or gas-to-particle

Dry and wet

Eddy diffusivities, or complex formulation

All terrain

Particle

Local or Regional

Time-dependent

Mixed La-

Nonreactive, reactive, or gas-to-particle

Dry and wet

Eddy diffusivities

All terrain

grangian and Eulerian

Cm

( I ,

TABLE 2.2-Continued Model Type

Geographical Scale

Steady-State or Time-Dependent

Frame of Reference

Reaction Mechanisms

Removal Mechanisms

Treatment of Turbulence

Topography Treated

Global

Global

Time-dependent

Eulerian

Nonreactive or reactive

Dry and wet

Eddy diffusivities

All terrain

Physical

Local

Time-dc-

Mixed Lagangian and Eulerian

Nonreactive

None

Not applicable

All terrain

pendent

"Modified from Drake rt aL. 1979, and Hosker, 1983.

i 4

8

?

z2 C

E

t]

$'4

where

x

(x, y, z ) = steady-state concentration a t a point (x, y, z ) , (g mV3or Ci m-3), Q = continuous release strength (g s-' or Ci s-'), u = mean (horizontal) transport wind speed in x-direction (m s-'), a,, a, = horizontal and vertical standard deviation of concentration distribution (m), and he = effective source height (m).

The double exponential term in z accounts for a conventionally assumed "reflectionn of the plume by the underlying surface. The dispersion lengths a, and a, are empirically-based functions of downwind distance, x, atmospheric stability conditions, source height, and surface roughness. The various series of diffusion field trials that provide values of a, and a, were made mostly a t atomic energy laboratories and field sites during the past 25 years or so. These experimental series have been reviewed in detail by Islitzer and Slade (1968) and Draxler (1979). The Gaussian plume model is illustrated in Fig. 2.2(a). Eq. (2-2) is an exact solution to the diffusion equation under certain conditions. For a stationary, homogeneous turbulent flow (i.e., for which statistical properties do not vary in time or space) it describes the near-field of diffusion exactly, based on statistical theory [see, e.g., Hinze (1959)l. Also, it is a solution to the Fickian or constant-K diffusion equation which makes it useful for global diffusion problems. For emissions not significantly affected by strong surface layer shears the theoretical credentials of the Gaussian-plume formula allow its strict application very near the source (out to a few hundred meters), and very far away ( 2 1000 km). Extension to regional-scales, i.e. distances from a source on the order of a few tens to hundreds of km, is accomplished by using the empirical a,- and a,-curves, which will be described below. Gaussian puff models assume that a plume element in the form of a three-dimensional Gaussian function is moved horizontally by the mean transport wind field u(x, y), i.e., the weather-map wind field, which is determined by standard principles of meteorological analysis and prediction. This kind of model can account for complicated wind transport paths, a situation illustrated schematically in Fig. 2.2(b), since it is not restricted to a constant value of u; and consequently it has been widely applied a t regional scales. There is comparatively little experimental diffusion data available a t these distances, so specifying any a-value is speculative. There is an important difference between puff models and the plume

6

14

/

2.

ASSESSMENT OF RADIONUCLIDES

Fig. 2.2(a) Coordinate system of the Gaussian plume model, showing distribution of concentration in the horizontal and vertical (after Twner, 1969).

yw

RELEASE POINT

Fig. 2.2(b) Schematic illustration of a "Puff" model (after Hanna et al., 1982).

model specified by Eq. (2-2). Models based on Eq. (2-2) attempt to simulate the time-average field of concentration, usually for an averaging time of the order of a few tens of minutes. In contrast, the socalled-puff models try to simulate the instantaneous plume spreading about its axial centroid, in the form of a sequence of overlapping puffs, resulting in a kind of "snapshot" of the plume. Fig. 2.3(a) and (b)

2.1 ATMOSPHERIC TRANSPORT MODELS

1

17

illustrate this conceptual difference by means.of actual instantaneous and time-exposure photographs of wind-tunnel generated smoke plumes. Because puff models portray the instantaneous plume concentration field, they are appropriate for estimating the maximum (shortterm) concentration a t a point. When combined with trajectory models, they also are useful in the important case of accidental releases, because releases may then vary in time or occur in brief bursts, such that a steady release cannot be assumed. Trajectory Models

At regional or greater travel distance, where an adequate empirical basis is lacking, trajectory models are frequently used. In these models, material transport is driven by the observed wind field, for instance that of a weather map, or by the output of a predictive or forecast wind-field model, as illustrated in Fig. 2.2(b) for the puff model. Diffusion is accounted for by moving-box, growing-puff, or small airparticle elements for which atmospheric diffusivity is specified according to one of the principles outlined in section 2.1.2 above, most often by some form of K-theory. Statistical-sampling, or "Monte-Carlo" forms of puff-trajectory models have also been proposed (Hanna, 1983). Trajectory models are quite flexible and can, in principle, account for wet- and dry-removal processes (washout and fallout), chemical transformations, and time-varying wind and stability conditions. Disadvantages of trajectory models arise from their sensitivity to errors in selecting values for the driving wind field, and from uncertainties associated with modeling time-variable diffusion and removal processes along the trajectory. To these should be added the problem that, although many trajectory models are in use, few have yet been adequately evaluated.

Grid Models Grid models are finite-difference approximations to the equation of motion, continuity, diffusion, and species conservation and removal. A region is covered by a grid of points at which solutions to the governing equation system are generated using standard finite-differencing techniques. There are several problems with the use of grid models. Computational instabilities, which can make nonsense of a solution in a few time steps, must be carefully controlled by proper choice of space and time grid intervals. To avoid this type of finite-

18

/

2. ASSESSMENT OF RADIONUCLIDES

differencing error, as well as to increase computational efficiency and reduce computer running time, pseudo-spectral models have been introduced. In these grid models, finite Fourier Transforms of the concentrations field are used to define derivatives in the diffusion equation. Christensen and Prahm (1976) discuss the computational advantages of the technique; and Prahm and Christensen (1977), and Mills and Hirata (1978) describe applications to long-range diffusion problems. Practical limitations are imposed on grid spacing in all such models by available computer capacity. Resulting grids are generally incapable of resolving important initial and boundary conditions in adequate detail, such as point sources or any but the largest of terrain features. This severely restricts the applicability of grid models to a large class of transport problems. Consider the fact that plumes from point sources (chimneys, tall stacks, etc.) are commonly observed to be as a rule 10 to 20 times as long as they are wide. (Otherwise they would not be commonly known as "plumes.") Typical grid-model spacings may be 0.5 to 5 km horizontally, often nearer the latter figure. Thus, a grid cannot resolve diffusion from a point-source plume until the plume has traveled many kilometers downwind. This puts quite real practical limits on what is in principle a modeling approach of great generality. Drake et al. (1979), Liu (1980), and Hanna (1983) have summarized existing grid models and their properties.

Particle-in-cell models attempt to overcome the numerical instabilities that affect grid models by calculating a "pseudo-velocityn field, which is composed of the actual velocity field plus a "diffusion velocity" (Lange, 1978). The wind field is assumed to be non-divergent, V . u = 0. The diffusion velocity, u ~ is , defined from gradient transport theory as UD = (Kij . Vxlx) where K is the diffusion tensor. From these definitions and thediffusion equation of K-theory, an equation for the concentration field can be written in terms of the pseudovelocity up: where u = the (vector) wind field (m s-'1,

uD = a diffusion velocity (m s-'),

2.1 ATMOSPHERIC TRANSPORT MODELS L C ~=

/

19

a pseudo-velocity, up = u + UD (m s-'1,

t = time (sec), and

x

= the concentration field a t a point ( x , y, z ) , (g m-3 or

Ci m-3). This equation is evaluated over a three-dimensional grid covering the region of interest. An initial distribution of a large number (on the order of lo4) of particles is specified over the grid; this might, for instance, be in the form of a Gaussian plume. These points are assumed to be transported to new cell locations each time step by u, according to Eq. (2-3). Then a new u~ is computed from the resulting concentration field and the process is iterated. This type of model readily accommodates processes such as a particle settling and deposition, washout, and radioactive decay. As with grid models, the ability of particle-in-cell diffusion models to resolve point-source plumes is constrained by the grid-cell size. In addition, the outer limit of material travel time that can be modeled is restricted by the larger number of points that must be followed to assure adequate definition of concentration gradients at great downwind distances. Finally, the basic theoretical limitations of K-theories, mentioned earlier, are equally applicable to these models.

BOXModels and Global Models Box models are based on mass conservation in a specified volume, in which the materials are assumed to be well mixed. This volume may range in size from a small portion of the boundary layer of a region, through that of the region itself, e.g., the Los Angeles basin (Friedlander and Seinfeld, 1969), to the entire atmosphere, in the example of global dispersion of nuclear weapons debris or COz (Machta, 1973). It is clearly essential in such a model that the time of turbulent mixing through the box be either much shorter or much longer than any time scales associated with removal or chemical transformation processes; otherwise the assumption of uniform mixing will be invalid. The generalization can perhaps be risked that the degree to which a class of models has been validated tends to be inversely proportional to model complexity. Box models, being inherently simple but physically sound, have been widely validated and in general found to perform well. The basic principles of box models have been discussed in the papers by Lettau (1970) and Tennekes (1976).

20

/

2. ASSESSMENT OF RADIONUCLIDES

Global models are not, strictly speaking, a distinct model class but rather are the global asymptotic limits of several of the above model classes. Global circulation models, originally aimed a t weather prediction, have been applied to the problem of climate change caused by anthropogenic increases in atmospheric COz (Smagorinsky, 1974; Manabe and Weatherald, 1967). Global reservoir-type box models have been applied to the climate change problem as has been mentioned; and the Gaussian plume model in a trajectory version has also been applied to material transport at large distances (Heffter and Ferber, 1975). Similar models have been used for many years to estimate long-range transport of radioactive clouds. Despite the fact that a penalty must be paid in terms of computer storage and running time to model the global atmosphere, a major theoretical simplification results from the fact that a constant K for diffusion can be assumed.

Physical Models By appropriate scaling of relevant dimensionless flow parameters, chiefly the Reynolds number for momentum, and Froude number for heat transport, so that laboratory wind- and water-tunnel flows corredly simulate the atmosphere, a large class of complicated flow and diffusion patterns can be studied in detail. Where this procedure applies, it is a much simpler and more economical way to model diffusion in complicated situations, such as in flow over rough terrain and flow in the wakes of buildings and other obstacles. Physical models are used mostly a t the local, short-range scales of diffusion, up to a few kilometers. This is because atmospheric turbulence and diffusion at larger scales are strongly influenced by accelerations arising from the earth's rotation. Abbey (1976) has summarized wind tunnel and related atmospheric modeling of wakes, and Hosker (1983) has provided a detailed discussion of the entire subject of physical modeling of atmospheric flows and diffusion. Particularly for wake and rough terrain flows, physical modeling seems under-utilized in comparison with purely numerical modeling studies. Indeed, for these intricate flows it may provide the main possibility of generating data adequate to validate numerical diffusion models.

2.1.4 Parameters of Atmospheric Models and Their Variability Any of the models so briefly described above could be used to simulate radioactive cloud transport and diffusion. However, the Gaus-

2.1 ATMOSPHERIC TRANSPORT MODELS

1

21

sian plume model has been by far the most widely applied. Hoffman et al. (1977), reviewing 83 computer codes for environmental radionuclide releases, remark that "Nearly all the codes dealing with atmospheric transport are based on the Gaussian plume dispersion model," Similar statements occur in many of the above-mentioned reviews. Turner's (1979) survey of atmospheric models contains 192 references, most of them to models described by some form of Eq. (2-2). The 18 "kinematic models" reviewed in detail by Liu (1980) make explicit use of the Gaussian distribution assumption. There are several reasons for this widespread use, among them the conservatism inherent in the regulatory process. The Gaussian model has been adopted as a standard method in regulating both radioactive (USNRC, 1977a; IAEA, 1980) and other (USEPA, 1978) airborne species. But more importantly, Gaussian models are firmly rooted in available experimental data, have a good if not perfect theoretical basis, and are simple enough to be easily adaptable to a wide variety of air pollution problems. Gaussian models also are the most extensively validated class of diffusion models, and their behavior, including their shortcomings, is comparatively well known. The following discussion of the parameters of atmospheric diffusion models accordingly centers on those of the Gaussian model; but the information applies equally to parameters of the other model types, since it is based on essentially all the available atmospheric diffusion data. Gaussian models have been developed to cope with a variety of pollution situations and regulatory requirements. Some of the factors that different models have addressed include: averaging period; source configuration; average concentration or maximum values vs frequency distribution; receptor configuration; and terrain type. Table 2.2, based on three of Liu's (1980) tables, summarizes the objectives, space- and time-scales, and documentation for the Gaussian models he surveyed. Each of these models contains modules (algorithms) designed to calculate the parameters appearing, explicity or implicitly, in Eq. (2-2) as applied to a particular kind of problem. These parameters might be classified as either basic, derived, or lumped. Basic parameters include: (1) basic fluid properties like viscosity, specific heat, and density-the kind of atmospheric properties normally available in tables; (2) field parameters, including gravitation and the rotational (Coriolis) parameter; and (3) basic measured or well-determined atmospheric quantities like wind-speed, direction, and gradient; temperature and its vertical gradient; humidity; surface heat flux. Derived parameters include: all the diffusivities and diffusion lengths, K,j, ay, a,; the parameters that characterize the stability of the atmosphere with respect to vertical turbulent motions, i.e., Richardson's number,

22 / 2. ASSESSMENT OF RADIONUCLIDES

Busse and Zimmerman (1973)

Busse, A.D. and J.R. Zimmerman, "User's Guide for the Climatological Dispersion Model," Publication No. EPA-RA-73-024 (NTISP B 227346/AS). Environmental Protection Agency, Research Triangle Park, North Carolina 27711, December 1973. Bmbaker, K.L., P. Brown and R.R Cirillo. "Addendum t o User's Guide for Climatological Dispersion Model," Publication No. EPA-460/3-77-105, Environmental Protection Agency, Research Triangle Park, North Carolina 27711, May 1977.

Long-term (monthly, seasonal, or annual) climatological average concentration a t any ground-level receptor from multiple point and area sources in urban areas. CDMQC estimates short-term (hourly or daily) average concentration a t any ground-level receptor from multiple point and area sources in urban areas.

Implicit, up to 100 km

10-month up to 1-year for CDMQC

1-hr up to 24hours

N

'

B% ~d

x

m

p, 0

5! Z

m

'a 0 P

r3

5 E

TALE 2.2-Properties Models

Developers

Reference

of selected goussian modelsa Objectives

tQ

A

Spatial Scales

Temporal Scales

Implicit, up to 100 km

1-hour u p to 1year

\

CRSTER

EPA (1977)

Environmental Protection Agency, "User's Manual for Single Source (CRSTER) Model," Publication No. EPA-450/2-77-013 NTIS PB 271360, Office of Air Quality Planning and Standards, Research Triangle Park, North Carolina 27711, July 1977.

Atmospheric conditions that lead to high ground-level concentration for a given set of emission characteristics over moderately complex terrain. Short-term (hourly or daily) and long-term (monthly or annual) arithmetic average concentration a t any ground-level receptor from single point source. Maximum short-term concentration (hourly or daily) a t any ground-level receptor. Frequency distribution for various concentration levels over different averaging periods.

h,

% E

CI) CI)

?i

Z 4

%

FE 0 2

C

0

5R

GEM

Fabrick et al. (1977)

Fabrick, A., R S . Sklarow and T. Wilson, 'Point Source Model Evaluation and Development Study", Science Application, Inc.. West Village. California. March 1977.

T o estimate short-term (hourly) average concentration a t any ground-level receptor.

ISC

Bowers et al. (1979)

Bowers, J.F., J.R. Bjorklund, and C.S. Chiney, "Industrial Source Complex (ISC) Dispersion Model User'e Guide," H.E.Cramer Company, Inc., Salt Lake City, Utah, January 1977.

Short-term (hourly, up to daily) and longterm (up to 1year) arithmetic average concentration at any ground-level receptor from point, area, and volume sources. Long-term (monthly, seasonal, or annual) climatological average concentration a t any ground-level receptors from point, area, and volume 80urces.

From 100 m up to 100 km

1-hour to 24hours, 1month to 1year

F CL

4

?i

%

tQ

TABLE 2.2-Properties of selected gaussian models' Models

Developers

Reference

Objectives

Pierce, T.E.and D.B.Turner, "Users Guide for MPTEFt," Publication No. EPA-6001 8-80-016, Environmental Protection Agency, Research Triangle Park, North Carolina, 1980.

Short-term (hourly), concentration a t ground-level receptor from multiple point sources.

Q,

Spatial Scales

Temporal Scales

Implicit, up to 100 km

1-hour to 1-day

\

MPTER

EPA (1980)

F)

% rn !2

Xz

Up to one-day arithmetic average concentration a t any ground-level receptor from multiple point sources. MSDM

MESO PLUME

Ermak and Nyholm (1978)

EPA (1979)

4

%

B

0

2

Ermak, D.L. and R.A. Nyholm, 'Multiple Source Dispersion Models," U.C. Lawrence Livermore Lab., Livermore, California, 1972.

T o estimate short-term (hourly) average concentration a t each grid cell within the modeling region.

Up to 100 km

Benkley, C.W.and A. Bass, "Users Guide to MESOPLUME (Mesoscale Plume Segment) Model," Publication No. EPA-60017-80057, Environmental Protection Agency, Washington, D.C.. 1979.

Short-term (hourly, up to several days) arithmetic average concentration a t each grid cell within the modeling region.

Up to several hundred kilometers

1-hour

2

E

U

E? 1-hour to several days

EPA (1979)

Benkley, C.W. and A. Bass, "Users Guide to MESOPUFF (Mesoscale Puff) Model," Publication No. EPA-600/7-80-058, Environmental Protection Agency, Washington, D.C.,

Short-term (hourly to several days) arithmetic average concentration a t each grid cell within the modeling region.

Up to several hundred kilometers

l-hour to several days

Short-term (hourly) concentration a t given ground-level receptor from multiple point sources, line sources, and area sources.

Implicit, up to 100 km

l-hour to l-day

1979.

PAL

Petersen (1979)

Petersen, W.B., "User's Guide for PAL: A Gaussian Plume Algorithm for Point, Area, and Line Sources," Publication No. EPA-600/ 4-78-013, Environmental Protection Agency, Research Triangle Park, North Carolina, February 1978.

Up to one day arithmetic average concentration at any ground-level receptor from multiple point sources, line sources, and area sources.

*

r

h)

TABLE 2.2-Properties of selected gaussian modeIsa Models

Developers

Reference

Objectives

OD

Spatial Scales

Temporal Scales \

PTDIS PTMAX PTMP

PTMAX

EPA (1973)

Turner, D.B.and A.D. Bussee, "User's Guide to the Interactive Versions of Three Point Source Dispersion Programs: PTMAX, PTDIS,and PTMTP," Meteorology Laboratory, EPA, Research Triangle Park, North Carolina, June 1973.

Short-term (hourly) centerline groundlevel concentration downwind from a point source a t distance specified.

See above.

Short-term (hourly) maximum groundlevel concentration under each combination of atmospheric stability and wind speed, conditions from a single point source. Downwind distance of maximum concentration for each combination of atmospheric stability and wind speed cond i t i o n ~from a single point source.

Implicit, up to 100 km

1-hour FJ

*

CI)

8

V)

X

z

4

2 Implicit, up to tens of kilometers

1-hour

See above.

RAM

Turner and Novak (1978)

Turner, D.B. and J.H. Novak, "User's Guide for RAM," Environmental Protection Agency, Research Triangle Park, North Carolina, 1978.

Short-term (hourly) concentration a t any ground-level receptor downwind from multiple point sources. Arithmetic average concentration (up to one day) a t any ground-level receptor downwind from multiple point sources. Short-term (hourly) concentration and up to 24-hour arithmetic average concentration a t any ground-level receptor from multiple point and area sources in urban areas.

Implicit, up to 100 km

1-hour to 24hour

b'

>

2 A

CO

3 z! 0

fi (I)

co

0

3

5u

TABLE 2.2-Properties of selected gaussian modelsa Models

Developers

Reference

Objectives

Spatial Scales

Temporal Scales

Koch and Stadsklev (1974)

Koch, RC. and G.H. Stadsklev, 'A User's Manual for the Sampled Chronological Input Model (SCIM)" GEOMET Report No. 3261, prepared for U.S. EPA under Contract No. 68-020281, December 1974.

Short-term (hourly) concentration and long-term (monthly) arithmetic average concentration a t any ground-level receptor from multiple point and area sources in urban mas. Maximum short-term concentration (hourly) at any ground-level receptor. Frequency distribution for various shortterm concentration levels.

Implicit, up to 100 km

1-hour to 1-year

u 0

SCIM

TCM

Christiansen and Porter (1976)

Christiansen, J.H. and R A . Porter, "User's Guide to the Texas Climatological Model," Texas Air Control Board, Austin. Texas, May 1976.

Long-term (monthly, seasonal, or annual) climatological average concentrations a t each ground-level grid cell from multiple point and area sources in urban areas. Identify high contributors to concentration a t each grid cell.

\

P

% rn !2

B

z

t-3

FE z

2r U

!2

2.1 ATMOSPHERIC TRANSPORT MODELS

32

/

2. ASSESSMENT OF RADIONUCLIDES

Ri, the Monin-Obukhov stability length, L, and the Pasquill class; and various other buoyancy and mechanical turbulence parameters. All these share the characteristic that they can be described by means of theoretically-deduced equations involving the basic parameters. Lumped parameters include quantities like deposition and resuspension velocities, washout coefficients, building-wake corrections, and entrainment velocities. Values of these parameters are more or less well known through experiment but may lack complete theoretical specification in the form of basic, defining equations, because of complexity. Details of how parameters are specified in Gaussian models are summarized in Liu's (1980) review. Although measurement of basic parameters in the field may present problems, and their representativeness must be carefully considered in relation to various model properties such as grid-point locations and spacing, the basic parameters are not usually major contributors to model output variability. T h e uncertainties attributable to the derived and lumped parameters of atmospheric models, particularly the diffusion lengths, stability class, and wet and dry deposition velocities, are usually the most significant factors. 2.1.4.1 Atmospheric Diffusion Categories

Pasquill (1961) proposed dividing all atmospheric turbulence conditions in terms of boundary layer stability into six approximately equally represented classes ranging from class A, very unstable, through class F, very stable. He based values of the diffusion lengths for these classes on existing experiments and theory. Pasquill's diffusion lengths are limited to diffusion from surface-level sources, to downwind distances of about a kilometer over uniform, level, fairly smooth vegetation, and to averages over a few minutes. Near-calm wind, very stable conditions, specifically excluded from Pasquill's original classes, are now sometimes called class G conditions. These classes have been widely applied in atmospheric modeling, in the form of curves of a, and a, vs downwind distance suggested by Gifford (1961), and are sometimes called Pasquill-Gifford (PG) curves. Several alternatives for determining the stability class a t any given time and place are in use. Pasquill's original proposal, a classification scheme based on insolation, cloud cover, and wind speed conditions experienced in the U.K., was modified by Turner (1964) for use with standard U.S. National Weather Service airport observations; this is conveniently expressed in the widely-used STAR code (Holzworth, 1976). Various researchers have proposed classifying stability condi-

2.1 ATMOSPHERIC TRANSPORT MODELS

/

33

tions on the basis of us, the standard deviation of the horizontal wind direction, as measured by a windvane sensitive to turbulent fluctuations. Vertical temperature gradient, as measured between standard heights of 10 and 60 meters, is the method recommended in the U.S. Nuclear Regulatory Commission's Regulatory Guide 1.23 (USNRC, 1972). Stability classification based on the fundamental physical parameters known to characterize atmospheric boundary layer turbulence, i.e. Richardson's number Ri, the Monin-Obukhov stability length L, and convective scaling parameters, is recommended for instance in the report of an American Meteorological Society workshop (Hanna et al., 1977). The remarkable expansion of environmental concerns in the past decade imposes problem conditions far exceeding the inherent limitations to horizontally homogeneous terrain, short distances, steadystate, etc., of the above scheme. Applications are required for great horizontal distances, elevated sources, averaging times up to a year, near-calm, stable conditions, time-variable sources, terrain ranging in type from somewhat irregular to mountainous, and from forests and coast lines to cities. Few of these extensions are supported by really adequate experimental data of the quality and amount that was available to develop the original diffusion categories. Reviews by Gifford (1976), Draxler (1983), and Pasquill (1978) address the basic theoretical issues involved in such diffusion parameterization schemes. Draxler (1979) has summarized important recent atmospheric diffusion experiments aimed at selecting the appropriate diffusion lengths, a, and a,, in all of the above non-ideal situations. Horst, et a1. (1979) and Briggs (1983), among others, have re-examined both the classical and more recent experimental diffusion data sets in detail from the standpoint of contemporary boundary layer theory, in efforts to provide optimum a-parameterizations. Interim practical recommendations are summarized in the workshop proceedings reported by Hanna et a1. (1977) and Crawford (1978). 2.1.4.2

Variability of a, and a,

Residual Scatter The following examples from current literature indicate the residual scatter of u-parameters that can be expected, given optimum specification of atmospheric turbulence type. Figure 2.4 is a plot of measured vs predicted a, values based on three independent series of diffusion

34

/ 2. ASSESSMENT OF RADIONUCLIDES

2.1 ATMOSPHERIC TRANSPORT MODELS

/

35

experiments re-analyzed by Horst, et al (1979). These observations cover a reasonably full range of stability conditions, sampling distances to about 3 km but to 25 km in some cases, and flat prairie or desert terrain. Stability class in this particular example was determined according to the NRC guidelines (USNRC, 1972) by the vertical temperature gradient (AT/Az) method. The predicted a,-values can be seen to be scattered about observed values to within a factor of approximately 2. This scatter is appreciably reduced, to a factor of perhaps 1.6, if account is taken of the effect of the dimensionless quantity S = a,/(xe), which is a complicated, empirically determined function of concentration-averaging time and boundary layer turbulence (i.e., stability properties). Specification of a,

Correct specification of a, proves to be a difficult problem because of the marked stability variation and vertical inhomogeneity of turbulence in the boundary layer. Briggs and McDonald (1978) have reanalyzed the Prairie Grass series of diffusion data (on which the original PG-curves were largely based) on the basis of similarity theory. An example of their results for vertical dispersion is illustrated in Figure 2.5. The quantity u, is the friction-velocity of boundary-layer theory, and h is a scale height for diffusion, defined in terms of the crosswind-integrated ground-level concentration; h e Q (Jxdy)-'. In terms of an equivalent Gaussian distribution, a, = 0.8h, so the scatter of those points reflects the scatter of a,. The logarithmic standard deviation in this case indicates a scatter of a factor of 1.2 to 1.4. This is slightly smaller than the previous result for a,, and probably represents the best that can be achieved with this kind of research-grade experimental data.

Variation of a, and a, with Source Height

The diffusion lengths uy and a, were originally based on empirical concentration data from plumes released near the surface at a height of one meter. Later experiments, for example those discussed by Vogt (1977), and Nickola (1979), indicate a dependence of a, on release height. Hanna (1980) estimates that during the day a, varies only slightly with release height but that a, increases by a factor of about two as source height increases from the surface to several hundred meters.

36

/

2.

ASSESSMENT OF RADIONUCLIDES

Fig. 2.6 Example of resulta from Briggs and McDonald's (1978) analysis of Prairie Grass diffusion data. The curves show vertical dispersion, h, as a function of downwind distance, x; circles are stable values (positive values of stability length, L)and dots are unstable values (negative L-values). Curves illustrate theoretical results from similarity theory (after Brigge and McDonald, 1978).

Effect of Non-Ideal Experimental Conditions An example of diffusion data scatter in non-ideal experimental conditions is shown in Fig. 2.6. These are a,-values, computed by Draxler (1979) using a u8-stability method, from the rough-terrain, Mt. Iron diffusion data series (Hinds and Nickola, 1967). For these data, the scatter of the computed values is about a factor of 2 relative to the observations. For other non-ideal situations, i.e., diffusion at shoreline sites, in complex forests, over cities, at extremely low wind speeds, and at long ranges, data are generally too sparse to support a reliable estimate of scatter (Draxler, 1979). Most studies report only a few experimental values, measured over a range of stability classes. Scatter of diffusion-length estimates will almost certainly exceed a factor of 2 in these cases, and will probably lie somewhere in the range of 2 to 5.

The source height, k,in Eq. (2-2) is termed an effective source height to account for the initial buoyancy and momentum created by

2.1 ATMOSPHERIC TRANSPORT MODELS

/

37

or OBSERVED (Y)

Fig. 2.6 Predictions of a, for Mt. Iron aeries of diffusion experiments, based on wind direction fluctuation, vs observed values (after Draxler, 1979).

the emission of radioactive gases a t high temperatures or under high pressure (Briggs, 1969,1975;Briggs and McDonald, 1978). If the plume is sufficiently radioactive, its buoyancy will be continually augmented by the resulting "self-heating" (Gifford, 1967). Initial plume buoyancy is usually the dominant effect because of the small radioactivity content of most releases. The Gaussian Model accommodates the buoyancy effect by defining an effective source height, h, = h, + Ah, as the sum of the actual source height, k , and the buoyant plume rise, Ah. The practical importance of Ah in concentration calculations can be appreciated from the fact that most large, coal-fired power plants could not meet currently allowable ambient SOn standards without taking credit for Ah. Plume rise in these plants roughly doubles the effective stack height, greatly reducing surface-level concentrations. For radioactive sources, such as operating nuclear power plants, the buoyancy effect is smaller, and is in many cases, negligible. In buoyant rise, the heated plume is moving relative to the surrounding air flow. Small-scale wind shear occurs at the plume's edge (the resulting eddies can often be seen at the edges of power-plant or cooling-tower plumes). This is assumed to result in an entrainment of cooler ambient air into the plume, gradually reducing its buoyancy. The actual rise of the plume, relative to the ambient flow, tends to be a regular phenomenon because it is controlled by the velocity of

entrainment. The plume is a t the same time carried along and deformed by the turbulence in the boundary layer. Thus, the resulting estimates of Ah, and of downwind concentration where the plume reaches the ground, exhibit scatter. Some idea of its magnitude can be gained from Fig. 2.7(a) and (b) (Briggs and McDonald, 1978). Nondimensionalized values of maxium downwind ground concentration, 0.0010

I

" , .c

0

\ R

-

-n LL

?

. .. . A

0

m

0.004

-

0 x

-

E

0

X

0.002 1

2

.v

4

U

e

+( ~ ~ / h , ) h

Fig. 2.7(a) Maximum ground concentration, x,,, sionalized (after Briggs and McDonald, 1978).

0

88. qv

-

v

10

vs wind speed, u, nondimen-

STABLE V

UNSTABLE 0 NORTHFLEET V TILBURY

Fig. 2.7(b) Effective stack height, he,vs wind speed, u, nondiiensionalized (after Briggs and McDonald. 1978).

2.1 ATMOSPHERIC TRANSPORT MODELS

/

39

X,,, and he are plotted as functions of wind speed; h, is source height and Fb is the total plume buoyancy flux at the source. These data are for stable and unstable ambient conditions a t the Northfleet and Tilbury (U.K.) power plants, and are further identified and described in the reference. The actual data scatter in Fig. 2.7(b) is quite small, and the fit of the observations to the various theoretical estimates is good. The scatter of these particular data points is no more than a factor of 1.2. On the other hand, the figure represents a highly optimized level of analysis, not all of which is at present reflected in the usual model parameterizations of he.This is in part because the derived parameter he depends on basic parameters that are not all routinely observed. In particular, the surface heat flux, H, which is especially significant in the unstable, low-wind speed cases, could, for these data, only be estimated to be somewhere between 25 and 75 ~m'sec-~, implying an uncertainty in he of a factor of about 1.4, according to Briggs.

Deposition Velocity The amount of radionuclide deposition on various kinds of vegetation, food crops, and other surfaces is taken into account in models by defining a "deposition velocity," ud, such that the (dry) deposition flux, F D , of airborne material to the surface is given by, F D = ud ( X A - XR). The latter two terms are the bulk air concentration and that at the receptor surface, respectively. Wet removal, or precipitation scavenging, can be treated in a similar way in the case of gases. Precipitation scavenging of particles (as well as highly reactive gases) is treated as a n exponential removal process, not unlike radioactivity decay. Thus, wet removal involves both wet-deposition velocities, u,, and scavenging rates, A. Deposited material can also be picked up and carried aloft from the surface by the wind. The aerodynamics of this phenomenon is handled in a way analogous to the above handling of deposition, by defining a "resuspension rate." Typical values of all these parameters, and further details of the many, complicated physical effects involved, are presented in Section 2.2.

2.1.5

Variability of Concentration Estimates

Many evaluations of the output of particular atmospheric models, especially the ground-level concentration values, x ( x , y, 0), have been made over the years. However, the points of view and objectives of

40

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2. ASSESSMENT OF RADIONUCLDES

such comparisons have been as diverse as the models themselves. Some model developers have been content with qualitative comparisons with experimental data, such as time series plots, isopleth analyses, and scatter diagrams. Others have used a variety of statistical measures of quality of agreement, such as mean absolute deviation, standard deviation, standard error of estimate, correlation coefficients, and so on. Bornstein and Anderson (1979) have surveyed these various statistics as applied in model validations. Several authors have performed sensitivity analyses and some of these studies have been summarized by Rote (1980). A workshop jointly sponsored by the Environmental Protection Agency and the American Meteorological Society emphasizes the desirability of using non-parametric statistical specifications of concentration distributions (Fox, 1981). An American Meteorological Society committee has also evaluated the technical aspects of air quality models (AMS, 1981). As a general comment on these and related studies it can be said that analysis of the error properties of atmospheric models in realworld applications (as opposed to sensitivity analyses, where no comparisons with observed data are involved) is a t a very rudimentary stage. After a decade of intensive model buildmg, atmospheric scientists have only recently begun to consider such questions as "What is the best statistical measure of model output validity?" The more fundamental question, "How does the structure of a given model affect the propagation of parameter errors and errors in the model output," has, rather surprisingly, not yet been raised in the considerations of this group. For this reason it is at present possible to discuss the error properties of atmospheric model outputs only in fairly general terms. Considering observed input parameter variabilities similar to those in the examples of the previous section, Pasquill (1974) gave estimates of the uncertainty of diffusion predictions based on Eq. (2-2). This question was subsequently considered further by the American Meteorological Society's 1977 Committee on Atmospheric Turbulence and Diffusion, which issued a position paper, and more recently a t the workshop reported by Crawford (1978). The conclusions of the workshop are summarized in Table 2.3, and these agree with the earlier estimates of model uncertainty. Little and Miller (1979) also surveyed a number of validations of specific atmospheric models. These include Gaussian model results for short-period and short-range concentration estimates, monthly to annual averages, long-range values (to 140 km), complex terrain, and low wind-speed conditions, and three non-Gaussian examples. Tables 2.4, 2.5, and 2.6 were adapted from Little and Miller (1979) and summarize the results of this survey. Although, as these authors are

2.1 ATMOSPHERIC TRANSPORT MODELS

TABLE 2.3-An -- .----. .- . .- -

/

41

estimate of the uncertuinty associated with concentration predictions made by the Gaussian plume modeP Range of the Ratio Predicted Observed

Conditions

0.8-1.2 Highly instrumented flat-field site; ground-level centerline concentration within 10 km continuous point source 0.1-10 Specific hour and receptor point; flat terrain, steady meteorological conditions; within 10 km of release point 0.5-2 Ensemble average for a specific point, flat terrain, within 10 km of release point (such as monthly, seasonal, or annual average) b Complex terrain or meteorology (e.g., sea breeze regimes) "After Crawford, 1978. b T h e group that assembled these estimates did not feel there was enough information available to make even a "scientific judgement" estimate under these conditions. -

TABLE2.4-Some

-

ualidation results for ensemble auerages predicted by the Gaussian plume mo&P Conditions

Range of the Ratio Observations Predictions

Annual average SO2concentrations for b a n e County, Tennessee; both point and area source emissions included

0.5-2.0

Continuous gamma-ray measurements 0.04-6.8 km downwind of a boiling water reactor

0.56-3.0

Gamma-ray doses downwide of Humboldt Bay Nuclear Power Plant

0.5-2.0

Monthly gamma-ray doses for four stations downwind of a nuclear power plant a t a n inland site

0.21-3.3 individual stations 0.65. mean of all data

Short term surface level releases of fluorescein particles under thermally stable atmospheric conditions a t Hanford, Washington

0.2-5.0.72% of samples

Short term SF6 releases from a 36-m high stack under stability categories B through F at the Rocky Mountain Arsenal, Denver, Colorado

0.33-3.0.8976 of samples 0.1-10,100% of 'samples

"From Little and Miller, 1979.

careful to point out, "not enough model validation studies have been performed to allow for a reliable statistical analysis," their results are important for several reasons. The data assembled, although sparse, represent the current state of the art. Moreover, these results generally

42

/

2. ASSESSMENT OF RADIONUCLIDES

TABLE 2.5-Validation results for Gaussian plume model predictions at distances to 140 km' Ran of the Ratio ~%ervations Predictions

Conditions

=Kr measurements 30-140 km downwind of the Savannah River Plant Weekly and annual averages Seasonal averages: Spring

0.25-4 0.25-0.5, 69% of samples 0.1-0.5, 100% of samples

Summer

0.25-2,46% of samples 0.1-2,85% of samples

Fall

0.25-2,31% of samples 0.1-2,85% of samples

Winter

0.25-0.5,69% of samples 0.1-0.5,92% of samples

Annual average

0.25-1, 77% of aamples 0.1-10,79-95% of samples

10-hour averages, six variations of the model

0.5-2.4245% of samples 0.1-10,79-95% of samples

" From Little and Miller. 1979. TABLE 2.6-Some validation results for Gaussian plume model predictions in both complex terrain and also under low wind speed inversion conditiod Conditions

Ran of the Ratio ~T~ervations

Predictions

Review of a number of experiments conducted in complex terrain for plume centerline concentrations

0.003-100, individual measurements close to the source 0.50-2, ~ 2 - 1 5krn downwind of source

Review of a number of experiments conducted under low wind speed, inversion conditions Smooth desert-like terrain Wooded flat terrain Wooded hilly terrain

'From Little and Miller, 1979.

Stability Category F G E 0.1-0.43 0.08-0.77 0.05-0.28 0.04-0.05 0.03-0.05 0.0334.05 0.003-0.02 0.002-0.003

2.2 RADIONUCLIDE DEPOSITION AND RESUSPENSION

1

43

agree with the earlier uncertainty estimates, which were largely based on the judgement of experts. Table 2.4 shows that the variability of short-term, short-range Gaussian model predictions ranges from factors of approximately 3 to 10, depending on sample percentage but that this decreases to factors of 2 to 4 for averaged data. Estimated average values of the predicted/ observed ratios for these cases indicate little or no model bias. For the long-range (Savannah River) experiments of Table 2.5, the variability of the Gaussian model output ranges from factors to 1.4 to 4 for various averaging periods, except that 10-hour averages for six different versions of the model show scatter by factors of from 2 to 10. Averaged ratios for seasonal concentrations in this table reveal a consistent bias, the reason for which is not well understood. Table 2.6 shows that, except for complex-terrain applications very close to the source, the variability of the remaining Gaussian model applications ranges between factors of 1 and 3. This is particularly interesting in the case of the light-wind, stable experiments, all of which have large biases that seem to increase sharply with terrain irregularity and slightly with increasing stability. The trajectory, particle, and grid models exhibit about the same amount of scatter as the Gaussian models when applied to the same (Savannah River) data, and are similarly unbiased, as Crawford (1978) has previously noted. 2.2 2.2.1

Radionuclide Deposition and Resuspension

Deposition

Dry Deposition Models

The dry deposition velocity, ud, relates the concentration, x , at some specified height (usually 1 meter) above the surface to the dry deposition flux, Fd, to the surface.

The dry deposition velocity includes effects of both atmospheric and surface processes between the reference height and the depositional surface. Current models for dry deposition fall short of a complete inclusion of all major recognized factors. Although specific mechanisms may

44

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2. ASSESSMENT OF RADIONUCLIDES

differ, the overall processes for dry deposition of gases and particles are similar enough to allow generic discussion. Ideally, input to a dry deposition model should be situation specific; controlling properties such as particle size distribution, solubility, roughness length, and displacement height should be used to predict the removal rate, rather than an invariant deposition velocity. Based on review of current models, there are two aspects of dry removal computation that may be improved in consequence models. These involve inclusion of the effect of the deposition-developed vertical concentration profile and a consistent definition of the magnitude and reference height of normalized dry deposition parameters. Dry deposition processes are conveniently separated into atmospheric and surface processes. This approach in different formats has been suggested by a number of authors. Actual dry deposition consists of a continuum of processes between the atmosphere and surface; division is accomplished by definition of a reference height. T h e specification of a reference height is basic to any proposed model. Atmospheric processes involve the delivery of material to the surface by the movements of the atmosphere. Surface processes such as impaction and sorption control the dry removal a t the receptors. Depending on ambient conditions and the characteristics of the depositing material, either the atmospheric or surface processes may be limiting. The modeling of these processes as resistances to dry deposition is a powerful alternative approach to the deposition velocity approach. The atmospheric resistance, r,, plus the surface resistance, r,, are equal to the total resistance, r,:

The deposition velocity is the inverse of the total resistance a t any reference height. The resistance approach is useful in understanding the processes controlling dry deposition. The question of the proper height for division of atmospheric and surface resistance is not a trivial problem. Failure to account for variation of these resistances as a function of height can lead to errors in dry deposition computations. The depth of the depleted plume will vary from case to case. The surface sink for a material results in the development of a vertical concentration profile with progressively lower concentrations near the surface. This directly influences the dry deposition computation and makes the consistent choice of heights and dry removal rates necessary. Literature data for dry deposition have been generally reported as deposition velocities relative to a one-meter reference height. As such,

2.2 RADIONUCLIDE DEPOSITION AND RESUSPENSION

/

45

these data contain information on both the atmospheric and surface processes under the reference height, but do not include information on atmospheric processes above the reference height. The current Nuclear Regulatory Commission (NRC) consequence model (USNRC, 1977a) allows for the mass of material removed by dry deposition by decreasing the total mass,in the plume a t progressive downwind distances. Since the reference height is defined as the division between surface and atmospheric resistances, the logical approach is to use a height near the surface. The wind profile can be used to define the height for which wind speed effectively is zero. This height, the roughness length, Zo (or displacement height for higher tree canopies), provides a consistent basis for separation of surface and atmospheric dry deposition processes based on an assumption of similarity of wind and airborne material profiles. It is beyond the scope of this report to define models for specific particles or gases (except for iodine which is presented below). Each should be considered on a case-by-case basis. The relative importance of atmospheric and surface processes defines the configuration and detail for a specific substance. For example, for materials that have a relatively low dry deposition rate, the atmospheric terms will be much less important than for a material with a higher deposition rate. Horst (1977) has developed a model for correction of the Gaussian plume model for the surface depletion of nonsettling particles. Although perhaps the most precise approach, this model requires considerable computation and applications are restrictively expensive. To overcome this problem, a hybrid source depletion model has been derived that allows for the surface depletion effects (Horst, 1978). This source depletion model compares quite well with the surface depletion model and has computationally reasonable algorithms. This simpler model reduces the source strength in the Gaussian model as a function of downwind distance to account for both the loss of airborne material and to account for the change in vertical profiles. The hybrid source depletion model may be applied in two ways. Either the approximation equation given by Horst (1978) is evaluated for each site, or a set of nomograms may be developed for generic application. The inclusion of the profile effects will significantly improve the estimates of surface flux, particularly for the more rapidly depositing materials. The model allows separate input of atmospheric and surface effects. Horst's profile approximation is the atmospheric resistance term. This model of the atmospheric processes includes both the ambient atmospheric and local surface characteristics. The procedure for defining a surface deposition velocity (given in

46

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2.

ASSESSMENT OF RADIONUCLIDES

Horst's paper) requires the definition of a deposition velocity a t a known height. The estimation of appropriate surface dry deposition velocities is an area where considerable improvement may be made. Sehmel's wind-tunnel study of particle deposition rates over various surfaces is one example of data for estimating surface deposition velocities. Gaseous, as opposed to particulate, dry deposition appears to depend on factors such as surface area, surface moisture, stoma openings, etc. Sehmel (1980) lists over 50 possible factors that enter into the determination of dry deposition velocity. These various factors need to be considered on a site-specific basis. From the wind-tunnel tests, Sehmel and Hodgson (1976, 1979) derived a generalized technique for estimating dry deposition of particles, which is only dependent on particle diameter, particle density, stable atmospheric roughness height and friction velocity, u* (see Section 2.1). This model describes particle motion in the atmosphere by a multidimensional, nonsteady-state continuity equation which can be represented by a three-box deposition model as a function of height above the surface. The first box represents the airborne vertical movement of the particles, which is described by standard meteorological diffusion equations. The second box represents the region just above the vegetative canopy or surface elements in a region where atmospheric transfer processes are modified by the canopy or surfaces. The third and final box is a t and within the deposition surface canopy. In the model, mass transfer resistances are calculated to describe the particle flux through the boxes from the reference concentration height (1meter) to the surface. The concentrations and fluxes are conserved a t the boundaries between the boxes (see Fig. 2.8). The results of the model computations are presented as graphs of deposition velocity a t one meter above the surface versus particle diameter (Sehmel, 1980). A typical graph is presented in Figure 2.9 for a particle density of 2.5 g cmP3,a friction velocity of 30 cm s-' and roughness heights from 0.001 to 10 cm. Sets of curves dependent on other particle densities and friction velocities from 10 to 200 cm s-' are given in Sehmel(1980). Table 2.7, adapted from the cited reference, gives surface roughness heights and friction velocities for various surfaces. Note the wide variation of surface roughness height with the type of surface. An alternate model for estimation of dry deposition of reactive gases onto a plant canopy has been presented by Heinemann and Vogt (1980). They define the deposition velocity of iodine by the semiempirical equation: vd =

ADu,F

(cm s-l)

(2-6)

2.2 RADIONUCLIDE DEPOSITION AND RESUSPENSION

/

47

Fig. 2.8 Conceptual three box model. (From Sehmel and Hodgson, 1976.)

where A = a quality factor (cm2 g-') representing a change in the plant canopy during its growing season which also incorporates a proportionality factor, D = areal density of the plant canopy in dry mass per unit ground surface area (g-dry cm-'), u, = the friction velocity (cm s-I), and F = the relative humidity (unitless).

From data derived in a series of experiments on grass and clover a t the Jiilich Nuclear Research Center, the above cited investigators were able to estimate an average u, = 26 cm s-' and A = 5.6 cm2 g-'. Other experiments in Germany gave D = 0.017 g cm-2 and F = 0.79 for Julich. The resulting product of these values gives a v d of 2 cm s-' for iodine vapor deposition on dry grass during the grazing period. Correcting for periods of high moisture on the grass such as early morning or during the night, a value for ud was obtained of 3 cm s-'. Preliminary investigations of the value of u d for elemental iodine attached to particles gives a value of 0.1 cm s-'. The above model concerns elemental iodine and not organic iodine compounds which may have a deposition velocity orders of magnitude less.

48

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2. ASSESSMENT OF RADIONUCLIDES

-

I

I

l

l

I

l

l

I

l

l

I

-

STABLE ATMOSPHERE WITH

20 (cm) 10

-

-

-

-

-

-

-

I

10-3 10-2

I

I

I

I

l

lo-'

l

I

l

l

I

1 o2

10

1 PARTICLE DIAMETER (pm)

Fig. 2.9 Predicted deposition velocities at 1 m for u, = 30 cm s-' and particlz -~ from Sehmel, 1980). density of 2.5 g ~ r n (adapted

TABLE 2.7-Aerodynamic surface roughness heights, z., and friction velocities, u - , for wind speeds, y of I and 5 m s-I at 2~metersabove the surface' Surface z.(cm) u,,(m 8-'1 Fnr

For

Smooth mud flata, ice Smooth snow or short grass

0.005

0.038

0.19

Smooth sea

0.02

0.043

0.22

Level desert

0.03

0.045

0.23

0.15

0.73

Mown grass 1.5 cm 3 cm 6 cm

60 cm

Long grass 60-70 cm Fully grown root crops

'From Sehmel, 1980.

14

/

2.2 RADIONUCLIDE DEPOSITION AND RESUSPENSION

49

Table 2.8 shows the wide range in experimental determinations of dry deposition velocities onto various media during varied atmospheric conditions for the various elements discussed in this report. Along with the ranges the values typically used in radiological assessments are listed. Note the exceedingly wide range of values reported for plutonium particles and for iodine in gaseous form-over three orders of magnitude. The wide ranges in deposition velocity are due to measurement technique as well as normal variation.

Wet Deposition The washout of particles and gasses from the atmosphere may, in some cases, be a significant contributor to ground deposition of the materials. Washout is defined as the scavenging of particles and gases by precipitation from a cloud. The deposition resulting from this process can be described by a "wet deposition velocity," v,, analogous to the dry deposition velocity discussed above. For particulate and gaseous material:

where

W = wet flux (pCi m-2s-'), and level air concentration of radioactive material (pCi m-3).

xo = surface

TABLE 2.8-Dry deposition velocities for selected elements in cm S-' Element

Cobalt Strontium Ruthenium Iodine Cesium Plutonium Uranium Radium

Fom

Particle Particle Particle Gas Particle Particle Particle Particle

Range

0.3-1.9" 0.002-0.01" 0.02-2.3' 0.02-26' 0.04-0.6' 0.0026-0.0 1 8 ~

. 0

Value

Typically Used 0.1' 0.1'.~ 0.1' lC 0.1' 0.1' 0.1' 0.1'

" Sehmel (1980) Craig et af. (1976) Soldat et al. (1974) Note that although the high value of the range for strontium is only 0.01 cm 8-l, the generic value for particle deposition velocity of 0.1 cm s-' is generally used in assessments " Range not available

50

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2. ASSESSMENT

OF RADIONUCLIDES

The wet flux may be estimated from two parameters: scavenging rate coefficient, $,, and washout ratio, w, (Slinn, 1978). The scavenging rate coefficient is usually defined as:

where

k = rate of removal of material from the air per unit volume (pCi m-3s-1), and

x = local air concentration of material (pCi m-3). The scavenging rate can be looked upon as analogous to the radioactive decay rate. It may be calculated from the collection efficiency of the precipitation (Slinn, 1978; Dana, 1980) or, alternately, derived from experimentally determined rain spectra (Dana and Hales 1976). The latter approach is more suitable for the accident case, because the parameters used to determine $, are measured during specific precipitation occurrences and not from averages over many days. A more suitable model for estimating wet deposition of long-term chronic releases of radionuclides is the washout ratio, w,. The washout (or scavenging) ratio is defined as the ratio of precipitation phase to air concentration of contaminant, with the concentrations normally evaluated a t the surface (Dana, 1980). For radioactive materials: xr w, = -

(unitless)

xo

where X, = concentration

of radionuclide in precipitation a t the surface (pCi mc3), and xo is as defined above.

The washout ratio is much more easily measured than the parameters of the scavenging rate coefficient. In essence, the washout ratio represents an integral of the scavenging rate and associated space dependent parameters over height z:

where x(z) = atmospheric air concentration as a function of height (pCi m-3), and

2.2 RADIONUCLIDE DEPOSITION AND RESUSPENSION

/

51

po= precipitation rate (rainwater equivalent) at the surface (m

s-I). The wet flux, W, may be given in terms of the washout ratio, w,: Then from Equations (2-7) and (2-11) the wet deposition velocity is: The wet removal of reactive gases (non-noble gases) depends on their chemical properties including solubility and gas and liquid transfer rates in addition to the rainfall rate and raindrop spectra. For gases that form simple solutions in water and are at equilibrium, the washout ratio is just the reciprocal of Henry's law constant, H. Washout ratios of particles and reactive gases may be obtained from values given in the literature (Slinn, 1978; Englemann, 1968; Dana, 1980). Table 2.9 shows the ranges of long-term average washout ratios for some representative materials. The washout ratio method, when used for long-term chronic type releases, is generally accurate to a factor of 2 using site-specific annual average data (Slinn, 1978). By the use of Eq. (2-12), and using an annual average PO,the wet deposition velocity may be approximated for washout on an annual basis. As an example, consider a site with an annual precipitation rate of 100 cm y-' (typical of the midwestern United States). Find the wet deposition velocity for iodine gas which has a washout ratio of 1000 (Table 2.9).

Thus, on an annual basis, u, is two orders of magnitude less than the typically used dry deposition velocity for iodine gas of 1.0 cm s-' (Table 2.8), so can, in general, be ignored in any radiological assessTABLE 2.9-Measured washout ratios for selected materials Material

had Iron Sodium Fallout Iodine Gas Calcium Manganese Chlorine

W.

Reference

Slinn, 1978 Slinn, 1978 Slinn, 1978 Slinn. 1978 Slinn, 1978 Dana, 1980 Dana, 1980 Dana. 1980

52

/

2. ASSESSMENT OF RADIONUCLLDES

ment. However, for short time periods during a rainfall, the wet deposition may indeed be greater than the average deposition rate. 2.2.2

Resupension

When a relatively insoluble material such as a long-lived radionuclide has been deposited on the ground, it may again in time be "resuspended" into the air and thus become a significant contributor to the inhalation or food chain pathway doses to persons long after the source term has ceased to exist. In addition, contaminated areas such as tailings piles, may erode through wind and water action thus spreading material over a large area, later to be resuspended. This resuspension process may be carried on by various mechanisms such as rainfall, winds, human and animal activity. The amount of material resuspended will depend on a great many parameters, as does the deposition process. Among the primary parameters are the nature of the surface, the age and chemical properties of deposited material and the magnitude and duration of wind, rain and other physical disturbances. Various models describing resuspension processes have been proposed. The earliest of these dealt more with the physics of particle interactions and forces between them. See the review article by Slinn (1978) for a summary of the complexities involved. Because of the uncertainty of these micro scale mechanisms over wide areas, more empirical models have been developed. Today two models are generally used: mass loading and resuspension factor. However, a third model, still under development, resuspension rate, may potentially be more useful (Healy, 1980).

Mass Loading In this model the amount of resuspended material in the air is estimated by measuring its concentration in the soil and the mass loading (concentration) of soil particles in the air above. Hence, the air concentration of the material of interest x, is given by: where

C, = concentration of the material of interest in soil (pCi pg-I), and C, = concentration of particulate matter in air (pg m-3).

2.2 RADIONUCLIDE

DEPOSITION AND RESUSPENSION

/

53

This mass loading method is primarily applicable to those instances in which the material of interest is mixed uniformly within the top 1 cm or more of soil. For instance, many years after the deposition of radioactivity, measured values of C, have been reported for various locations of the United States. They range from 9 to 79 pg m-3 (NAPCA, 1968). However, a value for C, of 100 pg m-3 has been recommended as a generic value for predictive purposes (Anspaugh et al.,1974). Although the above method has been used effectively for sites with aged deposits of material which have been mixed into the soil, it has not given realistic results when used to predict resuspension from relatively fresh layers of contaminant on the soil surface. Another deficiency of the mass loading method is that the implicit assumption that soil and contaminant are resuspended equally may be invalid in many instances (Linsley, 1978).

Resuspension Factor This model has been developed from studies of soil and air contamination after nuclear bomb testing in the southwestern United States. The resuspension factor K(t) is defined as a function of time after a contaminant was deposited on the soil surface.

where = air

concentration of resuspended activity at time t after the deposition has been completed (pCi m-3), and = surface deposition per unit area (pCi m-*). A simple exponential decay model was first proposed by Langham (1969,1971) and Kathren (1968): (m-'1 (2-15) K(t) = K(0) exp(-ln 2 t / k ) where K(0) = initial resuspension factor at time t = O'(m-'), t, = weathering half-time (d), and t = time after initial deposition (d). Stewart (1964) and Mishima (1964) have compiled measured values to of K(0) from various experiments and found a range of from m-'. m-'. However, only a few values were greater than Sehmel (1980), in a review of the literature has found mechanically-

54

/

2. ASSESSMENT OF RADIONUCLIDES

m-' and wind-caused factors caused factors ranging from lo-'' to ranging from to m-'. Weathering half-times of from 35 to 70 days have been measured from experiments lasting several weeks after deposition.' After long times, up to about 20 years after deposition, Eq. (2-15) drastically underestimates the resuspension factor. This phenomenon led Anspaugh et al. (1975) to develop a variation of this equation. From empirical data Anspaugh approximated the resuspension factor as: where X = a n empirical factor of 0.15 d-I/'. The second term was added based on the assumption that there would be no further decrease in the resuspension factor after 17 years. This period is the longest time after deposition for which measurements have been reported according to Anspaugh et al. (1975). This long-term component i: derived from limited experimental observations of resuspension of plutonium from undisturbed surfaces at nuclear weapons test sites in semi-arid conditions (Anspaugh, et al., 1975). The model used in the "Reactor Safety Study" (USNRC, 1975) is similar to Eq. (2-16), but with modifications to the time dependent term.

K(t)=10-5exp(-ln2t/0.977)+10-9 ( m ) (2-17) Here t is in years. The environmental half-time used is 0.977 y or about 50 weeks. However, K(0) has been lowered an order of magnitude from Anspaugh's formulation (Eq. 2-16). Another variation of this basic model has been used in the Liquid Metal Breeder Reactor Final Environmental Statement (USAEC, 1974) and the NRC UDAD code (Momeni et al., 1979). In this model K ( t ) is calculated for two periods: K(t)

=

loe5 exp(-ln 2 tlt,)

(m-I)

for t 6 664 d

and K(t) = lo-'

m

)

for t > 664 d

(2-18)

In Eq. (2-18), t, is taken to be 50 days, which is about midway between the two extreme values of 35 and 70 days. For a critical examination of these two models also see Lassey (1980).

'

These weathering half times derived from experimental measurements appear to some investigators as questionable (Sehmel, 1980); however, it appears that it is reasonable to expect that the resuspension source availability will decrease in some manner with time.

2.2 RADIONUCLIDE DEPOSITION AND RESUSPENSION I

I

I

I

I

1

/ I

55

-

-

-

REACTOR SAFETY STUDY (Eq. 2-17)

\

-

-

'4

-L/ UDAD (Eq. 2-18) -

-

/\

ANSPAUGH

-

et

-

al. (Eq. 2-16)

-

<-------\

-

-

-

I

I

I

I

I

I

20 25 30 (years) Fig. 2.10 Comparison of resuspension models as a function of time after deposition.

0

5

10

15

TIME SINCE DEPOSITION

Fig. 2.10 describes the dependence of the resuspension factor on time for the Anspaugh, Reactor Safety Study, and UDAD models. For times greater than 25 years after the deposition, they give essentially the same result: lo-' m-'. For times less than 25 years, the models vary greatly-especially for short times. Since the measurements data have such a wide variance due to the many factors involved, more precision for the model parameters will be hard to produce. It should also be pointed out that most of the measurements leading to these values were obtained in studies of dry, western regions of the U.S.,

56

/

2. ASSESSMENT OF RADIONUCLIDES

such as the Nevada Test Site, and may not be applicable to regions with greater moisture and ground cover. In addition, any subsequent disturbance of the ground such as farming, building, etc. may result in higher temporary resuspension factors than predicted. Also, the depth a t which soil samples are taken when measuring surface contamination may contribute a large variation in the resulting calculated surface concentration. It has been suggested that the uncertainty in the measured resuspension factors owing to the variability of soil concentration may be as high as two orders of magnitude (Anspaugh et al., 1975). The air concentration due to the resuspended material now can be calculated from Eq. (2-14): This resuspended air concentration then may be used to re-evaluate inhalation doses and concentrations in food crops, etc. using the appropriate deposition velocity method discussed in the previous sections.

Resuspension Rate The resuspension rate, A, is usually defined as A = fraction of the contaminant on the ground

(2-20)

that is resuspended per unit time (s-') The resuspension rate may be multiplied by the amount of contaminant in the soil of an area to produce a source term, Q, which may then be used in the various atmospheric diffusion equations discussed in Section 2.1. The air concentration downwind from the region of resuspension motion would then be:

when 0 = amount of contaminant in region (pCi) X

-=

Q

atmospheric dilution factor a t receptor point (s m-3).

Healy (1977) summarizes some typical experimental values for the resuspension rate of plutonium particles. For wind resuspension, values vary between 2 x 10-l2 t o 1 x s-', whereas those produced by mechanical disturbance, yield values from 3 x lop9to 1 x s-'; the latter values being due to normal operations a t a farm near the Savannah River Laboratory.

2.3 TERRESTRIAL TRANSPORT AND BIOACCUMULATION

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57

2.3 Terrestrial Transport and Bioaccumulation in Terrestrial Food Products Examination of terrestrial transport of radionuclides through the food chain to people is concerned with the study of the characteristics of various media along this pathway and the transfer and bioaccumulation factors which connect the media together. Radionuclides may be transported to vegetation by air or water. They may be deposited directly onto plants themselves through direct deposition and/or resuspension or taken up through the plant's root system from the soil onto which previous deposition has occurred. The plants or parts of them may be directly eaten by man or consumed by animals, which directly, as in the case of steers, sheep, etc. or indirectly, as in the case of milk cows, provide food for man. The following sections describe some typical models used and the parameters involved along with the values of these parameters, which may be used in a generic sense when specific site data are not available.

2.3.1

Transfer to Vegetation

The transfer of radionuclides from air and soil to vegetation has been usually estimated by two general models: transient model steady-state model.

Transient Model In the transient or dynamic model approach the plant, air, soil, etc. are considered as compartments containing varying amounts of radioactivity. The model then becomes a system of linear differential equations which describe the rate of change of the amount in each compartment as a function of the various transfer paths into and out of it. The general formula for these equations for a system with radioactive decay is given by:

where j is the compartment of reference and i designates all other compartments. The Xij and Xji represent the transfer coefficients in units of reciprocal time. The first term on the right represents all the flows entering compartment j; the second term represents all the flows

58

/

2. ASSESSMENT OF RADIONUCLIDES

leaving j. The constant, Xi, accounts for the radiological decay of activity in compartment j. The term Pj represents the input into compartment j from outside the system in units of activity per unit time. When the equations are integrated over long times with constant values of the Pj, the radionuclides in the various compartments approach constant concentrations. The system then is considered to be in equilibrium or in a steady state. An example of this approach and one of the early models developed especially for radionuclide transfer in the environment is given in Booth and Kaye (1971). Fig. 2.11 shows the multicompartmental system which was programmed for computer processing under the name of TERMOD. Here the input is from fallout and the final compartment is man. The rij represent the transfer coefficients between the compartments.

SUBSURFACE

SOIL POOL FOR

INPUT TO rvlm ~ ( ~ c i / d o y )

1

Block Diagram of the Terrestrial Food Pathways. Fig. 2.1 1 Block Diagram of the terrestrial food pathways (from Booth and Kaye, 1971).

2.3 TERRESTRIAL TRANSPORT AND BIOACCUMULATION

/

59

Later models have concentrated on estimating the concentrations in various subcompartments of soil and plants, and thus are much more complex. Needless to say, they have to be programmed for computer processing. Comprehensive discussion of transient models is given in ICRP 29 (ICRP, 1979). Examples of the more complex codes are given in Schreckhise (1980); Gallegos et al. (1980); Simmonds et al. (1979); Martin and Bloom (1980); and Garten et al. (1980). These models, when properly applied, and for which the transfer parameters have been carefully selected, give reasonable results for pulsed inputs of radionuclides and, after a reasonable integration time, give results similar to the more simple steady-state models.

Steady-State Model The steady-state or equilibrium model discussed here was developed by Soldat and Harr (1971) for a study of the potential radiation doses to people from nuclear facilities situated in the upper Mississippi River basin in the year 2000. A simplified version of the model was developed for ease of estimating doses for the various power reactor environmental statements published by the AEC/NRC (Soldat et al., 1974; Baker et al. (1979); Martin and Bloom (1980); and Garten et al. (1980). These models, when properly applied, and for which the transfer parameters have been carefully selected, give reasonable results for pulsed inputs of radionuclides and, after a reasonable integration time, give results similar to the more simple steady-state models. The approach was similar to that of Russell (1966) and others in that a relatively simple equilibrium model was developed to include the primary parameters controlling the uptake of radionuclides (except tritium and carbon-14) in plants. The model is composed of two components. The tirst describes the direct deposition of radionuclides onto plant foliage from air and in the case of sprinkler irrigation, water; and the second accounts for later uptake through the roots to the plant of long-lived radionuclides previously deposited on the ground. For short-lived nuclides such as 1311, the first component is generally of greatest concern; however, for certain long-lived nuclides and long buildup periods, the second component can control plant concentrations at a point in time, but not necessarily total accumulated dose in humans. The addition of these two components defines the total concentration, at the time of harvest, of a radionuclide i in the edible portion of the plant v in pCi kg-'; hence CiV= C,",+ C:

(pCi kg-')

(2-22)

60

/

2.

ASSESSMENT OF RADIONUCLIDES

where

C: =concentration of radionuclide i in edible portion of plant v through direct deposition (including that of resuspension) on foliage (pCi kg-'), and =concentration of radionuclide i in edible portion of plant v through soil to root uptake (pCi kg-').

cv

The expression for the concentration due to direct deposition is given by:

c:

d i f ~ T i v1 =-

yv

- exp(-X~it,)

(pCi kg-')

(2-23)

x ~ i

where d; = deposition rate or net flux of radionuclide i from the air to the ground surface (pCi m-'d-I), f R = interception fraction. The fraction of deposited material intercepted and immediately retained on foliage (dimensionless), Ti, = translocation factor. The factor for the translocation of externally deposited radionuclide i to edible parts of plants (dimensionless), Xi = radioactive decay constant of radionuclide i (d-I), and h ~ =i effective removal constant of radionuclide i from plant (d-I). X E ~ = XI + 0.693/tW,where t, = weathering half-life-the time required for l/z of the originally deposited material to be lost from the plant. t. = time of above-ground exposure of crop to contamination during growing season (d). This parameter would vary with plant type but would be around 60-90 days on the average. Y,, = standing plant biomass a t harvest (edible portion). The mass of the portion of the plant growing above a unit surface area (kg m-'). A few comments should be made to clarify the use of some of the above parameters (see Fig. 2.12). The deposition rate or net flux of radionuclide i from the air to ground surface may be calculated in various ways. The most common method is:

where Q: = release rate of radionuclide i (pCi d-I), (?/Qf) = atmospheric dilution factor (s m-3), and udi = deposition velocity of radionuclide i (m s-') (discussed in Section 2.2).

2.3 TERRESTRIAL TRANSPORT AND BIOACCUMULATION

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61

Fig. 2.12 Schematic of two component equilibrium model showing the parameters involved in direct deposition and uptake from soil.

Another method of calculating diis through the use of the parameter called the relative deposition factor, Si (m-2): Values of di are found in tables given in NRC Reg. Guide 1.111 (USNRC, 1977a). Also 6i may be calculated directly from the NRC Computer program XOQDOQ (Sagendorf and Goll, 1977). The value of the interception or retention fraction, fR,depends upon the nuclide, the type of plant material (and its density), and on how the deposition rate or flux was calculated. If diis calculated as the flux to the whole surface area of the ground, fR is then that fraction of this material intercepted and retained by the plant; however, if di accounts only for that flux impinging on plant surfaces, then f~ should be set to unity. Although the retention surface depends upon radionuclide and vegetation type, f~ is usually taken to be about 0.2 for wet and dry deposition of particles and 1for reactive gases such as iodine (USNRC, 1977b). Also, the translocation factor Ti,, although a function of both the particular nuclide and food type, is usually either set to unity for all cases (USNRC, 197%) or set to unity for leafy types of vegetables and to 1/10 for all other foods (Baker et al., 1976). This is because of the lack of data to determine this parameter adequately. Retention of particles on plant surfaces has been modeled by using a single exponential function incorporating a weathering half-life of

62

/

2. ASSESSMENT OF RADIONUCLIDES

around 14 days (Russell, 1966; Soldat et al., 1974; USNRC, 1977b). However, some investigators have concluded from experiments that for some crop types a variable weathering half-life would in many instances supply a better fit to the data (Miller, 1966; Krieger and Burmann, 1969). These investigators found that in the first few weeks, a weathering half-life of around 14 days would fit their data fairly well, but for longer growing periods, a much longer weathering half-life would be more appropriate. In fact, a small fraction of the deposited material may be retained for the life of the plant. Therefore, because retention varies widely with particle size and for various types of plants, shapes, sizes, and surface characteristics (smooth, irregular, hairy, spiny, etc.), there is wide variation in the experimental data (Cataldo and Vaughan, 1980). For this reason, a more refined model than a single exponential function does not seem to be warranted at present. The other component of uptake of radioactive materials by the plant is from the soil through the root system. This component becomes more important for certain long-lived nuclides and for deposition on and buildup in soils over an extended period. This component is given as the relation:

c =diBivp(1 - exp(-Xsitd) XB~

(pCi kg-')

(2-26)

where Bi, = concentration ratio for plant uptake of nuclide i from soil (pCi kg-' plant per pCi kg-' dry soil), see Section 2.4 for discussion of values, tt, = time for buildup of radionuclide in soil (d) depends on the duration of the deposition (for example, the operating lifetime of a nuclear facility-30-40 years), P = soil "surface density" the soil density divided by the depth of the plowed layer (kg dry soil m-'), see Section 2.4 for discussion of values, and Xgi = effective removal constant of radionuclide i from soil (d-'). In both of the above equations, the concentration is given per unit plant mass, which can be either on a fresh (wet) or a dry basis. Thus, if the standing biomass, Yv, is given on a fresh basis, then Ci, will also be on a fresh basis and vice versa. Similarly, if the concentration ratio, Bi,, is given on a fresh mass basis (for the plant), the Cj,will be on the same basis. Normally, soil surface density is given on a dry basis. Thus, it is imperative that the basis of these parameters is known. Generally, the dry mass is about 25% of the wet mass, so the param-

2.3 TERRESTRIAL TRANSPORT AND BIOACCUMULATION

/

63

eters may be converted from one basis to the other using this factor if required. A more complete listing of dry mass to wet mass ratios can be found in Till and Meyer (1983). In addition, the concentration ratio, Biv,is dependent on the plant part. Schrechkhise and Cline (1980) found that concentration ratios for Pu, Am, and Cm in barley seeds were 30-50 times and Np 5 times lower than in the entire plant. Pea seeds were some 70-230 times lower for Pu, Am, and Cm and 30 times lower for Np with respect to the entire plant. Thus, for dose estimates, the concentration ratio for the plant part that is ingested should be used. The effective removal rate from soil of a radionuclide used in Eq. (2-26) has usually been approximated by equating it to just the radioactive decay constant, Xi (USNRC, 1977b; Baker et al., 1976). For concentration ratios less than unity and for buildup times less than 100 years, this simplification has been reasonable. However, for long buildup times on the order of thousands of years and very long-lived nuclides (as in the cases of some waste-storage leaching scenarios), this simple approximation tends to be overly conservative, in that it predicts plant concentrations much higher than considered reasonable (Schreckhise, 1980). Thus, the inclusion of other losses into the equation is advisable. A loss constant may be derived for each loss mechanism so that the effective loss constant, Aei, includes more than one component. Two such losses are removal of radionuclides from the soil through harvesting and the leaching of radionuclides out of the root zone by water (this would include overwatering in the case of irrigation). Harvest loss has been discussed by Schreckhise (1980) and Hoffman and Baes (1979). Hoffman and Baes propose the relation for the loss constant due to harvest to be:

where

MH

= the

harvested biomass of vegetation per unit surface area per harvest (kg m-'), that amount of plant material which is removed during harvest and not returned to the land for recycle, and H,, = the number of harvests per year (assuming harvesting to be a continuous process occurring a t uniform intervals).

In Eq. (2-27) the concentration ratio, Bi,, should be related t o the total harvested biomass instead of just the standing biomass of the plant.

64

/

2. ASSESSMENT OF RADIONUCLIDES

For the pasture case H would be greater than one, but M H would have to be reduced to account for the waste products from the pastured animals being recycled back onto the soil. However, GI absorption depends on the element and compound ingested and this parameter should reflect those relationships. Losses through leaching have been suggested by Baes (Hoffman and Baes, 1979), whereas Schreckhise (1980) has discussed overwatering. Both of these investigators give essentially the same model and so both mechanisms shall be treated as one. Baes gives as a first order approximation the form of the loss constant to be:

where V , = velocity of water percolation downward through the soil (cm d-I), d, = depth of the soil-root zone (cm), p = soil bulk density (g ~ m - ~ ) , 0 = soil water content (mL cmP3),and K D= ~ equilibrium distribution coefficient for nuclide i. This term represents the ratio of the concentration of a radionuclide adsorbed to the soil particles to the concentration of that nuclide in the soil solution at equilibrium conditions (mL g-I). For very small KDi,nearly all the nuclide travels with water percolating through the soil column; for large KDi,the reverse is true-the nuclide is retarded for long periods of time in the soil. Range and median values of some of the above parameters, including KDi for some ions, are given in Table 2.10. See Sections 3.2 and 4.4 for further discussions of K D i . Thus, the effective removal constant for radionuclide i from soil, then, is the sum of the removal constants

When other types of removal mechanisms are considered important in specific situations, they may also be included as loss factors (d-') and then added to Eq. (2-29). The two-component model may be simplified for radionuclides of short half lives such as 13'I. Only the direct-deposition component is

2.3 TERRESTRIAL TRANSPORT AND BIOACCUMULATION

/

65

T A B L E2.10-Some ranges and means for parameters pertinent to the leaching loss constant. XI;.' Parameter

vw (cm Y - ' ) P

( g cm-?

0

(mL~ m - ~ )

KD, ( m L g-'1 Pu' TcO-4 ICS'

SrZ+ a

Renge

Mean

36.5-376 0.93-1.84 0.03-0.40

74 1.4 0.2

200-5000 0.007-2.8 0.08-525 36.5-30,000 2-1000 -

1000 0.14 6.5 370 81

From Hoffman and Baes. 1979.

usually required and if, in addition, we assume equilibrium, the exponential term approaches unity. Hence, for the concentration in the plant we may write:

c.

IV

=

Qi

($/Q)vdi YvXF,i

- Xivdi f~Tiv

f~Tiv

Yvx~i

(pci kg-').

(2-30)

Because of the high correlation found between fR and Yv, a transfer factor, VD~,combining deposition velocity and plant biomass may be defined (Hoffman and Baes, 1979; Bunch, 1966). This parameter, sometimes called the normalized deposition velocity or mass deposition, may be written as:

Here the product udi f~ describes the effective "deposition velocity" only t o plant foliage. If we further assume Ti, = 1, then we can write Equation (2-30) as: (pCi kg-'). This shortened form for the concentration in plants may be used for radionuclides with short half lives < 1 year; the root uptake component would have to be added to account for buildup in the soil from season to season. Alternately, Eq. (2-32) would have to be suitably modified to describe this additional contribution to the plant concentration. Note that for elemental iodine, Vl,i has been estimated a t 0.2 m:' kg-' s-'; for particles, VD 0.006 m q g - ' s-' (Heinemann and Vogt, 1980).

-

66

/

2. ASSESSMENT OF RADIONUCLIDES

2.3.2 Transfer to Animal Products The radionuclide concentration in a n animal product such as milk, meat, or eggs is dependent on the amount of contaminated feed or forage eaten by the animal and its intake of contaminated water (and air which is usually negligible compared to intake in feed and water for transportable radionuclides) (USNRC,1977b):

(pCi L-' or pCi kg-') where

Ci, = concentration of radionuclide i in animal product a (pCi L-') or (pCi kg-'), Fi, = transfer coefficient of radionuclide i from daily intake of animal to edible portion of animal product [pCi L-' (milk) per pCi d-'1 or [pCi kg-' (meat or eggs) per pCi d-'1, see Section 2.4 for discussion of range of values, C,i = concentration 'of radionuclide i in fresh pasture (pCi kg-'), f p = fraction of year animal on fresh pasture (dimensionless), C,i = concentration of radionuclide i in stored feed (pCi kg-'), f, = fraction of diet that is fresh while on pasture (dimensionless), QF = total diet consumed daily by animal (kg d-'1, see Section 2.4 for discussion of values, Ci, = concentration of radionuclide i in water consumed by animal (pCi L-'), f, = fraction of animal water contaminated a t concentration Ciw (dimensionless), and Qw = amount of water consumed daily by animal (Ld-' ). See Section 2.4 for discussion of values. An alternate method (Koranda, 1965) for calculating a radionuclide concentration in an animal product when the contaminated animal fodder is ingested from grazing and the effective half-life of the radionuclide is relatively short makes use of the "utilized area factor," U , which is the area (m2)of pasture foraged daily by a grazing animal. It is related to the amount of forage ingested, QF, and its standing biomass, Y,:

2.4 TERRESTRIAL TRANSPORT BIOACCUMULATION MODELS

/

67

Combining Eqs. (2-23, 2-33, and 2-34), we can write: (pCi L-' or pCi kg-') where Ti, = 1, f p , and f R = 1. It is also assumed that the animal does not drink any contaminated water. The advantage of this method is that sometimes utilized area factors are available, whereas the standing biomass areal density may not be available. The disadvantage of this method is that the biomass used for derivation of a reported utilized area factor may not be the same as the grazing animal's consumption.

2.4

Data Base for Terrestrial Transport Bioaccumulation Models

This section discusses the input parameters described in Section 2.3. Attention is first focused on the parameters of Eqs. (2-23) through (2-26) of Section 2.3, which are used to predict concentrations of a radionuclide in vegetation. Examples of site-specific values and default values that have been used when site-specific data are not available are presented for the parameters that are generally considered to be independent of radionuclide identity, including f~ the interception factor, Y, the standing crop biomass, t, the weathering half-life from plant surfaces, Ti,the translocation factor, t, the time of exposure during the growing season, P the surface density of soil, and t b the soil-buildup time. This is followed by the nuclide-independent parameters of Eq. (2-33) of Section 2.3, which is used to predict concentrations of a radionuclide in animal products. Examples of default values are presented for QF the daily intake of feed by the animal, Q,, the daily intake of water by the animal, f,, the fraction of the time the animal is grazing. Typical values of the utilized area factor U also are considered for use in Eq. (2-35) of Section 2.3. Finally, the radionuclide- or element-dependent transfer factors needed to predict nuclide concentrations in food and feed crops and in animal products are described. Attention is focused on Bi,, the concentration ratio for plant uptake from soil, and Fi,, the transfer coefficient to animal products from the daily intake by an animal. Transfer coefficients are considered for two kinds of animal products, . approaches used to obtain the milk (Fi,) and meat muscle ( F i f )The

68

/

2. ASSESSMENT OF RADIONUCLIDES

transfer factors are described, and the variability of individual parameter values are characterized, where possible. The adequacy of our present knowledge concerning these parameters and areas needing additional research are emphasized.

2.4.1

2.4.1.1

Transfer to Vegetation

Nuclide-Independent Parameters

Interception Fraction Eq. (2-23) of Section 2.3, the expression for the concentration of a radionulcide in (or on) vegetation due to deposition on aerial parts, requires several parameters. The interception fraction, f ~ is, not strictly nuclide-independent, although the interception and retention of radionuclides is frequently assumed to be common to all when they are transported as particulates. This parameter also depends on plant type and standing crop biomass and how the deposition rate or flux is calculated. If di is considered to be the flux to the total ground surface, then fR is the fraction of the depositing material that is intercepted and retained by plant surfaces. However, if di is considered to be the flux impinging only on plant surfaces, then fRshould be set to unity. Chamberlain derived a relationship between fR and Yv of pasture vegetation that yields reasonable results for particulates up to 88 pm in diameter (Miller, 1979):

In Eq. (2-36), y was found to range between 2.3 and 3.3 m2 kg-' (dry) when Yv was expressed as kg m-2 (dry). Because f~ and Yv for forage crops are strongly correlated and because these terms appear in Eq. (2-23) of Section 2.3 as the ratio fR/Yv,the variability of this ratio was evaluated (Miller, 1979). The ratio fR/Yv for forage plants was found to be log-normally distributed with statistical characteristics shown in Table 2.11. The use of Eq. (2-36) for estimating fR for crops other than forage crops may yield erroneous results and should only be considered on a case-by-case basis. It has been suggested that fR for vegetable crops cultivated in rows would be less than that of forage crops because of the soil surface exposed between rows (Moore et al., 1979). In the

TABLE 2.11-Distribution of values for selected parameters used to predict radionuclide concentrations i n vegetation and animal products 99th Observed Number of Mode Median Mean Obsewationa Percentile Range Ratio of Interception factorto biomasq fR/Yv'....................... m2 kgb1(drywt) ........................................................................

Parameter

Geom. S.D.

Forage grasses

1.6

10

1.5 (0.33)d

1.8 (0.50)

2.0 (0.59)

5.1 (0.99)

1.0-4.0

Forage gasses (at harvest)

1.8

527

2.1 (0.28)

3.0 (0.50)

3.6 (0.62)

12

0.63-25

(0.99)

Weathering half-life from plant surfaces, Tme------------------------------days ............................................................................... Iodine vapor (I2) on herbaceous vegetation Iodine particulates on herbaceous vegetation Other particulates on herbaceous vegetation

1.4

19

6.5 (0.38)

7.2 (0.50)

7.6 (0.56)

15.6 (0.99)

4.5-14

1.8

18

6.5 (0.30)

8.8 (0.50)

10.2 (0.60)

32 (0.99)

2.8-16

1.6

17

13.6 (0.32)

17 (0.50)

19.0 (0.59)

51.0 (0.99)

9-34

" Reference: Miller (1979). Reference: Baes and Orton (1979).

' Reference: Miller and Hoffman (1982).

* Values within parentheses are the percentile estimates within the distribution.

70

/

2. ASSESSMENT OF RADIONUCLIDES

TABLE2.12-Example and default ualrces for selected parameters used to predict radionuclides concentrations in vegetation and animal products T ical Default References Parameter glue Value ~ R / Y " Normalized interception fraction Forage vegetation (dry wt) f~

Y.

Interception factor Irrigation spray or particulates Irrigation spray Iodines Other particulates Crop yield Pasture vegetation (wet wt) Pasture vegetation (dry wt) Produce (fresh wt) Leafy vegetables (fresh wt) Other above ground vegetables (frest wt)

t,

Ti,,

te

P

0.25

Baker et d.,1976

0.25 1.0 0.2

USNRC, 1977b USNRC, 1977b USNRC, 1977b

0.7 kg m-2

USNRC. 197% Baes and Orton, 1979 USNRC, 1977b

2.0 kg m-2 2.0 kg m-' 0.60 kg m-2

Translocation factor Fresh forage, leafy vegetables Other produce

Produce

Miller, 1979

0.3 kg m-a

Weathering halflife All vegetation

Crop exposure period Pasture vegetation

2.0 m2 kg-'

Baes and Orton, 1979

14 d

Baker et al., 1976; USNRC 197%

1.0

Baker et al., 1976

0.1

Baker et al., 1976 Baker et al., 1976; USNRC 1977b USNRC, 19771,

30 d

60 d

Surface density of dry soil Based on 15-cm plow layer Based on 15-cm plow layer

240 kg m-' 224 kg m-2

USNRC, 197% Bakeret al., 1976

tb

Soil build-up time

15 Y

USNRC, 197%

QF

Daily intake of feed Dairy cattle (dry wt) Beef cattle (dry wt)

16 kg d-I 12 kg d-I

Comar, 1966 Comar, 1966

2.4 TERRESTRIAL TRANSPORT BIOACCUMULATION MODELS

Q..

Typical

Parameter

-

Daily intake of water Dairy cattle

Beef cattle

Value

Default Value

60 L d-'

/

71

References

Baker et al., 1976; USNRC 197% Baker et al., 1976; USNRC 1977b

50 L d-'

fo

Fraction of time cattle are on pasture

0.4

Shor and Fields, 1979

f~

Fraction of diet that is fresh while on pasture

0.4

Shor and Fields, 1979

U

Utilized area factor Dairy cows continuously grazing Dairy cows fed greenchopped forage

45 rn2 d-'

Koranda, 1965

30 m2 d-'

Koranda, 1965

absence of actual information, default values of 0.20 (USNRC, 197713) and 0.25 (Baker et al., 1976; USNRC, 1977b) have been assumed as the interception factor for food and forage crops (Table 2.12).

Plant Yield Yv is strictly the total yield of the above-ground parts of a crop. For forage plants and leafy vegetables the yield of the above-ground portions is equal to the yield of the edible portions, but for other produce the yield of the above-ground portions may exceed the yield of the edible portions. The total above-ground yield has been assumed to be three times the yield of the edible portions from above-ground parts of food crops and to be equal to the yield of edible portions from root crops (Ng et al., 1978). The variability of Y, of forage grasses is presented in Table 2.11, and default and example values of Yv of forage and food crops are presented in Table 2.12. The Yv of forage grasses appears to be lognormally distributed (Baes and Orton, 1979). Because Yv appears in the denominator of Eq. (2-23) of Section 2.3, statistical analysis was

72

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2.

ASSESSMENT OF RADIONUCLIDES

performed on l/Yv. In actual practice appropriate values of Yv are readily determined on a site-specific basis. Translocation Factor The translocation factor, Ti,, can be expected to vary with radionuclide and food type. Because Ti, cannot be determined directly, it has been implicitly set to unity for all cases (USNRC, 1977a), or set to unity for forage crops and leafy vegetables and to 0.1 for other crops (Baker et al., 1976; see Table 2.12). Ti, can be estimated as an empirical correction factor for Eq. (2-23) if measurements of concentrations in vegetation and deposition rates are available (Ng et al., 1978). Weathering Half-Life Miller and Hoffman (1982) evaluated the available data on the weathering half-life, t,, which can be expected to vary with crop type, stage of growth, climate and season. Average t, values derived from the effective weathering half-life of particulate nuclides on grasses and other vegetation, and iodine on grasses vary from 6.5 to 28 days and appear to be log-normally distributed (Table 2.11). Depending on the experimental methods used to derive t,, this parameter may also include the effects of growth dilution. A t, of 14 days is frequently used as a default value. The reader will note that an extreme case of a weathering half-life of the order of years has been measured in lichens in the arctic environment. Entry of 137Csand other nuclides into the lichen-caribou (reindeer)-man food chain has led to enhanced body burdens of 137Cs in arctic inhabitants that consume caribou (reindeer) meat (Hanson, 1967,1980). Other Nuclide-Independent Parameters The time of exposure during the growing season, t,, is readily determined on a site-specific basis. Example values are shown in Table 2.12. The surface density of soil, P , varies directly with the depth of the root zone, which is frequently assumed to coincide with a 15-cm plow layer (Table 2.12). A depth of 15 cm for the root zone corresponds to P = 200 kg m-2 for mineral soils assuming a bulk density of 1.3 g ~ m - and ~ , to P = 75 kg m-2 for peat soils, assuming bulk density of 0.5 g cmP3. The build-up time in soil, tb, is readily determined on a site-specific basis.

/

2.4 TERRESTRIAL TRANSPORT BIOACCUMULATION MODELS

2.4.1.2

73

Concentration Ratio for Plant Uptake from Soil

Estimation of Biv Soil-to-plant concentration ratios ( B i v )are obtained from radioisotope experiments on plants grown in pots or other containers in laboratory greenhouses, or in containers or field plots outdoors. In the absence of radionuclide data, they are estimated from the concentrations of stable isotopes in field-grown plants and associated soil. As noted in Section 2.3.1, concentration ratios have been reported as the concentration in fresh vegetation divided by the concentration in dry soil, and as the concentration in dry vegetation divided by the concentration in dry soil. Because the yield of forage crops and the intake of feed by livestock are typically reported on a dry weight basis, it is convenient to report the concentration ratio of forage crops on the basis of concentrations in dry vegetation. To distinguish concentration ratios reported on a dry mass basis from those reported on a wet mass basis the concentration ratio of dry vegetation is designated as CRi.

Default Values of B;, from Various Sources Table 2.13 lists default values of elemental Biv from various compilations of transfer factors expressed in terms of the wet mass concentration in vegetation and dry mass concentration in soil. The sources for Table 2.13 list the concentration ratios as a composite value for a variety of food and feed crops or separate values for forage vegetation and edible portions of various types of vegetables and produce. TABLE 2.13-Range of default values of Bi, the concentration ratio for plunt uptake from soil, F,, the transfer coefficient to cow milk, and Fil, the transfer coefficientto beef" Element Co Sr Ru

I cs Ra U

h

dFI, L-'

1 x lo-3 to 9.4 x lo-3 1.7 X lo-' to 1.0 3.8 x to 6.0 x 2.0 X to 5.5 X 6.4 x lo-' to 7.8 x lo-' 3.1 x lo-" 6.2 x lo-' 2.9 X to 2.5 X lo4 1 X 10" to 2.5 X

5.0 x 8.0 x 5.0 x 6.0 X 5.0 x 2.0 x 1.2 X 2.5 X

lo4 to 2.0 x lo4 to 2.4 x lo-' to 1.0 x to 1.0 X lo-=to 1.2 x lo4 to 8.0 x lo4 to 6.0 X lo-' to 2.0 X

Fu

d kg-'

lo-3 1 x lo-3 to 1.7 x lo-' 3.0 x to 2.0 X lo4 1.0 x to 4.0 X lo-' 2.9 X lo-' to 2.0 X lo-' to 3.0 X lo-' lo-' 4.0 X 2.0 x lo4 to 3.4 X 1 0 - q . 6 X 10-Bto 5.0 X 10" 4.1 X to 5.0 X

" References: Fletcher and Dotson (1971), Baker et al. (1976),USNRC (1977b),CEA/ NRPB (1979). Moore et aL (1979). McDowell-Boyer and Baes (1980). Values for forage crops and edible portions o f food crops.

74

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2. ASSESSMENT OF RADIONUCLIDES

A handbook assembled by Ng et al. (1968) has been a key reference for estimating Bivwhen experimental data are not available. Thus, the concentration ratios were estimated from stable element concentrations in the handbook as the ratio of the average concentration in the portion of human diet that is derived from plants and average concentration in dry soil (USNRC, 1977b). Bivvalues based on the handbook by Ng et al. (1968) are associated with a large uncertainty because they are based on concentrations in plants and unrelated soils. B;, values should be based on concentrations measured in plants and their associated soils. Variability of Concentration Ratios Table 2.14 presents ranges of Bivfor edible food crops and CRi for forage plants (grasses and legumes). The individual values within a range represent the mean values observed for single crop-soil combinations. The concentration ratios are generally based on radionuclide data for crops grown in laboratory green houses or in the field and include estimates for soils of virtually every texture classification from sand to clay. Some of the Bi, values are based on concentrations of naturally occurring radionuclides or stable nuclides in associated plants and soil. Except for some forage crops, the concentration ratios represent the edible plant part at maturity. The concentration ratio values are intended to reflect only plant uptake from soil via roots, although the effects of deposition of nuclides on plant surfaces following resuspension from soil may have contributed to some of the particularly high values from field studies. In this connection, the CRi values for Pu in crops grown adjacent to a reprocessing facility a t the Savannah River Plant were attributable mainly to aerial deposition of stack emissions and were about an order of magnitude greater than those for Pu in crops grown a t the White Oak Lake floodplain a t Oak Ridge where the Pu taken up by plants was exclusively via the soilroot pathway (Adriano et al., 1980). The concentration ratio of an element in crops varies in a very complex manner with soil texture and other soil properties, such as cation exchange capacity, exchangeable calcium, exchangeable potassium, pH, and organic matter content (Nishita et al., 1978). It varies with chemical and physical form of the nuclide, plant species, plant part, and stage of growth, as well as with experimental conditions such as management practice and the manner in which the isotope is introduced into soil. Consequently, Biv and CRi exhibit a variability that far exceeds that observed in transfer coefficients to animal

2.4 TERRESTRIAL TRANSPORT BIOACCUMULATION MODELS

1

75

products (to be discussed in Section 2.4.2.3). As noted in Table 2.14, the elemental concentration ratios commonly vary over two or more orders of magnitude. Statistical analysis of the relatively abundant data on concentration ratios for ST and Cs reveals that the B;, values are log-normally distributed (Fig. 2.13 and 2.14). The geometric standard deviation (GSD) of the Biv for food and forage crops over all agricultural soils is estimated to be in the range of 3.5 to 4.1 (Table.2.15), which is more than two times the GSD's for the milk transfer coefficients of these elements (see Table 2.18). Knowledge of the dominant crops and soil characteristics of an area may be useful in reducing the range of Bivat a particular location. The exchangeable calcium in soil is the most important factor in determining the extent of "Sr absorption by plant roots (Nishita et al., 1978; Biesold et al., 1978). The Biv for strontium in various crops has been shown to be negatively correlated with the exchangeable calcium in soil (Nishita et al.,1978; Sartor et al., 1966,1968; Hoffman, 1980).The B;, for strontium also decreases with increasing clay and organic matter in soil (Nishita et al., 1978). Uptake of 13'Cs by plants from soil decreases with increasing concentrations of exchangeable potassium (Nishita et al., 1978). However, other exchangeable cations also influence cesium uptake from soil (Nishita et al., 1978; Biesold et al., 1978). Elevated cesium concentration ratios are associated with soils of high organic matter content, low pH, or low clay content (Hoffman, 1980). With a knowledge of these factors one might expect a lower variability than Tables 2.14 and 2.15 indicate. It may be possible to reduce the variability shown in Tables 2.14 TABLE 2.14-Concentmtwn ratios for edible portions of food crops and pasture plants' Range of Values (pCi kg-' plant/pCi kg-' soil) Element

Eu'

Edible portion of food cmps (wet plant/* soil) B,.

1.2 x 10-I to 2.0 x lo-'

' From N g et d,1982a. Excludes sandy soils.

Pasture lanta (dry p l a n t b y mil)

CR;

76

/

2. ASSESSMENT OF RADIONUCLIDES B,: Sr (0) and Cc (+) in food crop

Cumulative probability (%)

Fig. 2.13 Concentration ratios Bbfor Sr and Cs in food crops (pCi kg-' fresh food per pCi kg-' dry soil).

CRi: Sr (0)and Cs (+I in forags crops

Cumulative probability (%)

Fig. 2.14 Concentration ratios CRi for Sr and Cs in forage crops (pCi kg-' dry vegetation per pCi kg-' dry soil).

TABLE 2.15- Variability of plant-to-soil concentration ratwe Element

Plant. soil

Sr . Food crops, all soils Cs Food crops, all soils Sr Cs

Forage plants, all soils Forage ~ l a n t sall . soils

Geometric

S.D?

Ne

Geometric Mean

...................................... 3.8 109 7.5 X lo-z 4.1 144 5.0 x lo-'

Mean

Standard Deviation B1,,pCi kg' fre& plant per pCi kg' &y mil

Observed Range

----------.----------.----------.-----.--

1.6 X lo-' 3.7 X lo-' 1.6 X to 1.7 9.5 x lo4 11.0x lo-3 1.5 x l o 4 to 5.9 x lo-2 ---.--.---.-----.----------.-----..--BIv,pCi kg-1 dry plmt per pCi kg-' dry soil ----------.-----------...------.-------.3.8 54 1.8 3.5 4.2 1.2 X lo-' to 2.3 x lo-' 3.5 42 8.9 X 10" 4.1 X 10" 3.8 x lo-' m 5.7 x 10-I 13.1 x lo-'

" Ng et al. (1982a). Geometric standard deviation. 'Number of mean Bi. estimates for single plant-soil combinations.

78

/

2. ASSESSMENT OF RADIONUCLIDES

and 2.15 by excluding or making adjustments for Biv derived from pot experiments. The Biv for '"Sr, 13" CS, 54Mn, and % ' o measured by Steffens et al. (1980) from pot experiments in greenhouses were higher than those from outdoor lysimeters. However, the existence of systematic differences between Biv from indoor pot experiments and Bi, from field studies needs further evaluation. 2.4.2 2.4.2.1

Transfer to Animal Products Nuclide-Independent Parameters

The daily intake of feed, QF, and the daily intake of water, Q,, by animals, the fraction of time that an animal is grazing on pasture, f,, and the fraction of feed that is fresh forage when an animal is grazing on pasture, f,, are readily determined on a site-specific basis. Example values of these parameters are presented in Table 2.12. In the case of commercial dairy herds, QF was found to be normally distributed with a mean value of 16 kg dry feed d-' (Shor and Fields, 1979). T o predict the area of forage utilized by an animal in Eq. (2-35), U = 45 m2 d-' has been suggested a reasonable value for dairy cows grazing on continuously used pasture (Koranda, 1965). For animals being fed green-hopped forage, U = 30 m2 d-' has been suggested (Table 2.12).

2.4.2.2 Fi,,,, the Transfer Coefficient from Feed to Milk As noted in Section 2.3.2, the transfer coefficient Fi, is the nuclidedependent parameter in equilibrium models used for predicting concentrations in animal products from those in feed. Experimentally based transfer coefficients have been derived for cow and goat milk, meat from various species, and chicken eggs. Of the transfer factors to animal products, those to cow's milk are the best documented.

Estimation of Fim The transfer coefficient of radionuclide i to milk Pi,,, (expressed in d L-' ) is the fraction of the nuclide ingested daily by a lactating animal that is secreted in 1 liter of milk under steady-state or equilibrium conditions. Milk transfer coefficients are estimated by the following

2.4 TERRESTRIAL TRANSPORT BIOACCUMULATION MODELS

/

79

approaches (Ng et al., 1982a): -Integrate the concentration in milk over time following a single intake of radionuclide. (The concentration in milk after a single intake is frequently described mathematically as a series of exponential~.) -Divide the total activity recovered in milk after a single intake of a radionuclide by the average daily milk secretion rate. -Divide the plateau concentration in milk after chronic or daily feeding of a radionuclide by the daily intake. -Divide the steady-state or equilibrium concentration in milk after continuous feeding of a stable or radioactive isotope by the product of the concentration in feed and the kg of feed ingested daily by the cow. Assumptions are frequently required regarding the milk secretion rate, the kg of feed ingested daily by the animal, or the total activity that wouldbe secreted in milk beyond the duration of an experiment. These considerations contribute to the uncertainty associated with estimates of Fi,. Default Values of Fi, to Cow's Milk

Table 2.13 lists default values of the elemental transfer coefficient to cow milk from various compilations. The Fh are reported as elemental transfer coefficients, which exceed the transfer coefficients of radioisotopes of the same element because transfer of radioisotopes to milk is accompanied by radioactive decay. However, the difference between elemental and radioisotopic transfer coefficients is significant only for short-lived radionuclides (Ng et al., 1977). Transfer coefficients to goat's milk have been suggested for several elements including Sr, I, and Cs (USNRC, 1977b). Variability of Fi, to Cow's Milk

The transfer coefficient to milk of an element can vary with its physical or chemical form in the animal's diet. The Fi, of various chemical forms of iodine, e.g., elemental iodine, methyl iodine, sodium iodide, and sodium iodate, are comparable ( ~ r e t t h a u eet r al., 1972). In the case of ruthenium, which is encountered in several species and oxidation states, both the trichloride (Ward et al., 1967; Kirchman and D'Souza, 1972) and nitrosyl trinitrate (Squire et al., 1958) are

80

/

2. ASSESSMENT OF RADIONUCLIDES

poorly transferred to milk (F, of about 6 x 10-I d L-'), while another unspecified chemical form is associated with an Fi, of about 1 x lo-' d L-' (Sirotkin et al., 1970). Plutonium citrate is transferred to milk more efficiently than the dioxide with the transfer coefficients differing by more than a factor of 10 (Stanley et al., 1974); however, both forms of Pu have very low milk transfer coefficients. Table 2.16 compares transfer coefficients based on radioisotope tracer data, those based on concentrations of the naturally occurring stable isotope in milk and the feed consumed by the animal, and those based on surveillance of fallout from weapons testing. Careful inspection of the individual Fimestimates suggests that, for some elements, the biological availability of the chemical form that occurs in feed differs from that of the chemical forms used in the tracer experiments. The Fimof Sr, I, and Cs, naturally present in feed are comparable to those of the elements in the chemical forms used in tracer experiments. For Co, the transfer coefficient of the stable isotope in feed exceeds that based on the radioisotope tracer. The Fi,of 89.90Srin fallout from weapons tests were comparable to those of the radioisotopes used in tracer studies. The Fimof 13'1and '37Csin fallout tended to be somewhat lower than those of the radioisotope tracers. With respect to the biological availability of radionuclides released from nuclear installations to dairy cattle, Hoffman (1978) reported Fi, estimates of l3'I emissions from nuclear power stations that are comparable to those of tracer 13'I. In view of the general lack of data for validating chronic exposure models, evaluation of the uncertainties in dose predictions has relied on statistical analyses of input parameters. Hoffman (1979) noted that the Fim of Sr, I and Cs were log-normally distributed and estimated the geometric standard deviation, mode, median, mean and 99th percentile values of Fi,(Table 2.17). Sufficient Fi,data for a meaningful statistical analysis are limited to only a few elements.

Assignment of Average Values of Fimto Cow's Milk Although data for statistical studies of Fimare limited, it is still desirable to adopt a single set of generic milk transfer coefficients for radiological assessments. Table 2.18 lists "average" milk transfer coefficients adapted from Ng et al. (1977, 1979). Generally, the Fi, in Table 2.18 are simply the unweighted mean of the mean values obtained for an isotope. If the maxima and minima differed by more than a factor of 10, the geometric mean was estimated. As noted above, the milk transfer coefficient can vary with the chemical form of the

E 3 22 P

TABLE 2.16-Effect of chemical and physical form on transfer coeffiient to cow's milka Radionucllde

YO 89.90Sr l",l"Ru ulI 134.137Cs

Chemical Form of

Radioisobpe Tracer Data

Radioisotope

x - 1.1 x 10-~m' x - 3.8 x x lo-1 - 1.0 x lo4 x 3.4 x lo-' x - 1.6 x

c0c12 SrC12 See footnote c NaI, KI, NaIO3 CaCl

8.7 3.5 5.0 3.6 1.9

Dioxide, citrate

2.7 x lo-'-

-

=Ra =?"U -F'u

Range of Individual Fb,d L - I Stable element concentration in associated milk and feed 2.9 x lo4 - 1.0 x 1.0 x lo-3 - 3.0 x lo+ 1.7 x - 1.4 x lo-' 3.6 x 1 0 - ~ 9.0 x - 7.0 x 6.9 X - 6.1 X lo4'*'

1.0 x lo-'

" Adapted from Ng et al. (1977). Based on data from Sam et al. (1978).

'Trichloride, nitrosyl trinitrate and unstated form studied by Sirotkin et al. (1970). *Takes into account data from Chapman and Hammons (1963).

t'

Radionuclide in Weapons Fallout

2

2:

n I

l

n l

N

0 4 z z X X X 2 2 2

3

n I

n

X

3 5

I

X

3

X

3 3

2.4 TERRESTRIAL TRANSPORT BIOACCUMULATION MODELS

/

83

TABLE 2.18-Elemental feed-to-milk transfer coefficients to cow's milP Element

co Sr

Ru I Cs

Ra

u

Pu

& L-'

Approachb

2.9 x 1 0 - ~ 1.4 x lo-3 6.1 x lo-''d)

3 2 1

9.9 x 1 0 - ~ 7.1 x lo-3 4 x lo-""' 4 x lo-"" 1.0 x lo-"*

2 2 2 3 1

d

Chemical Form'

Ruthenium trichloride Mitrosyl ruthenium trinitrate

Plutonium citrate

'Adapted from Ng et al. (1977, 1979). The Fi, values were established by the following approaches. 1. The Fi, is based on the recovery of a single administered dose of a radioisotope. 2. The Finis based on the recovery of a single administered dose of a radioisotope and on the concentrations of a radioactive or stable isotope in associated milk and feed. 3. The F;, is based on stable element concentrations in associated milk and feed. If the Finis based on a specific chemical form, the compound is listed in this column. An unstated chemical form of Ru was associated with an F, of 1 X lo-' d L-' (Sirotkin et d ,1970). Arithmetic mean of average values calculated by McDowell-Boyer et aL (1980)from each literature source. 'Takes into account data from Chapman and Hammons (1963). g T h e dioxide of P u was associated with an F;, of 2.7 x lo-' d L-' (Stanley et al., 1974). I,

element. If an Fimof Table 2.18 is based on a specific chemical form, the compound is noted in the table. Generally, when the Fim of two or more chemical forms of an element differ, the Fim of the form most readily transferred is listed in Table 2.18.

2.4.2.3

Fif,the Transfer Coefficient from Feed to Meat

The transfer coefficient of radionuclide i to meat (or another animal product besides milk), Fir,is the fraction of the nuclide ingested daily by an animal that is found in 1 kg of muscle (or other edible product) from the animal under steady-state or equilibrium conditions. The data base for Fir is more limited than for Fi,, and well-characterized Fif are few and largely undocumented.

84

/

2.

ASSESSMENT OF RADIONUCLIDES

Estimation of Fir to Meat Transfer coefficients to meat can be estimated by the following approaches (Ng et al., 1979): -Divide concentration (under steady-state or equilibrium conditions or at slaughter) in an animal product after continuous feeding of an isotope (stable or radioactive) by the daily intake. -Integrate the concentration in muscle over time for groups of animals that were given single doses of a radioisotope tracer and sacrificed at intervals. -Divide the accumulation factor (i.e., the ratio of the total radioisotope content in muscle and the daily intake after repeated or continuous feeding of the isotope) by the muscle mass. -Divide the concentration factor (i.e., the ratio of concentration of a radioisotope in flesh to that in feed after continuous feeding of a radioactive or stable isotope) by the kg of feed ingested daily.

Default Values of Fi, to Beef Table 2.13 lists default values of F i f ,the elemental transfer coefficient to beef, from various compilations. Most of the Fif to beef from Regulatory Guide 1.109 (USNRC, 197713) were estimated as the average concentration of the stable element per kg of meat divided by 50 times the average concentration of the stable element in food derived from plants. The concentrations in meat and food from plants were obtained from tables in the aforementioned handbook by Ng et al. (1968). Because 50 kg is the average wet weight of vegetation ingested daily by cattle, the Fir values from Regulatory Guide 1.109 implicitly represent the transfer coefficient to beef.

Variubility of Fir to Beef Estimates of the transfer coefficient to beef are summarized in Table 2.19. The estimates of Fifare based on radioisotope tracer data and on concentrations of radioactive or stable elements in beef and feed. Estimates of Fir to beef based on stable element concentrations in meat and feed are truly valid only when the concentrations are obtained for meat and the feed actually consumed by the animal providing the meat. The estimates of Fir to beef for Co and Sr are based a t least in part on stable element concentrations in beef and unassociated feed. The Fir for Co and Sr in Table 2.19 were estimated

2.4 SPECIAL CASE RADIONUCLIDES .(TRITIUM, CARBON-14)

Eleinent

Co Sr

/

85

TABLE2.19-Estimates of the elemental transfer coefficient to beef Meanm Range Approachb Reference FM,d kg-'

--.----.--.-..--.------------..-..--.-------.---------2 x lo-= to 6.9 x lo-' 2,3,4 Ng et aL, 1982b

RU

8 X lo-' 2 x lo4

I

7 x lo-3(')

Cs Ra

3

x lo-' 5 x lo-'

Pu

7-8 x lod

to 1.8 x

1,3 1

1

to 9.2 X lo-' 7.2 x undetectable to 2 x

4

5 X lo-'

1.4

to 2

X

2

Ng et a[., 1982b Ng, 1982: N g et al., 1982b Ng, 1982: Ng et al., 1982b N g et d.1982b McDowell-Boyer et d , 1980 Garten. 1978; Ng et d , 19821,

" Estimated value. The F,, values were estimated by the following approaches: 1. From radioisotope tracer data. 2. From concentrations of a radionuclide in associated meat and feed. 3. From stable element concentrations in unassociated meat and feed. 4. From collateral dab for cattle, caribou and reindeer. 'The elemental K was assumed to be two times the FZ for 13'I.

from the median concentrations in beef and a composite feed composed of fixed proportions of'grasses, legumes, and,concentrates (Ng et al., 1979). The uncertainty in the estimate of Fifwas evaluated in terms of a, the standard deviation of the log-transformed Fir values, which were calculated from the a's of the logitransformed concentrations in beef and feed, assuming statistical independence. The range of Fiffor Co and Sr is the 95% interval where the limits of the 95% range differ from the median by a factor of exp(2.00). Because of the scarcity of valid estimates of the transfer coefficient to animal products, opportunities for characterizing distributions of F i r are limited. Little (1979) found that the transfer coefficients of 13'Cs reported by Ward and Johnson (1965) for cattle were lognormally distributed. The range of Firexceeds an order of magnitude, and the geometric standard deviation is about 2.3 (Table 2.20). In general the variability of F,f to beef derived from stable element concentrations in unassociated meat and vegetation are characterized by geometric standard deviations ranging from 1.3 to 3.8. If data are not available to derive a transfer coefficient to beef, it can be estimated from the transfer coefficient to meat of another species and other collateral data. Transfer coefficients based on collateral data require certain assumptions relating to similarity in the meat-to-feed concentration ratio for different species, the feed con-

M

TABLE 2.20-Variability of transfer coefficient to beef a Element

Geometric

S.D.b

Nc

Mode

Median

Mean

99th

Percentile

NRC"

Range

2.3

24

5.8 X lo-$ (0.21)*

1.1 x (0.50)

1.5 X lo-' (0.66)

"Adapted from Little (1979). Geometric standard deviation. Number of animals studied. Values in parentheses are the percentile estimates within distribution. 'USNRC (1977b).

7.3 X (0.99)

4

8

Fx, d kg'

Cesium

z

4.0 X (0.10)

4.7 X lo-= to 9.7 X lo-'

ZJ

>

u E Z

-u

2r ?!

2.5 SPECIAL CASE RADIONUCLIDES (TRITIUM, CARBON-14)

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87

sumption rate and total body and muscle mass in different species, and similarity in the uptake and retention pattern of chemically related elements. These considerations enhance the uncertainty associated with estimates of Fif to beef that are based on collateral data. In general, estimation of transfer coefficients to beef and other animal products is a topic that needs integration and more complete documentation.

Fir to Other Kinds of Meat and Chicken Eggs Besides transfer coefficients to beef, Firto other animal products such as pork, lamb, chicken, and eggs also have been derived for terrestrial food chain models (Fletcher and Dotson, 1971; Baker et al., 1976; CEAINRPB, 1979; Ng et al., 1982b). Single doses of a tracer have been used to estimate the transfer coefficient for poultry. The transfer coefficient to eggs can be estimated by approaches similar to those for estimating transfer coefficients to meat. In addition, the Fir to eggs can be estimated by dividing the fraction of a single oral intake of radioisotope tracer recovered in eggs by the average mass of an egg in kilograms.

2.5 Special Case Radionuclides (Tritium, Carbon-14) Tritium and carbon-14 are handled as special cases because of their ubiquitous distribution once released to the environment. Environmental transport of these radionuclides is based on the assumption of their rapid and nearly uniform mixing with their stable element counterparts in nature in the vicinity of the release. Tritium is assumed to be transferrred in environmental media and incorporated into the body through its association with water as 3HOH. Carbon-14 is assumed to be converted to 14C0,, and to be fixed in vegetation, ultimately reaching man through ingestion. The approach used to calculate dose from 3H and 14C is based on the assumption that an equilibrium state exists between the concentrations in the atmosphere (or water), and food products for specified locations. Because of the small number of parameters used in the model, less uncertainty is introduced into the estimate of the dose. If the assessment is made for the point where the atmospheric concentration is highest and it is assumed that all food products are grown a t that point, an upper estimate of dose is established. However, if no account is taken of the possible dilution of 3H and 14Cin tissue due to

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2. ASSESSMENT OF RADIONUCLIDES

ingestion of food products grown at points where the atmospheric concentration is lower than where the individual resides, a n unrealistically high prediction of dose may result. I t is also noted that tritium specific activity in vegetation would normally be less than that of the water vapor in the ambient plume since the source of much of a plant's water is the soil moisture that is derived from rain. Therefore, the assumption of equilibrium between the plant and the ambient plume is likely to lead to overestimation of the specific activity in the plant and therefore overprediction of dose. In the case of 14C, however, a similar assumption of equilibrium of specific activity between plant tissue and the time-averaged C 0 2 in the plume may not lead to overestimation of specific activity in the plant because essentially all of the plant's carbon is derived from photosynthetic fixation of ambient C02.

2.5.1

Tritium

Numerous variations of the approach outlined above have been proposed to calculate the dose to man from tritium released to the environment (Evans, 1969; NCRP, 1979; Moore et al., 1979; USNRC, 197%). Till et al. (1980) reviewed four of these methodologies and included sample calculations of dose for each under chronic exposure conditions of tritium in the atmosphere. Based upon their study, an approach originally recommended by the National Council on Radiation Protection and Measurements (NCRP, 1979) was recommended with a minor modification, to permit the incorporation of site-specific data into the dose calculation. The concentration of 3H in the atmosphere at location (r, 8 ) is calculated using the expression

where

C+ = concentration of tritium in atmospheric water, (Ci L-'), Xcr,e) = atmospheric concentration of tritium, (Ci m-3), Ha = the absolute humidity, (g H 2 0 m-9, and 1000 = conversion factor (g H 2 0 L-I). The absolute humidity is a key parameter in the calculation of dose from tritium. Due to dilution of released tritium by airborne water vapor, dose is inversely proportional to absolute humidity. Actual values of absolute humidity may vary considerably depending upon

2.5 SPECIAL CASE RADIONUCLIDES (TRITIUM, CARBON-14)

1

89

geographical location and season. A default value of 8 g H20m-3 is recommended by the U.S. Nuclear Regulatory Commission Regulatory Guide 1.109 (USNRC, 197713); however, a recent report by Etnier (1980) summarized average values for geographic regions of the U.S. (Fig. 2.15). Report No. 62 of the National Council on Radiation Protection and Measurements (NCRP, 1979) proposes a methodology for calculating the dose from tritium when the concentration of tritium is known in the water, food products, and air to which the individual is exposed. This technique for calculating the dose applies to an equilibrium situation only and is not recommended to evaluate exposures resulting from pulse releases of tritium. The NCRP methodology assumes that the dose from tritium via the various pathways of exposure depends upon the relative contributions to total water intake as listed in Table 2.21. The annual dose per unit concentration for 3.0 L d-' water intake is described by the following expression:

MEAN ABSOLUTE HUMIDITY (cj/m3) D

4.7 6.6 8.4 10.6

RANGE OF VALUES (g/m3)

3.0 5.6 7.6 9.6 -

5.5 7.5 9.5 11.5

Fig. 2.15 Absolute humidity by geographic region (from Etnier, 1980).

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2. ASSESSMENT OF RADIONUCLIDES TABLE2.21-Contributions Source

to total water intake of the Reference Man' Intake Fraction

(Ld-')

Drinking Water Food productsb Oxidation of f o o e d Inhalationw Skin absorption' Total NCRP (1979). In food 0.72 L d-' In milk 0.53 L d-' In juice 0.02 L d-I. ' Oxidation of food 0.25 L d-' Oxidation of milk 0.04 L d-' Oxidation of juice 0.02 L d-'. Tritium entering body as organically bound hydrogen which is oxidized to 3HOH during metabolism. ' Assuming an absolute humidity of 6 g H 2 0 m-3 in air. a

where

Di

= annual dose rate to organ i due to inhalation and inges-

tion of tritium (mrem y-I), concentration of tritium in drinking water (pCi L-I), Cn concentration of tritium in water in food (pCi L-I), Cn = concentration of tritium oxidized to water upon metabolism of food (pCi L-I), C, = concentration of tritium in atmospheric water (pCi L-'), and (DRF)i = dose rate factor for organ (mrem y-'/pCi L-'). Cw

= =

One disadvantage of the methodology originally proposed by the NCRP to calculate the dose from tritium is that it does not allow for the incorporation of dose from food products grown a t more than one location. Two minor modifications to this methodology would improve its simplicity and yet allow for this more realistic situation. First, the oxidized and non-oxidized tritium components in food products in Eq. (2-38) are combined into a single value of 1.56 (1.27 + 0.29). This provides simplification of the model with only minor additional uncertainty. Second, the concentration of tritium in food products is broken into two parts: (1) that fraction grown a t the point where the dose is being calculated, and (2) that fraction grown a t another location where the air concentration is different than a t the point of interest. The model is described by the following equation, a modification of

2.5 SPECIAL CASE RADIONUCLIDES (TRITIUM, CARBON-14)

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91

which simplifies to

where

D i= annual dose rate to organ i due to inhalation and ingestion of tritium (mrem y-I), CW = concentration of tritium in drinking water (pCi L-'), Cm = concentration of tritium in water of food products grown at a location n (pCi L-I), 6, = fraction of food products grown a t location n (dimensionless), C a = concentration of tritiated water in air (pCi L-l), and (DRF); = dose rate factor for organ i (mrem y-l/pCi L-' H20). For airborne releases where measured concentrations of tritium in food products and in drinking water are not available, the concentration in food should be assumed to be equal to 100% that in air2 at location n, and that the concentration in drinking water should be assumed to be 1% of that in air at location n. The assumption that the tritium concentration in drinking water, C,, is 1%of that in air is strictly an arbitrary attempt to account for tritium that migrates from the atmosphere into drinking water supplies. If a drinking water supply is known to be contaminated by releases of tritium to the aquatic environment, then this assumption is no longer valid, and a separate calculation must be made to determine the concentration of tritium in the water. The modified NCRP model of Eq. (2-39) recommends a methodology that incorporates site-specific information on tritium concentrations in food products grown both locally and remotely. This This assumption is based upon a study by Murphy and Pendergast (1979) which was conducted in a warm, humid, forest environment. An earlier study by Anspaugh et al. (1973) suggested a value of 50%. which is widely used in assessment studies. However, because of the significance of this assumption and the importance of tritium in many source terms, the use of the 100% value would lead to a more conservative estimation of dose. Obviously, this assumption needs more attention through careful studies performed in several types of environments.

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2. ASSESSMENT OF RADIONUCLIDES

approach is considered an effective means for use in calculating dose to man from tritium released t o the environment. One possible source of error introduced in the calculation of dose from tritium is that of chemical form; when the precise chemical species is not known, it is generally assumed that all tritium released by nuclear facilities has the chemical form of tritiated water vapor, 3HOH. This assumption probably yields the maximum estimates of dose from tritium because of the rapid and complete mixing of 'HOH with water in the hydrologic cycle. Tritium in gaseous effluent. may also be present as tritiated hydrogen gas (3HH), elemental tritium ('H3H) or an organic compound such as tritiated methane ('HCH3). Experimental data on the chemical form of tritium released to the atmosphere by nuclear plants are limited but suggest that a combination of forms exists, and the relative proportions depend upon the type of facility being considered. The effect of chemical form of tritium released to the environment on estimates of dose has been addressed by Till et al. (1980), who showed that forms other than 3HOH such as tritiated gas, generally result in a lower dose in the vicinity of the release. Experimental data indicate that a release of 3HOH to the atmosphere results in higher tritium levels in vegetation relative to atmospheric levels than from a release of 3HH, although the levels resulting from release of 3HH are maintained in the environment for a much longer time (Sweet et al., 1983). Because of possible large releases of tritiated gases from fusion power reactors, this reduction is important and additional research in this area is needed. Another possible source of error is for exposures occurring near an elevated release. In this case, the specific activity in the atmosphere near ground-level will be less than in the plume overhead. The concentration of tritium in vegetation is then determined primarily by the ground-level atmospheric specific activity and the specific activity of tritium in rain (Vogt, 1979).

The model for calculating the dose from environmental releases of lJC assumes a steady-state relationship of carbon specific activities between the point of photosynthetic fixation and through the food chain to man. Details of such a model were discussed by KiIlough and Rohwer (1978). Carbon-14 is released in various chemical forms from nuclear facilities, the particular form depending on the type of facility. For boilingwater reactors (BWRs) the C02-bound component of 14C effluent

2.5 SPECIAL CASE RADIONUCLIDES (TRITIUM, CARBON-14)

1

93 -

constitutes more than 95% of the total emission, while for pressurizedwater reactors (PWRs), measurements have shown that the amount of 14C that is bound in COs varies over a factor of 100 between 0.8% and 80%, with the remaining I4C in carbon monoxide, methane, and other hydrocarbons (Schwibach et al., 1978). Only the COs-bound component is subject to entry into the food chain through photosynthetic fixation. It is assumed that the 14C02 in the effluent plume mixes with nonradioactive COs that is present in its ambient concentration. The concentration of COs varies considerably in diurnal and seasonal cycles and is locally influenced by residential and industrial COz sources. In the absence of site-specific data, a value of 0.18 g of C per m3 of air, corresponding to 330 ppm COz by volume, may be considered3 (Baes et al., 1977). If an atmospheric transport model is used to estimate the ground-level atmospheric concentration, X, (pCi m-3), of 14C,corresponding to release rate, Q (pCi s-l), in the vicinity of the point of release, then the ambient specific activity of the airborne carbon a t that point is calculated as

where the subscript n is used to denote the particular location. Since the photosynthetic processes are active only during daylight and (with certain exceptions) during a fairly well defined growing season-determined by the crops and the location-it is important that the meteorological data used in predicting the atmospheric transport of the 14C02from its point of release be typical of daytime and the months of the year constituting the growing season. Killough and Rohwer (1978) showed that a factor-of-three underestimate of the dose to a maximally exposed individual is possible if annually-averaged meteorological data, with night-time observations included, are substituted for the recommended season- and daytime-specific data. Photosynthetic reactions result in isotopic fractionation of 12C,13C, and I4C, the result of which is a 14C/12C ratio in plant tissue (and therefore specific activity) that is less than the ratio for the ambient airborne C01. The degree of fractionation varies among plant species and differs greatly between plants of the photosynthesis pathways designated as C3 (most food crops) and C4 (sugar cane, corn, sorghum). The maximum discrimination, however, occurs in the C3 plant pathway and is about 5%, with an average percentage that depends on the a This value should be interpreted as an estimated tropospheric average for the mid1970's; the current value would be higher because of the rising secular trend of C02 concentration in the atmosphere that results from combustion of fossil fuels.

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ASSESSMENT OF RADIONUCLIDES

particular diet. It is recommended that this effect be neglected and that the specific activity of carbon fixed in plant tissue a t location n be assumed equal to Aa,". Carbon-14 reaches man by consumption of plant matter, or meat or dairy products of animals that have fed on such plant matter. The fractionation effect in the assimilation of carbon by man and higher animals is insignificant in comparison with photosynthetic fractionation. Moreover, experiments with small animals indicate that nearly all of the carbon in the body (all but about 0.10%) is sustained by dietary intake of carbon as opposed to inhalation (Buchanan, 1951). Therefore, if animals feed on plant matter of specific activity A P , ' ~ " ~ , we assume for the steady-state model that the carbon in food products derived from these animals has the same specific activity, which in turn equals A"," We stress that the applicability of such a model is limited to the case of release a t a constant rate, so that the exchange of "C between plants and animals and their exposure environment exists in a state of equilibrium. To calculate the dose rate to man due to ingestion of 14Cunder the above conditions, we use the equation: N

Dig = (DRF)i,

C

(Gn/G) Aa,"

(mrem y-')

(2-41)

n-1

where Di, = annual dose to organ i (mrem y-') due to ingestion of 14C, (DRF)&= dose-rate factor for organ i (mrem y-'/pCi gC-'), G, = annual average intake of dietary carbon derived from the n-th location (gC y-'), G = total annual average intake of dietary carbon (gC y-'), and Aa," = estimated average daytime specific activity of ambient airborne carbon during the growing season at location n. The report on Reference Man by the International Commission on Radiological Protection (ICRP, 1975) recommends a value of G = 300 gC d-' (1.1 x lo5 gC y-') for a male adult. Estimation of the dose rate to an individual due to ingestion of 14Crequires an assumption about the reference individual's diet and the distribution of sources of dietary components that are grown in the area affected by the release. Table 2.22 is provided to assist in computing the Gn from the animal intake of each foodstuff once these assumptions are made.

2.5 SPECIAL CASE RADIONUCLIDES (TRITIUM, CARBON 1-4)

95

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TABLE 2.22-Fmctional carbon content (gC kg-') for edible portion of selected foods" Vegetables and Fruits

Vegetables and Fruits

Grain for Human Consumption

Lettuce Cabbage Celery Spinach Broccoli Cauliflower Brussels sprouts

20 32 24 28 42 35 65

Peaches Pears Plums Strawberries Snap beans Summer squash Blueberries

56 76 62 44 47 21 74

Potatoes Oranges

Blackberries Cranberries

69 57

Sweet cane Sugar cane Peanuts

Currants Gooseberries Black raspberries Asparagus

67 48 89

Carrots Dry beans Sweet potatoes Cantaloupes Dry Peas Pecans Tomatoes Grapes Apples

Corn Spring wheat Soybeans Oats Barley Rye

Miscellaneous

Eggs Honey

156 365

30 Dairy products

Meat and poultry Beef Lamb Pork Turkey Chicken

118 391 465 431 395 396

228 289 402 254 156

Milk (whole) Ice cream Cheese Cottage cheese Butter

67 196

350 99 620

"Unprepared food. Based on protein, carbohydrate, and fat content (50,44, and 76% carbon, respectively) given for the various foods by Watt and Merrill(1963).

Inhalation is ordinarily a minor exposure pathway for 14C, with dose-rate factors that are about 1%of those for ingestion. For completeness, we give the equation for the inhalation dose rate as:

Dih

=

(DRF)ihABnir

(mrem y-')

where

Dih = annual dose rate to organ i (mrem y-') due to inhalation of 14C,

(DRflih = dose-rate factor for organ i (mrem y-'/pCi gC-I),

K","

= annual-average specific activity of airborne carbon in

pCi gC-' where the exposed individual lives and works. Since the exposure pathway is not limited by the operation of photosynthesis, K","should be estimated on the basis of meteorological data sampled day and night through all seasons.

3. Assessment of Radionuclides Released to Surface Waters Radionuclides can occur i n freshwater systems either from atmospheric deposition, r u n offlsoil erosion or from releases of liquid effluents. Regardless of the source, two forms of potential radiation exposure can occur-external and internal. External exposure can occur from the surface of the water and sediment, and from immersion in the water. Internal exposure can occur from the ingestion of radionuclides, either directly as from drinking water, or as a result of transfer through aquatic food webs and consumption of aquatic biota. Current pathway models predict the concentration of radionuclides in the water as a result of dilution, dispersion and adsorption on sediments as a function of space and time. A number of transport models are available. T h e decision on the degree of complexity necessary depends upon the characteristics of the receiving water body, the potential exposure pathways, and how accurately the resultant dose needs to be known. I n current models, the adsorption of a radionuclide on sediments or the assimilation of a radionuclide by aquatic biota is calculated by using a single empirical relationship to represent the adsorption from water to sediment or the transfer of the radionuclide from water to a n organism. These dimensionless coefficients are known as Distribution Coefficients (KD) and Bioaccumulation Factors (BF) respectively. T h e rate of external exposure from the radionuclides per unit time is derived from the calculated concentration in the water or from the concentration i n the surface sediment and the pertinent usage factor. I n the case of internal exposure from drinking water, the rate of intake is derived from the calculated concentration i n the water and the usage rate. Where aquatic biota are consumed the rate of intake is derived from the calculated water concentration, the bwaccumulation factor and the pertinent usage factor. The intake derivations are all made using the pertinent parameters at the site of exposure. 96

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97

3.1 Surface Water Models

3.1.1 Introduction In addition to direct discharges, radionuclides can enter surface waters in several ways: 1. washout of atmospheric radionuclides directly to the water surface, 2. washout of atmospheric radionuclides deposited on the land and subsequently transported by overland flow or groundwater transport, 3. overland or groundwater transport of radionuclides residing on/ in the ground (e.g., waste disposal, mill tailings, reactor accidents). The present section does not deal with the mechanisms for release to surface water. Groundwater transport of radionuclides residing in the ground is covered in Section 4. Overland flow transport of dissolved or particulate radionuclides is not covered in this report. There are many overland transport or "watershed" models currently available, ranging from empirical approaches to complete numerical simulations. The interested reader is referred to Onishi et al. (1982~)and Haen et al. (1982). Many models have been developed to describe the changes in concentrations of radionuclides in aquatic systems as a function of space and time. These models vary in complexity from simple black-box time-concentration models in lakes or oceans to complicated threedimensional-dispersion-advection-particle resuspension models for streams, rivers, estuaries or coastal waters. The changes in concentration are dependent on dilution and changes in the chemical form of radionuclides in time and the degree of the interaction with bottom sediments or suspended particles. In the most conservative models for routine release analyses, it is assumed that all radionuclides entering the aquatic system remain in solation and their concentrations will decrease solely by radioactive decay or by dilution. Such models will overpredict the food chain dose for those radionuclides which are adsorbed onto particles such as 13'Cs in freshwater but reasonably describe the behavior of ions like "Sr in fresh water (Lerman, 1972) or 13'Cs in saline water (Jinks and Wrenn, 1975). After radionuclides are adsorbed onto particles in the water, they are ultimately transferred to the bed sediments. The bed sediments are often considered to be a sink for radionuclides. This may

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3. RADIONUCLIDES RELEASED T O SURFACE WATER

be true where contaminated bed sediments are rapidly covered by new sediment. However, the sediment/water interface can be disturbed by biological and physical processes such as biological mixing and physical and biological resuspension which will slow down the burial rate. Assuming that there is an equilibrium between water and bed suspended sediments, sediments will remain a source of radionuclides to the aquatic system, due to desorption, for much longer times than would be predicted from sedimentation rates alone. The effect of the mixed layer of sediments is to buffer the concentration of radionuclides in the water. For example, Edgington (1981) has shown that for plutonium in a wide range of aquatic environments, freshwater and marine, there is an equilibrium between water and sediment. Detailed studes of plutonium in water and sediments of the Great Lakes have shown that the respective concentrations at present are greater than would be predcted from a simple sedimentation model (Wahlgren et al., 1980). This concept has been validated in the Irish Sea, but the most striking example is the continued remobilization of plutonium and americium from the sediments of Eniwetok Atoll Lagoon even though there have been no new inputs over the last two decades. A detailed review of all radionuclide transport models applicable to rivers, estuaries, coastal waters, Great Lakes and impoundments has recently been completed by Onishi and his co-workers for the U.S. Nuclear Regulatory Commission (Onishi et al., 1981). This report summarizes the present state of the art. They considered not only models that have been specifically defined for radionuclides, but also the applicability of generalized sediment transport and water quality models to the problems of radionuclides in aquatic systems. Most models include terms to describe advection, dispersion, and radioactive decay. Consequently, they are limited to predicting the changes in concentration of water-soluble radionuclides resulting from short term migration where the association of individual radionuclides with particles is weak or the concentration of suspended particles is very low. Few of the models have included interaction terms for sediment/particle-radionuclideinteractions and none of the models at present considers the modifying effect of inorganic or organic ligands on the concentration of radionuclides in the water. However, the steady state contaminant transport model, EXAMS (Smith et al., 1977), and the geochemical model, MINTEQ (Felmy and Jenne, 1982). were recently coupled to include these effects on contaminant concentrations as an initial attempt (Felmy et al., 1983). Basically, a complete transport and fate model should have the capability to predict, as a function of space and time, the concentration of any radionuclide

3.1 SURFACE WATER MODELS

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99

species which can undergo transfer from the water to an aquatic organism or to sediments. While the major purpose of such aquatic transport models is usually to predict the persistence of soluble or biologically active species in the water column, it should be recognized that the adsorption of radionuclides on sediments needs to be included, as an important factor in calculating external dose. The models must, therefore, include terms to describe not only the transport, but also the fate of introduced radionuclides. When a radionuclide is introduced into an aquatic environment, a series of interactive physical, chemical, and biological processes are set into motion. For the most complete models the chemical and biological terms may be as important or more important than the physical advection and dispersion terms. Changes in chemical form can occur as a result of changes with time in the composition of the receiving water, seasonal, biological and biochemical reactions, and the concentration of suspended solids. For example, recent experimental work in freshwater environments has shown that the ratio of Pu(V)/Pu(IV) changes dramatically as a result of complexing with dissolved organic carbon compounds in the water (Wahlgren and Orlandini, 1982). Additionally, the ratio of oxidation states has been shown to change considerably as water flows through the Irish Sea around Scotland into the open Atlantic and the North Sea (Nelson and Lovett, 1978). However, it is at present unknown how individual oxidation states affect bioavailability. Where different water types interact, changes in the major chemical composition of the resulting water can alter the chemical complexing reaction of organic and inorganic ligands as well as the availability of adsorption sites on particulate material. The most dramatic changes in the chemical behavior of radionuclides occur where freshwater rapidly mixes with sea water. The adsorption/desorption behavior of 134Csand 13'Cs on particles in the Hudson Estuary is a prime example of the effects of a chemical transformation. Thus, a complete model must take account of all the major chemical and biological processes occurring in the water as well as the physical advection and dispersion processes. The transport of 137Csin the Hudson River was recently simulated by the unsteady, three-dimensional model, FLESCOT by changing the adsorption/desorption amount with salinity and sediment sizes (Onishi and Trent, 1982). It is clear that such aquatic models can be very complex. However, what degree of complexity is required? The complexity of the particular model required will depend largely on how accurately the dose needs to be known. In the present climate, where releases must be "as

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3. RADIONUCLIDES RELEASED T O SURFACE WATER

low as reasonably achievable" extremely conservative or complex models probably are not desirable. Conservative models tend to overestimate the resultant dose which leads in turn to an overestimation of the benefits to be realized from further reductions in releases. The adoption of too complex a model will require the collection, evaluation and validation of an excessive data set of environmental parameters. Such an effort may be more than can be justified by the benefits. A further degree of complexity is introduced when considering the amount of detail to be predicted in the time-dependent and spatial dispersion characteristics of the system. For example, radionuclides in the Great Lakes or oceans as a whole can probably be modeled with relatively simple time-concentration black-box models (Lerman, 1972; Jinks and Wrenn, 1975; Wahlgren et al., 1980). On the other hand, predictions of the concentration of radionuclides reaching a specific area of the water body, such as a municipal water intake or shellfishery downstream from a nuclear facility on a river may require a more sophisticated multi-dimensional advection-dispersion numerical model. Since extensive reviews have recently been made of all the models available (Onishi et al., 1981; USNRC, 1978), the purpose here will be to assess the data requirements for each term in the models, the data available for verification, and the additional data required for models of increasing complexity. 3.1.2

Model Types

In the development of models, it is necessary to be aware of (1) sources, i.e., location, form and rate of input; (2) removal and transformation mechanisms, i.e., volatilization, sedimentation, parentdaughter relationships and chemical changes such as oxidation state; and (3) water and sediment transport processes. Therefore, the application of the model requires a specification of the source term, the chemical properties of the radionuclide, the transport mechanisms and the choice of an appropriate averaging volume and time. The concentrations of radionuclides in any aquatic system will be determined in part by the balance between the rate of pollutant input and the rate of loss or removal. The processes likely to remove radionuclides from the water are: loss (or gains to the atmosphere) by volatilization, loss to the sediments, and radioactive decay. Additionally, transfers between the dissolved, particulate and sediment phases will also occur. The possible transformations are shown in Fig. 3.1 (NOAA, 1979).

3.1 SURFACE WATER MODELS Dumping

Atmpherit Dep8Sition

/

101

buoc

I

Volmtile

Compounds

I I I I

Fig. 3.1 Possible transformationsof a pollutant in the water column (from NOAA, 1979).

A generalized equation may be written:

where

C = concentration of dissolved, particulate, or sediment species, V = losses to the atmosphere, R = Losses by sedimentation, or return by resuspension, D = decay or growth of a daughter. T = transfer by complex formation, precipitation, adsorption, and/or diagenesis, W = advective processes, and M = diffusional or mixing processes. This generalized equation can be rewritten as a basic equation of mass conservation of a radionuclide in terms of the one dimensional advection-diffusion equation in Cartesian coordinates:

/

102

3. RADIONUCLIDES RELEASED T O SURFACE WATER

where C = the concentration in the water (Cd), or in sediment (C,),

s = the Cartesian coordinate, Ui = the velocity or advection term, t i = dispersion coefficient, CKjC = the sum of decay or other concentration dependent loss or gain terms where Kj is a rate constant, including V, the decay portion of R, and T (see Eq. 3-l),and CSj = is the sum of source/sink terms, and Sj is a flux per unit volume.

Typically, concentration Cd is expressed in pCi L-' and C, in pCi g-' or pCi kg-', Ui, ci and x are expressed in terms of lengths and times consistent with the scale of the water movement processes being modeled. A series of such equations can be defined for every form of each radionuclide (i.e., Cd, Cs, where C, includes inorganic or organic (biota particles) and in the required number of coordmates (i) and then solved simultaneously. In general, it is impossible to solve the equations analytically and numerical techniques must be used (Onishi et al., 1981). This general equation can be simplified in certain special cases SO that an analytical solution is possible (USNRC, 1976; Codell et al., 1982). These cases include the transport of dissolved radionuclides with and without radioactive decay as a result of an instantaneous point release, or continuous point sources with a time dependent or steady-state solution. Such solutions of the advection diffusion equation can be applied to a situation approximating an infinite domain with constant depth and velocity. Thus, they can be applied to soluble radionuclide transport in water bodies such as lakes, estuaries, and oceans where the assumptions implied in formulating the solution equations can be met. Many models have been developed to describe water quality and sediment transport that can be used or applied to the behavior of radionuclides. These models can be summarized in terms of six general types described below. (1) Aduection-diffusion with decay and sourcelsink terms (Eq. 3-2)

This is the most general equation, and provided that the input constants can be measured, it can be solved numerically for all situations involving dissolved species and the reduction in concentration due to interactions with fixed adsorbers (bed sediment or biota). It is

3.1 SURFACE WATER MODELS

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not directly applicable to problems involving transport of radionuclides adsorbed to sediments. Many models of this type have been developed for water and sediment transport and applied to rivers and estuaries (Onishi et al., 1981). In general, these models are one-dimensional and unsteady. While adsorption to sediments can be included, very few models incorporate a coupling of water and sediment transport. Buchner and Hayes (1975) used a model of this type to simulate the concentration of tritium in the Savannah River after a single discharge, and Norton et al. (1974) simulated common water quality parameters such as DO (dissolved oxygen) and BOD (biological oxygen demand) in the Truckee River. The U.S. Nuclear Regulatory Commission has developed a simple one-dimensional estuary model, including sedimentation, that accounts for the net velocity downstream of the sediment bed as well as the interaction with sediment (USNRC, 1978). A similar model by Baca et al. (1973) can simulate up to 16 water quality parameters including soluble radionuclides and is applicable to tidal rivers. The transport of sediments in rivers is a major problem and therefore many models have been developed to simulate these processes. Among the more successful models were those developed by Thomas (1974) for the U.S. Corps of Engineers and Hetrick et al. (1979) as part of the ORNL unified transport of suspended and bedload sediments. More recently Onishi et al. (1980a) have developed an unsteady twodimensional model that attempts to simulate more accurately the migration of radionuclides by coupling water and sediment transport. The model includes components for sediment/radionuclide interactions together with transport terms for dissolved species, suspended solids and sediment, thus allowing for adsorption/desorption, and deposition/erosion and instantaneous/continuous releases of 137Csand 'OSr. A comparison of measured and simulated concentrations of 137Cs in the Clinch River is shown in Fig. 3.2 (Onishi et al., 1980a). A similar model has been used to simulate the behavior of kepone in the James River (Onishi, 1981). (2) Advection with or without decay and sourcelsink terms

This model assumes that the resolution of the time scale is such that diffusive mixing processes are unimportant, as might occur in a fastflowing river. These models can be used to simulate water quality or

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3. RADIONUCLIDES RELEASED TO SURFACE WATER

-.-

J

DISSOLVED~~~CS

0 MEASURED TOTAL'~'CS

1 I

1 I

MEASURED P A R T I C U L A T E ~ ~ ~ C S MEASURED D I S S O L V E D ~ ~ ~ C,S

RIVER KILOMETERS Fig. 3.2 Model simulation in longitudinal distributions of dissolved, particulate and total cesium-I37 concentrations in the Clinch River, Tennessee (from Onishi et aZ., 1980a).

radionuclide concentration in rivers or estuaries and can include adsorption to sediments (Hydroscience, Inc., 1978). The liquid pathway model of Fletcher et al. (1973)calculates the dissolved radionuclide concentration at a given location and time by applying the mass conservation equation with radioactive decay:

where C x ,= concentration for dissolved radionuclides at location x at time

t, Q,, = flow rate at location x a t time t,

Ci =concentration of dissolved radionuclide of tributary i, = flow rate of tributary i, and X = radioactive decay rate. Sediment transport rate, S, is found empirically by Qi

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105

where a and b are constants for each sediment size range, and the concentration of radionuclide, C, transported on sediment is calculated from C,, and the value of,the Ko (see Section 3.1.3). (3) LaGrangiun routing models with decay and sourcelsink terms

In this model it is assumed that the longitudinal coordinate system is moving with the flow velocity. This is also a comparatively simple model that can be applied to fairly uniform non-tidal rivers, but is limited to transport of dissolved radionuclides with decay or adsorption by other substances at a constant rate or with fixed particulate radionuclide concentrations. This type of model has been used by Waddel et al. (1974) to study water quality in the South Platte River Basin. A special case of this model is the U.S. Nuclear Regulatory Commission Plug Flow Model in which it is assumed that radioactivity from the source is moving as a plug in a uniform channel and losses are only due to radioactive decay or transfer to sediment (USNRC, 1976). ( 4 ) Complete mixing model

This is mathematically the same as the previous type. There are no spatial coordinates and the change in concentration of the radionuclide is due to decay proportional to the concentration and sinklsource strength. This is a simple black-box time concentration model which can be applied to well-mixed lakes or the oceans where concentration can be assumed to change with time but not with location. This model permits coupling of the boxes as in a series of lakes, in permanently stratified situations within lakes, or rivers and estuaries which can be compartmentalized. Several groups have attempted to simulate the behavior of radionuclides in rivers, estuaries, and lakes using the complete mixing model and it is possible to include a wide variety of parameters and processes, such as transfer between compartments, suspended sediment interactions, sediment deposition, bioturbation, and deposition. Onishi et al. (1980b) have developed a model with a series of mixed tanks connected to simulate the behavior of pesticides in streams which includes adsorption onto sediment but no deposition or resuspension. Several models have been developed to describe the behavior

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3. RADIONUCLIDES RELEASED TO SURFACE WATER

of radionuclides in lakes. Lerman (1972) developed a time-concentration model for 'OSr in all the five Great Lakes. In order to account for apparent large variations in the 'OSr in the water column, he included as a source term not only the upstream and atmospheric inputs, but also transport overland and through groundwater from the watershed. More recently, Walgren et al. (1980) have modeled on an annual basis the behavior of plutonium in the Great Lakes. The results are shown in Fig. 3.3. The deviations between the predicted and observed values point to the need to better understand the true nature of the adsorption/ desorption reaction with sediments. Several more complicated models have been developed to simulate the transfer of pollutants between different compartments within one lake. The components of such a model developed by Vanderploeg et al. (1976) are shown in Fig. 3.4. This model calculates the concentration of radionuclides in a stagnant, non-stratified, shallow eutrophic lake through the food web to fish. Interactions with sediment and interstitial water are also included. The model was applied to White Oak Lake to simulate the behavior of '37Cs,but is limited to lakes with no measurable inflows or outflows. Similar models have been constructed by Thomann and DiToro (1979) to simulate the response of the Great Lakes to pollution abatement.

4

4

-1

1 1 1 1 1 1 1 1 1 1 1 1 1

- 10

Lake Michigan Tk = 2.4 yr

-

-

Lake Huron

-

1950

Lake Superior

Tk

1970

1860 YEAR

2.3 yr

4

1950

1960

1970 YEAR

Fig. 3.3 Comparison of concentrations of 238.B0P~ in the water column predicted by the coupled-lakes model with available experimental data points (0). The best estimate of the residence time for deposition in the sediments is given for each lake (from Wahlgren et al., 1980).

1

4 bVATER PLANTS

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3.1 SURFACE WATER MODELS

4

INTERSTITIAL WATER

PHYlOPLANKTON

?iATER b

1 I _ I' 1

1

POM

SEDIMENT

ZOOPLANKTON

ON BOnOM

I

1

DETRITUSFEEDING INVERTEBRATE

FlSH I Ill

T

& OETRITUS-

-+ FEEDING F l S H

-

ill

I

T

FlSH 1 (21

1

DETRITUSFCtDlNG F I 5 H (2)

-

1;, FlSH 2

Fig. 3.4 Compartments of the Lake Ecological Model of Vanderploeg et d.(1976).

Comparable well-mixed compartment models can also be utilized to simulate the behavior of radionuclides in the oceans. In the model recommended by the Commission of the European Communities (CEC, 1979), water movements, sediments, and radioactive decay are considered. The variation in concentration of such radionuclides in the ith compartment is a differential equation of the form:

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3. RADIONUCLIDES RELEASED TO SURFACE WATER

for all i = 1 to N, where A; = the activity a t time t in the ith compartment, Kij and Kji(i # j) = the rates of transfer between compartments, Ki = the rate of loss due to decay and sedimentation, and S; = the rate of new input to compartment i. The fraction of activity not adsorbed on suspended sediments (Fw)is also calculated so that food chain transfer may be correctly assessed: (3-9) J'w = 1/(1 + K D ~ s s ) , where CSS is the suspended sediment load (g L-') and KD is the distribution coefficient (Lg-') discussed in Section 3.1.3. Removal of activity to bottom. sediments is estimated using a particle scavenging model discussed in Section 3.1.3.

( 5 ) Diffusion or mixing with or without decay or sourcelsink terns

This model includes no advective terms and is only applicable to quiescent water bodies. Thus its use is very limited. ( 6 ) Monte Carlo model

Such models are not based on a solution to a differential equation but rather describe the transport of contaminants phenomenologically using a computer memory to store information on the movement of constituents a t each time step. This model can be applied to either dissolved or particulate radionuclide transport, but a considerable complication is introduced when requirements are incorporated for the coupling of both dissolved and particulate radionuclides with transport by both sediment and biota (Ahlstrom, 1975). Advection-diffusion models and Monte Carlo models can be applied without difficulty to the transport of dissolved radionuclides. Considerable modifications would have to be made to existing dissolved-only contaminant transport models to incorporate particle and sediment association. I t is clear that advection-diffusion models and Monte Carlo models have a general applicability and models of other types are of a more limited applicability. However, the application of the latter may be more useful in those cases where the modgl parameters are well known and the simplifications may be justified. A summary of these model types and their applications is presented in Table 3.1.

TABLE 3.1-Examples of the mnge of models used to evaluate the changes in concentratwn of mdtonuclides in aquatic environments. Model Type

Simple Box Models

Time dependent

Application

Lakes, impoundments Lakes, Rivers

Simple Flow Models

Two dimensional flow

Rivers

Assumptions and Parameters

Completely mixed above and below thermocline. Completely mixed with sediment interaction. Assumes river can be divided into a series of well-mixed compartments, i.e., between dams includes equilibration with suspended sediments. Calculates dilution factor and radioactive decay Estimates fraction adsorbed to sediments. Two dimensional model for mixing across a river with vertical variation in concentration and velocity averaged.

Comments

References

Used to predict wSr in Gt. Lakes.

Lerman, 1972

Used to predict Pu in Gt. Lakes.

Wahlgren et al. 1980

Used to describe pesticides in rivers. 13'Cs in Clinch R.

Onishi et d ,1980b NRC, 1978

Appried to 3H releases into Savannah

Soldat et al., 1974 Buckner & Hayes, 1975 Jinks & Wrenn, 1975

Behavior of Ia7Cs Applied to Missouri River for water quality

Yotsukura and Sayre, 1976

TABLE 3.1-Continued Model Type

Application

Assumptions and Parameters

Comments

Steady, one-dimensional convection equation with decay and source/sink terms. Simulates transport of trace contaminants in the dissolved form and on particulates. Combines Wisconsin hydrologic transport model with a sediment transport model.

Diffusion is not considered, since the cross-sectional area of the river is considered constant. Uses KI, to simulate first-order exchange between sediment and water. Couples water transport and sediment transport using three submodels and has been used to simulate the behavior of I3'Cs and *Sr in the Clinch R (see text).

References

-

Complicated Flow Models One dimensional

Two dimensional

Rivers, estuaries

Simulate the transport of sediment and contaminants with their interactions. Finite element model including sediment transport, dissolved contaminant transport and interaction of contaminant with sediment. Includes

Applied to canyons in Los Alamos National Lab. to simulate =F'u migration. Handles linear or quadratic approx. to velocity and depth distribution so as to be compatible with other hydrodynamic models.

Hydroscience, 1978

Fields, 1976 Hetrick et d,1979

Onishi et al., 1980a Onishi et aL, 1982b

Three dimensional

advection and dispersion, longitudinal and lateral, wave motion to resuspend eediments, sediment cohesion, sediment deposition and resuspension, sediment sources and mixing. Numerical model computing the velocity field from vertically integrated two-dimensional equation of mass and momentum conservation which then becomes the advective mechanism. Finite difference model computing unsteady distribution of flow, water temperature, salinity, sediment, dissolved contaminated particulate contaminant.

Has been used to pre-

Onishi, 1981

dict the migration of *9Pu,I3'Cs, and Kepone.

Applicable to cases of non-steady-state flow, particularly in estuaries. Used to calculate bacteria distribution in the NY Bight

Leendertse et al., 1973

Has been used to predict the migration of 13'Cs in the Hudson River estuary with KDchanging with salinity.

Onishi & Trent, 1982

o +

m C

%

b M

2 2z

5u M

F

ul

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3. RADIONUCLIDES RELEASED TO SURFACE WATER

3.1.3 Evaluation of Parameters and Data Bases There are many different mathematical and computational approaches that can be applied to solving the generalized advectiondiffusion equation (Eq. 3-2) and these have been summarized by Onishi et al. (1981). However, it is clear that the most important problems in assessing the value of the different approaches to obtaining a solution is the correct assessment and assignment of reasonable values to the various parameters required for solution of the model equation. The more simplifications that can be made in the equation, the fewer the number of parameters required. Such simplifications might include, for example, in the case of stream releases, the assumption of instantaneous dispersion across a river, interaction with suspended solids but no settling in the longitudinal flow. For lakes or impoundments, simplifications may include the assumption of instantaneous dispersion and no resuspension of bottom sediments. The most complete models will have to include parameters for,(i) diffusional dispersion within the water column, (ii) advection as a result of flow, (iii) adsorption/desorption on sediments, (iv) transport settling and resuspension of sediments, (v) the hydraulic behavior of water in lakes and oceans-water balance, stratification, upwelling, etc., (vi) hydraulic and sediment properties of rivers-water flow, sediment movement and sinks, (vii) the hydraulic' behavior of estuaries, and (viii) evaluation of sources and sinks.

Diffusional Dispersion (ei) An accurate evaluation of the dispersion coefficients and advective vectors will be important if the accurate evaluation of radionuclide distribution is to be made. Within estuaries, the dispersion, for example, will be a function of many competing physical factors such as geomorphology, tidal flow, effects of freshwater flow, mixing conditions, and salinity. Many of those factors will be influenced by weather conditions prior to, during, and after the event. Similarly, in lakes, dispersion is a complex product of the behavior of currents, waves and the wind, and may be variable by season due to the formation of a thermal bar or stratification (Rodgers and Sato, 1970; Hamblin, 1971). Wind driven waves will resuspend sediments in the nearshore zone which then will considerably alter the ultimate behavior of the radionuclides in the dispersing plume. Models strongly dependent on dispersion and advection are perhaps the most complicated to parameterize and most difficult to validate. Considerable effort is expended

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to obtain data sets to validate models of the physical dispersion process, such as the use of dye (Hamblin, 1971), thermal releases (Romberg et al., 1971) or turbidity plumes (Johnson et al., 1977). While the result of model calculations agree fairly well with measurements in the nearshore zone, the far-field calculations are not as successful. However, more critical is the question of of how well such models can accurately predict the movement of a plume. The question of dispersion within a finite length of a river channel is less important, and a majority of the models do not include a parameterization of these advective/diffusion terms for this case. The rate of dispersion in a river or estuary will be dependent to some extent on the shape and roughness of the channel, the rate of flow, and external wind stress. Again these parameters are highly sitespecific and the rate of dispersion also will be strongly dependent on the time dependent factors such as flow. Aduection (Ui)

The advective terms are the most critical for models of the transport of radionuclides in rivers and estuaries. The correct parameterization of this term in relation to the water-soluble radionuclides in rivers depends solely on how well the rate of flow may be predicted downstream on the basis of prior experience and weather conditions prior to, during, and after a release. In estuaries, these terms must be modified to account for variations in velocity, water volume, and mixing due to tides and tidal currents. The correct parameterization of this term becomes even more critical for radionuclides which are strongly adsorbed by and transported with the suspended sediments. Under these conditions, the sediments can also act as source or sink depending on the hydrodynamic properties of the individual river. The more complete models have attempted to estimate the resuspension of bottom sediments and transfer downstream (Onishi and Wise, 1979 and Onishi, 1981). A considerable effort has been made to characterize these processes in terms of simple parameters such as particle size distribution and particle-particle cohesiveness for sediments in rivers and estuaries (Thomas, 1974; Onishi and Wise, 1979; Fields, 1976). The coupling of these parameters with river flow requires further development of transfer coefficients based on Stokes settling velocities (Fields, 1976) or non-uniform vertical distribution of longitudinal velocity (Onishi and Wise, 1979). In general, this process has been parameterized by assuming that there are certain flow rates which will resuspend, or keep in suspension

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sediments of given ranges in particle size. Sediments are first classified as cohesive or non-cohesive and then divided according to particle size. The CHNSED model developed by Fields (1976) includes 12 size fractions from 4 pm for clay to 100 pm for sand while the models, SERATRA (Onishi and Wise, 1979), FETRA (Onishi 1981), FLESCOT (Onishi and Trent, 1982) and TODAM (Onishi et al., 1982b,c) specify three size fractions. In the Fields model, transport of suspended sediment is parameterized in terms of flow rate and Stokes settling velocity, while bedload transport requires the estimate of an effective diameter (Thomann, 1978). The SERATRA, FETRA, FLESCOT and TODAM models express deposition and source of cohesive and noncohesive sediments separately with empirical relationships based on bed sheer-stresses, flow rates, sediment diameters and settling velocities. It is further assumed that any pollutant or radionuclide adsorbed onto these sediments will equilibrate with the water a t some reasonable rate. This problem will be discussed in more detail later in the Section Adsorption/Desorption Properties of Sediments. At the present time, the parameterization of these processes has been considered mostly in terms of the physical properties of particles. There is a growing body of information which suggests that the physical properties of sediments are strongly influenced by biological and chemical processes changing, in particular, the cohesiveness of sediments and the distribution of particle sizes. The coagulation of small clay-mineral and organic particles into larger particles is extremely important in removing pollutants from the water column (Lerman, 1979). This process is even more important in estuaries where changes in the surface properties and chemistry of the particles occur because of the changes in the chemical composition of the water (Duinker, 1980). The most obvious example of this is the difference in the behavior of '37Cs for adsorption onto, and desorption from, clays in fresh and marine waters (Jinks and Wrenn, 1975). The resuspension of sediments from the bottom of large lakes, rivers and estuaries will also play a large role in the transport and control of the behavior of radionuclides in the water column (Wahlgren et al., 1980). Here the resuspension mechanism could be described as an advective term. Little is known about this process in lakes other than evidence of intermittent strong currents and massive sediment disturbances in the historical sediment record (Robbins et al., 1978). However, if the controlling process for the concentration of radionuclides in water is an equilibrium between water and sediments, a detailed knowledge of the magnitude of this resuspension process and mixing within the water column will be necessary.

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Hydraulic Properties of Lakes and Estuaries In order to adequately define the parameters for lake and estuarine models it is necessary to include terms for: the presence of permanent or non-permanent thermoclines or chemoclines, physical mixing between the upper and lower layers of the water column, chemical and biological exchange or transport between layers, and changes in water level (or volume). In estuaries, there are additional problems related to estimating the effects of tidal flow, river flow, the formation of a salinity wedge, and the associated changes in the physical and chemical properties of the suspended particles between fresh and salt water (Duinker, 1980).

Sediment Deposition and Resuspension In terms of the physical parameters, estimations of the rates of sediment deposition and resuspension are the least well characterized. In lakes, where the advective term is relatively small, it is comparatively simple to determine sedimentation rates both within the water column and at the sediment water interface, using sediment traps and radionuclide geochronological techniques, respectively (Wahlgren et al., 1980; Krishnaswami et al., 1971; Robbins and Edgington, 1975). The modeling of suspended particles in deep lakes and the oceans is complicated by seasonal changes in particle composition and remineralization within the water column (Thomann, 1978; Wahlgren et al., 1980). In terms of the surface sediments for those areas where strong advective forces are largely absent, recent experimental evidence has shown that biological activity and infrequent storm events disturb the sediment record and induce resuspension (Edgington and Robbins, 1976).

Adsorption/Desorption Properties of Sediments It has long been recognized that many radionuclides (or other contaminants) are readily adsorbed by (both organic and inorganic) sediment particles in the environment, where, depending on other conditions (i.e., currents, sedimentation rate, biological mixing, etc.), the contaminated sediment is either buried or returned to the water column. Therefore, in many of the models summarized by Onishi et al. (1981), a parameter is introduced to linearly relate the concentration of a constituent on sediment to its concentration in the water.

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3. RADIONUCLIDES RELEASED T O SURFACE WATER

This parameter is commonly defined as the distribution coefficient ( K D )similar to that used to describe ion-exchange equilibria, i.e.,

KD =

conc. of constituent per gram sediment -

C,

cone. of constituent per milliliter water

Cd

-

For some dissolved species, the linear equilibrium relationship is not appropriate (e.g., cesium). In this case, the adsorption can be better represented by the Freundlich isotherm:

C, = k CAI" I t can readily be seen that if n = 1, k = KD. There is a real problem in applying equations and constants which have been derived for simple ion-exchangers or adsorbers to natural material such as soil or sediment. The chemical composition of these materials is both complex and variable, and a natural sediment may contain varying proportions of different geochemically definable minerals, hydrous oxides, and detrital complex organic compounds (generally humic and fulmic acids) which have widely different ion-exchange or adsorption properties (Gibbs, 1973). As for well-characterized ion-exchange resins, the effective exchange capacity will depend on surface area, and the size distribution of the particles. Furthermore, it is possible that the adsorption properties of the sediment will not depend on bulk properties, but on the presence of an ill-defined surface layer on all particles, one or more molecules thick, for example, of hydrous ion oxides or organic materials. The factors governing the uptake of radionuclides by sediments can be complex, and the nature of the process will depend not only on the chemical properties of the individual radionuclides and the formation of complexes in the aqueous phase, but also on the complicated geochemical properties of the sediments. The assumption that there is one KD for each radionuclide with sediments is somewhat naive a t best. There is a further complication: the definition of KD implies that there is a true equilibrium between the ion in question and the sediments and this definition is inherent in all models except several models to describe the aquatic transport of radionuclides (Onishi and Wise, 1979; Onishi, 1981; Onishi and Trent, 1982; Onishi et al., 1982b,c). A more rigorous approach to handle radionuclide adsorptionldesorption mechanisms is to model detailed chemical reactions of the radionuclides in the aqueous and sediment phases. If this detailed chemical modeling approach is used, the user will need information about the Eh, pH, and the natural geochemical equilibrium of the

3.1 SURFACE WATER MODELS

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117

chemical in the water, as well as a complete mineralogic description of the soil, water quality parameters, and a large number of chemical reaction constants, including the spatial variation of these parameters. Currently, several geochemical models are used to simulate radiochemical reactions to obtain aqueous chemical species and adsorption/ desorption and precipitation/dissolution values. This takes the place of using KD as a bulk expression of adsorption/desorption (Krupka and Jenne, 1981; Felmy and Jenne, 1982). There is considerable literature describing the uptake of radionuclides by soils and sediments. There has been little effort made to synthesize this information, and few attempts have been made to determine whether the assumption of a reversible KD is acceptable. Onishi et al. (1981) have developed a list of almost 30 parameters that must be evaluated to determine the functional dependency of KD on sediment composition; however, they failed to recognize the most critical one-the not-complete reversibility of the adsorption reaction-when they applied SERATRA to the Clinch River (Onishi et al., 1980a). The current version of the SERATRA models (Onishi et al., 1982a) as well as the FLESCOT model (Onishi and Trent, 1982) handle this not-complete reversibility of adsorption/desorption mechanisms. As has been mentioned earlier, the uptake of 137Csby sediments is dependent on the geochemical environment. In the Great Lakes, where there are significant concentrations of illite in natural clays, '37Cs is very strongly adsorbed, and little can be extracted (Alberts et al., 1975); in this situation, the adsorbed cesium is not readily available to aquatic biota. In other locations, such as the waters of the southeast U.S.and the ocean, very little '37Cs is adsorbed, i.e., the KD is small, and it is readily desorbed. The differences in behavior are simply explained in that for the Great Lakes sediments the '37Cs becomes irreversibly bound at interlayer sites in the clay mineral illite, while the southeastern U.S. clays do not contain illite (Wahlberg and Fishman, 1962). In oceanic sediments, these sites are already occupied by K+ and ions. Therefore, in the ocean and southeastern U.S.sediments, 137Csis absorbed reversibly by an exchange mechanism on the natural clay ion-exchanger. Sediments in the Hudson River estuary exhibit a reversible trend of sorption caused by diurnally and seasonally changing salinity. The relationship between KD and chloride content of the water in the Hudson River is illustrated in Fig. 3.5 (Jinks and Wrenn, 1975). In contrast, extensive measurements of the uptake of plutonium onto sediments of widely different composition in a wide variety of environments have resulted in values of KD that are remarkably

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3. RADIONUCLIDES RELEASED TO SURFACE WATER

Fig. 3.5 Relationship of I3'Cs distribution coefficients (KD) and chloride concentrations in continuous water samples at Indian Point, New York in 1971 (from Jinks and Wrenn, 1975).

constant (Edgington, 1981). Other measurements indicate that the uptake of plutonium is rapid and reversible. Therefore, it is reasonable to assume that the value of KDis a true reversible constant (Edgington et al., 1979). The nonvariability of the value of K D with sediment composition suggests that the mechanism of uptake is independent of the gross composition of the sediments. Experiments have shown that plutonium (and other elements such as americium) are uniquely associated with reducible hydrous oxides which occur ubiquitously as coatings on particles (Edgington et al., 1976). It is clear then that one cannot correctly assume that all radionuclides which become associated with sediments will behave in a simple, easily predictable manner, even when present a t essentially tracer concentrations. This can be resolved by a careful evaluation of the chemical properties of important radionuclides in freshwater environments in relation to inorganic and organic complexing agents, and then critically evaluating the interactions of these species with carefully characterized sediments. In general, the effect of radionuclide interaction with sediments, where the KD value is large, is to considerably reduce the overall concentration in water and thus the exposure to man. The relative importance of the various factors involving sediments (i.e., suspended particle concentration, sedimentation rate and biolog-

3.1 SURFACE WATER MODELS

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119

ical mixing, resuspension, and KD) can be illustrated in terms of the simple model outlined in Fig. 3.6. In this model it is assumed that (1) the total concentration of suspended particles in the water column is constant and is made up of three parts-steady-state suspended material, a resuspended fraction of the prior year's deposition and new sediment; (2) these particles are uniformly distributed in the water column; (3) the radionuclides adsorbed on the particles are in equilibrium with the water; and (4) the mixed sediment layer is uniformly mixed a t all times. The curves shown in Fig. 3.7 were calculated for a lake having an average depth of 100 m of water and a water residence time of 100 years (i.e., Lake Michigan), and illustrating the effects of KD, resuspension, and total suspended particle concentration, and mixing on the fraction of activity remaining in solution as a function of time following a single acute input. The calculations indcate that resuspension (R) will have the effect of permitting of a higher fraction t o remain in solution than would be the case for zero resuspension. Similarly a higher steady-state concentration of suspended particles ( S )would also lead to higher concentrations of radionuclides remaining in solution following an acute release. SEDl MENTATION MODELS

Sediment

Mixing Fig. 3.6 Key components of sedimentation models.

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RADIONUCLIDES RELEASED TO SURFACE WATER

m .-C .-C

S = 0.002

----0.001

0

5

10

15

Years ofter event Fig. 3.7 An illustration of the use of a simple time concentration model to predict the concentration of a radionuclide in Lake Michigan following a single input. The curves illustrate the effect of KD, mixing (M), resuspension (R), and suspended sediment concentration as the fraction of activity remaining in solution as a function of time. For these calculations it is assumed that the average sedimentation rate is lo-' g cm-' y the resuspension (R) is expressed as a fraction of this rate, and mixing is expressed in terms of years of sedimentation. S (the concentration of suspended particles) is expressed in g L-'.

-',

The effect of biological mixing (M), a process shown to be important in the Great Lakes and even the deep oceans (Edgington and Robbins, 1975; Robbins et al., 1978; Guinasso and Schink, 1975) is to increase considerably the total quantity of sediment in contact with the water. In freshwater lakes, for example, where the sedimentation rate varies between a fraction to several millimeters per year, mixing depths up to 4 cm are common, resulting in up to 40 or more years of sediment deposition remaining in contact with the water. The effect of mixing then is to reduce dramatically the fraction remaining in solution. However, this mixed layer acts as a buffer where the concentration on the particles changes very slowly with time, the concentration, as such, does not decrease as rapidly as would occur if there were no mixing. Thus, while the sediments exert considerable control on the fraction

3.1 SURFACE WATER MODELS

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121

of activity remaining in solution, there is no evidence to suggest that radionuclides buried below the active zone can re-enter this zone by diffusional/advective processes (Edgington et al., 1979). There is evidence though that freshwater and estuarine sediments are subject to major disturbances (such as storm events or hurricanes). The effects of such disturbances can be to remove several years of sediment deposition and expose the annual layers containing the major fraction of an acute release (Edgington and Robbins, 1975; Goldberg et al., 1979). In this situation, the concentration in solution could increase dramatically. 3.1.4

Distribution Coefficients

(KD)

The definition and application of this parameter have been discussed earlier (see Section 3.1.3). Many measurements have been made of the adsorption, and in some cases of the desorption, of radionuclides by sediments. A review of some of the measurements of KD for the radionuclides of interest is presented in Tables 3.2 to 3.8. A direct comparison of the magnitudes of these measured values is difficult because of the disparate experimental conditions.

3.1.5

Verification of Modek;

Onishi et al. (1981) have summarized the many different approaches and simplifying assumptions which have been employed to describe the transport of radionuclides in the aquatic environment as well as the data bases which are available to test the validity of the models. While they have evaluated the models in terms of their completeness and the rigorousness of the mathematical description of the system, it was not within the scope of this report to address or evaluate the possible variations in the values of the concentration of radionuclides which would come about from the application of one or another of the models and the effect this would have on estimated exposure. The largest number of models have been developed to describe the transport of radionuclides (or other contaminants) in rivers; of these, the majority simulate only the transport of dissolved radionuclides. There are, however, a few models which simulate the transport and fate of both soluble and particle associated radionuclides. These require the simultaneous solution of equations for soluble and particulate forms, including sedimentlwater interactions and sediment settling, scouring and transport. In such models, the governing equations for

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RADIONUCLIDES RELEASED TO SURFACE WATER

dissolved and adsorbed (but immobile) radionuclides respectively are:

and

where

C = concentration of dissolved radionuclide, CSj= concentration of radionuclide attached to jth adsorbent (e.g., sediment), KD = the distribution coefficient, lz, = the mass transfer coefficient for jth adsorbent, n, = the mass of the jthadsorbent, U = the velocity of the x direction, 6 , = the dispersion coeffient, and X = radionuclide decay rate. In these equations, it is assumed that the concentration is constant across the river and with depth in the water column. Models which do not calculate the effects of adsorption by sediments (or biota) will predict that the rate of clearance of the radioactivity will be equal to the flushing rate of the stream. The effect of sediment adsorption will be to cause adsorbed radionuclides to flush more slowly from the river. Another important effect of sediment adsorption will be to reduce the concentration of radionuclides in true solution and the absorption by biota, with the possible exception of bottom feeders. While not considering the effects of sediment adsorption may preclude the accurate prediction of the changes in the total concentration of radionuclides in time and space, a more serious effect of not including the sediment effects may be an overly-conservative estimate of exposure via food chains. Another problem associated with radionuclides on sediments is the inability to predict areas where the external dose from sediments could become critical in assessing total exposure. However, such areas of deposition of fine-grained sediments which accumulate radionuclides are readily discernable, and in those cases where such deposits can be identified, a model including adsorption by sediment and sediment transport must be included. Equations similar to (3-11) and (3-12) can be set up to describe the behavior of radionuclides in situations where it cannot be assumed

3.1 SURFACE WATER MODELS

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123

dC dC that - and - are zero, i.e., in wide rivers or lakes. In the Great

ay

Lakes, where the water column is well mixed for a large proportion of the year and few detailed data are available for verification, a simple box model may suffice to determine the long-term effects of releases on critial water intakes (Lerman, 1972). But if it is necessary to predict the immediate effects of an accidental release in the lake coastal zone, then a more complex advection-diffusion model is clearly required. The power of such a simple model is illustrated in Fig. 3.8. The change in concentration of '"Sr in each of the Great Lakes is calculated using the time-concentration model of Lerman (1972) and fall-out monitoring data input (HASL, 1977). The solid lines were calculated assuming no contributions from the watershed, and the broken lines

1950

1960

1970

1980

1990

2000

Year Fig. 3.8 Concentration of %r as a function of time using a simple compartment model, calculated assumingcontribution from watershed is zero; - - - - - calculated assuming the addition of 0.5%of the total deposition in the watershed each year. The symbols are experimental data points.

-

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3. RADIONUCLIDES RELEASED TO SURFACE WATER

assumed a n annual leakage of a fraction of 0.005 the total deposition in the watershed. The experimental data points were chosen such that the analysis represented time periods when the lakes are well-mixed (the 1976 data are unpublished data from Argonne National Laboratory). The difference between calculated and observed concentrations are small and may reflect an unrealistically low contribution from the watershed. The value of 0.005 for the fraction of radioactivity leaking from the watershed is based on field measurements of plutonium (Sprugel and Bartelt, 1978), but since the KD for 'OSr is low compared to plutonium, the watershed leakage of this radionuclide may be larger or smaller depending on whether or not there has been deep penetration into the soil. The complexity of the model required is, therefore, very dependent on the nature of the effects to be predicted. If time scales of dominant phenomena for radionuclide transport and fate are days, weeks, months or even years, then it is clear that any formulation with a time scale smaller than these is too complex. Thus, the solutions to Eq. (311) can vary considerably in complexity. A summary of the various models discussed in this section, together with the methods used to solve these equations and assumptions are given in Table 3.1. This review is not meant to be exhaustive, but is meant to be representative of the range of available solutions. For additional information see the review by Onishi et al. (1981). 3.1.6 Validation and Data Sets

At a workshop on the evaluation of models used for radiological assessment of radionuclide releases it was concluded that, in order to improve aquatic transport models, better calibration and verification are required (Hoffman et al., 1978). The next conclusion that may be drawn is that there are insufficient data relating to critical processes and parameters for many of the environments where modeling is attempted. In spite of all the measurements that have been made of radionuclides in the Columbia, Clinch and Savannah Rivers over the last three decades, there are very few self-consistent data sets that are extensive enough to be used to validate models. Virtually no measurements were made in the Great Lakes before 1970 other than monitoring of water supplies for 90Sr.A tabulation of the data sets which have been accumulated has been made by Onishi et al. (1981). A detailed study of this literature would indicate that the data sets are sparse at best in terms of either the length or depth of the study. There are very few systems in the world today where sufficient concentrations of

3.1 SURFACE WATER MODELS

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125

radionuclides have been or are being released to permit the gathering of more complete data sets. A particular exception is the release of fission products and transuranic elements from the Windscale plant into the Irish Sea. In this environment, comparatively simple models have been shown to be sufficient to describe the behavior of the release (Hetherington et al., 1975). Studies of radioactivity in the environment elsewhere are concerned with following the residual activity from the weapons testing in the 1950's and 1960's. The data sets being generated in these studies, particularly in the Great Lakes, will provide valuable input to models for large water bodies. But in large lakes and oceans the major vertical movement of radionuclides like plutonium and americium may be complicated by their resolubilization due to the remineralization (oxidation of organic material back to inorganic material) of biological particles, a process not completely understood and also not included in present models (Edgington, 1981). However, at present it is not clear as to whether it will be necessary to model such processes in detail. In general, it must be recognized that a simple model with very conservative assumptions may be all that is needed if the calculated concentrations do not exceed limit guidelines. If these conditions are exceeded, then more complicated but still relatively simple models can be applied utilizing carefully evaluated parameters, and should lead to more realistic results. As a rule, complex models generally give acceptable results. The data requirements for such models in terms of input parameters and data sets for validation are much more stringent and, therefore, the use of sophisticated complex models gains little over much simpler models where input parameters are poorly defined. Data for individual radionuclides are discussed below.

Cesium As can be seen from the data given in Table 3.2, the behavior of 13'Cs is very variable and highly dependent of the composition of the sediments. It is clear, however, that, in general, values of KDare lower in the marine environment than in freshwater environments. I t also appears that the uptake of 13'Cs in seawater is by an ion-exchange mechanism where counter ions such as I$+ and Rb+ can have a large effect on the uptake, and the process is reversible. In many freshwater environments, the large uptake of 13'Cs appears to be due to the presence of illite in the sedimentary material (Wahlberg and Fishman, 1962). Experiments have shown that while the uptake of 137Csmay be affected by the presence of competing ions such as Na+ or K+, the process is not entirely reversible and the effective KD'Smay increase

Conditions -

Laboratory: Seawater, pH 8 illitic sediment carbonate sediment Seawater & sediments, Cape Thompson, Alaska Marine, red clay, seawater, distilled water, pH 7-9

TABLE 3.2-Summary of measured ualues of KD for 13'Cs KO Comments

450-900 40 v. high

Rhine River basin Oceanic sediments Nitelva River, Norway White Oak Creek Pacific Ocean Belgian sediments Rhine River Freshwater and marine sediments: Lake Michigan sediment Clinch River Hudson River Marine sediments, seawater distilled Variety of clays with differing Cs concentrations Illite and other clays Field studies: Lake Michigan, pH 8.0 Freshwater pond Clinch River, pH 6

800-1000 42-559 (ads) 4-590 (des)

Independent of sediment core Below 200 mg/L uptake only. Represented by mass action. Adsorption/desorption studied Competition with K, Ca, Mg and mass action. Controlled by ion-exchange KD correlated with exchangeable K'. High [K], KD. KD increases with decreasing concentration of sediment Illite controls adsorption. Adsorption is reversible.

Aston & Duursma, 1973 Baker et al., 1964 Cheng & Hamaguchi, 1968 Collet et d , 1968 Duursma & Eisman, 1973 Garder & Skulberg, 1964 Jenne & Wahlberg, 1968 Kuznetsov & Schebetkovskii, 1971 Meeusen et aL, 1975 Schneider & Block, 1968

v. high 510 (ads) 560 (des) 1360 350-880 114 250

References

Schell et al., 1980a. 1980b Decreases with increasing salinity. Cerrai et d ,1969 Competing cations such as K', Ca", Mg+2used illite included Various [Na+] -- 0.02 M-0.5 M

Wahlberg & Fishman, 1962 Tarnura, 1972

Irreversible only brought into solution with fusion 99.4% in sediments after 80 days

Alberts et al, 1974

Long time high K D 13'Cs desorbed only by strong acids

Tamura, 1972

Brungs, 1974

3.1 SURFACE WATER MODELS

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127

in time as the exchangeable fraction decreases. In areas where illite is not prevalent, the behavior in freshwater appears to be similar to that in seawater. The choice of a KD value for 13'Cs, therefore, depends on the sediment types and the watershed to be modeled. Iodine

There are three isotopes of iodine which can contribute to the dose to man and should be considered in aquatic pathway models. They are the short-lived '1 and 1311with half-lives of 60 and 8 days, respectively, and the long-lived lZ9Iwith half-life of 1.7 x lo7 years. This element can exist in several different oxidation states and form covalent compounds with organic materials. The most common oxidation state in the aquatic environment is I-, and, as a result, it is not expected to adsorb strongly to sediments. There are few studies of the adsorption of iodine by sediments (Table 3.3). Because the anion exchange capacities of most sediments are minimal over the pH range 6-8, the desorption of iodine is small, as expected. Studies of the distribution of iodine in sediments suggests that there is a strong correlation between iodine and total organic carbon content. Therefore, while this element tends to act as a simple anion like OH- or C1- with a very small KD in the aquatic environment, users of sediment-interaction models should be aware of the possibility of iodine becoming covalently associated with natural organic compounds. Plutonium A large nilmber of measurements have been made of the association of plutonium with sediments and soils (Table 3.4). Interpretation of these data has been complicated by the large variations which can occur in the apparent behavior of plutonium a t neutral pH, due mainly to differences in the method of preparation of the Pu tracer solutions. However, recent measurements of plutonium in aquatic environments, marine and freshwater, from all around the world suggest that the adsorption behavior of this element can be explained in terms of several relatively simple parameters. For ocean water and the Great Lakes, the experimental data lead to values of KDwhich vary by less than two orders of magnitude, a variation explicable by differences in the size distribution of the sediment particles alone (Edgington, 1981a; Duursma and Gross, 1971). Further experimental evidence has shown

Conditions

TABLE 3.3-Summary of measured values-of KD for iodine Pm1, 1251, 13'1) -- Comments KD

References

Laboratory

1311with I- carrier clay soils French River 59 different soils Rhine sediments Pure clay & other minerals Soils a t different pH values Iodide solutions, different concentration 0.12-1.27 g L-' Rainer tuff Different soil types lalI-, Ch3 I3lI in 0.01 M CaCll solution

Little fixation of iodine Differences found for different soils. negligible

1.1 0.007-52.6

Uptake dependent on clay content. Negligible uptake except, on clay minerals. Used simulated groundwater. Iodide adsorption function of silt content. Methyl iodide function of organic content.

Harnid and Warkentin, 1967 Juguet et al., 1966 Knaelmar, 1970 Schneider & Block, 1968 Schneider, 1970 De et aL, 1971 De et d., 1971 Goldberg et al., 1962 Wildung et aL, 1975

3.1 SURFACE WATER MODELS

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/ 3. RADIONUCLIDES RELEASED TO SURFACE WATER

3.1 SURFACE WATER MODELS

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131

that the important equilibria involved in these reactions are a redox equilibrium between Pu(1V) and Pu(V) and the equilibrium between Pu(1V) and the sediment particle surfaces (Edgington, 1981a). The behavior of Pu(V) may be compared to that of Np(V) which does not strongly adsorb to sediments (Harvey, 1981). Additional experiments have shown that in many freshwater systems containing larger concentrations of dissolved organic carbon, a significant proportion of the plutonium, in direct contrast to the situation in the oceans, is present as complexes of Pu(1V) which do not adsorb as strongly to the sediments (Nelson et al., 1981). Up to now, such behavior has been observed only in aquatic systems which are not utilized for drinking water (Wahlgren and Orlandini, 1981). In order to utilize a value of KD for plutonium in aquatic transport models it is therefore necessary to know the ratio of oxidation states (Pu(V)/Pu(IV)) and the probability of the formation of organic complexes which can not only change this ratio but also the total concentration of plutonium in solution. For a large fraction of water bodies, where application of a model is contemplated, consideration of complexing does not appear to be critical. But in those areas where the concentration of organic carbon is large, more work must be carried out to characterize the nature and stability of complexes with these natural ligands. In general, the adsorption of plutonium by sediments appears to be reversible and the KD concept in models is applicable for this element.

Radium Isotopes of radium are ubiquitous in the environment o~curringin association with stable calcium, strontium and barium. Significant quantities of radium, in equilibrium with uranium, are remobilized in the mining and processing of uranium ores. The majority of the large number of studies of radium in the environment have been concerned with the leaching properties of sediments of ores. The few studies that have been made of the adsorption of radium by sediments indicate that the reaction is reversible and the magnitude of the KD is dependent on the cation capacity of the soil or sediment and radium will behave like Sr2+or Ba2+(Table 3.5).

Ruthenium The chemistry of ruthenium is complex, and several different oxidation states can exist in the environment (Ginzberg et al., 1975).

5

z

TABLE 3.5-Summary of measured values of KDfor r d k m KD

Conditions

Deep sea red clays, etc. Clay sediments NTS tuff Utah soils with simulated river water, pH = 7.8

Comments

Adsorption independent of conc of Ra tracer Adsorption is exchangeable 6700

214-467

River water contained 82 mg/L calcium. Soils contained 2-5% calcite, Ko correlated with cation capacity of soils.

References

Holland and Kulp, 1954 Titaeva, 1967 Stead, 1964 Serne et d,1974

sc a

E

"A

P

m r m

% M u

4

0

3.1 SURFACE WATER

MODELS

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133

There is little evidence for simple aqueous ruthenium ions, and the behavior of ruthenium in the environment will be strongly dependent on the identity and cornplexing ability of the anions present in the water. Measurements of ruthenium in natural water such as the Columbia River have shown that a small proportion (20%) is associated with suspended particles and that a majority is in a non-ionic form (Perkins et al., 1966) (Table 3.6). Additional studies have shown that while lo6Rumoves at essentially the same speed as groundwater, a large proportion of this dement released to the environment is in a particulate form and is readily adsorbed by soils (Brown, 1967). Measurements of the KD for ruthenium in White Oak Creek sediment indicated that the lo6Ru in the water is not desorbed by sediments (Jenne and Wahlberg, 1968). However, laboratory studies using marine sediments indicate a significant uptake on marine sediments, the KD varying with the cation exchange capacity of the sediments used (Aston and Duursma, 1973). Thus, it is clear that while many studies of the behavior of ruthenium in the environment are contradictory; some indicate that it will remain in solution and will be adsorbed by sediments, and there is other evidence suggesting that this element is strongly bound by sediments. There is no doubt that the chemical behavior of this element is complex and is strongly affected by the chemical form released. Knowledge of its redox reactions and cornplexation in natural waters and its adsorption to sediments is fragmentary at best. Strontium

A large amount of experimental data has been accumulated over the last 30 years on the interaction of '"Sr with sediments. A selected summary of some of those results is given in Table 3.7. The adsorption of @OSrappears to occur by a simple cation-exchange mechanism, and therefore KD'Sare dependent on the cation-exchange capacity of the sediments, the pH, and the concentration of competing cations such as Ca2+,and Na+. There is no doubt that, even though strontium is present in solution as a simple ion and will undergo ion-exchange reactions with soil or sediment particles, the sediments either in fresh or marine waters are not a sink for this radionuclide. This is a result of competition for exchange sites with the other divalent ions in solution such as Ca2+ and MgZ'. Thus, the adsorption of 'OSr will be limited by the ratio of its concentration in relation to the total concentration of stable calcium, magnesium and strontium.

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3. RADIONUCLIDES RELEASED T O SURFACE WATER

Uranium There are few measurements of the adsorption of uranium by soils and sediments (Table 3.8), however the leaching of uranium from soils, sediments, and ores has been well studied. The concentration of uranium is greater in ocean water than would be expected based on the concentration of radium. This is believed to be due to the formation of an anionic uranium-carbonate complex which does not take part in ion-exchange reactions with clays. 3.2 Bioaccumulation Factors (BF) The bioaccurnulation factor of an organism or tissue is the ratio of radionuclide concentration in the whole organism or tissue to that in water: where

CF = concentration of element or radionuclide ( j E i g-' fresh weight) in the organism or tissue, and CW = concentration of element or radionuclide in water (&i g-I). Assimilation of radionuclides by aquatic biota is a complex phenomenon especially in those organisms that absorb radionuclides directly from water as well as from food in the gastrointestinal (G.I.) tract. The ratio of the equilibrium concentration of the assimilated nuclide in the organism or tissue to the average concentration of that nuclide in the water during the history of exposure is the true bioaccurnulation factor. A variety of environmental factors can influence the assimilation of radionuclides, and hence the bioaccurnulation factors in aquatic organisms. This section reviews data that are available for bioaccurnulation factors for freshwater biota and identifies the uncertainties associated with the values reported in the literature. Included in this section are: tables containing ranges of bioaccurnulation factors from the data bases reviewed; a listing of environmental factors; and an example of an imprecision analysis that can be used to evaluate the uncertainties associated with bioaccurnulation factors. Available data bases for radioisotopes of Co, Cs, C, H, I, Pu, Ra, Ru, Sr and U will be reviewed. In most cases the review is restricted to bioaccurnulation factors determined for natural systems. Although the bioaccumulation factors reported for some radionuclides may vary by several orders of magnitude (Ophel, 1978), a single

c

TABLE 3.8-Summary of measured values of KDfor uranium Conditions

KO

Adsorption on different soils; studied effects of pH and soil type on uptake

0 quartz 33, clay, pH 12 270, alkaline peat 2000, clay, pH 10 300, clay, pH 5.5 1000

Adsorption of suspended particles, Great Lakes

Comments

KD varies depending on clay type, presence of carbonates, reduced uptake. KD varies with

References

Rancon, 1973

suspended particles and concentrated in water.

0

P

C) C)

c 3

pH.

KD calculated from extractable uranium on

?!

Nelson (unpubl.)

Br! 0

Z

2

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3. RADIONUCLIDES RELEASED TO SURFACE WATER

value for each element is usually recommended for dose calculations when there is an absence of site-specific data. No one data base contains information on all of the nuclides being considered in this section. Many of the studies reviewed were limited to bioaccurnulation factors for a single species with little supporting environmental data. The most complete data bases are usually from research conducted at the large national laboratories and their surrounding environments.

3.2.1 Bioaccumulation Factors for Cesium, Cobalt, and Strontium Bioaccumulation factors for cesium, cobalt, and strontium for different classes of aquatic biota are provided in a review by Vanderploeg et al. (1975).The study also considers environmental factors that influence the concentration of radionuclides in aquatic biota and, therefore, is relied upon for much of the information in this section. However, in most cases the original data bases were examined. Because fish are considered the primary source of food for man from freshwater ecosystems, the data bases emphasize bioaccurnulation factors for fish.

Cesium More information is available on the concentration of cesium in aquatic biota than for any of the other nuclides considered in this section. Unfortunately, much of the information is not suitable for calculating bioaccurnulation factors. Bioaccumulation factors for 137Cs are listed in Table 3.9 for the following data bases: Lake Michigan (Wahlgren and Marshall, 1975);White Oak Lake (Kolehmainen and Nelson, 1969);Clinch River (Nelson, 1967);Wintergreen Lake (Spigarelli, 1971); English Rivers and Lakes (Preston et al., 1967); and Lake Maggiore (Bortoli et al., 1967;1966).Sources of 137Csin White Oak Lake and the Clinch River are primarily from waste disposal operations and nuclear facilities. In the other environments, the source of 137Csis primarily fallout from nuclear weapon tests. Because they are chemically similar, the bioaccurnulation of cesium is influenced by the potassium concentration in water. Also, the bioaccurnulation of cesium appears to be related to the suspended solids concentration (both organic and inorganic). The highest bioaccumulation factors for fish are found in oligotrophic lakes having a potassium concentration of 1 ppm or less. Vanderploeg et al. (1975) developed a relationship between the bioaccurnulation factor for cesium in fish and the concentration of potassium in water for environ-

TABLE 3.9-Range of bioaccumuhtion factors for cesium, cobalt, and strontium Biota

Fish Piscivorous Planktivorous Omnivorous Benthic omnivores Zooplankton Phytoplankton Filamentous Algae Benthic Invertebrates Aquatic Macrophytes References

" Fish flesh.

Cesium

400-14,000 514-4098 407-3541 272-4426 501-586 1900-2672 1016830-3370 130-1500

Bortoli et a l , 1966, 1967 Nelson, 1967 Kolehmainen et aL, 1968 Kolehmainen & Nelson, 1969 Spigrelli, 1971 Wahlgren & Marshall, 1975 Preston et al., 1967

Cobalt

Strontiuma

5-280 27-600 17-650 14-385 700 500-30,000 250-2800 200-23,000 200-15,000

1.3-125 280.7-198 105 61 37 120-600 300-720 30-220

Morton, 1965 Merlini et al., 1967, 1971 Nelson et a l , 1971 Copeland & Ayres, 1972 Mathis & Cummings, 1973 Ophel et d , 1972

Templeton & Brown, 1964 Agnedal, 1966 Nelson, 1966 Ophel & Judd, 1973 Wahlgren & Marshall, 1975 Vanderploeg, 1975

g E

0 0 >

C3

EF 8z

P % C]

c3

-P -g

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3. RADIONUCLIDES RELEASED TO SURFACE WATER

ments with high suspended solids (>50 ppm) and low turbidity (Fig. 3.9). Based on that relationship, piscivorous fish from waters low in suspended solids have cesium bioaccumulation factors about five times those of piscivorous fish from water high in suspended solids. Thus, suspended solids appear to compete with the biota for the Cs ion. Cobalt Although the data bases for cobalt are not as extensive as those for cesium, considerable data are available for different aquatic environments. According to Vanderploeg et al. (1975) the proportion of cobalt in the particulate phase increases as suspended solid concentrations increase. The proportion decreases with eutrophy. Bioaccumulation ORNL-DWG 74-8724

POTASSIUM CONCENTRATION IN WATER ( p p m )

Fig. 3.9 Bioaccumulation factors for cesium in freshwater fish as a function of potassium concentration in water (from Vanderploeg et aL, 1975).

3.2 BIOACCUMULATION FACTORS (BF)

/

141

T A B L E3.10-Range of bioaccumulatwn factors for cobalt in fish from mesotrophic and eutrophic watersa Fish

Piscivorous Planktivorous Omnivorous Benthic omnivores

Eutrophic

Mesotrophic

5-50 27-53 17-19 14-29

23&280 600 290-650 230-385

" A f t e rVenderploeg et al., 1975.

factors listed in Table 3.9 represent data bases from the following eutrophic and mesotrophic environments: Perch Lake (Ophel et al., 1972); White Oak Lake (Nelson et al., 1971); Illinois River (Mathis and Cummings, 1973); Lake Maggiore (Merlini et al., 1971,1967); and Lake Michigan (Copeland and Ayres, 1972). Most of the bioaccumulation factors reported for cobalt were based on filtered water samples. Generally, the use of filtered water samples to calculate bioaccumulation factors would lead to overpredictions of radionuclide concentration in organisms; however, in nonturbid waters, most of the cobalt is in the soluble phase. The tendency of cobalt to form soluble complexes with dissolved organic matter may serve to keep it in solution in eutrophic water with its high concentrations of dissolved organic matter. In Table 3.10 the data bases show bioaccumulation factors for eutrophic and mesotrophic environments separately.

Strontium Bioaccumulation factors derived for strontium from four data bases are listed in Table 3.9. With the exception of the Lake Michigan data (Wahlgren and Marshall, 1975), the other data bases (English Lakes and Rivers, Templeton and Brown, 1964; Swedish Lakes, Agnedal, 1966; the Clinch River, Nelson, 1966; and Perch Lake, Ophel and Judd, 1973) were reviewed by Vanderploeg et al. (1975). Because strontium absorption and metabolism are similar to calcium, calcium concentration in water can influence the bioaccumulation of strontium. The data bases listed in Table 3.9 include environments with high and low concentrations of calcium in the water. Bioaccumulation factors for strontium in fish have been shown to be negatively correlated with calcium in water. This is not true for algae and plants because concentration of calcium in water appears to have little influence on their bioaccumulation of strontium.

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3. RADIONUCLIDES RELEASED TO SURFACE WATER ORNL-OWG 75-4447R

2 lo'

5

5 0.4

0.2

0.5

2

5

40

20

50

I00

CALCIUM CONCENTRATION IN WATER (ppml

Fig. 3.10 Bioaccumulation factors for strontium in freshwater fish as a function of calcium concentration in water (from Vanderploeg et al., 1975).

Vanderploeg et al. (1975) derived for all of these data a linear relationship between the bioaccumulation factor for strontium in fish flesh and bone and the concentration of calcium in water. The relationship indicated that a decrease in calcium concentration in water from 50 ppm to 1 ppm increased the bioaccumulation factor by two orders of magnitude (Fig. 3.10). Bioaccumulation factors based on the concentration of strontium in bone were about two orders of magnitude higher than those calculated for tissue.

3.2 BIOACCUMULATION FACTORS (BF)

3.2.2

1

143

Bioaccumulation Factors for Iodine and Ruthenium

Iodine A considerable amount of data is available on iodine in the aquatic environment; however, most of the studies are physiological in nature and are not useful for calculating bioaccurnulation factors. Nevertheless, by using marine and freshwater data, Vanderploeg et al. (1975) calculated stable iodine bioaccumulation factors for fish flesh and thyroid tissue. The most comprehensive data base for determining bioaccurnulation factors for iodine is from Lake Michigan (Copeland et al., 1973). In addition to the Lake Michigan data, 1311 tracer studies conducted on small freshwater lakes provide data for Table 3.11 (Short et al., 1969; Kolehmainen et al., 1973). Ruthenium Data on the bioaccumulation of ruthenium by freshwater biota are limited in comparison to the amount of information on marine environments. Woodhead (1972) reported on the concentration of 'OGRu from waste disposal operations in the Irish Sea, and Schelske (1971) determined the concentrations of 'OGRu in marine biota from fallout. The data bases for freshwater biota listed in Table 3.11 are from White Oak Lake (Cooley and Nelson, 1970) and the Clinch River (Churchill et al., 1965; Morton, 1962; Cowser and Snyder, 1966). Although in some cases concentrations of '06Ru have been measured in biota near the effluents of nuclear plants, water concentrations were not available to calculate bioaccumulation factors (Yaguchi et al., 1973).

3.2.3

Bioaccumulation Factors for Plutonium, Uranium and Radium

Plutonium In recent years, a major effort has been made to document the environmental cycling and transfer of plutonium through aquatic food chains. Studies are continuing and analyses of the results should improve our understanding of plutonium behavior in the aquatic environment. As a result of this effort, information is now available

9 TABLE 3.11-Range Biota

Fish Piscivorous Invertebrates Algae Macrophytes

Stable Iodine"

Vanderploeg et aL (1975)

15-170 17-140 10-565 130-380 71-209

of bioaccumulationfactors for iodine and ruthenium in freshwater biota 1211 1x11 lmRu Finis4 Lakeb Fern Lakeb Clinch River' Short et aL Morton Kolehmlunen et d (1971)

(1969)

(1962)

7.9-110

0.3 0.2-3.5

25-60

200 60

"Calculatedfor Lake Michigan (Copeland and Ayres, 1972) and other data. Small oligotrophic lake. 'Large productive river with high level of suspended solid. Small entrophic reservoir, maximum depth 3 m.

150-450 150-530

z0

ImRu

White Oak Laked Cooley and Nelson (1970)

Z C

cu

t,

m

(I)

46 57

Er'

Emu d ~ 1 3

C

2

3.2 BIOACCUMULATION FACTORS (BF)

/

145

on plutonium in different environments. The bioaccumulation factors listed in Table 3.12 represent data from the following environments: Great Lakes (Wahlgren et aC, 1976); Hanford Pond (Emery et al., 1974);Miami River (Bartelt et al., 1976);and White Oak Lake (Eyman and Trablaka, 1976). Most of the information from these data bases was summarized in a recent publication by Hanson et al. (1980). Probably more plutonium analyses have been conducted on the aquatic biota from U Pond at the Hanford Plant (Emery et al., 1974) than on any other aquatic environment. This pond is very shallow and has been described as an ultra eutrophic system that receives nutrients supplied by laundry waste. The bioaccumulation factors from the Hanford pond, although listed in Table 3.12, are not necessarily representative of natural systems. The complex environmental chemistry of plutonium was reviewed for freshwater ecosystems by Watters et al. (1980). In shallow bodies of water, more than 96 percent of the plutonium released to that environment is rapidly transferred to sediments. Apparently physical and biological processes may rework the sediments resulting in a resuspension of plutonium in the water column. Although the different chemical forms of plutonium that occur in freshwater ecosystems undoubtedly influence the bioaccumulation of plutonium in aquatic biota, that influence is not yet well documented. Uranium and Radium Data bases for uranium and radium are fragmentary, and comprehensive studies of the relative concentration in aquatic biota and movement through aquatic food chains are not available. The most is from Lake Michigan (Wahlcomplete set of data collected for 238U gren et al., 1976). A more recent report (Stegner and Kobal, 19811, provides substantial information on the concentration of uranium in fish from a uranium mining area in Yugoslavia. In addition, data that were reviewed by Bondietti et al. (1979) for the Jaduguda area in India and for Lake Issyka-Kul and Lake Sevan in the Soviet Union are included in Table 3.13. Data available on the concentration of radium in aquatic biota from natural environments are associated with uranium mining and milling operations. In general, these data are limited by sample size and number of species. The data for radium in Table 3.13 are from the Animas River, Colorado-New Mexico (Anderson, 1963); Jaduguda mining area, India (Bondietti et al., 1979); Zirovski mining area in Yugoslavia (Stegner and Kobal, 1981); and the Pathfinder mining area in Colorado (Rope and Whicker, 1980).

TABLE 3.12-Range Biota

Piscivorous Planktivorous Omnivorous Benthic omnivores Zooplankton Phytoplankton Filamentous algae Benthic invertebrates Aauatic macro~hvtes

o/ btoaccurnulntion factors /or as*240Pu in freshwater biota Lake Michi an" White Oak Lakeb Miami River' Wahlgren & darshall Eyman & Trabalka Bartelt et aL (1976) (1976) (1976)

1-7 17-30 5-23 128560 122-653 62615,300 1060-6930 587-1830 16569000

" Large, deep, oligotrophic lake. *Small eutrophic reservoir, maximum depth 3 m. 'Medium size highly productive industrialized river. Highly eutrophic settling pond, maximum depth 1 m.

0.4 4 3 3

0.4-0.5 0.1-0.3 0.4-1

800 1000

340-28,000 0.2-0.4 230-690

U-Pondd Emery et al. (1974)

6

%

2

0 b

u < Z

0069-096 099 OOSEQOII

S

@

3

3

5

SEI E'E-F'O

OOZI-Z9L OOOI-009 0082-002 OOZI-OOP

8-E

Z-1

.m p qqdap mnm!xvm 'puod Bu![qqas iqvm p103 ~ [ e m s , .sp!los papuadsns jo p a [ q8!q ql!m mo[@qs (633 OOL) [pms, .ia~!iJ ~ P M pro3 a~!qmpoid~ p m s ,

9E-1

00 P OP

0092-OP 08

8-E

LEI-ZP

.aye[ 3!qda~o8!lo daap aldiv?. 912-29 swqdomv~y 8-2 saleiqwanuI 19 ~ ~ B I V 991-88 u~9u~ldMqd

PP-91

8'2-L'O 8

0 U

9'0-E'O L.0-9.0

U~)VI~~OZ

aloAo!umo >!q?uaa snaoaopmo snornoqquqd Sn010A!3S!d

V!l

4

2 a

?

(0861)

JaV'!qM Pm Smqq Japogqlnd

(8861) lBQOW Pun ramalg ,nary au!myy !9sAFZ

(B961)

U'=aPV o~!xam~a~

-ope10103 ,'a,,!a

(6L61)

7D la

!~~yp V"I

w au!"!m

~P*P~P

(Z861)

lsqo PUS ~ n~ryaa1dsmo asn ~ , n w XU!"!K !98""J!Z

(6L61)

uafi19s~ .'JBs!qJ!yY a m

!Ua!PUOa assn '.lnW-'IamI aqel

(9L61)

70 la

7D la

W0!8

-!PB)I mn!mm q q q ~ a $ o m y s au!~ w j n ! p ~ puo wn!uom ~ os ~j o $ mujm $ ~ w n 3 m qjo q a & r o ~ - - ~ 1a. ~~ e v ~

148 3.2.4

a

/

3. RADIONUCLIDES RELEASED TO SURFACE WATER

Bioaccumulation Factors for Carbon and Tritium

Carbon-14 and tritium are considered special case radionuclides in this report and are discussed in Section 2.5. Data bases are not available for the bioaccurnulation of carbon in freshwater biota; therefore, the reported bioaccumulation factors are default values based on the carbon content of muscle tissue of the organism and the carbon content of water. In contrast to carbon, several studies have been conducted on tritium in freshwater biota. The review by Vanderploeg et al. (1975) concluded that the bioaccurnulation factor for tritium was approximately one. According to Elwood (1971), the biological half-life of tritium in fish is less than one day; thus, the concentration of tritium in fish will follow closely the concentration of tritium in ambient water. The ratio of tissue-water tritium to lake water tritium in biota from White Oak Lake, which received a chronic input of tritium, ranged from 0.8 to 1.2 (Blaylock and Frank, 1979). The value of 1.2 probably reflected nonequilibrium conditions a s a result of spatial and temporal variations in tritium concentrations in the lake water. 3.2.5

Factors Influencing the Variability of Reported Bioaccumulation Factors

Wet Weight, Dry Weight The method used to determine bioaccurnulation factors can have a significant influence on the calculated value. Although the bioaccumulation factors are simple to calculate-radionuclide concentrations in the organism divided by the concentrations in water-they are variously calculated using wet weight, dry weight, or ash weight o t t h e biota. Conversion factors are available for converting dry weight to wet weight for most biota. Bioaccumulation factors based on dry weight are necessarily higher than those based on wet weight. Reporting bioaccurnulation factors on dry weight increases the value of the bioaccumulation by factors of approximately 5 for fish and 10 for plants. Conversion factors for ash weight are not commonly available and may vary from species to species.

Analytical Errors and Sampling Errors Although analytical accuracy of bioaccurnulation factors is seldom reported, for the purpose of this section, the reported bioaccurnulation

3.2 BIOACCUMULATION FACTORS (BF)

1

149

factor in the data bases reviewed are assumed to be without analytical error. Sampling errors are a significant influence on bioaccurnulation factors. Because aquatic organisms are mobile, they can move in and out of contaminated areas. As a result, equilibrium conditions with respect to concentration of the isotope in the contaminated area may never be reached. Also, concentrations of radionuclides in the environment can be the result of an acute release; thus, inadequate sampling on an appropriate time scale will not reflect the correct concentration of the radionuclide in the environment. The lack of a sufficient number of samples and a properly designed sampling program are probably the greatest sources of errors in determining bioaccurnulation factors.

Filtered and Unfiltered Water Reported bioaccurnulation factors are based on either filtered or unfiltered water samples. Since a significant fraction of some elements in water may be in the suspended phase, bioaccurnulation factors based on filtered samples may be much greater than bioaccurnulation factors based on unfiltered samples. For example, the fraction of cesium in water in the suspended phase has been shown to range between 19 and 92 percent; furthermore, the fraction appears to be correlated with suspended particulate matter in the water (Vanderploeg et al., 1975). In contrast, strontium is not strongly adsorbed by suspended particulates in water and the fraction in the suspended phase ranges from 0.9 to 10 percent. Thus, filtration of water which could have a significant influence on the bioaccurnulation factor of cesium would have little effect on the bioaccurnulation factors for strontium. The ratios for bioaccurnulation factors based on filtered and unfiltered water samples for cesium are shown in Table 3.14. Bioaccumulation factors for stable cesium based on filtered water samples were greater than bioaccurnulation factors based on unfiltered samples by a factor of 12.5. Ratios listed in Table 3.14 are usually the maximum ratios available in the data bases that were reviewed. TABLE 3.14-Ratw of bioaccumulation factors for cesium based on filtered and unfiltered water Cesium

Stable la7Cs Stable

" Mean

Filtered Unfiltered

12.50 +. .24' 2.63 .07 2.50

+

* 1 Standard error.

Organism

No. Species

Reference

Fish Fish Insect Larvae

5 7 1

Nelson, 1967 Kolehminen, 1972 Kolehminen. 1972

150

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3. RADIONUCLIDES RELEASED TO SURFACE WATER

The influence of using filtered or unfiltered samples for bioaccumulation factors may vary among environments. Plutonium has an affinity for particulate matter in freshwater ecosystems; thus, the use of filtered or unfiltered water samples can influence the bioaccumulation factor. In goldfish from the Hanford U Pond (Emery et al., 1974), the use of filtered water samples influenced the bioaccurnulation factor of 2393mP~ by a factor of 2.5. In contrast, the use of filtered water samples did not significantly influence bioaccumulation factors for 239,240P~ in Lake Michigan because of the lack of suspended particulate matter (Wahlgren et al., 1976).

Tissue Distribution of Radionuclides Calculating radiation doses to man from aquatic food chains ususally requires that bioaccurnulation factors be only for the edible portion of the organism. In the data bases examined bioaccurnulation factors are reported variously for whole fish, whole fish minus viscera, muscle tissue, thyroid, ovaries, and bone. Because some tissues and organs have metabolic requirements for certain elements, bioaccurnulation factors for these elements are incomplete without reference to the specific tissue analyzed. T h e whole-body bioaccurnulation factors may be quite different from those reported for muscle tissue. The concentration of cesium does not vary greatly among the organs of fish; therefore, bioaccurnulation factors apply equally well for whole fish and muscle tissue (Nelson, 1967). In contrast, strontium, radium, uranium and plutonium accumulate in bone, and contribute to a wholebody concentration that is greater than their concentrations in muscle. Ratios for the whole-body/muscle tissue bioaccurnulation factors are shown in Table 3.15. TABLE3.15-Bioaccumulahbn factors for whole-fuh-and tissues Nuclide

13'Cs 60Co 90Sr

Ft,"ie 612 20.8 981.

'06Ru

1.8(s' 2 3 9 - 2 4 0 ~ ~2 106(a) -

190(')

Tissue

734 12.5 1 0.1

Bone

8.3 8000 3384 0.3

5 x lo' 3

"Whole fish less viscera.

112

BF Whole Fish -

BF Muscle Tissue

0.8 1.6

18 40 63

Reference

Kolehminen & Nelson, 1969 Morton, 1962 Ophel & Judd, 1973 Nelson, 1967 Morton, 1962 Emery et al., 1974 Anderson. 1963

-

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3.2 BIOACCUMULATION FACTORS (BF)

151

Chemical State of the Radionuclides Reported bioaccumulation factors based on stable element concentrations may be different from bioaccumulation factors based on radionuclide concentrations. Radionuclides exist in a wide variety of physiochemical forms in nature, and their different forms have different availabilities to aquatic biota. For example, fallout-derived 13'Cs appears to be more available to aquatic organisms than stable cesium. Apparently, a greater proportion of fallout 13'Cs entering a watershed from the atmosphere is in soluble form or on exchangeable sites, making it more available to aquatic biota. Bioaccumulation factors calculated from fallout-derived 137Csare from 1to 8 times greater than those calculated for stable cesium (Table 3.16). Eventually, for longlived nuclides, there should be a n approach to the stable isotope state.

Chemical Composition of the Water The chemical composition of water can influence the bioaccumulation of radionuclides by freshwater biota. After a comprehensive review of the literature, Ophel (1980) recommended using different bioaccumulation factors for some elements in freshwater fish flesh depending on whether the fish were from waters of low mineral content (
White Oak Lake, Tenn.' Wintergreen Lake, Mi~h.~ Lake Haggiore, Italye Lake Varese, Italyf White Oak Lake, Tenn.'

Tme I3'ofCs Release

Organisms

Number of Species

BF "'Cs BF Stable

+ .20'b'

Reference

Chronic

Fish"

7

0.63

Fallout

Fish

4

2.06 & .94

Eyman, 1972

Fallout

Fish

2

2.48 + .23

Bortoli et d ,1967

Fallout Chronic

Fish Insect Larvae

2 1

8.18 + .257 2.90

Bortoli et al, 1966 Kolehminen, 1972

Bortoli et al., 1967

" Bioaccumulation factor of whole fish based on unfiltered water samples. Standard error.

' Small entrophic reservoir, maximum depth 3 m. Small eutrophic lake.

' Mesotrophic lake. 'Oligotrophic lake.

152

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3.

RADIONUCLIDES RELEASED TO SURFACE WATER

TABLE3.17-Bioaccumulntion factors in low and high

H C Co Srb Ru I Csb

RB

u

Pu

mineral content fresh waters ' Water of High Water of Low Mineral ContentMineral Content 1 1 5 x lo4 5 x lo3 1 x lo3 1 x 102 1 x lo2

50 1 x lo2 20 50

10 50 50

2 10

'After Ophel (1980). Related to calcium or potassium concentration in water (see Fig. 3.9 and F i g . 3.10).

For some radionuclides, such as Cs and Sr, the relationship between the bioaccumulation factor and the concentration of other elements in water has been established.

Species-Specific Characteristics of Organisms The feeding habits of an individual species, which may vary from ecosystem to ecosystem, can influence the bioaccumulation of radionuclides. Also, in deep bodies of water where stratification occurs, the depth of the habitat can affect the bioaccumulation factor. Benthic feeding organisms may be exposed to high concentrations of radionuclides that accumulate in the sediments. The gut content of benthic feeders and adsorption of particulate material on the surfaces of organisms, particularly invertebrates and plants, can significantly influence the whole-body bioaccumulation factor. These factors undoubtedly account for some of the variability associated with the reported bioaccurnulation factors for these organisms. The size and the age of the fish and the season of the year can influence the concentration of cesium in fish. Bluegill weighing more than 70 g contained concentrations of Cs four times greater than fish that weighed 2 g (Kolehmainen and Nelson, 1969). Changing food habits as the fish increased in size appears to be responsible for the difference in concentration. Also, the season of the year that bluegill were collected influence the concentration of 13'Cs by a factor of two. However, seasonal variations would be of little consequence in calcu-

3.2 BIOACCUMULATION FACTORS (BF)

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153

lating average annual doses for man, if the bioaccurnulation factors were established from data collected throughout the year.

3.2.6 Uncertainties Associated with Bioaccumulation Factors The uncertainties associated with bioaccurnulation factors for freshwater biota are discussed in this section. The methodology used to determine bioaccurnulation factors, various environmental parameters, the chemical form of the radionuclide, and individual species characteristics can significantly influence the values reported in the literature. Much of the data used to determine bioaccumulation factors was derived from studies that were not designed specifically for that purpose; therefore, all the data necessary for determining reliable bioaccurnulation factors were not available. The use of a conversion factor to change dry weight values to wet weight values can reduce the variability of bioaccurnulation factors by a factor of five. The use of whole fish instead of muscle tissue can influence the bioaccurnulation factor for some radionuclides by an order of magnitude. The influence of the chemical composition of the water on the bioaccurnulation of cesium and strontium in fish has been established but, in most cases, the environmental chemistry of radionuclides and its influence on bioaccurnulation has not been determined. Because of all the uncertainties associated with bioaccurnulation factors, there is a tendency to select values that will usually overestimate the bioaccurnulation factors; therefore, one cannot expect validation studies to show close agreement between many of the values found in the regulatory guide and experimentally measured values for fish in the outfall of a nuclear facility. A partial validation, under such circumstances, is shown in Table 3.18 (Feldt, 1980). In this study, the computed value for three of the four isotopes overestimated the measured concentration by a factor of two; as a result, dose calculations TABLE 3.18-Comparison Radionuclide

3H "C @Co '"Cs

of computed and measured radionuclide concentrations in fish muscle in the outfall . of . a nuclear Dower ~ l a n t . " Compute+ Measured Mean Bioaccumulation Concentrat~on Concentration Factorsb (pCi Kg-') (pCi Kg-') 0.9 4,500 20 400

8,700 200 11 200

" Adapted from Feldt, 1980. Bioaccumulation factors from Thompson et aL, 1972.

3,600 & 1,600 100 -C 150 <20 100 k 50

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3. RADIONUCLIDES RELEASED TO SURFACE WATER

based on the computed values would be in error by at least a factor of 2. This partial validation is one of.the few attempts to compare computed and measured radionuclide concentrations in fish muscle in the vicinity of a nuclear power plant! More studies of this type are needed, otherwise bioaccurnulation factors that have become established in regulatory guides, which in general contribute to the overestimation of dose, continue to be used for dose calculations for man. Where validation information is not readily available for bioaccumulation factors, an imprecision analysis can be used to evaluate the uncertainties. Imprecision analyses, which are discussed in more detail in Section 6, involve the estimation of the variability associated with each model parameter to determine the influence of the total parameter variability on the model's predications. A type of imprecision analysis is shown in Table 3.19. After Hoffman and Baes (1979) noted that the bioaccurnulation factors for Cs, Sr, and I, primarily from Vanderploeg et al. (1975), were log-normally distributed, they estimated the geometric standard deviation, mode, median, mean, and 99th percentile value for the bioaccumulation factors (Table 3.19). This probability distribution. of a given set of observations is useful for comparison with the default values recommended by the NRC in Regulatory Guide 1.109 (USNRC, 197%). For example, the median value for the bioaccurnulation factor of Sr (2.4) at calcium concentrations of 20-60 ppm in water, is one order of magnitude less than the 99th percentile (24). This 99th percentile value is comparable to the default value of 30 recommended by the NRC which, based upon this analysis, would include 99 percent of all the observed bioaccurnulation factors for Sr. A larger proportion of the uncertainty associated with bioaccumulation factors could be eliminated by re-evaluating the data used to establish values in the regulatory literature. This would assure the use of a standard method to derive bioaccumulation factors for all radionuclides. Also, a re-evaluation could eliminate values that are based on studies with insufficient or incomplete environmental data. Although this would reduce some of the uncertainties associated with bioaccurnulation factors, there would still be gaps in our knowledge that would require experimentally measured factors. Uncertainties associated with experimentally measured bioaccumulation factors can be reduced. This review provides some general guidance for collecting data that could reduce the variability of bioaccumulation factors. For example, concentrations of the radionuclide should be measured in the edible portion of the organism at the time of equilibrium. Water and aquatic organisms should be sampled several times a year to determine seasonal trends and to measure both radio-

3.2 BIOACCUMULATION FACTORS

(BF)

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155

156

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3.

RADIONUCLIDES RELEASED TO SURFACE WATER

active and stable elements. Concentration of the radionuclide should be measured in filtered and unfiltered water samples along with supporting data on other water quality and ecological parameters that might influence bioaccurnulation. Sampling protocols should ensure that edible tissue is not contaminated during sample preparation or storage. Partial validation of aquatic pathway exposures can be accomplished by measuring bioaccurnulation factors. In order to reduce the uncertainties associated with experimentally measured bioaccumulation factors, field validation studies should be conducted at a number of sites representative of the range of identified environmental parameters. Bioaccumulation factors may span several orders of magnitude depending upon water quality and water chemistry. The available data on bioaccumulation factors should be re-examined from the standpoint of establishing correlation with environmental factors such as concentration in the water of the related stable element (if any) and, analogue elements, suspended matter, nutrient levels, etc. Current values of bioaccurnulation factors in Regulatory Guide 1.109 (USNRC, 1977b) are conservative values largely derived from a publication by Thompson et al. (1972). Field data on bioaccurnulation factors have continued to accumulate a t a variety of sites since the study by Thompson et al. (1972) was published. These more recent data should be used to correct and update the bioaccumulation factors in the regulatory literature. One of the factors contributing to the degree of uncertainty associated with bioaccumulation factors is that few efforts have been made to validate the bioaccurnulation values listed in the regulatory guide with field data. Validation studies are needed; otherwise bioaccumulation factors that have become established in the regulatory literature, which in general contribute to the overestimation of dose, will continue to be used for dose calculations for man.

4. Assessment of Radionuclides Released to Groundwater Groundwater flow is the predominant pathway for radionuclides released from controlled solid waste disposal operations o n land, certain classes of accidental and normal releases from nuclear reactors, and from some of the early liquid waste disposal operations. Transport of radionuclides released to ground water can be predicted using mathematical models that account for the chemical form, radioactive half life, and geologic and hydrologic parameters of the environment. The ultimate objective of groundwater models is to predict the quantity per unit time of radionuclides released from a source which is subsequently ingested by humans directly i n drinking water or enter the food chain after becoming dispersed in surface or drinking waters. The time scale over which the predictions may be made ranges from a few years to thousands of years and beyond. 4.1 Introduction Groundwater flow is one of the likely pathways of radionuclides released from waste disposal areas. Groundwater transport is also a major pathway for certain classes of accidental and normal releases from nuclear power plants, and mining and milling operations. The primary emphasis of this section will be groundwater transport of radionuclides using waste disposal as an example. Concentrations of radionuclides that could reach the biosphere and the resulting consequences must be predicted using scenarios of events and processes that are possible but unlikely to occur at the disposal site. Estimation of groundwater flow and transport are important in assessing the performance of a disposal system because they simulate a probable migration pathway between the nuclear waste and the biosphere. The transport of radionuclides through the ground can be estimated by the use of tracers, groundwater dating, mathematical models, or by a combination of all of the above. Chemical or radioactive tracers may 157

158

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4.

RADIONUCLIDES RELEASED TO GROUNDWATER

be deliberately introduced to the groundwater and monitored through wells for the direct determination of groundwater velocity and transport. Alternatively, pollutants or natural contaminants not deliberately introduced to the groundwater may also be traced. Groundwater dating is a technique by which the age of a particular groundwater sample is estimated from the concentration of an atmospheric radionuclide it contains. Tritium released since the beginning of the nuclear era can be used to date water up to several decades old. Carbon-14 may be used to date water for periods of hundreds to thousands of years. Chlorine-36 may be used to date older water. Direct measurements of the migration of radionuclides released from naturally occurring uranium and thorium ore bodies provide evidence of groundwater migration and can be used as a close analog to manmade radioactive waste disposal situations. Groundwater flow and transport models provide a means of calculating the expected concentrations of radionuclides following release to the environment. Where contamination of wells or surface water bodies such as lakes, streams, or rivers occurs, the radionuclide concentrations can be used in biosphere pathway models to calculate the consequences of the release. Pathway models consist of surface water transport models and biological pathway models which in turn provide the basis for dose calculations. Radiation doses to people arise from the penetration of radionuclides into drinking water, food, and also to surfaces such as flood plains and beaches. This section discusses current practice in groundwater flow and transport modeling along with data requirements, and possible misuses of models.

4.1.1

Types of Groundwater Assessments Needed

Geologic Isolation of High-Leuel Waste (HLW)

Actual tests and demonstrations of the behavior of a potential HLW repository system cannot be performed over the operational lifetime of the repository. In this case, mathematical models must be relied on for assessments of performance using data collected over comparatively short periods of time, to predict the long-term performance of the system. This is the only means by which the cumulative effects of changes in the properties of the repository system, the effects of changes in the properties of the repository, and the effects of the repository on the environment can be analyzed. Performance assess-

4.1

INTRODUCTION

/

159

ment not only provides this type of analysis, but also provides information that is useful in guiding research and development activities in site selection, repository design, and waste package design. Performance assessment treats concepts that can be quantified, i.e., failure analysis and consequence assessment (Klingsberg and Duguid, 1980). An assessment of the long-term performance of a repository analyzes the events and processes that could release radionuclides from the waste and the phenomena that might transport radionuclides to the biosphere. These phenomena may be roughly classified as those that occur in the near-field (where waste and repository phenomena dominate) and those that occur in the far-field (at a greater distance from the repository where natural phenomena dominate). Although these two regions are not separated by a precisely defined boundary, the distinction is useful because the physical and chemical effects of heat and radiation from the waste are limited to the near-field (Klingsberg and Duguid, 1980). Different methods of analysis are, therefore, appropriate for the two regions. Near-field analysis studies the combined effects of heat, radiation, repository design and construction, and the behavior of the waste package. In the near-field, the thermal effects of the waste can provide the driving force for radionuclide migration (i.e., thermal gradients, increased rock stress and increased rates of chemical reaction) for periods of up to hundreds of years after closure. Far-field analysis studies the effects of natural phenomena and potential human actions after the repository has been sealed. These farfield phenomena usually appear in the geosphere and the biosphere outside of the repository where ambient conditions exist. Near-field and far-field performance must both be considered in determining how well the natural and the man-made components of the disposal system meet the criteria for repository performance. Shallow Land Burial For near-surface disposal such as shallow land burial, the analysis of system performance is similar t o that of isolation of high-level waste with two major exceptions: (1) groundwater flow and transport models must frequently consider the unsaturated zone and (2) the wastes are not heat producing (Aikens et al., 1979). The analysis proceeds in much the same fashion as for high-level waste and includes: the development of a source term through corrosion or breaching of waste containers; defining an appropriate leach rate for the waste form; developing a system release scenario; and calculation of groundwater flow and radionuclide transport for use in the biosphere models and dose codes.

160

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RADIONUCLIDES RELEASED M GROUNDWATER

Uranium Mining and Milling There are several potential groundwater contamination problems associated with the mining, milling and waste disposal operations necessary to produce uranium fuels (USNRC, 1979, Shepard and Cherry, 1980). Frequently, the nonradioactive by-products of the mining and milling operations, such as selenium and sulfates, present more of a pollution problem than the radioactive uranium and its daughter radionuclides (Kaufman et al., 1976). The greatest contamination hazard to groundwater is the seepage from tailings ponds used in conventional milling procedures. The mill waste stream contains about half solids and half water, which is usually disposed of in ponds (tailing ponds) which are formed behind earth or rubble dams. Tailings are sometimes reburied in the ore pits. Acid leach mills are the most prevalent type. Tailings ponds usually receive highly acidic (pH 0.5 to 2) water and tailings, but in some cases tailings are first neutralized. The wastes from the tailings ponds will differ most from other forms of nuclear waste because of their unique chemistry. In acidic tailings, most of the radioactive and other chemical wastes will be in the dissolved state. Acidic wastes are sometimes neutralized to reduce the solubility of pollutants, but in some cases the wastes slowly become acidic again because of oxidation of pyrite (iron sulfide). The behavior of the radioactive contaminants varies from very simple to very complex. Probably the most radiologically significant radioactive waste component present is radium which has a fairly simple chemistry since it exists only in the +2 valence state. Uranium and other radioactive minerals behave in a much more complicated fashion, because they exist in several oxidation states, and form complexes. The solubility of all of the contaminants is high for low-pH conditions and decreases markedly at higher pH. Neutralization by carbonates, such as limestone either added deliberately or encountered in the environment, however, can mobilize uranium in the form of carbonate complexes. Uranium may also be mobilized by certain natural or manmade organic chemicals in groundwater (Mo, 1980).

Nuclear Power Plant Accidents Postulated accidental releases of radioactivity to the groundwater pathway have been evaluated for a wide range of nuclear facilities either for generic sites or in actual reactor licensing reviews. The accidental releases considered range from small leaks from radwaste storage tanks in nuclear plants to major releases postulated to result

4.2

TYPES OF GROUNDWATER MODELS

/

161

from a core meltdown accident (USNRC, 1975, 1978; Niemczyk et al., 1981; Codell, 1983). Consideration given to nuclear power plant accident releases to groundwater differ from those for high- and low-level waste disposal or other fuel cycle problems in several important respects: (1) The risk of contamination would exist only for a period approximating the lifetime of the plant. Administrative controls would be in effect during this period so mitigative measures could presumably be taken should an accidental release occur. (2) The isotopes of importance in nuclear power plant accidents are generally those with high dose factors and/ or half-lives of years to tens of years, notably tritium, 13Ts,137C~, "Sr, 'OSr and 'OGRu.Unlike nuclear waste, long lived radionuclides, actinides and transuranics have been shown to be of much lower importance (USNRC, 1978). (3) For a given event, consequences of radioactive release to the groundwater pathway typically present much smaller risks than release to the airborne pathway (Codell, 1983). These consequences should not be neglected in siting studies for nuclear power plants, however.

4.2

4.2.1

Types of Groundwater Models

Groundwater Models for Low-Level Waste

The assessment of a low-level waste burial ground requires three types of models: (1) models to determine the portion of the radioactive source released if infiltrating water contacts the waste, (2) mathematical models in terms of measureable hydrologic parameters which predict the migration of radionuclides from the source to locations accessible to the public, and (3) models for determining the potential radiation dose using the radionuclide concentrations that reach accessible locations. In this section only items 1 and 2 will be discussed. Although difficult to analyze, the near-field is as important and complex for shallow land disposal as for deep geological disposal. The interaction of the waste in the disposal trench with its immediate environment determines what is available for future groundwater transport. Determining the water balance and the amount of water infiltrating is difficult. Determining the leaching and release from chemically and physically heterogeneous wastes such as low-level wastes is even more difficult. T o date, no model adequately addresses the problem of modeling the near-field environment for shallow land burial.

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The calculation of transport of radionuclides from shallow land burial sites is complicated by the waste frequently being leached in the unsaturated zone. The movement of waste to the water table must consider both flow and transport through the unsaturated zone. In the simplest case, flow and transport may be assumed to be downward in one dimension. Water flow rates from a water balance can be used to approximate the unsaturated flow which is used as input to the radionuclide transport model. Radionuclide transport in the unsaturated zone can also be assumed to be downward and one-dimensional, although there are cases where the flow is clearly multidimensional in nature (Segol, 1982). These simplifying assumptions can be used to calculate the concentrations of radionuclides being released to the water table as a function of time. More rigorous calculations can also be done using two- and three-dimensional models of unsaturated flow and transport. However, considering the uncertainty in the magnitude of the source term these sophisticated calculations are only warranted when a large amount of data is available and/or detailed results are required. Multidimensional models, however, can demonstrate the sensitivity of the results t o the assumption of one-dimensional flow. Below the water table either numerical o r analytical models of two- or three-dimensional groundwater flow and radionuclide transport can be used to calculate the concentration of radionuclides released a t locations accessible to the public. The radionuclides of interest in shallow land burial for which leach rates should be obtained and used in the performance assessment are: ''Sr, "Tc, 137Cs,"CO, lo6Ru,3H, 14C, '"1, actinides such as thorium, and transuranics such as plutonium where appropriate. 4.2.2

4.2.2.1

Groundwater Models for High-Level Waste Repositories Far-Field Performance

Although there are significant differences in the state of development and verification of different far-field models, these models are sufficiently well advanced t o be used in assessments of repository performance a t either generic or specific sites (Klingsberg and Duguid, 1980). In general the procedure for calculating the far-field effects of a respository breach is shown in Fig. 4.1. After the scenarios that have to be modeled have beep identified, the next step in a performance assessment is to predict their consequences. Whether the scenarios will actually occur cannot be predicted

4.2 TYPES OF GROUNDWATER MODELS

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RELEASE SCENARIO

TRANSPORT THROUGH GEOSPHERE

TRANSPORT THROUGH BIOSPHERE

I

CALCULATIONS

I

Fig. 4.1 Elements of far-field performance assessment (from Klingsberg and Duguid, 1980).

with complete certainty, but where possible, the probability of their occurrence is estimated. Probabilities are, however, highly uncertain for the events that have occurred in the region around the repository site only a few times in geologic history, or that may not have occurred there a t all. For this reason, the assessment of repository performance relies heavily on predictions of the consequences of scenarios rather than on predictions of their probabilities, in order to bound the risk (Klingsberg and Duguid, 1980). The source term describes the waste a t all times. It specifies the radionuclides present and the physical and chemical conditions of the waste. The radionuclide concentrations a t the time of the breach can

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RADIONUCLIDES RELEASED TO GROUNDWATER

be calculated from their original concentrations in the waste. Some of the physical and chemical information required for this source term can be predicted from studies of near-field waste-rock interactions. Source term evaluation is highly site-specific, depending on such factors as the chemistry of the waste, the host rock, and the groundwater. Also, interaction between natural and man-made components can play an important role in defining release mechanisms. Near-field phenomena are important to defining the source term and are discussed in Section 4.2.2.2. Further discussion of the near-field aspect of waste-migration modeling is beyond the scope of this report but is discussed by Klingsberg and Duguid (1980). Once the source term has been defined, transport through the geosphere includes modeling of fluid flow into and away from a repository. The output from the geosphere transport codes is a prediction of the radionuclide concentrations reaching the biosphere as a function of time. As contaminants move with groundwater, they may be sorbed and thus retarded by the rocks through which they pass. The parts of the contaminant transport models that describe sorption generally assume equilibrium between the concentration of contaminants in the fluid and the concentration of the rock surfaces, but this relationship is frequently much more complicated. Because models of flow through fractures tend to be specific to particular types of fracture systems, they are less universally applicable than porous media models (Duguid and Lee, 1977). There are two basic problems for the modeling of material transport in fractured media. One problem is to assemble sufficient data to be able to adequately describe the hydrology of the far-field region surrounding a repository site. The determination of effective permeabilities and fracture interconnections is difficult, and a considerable amount of research remains to be done before reliable methods will be available. The second problem is to understand the sorption process in the fractured rocks; although sorption is effective in porous rocks, it might be much less effective in fractured rocks. Successful modeling of transport in fractured aquifers is non-existent a t the present time. Current models for porous media are being used with equivalent formulations and conservative assumptions to establish bounds on the effects of flow through fractured media (Klingsberg and Duguid, 1980). 4.2.2.2

Near-Field Performance

Models for assessing the performance of high-level waste repositories in the near-field must take into account mechanical stresses, heat

4.2 TYPES OF GROUNDWATER MODELS

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flow, chemical interactions, and radiation-induced physical and chemical processes. All of these phenomena, in addition to the properties of the host rock, affect the environment of the emplaced waste. The following sections discuss the status of the three principal types of models required for near-field analysis: Heat transfer models, thermomechanical models, and models of physical and chemical interactions between the emplaced waste, the components of the waste package, and the host rock.

Heat Transfer Models Thermal models based on physical laws provide an accurate portrayal of heat flow and changes in temperature. For simplified configurations, the experimental temperatures to date have been predicted to within a few percent of measured values. Consideration of heat transfer is important because temperature gradients, which can be large in early times, can be a driving force in groundwater flow. Over 40 such models are identified as useful in the studies of waste disposal (SAI, 1981).

Thermornechanical Models These models are based on relations derived from laws of physics and functional relationships between stress and strain that are obtained from laboratory tests. Because repository rocks are inhomogeneous and may be fractured, generic functional laws are more difficult to obtain for rocks than for most other construction materials. Thermomechanical codes are currently being used to analyze the uplift and subsidence, storage room stability and rate of closure, hole stability and rate of closure, waste canister movement, pillar stability, thermomechanical effects on groundwater flow, stresses and strains at critical locations in the rock mass, and mechanical failure of the rock mass. These phenomena are most important to flow in fractured rock. Current research emphasis is on the relationship between permeability and changes in fracture geometry due to stress (SAI, 1981).

Chemical Models To predict the near-field behavior of a repository requires analyses of the interactions between the emplaced package components and the host rock. These interactions fall into six general categories: (1)

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the movement of fluids to the vicinity of the waste package, (2) the corrosion of the canister and sleeve materials by these fluids, (3) the dissolution of the waste form by groundwater containing the added corrosion products, (4) the sorption of radionuclides by the rocks and the engineered components of the repository, ( 5 ) the absorption of radiation emitted by the waste, and (6) the alteration of chemical phases and properties in the vicinity of the canisters. A study of these interactions predicts the kinds, amounts, and chemical state of the radionucludes available for entry into the groundwater system (Jenne, 1979). 4.2.3

Performance Assessment for Mill Tailing Waste Migration

The modeling of transport from mill tailings is similar in many ways to other types of groundwater migration problems such as low-level radioactive waste disposal. The unique aspects of the modeling of mill tailings wastes may be their complex chemistry and the process of neutralization, especially by rocks along the transport pathway. Typical linear equilibrium concepts such as the retardation factor and distribution coefficient ( K d )will generally not work well. While retardation factors are not always appropriate for high- and low-level waste transport either (see Section 4.4.4), the problems are exacerbated for mill tailings because of the high ionic concentrations and low pH typical of these wastes, which make the interaction of the dissolved radionuclides with the soil or rock highly nonlinear and time dependent (i.e., non-equilibrium). Unsaturated flow in some of the pond settings and the transient existence of the milling operations may present special modeling problems. Non-radioactive pollutants, such as selenium and sulfates, are often a greater problem than radioactive pollutants (Shepard and Cherry, 1980; USNRC, 1979; Kaufman et al., 1976).

4.3 Equations for Groundwater Flow and Radionuclide Transport The movement of radionuclides in groundwater can be described by two equations: one for the movement of the carrier fluid (water) and one for the mass transport of the dissolved constituents (radionuclides). In some cases, where temperature effects are important, such as in high-level waste repositories, a third equation for heat transport

4.3 EQUATIONS FOR GROUNDWATER FLOW

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is coupled to the flow equation. Models including heat transport are beyond the scope of this report, but the reader is referred to a recent Lawrence Berkeley Laboratory report (LBL, 1981). In using transport equations, the movement of the carrier in the region under consideration must be known before the transport equation can be solved. The following discussion of equations can only be used as a general guide. Use of these models requires a considerable amount of experience.

Radioactive releases may travel in the unsaturated region (i.e., region above the water table) before entering the zone of saturation (i.e., below water table). However, the release can also be directly into the zone of saturation. The predominant direction of the flow in the unsaturated region is downward until the flow reaches the zone of saturation. Within the zone of saturation the flow is predominantly lateral. The governing equations in the unsaturated zone consist of a set of coupled equations for the movement of gas and water. T o date, only computer codes of limited applicability are available for the solution of these coupled gas-water equations (Lappala, 1981). When the assumptions are made that the water moves as a single phase and that no trapped air pockets exist, a single governing equation for saturatedunsaturated flow is obtained (ANS, 1980).

[$

.'

2 ah = V . [ R ( h ) . (Vh + Vz)]

+ " ' + (dh)] d t

(4-1)

where

0 = the moisture content (dimensionless), n' = total porosity (dimensionless), a' = the modified coefficient of compressibility of the medium (cm-I), p' = the modified coefficient of compressibility of water (cm-I), h = the pressure head (cm), t = the time (sec), I? = the hydraulic conductivity tensor (crn s-I), z = the elevation head (cm), and V = the Del operator. Eq. (4-1) is nonlinear because, for unsaturated flow, both hydraulic conductivity and moisture content are functions of pressure head. The solution of Eq. (4-1) in three dimensions is generally imprac-

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RADIONUCLIDES RELEASED TO GROUNDWATER

tical. Simplifications must usually be found (Lappala, 1981). Depending on the nature of the problem, analytical or numerical methods such as the ones described in Reeves and Duguid (1975), and the survey report by Oster (1982), can be used to analyze saturatedunsaturated flow. The hydraulic conductivity is a tensor which accounts for directional properties (anisotropy) that arise in formations such as layered sediments (i.e., hydraulic conductivity is different in different directions). If the coordinate system is oriented parallel to the principal components of hydraulic conductivity, only the principal components of the tensor are required. If the medium is further assumed to be homogeneous and isotropic, hydraulic conductivity becomes a scalar and Eq. (4-1) becomes (ANS, 1980):

where

H = the total head (cm), Ss = pg ( a + n1 P ) = specific storage coefficient (cm-I), P = the water density (gm ~ m - ~ ) , K = the scalar hydraulic conductivity (cm s-'), g = the acceleration of gravity (cm s - ~ ) , a = the coefficient of compressibility of the medium (cm sec2 gm-I), and @ = the coefficient of compressibility of water (cm sec2 gm-I). This equation is valid for saturated flow in confined aquifers. For a confined aquifer of thickness b, the storage coefficient (s) and transmissivity ( T ) are defined as S = S,b

(dimensionless)

(4-3)

T =Kb

(cm2 S-l)

(4-4)

and Eq. (4-2) becomes

In simulations using Eq. (4-5), the boundary conditions of leakage should be used when appropriate. For problems involving "leaky" aquifers, for which there would be flow between layers, methods such as those described by Bredehoeft and Pinder (1970) can be used. For unconfined aquifers where compressibility of the medium and the water is relatively unimportant compared to the vertical movement of the free surface (water table), the continuity equation can be written

4.3 EQUATIONS FOR GROUNDWATER FLOW

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169

as (ANS, 1980):

where S, = the specific yield of the aquifer

(dimensionless).

Specific yield is also sometimes called "effective porosity, n,," and can be interpreted as the ratio of the drainable volume to the bulk volume of the medium (McWhorter and Sunada, 1977). Effective porosity is the porosity of the medium available for flow. For steady flow in either confined or unconfined aquifers, Eqs. (45) and (4-6) reduce respectively to the following equations:

V2H = 0

(4-7)

V2H2 = 0

(4-8)

For simplified cases, analytical solutions of Eqs. (4-5), (4-6), (4-7) and (4-8), such as those given in Carslaw and Jaeger (1959), ANS (1980), and groundwater textbooks such as Davis and De Weist (1965) and Bear (1979), can be used. For more complex situations, numerical solutions such as those described in Gray et al. (1977) should be used. An approximation of the flux (volume of flow per unit cross sectional area) in the major flow direction can be obtained using Darcy's law:

where AH/& is the hydraulic gradient in the direction of flow. Use of this equation assumes a homogeneous isotropic medium in which the hydraulic conductivity and gradient are constant over the increment. The pore velocity (seepage velocity) which would be the approximate speed at which a chemically-neutral tracer would move in a saturated medium, may be approximated by dividing the flux, V,, by the effective porosity, n,:

The difficulty associated with the solution of the flow and transport equations in the unsaturated zone leads naturally to approximation methods. The time of travel can be estimated by assuming that the mean downward velocity is proportional to the rate of recharge of water a t the surface, r, and inversely proportional to the mean volumetric moisture content, 0:

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The recharge rate, r, can be estimated by methods described in Section 4.3.4. The volumetric moisture content can be conservatively assumed to be equal to the field capacity which is the water content a t which moisture can no longer be held against gravity. Field capacity is equal to the specific retention, S,, which is the difference between the total porosity, n, and the effective porosity, ne: Representative values of n, and n are tabulated in Section 4.4.2. 4.3.2

Mass Transport

The most general form of the mass transport equation is for transport in saturated-unsaturated media. If local equilibrium of mass transfer and first order chemical reactions are assumed, sorption can be represented as a linear relationship and the general mass transport equation can be written as (ANS, 1980)

where

Rd = the retardation factor (dimensionless), c = the concentration of dissolved constituent (gm ~ m - ~ ) , 5 = the dispersion tensor (cm2 s-I), P = the flux (cm s-'), X = the radioactive decay constant = 0.693/halflife of isotope, (Y-]) The retardation coefficient is defined

pb

=

the dry bulk density of the medium,

n = the total porosity, and n, = the effective porosity.

Kd =

radioactivity/unit mass of solid (mL g-I) radioactivity/unit volume of water

(4-15)

4.3 EQUATIONS FOR GROUNDWATER FLOW

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More conservatively, by assuming n = G , & can be estimated as:

An equivalent retardation factor may be defined for fracture flow where the exposed area of the fracture is used rather than the porosity (Freeze and Cherry, 1979). It should be recognized that the assumption of equilibrium linear sorption is, in many cases, inappropriate (Seitz et aL, 1979, McKinley, 1982). The chemical interactions between the radionuclide and the soil or rock can be highly complex (see Sections 4.2.3 and 4.4.4). For the important case when the medium is assumed to be fully saturated, the mass transport equation becomes

When the fluid flux is assumed to be uniform and steady, Eq. (417) becomes:

If the dispersion tensor is assumed to be homogeneous and isotropic, and the flux is assumed to be parallel to the x-axis, Eq. (4-17) can be written as:

where U is the pore velocity defined by Eq. (4-10) and Bj = fraction of species j that decays to species i. The approximate rate of movement of the radionuclide is U/%, which may be used to estimate the travel time. D,, D, and D, are the dispersion coefficients defined in Section 4.4.1. The above equations are strictly valid only for isotropic media (i-e., dispersivity equal in all coordinate directions), but may be applied to slightly anisotropic formations when dispersivities are obtained from field studies.

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Chain Decay of Radionuclides

4.3.3

In order to account for the chain decay of radionuclides to a stable element, one transport equation must be written for each original species and each daughter product to yield the concentration of each radionuclide (original species and daughter products) at points of interest along the flow path. In a constant one dimensional velocity field the general transport equations can be written as (Burkholder and Rosinger, 1980):

where Rdi =

U

the retardation factor for species i,

q

= the seepage velocity, = the concentration of species i (g m-3),

D Xi

=

=

the coefficient of dispersion, and the decay coefficient for species i

=

0.693fialflife.

Eq. (4-20) describe the material balances of the "inth member of a decay chain and its immediate predecessor. Analytical models incorporating chain decay with different sorption properties for each daughter are available for up to a three-component chain (Burkholder and Rosinger, 1980). A simpler analytical formulation applies if all daughters are assumed to have equal sorption properties. If its initial concentration is zero, q, of the ith daughter product in terms of parent concentration cl is (Codell et al., 1982):

For long chain decays with sorption considerations, numerical solutions are practically mandatory (Burkholder and Rosinger, 1980; Dillion, et al., 1978).

4.4

PARAMETERS FOR TRANSPORT FLOW EQUATIONS

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173

4.3.4 Percolation of Water into the Ground An important part of the analysis of the migration of contaminants in groundwater is determination of the rate of release of the contaminant at the source (e.g., leaching of low-level waste) and determining the speed of transport by the groundwater. Both of these aspects of the migration problem frequently involve knowing the rate at which water infiltrates into the ground either from a surface water body such as a river or pond or directly from precipitation. Infiltration is most important for shallow land burial, but not relevant for a deep repository not affected by local recharge. For example, the source of radioactive contamination a t a low-level waste site may by limited by the amount of rainfall that penetrates the land surface and comes into contact with the buried waste (Aikens et al., 1979). In addition, lateral groundwater flow in the saturated zone is driven by recharge caused by the infiltration of precipitation over a wider area than the disposal site itself. Percolation of rainwater is frequently estimated by calculating the water budget for the root zone. Water enters the root zone through infiltration of rainfall and is removed by the evaporation directly from the surface, by transpiration from vegetation, and by seepage vertically downward to the water table. The water budget for this system is illustrated in Fig. 4.2. Both rigorous (Gupta et al., 1978) and empirical (Thornthwaite and Mather, 1957) methods of performing a water budget are in common use. Empirical methods can be found in standard hydrology textbooks along with coefficients that apply to a variety of soil and vegetation types and climates (Chow, 1964).

4.4. Parameters for Transport and Flow Equations In discussing parameters for transport and flow equations, it is first necessary to realize that there is often great uncertainty in the description of the physical and chemical properties of the porous medium. The collection of high-quality groundwater data is much more difficult and costly than for other environments such as air and surface water. T o collect sufficient data for accurate deterministic modeling is frequently impossible. Therefore, it is important to attempt to quantify the uncertainty in transport model predictions and correlate it with the uncertainty in the various model parameters (Grove and Kipp, 1981). Problems of uncertainty in the collection of data lead to a class of

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I Precipitation

Root zone

storage

Fig. 4.2 The water budget in root zone.

models known as "stochastic" (Gelhar et al., 1979; DeMarsily, 1982; Simmons, 1982; Cranwell and Helton, 1982). These models are solutions of differential equations whose parameters and inputs are random variables, and whose outputs (e.g., concentration) are'also expressed as random variables. Stochastic models are among the most

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PARAMETERS FOR TRANSPORT FLOW EQUATIONS

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175

recent developments in groundwater transport modeling, and are well beyond the scope of this report. The following discussions refer mainly to data applicable to more conventional deterministic models, but the uncertainty of data should be kept in mind. 4.4.1

Dispersion and Diffusion in Porous Media

Molecdar Diffusion Dispersion in Eq. (4-13) is actually a combination of molecular diffusion and mechanical dispersion which are processes that irreversibly distribute dissolved constituents within porous media. Molecular diffusion results from the random movement of molecules at a very small scale. Diffusion within fluids depends on fluid properties such as temperature, concentration, and viscosity as well as temperature and concentration gradients. In a one dimensional non-flowing diffusion process, transport due to diffusion is usually related to Fick's law

where D' is the effective diffusion coefficient for porous media which typically varies from about to lo-' cm2 s-'. The effective diffusion coefficient D' will be lower than the molecular diffusion coefficient in a free liquid because diffusion will be inhibited by the pore structure (Evenson and Dettinger, 1980).

Dispersion Dispersion describes the mechanical mixing of dissolved constituents caused by the complex flow paths the fluid must take in the porous medium. Variability of path length and velocity from the mean, results in longitudinal and lateral spreading of the dissolved constituents. Laboratory investigations have shown that in porous media longitudinal dispersion is related to the seepage velocity of flux. For an isotropic medium, the dispersion coefficient Dij can be described in terms of the longitudinal and transverse dispersivity (Scheidegger, 1961).

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where

i, j

= directional indices

6,

=

= a~ = V = Vi, Vj =

at

1 for i = j, Aij = 0 for i # j

(Kronecker delta function) transverse dispersivity (cm), longitudinal dispersivity (cm), magnitude of the flux (cm s-I), and directional components of the flux (cm s-').

Even in small scale laboratory experiments in uniform porous media, dispersion processes usually dominate the diffusion processes. Dispersion depends on flow, however. For sufficiently low flow rates, molecular diffusion, which is independent of flow, will dominate the dispersion (Evenson and Dettinger, 1980). Macrodispersion

Experiments with packed laboratory columns generally yield dispersivities which have dimensions on the order of the median grain diameter, ranging from millimeters to centimeters. If the dispersivities measured in the laboratory were used in a model of dispersion in a large aquifer, dispersion would be grossly underpredicted. At the aquifer scale, it appears that the heterogeneities in permeability, fracturing, stratification of the medium, sampling errors, model approximations, and other properties of the medium, are more important to producing dispersive behavior than mixing around individual grains and pores in the laboratory scale experiments (Evenson and Dettinger, 1980, Anderson, 1979). Field studies tend to support the hypothesis that macrodispersion is largely a result of heterogeneity in hydraulic conductivity. Dispersivity also apparently increases with the length scale of the experiment. There is a tendency for large dispersivities to coincide with experiments involving large distances (Sauty, 1980). The Fickian analogy for dispersion does not always behave satisfactorily and the dispersion cannot be characterized with a parameter as simple as the dispersivity. The assumption of homogeneity of the medium breaks down if the heterogeneities are not random or if they are large in comparison to the scale of the aquifer being modeled (Winograde and Pearson, 1976). The cases in which the simple dispersion models are likely to fail are: 1. Media in which a few extensive conductivity variations dominate the transport process.

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177

2. Media in which conductivity variation are abrupt, severe and tend to follow well-defined paths. 3. Media for which observations were made on a scale that is small compared to the scale of the variation. 4. Media that show variations in conductivity that cannot be modeled as a random field with apparently random values, spatial extents and orientations assumed by the aquifer properties (Evenson and Dettinger, 1980).

Determination of Dispersion It is frequently the case that the only way that values of dispersion coefficients can be determined for a given site is by direct observations of either man-made or naturally. occurring tracers. However, direct tracer methods have several disadvantages in groundwater studies: 1. Because groundwater velocities are rarely large under natural conditions, undesirably long times are normally required for tracers to move significant distances through the flow system. For this reason, only small, nonrepresentative portions of the flow field can be measured. 2. Because geological materials are typically quite heterogeneous, numerous observations are usually required to adequately monitor the passage of the tracer through the portion of the flow field under investigation. The measurements themselves may actually disturb the flow field significantly. As a result of these factors, large-scale tracer experiments over extended periods of time are rarely performed (Anderson, 1979; Evenson and Dettinger, 1980). Deliberately-introduced tracers are used in single- or double-well pumping experiments, and can be performed in much shorter times than the direct observation of tracers. De Marsilly (1982) suggests, however, that dispersion determined from any test where the flow field is disturbed by pumping can be grossly misleading. Values of dispersivities obtained from a wide range of tracer experiments and also those backed out of numerical models of observed groundwater solute transport cases are presented in Tables 4.1 and 4.2, respectively (Anderson, 1979; Evenson and Dettinger, 1980). These values represent site specific cases and may be extrapolated to other cases only with extreme caution. Furthermore, the dispersivities reported in Table 4.2 probably reflect, to a degree, processes such as numerical dispersion which are inaccuracies of the mathematical model and not measured in nature.

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4. RADIONUCLIDES RELEASED TO GROUNDWATER

TABLE 4.1-Dispersiuity values, aL and n ~ obtained , directly through measurements of trAer breakthrough curves in groundwater solute transporl Setting

(m)

4 (m)

(m)) $ ' , (

Method

Single well tracer test Single well

Chalk River, Ontario alluvial aquifer Chalk River, strata of high velocity alluvial aquifer alluvial aquifer, strata of h k h velocitv

Two well Two well Single well

Lyons, France alluvial aquifer (stratum) Lyons, France, (full aquifer)

Single well Single well test with resistivity

Environmental tracer

Alsace, France alluvial sediments Carlsbad, NM Fractured Dolomite Savannah River, SC fractured schistgneiss Barstow, CA alluvial sediments Dorset, England chalk (fractured) (intact) Berkeley, CA sand/gravel

38.1111

nr

38.1

0.15

Two well

134.lm

nr

538

0.4

Two well

15.2111

nr

6.4

nr

Two well

3.1 1.0 2-3

nad na nf

8 8 8

Two well

~ississippiLimestone NTS, Carbonate aquifer Limestone Pensacola, FL

11.6 15 10

nr nr nr

nr na 312

na na 0.0036 0.016 nr na 0.6

"

Multiwell tracer test Single well Two well tracer Two well

'Taken from Evenson and Dettinger, 1980. Distance between wells in 2-well test.

'Groundwater seepage velocity.

* Reference not available for inspection. 'No reference to the particular quantity in the reference

4.4.2

Porosity and Effective Porosity

The parameters porosity and effective porosity (sometimes equated to "specific yield") are necessary for the solution of the flow and solute

4.4

PARAMETERS FOR TRANSPORT FLOW EQUATIONS

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179

TABLE 4.2-Dispersivity

values aL and aT obtained by calibration of nuherical transport models against observed groundwater solute transport" Setting

Rocky Mtn. Arsenal alluvial sediments Arkansas River Valley codluvial sediments California alluvial sediments Long Island glacial de~osits

AX' (m)

(mV d-l)

Methodd

a= (m)

(YT(m)

30.5

30.5

305

nP

Areal (moc)

30.5

9.1

660 x 1320

nr

Areal (moc)

30.5 21.3

9.1 4.3

305 variable (50-300) variable 640 640 nr 305 na variable 3 X 152 nr variable (2-20 km)

na' 0.4

Areal Areal (fe)

nr na na na nr nr na nr nr nr nr

Areal (moc) Areal Areal (fe) Areal (rw) Areal (fe) Areal (fe) Areal Profile (fe) Profile Profile 3-D (fe)

B ~ n s w i c k GA , Limestone 20 Snake River, ID fractured basalt 136.5 Idaho, fractured basalt 91 Hanford site, WA fractured basalt 18 Barstow, CA alluvial deposits 18 Roawell Basin. NM limestone nr Idaho Falls, lava flows and sediments 137 Barstow, alluvial sediments 0.18 Alsace, France alluvial sediments 1 Florida (SE) limestone 0.7 Sutter Baa~n,CA alluvial sediments 8-20 ' From Evenson and Dettinger. 1980. Reference not available for inspection. 'No reference to the particular quantity in the reference. (fe) indicates use of a finite element model (moc) indicates method of characteristics (rw) indicates a random-walk model " Ax = grid fiize in program ' a = groundwater seepage velocity

transport equations. The porosity of a soil or rock is a measure of the interstitial space relative to the space occupied by solid material, and is expressed quantitatively as the fraction of the total volume occupied by the interstices. The porosity of a sedimentary deposit depends chiefly on the shape and arrangement of its constituent particles, the degree of assortment of its particles, the cementation and compaction to which it has been subjected, the dissolution of mineral matter by water, and the fracturing resulting in open joints other than interstices. The porosity of many sedimentary deposits is increased by the irregular angular shapes of its grains. Porosity of a material is usually determined in the laboratory from measurements of the volume of an undisturbed sample, its dried weight and the known density of the minerals from which it is composed (Bouwer, 1978). Porosity decreases with increases in the variety of size of grains because small grains fill interstices between larger grains. Table 4.3 gives representative values of porosity for a wide range of soils and rocks. The effective porosity or %pecific yield" is the portion of the porosity which can be considered to be available for the flow of groundwater through a porous medium. Not all of the water in the interstices of

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4. RADIONUCLIDES RELEASED TO GROUNDWATER TABLE 4.3-Typical - - - --

Aquifer Material Igneous Rocks Weathered granite Weathered gabbro Basalt Sedimentary Materials Sandstone Siltstone Sand (fine) Sand (coarse) Gravel (fine) Gravel (coarse) Silt Clay Limestone Metamorphic Rocks Schist

values-of porosity of aquifer materialsa .- . - . Arithmetic No. of Range Analyses Mean -

8 4 94

0.32-0.57 0.42-0.45 0.03-0.35

0.45 0.43 0.17

65 7 243 26 38 15 281 74 74

0.14-0.49 0.21-0.41 0.25-0.53 0.31-0.46 0.25-0.38 0.24-0.36 0.34-0.61 0.34-0.57 0.07-0.56

0.34 0.35 0.43 0.39 0.34 0.28 0.45 0.42 0.30

18

0.04-0.49

0.38

" From McWhorter and Sunada, 1977.

saturated rock or soil is available for flow. Part of the water is retained in the interstices by the forces of molecular attraction, or is trapped in dead-end pores. The amount of water trapped is greatest in media which have small interstices. Specific yield is often obtained by pumping tests in an unconfined aquifer. A well is pumped at a constant rate, and the resulting drawdown of the water table is measured as a function of time a t certain distances from the pumped well. The specific yield (also hydraulic conductivity) can then be backed out of the data by using analytical or graphical solutions to the transient flow equations (Bouwer, 1978). Table 4.4 gives representative values of effective porosity for a wide range of soils and rocks.

4.4.3

Hydraulic Conductivity for Saturated Flow

The hydraulic conductivity, K for an isotropic, homogeneous saturated medium, determines the rate a t which water moves through the porous medium for a given hydraulic gradient. Hydraulic conductivity is a property which depends on the properties of both the fluid and the medium, and has units of velocity. A measure of the hydraulic conductivity which is a property of the porous medium alone is the intrinsic permeability k, which has units of length squared and is usually expressed in Darcys. Hydraulic conductivity, K, and intrinsic permeability, k, are gener-

4.4 PARAMETERS FOR TRANSPORT

FLOW EQUATIONS

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TABLE 4.4-Typical values of effective porosity (or specific yield) of aquifer materials. Arithmetic No.of Aquifer Material Range Analyses Mean Sedimentary Materials Sandstone (fine) Sandstone (medium) Siltstone Sand (fine) Sand (medium) Sand (coarse) Gravel (fine) Gravel (medium) Gravel (coarse) Silt Clay Limestone Wind-Laid Materials Loess Eolian Sand Tuff Metamorphic Rock Schist 'From McWhorter and Sunada, 1977.

ally related by the equation:

where g is the acceleration of gravity, p is the density of the fluid, and p is the viscosity of the fluid. Hydraulic conductivity can be determined either in the laboratory or in the field. Laboratory measurements use a device called a permeameter, which enables measurements of the flow rate and head loss across the sample. Field measurements of permeability generally employ well pumping tests with measurements of the response of the water table (unconfined aquifer) or piezometric surface (confined aquifer), and an analytical or graphical solution of the equations for groundwater movement (Bouwer, 1978).Table 4.5 gives representative values of saturated hydraulic conductivity for a sampIe of common porous materials (McWhorter and Sunada, 1977). Environmental factors may affect the hydraulic conductivity of a given porous medium. For example, ion exchange on clay and colloid surfaces will cause changes of mineral volume and pore size and shape. Changes in pressure may cause compaction of the material or may cause gases to come out of solution which would reduce the hydraulic conductivity (Davis and De Wiest, 1965).

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TABLE4.5-Typical values of hydraulic conductivity of porous materials" Material

Igneous Rocks Weathered granite Weathered gabbro Basalt Sedimentary Materials Sandstone (fine) Siltstone Sand (fine) Sand (medium) Sand (coarse) Gravel Silt Clay Metamorphic Rocks Schist

No. of AnalYWS

Range

(cms-'1

Arithmetic Mean

(cm s-')

7 4 93 20 8 159 255 158 40 39 19

17

"From McWhorter and Sunada, 1977.

4.4.4 Adsorption and Retardation Coefficients An important mechanism in retarding the migration of radionuclides in groundwater is sorption, which is defined to include all rock-water interactions that cause the radionuclides to migrate at a slower rate than the groundwater itself. The amount of sorption is dependent on both the chemistry .of the water and of the rocks. Because some of the chemical reactions are slow, it is a function of time as well. Values of sorption coefficients are required to calculate the travel times of key radionuclides from the source to the biosphere. The sorption coefficients are usually obtained using a standard batch test where rocks are put in contact with groundwater in which small amounts of radionuclides have been mixed, or in similar experiments with packed columns. The problem with this type of approach is that more detailed geochemical data are necessary to support the validity of the sorption measurement over the expected travel time of the radionuclides (which may be of the order of thousands of years). To provide the justification for using simple sorption coefficients a detailed understanding of the geochemical mechanisms of rock-water interactions must be attained. Such mechanisms as dissolution/precipitation, complexing, adsorption/desorption, phase transformations, and solubility should be understood for radionuclides of interest in the geochemical environment. The effect of heat, radiation, or high conceotrations of chemicals will be particularly important close to the source of release in some situations. Much of this understanding for

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PARAMETERS FOR TRANSPORT FLOW EQUATIONS

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shorter periods of time and close to the points of release can be obtained through a combination of laboratory and field experiments (Pickens et al., 1981) combined with data from natural systems that can be used as analogs. However, over longer time periods or far from the points of release all of the data must be obtained from studies of the natural system. Natural analogs of interest for application to radionuclide migration include: hydrothermal ore deposits, intrusive magmas into generic host rocks, uranium ore bodies, rich thorium deposits, "natural" fission reactors and underground nuclear explosions (Klingsberg and Duguid, 1980). Also, the behavior of natural radionuclides and their decay products in host rock formation can provide the data necessary to demonstrate that the sorption coefficients used in the transport models are conservative over the range of geochemical conditions and the transport time expected. Tables 4.6 and 4.7 demonstrate typical ranges of distribution coefficients (Kd) for several significant radionuclides, in an assortment of rocks and soils (Isherwood, 1981). This table illustrates some of the sensitivity of & to factors such as particle size and chemistry of the water phase. Values of Kd should be extrapolated to situations other than those for which they were determined only with extreme caution. TABLE 4.6-Distribution

coefficients: strontium and cesium"

Material and Conditions

Basalt, 32-80 mesh Basalt 0.54mm, 300 ppm TDSb Basalt-0.5-4mm, sea water Basalt-fractured in situ measurement Sand, Quartz - pH 7.7 Sands Carbonate, greater than 4mm Dolomite, 4000 ppm TDS Granite, greater than 4mm Granodiorite, 100-200 mesh Granodiorite, 0.5-lmm Hanford Sediments Tuff Soils Shaley siltstone greater than 4mm Sandstone, greater than 4mm Aluvium, 0.5-4mm Salt, greater than 4mm, saturated brine -. "Taken from Isherwood (1981). Total Dissolved Solids.

j6 (mLg-'I

Sr

1.4 48-2454 0.19

Cs

102 121-3165 0.027

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4. RADIONUCLIDES RELEASED T O GROUNDWATER

TABLE 4.7-Distribution coefficients: thorium and uranium" K.i (mLe-')

Conditions

Thorium Silt loam, Ca sat. clay. pH 6.5 Montmorillontie, Ca sat. clay, pH 6.5 Clay soil, 5mM Ca(NO&, pH 6.5 Med. sand, pH 8.15 Very fine sand, pH 8.15 Silt/clay, pH 8.15 Schist soil, 1 g/liter Th, pH 3.2 Schist soil, 0.1 g/liter, Th, pH 3.2 Illite, 1 g/liter Th, pH 3.2 Illite, 0.1 g/liter Th, pH 3.2 Illite, 0.1 g/liter Th, pH >6 Uranium 62,000 4400 300 2000 270 4.5 2.9

Silt loam, U(VI), Ca sat., pH 6.5 Clay soil, U(VI), 5mM Ca(N0J2, pH 6.5 Clay soil, 1 ppm U0+', pH 5.5 Clay soil, 1 ppm U0+2,pH 10 Clay soil, 1 ppm U0+', pH 12 Dolomite, 100-325 mesh, brine, pH 6.9 Limestone, 100-170 mesh, brine, pH 6.9

"Taken from Isherwood, 1981.

4.5

4.5.1

Methods of Solution f o r G r o u n d w a t e r Movement and Solute T r a n s p o r t

Introduction

The basic differential equations which describe the movement of water and dissolved radionuclides have been addressed in Section 4.3. The solution of these differential equations by analytical (closed form) or numerical methods will be described in this section. Over the past several years, numerous mathematical.models have been developed to simulate the flow of groundwater and the transport of radioactive and chemical substances, particularly in the field of waste management and new models are being introduced at a rapid rate. Discussion of the virtually hundreds of groundwater models is beyond the scope of this report, but several excellent compilations of analytical and numerical groundwater models are available (Bredehoeft, 1978; SAI, 1981; Lappala, 1981; Oster, 1982; Cleary and Ungas,

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1978;Codell et al., 1982). Some representative models in each category will be referenced, but the reader should recognize that the example cited may not be the only, or even the most appropriate model for a given situation. Groundwater models can be broadly classified as either numerical or analytical. Numerical techniques are usually direct solutions of the differential equations describing water movement, solute transport, and, in some cases, heat transport, using methods such as finite differences, finite elements, or network analysis. These methods always require a digital computer, an experienced modeler-hydrologist, and generally a large quantity of data. The validity of the results from numerical models depends strongly on the quality and quantity of the input parameters. Analytical models are usually approximate or exact solutions to simplified forms of the differential equations for water movement and solute transport. Such models are simpler to use than numerical models and can generally be solved with the aid of only a calculator, although computers are also used. Analytical models are much more severely limited to simplified representations of the physical situations. However, they are extremely useful for scoping the problem to determine data needs or the applicability of more detailed numerical models.

4.5.2 Numerical Methods Several of the more important types of numerical solution techniques are discussed below.

4.5.2.1

Finite Difference

One approach that has been applied to the solution of groundwater equations involves finite-difference approximations. To apply these approximations, the region under consideration is usually divided into a rectangular grid. The intersections of the grid are called nodal points and represent the position a t which the solution for unknown values such as hydraulic head are obtained. When difference equations are written for all nodes, and boundary conditions are applied, a system of n algebraic equations in n variables can be solved for each node and each time increment (Faust and Mercer, 1980).

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RADIONUCLIDES RELEASED TO GROUNDWATER

Finite Element

In the finite element method, a region is divided into subregions, called elements, whose shapes are determined by a set of points called nodes (similar to the finite difference grid). The first step is to derive an integral representation of the partial differential equations. This is commonly done by using the method of weighted residuals or the variational method. The next step is to approximate the dependent variables (head or concentration) in terms of interpolation functions called basis functions. Once the basis functions are specified and the elements defined, the integral relationship must be expressed for each element as a function of the coordinates of all nodal points of the element. Then the values of the integrals are calculated for each element. The values for all elements are combined and boundary conditions applied to yield a system of time-dependent first-order linear differential equations (Faust and Mercer, 1980). 4.5.2.3

Method of Characteristics

The method of characteristics is used in convection-dominated transport problems where finite-difference and finite-element approaches suffer from "numerical dispersion" or solutions that oscillate. The approach is not to solve the transport equations directly, but to solve an equivalent system of ordinary differential equations which are obtained by rewriting the transport equation using the fluid particles as reference points. This is accomplished numerically by introducing a set of points moving with the fluid (reference particles) that can be traced within the stationary coordinates of a finitedifference grid. In two dimensions this results in three equations; two for the velocity components and a concentration equation. Particles are placed in each finite-difference grid block and allowed to move a distance proportional to the velocity and elapsed time. The moving particles simulate the convective transport because concentration is a function of spreading or condensing of the particles. Once the convective effects are known, the remaining parts of the transport equation are solved using finite difference approximations (Faust and Mercer, 1980). 4.5.2.4

Random Walk Method

A method similar in many ways to the method of characteristics is the "random walk method." In this approach, a particle-tracing model

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SOLUTION METHODS FOR GROUNDWATER MOVEMENT

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is used to simulate convection. At the end of each time step, the particles are dispersed by being displaced a random distance in a random direction. Concentrations are calculated by counting the resulting number of particles in each cell and comparing this to the initial conditions. This solution technique is based on the realization that a normal probability distribution is a solution to Fick's Law. This method of transport modeling is easily implemented and provides simulations whose accuracy is limited only by the number of particles that can be traced. The main advantages of the method are its inherent stability, lack of numerical diffusion and simplicity. The main disadvantage of this method (and the method of characteristics) is the expense involved in keeping track of large numbers of particles (Evenson and Dettinger, 1980).

4.5.2.5 Distributed Velocity Method The Distributed Velocity Method (DVM) is a procedure useful for one-dimensional dispersion, especially of radionuclides which have long decay chains and where computational efficiency and stability are especially important. The DVM has found application in radioactive waste risk assessments where large numbers of calculations are conducted over wide ranges of input parameters. The underlying concept on which the DVM is based is the realization that the lateral and longitudinal dispersion of a contaminant introduced to the groundwater is largely caused by the heterogeneity of the flow field which results in a number of alternative paths. Such paths may be characterized by a continuum of migration times and average velocity components in the direction of flow. Extension of the DVM to radioactive decay chains, in which each member of the decay chain may have a different retardation coefficient, is straightforward and avoids many of the difficult problems encountered with other analytical and numerical methods in solving such problems. Two disadvantages of the DVM are that some numerical dispersion is introduced in the solution and the method has not yet been extended to more than one dimensional, time-dependent flow fields (Campbell et al., 1980b). 4.5.2.6

Flow NetworkModels

The numerical simulation by finite differences or finite elements of groundwater flow and solute transport problems in two and three dimensions can be costly in terms of computational resources. Flow network models such as the Network Flow and Transport Code

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(NWFT) (Campbell e t al.,1980; Cheung et al., 1982) are models which can be used to describe two- or three-dimensional fields in a much more efficient way by a network of interconnecting one dimensional flow segments. Fluid discharge and velocity are determined by requiring conservation of mass a t the segment junctions. Radionuclide migration from the points of release is calculated by assuming that transport occurs along a single one dimensional path having a length equal to the total migration path length. Where numerically feasible, the network model is particularly useful when it is used in conjunction with a more-complicated two- or three-dimensional model to first define the flow and concentration field for a particular example. The network model is first matched or "tuned to the results of the traditional model. The tuned network model may then be used for further computations, with a much smaller commitment of resources than the original model, for other runs and sensitivity experiments. 4.5.2.7 Advection Models There are groundwater solute modeling situations where the phenomenon of dispersion, together with its many uncertainties, is only a minor factor in describing the transport of contaminants in groundwater. For example, the flux of contaminant entering a river which is recharged from a contaminated aquifer is much less sensitive to dispersion than the concentration in a particular well. In the former case, the contaminated groundwater would enter the river over a wide area which would tend to "smear out" the effect of transverse dispersion. For simlar reasons, the transport from non-point sources of contamination such as large low-level radioactive waste landfills would diminish the sensitivity of modeled results to dispersion especially for relatively short flowpaths. First a flow model generates a potential field and streamlines. The flow patterns from the sources to the sinks are then used to formulate the "arrival time distributionn which subsequently can be used to calculate the concentration or flux of a contaminant a t downgradient points. Either numerical or analytical solutions of the flow equations are used to estimate groundwater velocities, the length of the path of a contaminant and the arrival time distribution (Nelson, 1978). 4.6 4.6.1

Model Validation, U s e a n d Misuse

Introduction

Before beginning a model study of a particular groundwater problem, the following points should be considered: (1) what a1.e the study

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objectives, (2) how much is already known about the groundwater system and source of potential contamination, and (3) does the study include plans to obtain additional data. The study objectives may require only a very simple model, or the lack of data may make a sophisticated model fruitless. If a field study is in its initial stages, a concurrent model analysis can be useful for determining the direction and needs of data collection efforts (Mercer and Faust, 1980a).

4.6.2 Model Validation Before a model can be used with confidence it must be validated. In general, the model is the solution of a set of equations, and validation consists of comparison of the solution with field-measured data. Agreement of a numerical model with known analytical solutions for simplified situations can be used to show that the numerical techniques work and that no serious errors exist in the computer code, but the ultimate test of the model is how well it compares to actual field data, or to other models which have previously been validated with field data. 4.6.3

Examplesof Validation

High quality field data on contaminant or radionuclide transport in groundwater are scarce. The collection of data necessary for very detailed modeling efforts is extremely costly, since the aquifer in which the dispersion is taking place can only be measured indirectly from wells. Determining the parameter distribution for a real system from a sparse data set can limit the quality of the model predictions (Grove and Kipp, 1981). Two of the best-documented examples of model-prototype comparisons of the transport of dissolved contaminants under saturated-flow conditions are illustrated below. Other validation efforts are discussed by Evenson and Dettinger (1980), Anderson (1979), Konikow (1977), Mercer and Faust (1980b), and Isherwood (1981). Unsaturated flowmodels have been validated with laboratory data (largely one-dimensional infiltration column data), but rarely with field data '(Oster, 1982).

The Snake River Plain Aquifer One of the most comprehensive studies of radioactive waste dispersion in groundwater was performed at the National Reactor Testing

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Station (NRTS) in southeast Idaho. The Snake River Plain is composed of basaltic lava flows and interbedded sediments. It is underlain by the Snake River Plain Aquifer, in addition to regions of perched water contained in sediment layers above the water table. The chemical and physical properties of the Snake River Plain are extremely complicated. The aquifer is apparently highly anisotropic. Although the permeable zone is more than 1000 feet (305 m) thick, dispersion from waste discharge appears to be largely confined to roughly the upper 250 feet (76 m) because of layering. The regional aquifer and perched ,?quifershave been extensively monitored in order to trace the migration of chemical and low-level radioactive wastes released to the groundwater from fuel reprocessing operations at the site. In.addition, there have been extensive long-term measurements of physical, chemical, and hydrological properties of the Snake River Plain Aquifer (Barraclough et al., 1967; Robertson et al., 1974). Since 1952, low-levelradioactive and chemical wastes from the Idaho Chemical Processing Plant have been discharged to the Snake River Plain Aquifer by means of deep well injection and a covered disposal seepage pit. An estimated 22,000 curies of tritium were released in the period from 1952 to 1970. Other important relatively long-lived radionuclides released a t the site since 1952 were approximately 53 curies of and 52 curies of 137Cs.In contrast to the tritium releases, which were largely to the deep injection well, most of the cesium and strontium releases were to the disposal pit. Radioactive wastes released to the pit must percolate through about 130 meters of ground cover, including areas of perched water, before reaching the regional water table (Robertson et ad.,1974).

Numerical Model Numerical models of two-dimensional groundwater flow and transport were applied to the Idaho Nuclear Engineering Laboratory site (Robertson et al., 1974). The groundwater flow simulation was tested by calculating the distribution of released chlorides and comparing it with the measured distribution. This simulation provided values of dispersivities so that the transport of tritium could be modeled. The results compare favorably with the concentration of tritium in the aquifer observed in monitoring wells (Fig. 4.3). Simulations were also done for where sorption was considered. The results for strontium were somewhat less accurate when compared with field measurements (Robertson, 1974).

4.6 MODEL VALIDATION,

USE AND MISUSE

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191

Equal Tritium Concentration in pic0 curles per m i l l i l i t e r for 1968 0 Well sarnples Digital model INEL = Idaho National Engineering Laboratory ICPP = Idaho Chemical Processing Plant (nuclear fuel reprocessing) TRA = Test Reactor Area EBR-1 = Experimental Breeder Reactor 1 s i t e (inactive) CFA = Central Facilities Area

l 5 '\'-SO

Fig. 4.3 Comparison of ICPP-TRA waste tritium plumes in the Snake River Plain aquifer for 1968based on well sample data and computer model (from Robertson, 1981).

Analytical Model

Code11 and Schreiber (1978) applied a two-dimensional time dependent analytical model to the transport and dispersion of tritium a t the Idaho disposal site. Analytical models in this complicated system are risky at best since they are usually able to incorporate only uniform coefficients. Much of the success of the numerical simulation of Robertson et al., (1974) is attributable to the model's ability to accept distributed values of the parameters governing flow and dispersion.

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Although the direction and velocity of groundwater flow in the aquifer were both time and position dependent, a single steady average velocity and average direction were estimated from Darcy's law, Eq. (4-9), based on the hydraulic gradient, permeability and porosity. The dispersivities were taken from the value determined in Robertson's finite difference simulation. Comparison of the model and prototype results is reasonable, and as good as could be expected for a model with non-distributed parameters. A model-prototype comparison is shown in Fig. 4.4 for October 1961 data.

Long Island Chromium Disposal Case Numerical Model Chromium wastes arising from the aircraft industry were released to an aquifer on Long Island, New York, in the 1940's, through disposal ponds. The aquifer is composed of glacial outwash material of Pleistocene Age which is underlain by a clay unit that acts as an aquitard. The aquifer discharges to a small surface stream down-gradient from the disposal basins. Hydrologic and transport parameters were obtained from field investigations of the contaminated site and then used in the flow and transport simulations. The two-dimensional groundwater flow and the transport of the nonsorbing chromium were simulated using a two-dimensional finite element model (Pinder, 1973). Groundwater flow was simulated to correspond with the hydrologic history of the site. Flow data were then used, with chromium release data to the ponds, to simulate the chromium transport. Monitoring data for chromium in the down-gradient plume were used to obtain values of dispersivity for the aquifer. The simulation of the chromium plume movement was then used to predict transport between 1949 and 1972 with excellent agreement to the data of Perlmutter and Lieber, (1970), as demonstrated in Fig. 4.5. Wilson and Miller (1978) applied an analytical solution of convective dispersion to the Long Island chromium contamination problem. They assumed a continuous point source, constant aquifer thickness and a steady groundwater velocity. Dispersion coefficients for their model were taken from the numerical model study by Pinder (1973). The model predictions were compared to the observed data of Perlmutter and Lieber (1970) for mid-1949 as shown in Fig. 4.6. Agreement is generally good, considering the simplicity of the model and the nondistributed nature of the input parameters.

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193

SCALE

+

0

NORTH

1 O O O M O O MOO

FEET

Fig. 4.4 Analytical Model-prototype comparison for tritium concentration in pCi mL-', October 1961.

4.6.4

Use of Models

Once it has been determined that a model study is, in fact, needed, and a validated model has been chosen, the procedures shown in Fig. 4.7 are generally followed. Data preparation first involves determining the boundaries of the

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Fig. 4.5 Comparison of observed areal extent and calculated isopleths for chromium contamination in 1953 (from Pinder, 1973).

Shaded area reprlaenls rnaanurld a s t m l of Contornlnat~on Con?ourr are af equal Cgncanlro1,an l m a l t 1

Fig. 4.6 Hexavalent chromium contamination: measured extent of contamination and predicted concentrations, Mid-1949 (from Wilson and Miller, 1978).

region to be modeled. If the model is numerical, the region must be discretized into subelements (e.g., grid blocks, finite elements or networks), depending on the model used. Once the region is discretized, it is necessary to specify the parameters and data for the model. Initial estimates of aquifer parameters constitute the first step in a trial-and-error procedure as "history matching" or "model calibration" (Mercer and Faust, 1980a,b). Predictions of the model are compared with available field data. If the comparison shows significant differences between predictions and

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OF NUMERICAL MODEL

AVAILABLE DATA

COLLECT DATA AND OBSERVE SYSTEM \,

*

Cmceplualirdlion

7

Hislory Mdlching (Field Problem)

PREPAREDATA FOR MODEL USING ESTIMATED PARAMETERS

PREPAREDATA FOR MODEL USING ESTIMATED PARAMETERS

*

4 COMPARE RESULTS WITH OBSERVED DATA

INTERPRETRESULTS Conceptual Model

Poor Comparison SENSITIVITY RUNS

*

IS MORE DATA NEEDED?

SIMULATION RUNS

Fig. 4.7 Diagram showing model use (from Mercer and Faust, 1980a).

observations, the model is modified and tested again. This iterative process of modification and verification continues until a satisfactory agreement between prediction and observation is obtained, a t which point the model is considered "calibrated." The chteria used to determine that the model is sufficiently calibrated depend on a number of factors such as the limitations of the model, the uncertainties of the field data, the needs of the modeler, the budget available for field and computer studies, and the time allowed for the study. The modification of boundary conditions and parameters is subjective and requires a considerable amount of knowledge of the region being simulated and experience on the part of the modeler. The boundary conditions and parameters used in the final simulation must still be in agreement with the knowledge and understanding of the geology and hydrology of the site. Through this process the equations of groundwater flow through porous media have been well tested and verified. The equations of flow through fractured media have been tested to some extent,

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but the equations of transport through fractured media still remain largely untested. Where enough data on hydraulic heads and variation of groundwater flow over long time periods are available, the inverse of the equations for head can be solved for the spatial distribution of permeability. The solution of the "inverse problem" (Neuman, 1973, 1980; Neuman and Yakowitz, 1979; Neuman et al., 1980) is useful because it yields a spatial distribution of parameters that are consistent with the hydrology of the site under consideration. In this process field measured parameters are useful for comparison with computer-generated parameters to ensure that generated values are realistic. For the radionuclide transport equations, the inverse problem has not been solved because the results are not unique. The calibrated model can be used to predict the future behavior of the modeled system, or to test the effects of modification to the system. A typical example of this type of modeling is the predication of tritium plumes in the Snake River Plain aquifer (Robertson, 1974). Such predictions can usually be made simply and cheaply once the model has been developed, verified and calibrated. Models can also be used to examine problems for which they have not been calibrated, or no calibration is possible. An example of this type of modeling is the study by Reisenauer (1981) the effect of different management alternatives (e.g., clay liners) on the unsaturated-flow migration of pollutants from a uranium tailings pit, even though the model used had not been calibrated to the field situation. In addition to site-specific applications, hypothetical groundwater situations can be modeled in order to explore various types of behavior which might not be intuitively obvious, and to test the sensitivity of the modeled phenomena to variations in the model parameters (Mercer and Faust, 1980a,b). An example of this type of modeling would be the studies of a hypothetical high level waste repository in bedded salt (Campbell et al., 1978). 4.6.5

Misuse of Models

The three most common misuses of models are overkill, inappropriate prediction, and misinterpretation. Overkill is defined as using a more sophisticated model than is appropriate for the available data or the level of results desired.. The temptation to apply the most sophisticated computational tool to a problem is difficult to resist. A question that often arises is: "When should three-dimensional models be used as opposed to two-dimen-

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sional or one-dimensional models?" Inclusion of flow in the third dimension, usually vertical, is recommended only in thick aquifers or if permeability changes drastically across the thickness of the aquifers. Inclusion of the third dimension requires substantially more data than for one- and two-dimensional models. For example, saturated-unsaturated flow through a shallow land burial site is truely a threedimensional problem. However, the data are seldom available to consider more than one-dimension above the water table. In many cases, sophisticated models are used too early in the analysis of a problem. One should begin with the simplest model appropriate to the problem and progress toward the more sophisticated models until the desired level of results is achieved. In transport problems, the flow modeling should be completed and checked against the understanding of site hydrology before a transport model is applied. Misinterpretations usually arise because inappropriate boundary conditions were selected or the hydrologic history of a site has been misread. Under either of these conditions the simulated data will not match the hydrologic history of the site. Perhaps the worst misuse of a model is blind faith in model results. Simulated data that contradict hydrologic intuition almost always arise from a mistake in some data entry, an error in the computer code, or application of a model to a problem for which it was not designed. The latter case usually occurs in application of an analytical solution that was obtained using boundary conditions that are different from those to which the solution is being applied (Mercer and Faust, 1980a).

5 . Usage Factors for Predicting Exposure to Man Once the concentration of radionuclides i n the atmosphere, water, and food products has been established using techniques described i n Sections 2-4, the amount taken i n by people can be determined by applying usage factors for dietary intake, breathing rates, and living habits. Site-specific data for usage factors are always preferable to the default values discussed in this chapter. However, in many cases, these data are not available or are difficult to obtain. Knowing the intake rate of radionuclides per unit time, internal exposure may then be calculated using dose conversion factors for ingestion (mrem y-' per pCi ingested) or inhalation (mrem y-' per pCi inhaled). External exposure is calculated using a separated set of dose conue~sionfactors for submersion i n air or water (mrem y-' per PC m-3) or living o n contaminated surfaces (mrem y-' per PCi m-').

5.1 Dietary Pathway Usage Factors 5.1.1 Introduction

Evaluation of the intake of radionuclides by the ingestion of contaminated food and water requires a detailed knowledge of the patterns of food and water consumption, commonly referred to as usage factors. In this section the available data on dietary intake rates of terrestrial foods, aquatic foods, and water and other beverages are summarized for individuals of various ages. The data, which are abstracted from three reports, Rupp (1979, 1980) and Rupp et al. (1980), are based on market basket surveys and surveys of individual eating habits. Although average intake rates are often the only data reported, ranges as well as averages are included whenever possible. Frequency distribution of usage factors for individuals of various age groups are 198

5.1 DIETARY PATHWAY USAGE FACTORS

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characterized only for milk and fish, the two food items which have been more thoroughly evaluated. 5.1.2 Generic Usage Factors Although site-specific values of dietary usage factors are most appropriate for evaluating the intake of radionuclides via foodstuffs, the effort and expense of a detailed survey for a particular area may not be justified. If the food consumption pattern of a population group is not unusual, generic values of dietary intake rates may be used. The Nuclear Regulatory Commission has recommended a set of default values of usage factors to be used in lieu of site-specific data when evaluating compliance with regulations limiting routine releases from light-water reactors. Tables 5.1 and 5.2 summarize the generic values for the average individual and for the maximally-exposed individual, respectively (USNRC, 197%). TABLE 5.1-Values for dietary usage factors from Regulatory Guide 1.109 to be used for the average indiuidual in lieu of site specific data" Pathwav

Child

Fruits, vegetables & grain (kg Y-') Milk ( L y-') Meat & poultry (kg y-') Fish (kg y-')b Seafood (kg y-')' Drinking Water (L y-') . -

Teen

Adult

200

240

190

170 37 2.2 0.33 260

200 59 5.2 0.75 260

110 95 6.9 1.0 370

"From USNRC, 1977b. Fish includes freshwater and marine. ' Seafood includes aquatic invertebrates.

TABLE 5.2-Values for dietary usage factors from Regulatory Guide 1.109 to be used for the maximum exposed indiuidual in lieu of site specific data." Pathway

Fruits, vegetables & grain (kg Y-' Leafy vegetables (kg y-') Milk (L y-') Meat & poultry (kg y-') Fish (fresh or salt) (kg y-') Other Seafood (kg y-') Drinking Water (L y-')

" Adapted from USNRC (1977b).

Infant

Child

Teen

Adult

-

520

630

520

330

26 330 41 6.9 1.7 510

42 400 65 16 3.8 510

64 310 110 21 5 730

-

330

200

/

USAGE FACTORS FOR PREDlCTING EXPOSURE T O MAN

5.1.3 Usage Factors for Terrestrial Foods Table 5.3 summarizes Rupp's (1980) "best estimate" average daily intake of a variety of foods by age group. Although several sources were used to determine the average, the majority are based on the U.S. Department of Agriculture (USDA) survey of 1965. The values in Table 5.3 are based on weighted averages of all persons in each data base. Because the "best estimate" average daily intake values are based TABLE5.3-"Best

estimatesn of werage daily intake of various foods by age" Age (years)

Food <1

Milk, fluid Milk and milk products (Ca equivalent)

1-11

>11-18

m L d-' 485 594

>18

696 795

542 606

261 306

17

25

31

41

7 4 34 3

38 41 39 18

66 69 52 27

86 76 70 26

-

6

0.49 4.33 0.93 49

0.84 7.23 1.45 67

1.48 10.68 3.59 69

2 12 12 50

20 7 22 58

30 7 28 82

50 8 25 99

23 112 3 21

74 112 2 87

93 116 1 113

99 87 1 97

g d-'

Eggsb Meats Beef Pork Other and Mixtures Poultry Fish' Freshwater fin Saltwater fin Shellfish (all) Potatoes Vegetablesd Leafy, mixturesd Deep yellow, mixturesP Legumes, mixtures Other, mixtures Fruit Citrus, tomatoes Other, mixtures Dried Grain (flour equivalent)

-

"Adapted from Rupp (1980). An average egg weighs 48 g (Blanchard, 1978). The egg group includes egg salads, creamed eggs, omelets, and mixtures which are primarily eggs. ' National Marine Fisheries Service Survey, 1973-1974 raw data. Blanchard, 1978. 'These quantities are considered by the U.S.D.A. to be relatively low compared to previous surveys.

5.1 DIETARY PATHWAY USAGE FACTORS

/

201

TABLE 5.4-Relative frequency of types of milk consumed by infants of various Age (Months)

Feeding

Otol l t o 2 2 t o 3 3 t o 4 4to5 5 t o 6 6 t o 9

Relative Percent

Breast-fed Milk-based formulac Milk-free formulac Evaporated milk formula Evaporated milk and water Fresh cow's milk

20 64 10 4 2

15 65 10 4

6

12 59 10 3 2 14

10 49 10 2 29

8 41 8

5 29 6 2 2 41 58

2

3 2 1 92


" Adapted from Rupp (1980). Fomon (1975). These estimates were based on market research data and modified slightly by findings from 15 published reports in the open literature. 'Commercially prepared.

primarily on the USDA survey of 1965, they are not necessarily valid today. Rupp (1980) compared consumption rates from the 1955 and 1965 household surveys and noted changes in the per capita consumption rates of specific food categories. Among the differences in the 1955 and 1965 surveys were the increased use in 1965 of meat, poultry, and fish and the decreased use of dairy products, vegetables and fruit, and grain products. The changes in per capita food consumption since 1965 have not yet been characterized.

Milk Consumption In the United States, milk is an important nutrient source not only in the infant diet but also in the diet of other age groups. Rupp (1980) evaluated data on milk consumption by infants and found from studies on individual subjects that infants 0 to 4 months of age consume milk a t a rate of 750 mL d-' with a range of 550 to 1060 mL d-'. Infants 4 to 6 months of age consumed milk at a rate of 800 mL d-' with a range of 480 to 1180 mL d-'. For infants 1year of age, the average consumption rate of fluid milk is between 600 and 700 mL d-'. The relative frequency of consumption by infants of human milk, dairy milk, evaporated milk and powdered formula is presented in Table 5.4. A t 1 month of age, only 2 % of infants are using fresh cow's milk. A t 4 to 5 months of age, about half of the infants are drinking fresh milk. At 1 year of age, almost all infants are using fresh milk. These considerations can be important when evaluating the radiation dose to infants from ingestion of nuclide-contaminated milk.

202

/

USAGE FACTORS FOR PREDICTING EXPOSURE TO MAN

Age Variation of Dietary Intake The age dependency and sex difference in the consumption rates of milk, of meat and poultry, and of vegetables, fruits and grains are shown graphically in Fig. 5.1, 5.2, and 5.3, respectively. The average milk consumption (Fig. 5.1) declines after the first year until 3 years of age when it starts to rise again in children and teenagers and then falls in adults. Consumption of meat and poultry (Fig. 5.2) is highest in adults, and consumption of vegetables, fruits and grains (Fig. 5.3) is highest in teenagers and adults.

Variability of Dietary Usage Factors Rupp (1979) analyzed the distributions of milk consumption by individual infants and the mean consumption by groups of infants. Milk consumption by infants varied over a small range of less than a factor of 2 and was log-normally distributed with a geometric standard deviation of 1.2 or less (Table 5.5). Milk consumption by older individuals varies over a much greater range. Table 5.6, reproduced from Rupp (1980), shows the frequency distribution of milk consumption by individual males and females in selected age groups based on Pao and Burk (1975). Because the data are from a one-day recall survey, they are not strictly valid when extrapolated to annual. average consumption rates.

t

FEMALE

1

AGE ( y r )

Fig. 5.1 Consumption rate of milk and other dairy products by age and sex of individuals (from Rupp, 1980).

5.1 DIETARY PATHWAY USAGE FACTORS

I

I

-

I

I

I

I

-

*/-*-

-

FEMALE 0

0

r'H0-0-

203

1

f 0

0

--

C

-

-

-

a-

-

---

I I0

20 0

20

I

I

30

40

50

70

60

AGE ( y r )

Fig. 5.2 Consumption rate of meat and poultry by age and sex of individuals (from Rupp. 1980).

-

I

I

I

I

I

I

-

-

MALE

-

a' 0

-

-

I

loo 0

10

--* I

I

20

30

I 40

I 50

I

60

AGE ( y r )

Fig. 5.3 Consumption rate of vegetables, fruits and grains by age and sex of individuals (from Rupp, 1980).

204

/

USAGE FACTORS FOR PREDICTING EXPOSURE TO MAN

TABLE 5.5-VariabilityAge Group -- months

Individual Data 0-4 4-6 Grouped Data 0-4 4-6 6-12

of. individual and averme . - milk w ~ u m p t i o nby- infants" -

Geometric S.D.b

W

Mode

Median

Mean

p,:",","ti,e

Range

mL d-'

1.1 1.2

100 45

620 790

740 820

750 840

1000 1300

550-1060 480-1180

1.1 1.1 1.2

12 7 4

730 810 710

740 820 740

750 820 760

930 1080 1210

650-890 700-990 670-1030

Adapted from Rupp, 1979. Geometric standard deviation. 'Number of individual or mean estimates (derived from report averages).

5.1.4

Usage Factors of Aquatic Foods

The pattern of fish consumption by children, teenagers and adults in various regions of the U.S. was recently reported by Rupp et al. (1980) who examined the extensive data base on fish consumption compiled by the National Marine Fisheries Service. The data include fish consumption in number of meals and serving sizes for each type of fish eater for a 1-month period. Consumption rates for 80 species of fish are reported for at hdme and away-from-home consumption. Table 5.7, which summarizes these data, presents fish consumption for children (1 to 11 y), teenagers (12 to 18 y), and adults ('19 to 98 y), respectively, based on over 23,000 individuals. Table 5.7 considers three categories of fish: freshwater finfish, saltwater finfish, and shellfish, and lists the 50th, 90th and 99th percentiles, as well as the maximum and average consumption for all states. Fish consumption increased with age, and saltwater finfish ranks first in terms of consumption rate and percent of the population eating this type of fish. Based on population averages, only 10% of the population eat no marine finfish, while 65% eat nodhellfish and 86% eat no freshwater fish. The consumption patterns of individual shellfish species vary greatly by region. Table 5.8, which is also reproduced from Rupp et a!. (1980), is a regional summary of the average per capita consumption of the three categories of fish. Because the average per capita consumption includes zero values from persons who eat no fish or shellfish, the average consumption of individuals who eat fish or shellfish is greater than the average of Table 5.8. The maximum is several times the average value.

TABLE 5.6-Fluid whole and partinlly skimmed milk consumed in a day by selected sex-age groups"

-

Selected Sex-Age Groups Item and Unit

Individuals sampled Percent consuming on day surveyed

3-5 y

15-17 y

9-11 y

20-34 y

65-74 Y

35-54 y

(M a n d F ) b

M

F

M

F

M

F

M

F

M

F

1397 89.4

663 88.5

597 86.4

561 81.8

532 75.4

1396 69.5

1676 60.3

2050 62.2

2444 56.9

450 68.4

599. 59.9

14.5 9.0 16.6 4.8 9.7 3.7 2.4 1.3

17.9 14.6 13.4 3.3 5.8 1.1 0.6 0.2

15.8 16.4 14.4 5.3 9.8 4.2 2.0 0.4

21.0 13.2 14.4 3.2 5.8 1.8 0.5 0

Relative Percent

Quantity consumed (mL d-') 1-120 121-240 241-360 361-480 481-730 731-970 971-1330 1331-3472

2.2 8.6 14.3 12.9 26.9 16.3 7.0 1.1

1.5 4.8 15.1 8.6 21.8 22.5 11.7 2.4

0.8 5.9 15.6 12.1 25.8 19.2 6.5 0.5

3.2 2.8 12.6 4.4 21.0 18.5 14.1 5.0

" Reproduced from Rupp, 1980. Reference: Pao and Burk, 1975. M = Male, F = Female.

5.6 4.7 20.7 7.3 19.7 11.8 4.9 0.6

14.9 7.6 16.0 6.0 12.6 5.4 4.3 2.6

14.0 10.1 16.0 4.6 11.1 2.5 1.8 0.1

Age Group

1-llyoldchild

Total (a, b, c) 12-18 y old teenager Total (a, b, c) 1&98 y old adult

Total (a, b, c)

%z a b c

TABLE 5.7-Fish Percentiles 50%

a b

0 1.10 e 1.10 0 1.88

C

0

a b

1.88 0 2.66

c

0 2.66

90%

99%

consumption in the United Statesd Maximum

Average

Sample Size

0.55 3.59 1.37 5.51 1.01 5.77 1.88 8.66 1.87 8.66 4.00 14.53

Adapted from Rupp et d., 1980. Based on National Marine Fisheries Service Survey, 1973-1974 raw data. " a = freshwater finfish. b = saltwater finfish. c = shellfish.

Percent Consuming

660'B EEO'I 821'2 GOB'Z ZOP'P FLO'I ~ ~ 8 ' 2 966'P OEB'1 CIZ'EZ 01dOad =PnN

8'PIT 2'8L KZI1 P'61; P'09 2'18 9'1PT 0.90T E'L91

WOOI S e i a ~ y[BUO!~ -BN$0 a ~ u a x a d

91'1 6L'O P1'1 09'0 19'0 28'0 EP' 1 90'1 69'1 10'1

L'601 8'98 8'26

9'08 8'26 L'68 Z'LO1: L'PIT 7.811 0.00~ S a a ~ [sue!? y

I-'

VL?II~~S

-RNp a s t q u a ~ a d

IS'€ EL'? L6-Z 8SZ L6'2 L8'2

BP'B L9'E 8L'O OZ'E I-'

7'

qm~u!da a ~ e m ~ l ~

,,a%orann p u m ~ mq?10 ? u a ~ a pun d ytxj~layspun yq/ul/jo

L'9L WL01 P'S61 8'8PI Z'OE1 8'291 L'9L 8'29 9'8 I 0.001 aSera~ypuog -BNJO a~~n?uaxad

68'0 9VO W0 PYO %'O OL'O €6'0 LZ'O 80'0 FP'O 1-'

3'~!38d uyuno~ PJ2Ua3'S'M p ~ 2 u a 3'N'M 18JWa3 'N'3 18a7Ua3 .s'3 3!3UBpv

's

3!3U8DV P!N puelSu3 ma^ s a w s pal!un u o g a ~s n s u ~

~ ( ~ l l~ua !) s~m q s a ~

a m uoydwnsum v?!du3 lad a8v~annaq? jo Xlmuwns puqri7ag-8.1;

a~av~,

208

/

USAGE FACTORS FOR PREDICTING EXPOSURE T O MAN

5.1.5 Usage Rates for Water and Other Beverages The patterns of consumption of water and other beverages were recently reviewed by Rupp (1980). A summary of the average intake and range of intake of water and other beverages by age group is reproduced as Table 5.9. The data in Table 5.9 were selected to average out differences in climate and season. Fluid intake is greater in summer than in winter, as one would expect. Fluid intake was noted to increase with age while proportionately the intake of tap water decreases.

5.2 Inhalation Pathway Usage Factors 5.2.1 Introduction Evaluation of the quantity of radionuclides transmitted to the whole body or specific organs from inhalation of air contaminated with various radionuclides requires the following data: (1) Concentration of each radionuclide in the air. (2) Breathing rates in L min-' or m3 d-' of the exposed individual. (3) Fraction of the inhaled radionuclide deposited in the lung. TABLE 5.9-Average and range of daily intakes of tap water and beverages other than

- - (Y)~

Aee Grouns ----r-

milk for various age&qx* -.

Infantb <1

Childb 1-12

-

Teenc

Adult‘

12-17

>18

Tap Water (mL d-') Average 223 329 279 255 Range 159-340 208-493 216-332 192-411. Other Beveragesd (mLd-I) Average 726 1096 Range 547-917 729-1436 Total Aver1005 1351 age " From Rupp, 1980. Walker et a l , 1963. Water intake for infants also includes water used for mixing formulas and fruit juices (infant, child). 'Cook et a!., 1975 (teenager, adult). Other beverages include soft drinks, coffee, tea, beer, wine, distilled alcoholic beverages, and water used in fruit juices and fruit-flavored drinks (Data not available for infants and children).

5.2 INHALATION PATHWAY USAGE FACTORS

1

209

(4) Fraction of the inhaled radionuclide absorbed from the lung and

distributed to the body (organ). (5) Retention time (or removal rate) of the radionuclides in the body organ. The first item has been addressed in Section 2. Here the focus is on the second item, namely the breathing rate and its variation with age, sex, state of exertion, etc. Items 3-5 are not considered in this report. Often an assumed average breathing rate of an adult population is used to estimate the quantity of a radionuclide that may be inhaled in a particular situation. Although this approach is sometimes adequate to estimate the magnitude of the problem, it is often insufficient for decision criteria because it does not provide an estimate of the range ar distribution of the possible inhaled quantities of radionuclides for the adult population. It certainly does not provide information on ranges and distributions that might be expected for various age groups or for difference in sex, physical condition, and activity levels within age groups. The purpose of this discussion is to summarize available ventilation rate (minute volume) information and, where possible, define the distributions and show the differences that exist as functions of age, sex, and activity level. Thus if demographic data are available for a given release situation, a better estimate of the possible range and distribution of dose might be made for the inhalation pathway. Maximum inspiration

1 1

t

t

.-> 0

lnspiratory reaene volume (complementary air)

m P

rnU

Normal inspiration

>

.-

P

-

->u 3.-

3 I;; En U ria.4.

J

L

Collapsed lung

Fig. 5.4 Lung capacities and volumes.

210

/

USAGE FACTORS FOR PREDICTING EXPOSURE TO MAN

Several terms are frequently used to describe the volumes and capacities of the lungs and data are presented in a variety of ways. Therefore, brief definitions of the terms for lung volumes, capacities, and rates are given in the glossary (Appendix B) and are schematically displayed in Fig. 5.4. Data are frequently expressed in terms of vital capacity, tidal volume ventilation or minute volume and daily or annual inhalation rate. The dynamic volumes-those volumes comprising the vital capacity-vary considerably with the physical exertion of an individual and with size, age, sex, altitude and health status. The critical parameter for estimating the quantity of inhaled radionuclide is the minute volume for an individual a t the time of exposure. Ventilation rate and minute volume, expressed as L/min, are both used in the published literature. In this report we only refer to minute volume.

5.2.2 Minute Volumes A report by Thompson and Robison (1983) summarizes the minute volumes by sex, age, physical exertion, etc; a summary of some of the findings is given in Table 5.10.

Infants - Newborn (1 week or younger)

The International Commission on Radiological Protection (ICRP, 1975) lists a minute volume of 0.5 L min-' for a resting newborn and TABLE 5.10-Summary of ventilation rates (minute volumes) at normal body temperature and pressure, saturated in L min-'--and in m3 d-'' Subject

Age

Newborn Infants Infants Children Children Teenage Boys Teenage Girls Adult Men Adult Women

1 hr. to 1 wk. 2 wk. to 1 mo. 1 to 12 mo. 1t04y

5 to 12 y 13 to 19 y 13 to 19 y 20 Y 20 Y

Resting 0.7 ( 1 . 0 ) ~ 0.9 (1.3) 1.5 (2.2) 3.3 (4.8) 7.1 (10) 7.6 (11) 5.6 (8.1) 8.8 (13) 6.4 (9.2)

Active 2.1' (3.0) 2.7' (3.9) 4.5' (6.5) 10' (14) 20 (36) 30 (43) 25 (36) 30 (43) 25 (36)

Maximum work

-

-

63 (91) 130 (187) 89 (128) 132 (189) 98 (141)

'Average ventilation rates based on studies reviewed by Thompson and Robison (1983). Numbers in parentheses are the equivalent breathing rates in m3 d-'. ' Bawd on three times the resting minute ventilation (Deming and Washburn, 1935).

211

/

5.2 INHALATION PATHWAY USAGE FACTORS

TABLE5.11-Currently adopted minute volumes (L min-') for the r e s t i s state Newborn

ICRP (1975) USNRC (1977b3

Infant

1.5 (4.2) 2.7

0.5 (1.5)" -

Child

4.8 (13) 7.0

"Minute volumes for nonresting, light activity conditions are shown in parentheses.

TABLE5.12-Currently proposed daily ventilation rates in m3 d-' Source

Newborn

Infant

Child

Teen

ICRP (1975) USNRC (1977b3

0.8 -

3.8 3.8

15 10

22

Men Adult &

23

21 22

1.5 L min-' for an active newborn (Table 5.11). They assume that the 0.5 L.min-' rate applies 23 hours per day and the 1.5 L min-' for 1 h for a total daily volume of approximately 0.8 m3 (Table 5.12). From the studies of Bolton and Herman (1974), Hathorn (1974, 1978), and Brady et al. (1964) it would appear that an average value for resting newborn infants would be more in the range of 0.6 to 0.8 L min-I with a mean of 0.7 L min-'. This is a 40% increase over the ICRP value (ICRP, 1975). In view of the fact that the general assessments of the inhalation pathway for newborns assume that the breathing rate for the resting condition applies 23 hours per day, it would seem a higher average breathing rate for the resting condition should be used for newborn infants. Deming and Washburn (1935) have reported that the average minute volume for infants who are awake but quiet is about 22% greater than in the sleep state; they also provide data which indicates that the minute volume during crying is 3 to 3.5 times that observed in the sleep state. Thus the minute volumes for a crying active state would be 2 L min-'. The distribution is log-normal with an arithmetic mean of 0.63 L min-l, a geometric mean of 0.60 L min-' and a geometric standard deviation of 1.35. Infants - 1 week to 1 month

Data on minute volumes for infants and children more than just a few days old are very limited. Most of the literature addresses newborns or children over 5 years of age. Data from Deming and Washburn (1935) indicate that the average resting minute volume for infants 2 to 4 weeks (1month) of age is 0.9 L min-' with a range from 0.88 to 0.92 L min-'. Insufficient individual data are available to determine the distribution. If one assumes that

212

/

USAGE FACTORS FOR PREDICTING EXPOSURE TO MAN

the minute volume in the active state is 3 times that in the resting state (Deming and Washburn, 1935), then the active minute volume is about 2.7 L min-'.

Infants - 2 to 12 months Deming and Washburn (1935) reported data from which it was calculated that the resting minute volume for infants age 1to 3 months and infants 4 to 12 months is 1.6 L min-'. The average for 2 to 12 months was 1.3 L min-'. It is clear from both Deming and Washburn's (1935) and Krieger's (1963) studies that the minute volume increases rapidly with age during infancy. Therefore, a reasonable average resting minute volume for the 2- to 12-month age group would be about 1.5 L mine'. The active state minute volume would be about 4.5 L min-' assuming, again, that the active state minute volume is three times that for the resting state (Deming and Washburn, 1935). The distributions for the data from Deming and Washburn's study are log-normal with an arithmetic mean of 1.4 L min-', the geometric mean of 1.33 L min-' and the geometric standard deviation of 1.44.

Children - Ages 1 to 4 y Few data are available on the minute volumes either at rest or at maximum exercise for children between 1 and 4 years of age. The data of Kattan et al. (1978) and Krieger (1963) would suggest that 3.3 L min-' is the average resting volume for this age group and if it is assumed that the active minute volume is three times the resting rate (Deming and Washburn, 1935), then the average active minute volume would be about 10 L min-'. Insufficient individual data were available to assess the distribution of minute volumes in this age group.

Children - Ages 5 to 12 y Resting minute volumes for boys between the ages of 5 and 12 were found to be about 7.1 L min-' by both Orzalesi et al. (1965) and Eriksson (1972). Onalesi et al. (1965) also found that girls in this age range had similar volumes of 7.1 L min-I; this rate is based on only four subjects and is a bit higher than the average for teenage girls and adult women.

5.2

INHALATION PATHWAY USAGE FACTORS

/

213

For maximum exercise in this age group, average minute volumes, derived from the studies reviewed by Thompson and Robison (1983) are 61 and 63 L min-' for boys and girls, respectively. Average minute volumes for routine play and activity would be less than these values. Assuming that the minute volume during average childhood play and exertion would be about 3 times the resting rate, then 20 L min-' would be a reasonable estimate, which is consistent with results reported by Gadhoke and Jones (1969). Insufficient individual data were available to determine the distribution of minute volume in this age group.

Teenage - Ages 13 to 19 y The average minute volumes derived from the studies reviewed by Thompson and Robison (1983) are 7.6 L min-' for boys and 5.6 L min-' for girls for the resting state and 130 L min-' and 89 L min-' respectively for the maximum work state. Gadhoke and Jones (1969) report sub-maximal work minute volumes ranging from 25 to 49 L min-'. The minute volumes under submaximum and maximum work are very similar to the comparable same-sex values for adults. Very few minute volume data are available for teenagers for submaximal work conditions; however, because teenagers tend to approach adult minute volumes under maximum work conditions, it can be assumed that under light-to-moderate activity the rates would be similar. These distributions are log-normal with an arithmetic mean, and geometric mean of 8.3 and 8.2, respectively, and a geometric standard deviation of 1.3.

Adults Average values for the minute volume for adult men and women for both resting and maximum work conditions have been reviewed by Thompson and Robison (1983). The minute volumes for the resting, submaximum work, and maximum work conditions are summarized in Table 5.10. Several studies have been directed toward evaluating the minute volumes as a function of work and exercise. Studies reviewed by Thompson and Robison (1983) report results for men in light-tomoderate exercise on treadmills, ergometers, and controlled exercise, and the results all fall between 17 and 45 L min-'. At higher work

214

/

USAGE FACTORS FOR PREDICTING EXPOSURE T O MAN

loads, the minute volume begins to increase and approach the average maximum work load values of about 130 L min-'. Studies t o determine the minute volume a t submaximal work load for women indicate a range from about 12 to 36 L min-'. Skubic and Hodgkins (1966) and Michael and Horvath (1965) both report results within this range. The distribution of minute volumes for males over the age of 20 for the resting state is log-normal, has an arithmetic mean of 8.8 L min-', a geometric mean of 8.5 L min-', and a geometric standard deviation of 1.28. The minute volume distributions for males for age groups 20 to 30, 31 to 40, 41 to 50, and older are all log-normal with geometric standard deviations ranging from 1.22 to 1.45. T h e distribution of minute volume for men over the age of 20 for maximal work conditions appears to be log-normal with an arithmetic mean of 127 L min-', a geometric mean of 125 L min-', and a geometric standard deviation of 1.22. Resting minute volumes for adult women between, 20 and 60 are log-normally distributed. The arithmetic mean, geometric mean and geometric standard deviation are 7.3 L min-', 7 L min-' and 1.34, respectively. The limited number of data points for maximum-work minute volumes for women make the distribution uncertain. However, because minute volume distributions for the resting conditions for women, men, and infants all appear to be log-normal, we assume these have the same distribution, with a geometric standard deviation of 1.42 L min-' and an arithmetic and geometric mean of 109 and 104 L min-', respectively. The age ranges selected for analysis above were arbitrary; however, they do show how the minute volume changes with age. Although these rates can be used in assessment for the particular age group, the minute volumes do vary within a group. For example, the volumes for 18- and 19-year-old subjects is generally a bit higher than those for the 13- and 14-year-old subjects and, therefore, slightly higher than the listed average for the entire age group. Similarly, the 11- and 12year-old children have slightly higher minute volumes than do the 5and 6-year-old children.

5.2.3

Significant Factors Affecting Minute Volumesfor Radionucltde Intake via Inhalation

Age Distribution The data in Table 5.10 indicate a range of average resting minute volumes from 0.7 L min-' for newborn infants to 8.8 L min-' for adult

5.2 INHALATION PATHWAY USAGE FACTORS

I

215

males. Therefore, it is necessary to have some idea of the age distribution of the population because the difference in range of average minute volumes between infants and adults is about a factor of 13, while the difference between young children and adults is less than a factor of 3. For both sexes, the resting ventilation rates are not greatly different as a function of age after about 13 or 14 years of age. However, maximum minute volumes do tend to decrease with age (Dill et al., 1963). Sex Resting minute volumes are not very different between sexes through about 12 years of age. From teenage on through adulthood, however, the males have resting volumes that are about 40 to 50% higher than females. Men also have 35 to 40% higher volume under maximum work conditions than women. Therefore, the sex ratio in a population will make some difference in an inhalation assessment. State of Physical Activity The most significant parameter that needs to be determined is the state of activity of the population during a period of radionuclide inhalation. For example, differences in resting minute volumes between sexes and among ages is not large, the greatest being that between young children and adults, about a factor of 3. However, minute volumes under maximum work are about 15 times those a t rest for both sexes and all ages greater than 5 years (Table 5.10). The minute volumes observed under average working or activity conditions are four to eight times those observed a t rest. Thus, it is clear that the state of exercise or level of activity is very important in determining the quantity of radionuclide inhaled over periods of a few hours or days. For continuous chronic exposure, average values for the percentage of time spent in the resting and active states may be used with the appropriate minute volumes for developing general assessments. Other Variables Other variables that can alter the minute volume for both the resting and submaximal work state have been reviewed by Thompson and Robison (1983). These include temperature (hot vs cold environment);

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USAGE FACTORS FOR PREDICTING EXPOSURE T O MAN

altitude; weight; height; smoking and general health state-especially pulmonary-related diseases. Many papers discuss the effects of these and other variables on minute volumes. However, they are perturbations of the basic results already discussed for the various age groups and sexes, and of lesser magnitude than the evaluation of whether resting- or active-state minute volumes should be applied to a given situation. 6.2.4 Average Time Spent at Rest and Light-to-Moderate Activity The most common assumptions for the average number of hours spent at rest and at work or in light-to-moderate exercise is 8 hours per day at rest, 8 hours per day at work, and 8 hours per day at personal light-to-moderate activity (ICRP 1975); and for a large population, this is generally adequate. To be more precise would require a detailed knowledge of the daily habits of the exposed population. These habits, even for an individual, will vary depending on the time of year, climatic conditions, time of day, etc. If such details were available, it might be possible to also determine the percentage of time that a small portion of the population would be at maximum ventilation rates. Unless such data are available, so that the distribution and standard deviations of the time spent at rest or at various stages of exertion can be determined, it is necessary to use the general approach with specific fractions of time allocated for each state of minute ventilation. 6.2.6 Summary and Discussion Data are available to evaluate infants and adult men and women for both the resting and maximum activity states; however, limited data are available for evaluating the distribution of the minute volumes for children 1 through 12 years of age and for teenagers. The distributions of the available data are log-normal with geometric standard deviations in the range 1.3 to 1.5. Therefore, it can be assumed that minute volumes in the other age groups will also be log-normally distributed with similar standard deviations. Observed, average minute volumes, a log-normal distribution, and a geometric standard deviation of 1.4 will provide an estimate of the distributions of inhaled radionuclide for the children and teenagers. Because the distributions are lognormal, use of the arithmetic mean includes more than 50% of the population. For example, for infants the mean value of 0.7 L min-'

5.3 REDUCTION IN EXTERNAL EXPOSURE

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217

falls a t about the 62"* percentile of the distribution. For the resting state of adult males, the mean falls a t about the 60thpercentile. For the resting state of women and the maximum activity state of men and women, the mean minute volume falls a t the 60th, 67th,and percentiles, respectively. The arithmetic mean value of the minute volumes for resting and active states for the selected age groups are listed in Table 5.10. These data, when used in conjunction with the assumptions that the data are distributed log-normally with geometric standard deviations of about 1.4, can be incorporated in stochastic models for the distribution of inhaled radionuclides in a population. 5.3

Reduction in External Exposure from Shielding Due to Buildings, Homes, and Vehicles

On the average, people in the U.S. are reported to spend 95% of their time indoors either a t home or in large buildings for work or pleasure (Oakley, 1972). This estimate is based upon a large scale international study reported by Szalai (1972) in which the U.S. portion was conducted by Robinson and Converse (1966). These data have been summarized in a report for the Environmental Protection Agency by Moeller and Underhill (1976). Some occupations obviously require that more time be spent outdoors. Farmers, ranchers, road and building construction crews, linemen for telephone and electric companies, etc. are examples. Assuming an &hour work day, it is reasonable to assume that 70 to 75% of such a person's wake time may be spent outdoors. However, for people who spend considerable time in their cars for occupational purposes, this time is considered to be time indoors since vehicles provide a similar degree of protection from external radiation as do houses. To predict the amount of time an individual in a population spends indoors requires a detailed knowledge of that person's occupation and habits. However, to determine an average distribution of time individuals might be expected to spend indoors, it is probably reasonable to assume that the general distribution is uniform within an estimated range of 70 to 95%. There will be only a small percentage of the population at each end of the spectrum that will spend on average 100% of their time indoors or less than 70% of their time indoors. If such a significant fraction of a person's time is spent indoors, then it may be necessary to know the reduction in absorbed dose relative to open air exposure which would occur from the shielding afforded by the buildings and vehicles. A report by Burson and Profio

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USAGE FACTORS FOR PREDICTING EXPOSURE TO MAN

(1975) provides original data, as well as a summary of several other studies, on shielding provided by structures such as homes, office and industrial buildings and vehicles. Shielding factors vary for a structure depending on whether the source of radiation exposure is ground deposited or is a cloud. The reported reduction factors (ratio of the exposure rate in the structure to the exposure rate in open air) for radionuclides deposited on the ground range from an average of about 0.27 for single story wooden houses to 0.06 for reinforced concrete and brick homes. Basements provide more protection than other areas of the house and average reduction factors range from 0.003 to 0.08. Large office buildings provide more shielding, and, therefore, lower reduction factors than homes (other than basements). For example, average reduction factors in one- and two-story office buildings range from 0.01 to 0.12. Vehicles provide reduction factors in the range observed for onestory houses. The range for cars, pickups, buses, trucks and trains is 0.15 to 0.6. The range for trucks and trains is encompassed within the observed range for automobiles, pickups and buses. In the case of cloud sources, only average reduction factors are available for buildings and vehicles. These values are probably representative of the upper range for a particular structure. If i t is assumed that a range similar to that observed for ground deposits applies, then reduction factors might be as follows; wood frame homes, 0.6 to 0.9; masonry houses and masonry houses with basements, 0.3 to 0.6 and 0.2 to 0.4 respectively; and large office buildings, 0.05 to 0.2. The distribution between these ranges for both ground deposited and cloud sources could be considered to be uniform because there is likely to be a continuous range of values due to difference in materials and architecture. A precise analysis of reduction' factors for individuals in a specific area would require information on the percentage of the different type dwellings in the area. Data on the numbers of one- and two-story single family dwellings in different regions of the United States are given for 1970 by Moeller and Underhill (1976). For individuals, it is also necessary to determine how much time is spent at home (in one- or two-story wood or masonry dwellings) and how much time is spent in large office or industrial buildings; a general range of 6 to 10 hours per day or 30 to 50 hours per week can be assumed. Seventy to 95% of a person's time spent indoors is the equivalent of 118to 160 hours per week, of which 30 to 60 hours would be in office or industrial buildings. These time distributions and ranges can be used in.conjunction with the range of reduction factors of Burson and Profio (1975) to estimate the range of effective reduction factors expected for individuals.

6. Identification of Uncertainties Associated with Model Predictions The models and parameters described i n Sections 2-5 are only mathematical approximations of real environmental situations and processes. Furthermore, the parameters used i n these mo&ls are highly variable. Therefore, it is important to conszder the level of uncertainty associated with model calculations. Only a few specific quantitative examples of model uhcertainty can be given because of the limited extent to which environmental transport models have been validated i n the field or evaluated through statistical studies. 6.1 Introduction Few efforts have been directed toward the analysis of the uncertainty associated with environmental radiological assessment models. The necessary amounts of detailed data have rarely been available, and a need for such efforts has not always been apparent, since dose predictions for routine operation of nuclear facilities generally have been well below applicable standards. The models as applied were generally biased to produce results intended to overestimate actual doses. This "conservative" bias was often embodied in the assumptions.underlying the design of the model as well as in the choice of values for the independent variables, or model parameters. With increasing emphasis on restricting release and dose to levels considered "as low as reasonably achievable" (the ALARA concept), concurrent importance is being placed on decreasing the amount of deliberate conservatism in assessment calculations. However, removal of conservative assumptions from assessment models may increase the possibility of underestimating actual dose unless the magnitude of uncertainty in model predictions is taken into account. Quantifying the uncertainty associated with dose assessment models is, therefore, receiving growing attention. 219

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6. IDENTIFICATION OF MODEL PREDICTIONS

6.2 Sources of Model Uncertainties Uncertainties exist in environmental transport and exposure models because they are mathematical approximations of the real world (Schwarz, 1980; Shaeffer, 1980; ICRP, 1979). Model uncertainties may lead to improper extrapolations due to either incorrect formulation of the mathematical equations and/or selection of incorrect parameter values. Incorrect extrapolations are most likely to occur when models are used to predict the transport of radionuclides among different geographical locations and over periods of time that are different from the conditions for which the models and data bases were initially developed. For example, models used to evaluate the geological disposal of high-level wastes may be especially subject to incorrect extrapolation because predictions are made far into the future using data bases derived from short-term experiments (Section 4). Much uncertainty is due to a lack of relevant data or large variability in the available data for quantifying model parameters. Parameter variability is especially significant in present environmental radiological assessment models which are "deterministic" rather than "stochastic." Deterministic models use single values for each parameter to produce a predicted quantity. This ~redictedquantity cannot reflect the influence of parameter variability. Stochastic models, on the other hand, can produce a range or dstribution of predicted values as a function of parameters which are defined as random variables. In stochastic models, parameter variability can be considered explicitly. Most models used for environmental radiological assessments are, however, deterministic. In deterministic models, parameter values may be selected from the upper end of the reported range to reduce the probability of underestimation. This procedure introduces a strong bias in model predictions resulting in substantial overestimation of actual events. More often, however, values are selected based on a n average of data reported in the literature (see Sections 2.3 and 3.2). This is also a source of bias, because such average values may be significantly different from values best representing a specific situation.

6 . 3 Determination of Model Uncertainties 6.3.1 Model Validation The best method to determine model uncertainty is through testing the model against accurately measured, independent sets of field or

6.3 DETERMINATION OF MODEL UNCERTAINTIES

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221

laboratory observations made over the range of conditions for which application of the model is intended. This procedure is referred to as "model validation." As discussed in preceding sections, only limited validation studies have been performed on radiological assessment models. Furthermore, model validation experiments are not always feasible. For example, low-level environmental concentrations of radionuclides and radiation exposures resulting from routine operations of nuclear fuel cycle facilities are often extremely difficult to measure. Even when detection of low-level concentrations of radionuclides is possible, the high costs encountered usually limit the extent of validation to only a few situations.

6.3.2 Parameter Imprecision Analyses In situations where validation information is not readily available or sufficiently complete, a procedure referred to as a "parameter imprecision analysis" can be used to evaluate model predictions (Schwarz, 1980). This procedure involves estimating the variability (or imprecision) associated with each model parameter to ascertain the influence on the model output of the combined variability of all model parameters (Fig. 6.1). This requires transforming a deterministic model into a stochastic model. The term "imprecision" is used because the analysis only provides an evaluation of the model's uncertainty due to uncertainties in parameter estimation. It does not provide an evaluation of uncertainty due to the use of an inappropriate equation or set of equations. T o provide a reasonable indication of predictive uncertainty, the mathematical structure of the model must be an appropriate representation of the real world and estimates of parameter variability must be unbiased. Scientific judgment must be used to ensure that the model and its parameter estimates satisfy these criteria. Analytical error propagation formulae can be used to perform parameter imprecision analyses on relatively simple models (Shaeffer, 1980; Collee et al., 1980; Schubert et al., 1967). For more complex models, numerical techniques employing the use of a computer may be more convenient than complex analytical solutions (Rubinstein, 1981; Iman et al., 1980,1981a, b; Schwarz and Hoffman, 1981; O'Neill, 1979; McKay et al., 1979). Most work using parameter imprecision analysis for radiological assessments has focused on the air-pasture-cow-milk-child pathway for 13'1 (Stocum, 1970; Shaeffer and Hoffman, 1979; Hoffman and

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6. IDENTIFICATION OF MODEL PREDICTIONS (1) Descrlbe uncertain model parameters as random variables

:kikg Parameter x

Parameter y

C 3

Parameter z

3

w

B

LL

E'

LL

LL

Values of y

Values of x

\

Values of z

/ (2) Distributions of parameter values are then used as input to a model I

1

MODEL

1

I (3) The model produces a distribution of dose estimates

Values of Dose

Fig. 6.1 Parameter imprecision analysis.

Baes, 1979; Schwarz and Hoffman, 1981), and the transport of 13'Cs and in aquatic and terrestrial systems (Schubert et al., 1967; Matthies et al., 1981; Hoffman et al., 1982). For the 1311 air-pasturecow-milk-child pathway simple analytical procedures have been used (Hoffman and Baes, 1979; Schaeffer and Hoffman, 1979). Table 6.1 shows the results obtained using a simple analytical approach. This approach reduces the model to a linear multiplicative chain of independent parameters.

Table 6.1-Results of an analytical approach to a parameter imprecision anolysis for the and Baes 1979) Parameter

Biomass normalized deposition parameter for Iz Effective mean residence time on pasture vegetation Total dry matter intake by a dairy cow Fraction of dairy feed composed of fresh forage Milk transfer coefficient Fraction of time during a year a cow receives fresh forage Annual milk consumption of children (ages 0.5-2 yrs.) Fraction of ingested iodine that deposits in the thyroid gland Fkciprocal of the thyroid mass Effective mean residence time of la'I in the thyroid Dose to air concentration ratio Distribution of dose to air concentration ratioc D/x (mrem m3 pCi-' y-')

Symbol

Geometric Mean (units)

I3'I2

air-pasture-COW-infant pathway (after Hoffman Percent Contribution to Total Imprecisionc

II

VD

0.12 (m3 kg-Is-')

l/xvem

6.1 (d)

QT

15 (kg d-') 0.42 (-)

FP

0.01 (d L-') 0.37 (-)

UM

300 (L y-')

FTh

0.30 (-)

l/m l/h?i

0.57 (g-') 6.5 (d)

D/x

5100 (mrem m3 pCi-' y-')

8.53d

1.09'

Mode Median Mean

1700 5100 8700

XM"

14000 28000 57000

F, Fm

-2.1

0.002

0.18

0.02

1.8

2.7 -0.87

0.014 0.058

1.3 5.3

-4.6 -1.0

0.3 0.17

27.6 15.6

0.04

3.7

-1.2

0.W

7.7

-0.56 1.86

0.25 0.15

23.0 13.8

1.8

5.7

z m U 4

m

Z

S

54

3

0 z

g E t-

d

xw xm

100

" p , mean of logarithms of parameter values. All values are accurate to only two significant figures. 2, variance of logarithms of parameter values. 'These values are based on assumption that all parameters are statistically independent; changes are expected with future quantification of parameter covariance. Calculated by adding ln(897 millirem g s pCi-' d-') to 1.77, the sum of the means of logarithms of values for each parameter. "Xu,X95,2& are the upper 84th, 95th and 99th percentiles, respectively, of the predicted distribution of the D/x ratio.

3 3 2 4

C(

m

c/i

\

N

N

w

224

/

6. IDENTIFICATION OF MODEL PREDICTIONS

where

D/x

K

= the thyroid dose resulting from a given concentration of 13'Iz in air ( x )and the subsequent transport over the pasture-cowmilk pathway prior to ingestion of 13'1 in milk by children within the age group 0.5-2 y. is a constant (897 mrem g sec pCi-' day-'), with all other parameters being described in Table 6.1.

Assuming that the variability of parameter values is reasonably approximated by a log-normal distribution, log-transformation permits simple analytical propagation of errors using normal statistics. In this example, the sum of the means of log transformed parameter values, pp, equals the mean of the log transformed dose, PD,

The sum of the variances of the independently distributed log transformed parameter values, a:, equals the variance of the log transformed dose VD,

If covariance exists between model parameters, additi6nal terms would be required, affecting the results in Table 6.1. Covariance between many of these parameters, especially UM,FTh, m, and AT;, is suspected but experimental quantification is not documented (Dunning and Schwarz, 1981). In this example, the geometric mean or median (X,) of the distribution of dose predictions is: The mode (X,), arithmetic mean, (X),84th (XS4), 95th (X95), and 99th (X*) percentiles of the distribution of dose predictions is:

6.3 DETERMINATION OF MODEL UNCERTAMTIES

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225

The contribution of parameter variability to the total predictive imprecision is estimated by dividing the variance of the log transformed parameter values, u2,, by the variance of the log transformed distribution of dose predictions, a;. The results in Table 6.1 indicate that the 99th percentile (5.7 x lo4 mrem y-' per pCi m-3) of the estimated distribution of thyroid dose incurred from a given air concentration of 13'12is about one order of magnitude greater than the median value (5100 mrem y-l per pCi mP3) of the predicted dose. Most of the imprecision involves the parameters (F,, m, As!) for which site-specific information will be most difficult to obtain. The results of other studies are presented in Table 6.2 for a variety of exposure pathways and radionuclides. Table 6.2 indicates that parameter imprecision may contribute to a range of about one to two orders of magnitude about the geometric mean.

6.3.3 The Effect of Bias in the Selection of Parameter Values Bias (i.e., the tendency to over- or underestimate) in the predictions of deterministic models can be evaluated by comparing their results with the distribution of predicted doses produced through parameter imprecision analyses (Fig. 6.2). As mentioned previously, substantial overestimation is expected when conservatism is applied in the selection of each parameter in a deterministic model. For example, in a model composed of ten or more multiplicative parameters (where each parameter contributed equally to the total model uncertainty), the selection of only the 84th percentile for each model parameter results in a predicted value that exceeds the 99.9th percentile of the distribution of model output (Hoffman and Baes, 1979). Thus, bias in the selection of parameter values may have a pronounced effect on the total conservatism in the final model prediction.

6.4 Uncertainties Among Various Types of Models The examples of parameter imprecision analysis (Tables 6.1 and 6.2) demonstrate the potential for considerable discrepancies between a single deterministic estimate produced by a model and the actual value or range of values which are possible for a given situation. Among the models reviewed in this report, the largest uncertainties are expected to be associated with the prediction of deposition, sedi-

TABLE 6.2-A summary of results for parameter uncertainty analysis performed on a variety of environmental exposure pathway models. Valuespresented are the 5th percentile (La), geometric mean (X,), and upper 95th (XW) percentile of the predicted distributions of model results. Radionuclide

2aDh 2JOPu 131~2

"Sr "Sr

'"Cs '"Cs 137Cs

Exposure Pathway

Soil-air-inhalation-lung" (mrad y-I per pCi g-' soil) Soil-vegetation-ingestion-bonew (mrad y-' per pCi g-I soil) Air-pasture-milk-ingestion-thyroidd* (rem y-' per pCi m-3 air)

Water-fmh-ingestion-bone-surfacek (mrem) y-I per pCi L-'water) Deposition-multiple terrestrial food pathways-bone surfacebd (mrem y-' per p c i m-2 d-1 1 Deposition-soil-pasture-milkd.' (pCi L-I per Ci km-') Water-fish-ingestion-total bodyb (mrem y-' per pCi L-'water) Deposition-multiple terrestrial food pathways-total bodyb-d(mrem y-' per pCi m-2 d-I)

& 2.5 x 4.1 x

lo4

\

x, 9.4 x 1.1x

X,

Reference

lo-'

Garten (1980)

3 x 10-1

Garten (1980)

23

Schwan and Hoffman (1981) Hoffinan e t al. (1982) Hoffman et al. (1982)

3.5 x

lo-2

M

p

Z

0.66

9.6

3.9

0.26

6.5

10

50

220

0.28

1.2

5.1

0.67

4.8

X

9.3 x 1.2 X

10"

lo-'

4.4 x

lo-'

"Estimated dose rate a t age 70 from a lifetime exposure. Estimated dose rate to age 70 years as the result of a continuous exposure beginning at age 20. ' Simple analytical procedures used to propagate parameter error. Monte Carlo computer techniques used to propagate paramater error. "Estimated thyroid dose rate for children of the age group 0.5 to 2.0 years. 'Values approximated from published figures using lognormal statistics.

0.16

Matthies et al. (1981) Hoffman e t al. (1982) Hoffman et al. (1982)

=!

z

C,

3-

3Z

8

z

0 0

r M

E~j

2 5 5

6.4 UNCERTAINTIES AMONG VARIOUS TYPES OF MODELS

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227

VALUES OF PREDICTED DOSE (D,)

Fig. 6.2 A frequency distribution of predicted doses (D,), produced through parameter imprecision analyses, compared with a deterministic model prediction of dose (Dd). The probability of the deterministic prediction being underconservative is indicated by y. The expression 1 - y indicates the probability of the deterministic model prediction being conservatively biased.

mentation, resuspension, food chain bioaccumulation, and ground water transport. These uncertainties are predominantly due to the use of generic or default values for model parameters that depend, to a large extent, on the characteristics of the site and the biogeochemical behavior of the various physico-chemical forms of the radionuclides. Improved estimates for these parameters are difficult, requiring a considerable investment in site-specific research. Less uncertainty is expected for predictions of atmospheric and surface water dispersion of prolonged (or chronic) releases of radionuclides. These calculations are dependent on known physical parameters whose variability is reduced by the effects of temporal and spatial averaging. Although some models may have larger uncertainties than others, the importance of these uncertainties will vary depending on the amount and composition of the released radionuclides, the magnitude of the dose received by members of the general public, and the relative contribution to the dose by each exposure pathway. 6.4.1 Atmospheric Transport Models

Gaussian plume models appear to be relatively accurate (within a factor of 2 to 4) for predicting long-term average air concentrations over flat terrain (Section 2.1), especially when site-specific meterological data are used for values of model parameters and the location of the predicted concentration is relatively close to the point of release (within 10 km). There is less certainty for short-term predictions under complex conditions of meterology and terrain. Under these conditions, uncertainties of one to two orders of magnitude may be encountered (Miller and Little, 1982). The major sources of uncer-

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6. IDENTIFICATION OF MODEL PREDICTIONS

tainty are related to the specifications of wind patterns at sites with complex terrain and complex meterological characteristics, the classification of atmospheric stability, the values selected for the dispersion parameters a, and a,, and the values selected for wet and dry deposition. The prediction of the rate a t which radionuclides are transferred from the atmosphere to the terrestrial system is influenced by values assumed for parameters that determine wet and dry deposition. These calculations can be associated with one to three orders of magnitude uncertainty for gases and particulates when predictions are made for short-term releases. Less uncertainty is expected for deposition calculations of prolonged releases because of the effects of time averaging (Section 2.2). Although the parameters involved with the calculation of resuspension also span several orders of magnitude, this exposure pathway is usually of secondary importance, with the exception of those circumstances where the ground surface is the primary source of contaminated material. 6.4.2

Terrestrial Food Chain Transport Modek;

Validation of terrestrial food chain models has generally been restricted to isolated testing of a few model parameters. Some attempts have been made to test the aggregation of models which consider all variables from source term to concentrations in air, water and foods. These tests have only met with partial success, because contamination from atmospheric weapons testing interferes with measurements of the amounts of radionuclides, and because actual releases of radionuclides from nuclear facilities are intermittent rather than constant. For radioiodine releases, partial validation information indicates that the assumption of dry deposition parameters for iodine in elemental form (I2) tends to overpredict concentrations of 13'1 in milk (Weiss and Keller, 1977; Weiss et al., 1975; Riedel and Von Gadow, 1976; Erb, 1979; Golden et al., 1982; Voilleque et al., 1981). This tendency is expected because 13'1 released in chemical forms other than elemental iodine are associated with substantially lower rates of atmospheric deposition (see Sections 2.2 and 2.3, and Hoffman, 1977). Most of the uncertainty associated with terrestrial food chain models is due to bias in the selection of parameter values and the lack of data for transfer coefficients for specific foods (Section 2.3). The variability of values for parameters used to predict the transfer of radionuclides into major food categories (milk, meat, and vegetables) is large. Therefore, discrepancies between field measurements of concentrations in foods and predicted concentrations of "deterministic" models are

6.4

UNCERTAINTIES AMONG VARIOUS TYPES OF MODELS

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229

expected. The use of conservative assumptions in the absence of sitespecific data should, however, result in predictions that tend to overestimate the concentration in terrestrial foods. Although site-specific data can be readily obtained for agricultural parameters such as vegetation biomass and its later consumption by animals, uncertainty still remains in the selection of appropriate food chain transfer factors for specific radionuclides (Section 2.3). Derivation of isotope-specific transfer factors on a site-specific basis through empirical measurements or through correlation with readily available environmental factors such as soil characteristics, climate, vegetation species, animal type, etc., should help reduce a substantial amount of the uncertainty inherent in terrestrial food chain models. More complete validation studies, however, will be necessary to document the overall uncertainty associated with these models. 6.4.3 Specific Activity Models for 3H and 14C

If dose assessments of 3H and 14C are performed using the specific activity approach, reasonable confidence can be placed in the dose estimate being equivalent to an upper limit when the specific activity (i.e., the ratio of the mass of the radioisotope to the mass of its related naturally occurring stable element) in environmental media is assumed to be equal to the specific activity within the human body a t the point of interest (Section 2.5). This assumption ignores the likely dilution of the body content of 3H and 14Cthrough intake of less contaminated sources of hydrogen and carbon. Sources of error which could offset this maximum conservatism are related to: (a) the estimated release rate, (b) the estimated physical dispersion from the point of release, (c) the concentration of stable hydrogen and carbon in air and water at the location of assumed exposure, and (d) the estimated fraction of the receptor that is hydrogen and carbon. Accounting for dilution in the body and intake of less contaminated sources of stable hydrogen and carbon (Section 2.5) reduces the conservatism provided by the specific activity approach, but also increases the probability of underpredicting the dose, given that sources of hydrogen and carbon may be highly variable for any specific individual. Additional uncertainty will also be encountered if the specific activity approach is only used .to estimate the concentration of 3H and 14C in air, water, and food. Dose calculations will then be a function of intake rates (ingestion and inhalation), conversion factors relating dose to a unit intake of 3H and 14C, and estimates of the fractions of food and beverages composed of hydrogen and carbon.

230

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6. IDENTlFICATION OF MODEL PREDICTIONS

Such an approach includes sources of uncertainty due to variability in diet and physiology, including the effects of age-dependen~e.~ These sources of uncertainty are not encountered when the specific activity within the human body is related directly to the maximum specific activity in the environment, with no account given for dilution from intake of relatively uncontaminated sources of stable hydrogen and carbon. 6.4.4

Surface Water Transport Models

For surface water transport models, accuracies to within a factor of two are likely (Section 3.1, Little and Miller, 1979). Although few validation studies have been conducted, the prediction of physical dispersion in surface waters is reasonably well known. This is because, for most situations, boundary conditions are well defined and the impact of time averaging of discontinuous releases is small. For most assessment situations, simple box models are adequate. A major source of uncertainty is the amount of interface between the soluble fraction and suspended and deposited sediment. The usefulness of highly variable distribution coefficients (Kd), for predicting the behavior of radionuclides in natural aquatic systems is tenuous. Values of Kd are frequently determined under laboratory conditions for specific sediment types and chemical elements. Usually, the impact from contamination of sediments is small enough to offset concerns about gross uncertainty in model predictions. However, for some radionuclides, the potential for sediments to act as a secondary source of input into aquatic food chains needs to be evaluated. 6.4.5

Aquatic Food Chain Transport Models

For aquatic food chain models, the largest uncertainty is in estimating the coefficient for the transfer of radionuclides from water to edible

,

'Although this report has not specifically addressed the issue of uncertainties associated with the external and internal dose factors, much of the total uncertainty in assessing radiological impacts on humans may be due to these factors. Dose factors are used to convert exposure rates to contaminated air, water, foods and surfaces into values of dose equivalents. In the example of the imprecision analyses for the transport and dose of 13'Iz over the pasture-cow-milk-child-thyroid pathway, more than 40% of the total variability in the model prediction was due to the variability in the biological parameters used to estimate the internal dose factor, assuming statistical independency among the parameters of the internal dose factor (see Table 6.1). The importance of this source of variability is especially noteworthy because, although site-specific investigations may be used to reduce the uncertainty in the environmental transport models, it is not likely that such investigations will modify the estimate of the internal dose factors.

6.4

UNCERTAINTIES AMONG VARIOUS T Y P E S OF MODELS

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aquatic organisms, i.e., the bioaccumulation factor (Section 3.2). The variability in values of the bioaccumulation factor may span several orders of magnitude. Generic values for bioaccumulation factors currently used in assessment models ignore dependence on measurement technique, species of organism, water quality and water chemistry. Usually, these generic values have been derived from fallout contamination or from stable element concentrations. Their use in deterministic assessment models generally leads to overestimates of the concentration of radionuclides in aquatic foods; however, overprediction for all aquatic environments cannot be assumed a priori. Estimation of bioaccumulation factors can be improved substantially by establishing correlations with environmental factors such as water concentration of the related stable element, water concentration of an analogue element, suspended matter, nutrient levels, etc. 6.4.6 Groundwater Transport Models

For the most part, models which predict groundwater flow and pressure have been used and tested for several decades and have been shown to provide reliable predictions over time periods of 20 to 30 years. Hydrologists also believe that these models will provide reliable estimates of porous flow in simple geologic settings over the longer time period needed for assessing waste disposal systems (i.e., more than 1000 years). However, in situations of unsaturated flow and transport, and fracture flow and transport, the models are not as reliable and validation is extremely difficult to achieve (Section 4). Uncertainties in describing boundary conditions, and in characterizing environmental conditions over geological time scales are particularly troublesome. Few other pathways require predictions extending so far into the future, and few include components, that, like host rock, are difficult to test nondestructively. Major efforts, however, are currently underway to address the issue of predictive uncertainty in ground water transport models as a function of parameter imprecision (Kocher, 1982; Cranwell and Helton, 1982).

6.4.7 Human Factors The exposure to environmental radioactivity is greatly influenced by human dietary habits, inhalation rates, and occupancy rates. Although the types of foods and intake rates assumed in model calculations are based upon reference members of critical groups of the

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population, site-specific habits for any given individual may differ substantially from reference values (Section 5). In the past, attempts have been made to offset large uncertainties associated with food chain transfer factors by postulating conservative (i.e., tending to maximize dose) usage factors for the critical population group. More recently, attempts to increase the realism of model predictions have eliminated conservative usage factors and have replaced them with averaged values derived from site-specific or regional surveys. In view of the large uncertainty associated with generic food chain transfer factors, the intended realism associated with these new estimates of human usage factors may be misleading. This is especially apparent in cases where the selection of default values for other model parameters has not been conservative. Unlike human usage factors, many parameters currently used in environmental radiological assessment models cannot be readily determined on a site-specific basis (Sections 2, 3, and 4). With the exception of data on infant and child milk consumption, the variability of values for dietary habits is difficult to assess because literature data frequently 'are derived from daily recall surveys and have not attempted to follow individual usage patterns over extended time periods (Section 5). These data can be expected to overestimate the variability associated with annual average factors for actual individual members of population groups. In general, more variability in dietary habits, and occupancy factors are expected for adult members of the population than for younger age groups, with the least variability expected to occur among infants.

6.5 Conclusion The overall uncertainty in the calculation of dose is recognized as an issue requiring continued attention. Concentrations of radionuclides in the terrestrial and aquatic environment may be determined through measurements rather than model calculations but estimates of dose from radionuclides deposited in the body will depend on the continued use of internal dosimetry models. Therefore, the accuracy attainable by environmental radiological assessment models likely will be limited by the uncertainties inherent within the calculation of dose conversion factors for internally deposited radionuclides.

7. The Application of Models for Environmental Assessments Models developed for assessment purposes are distinctly different from those intended to serve as research tools. Usually, the best model for a given assessment is the easiest one to use that produces results within a n acceptable degree of accuracy. Simple screening models are useful for identifying potentially important radionuclides and pathways. Research model. are typically more complex and attempt to explicitly simulate individuul mechanisms and processes involved with enuironmental transport; however, their accuracy is not necessarily improved by increased complexity. The utility of assessment models is optimized when the uncertainty in the results is reduced while mathematical simplicity is maximized.

7.1 Classes of Models Although various classifications of the models reviewed in this study are possible, two basic categories are recognized here: models specifically developed for use in assessments (environmental assessment models) and models developed as tools for research (research models).

7.1.1 Environmental Assessment Models The purpose of radiological assessment models is to predict concentrations of radionuclides in various environmental media (i.e., air, water, sediment, soil, and terrestrial and aquatic foodstuffs). To be useful, the predictions made by assessment models must be defensible. T o be defensible, they must be sufficiently complete in that all important exposure pathways are included and the range of uncertainty in the results has been confirmed through validation tests. Ideally, parameter values and model predictions should be capable of being tested 233

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through field validation. Untested assessment models should be given an intentional and clearly stated degree of conservative bias to reduce the probability of underestimation.

7.1.2 Research Models In contrast to models specifically developed for assessment purposes is the class of models developed as research tools. Research models differ from assessment models in their objectives. Emphasis is placed on their ability to explicitly simulate the processes and mechanisms affecting the behavior of radionuclides in the environment. Because these models are usually developed to identify all distinct physical processes and biological mechanisms, they are mathematically more complex than is typical of assessment models. However, the ability to field test the parameters and predictions of research models is not important as a constraint for their development. Intentionally conservative bias is also absent because of the desire to describe environmental transport mechanisms realistically, and to understand them. Furthermore, unlike radiological assessment models, the development of research models is not constrained by the limitations set by potential users. Although research models are often adapted for assessment purposes, their use is usually restricted t o situations where either an assessment model does not exist or where there are insufficient data to quantify critical parameters. Caution should be exercised before considering adaptation of a research model for a given assessment problem. In Section 4, the application of complex research-level models for geological waste isolation is described as model "overkill." For complex dynamic models, the experimental determination of many coefficients describing the transfer of a given material between compartments may be impractical. Research models often are dependent on parameters that cannot be readily measured in the field without significantly perturbing of the ecosystem. Also, without specification of parameter covariances, increasing model complexity increases the sensitivity of predictions to parameter error propagation (O'Neill et al., 1980; Gardner et al., 1980). Examples of complex research models are illustrated in Fig. 3.1 and 3.4 of Section 3.1 for aquatic systems. In contrast to these complex models is the use of the simple "bioaccumulation factor" in Section 3.2 to describe the multiple processes of radionuclide transport directly from water to fish.

7.3 IMPROVEMENT OF RADIOLOGICAL ASSESSMENT MODELS

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7.2 Application of Environmental Assessment Models for Screening

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Realizing that quantitative predictions are based on simplifying assumptions and generalizations of complex real-world behavior, a useful application of assessment models is to screen for the more important radionuclides and exposure pathways. Typically screening involves comparison of conservatively biased model predictions (predictions expected to be on the high side) with established limits. A radionuclide and exposure pathway can be considered insignificant when predicted concentrations are less than a small fraction of the protection limit (Hoffman and Kaye, 1976). On the other hand, radionuclides and pathways predicted by screening models to result in concentrations that approach or exceed limiting values indicate the need for further analysis. The amount and type of conservatism applied for screening will depend on the level of understanding of the radionuclides behavior in the environment, the amount and quality of available data, and the history of model validation. Many environmental models used for assessment and research purposes can be adapted for screening calculations. Usually, however, calculation procedures are not extensive and the data base includes generic default parameter values for use in the absence of site-specific information. Sometimes research models are proposed for screening calculations. Research models are often implemented incorrectly when the actual behavior of the radionuclide in food chains is not well understood or when relevant parameter values and model validation results are lacking. However, unless available data can justify the need, increased mathematical complexity for screening purposes is likely to be unwarranted (Hoffman et al., 1978; Kaye et al., 1982).

7.3 Improvement of Radiological Assessment Models 7.3.1 Reduce Uncertainties Improvements in environmental models are needed to reduce the uncertainties of their predictions. The use of screening models can facilitate these improvements by identifying those radionuclides and pathways requiring better data. Once the important radionuclides and pathways are identified, field validation tests can quantify the degree

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of the uncertainty. Further improvements may be made through better estimation of parameters, adjustments in model structure, and calibration of model predictions against data sets obtained from validation tests. Additional field validation tests can confirm these improvements. Reduction in predictive uncertainty can also be accomplished by using site-specific parameters whose values may be readily determined for a specific site, such as standing vegetation biomass, the bulk density of surface soil, and some aspects of cattle management practices (Section 2.3). However, radionuclide-specific environmental transfer factors or rate constants such as deposition velocity, distribution coefficients, weathering rates, and food chain transfer coefficients cannot be determined for a specific site without extensive monitoring or experimental investigation (Kaye et al, 1982). Matching these model parameters with easily measurable environmental variables such as temperature, pH, soil type, and specific food products should improve the accuracy of model predictions.

7.3.2

Model Simplification

Perhaps the most effective improvements in environmental assessment models can be made in achieving an optimum level of model simplification. As mentioned in many of the previous sections, the "best" model for a given assessment will be the model that is easiest to use and which produces results within an acceptable degree of accuracy. Thus, relatively simple model formulations have prevailed in environmental radiological assessments despite the availability of models described in the previous chapters which are substantially more complex but not necessarily more accurate. Simple models consisting of few parameters for important radionuclides and pathways should be more amenable to field validation than more complex models because of reduced demands on simultaneous parameter measurement. Thus, an optimum level of complexity can be envisioned when all parameters are readily measurable and the possibility of predictive error due to unforseen correlations among the parameters is small. However, an optimum level of simplification will be determined by the amount of predictive uncertainty accepted by the user and the ease of model implementation.

8. Conclusions and Recommendations 8.1 Conclusions The objective of this report has been to analyze the current status of the application of models used for radiological assessments. Several conclusions are drawn based upon our evaluation of the models and their use. Because of the general nature of these conclusions, they are not explicitly mentioned within the body of the report and are summarized in the following statements. The order in which they appear does not reflect any order of their importance. (1) Models are available to address all significant pathways of potential importance to the radiological exposure of humans in the vicinity of the release of radionuclides. The models utilize a broad data base derived from studies of stable elements and radioactive tracers performed over several decades. (2) Radiological assessment models are essential for a priori evaluation of the acceptability of planned and unplanned releases of radioactivity to the environment. In addition, they are the only mechanism available to estimate the impact of releases that are below detectable levels in the environment. (3) Further development of radiological assessment models and improvements in the data base should be pursued selectively by considering the radionuclides, pathways, and exposure groups that are of most importance in terms of the final estimated dose. As a part of this selection process, emphasis must be given to improving the data that a t present introduce the greatest uncertainty in dose. (4) It is recognized that models and data bases for some environmental transport mechanisms are more complete than others (e.g., the state-of-the-art for atmospheric transport models is more advanced than those for groundwater transport, etc.); however, this disparity is a normal scientific response' to fulfilling the most immediate needs first, as development of the nuclear industry progressed. This is not to imply that future

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research should automatically focus on radiological assessment models and data bases that are less developed, rather, the emphasis in the future for research must be based upon the criteria previously stated in item (3), pathways, radionuclides, and exposure groups contributing the most to total estimated dose. (5) Additional work is needed to improve our confidence in the results of model calculations and make them more defensible. Also, more emphasis must be given to better documentation of models and making models and data bases more useable by individuals involved in day-to-day calculations. This report is unique in that it attempts to show the interrelationship of each of the major pathways of exposure in the assessment process, the strengths and weaknesses of the models, and uncertainty associated with the data base. Additional work is needed to provide a complete manual or handbook that covers the entire spectrum of radiological assessment from source term to analysis of health effects.

8.2 Recommendations In order to enhance the use of radiological assessment models and better understand their capabilities, it is recommended that future research emphasize two vital areas, model validation and model simplification. Justification for these two recommendations is elaborated below.

Model Valufation This study indicates that there is a high degree of uncertainty in the accuracy and precision of methods used for environmental radiation assessments. One factor contributing to this high degree of uncertainty is that few concerted efforts have been made to validate with field data the transport models or basic environmental parameters used in the models. The technique of radiological assessment has now reached the point where model development has greatly exceeded the efforts to validate the models. Although validation research would be extremely beneficial in terms of derived benefits, this research has typically been given low priority because of anticipated high costs, and the long times normally required to accumulate statistically valid results. It is recommended that priority for future research be given to the

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validation of radiological assessment models. It is also recommended that this validation effort be carefully planned and carried out as a unified effort includng all agencies and groups involved in the development and application of radiological assessment models. Therefore, a comprehensive long-range plan for validation is needed to determine priorities for validation research and the projected cost vs. anticipated benefits. Priorities need to be carefully established, because validation experiments will require considerable commitment of time and financial resources. Model Simplification In recent years, the trend has been toward more complex models; however, the increased complexity has not necessarily improved the accuracy of estimates of dose and, in certain cases, has had the opposite effect. It is recommended that future model development be directed toward the simplest model that will adequately address each assessment situation. Currently, there is no comprehensive set of simple screening models that would provide a preliminary estimate of dose. Screening models should be developed for use in the preliminary evaluation of radionuclide releases. To be effective, screening models should have a predetermined level of uncertainty and should be the only model required if the resulting dose is less than a prescribed level.

APPENDIX A

Applicability of Models for Routine Releases to the Accident Situation The majority of models that predict the behavior of radionuclides in the environment are based upon concepts that simulate steadystate conditions. The source term for assessing routine releases is generally assumed to be uninterrupted and without significant perturbations for a long period of time such that near-equilibrium conditions exist for the duration of the release. Accidental releases, on the other hand, involve injection of a pulse of radioactivity that results in a high concentration in environmental media which may be rapidly eliminated from some compartments and persist in others for many years. Therefore, it is important to consider the applicability and limitations of the models discussed in this report to the accident situation in which equilibrium conditions may not exist. Methods for evaluating accidental releases of radionuclides are needed to predict the severity of accidents before they occur and to assist in determining protective action and health implications during and after a contaminating event. The evaluation of postulated accidents is also of considerable interest both in the assessment of risk from commercial nuclear plants (USAEC, 1975) and in establishing criterion for siting nuclear facilities (CFR, 19711). In any accident analysis, it is reasonable to assume that pathways of exposure to man would be limited by constraints placed upon individuals to restrict the amount of time spent in the area and to minimize the consumption of contaminated food products. I t is our opinion that for generic accident analyses, the models discussed in this report could be used for initial estimation of the total integrated dose, provided that conditions expected to prevail during the time of the accident are taken into account. For example, models developed for routine releases (perhaps with minor modifications) could be useful in identifying potentially important pathways of ex240

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posure, areas where interdiction of land use might be necessary, and sites which should be evacuated. In the case of the actual event, we recommend that emphasis be placed on a comprehensive environmental monitoring program as an integrated part of the emergency response plan. This program should not preclude the use of models discussed in this report to assist in identifying and prioritizing pathways of exposure to monitor during or following the accidental release. Therefore, for analysis of accidental releases, emphasis should be given to developing realistic source terms and providing immediately available meteorological and demographic data rather than creating new models specifically for the accident case.

APPENDIX B

Glossary

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absolute humidity: Vapor content of water in air expressed as g m-3. A key parameter in the calculation of dose from tritium released to the atmosphere. acceptable degree of accuracy: The amount of error or uncertainty in model predictions tolerated for any given assessment situation. Usually, a greater degree of accuracy is required for potential outcomes involving high risks and/or economic costs. accuracy: As applied to environmental assessment models, accuracy implies agreement between the model prediction and actual events. An "accurate" model should be precise and unbiased. algorithm: An explicit step by step procedure for producing a solution to a given problem. In a computer model, an algorithm may be any statement or set of statements expressing the functional operation of a model which enables a set of input data to produce a given output. anisotropy: Referring to the character of a medium in which, at any point, the properties are different in different directions. aquifer: A formation or group of formations, or part of a formation that contains sufficient saturated permeable material to yield significant quantities of water to wells and springs. aquitard (confining bed): A body of impermeable material stratigraphically located adjacent to one or more aquifers, which tends to isolate the water in a permeable portion of the aquifer from another portion. benthos: Aquatic bottom-dwelling organisms (benthic organisms). bias: The tendency for an estimate to deviate from an actual or real event. Bias may be the tendency for a model to over- or underpredict. bioaccumulation factor (BF):The ratio of radionuclide concentration in an organism or tissue to that in water or food products. boundary layer: That portion of a moving fluid in which turbulent diffusion is taking place. This turbulence may be due to mechanical effects, thermal effects, or some combination of both. ?A2

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box model: A pollutant transport model based on mass conservation of the pollutant in a specified volume. Such models are inherently simple but physically sound. concentration factor: See bioaccumulation factor. conservative bias: A tendency to overestimte rather than underestimate. default value: A value prescribed for a model parameter in the absence of data directly relevant to the assessment situation. deterministic model: A model whose output is predetermined by the mathematical form of its equations and the selection of a single value for each input parameter. diffusion: The spreading out of a material in a fluid due to thermal or mechanical agitation. dispersion coefficient: A measure of the spreading of a flowing substance due to the nature of the porous medium. dispersivity: A geometric property of a porous medium which determines the dispersion characteristics of the medium by relating the components of pore velocity to the dispersion coefficient. distribution coefficient: The quantity of the radionuclide sorbed by the solid per unit weight of solid divided by the quantity of radionuclide dissolved in the water per unit volume of water. environmental assessment model: A type of model specifically designed to address questions formulated in the context of an environmental assessment. Environmental assessment models are usually less complex mathematically than are models used as tools in research. e r r o r propagation: The translation of input errors into estimates associated with modeling art; in this context, statistical and numerical error propagation techniques are the fundamental methods used to combine parameter uncertainties into an estimate of the overall uncertainty in model pAdictions. This process is referred to in this report as a "parameter imprecision analysis." eutrophic: Waters with good supply of nutrients and hence a rich organic production. extrapolation: The projection of model calculations to situations outside the realm of past experience or known data. Model calculations performed within the realm of experience and pertinent data are considered to be interpolations unless verified by measurement. flux (specific discharge, darcy velocity): The volume of discharge from a given cross-sectional area per unit time divided by the area of the cross section. fracture flow: Groundwater flow through a fractured medium. The

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medium itself may be porous and permeable, but the flow would be dominated by fractures, cracks or solution cavities. Gaussian model: A pollutant diffusion model based on an assumption of stationary, homogeneous turbulent flow. The distribution of material in the plume or puff is assumed to be gaussian in shape. gradient-transport theory: A theory of pollutant transport which assumes that the pollutant flux is proportional to the local concentration gradient in the direction of the mean fluid flow and from this derives a diffusion equation based on mass continuity. grid model: A pollutant transport model that is a finite-difference approximation to the equation of motion, continuity, diffusion, and species conservation and removal. Grid models are severely restricted in their applicability to a large class of pollutant problems. high-level waste: High-level radioactive waste is defined by 10 CFR 60 (May 1983) as: "(1) irradiated reactor fuel, (2) liquid waste resulting from the operation of the first cycle solvent extraction system, or equivalent, and the concentrated waste from subsequent extraction cycles, or equivalent, in a facility for reprocessing irradiated reactor fuel, and (3) solids into which such liquids have been converted." higher-order closure theory: A theory of pollutant diffusion which is based on the principle that knowledge of all the moments of the distribution of a quantity is fully equivalent to knowing its distribution. homogeneity: The properties, or conditions of isotropy or anisotropy are constant from point to point in the groundwater medium. hydraulic conductivity (permeability): The volume of water that will move per unit time in the aquifer under a unit gradient through a unit cross sectional area perpendicular to the direction of flow. intrinsic permeability: The measure of the ability of a rock or soil to transmit fluid under a fluid potential gradient (see definition of hydraulic conductivity). isotropy: As applied to groundwater, referring to the character of a groundwater medium in which the properties a t any point within the medium are the same in all directions. K-theory: See gradient-transport theory. leaky aquifer: An aquifer which consists of a t least two permeable units separated by a less permeable layer which partially separates the water in each unit, but allows for a certain amount of leakage between units. low-level waste: Low-level waste is defined by 10 CFR 61 (December 1982) as ".. . radioactive waste not classified as high-level radioac-

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tive waste, transuranic waste, spent nuclear fuel or byproduct material (uranium or thorium tailings and waste) . . . . ." macrophyte: Plants that can be seen with the unaided eye. minute volume or ventilation rate: The volume of air expired per minute. It is the product of the tidal volume and the breathing frequency. mixed layer: See boundary layer. model: A mathematical abstraction of an ecological or biological system, sometimes including specific numerical values for the parameters of the system. model overkill: The inappropriate applications of complex models for problems that can be adequately addressed using simpler approaches. model prediction: The result or dependent variable produced by a model calculation. model structure: The conceptual design, mathematical equations and set of algorithms that control the results or predictions produced from a given set of input data or assumptions. model validation: Documentation of the discrepancy (or agreement) between model predictions and actual events through comparison of predicted values with accurately measured field data obtained over the range of conditions representing the extent of intended application of the model. moisture content: The volumetric fraction of the groundwater medium "occupied by liquid water." molecular diffusion: The spreading out of molecules or ions in a fluid, in a direction tending to result in uniform concentrations in all portions of the system. oligotrophic: Waters deficient in nutrients. omnivorous: Feeding on both plants and animals. parameters: Any one of a set of independent variables in a model whose values determine the characteristics or behavior of the model. parameter imprecision analysis: An analysis of uncertainty using error propagation techniques to produce a stochastically variable prediction as a function of stochastically variable parameters. percolation (infiltration): The process of downward movement of water from the surface into underlying materials. periphyton: The aquatic community of diatoms and other algae, bacteria, fungus and protozoa, which is attached to substrates. phytoplankton: T h e plant organisms of plankton. piscivorous: Feeding on fish. plankton: Aquatic organisms, usually microscopic, which float pas-

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sively or exhibit limited locomotor activity. pore velocity, seepage velocity: The average rate -of flow in the pores of a given groundwater medium. This is approximated by dividing the flux by the effective porosity. porosity: The property of containing interstices. Total porosity is expressed as the ratio of the volume of interstices to total volume. Effective porosity refers t o the porosity through which flow occurs. porous flow: Goundwater flow which is predominantly through pores in the medium, or through the interstitial spaces between small grains of material (as opposed t o fracture flow, defined previously). pressure head: The height above a standard datum of the surface of a column of water that can be supported by the pressure a t a given point. The gradient of the pressure head is usually the driving force for ground water flow. probabilistic model: See stochastic model. research model: Any model developed to fulfill research objectives. Usually research models are developed to provide insight into explicit processes and mechanisms and thus are mathematically more complex than assessment models. retardation coefficient: The measure of the capability of the porous medium to impede by sorption the movement of a particular radionuclide being carried by the fluid. saturated zone: T h e portion of the porous medium in which only fluid occupies (fills) all of the interconnecting interstices (void space or pores) which can interact with other portions of the medium. screening: The process of rapidly identifying potentially important radionuclides and exposure pathways by eliminating those of known lesser significance. screening models: Simple models employing conservative assumptions for the expressed purpose of screening out radionuclides and exposure pathways of negligible importance. sensitivity analysis: Analysis of the mathematical sensitivity of the model predictions to selected perturbations of model parameters. similarity theory: A theory of pollutant diffusion based on dimensional analysis of the physical variables that control boundary layer turbulent flow. site-specific data: Data used in radiological assessment models which are obtained to describe the particular location for which the assessment is being performed. W.hen site-specific data are not available, default values must be used. soil-to-plant concentration ratio: Bi,, the ratio of the concentration of a radionuclide (i) in fresh vegetation to that in dry soil. CRi, the

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ratio of the concentration of a radionuclide (i) in dry vegetation to that in dry soil. sorption: All mechanisms, including ion exchange, that remove ions from the fluid phase and concentrate them on the solid phase of the medium. specific activity method: A model which estimates dose from a radionuclide by assuming the specific activity in food or water is equal to or a fraction of the specific activity in air for a given location. This approach bypasses the steps normally used in radionuclide transport models; however, it is primarily applicable to radionuclides that have a n abundant stable carrier in nature such as water for tritium and carbon dioxide for carbon-14. specific retention: The ratio of the volume of water which the rocks or soil, after being saturated, will retain against the pull of gravity to the unit volume of rock or soil. specific storage: The volume of water released from or taken into storage per unit volume of the porous medium per unit change in head. specific yield: The ratio of (1) the volume of water which the rock or soil, after being saturated, will yield by gravity, t o (2) the volume of the rock or soil (sometimes referred to as "effective porosity"). stability class: A measure of the state of atmospheric turbulence conditions. statistical theory: A theory of diffusion in a fluid which assumes a stationary, homogenous turbulence field and derives the pollutant concentration in terms of the mean-square displacement of a fluid "particle" from its average position. stochastic model: Any model whose input and output are expressed as random variables. Contrast with deterministic model. stratification: The phenomenon occurring when a body of water becomes divided into distinguishable layers. tidal volume: The volume of air breathed in and out under any condition. trajectory model: Atmospheric transport model which is driven by an observed or predicted wind field, generally for distances beyond 10 km. Diffusion is accounted for using a moving-box, growing puff, or small air-particle elements. transfer coefficient to milk (Fi,): The fraction of element (i) ingested daily by a cow that is secreted in milk at steady-state or equilibrium. transfer coefficient to other animal product (e.g., meat, eggs) (Fir):The fraction of element (i) ingested daily by a herbivore that

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can be measured in 1 kg of animal product a t steady-state or equilibrium. transmissivity: The rate a t which water is transmitted through a unit width of the aquifer under a unit hydraulic gradient. transport:The movement .of a material within a single environmental medium, e.g., dispersion in the atmosphere. uncertainty: The lack of sureness or confidence in the predictions of models. uncertainty analysis: Analysis of the uncertainty in model predictions. unsaturated zone: The portion of a porous medium where the interconnecting interstices are only partially filled with fluid. utilized area factor (U): The effective area of pasture grazed daily by a herbivore. ventilation rate: See minute volume. water table: The surface in an unconfined groundwater body at which the water pressure is atmospheric (e.g., the level reached in dug wells). zooplankton: The animals of plankton.

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SEGOL,G. (1982). "Unsaturated flow modeling as applied to field problems," page 35 in Symposium on Unsaturated Flow and Transport Modeling. Report No. NUREG/CP-0030 (U.S. Nuclear Regulatory Commission, Washington, D.C.). SEHMEL,G. A. (1980). "Particle and gas dry deposition: A review," Atmos. Envir. 14, 983. SEHMEL,G. A. A N D HODGSON,W. H. (1976). "Predicted dry deposition velocities," page 399 in Proceedings of the Atmospheric Surface Exchange of Particulate and Gaseous Pollutants-1974 Symposium, ERDA Symposium Series 38, CONF-740921 (U.S. Energy Research and Development Administration, Washington, D.C.). SEHMEL,G. A. AND HODGSON, W. H. (1979). A Model for Predicting Dry Deposition of Particles and Gases to Environmental Surfates, Report No. PNL-SA-6721, Rev. 1 (Pacific Northwest Laboratory, Richland, Washington). SEITZ,M. G., RICKERT,P. G., FRIED,S. M., FRIEDMAN, A. M. AND STEINDLER, M. J. (1979). Studies of Nuclear Waste Migration in Geologic MediaAnnual Report October 1977-September 1978, Report No. ANL-79-30 (Argonne National Laboratory, Argonne, Illinois). D. A. (1974). Experimental SERNE,R. J., ROUTSON,R. C. A N D COCHRAN, Methods for Obtaining PERCOL Model Impact and Verification Data, Report No. BNWL-1721 (Battelle Pacific Northwest Laboratory, Richland, Washington). SHAEFFEB,D. L. (1980). "A Model evaluation methodology applicable to environmental assessment models," Ecological Modeling 8, 275. F. 0. (1979). "Uncertainties in radiological SHAEFFER, D. L. AND HOFFMAN, assessments a statistical analysis of radioiodine transport via the pasturecow-milk pathway," Nuc. Technol. 45,99. T. A. AND CHERRY, J. A. (1980). uContaminant migration in seepage SHEPARD, from uranium mill tailings Impoundments-An overview," page 299 in Uranium Mill Tailings Management, Proceedings of Third Symposium, Nov. 2425, 1980 (Civil Engineering Department, Colorado State University, Fort Collins, Colorado). SHOR,R. W. A N D FIELDS,D.E. (1979). "The fraction of total feed composed of fresh forage, F., and the Fraction of the Year Fresh forage is Utilized," page 59 in A Statistical Analysis of Selected Parameters for Predicting Food Chain Transport and Internal Dose of Radionuclides. Hoffman, F. 0. and Baes, C. F. I11 Eds., Report Nos. NUREG/CR-1004,ORNL/NUREG/TM282 (Oak Ridge National Laboratory, Oak Ridge, Tennessee). R. F., OLSON,P. R. A N D DONALDSON, J. R. (1969). SHORT,Z. F., PALUMBO, "The uptake of Iodine-131 by the biota of Fern Lake, WA, in a laboratory and field experiment," Ecology 50,979. J. R., LINSEY,G. S. A N D JONES,J. A. (1979). A General Model SIMMONDS, for the Transfer of Radioactive Materials in Terrestrial Food Chains, Report No. NRPB-R89 (National Radiological Protection Board, Harwell, Didcot, Oxon). SIMMONS, C. S. (1982). "A Stochastic Convective Transport Representation

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The NCRP The National Council on Radiation Protection and Measurements is a nonprofit corporation chartered by Congress in 1964 to: 1. Collect, analyze, develop, and disseminate in the public interest information and recommendations about (a) protection against radiation and (b) radiation measurements, quantities, and units, particularly those concerned with radiation protection; 2. Provide a means by which organizations concerned with the scientific and related aspects of radiation protection and of radiation quantities, units, and measurements may cooperate for effective utilization of their combined resources, and to stimulate the work of such organizations; 3. Develop basic concepts about radiation quantities, units, and measurements, about the application of these concepts, and about radiation protection; 4. Cooperate with the International Commission on Radiological Protection, the International Commission on Radiation Units and Measurements, and other national and international organizations, governmental and private, concerned with radiation quantities, units, and measurements and with radiation protection. The Council is the successor to the unineorporated association of scientists known as the National Committee on Radiation Protection and Measurements and was formed to carry on the work begun by the Committee. The Council is made up of the members and the participants who serve on the eighty-one Scientific Committees of the Council. The Scientific Committees, composed of experts having detailed knowledge and competence in the particular area of the Committee's interest, draft proposed recommendations. These are then submitted to the full membership of the Council for careful review and approval before being published. The following comprise the current officers and membership of the Council: 284

THENCRP Officers President Vice President Secretary and Treasurer Assistant Secretary Assistant Treasurer

WARRENK. SINCLAIR S. JAMES ADELSTEIN W. ROGERNEY EUGENE R. FIDELL JAMES F. BERG

Members GEORGER. LEOPOLD THOMASA. LINCOLN RAYD. LLOYD ARTHURC. LUCAS CHARLES W. MAYS ROGER0.MCCLELLAN JAMESMCLAUGHLIN BARBARA J. MCNEIL F. MEANEY THOMAS CHARLES B. MEINHOLD MORTIMERL. MENDELSOHN WILLIAME. MILLS DADEW. MOELLER A. ALANMOGHISSI ROBERTD. MOSELEY,JR. JAMES V. NEEL WESLEYNYBORG MARYE. O'CONNOR FRANKPARKER ANDREWK. POZNANSKI NORMAN C. RASMUSSEN WILLIAMC. REINIG CHESTERR. RICHMOND JAMES T. ROBERTSON ROBERTE. ROWLAND LEONARD A. SAGAN J. SCHULL WILLIAM GLENNE. SHELINE ROYE. SHORE WARRENK. SINCLAIR LEWISV. SPENCER J O H NB. STORER ROYC. THOMPSON JOHNE. TILL ARTHURC. UPTON GEORGEL. VOELZ EDWARD W. WEBSTER GEORGEM. WILKENING H. RODNEY WITHERS

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THENCRP Honorary Members LAURISTON S. TAYLOR, Hommty President

Currently, the following subgroups are actively engaged in formulating recommendations:

SC-48: SC-52: SC-53: SC-54: SC-55: SC-57:

Basic Radiation Protection Criteria Medical X-Ray, Electron Beam and Gamma-Ray Protection for Energies Up to 50 MeV (Equipment Performance and Use) X-Ray Protection in Dental Offices Standards and Measurements of Radioactivity for Radiological Use Waste Disposal Task Group on Krypton-85 Task Group on Carbon-14 Task Group on Disposal of Accident Generated Waste Water Task Group on Disposal of Low-Level Waste Task Group on the Actinides Task Group on Xenon Biological Aspects of Radiation Protection Criteria Task Group on Atomic Bomb Survivor Dosimetry Subgroup on Biological Aspects of Dosimetry of Atomic Bomb Survivors Industrial Applications of X Rays and Sealed Sources Radiation Associated with Medical Examinations Radiation Received by Radiation Employees Operational Radiation Safety Task Group 1on Warning and Personnel Security Systems Task Group 2 on Uranium Mining and Milling-Radiation Safety Programs Task Group 3 on ALARA for Occupationally Exposed Individuals in Clinical Radiology Task Group 4 on Calibration of Instrumentation Instrumentation for the Determination of Dose Equivalent Apportionment of Radiation Exposure Conce~tualBasis of Calculations of Dose Distributions ~iolo'ical Effects and Exposure Criteria for Radiofrequency Electromagnetic Radiation Bioassay for Assessment of Control of Intake of Radionuclides Experimental Verification of Internal Dosimetry Calculations Internal Emitter Standards Task Group 2 on Respiratory Tract Model

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Task Group 3 on General Metabolic Models Task Group 4 on Radon and Daughters Task Group 6 on Bone Problems Task Group 7 on Thyroid Cancer Risk Task Group 8 on Leukemia Risk Task Group 9 on Lung Cancer Risk Task Croup 10 on Liver Cancer Risk Task Group 11 on Genetic Risk Task Group 12 on Strontium Task Group 13 on Neptunium SC-59: Human Radiation Exposure Experience SC-60: Dosimetry of Neutrons from Medical Accelerators SC-61: Radon Measurements SC-62: Priorities for Dose Reduction Efforts SC-63: Control of Exposure to Ionizing Radiation from Accident or Attack SC-64: Radionculides in the Environment Task Croup 5 on Public Exposure to Nuclear Power Task Group 6 on Screening Models SC-65: Quality Assurance and Accuracy in Radiation Protection Measurements SC-67: Biological Effects of magnetic Fields SC-68: Microprocessors in Dosimetry SC-69: Efficacy Studies SC-70: Quality Assurance and Measurement in Diagnostic Radiology SC-71: Radiation Exposure and Potentially Related Injury SC-72: Radiation Protection in Mammography SC-74: Radiation Received in the Decontamination of Nuclear Facilities SC-75: Guidance on Radiation Received in Space Activities SC-76: Effects of Radiation on the Embryo-Fetus SC-77: Guidance on Occupational and Public Exposure Resulting from Diagnostic Nuclear Medicine Procedures SC-78: Practical Guidance on the Evaluation of Human Exposures to Radiofrequency Radiation SC-79: Extremely Low-Frequency Electric and Magnetic Fields SC-80: Radiation Biology of the Skin (Beta-Ray Dosimetry) SC-81: Assessment of Exposure from Therapy Committee on Public Education Committee on Public Relations Ad Hoc Committee on Policy in Regard to the International System of Units Ad Hoc Committee on Comparison of Radiation Exposures Study Group on Acceptable Risk (Nuclear Waste) Study Group on Comparative Risk Task Group on Comparative Carcinogenicity of Pollutant Chemicals Task Force on Occupational Exposure Levels

In recognition of its responsibility to facilitate and stimulate cooperation among organizations concerned with the scientific and related aspects of radiation protection and measurement, the Council has created a category of NCRP Collaborating Organizations. Organizations or groups of organizations that are national or international in

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scope and are concerned with scientific problems involving radiation quantities, units, measurements, and effects, or radiation protection may be admitted to collaborating status by the Council. The present Collaborating Organizations with which the NCRP maintains liaison are as follows: American Academy of Dermatology American Association of Physicists in Medicine American College of Radiology American Dental Association American Industrial Hygiene Association American Institute of Ultrasound in Medicine American Insurance Association American Medical Association American Nuclear Society American Occupational Medical Association American Podiatry Association American Public Health Association American Radium Society American Roentgen Ray Society American Society of Radiologic Technologists American Society of Therapeutic Radiologists Association of University Radiologists Atomic Industrial Forum Bioelectromagnetics Society College of American Pathologists Federal Emergency Management Agency Genetics Society of America Health Physics Society National Bureau of Standards National Electrical Manufacturers Association Radiation Research Society Radiological Society of North America Society of Nuclear Medicine United States Air Force United States Army United States Department of Energy United States Department of Labor United States Environmental Protection Agency United States Navy United States Nuclear Regulatory Commission United States Public Health Service

The NCRP has found its relationships with these organizations to be extremely valuable t o continued progress in its program. Another aspect of the cooperative efforts of the NCRP relates to the special liaison relationships established with various governmental organizations that have an interest in radiation protection and meas-

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urements. This liaison relationship provides: (1) an opportunity for participating organizations to designate an individual to provide liaison between the organization and the NCRP; (2) that the individual designated will receive copies of draft NCRP reports (at the time that these are submitted to the members of the Council) with an invitation to comment, but not vote; and (3) that new NCRP efforts might be discussed with liaison individuals as appropriate, so that they might have an opportunity to make suggestions on new studies and related matters. The following organizations participate in the special liaison program: Defense Nuclear Agency Federal Emergency Management Agency National Bureau of Standards Office of Science and Technology Policy Office of Technology Assessment United States Air Force United States Army United States Coast Guard United States Department of Energy United States Department of Health and Human Services United States Department of Labor United States Department of Transportation United States Environmental Protection Agency United States Navy United States Nuclear Regulatory Commission

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American Osteopathic College of Radiology American Podiatry Association American Public Health Association American Radium Society American Roentgen Ray Society American Society of Radiologic Technologists American Society of Therapeutic Radiologists American Veterinary Medical Association American Veterinary Radiology Society Association of University Radiologists Atomic Industrial Forum Battelle Memorial Institute Bureau of Radiological Health College of American Pathologists Commonwealth of Pennsylvania Defense Nuclear Agency Edison Electric Institute Edward Mallinckrodt, Jr. Foundation Electric Power Research Institute Federal Emergency Management Agency Florida Institute of Phosphate Research Genetics Society of America Health Physics Society James Picker Foundation National Association of Photographic Manufacturers National Bureau of Standards National Cancer Institute National Electrical Manufacturers Association Radiation Research Society Radiological Society of North America Society of Nuclear Medicine United States Department of Energy United States Department of Labor United States Environmental Protection Agency United States Navy United States Nuclear Regulatory Commission

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Title Perceptions of Risk, Proceedings of the Fifteenth Annual Meeting, Held on March 14-15, 1979 (Including Taylor Lecture No. 3) (1980) Quantitative Risk in Standards Setting, Proceedings of the Sixteenth Annual Meeting Held on April 2-3, 1980 (Including Taylor Lecture No. 4) (1981) Critical Issues in Setting Radiation Dose Limits, Proceedings of the Seventeenth Annual Meeting, Held on April 8-9, 1981 (Including Taylor Lecture No. 5) (1982) Radiation Protection and New Medical Diagnostic Procedures, Proceedings of the Eighteenth Annual Meeting, Held on April 6-7, 1982 (Including Taylor Lecture No. 6) (1983) Environmental Radioactivity, Proceedings of the Nineteenth Annual Meeting, held on April 6-7, 1983 (Including Taylor Lecture No. 7) (1984)

Symposium Proceedings

The Control of Exposure of the Public to Ionizing Radiation in the Event of Accident or Attack, Proceedings of a Symposium held April 27-29, 1981 (1982) 291

NCRP PUBLICATIONS

Lauriston S. Taylor Lectures No. 1

Title and Author The Squares of the Natural Numbers in Radiation Protection by Herbert M . Parker (1977) Why be Quantitative About Radiation Risk Estimates? by Sir Edward Pochin (1978) Radiation Protection-Concepts and Trade Offsby Hymer L. Friedell (1979) [Available also in Perceptions of Risk, see above] From "Quantity of Radiation" and "Dose" to ''Exposure" and "Absorbed Dose"-An Historical Review by Harold 0.Wyckoff (1980) [Available also in Quantitative Risks in Standurds Setting, see above] How Well Can W e Assess Genetic Risk? Not Very by James F. Crow (1981) [Available also in Critical Issues in Setting Radiation Dose Limits, see above] Ethics, Trade-offs and Medical Radiation by Eugene L. Saenger (1982) [Available also in Radiation Protection and New Medical Diagnostic Approaches, see above.] The Human Environment-Past, Present and Future by Merril Eisenbud (1983) [Available also in Environmental Radioactivity, see above.]

NCRP Reports No. 8

Title Control and Removal of Radioactive Contamination in Laboratories (1951) Recommendations for Waste Disposal of Phosphorus-32 and Iodine-131 for Medical Users (1951) Recommendations for the Disposal of Carbon-14 Wastes (1953) Radioactive Waste Disposal in the Ocean (1954) Maximum Permissible Body Burdens and Maximum Permissible Concentrations of Radionuclides in Air and in Water for Occupational Exposure (1959) [Includes Addendum 1issued in August 19631 Measurement of Neutron Flux and Spectra for Physical and Biological Applications (1960) Measurement of Absorbed Dose of Neutrons and Mixtures of Neutrons and Gamma Rays (1961) Stopping Powers for Use with Cavity Chambers (1961)

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Safe Handling of Radioactive Materials (1964) Radiation Protection in Educational Institutions (1966) Medical X-Ray and Gamma-Ray Protection for Energies Up to 10 MeV-Equipment Design and Use (1968) Dental X-Ray Protection (1970) Radiation Protection in Veterinary Medicine (1970) Precautions in the Management of Patients W h o Have Received Therapeutic Amounts of Radionuclldes (1970) Protection against Neutron Radiation (1971) Basic Radiation Protection Criteria (1971) Protection Against Radiation from Brachytherapy Sources (1972)

Specification of Gamma-Ray Brachytherapy Sources (1974) Radiological Factors Affecting Decision-Making in a N u clear Attack (1974) Review of the Current State of Radiation Protection Philosophy (1975) Krypton-85 in the Atmosphere-Accumulation, Biological Significance, and Control Technology (1975) Natural Background Radiation in the United States (1975) Alpha-Emitting Particles in Lungs (1975) Tritium Measurement Techniques (1976) Radiation Protection for Medical and Allied Health Personnel (1976) Structural Shielding Design and Evaluation for Medical Use of X-Rays and Gamma-Rays of Energies U p to 10 MeV (1976) Environmental Radiation Measurements (1976) Radiation Protection Design Guidelines for 0.1-1 00 MeV Particle Accelerator Facilities (1977) Cesium-137 From the Environment to Man: Metabolism and Dose (1977) Review of NCRP Radiation Dose Limit for Embryo and Fetus in Occuptionally Exposed Women (1977) Medical Radiation Exposure of Pregnant and Potentially Pregnant Women (1977) Protection of the Thyroid Gland in the Event of Releases of Radioiodine (1977) Radiation Exposure From Consumer Products and Miscellaneous Sources (1977) Instrumentation and Monitoring Methods for Radiation Protection (1978) A Handbook of Radioactivity Measurements Procedures (1978)

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NCRP PUBLICATIONS

Operational Radiation Safety Program (1978) Physical, Chemical, and Biological Properties of Radiocerium Relevant to Radiation Protection Guidelines (1978) Radiation Safety Training Criteria for Industrial Radiography (1978) Tritium in the Environment (1979) Tritium and Other Radionuclide Labeled Organic Compounds Incorporated in Genetic Material (1979) Influence of Dose and Its Distribution in Time on DoseResponse Relationships for Low-LET Radiations (1980) Management of Persons Accidentally Contaminated with Radionuclides (1980) Mammography (1980) Radiofrequency Electromagnetic Fields-Properties, Quantities and Units, Biophysical Interaction, and Measurements (1981) Radiation Protection in Pedintric Radiology (1981) Dosimetry of X-Ray and Gamma-Ray Beams for Radiation Therapy in the Energy Range 10 keV to 50 MeV (1981) Nuclear Medicine-Factors Influencing the Choice and Use of Radionuclides i n Diagnosis and Therapy (1982) Operational Radiation Safety-Training (1983) Radiation Protection and Measurement for Low Voltage Neutron Generators (1983) Protection in Nuclear Medicine and Ultrasound Diagnostic Procedures in Children (1983) Biological Effects of Ultrasound: Mechanisms and Clinical Applications (1983) Iodine-129: Evaluation of Releases from Nuclear Power Generation (1983) Radiological Assessment: Predicting the Transport, Bioaccumulation, and Uptake by Man of Radio-nuclides Released to the Environment (1984) Exposures from the Uranium Series with Emphasis on Radon and its Daughters (1984) Evaluation of Occupational and Environmental Exposures to Radon and Radon Daughters in the United States (1984)

Binders for NCRP Reports are available. Two sizes make it possible to collect into small binders the "old series" of reports (NCRP Reports Nos. 8-31) and into large binders the more recent publications (NCRP Reports Nos. 32-71). Each binder will accommodate from five to seven reports. The binders carry the identification " N C W Reports" and

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come with label holders which permit the user to attach labels showing the reports contained in each binder. The following bound sets of NCRP Reports are also available: Volume I. NCRP Reports Nos. 8, 9, 12, 16, 22 Volume 11. NCRP Reports Nos. 23, 25, 27, 30 Volume 111. NCRP Reports Nos. 32, 33, 35, 36, 37 Volume IV. NCRP Reports Nos. 38,39,40,41 Volume V. NCRP Reports Nos. 42,43,44,45, 46 Volume VI. NCRP Reports Nos. 47,48,49,50,51 Volume VII. NCRP Reports Nos. 52, 53, 54, 55, 56, 57 Volume VIII. NCRP Report No. 58 Volume IX. NCRP Reports Nos. 59, 60,61,62,63 Volume X, NCRP Reports Nos. 64,65,66, 67 (Titles of the individual reports contained in each volume are given above). The following NCRP Reports are now superseded and/or out of print: No. 1

Title X-Ray Protection (1931). [Superseded by NCRP Report No. 31 Radium Protection (1934). [Superseded by NCRP Report No. 41 X-Ray Protection (1936). [Superseded by NCRP Report No. 61 Radium Protection (1938). [Superseded by NCRP Report No. 131 Safe Handling of Radioactive Luminous Compounds (1941). [Out of Print] Medical X-Ray Protection U p to Two Million Volts (1949). [Superseded by NCRP Report No. 181 Safe Handling of Radioactive Isotopes (1949). [Superseded by NCRP Report No. 301 Radiological Monitoring Methods and Instruments (1952). [Superseded by NCRP Report No. 571 Maximum Permissible Amounts of Radioisotopes in the Human Body and Maximum Permissible Concentrations i n Air and Water (1953). [Superseded by NCRP Report No. 221

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Protection Against Radiations from Radium, Cobalt-60 and Cesium-137 (1954). [Superseded by NCRP Report No. 241 Protection Against Betatron-Synchrotron Radiations U p to 100 Million Electron Volts (1954). [Superseded by NCRP Report No. 511 Safe Handling of Cadavers Containing Radioactive Isotopes (1953). [Superseded by NCRP Report No. 211 Permissible Dose from External Sources of Ionizing Radiation (1954) including Maximum Permissible Exposure to Man, Addendum to National Bureau of Standards Handbook 59 (1958). [Superseded by NCRP Report No. 391 X-Ray Protection (1955). [Superseded by NCRP Report No. 26 Regulation of Radiation Exposure by Legislative Means (1955). [Out of print] Protection Against Neutron Radiation U p to 30 Million Electron Volts (1957). [Superseded by NCRP Report No. 381 Safe Handling of Bodies Containing Radioactive Isotopes (1958). [Superseded by NCRP Report No. 371 Protection Against Radiations from Sealed Gamma Sources (1960). [Superseded by NCRP Report Nos. 33, 34, and 401 Medical X-Ray Protection Up to Three Million Volts (1961). [Superseded by NCRP Report Nos. 33, 34, 35, and 361 A Manual of Radioactivity Procedures (1961). [Superseded by NCRP Report No. 581 Exposure to Radiation in an Emergency (1962). [Superseded by NCRP Report No. 421 Shielding for High Energy Ebctron Accelerator Installations (1964). [Superseded by NCRP Report No. 5111 Medical X-Ray and Gamma-Ray Protection for Energies Up to 10 MeV-Structural Shielding Design and Eualuation (1970). [Superseded by NCRP Report No. 491

Other Documents The following documents of the NCRP were published outside of the NCRP Reports series: "Blood Counts, Statement of the National Committee on Radiation Protection," Radiology 63, 428 (1954)

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"Statements on Maximum Permissible Dose from Television Receivers and Maximum Permissible Dose to the Skin of the Whole Body," Am. J. Roentgenol., Radium Ther. and Nucl. Med. 84, 152 (1960) and Radiology 75, 122 (1960) X-Ray Protection Standards for Home Television Receivers, Interim Statement of the National Council on Radiation Protection and Measurements (National Council on Radiation Protection and Measurements, Washington, 1968) Specification of Units of Natural Uranium and Natural Thorium (National Council on Radiation Protection and Measurements, Washington, 1973) NCRP Statement on Dose Limit for Neutrons (National Council on Radiation Protection and Measurements, Washington, 1980) Krypton-85 in the Atmosphere- With Specific Reference to the Public Health Significance of the Proposed Controlled Release at Three Mile Island (National Council on Radiation Protection and Measurements, Washington, 1980) Preliminary Evaluation of Criteria For the Disposal of Tmnsuranic Contaminated Waste (National Council on Radiation Protection and Measurements, Bethesda, Md, 1982)

Copies of the statements published in journals may be consulted in libraries. A limited number of copies of the remaining documents listed above are available for distribution by NCRP Publications.

Index Adsorption/desorption properties of sedi- Data sets, terrestrial, 67 ments, 99, 101,106, 112, 115, 117 concentration ratios, 73, 75, 81, 85, 89, Adsorption/retardation properties of soils, 95 182 transfer coefficients, 78,81, 85,89, 95 Advection, 99, 103, 113 Data sets, usage factors, 199 Advective-diffusion, 101, 102, 103, 108, aquatic, 204 112 external exposure, 217 with decay and source/sink terms, 102 generic, 199 without decay and source/sink terms, inhalation, 208 103 terrestrial, 200 Applications of models, 233 water consumption, 208 environmental, assessment, 233 Deposition from atmospheric, 43 research, 234 dry, 43 screening, 235 reactive gases, 46 Aquatic pathways, 204 wet, 49 bioaccumulation factors, 136 velocity of. 49 usage factors, 204 Diffusion models, atmospheric, 5 uncertainties in, 230 basic parameters for, 21 UAslow as reasonably achievable" higher closure theory, 9 (ALARA), 99 k-theory, 8 Atmospheric transport models, 5 lumped parameters for, 32 wet, 39, 49 velocity, 18 Bioaccumulation factors, aquatic, 96,136 Distribution coefficients (Kd), 96,115,121, factors influencing variability, 148 182 uncertainties associated with, 153,230 validation, 153 External exposure. usage factors, 217 Bioaccumulation, terrestrial, 57 Food consumption rates, see Usage factors

Concentration ratios, terrestrial, 73 Consumption rates, see Usage factors Data sets, atmospheric, 34 Data sets, groundwater, 177 dispersion, 177 182 distribution coefficient (L), hydraulic conductivity, 180 porosity, 178, 180 Data sets, surface waters, 125 bioaccumulation factors, 136 distribution coefficients (Kd), 118, 126, 128, 132,134 298

Gaussian plume models, 6 properties of, 22 Global models, 17 Grid models. 17 Groundwater assessments, need for, 158 geological isolation of high level waste (HLW), 158 nuclear power plant accidents, 160 shallow land burial, 159 uranium milling and mining, 160 Groundwater flow and radionuclide transport, 166

INDEX Groundwater flow (Continued) groundwater flow, 166 mass transport, 170 decay of radionuclides, 172 Groundwater models, 157 data sets, 177 uncertainties in, 231 percolation, 173 Hydraulic, conductivity, 180 properties of lakes and estuaries, 115 Imprecision analyses, parameters, 221 Improvement of models, 235 Inhalation pathway, usage factors, 208

Kd, (distribution coefficient), 96,125,182 Models, atmospheric transport, 10 box, 19 data sets, 34 deposition and resuspension, 43 diffusion, 5 eddy diffusivity in, 8 effective source height for, 36 friction velocity in, 46 Gaussian plume and puff, 10 global, 19 grid, 17 Monin-Obukhor stability length, 33 parameters for, 20 particle in cell, 18 Pasquill-Gifford (PG) curves, 32 physical, 20 plume reflection, 13 precipitation scavenging, 39 pseudo-spectral, 18 Richardson's number, 33 types of, 10-20 uncertainties in, 227 variability of concentration estimates in, 39 validation of, 39 Models, groundwater, 161 data sets, 177 decay of radionuclides, 172 groundwater flow, 166 high level waste, 162 low level waste, 161 mass transport, 170 mill tailing waste, 166

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299

Models, groundwater (Continued) misuse of, 196 parameters for, 173 percolation, 173 uncertainties in, 231 validation of, 188 Models, screening, 239 Models, simplification of, 239 Models, surface waters, 98 advection, 113 advection-diffusion with decay and source/sink terms, 102 advection-diffusion without decay and source/sink terms, 103 advective diffusion, 101,108 CHNSED, sediment transport, 114 complete mixing, 105 contaminant transport, 98 data sets, 125 diffusion-dispersion, 112 diffusion with or without decay and source/sink terms, 108 EXAMS, contaminant transport, 98 FETRA, sediment transport, 114 FLESCOT, three-dimensional, 99,114, 117 geochemical, 98 liquid pathway, 103 Lagrangian routing with decay and source/sink terms, 15 MINTEQ,geochemical, 98 Monte Carlo, 108 one-dimensional estuary, 103 particle scavenging, 108 plug flow, 105 SERATRA, sediment transport, 114, 117 sediment transport, 98 three dimensional, 99 time concentration, 100,105 transport and fate, 98 transformation, 100 TODAM, sediment transport, 114 uncertainties in, 230 validation of, 124 verification of, 121 water quality, 98 well mixed compartment, 106 Models, terrestrial, 57 air-vegetation. 57 data sets, 67

300

1

INDEX

Models, terrestrial (Continued) direct deposition, 59 harvest loss, 63 simple equilibrium, 59 soil-vegetation, 59, 62 steady-state, 59 TERMOD, pathway, 58 transient, 57 two-compartment, 64 uncertainties in, 228 vegetation-animal, 66 weathering half-life, 61 XOQDOQ, deposition/retention, 60 year-2000, radiation dose, 59 Model uncertainties, 219 among model types, 225 bias, 219 determination of, 220 sources of, 220 Models, validation of, 238 Pathways, 5-56, 57, 136 aquatic, 136 atmospheric, 5 dietary, 57-95 groundwater, 157 imprecision analyses, 221 surface waters, 96 to animal products, 66 to vegetation, 57 uncertainty analysis, 225 Radionuclides, special cases, 87 carbon-l4,92 tritium, 88 Reactive gases, 46 wet removal of, 51 Resuspension, 52 mass loading, 52 factor, 53 rate of. 56 Scavenging, atmospheric, 39 rate coefficient for, 50 Sediments, 96 adsorptionldesorption properties, 106, 115,117 data sets, 118, 126,128,132,134 CHNSED model, 114 deposition and resuspension, 115 FETRA model, 114 FLESCOT model, 114, 117

Sediments (Continued) particle cohesiveness, 113 particle size, 113 precipitation/dissolution values, 117 resuspension and transport, 113, 119 SERATA model, 114, 117 suspended, 119 TODAM model, 114 transport, 103 water interface, 98 Specific activity approach, 87 uncertainties in, 229 Surface water models, 96 Terrestrial pathways, 57 models, 57-96 transfer coefficients, 78 usage factors, 200 uncertainties in, 228 Transfer coefficients, terrestrial, 78 Uncertainties in models and parameters, 153, 219

aquatic food chains, 230 atmospheric transport, 227 bioaccumulation factors, 153 groundwater transport, 231 human factors, 231 specific activity approach, 229 surface water transport, 230 terrestrial food chains, 228 Usage factors, 198 aquatic, 204 external exposure, 217 generic, 199 inhalation, 208 terrestrial, 200 water and other beverages, 208 Validation of atmospheric transport models, 39 Validation of models. 124, 220 Variability, factors influencing parameters, 74, 148, 202 bioaccumulation factors, 148 concentration ratios, 74 transfer coefficients, 78 usage factors, 202 Variability of atmospheric concentration estimates, 39 Verification of surface water models, 121 Water quality models, 98