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'IJ 2| 7| a. :- IL..<.‘ O ; lion . < ..L h: }.| 1 1“ «I. n kl . 1"). “Lil ablrl . \ AN... . ... ‘ . 4|.IP. y l. l .1. \10” I‘liau‘a ~ . l (I . 10-. I { \l y ‘9). 0". .v. VI. - Unix»: Lu. 391-01-- ‘ INUIIo. . ,l t .1]! ‘ .l‘. wail». .o i --1 -.- n4.uw.I04.m‘.f\|h :1...th V. I! II: - I! ‘x ..v I. :c .' 3- :1 I - t f ' I . i l I u h - ‘l . ‘N OI ...IIQ ~uv00 . . 2!.) ti!!! 1.. 53...... on o y.“ 01r.;9| fh'.‘ 55?».fi1 ‘§, 2 - - . . .. a .. x. . .. . . maamfiwdambwckéwm.Ehn’2Lth4l». .. It. J v . . . y . . . . A . . p. 4 3-K». hm” 1.4.3.3.. 1.35-! LIBRARY Michigan State University This is to certify that the dissertation entitled MINIMIZING THE RISK AND COST OF TRANSPORTING RADIOACTIVE MATERIAL presented by James Thomas Carrick has been accepted towards fulfillment of the requirements for Doctor of Philosophy degreein Civil Engineering gym“ a . fad/é? Major professorg/ DateJuly 21 . 1987 MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 MSU LIBRARIES “ ,‘v-v-J ' RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. mimetic in} Jig-1.. A) MINIMIZING THE RISK AND COST OF TRANSPORTING RADIOACTIVE MATERIAL By James Thomas C arrick A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Civil and Environmental Engineering 1987 Copyright by . JAMES THOMAS CARRICK © 1987 To my wife, Mary and to my parents, Thomas and Helen Carrick ACKNOWLEDGEMENTS I would like to thank all who have contributed to this research. John Z. Reynolds of Consumers Power Company along with Roger Sinderman, Dr. Robert English and William Beckius were instrumental in securing financial support for this project. Michael Bandrowski of the U. S. Environmental Protection Agency, Dr. Marcus Voth of the Pennsylvania State University and James McClure of Sandia National Laboratories provided much of the back- ground material. Dr. Michael Chial’s insights have been incorporated into the discussion of risk, perception and philosophy. Robert Christie, David Fugere, Mark Moore and Thomas Neal of Consumers Power Company supplied technical assistance during the development of the risk assessment model. Charles Bodwell, Dr. Frank Hatfield and Dr. Abdol Esfahanian shared their experience in network analysis with me. George Bruchmann of the Michigan Department of Public Health and Richard Esch of the Michigan Department of Transportation provided data specific to the Midwest Interstate Low-Level Radioactive Waste Compact. I would also like to express my gratitude to my guidance committee, Dr. Herman Koenig, Dr. Milton Steinmueller, Dr. Bruce Wilkinson and espe- cially my advisor Dr. William Taylor. Each has been a friend as well as counselor through the years. ABSTRACT MINIMIZIN G THE RISK AND COST OF TRANSPORTIN G RADIOACTIVE MATERIAL By James Thomas Carrick A method is developed to minimize the risk and cost of shipping radioactive material. The model includes a procedure to assess the risk of transporting radioactive material during accident and accident-free situations. An algorithm for routing the shipments on a network by minimizing the risk or cost is also provided, as is its implementation as a computer program. The method is applied to shipments of low-level radioactive waste in the Midwest Interstate Low-Level Radioactive Waste Compact. The ship- ments flow from the waste generators in the region to potential repository sites. The risk and cost of these shipments is evaluated for numerous sites within the region. Maps of the region are generated in which repository sites of equal risk or cost are connected to produce contour lines. The risk and cost estimates of each potential repository are then combined through a normali- zation procedure to provide a relative ranking of the combined risk and cost index. Areas with extreme values of risk, cost or combined index are noted. James Thomas Carrick The model is also applied to the state of Michigan for low-level radio- active waste shipments originating within Michigan. The results are dis- played in the manner previously described. Sensitivity analyses are performed to test the behavior of the model. Conditions tested are: the withdrawal of one state from the Compact, accident rates reduced by a factor of 10, shipment volumes reduced by a factor of two and requirement of high-integrity containers during shipment. The model performs as expected during the sensitivity analyses. Volume reduction appears to be the policy with the greatest impact on reducing transportation cost, requiring high-integrity containers provides the greatest reduction in risk estimates. General conclusions are: 1. The risk of transporting radioactive material can be quantified, 2. Risk is useful as a criterion for routing radioactive material shipments, 3. Parameters such as risk and cost can be combined through a normalized index, 4. The risk associated with shipping low-level radioactive waste is small in comparison with other transportation risks, and 5. The method used in this research may be applicable to the shipment of other hazardous material with the formulation of appropriate risk models. TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES 1 LOW-LEVEL RADIOACTIVE WASTE ISSUES HISTORICAL PERSPECTIVE REGIONAL COMPACT S FORMED PROBLEM STATEMENT AND RESEARCH OUTLINE 2 LITERATURE REVIEW SITING OF LOW-LEVEL WASTE REPOSITORIES NETWORK MODELS Theoretical Basis Application of Network Models to Hazardous Materials Application of Network Models to Radioactive Materials RISK OF TRANSPORTING MATERIALS Risk of Shipping Hazardous Materials Risk of Shipping Radioactive Materials INTEGRATING DISTINCT MODELS OR METHODS SUPPORT FOR THE CURRENT RESEARCH 3 RISK and PHILOSOPHY DEFINING RISK PERCEIVED RISK Perceiving is Understanding Perceiving is Sensing CULTURE AND BELIEFS DETERMINE RISK Cultural Perception Relativism Cultural Consensus CULTURAL ISSUES TO RESOLVE Control and Voluntary/ Involuntary Risk Distribution of Risk THE DESIRE TO SHAPE SOCIETY WHERE DOES ALL OF THIS LEAD? BASIS FOR THE CURRENT RESEARCH iv vii ix 11 11 12 12 16 18 21 21 26 3O 32 33 33 34 34 38 39 4O 4O 41 43 43 47 50 55 4 RESEARCH METHODS OVERVIEW LOW-LEVEL WASTE SHIPMENT INVENTORY TRANSPORTATION NETWORK RADIOLOGICAL RISK ASSESSMENT MODEL Risk Modeled by Exposure Overview of the Radiation Exposure Model Accident-Free Exposure Exposures from Accidents NETWORK OPTIMIZATION MODEL Optimization Algorithm Weight Functions COMBINING COST AND RISK MODEL IMPLEMENTATION 5 MODELLING THE MILLRWC RESULTS Cost Risk Combined Cost and Risk Cost-Risk Correlations SENSITIVITY ANALYSES One State Withdraws from MILLRWC Accident Rate Reduction Volume Reduction Improved Package Integrity MODEL APPLIED TO SINGLE STATE SUMMARY 6 CONCLUSION ASSUMPTIONS UPON WHICH THE RESULTS ARE BASED Low-Level Waste Shipment Inventory Transportation Network Radiological Risk Assessment Model Network Optimization Model CONCLUSIONS APPLICABLE TO RISK AND TRANSPORTATION CONCLUSIONS SPECIFIC TO THE MODEL USED IN THIS RESEARCH APPENDICES A ANNUAL INVENTORY OF LOW-LEVEL WASTE SHIPMENTS IN THE MILLRWC B NODE DATA FOR THE MILLRWC TRANSPORTATION NETWORK C LINK DATA FOR THE MILLRWC TRANSPORTATION NETWORK U 57 57 58 59 60 61 62 72 84 86 88 94 97 98 98 99 100 102 103 105 106 108 109 110 111 116 118 118 118 119 119 121 121 123 125 134 137 MASS ATTENUATION AND DOSE BUILDUP FACTORS CALCULATION OF ATMOSPHERIC DISPERSION AND DEPOSITION RISK FACTOR COMPONENTS UNTT RISK FACTORS momma VERIFICATION OF THE NETWORK OPTIIVIIZATION ALGORITHM H RISK AND COST OP'IMZATION PROGRAM J COST, RISK AND INDEX RESULTS: MODELLING THE MILLRWC K COST, RISK AND INDEX RESULTS: MODELLING MICHIGAN LIST OF REFERENCES vi 150 152 157 164 166 170 184 187 189 9. LIST OF TABLES . Values of C31 . Parameters Specific to Population Density Class . Pasquill Category—Fraction of Occurrence . Dose Component Examples . LLW Rates in Cents per Mile Michigan Withdraws Minnesota Withdraws Ohio Withdraws Risk Estimates (person-rem) with Accidents Reduced by a Factor of 10 IO. Fraction of Base 11. Cost and Risk with Volume Reduced 50% 12. Fraction of Base 13. Cost and Risk if Casks are Required 14. Fraction of Base D-l. e1” Butt) at 0.5 MeV D-Z. e4” B01!) at 1.0 MeV E-l. Plume Depletion Calculation E-2. X and Deposition Values F-l. Population Zone Parameters F-2. Isotope Data F-3. Package Shielding Factor vii 68 68 78 85 91 106 107 107 108 108 109 109 111 111 150 151 153 156 157 157 158 F4. F5 . F-6. F-7 F-8. G-l. G-2. H-1. Accident-Free Dose Components Non-Dispersal Accident Risk Components (Cask Shipments) Atmospheric Dispersion Data Resuspension Dose Factors Dispersal Accident Risk Components (LSA 8: Drum Shipments) Risk Factors: Person-Rem per Kilometer Risk Factors: Person-Rem per Mile Test of Algorithm viii 158 160 161 162 162 164 165 166 \ON\10\UIuhbJNv—I Nv—lv—II-JHt—lv—l—Jt—lr—IH OOQVChmAva-io 21. LIST OF FIGURES . The MILLRWC . Transportation Network for the MILLRWC . Perception vs. Reality . Errors Resulting from Incorrect Evaluation of Risk . Displacement of Hazards in Space and Time . Four Problems of Risk . Model Outline . Accident—Free Exposures . Accident Exposures . Annular Element . Dispersal Accident Methodology . Optimization Algorithm Flow Diagram . Iso-Cost Lines (in Millions of Dollars per Year) . ISO—Risk Lines (in Thousands of Person-Rem per Year) . Normalized Cost + Normalized Risk (Arbitrary Units) . Regression of All Data Points . Regression of Eastern Data Points . Regression of Western Data Points . Iso-Cost Lines if Michigan Goes Alone (in Hundred Thousand Dollars per Year) . Iso-Risk Lines if Michigan Goes Alone (in Hundreds of Person-Rem per Year) Normalized Cost + Normalized Risk if Michigan Goes Alone (Arbitrary Units) E-l. Nested Ellipses H- 1. Test Network H-2. Solution 14 36 38 48 55 62 63 63 73 76 89 100 101 102 104 104 105 112 113 114 152 166 169 Chapter 1 LOW-LEVEL RADIOACTIVE WASTE ISSUES Historical Perspective Beginning with the Manhattan Project during World War II, scientists and engineers have recognized the need to separate radioactive materials from normal waste materials for disposal. The disposal method first chosen for the radioactive waste generated by the Manhattan Project was shallow land burial. During the post-war period, the burial grounds were located on the Project sites to satisfy security needs. An added benefit to this method of site selection was the minimization of risk to the public during transportation of the waste since the disposal sites were adjacent to the facility generating the waste [7]. With the expansion of the Federal nuclear weapons and power programs during the 1940’s and 1950’s, more than a dozen government Oper- ated disposal sites were established at the laboratories, test and production facilities engaged in nuclear research. 2 Refinements in the understanding of the health effects of radiation led to the classification of radioactive wastes by such categories as isotopic con- tent, Curie content, waste form or source of waste. Accordingly, wastes were classified as spent fuel, high-level waste (HLW), transuranic waste, mine and mill tailings, or low-level waste (LLW). Classifying the wastes allowed for their separation at the waste generating facilities. Thus each waste class could be handled in a manner which limited the amount of radiation exposure received by the workers and yet was effective and economical for each class. Spent fuel is exactly that, fuel that has been used in a nuclear reactor. Spent fuel typically contains large quantities of fission and activation products and as a result is highly radioactive for a number of years following its removal from the reactor in which it was used. This radioactivity is generally allowed to decay for a number of years prior to the treatment or final disposal of the spent fuel. Spent fuel generally emits energetic beta and gamma radiation which is highly penetrating. High-level waste (HLW) is the waste stream generated during the reprocessing of spent fuel. During reprocessing, spent fuel is cut into sections and the fissionable isotopes remaining in the fuel matrix are chemically sepa- rated from the non-fissionable isotopes. The uranium and plutonium thus recovered can be reloaded into new fuel bundles. The HLW comprises the remnants of the fuel following this separation. HLW is also highly radioac- tive as it contains the fission and activation products found in the spent fuel. Transuranic waste (TRU) is material other than spent fuel or HLW which contains elements with atomic number (Z) greater than that of ura- nium (2:92). The concentration of transuranic elements must exceed a limit established by the Federal government to be considered transuranic waste. TRU decays through the emission of alpha particles which is not a 3 penetrating form of radiation. The gamma radiation emitted during the alpha decay process is generally of low energy. Mine and mill tailings are wastes generated in the mining of uranium or thorium ore or in the processing of uranium ore into a substance known as yellowcake. Alpha decay is the primary mode of decay for tailings. Treat- ment of tailings is relatively simple because of the low concentration of radioactivity in the ore. The main concern with tailings is to limit inhalation of dust because of the hazard posed by alpha particles absorbed by lung tissue. Low-level waste (LLW) is defined by exclusion, that is, LLW is any radioactive waste not defined by the other waste classes. The shallow land burial method of disposal was found inappropriate for highly radioactive classes of waste like HLW and spent fuel because of the poor radiation shielding qualities of soil. This method however, was still useful for the disposal of LLW and during the 1950’s the government con- tinued to dispose of its LLW at government owned and Operated sites. The late 1950’s brought the advent of commercial nuclear power and the use of radioisotopes in industry and medicine. The LLW generated by these commercial enterprises was initially disposed of by ocean disposal firms at a small number of Atomic Energy Commission (AEC) approved ocean disposal sites. In 1960, due to potential problems with ocean disposal (such as monitoring of the waste), the AEC allowed commercial waste to be disposed at government sites while commercial shallow land burial sites were being developed [7,21]. The first commercial LLW disposal site was opened in 1962 at Beatty, Nevada. This site was followed over the next nine years by sites in Kentucky, New York, Washington, Illinois and South Carolina. To promote the opening and use of commercial sites, waste generated by government nuclear operations were frequently shipped to those sites between 1963 and 4 1979 [7]. With the opening of commercial sites, the federally operated disposal sites no longer accepted commercial waste. In retrospect, the major criteria for site selection by the commercial disposal site operators appear to have been the site’s soil and hydrogeological characteristics and the proximity of the site to potential users [7,21]. The Beatty, Nevada site is located close to the Nevada Nuclear Weapons Test Site. The Maxey Flats, Kentucky location is near a number of facilities in the front end of the nuclear fuel cycle such as the Paducah Gaseous Diffusion Plant and the Portsmouth Gaseous Diffusion Plant. The West Valley, New York facility is located adjacent to a nuclear fuel reprocessing plant. The Richland, Wash- ington site is within the Hanford Reservation, a large government facility involved in nuclear power and weapons research. Sheffield, Illinois is centrally located for a number of commercial nuclear power stations, research universities and pharmaceutical manufacturers. Barnwell, South Carolina is next to another major government facility, the Savannah River Plant. It is apparent that the commercial disposal site operators gave considerable importance to being located near the waste generators [21]. While this may have been economically motivated, at least initially it also limited the risk of public exposure to the transportation of LLW. Operational problems drastically changed the LLW disposal situation during the 1970’s. The first problem to occur was the detection of radionu- clides leaching from both the Maxey Flats, Kentucky site and the West Valley, New York site. As a result both sites were closed, West Valley in 1975 and Maxey Flats in late 1977. In 1978 the Sheffield, Illinois site reached its licensed capacity and was closed pending the outcome of a site expansion application filed in 1976. During the licensing process the site operator, U.S. Ecology, Inc., requested that the process be terminated. The site has remained closed [8,21]. 5 Since the mid-1970’s the volume of waste generated steadily increased. The generating facilities were concentrated in the areas of the country (the Northeast and Great Lakes regions) which following 1978 had no disposal sites. In 1979, the section of the country north of Tennessee and North Carolina and east of the Mississippi River produced 58% of the total volume of LLW. The Barnwell, SC site (operated by Chem-Nuclear Systems, Inc.) bore the brunt of the northern and eastern site closures. In 1979, 80% of the LLW generated in this country was sent to there for disposal [43]. These factors combined with poor shipping practices on the part of the waste generators to cause a crisis in mid-1979. Between April and July of 1979, 63 packaging deficiencies were noted during a receipt package inspection pro- gram at the Barnwell site [9]. In July, 1979 the Governor of Nevada ordered the Beatty site closed after two major shipping incidents occurred at the site. The first incident was a fire on a truck carrying improperly packaged medical waste into the site. The second incident involved contaminated water leaking from a shipment of demineralizer resin originating at a nuclear power plant [10,22]. The site was reopened late in the month after the gover- nors of Nevada, South Carolina and Washington jointly demanded stricter enforcement of the federal rules governing LLW shipments. The Beatty site was again closed from October to December, 1979 when several waste drums were discovered buried outside of the site fence. It was decided that these drums had most likely been buried at the end of one of the older trenches and the fence was later built without finding the exact location of the end of the old trench [21,22]. Also in October of that year, the Governor of Washington closed the Richland site because of three packaging or shipping problems. The site was reopened in November, 1979 when Federal regulatory agencies made assurances that transportation regulations would be enforced [10]. 6 While the Beatty and Richland sites were closed, the Governor of South Carolina announced that the volume of waste accepted by the Barnwell site would be cut in half from the amount received in October, 1979. This reduction would be phased in over a two year period [43]. In response to the governors’ actions and with the support of the National Governors Conference and the National Conference of State Legis- latures, Congress enacted the Low-Level Waste Policy Act (PL 96-573) in December, 1980. This legislation [56] set the Federal policy on LLW as: 1. Each state is responsible for the disposal of commercial LLW generated within its borders, 2. A regional basis for the management of LLW is the most efficient and safe method, 3. States may enter into compacts to establish and operate regional LLW disposal facilities, 4. Congress must consent to the compacts, and 5. After January 1, 1986, any approved compact may restrict the use of the regional disposal facilities under the compact to the disposal of LLW generated within the region. Since this Act was passed, the three remaining disposal sites have continued to accept shipments of LLW [22]. Because of delays in meeting the 1986 deadline, the Act was amended in December, 1985 and a new deadline of January 1, 1993 was set. Further provisions were: 1. Annual capacity for LLW was fixed at 2.8 million cubic feet, 2. Disposal volume is allocated to utility generators based on type of nuclear reactor, the remaining generators are served on a first- come, first-served basis, 3. Open disposal sites are allowed to add a surcharge on wastes from outside the region containing the site, and 4. Milestones for opening additional sites were established. Penal- ties for failure to meet these milestones were also established. Regional Compacts Formed In response to the Low-Level Waste Policy Act, states have been forming compacts to manage the disposal of LLW. Generally these compacts are based on geographic location although the states need not be contiguous. Geography was the basis for the formation of the Midwest Interstate Low-Level Radioactive Waste Compact (MILLRWC), comprised of Indiana, Iowa, Michigan, Minnesota, Missouri, Ohio and Wisconsin (figure 1). The MILLRWC is one of the largest compacts both in terms of area and number of states. Smaller com- MN ' pacts are more common, for example, WI Illinois has established a compact with Kentucky, creating a gap along the IA southern rank of the Midwest Regional Compact. Other states, Texas MO is an example, have chosen to go it alone. Figure 1. The MILLRWC Once a compact is established, the states forming the compact accept the responsibility for managing LLW in that compact. This includes establishing a site or sites within the compact area for disposal or processing of the LLW generated within that area. The operation of the sites and long-term care for those sites are other responsibilities of the compact. Site selection will be both a technical and a political process. The opportunity exists to make this process one based on reason and knowledge gained from past experience at the com- mercial facilities and the government sites. Clearly factors such as the geology and hydrology will determine if a site is or is not suitable. Also of concern are 8 the land use and resource use plans of the proposed sites. While these con- cerns will at least partially determine the capital costs of preparing a site as a LLW disposal facility, the location of the site chosen will also affect the oper- ating costs. The labor and transportation components of the site operating costs will depend on where the site is located within a region. Problem Statement and Research Outline This research will provide a method to estimate the impact of trans- porting LLW to proposed disposal sites and then optimize the choice among alternative sites by selecting the site which minimizes the effects of transpor- tation. To do this, a transportation model will be developed, the major components of which are a catalog of LLW shipment origins in a region, a definition of possible shipping routes in that region, a cost function to pro- duce both out-of-pocket costs and the costs to society of LLW shipments, and finally, an algorithm to choose the optimal routes from all generators to each proposed disposal site, allowing the selection of the site with the smallest transportation impact. The shipment catalog will be used to characterize the LLW shipments within the region of interest. Three major categories of waste generator will be considered: Commercial nuclear power plants, Institutional generators and Industrial generators. Institutional generators include universities, hospitals and research facilities. Industrial generators include radiopharmaceutical manufacturers, fuel—fabrication facilities and manufacturers of industrial and consumer products which use radioactive material. Cataloged for each generator will be: 9 Annual number of shipments, Annual volume shipped, Isotopic content of waste shipped, and Physical form of waste shipped. The cost function will allow the direct cost to the shipper to be combined with the cost borne by society due to the radioactive nature of the LLW shipments. The direct cost is based on the distance over which the waste is shipped and the type of waste shipped. The radiological cost or risk will be determined by assessing the probability of a LLW shipment being involved in an accident and then quantifying the consequences of such an accident. Also quantified will be the radiological impact of incident-free shipments. The radiological consequences will be estimated through the use of internal and external dose models. The expected radiological impact of shipping LLW will be calculated by multiplying accident consequence with the probability of an accident on each link. Once the shipping cost or risk for each link has been determined, the optimization algorithm will route the shipments from each waste generator to a proposed disposal site. A dynamic programming model will be used to optimize the network. The lowest cost (risk) routes to each disposal site will then be totalled to produce the transportation cost (risk) for that site. The proposed repository sites will then be compared to determine the least costly alternative. Cost and risk estimates will be combined to allow optimization of the network with respect to the resultant combined total impact parameter. To test the model, data from the Midwest Regional Compact will be used. The Compact has contracted ERM Midwest, Inc. to produce a shipment catalog. The remaining data will be gathered specifically for this research. Potential disposal sites will be assumed to exist in each state of the compact. 10 The model will then be used to choose the optimal location from among these assumed sites. Chapter 2 of this dissertation presents a review of literature relevant to the problem. Chapter 3 is a discussion of risk assessment as it relates to the problem. The components of the transportation model are developed in Chapter 4 and then combined into a method capable of solving the problem at hand. The application of the model to the Midwest Regional Compact is presented in Chapter 5. Finally, Chapter 6 presents the conclusions drawn from this research. Chapter 2 LITERATURE REVIEW Siting of Low-Level Waste Repositories Little has been written about siting LLW repositories because the need for such studies did not exist until recently. Clancy, Gray and Oztunali [7] re— viewed the history of LLW disposal for the Nuclear Regulatory Commission. Their review included the major Federal sites as well as the six commercial repositories. Generally, they found that disposal areas have been situated near waste generators either for reasons of security or to minimize the trans- portation of the wastes. For example, the Federal Government established a disposal site on the Hanford Reservation near Richland, Washington during World War H to accept the wastes from plutonium production at nearby facilities. Another example is the Barnwell, South Carolina site which is located adjacent to the U. S. Department of Energy Savannah River Plant and is in close proximity to a number of commercial nuclear power plants. 11 12 Similar reasoning is being explicitly incorporated into the siting processes currently under consideration by some compacts formed as the result of the LLWPA. Colglazier and English [11] report that waste transpor- tation is an issue to be dealt with by the Illinois Department of Nuclear Safety as part of the siting process used by the Central Midwest Compact. They also note that the Southeast Interstate Compact is to consider ”the minimization of waste transportation” in its site selection. This is also one of the factors to be used in identifying the host state in the MILLRWC. Network Models Theoretical Basis Networks, or their geometric equivalents, graphs, have. long been the object of study by mathematicians. Euler applied graph theory to the problem of traversing the seven bridges of Kbnigsberg in 1736. In the Nineteenth Century, the mathematician W. R. Hamilton introduced a game based on his work in networks and graphs. These and dozens of other applications of network theory are described in a text by Busacker and Saaty [4]. This text, one of many on the topic, describes both the graphical representation of networks and their representation by matrix methods. A more detailed description of the matrix formulation of networks is given by Fenves and Branin [23]. This formulation uses network properties such as connectivity, incidence and circuitry to define matrices which provide a mathematical description of the network. For example, an incidence matrix relates the nodes on the network with the segments entering each node. This matrix gives rise to a tree matrix in which all nodes in the network are connected. The path from any node to another along the tree can be derived from the tree matrix: the inverse of the tree matrix equals the transpose of the path matrix. So, from a theoretical 13 viewpoint, it is a short exercise in matrix algebra to move from a network description to solving for paths through the network. From a practical point of view however, complications arise due to the large size of the incidence matrix for even modest networks such as the one being studied in this research. The limited access highway network in the eleven state area containing the Midwest Regional Compact along with Illinois, Kentucky, Tennessee and West Virginia is composed of about 300 nodes (or inter- changes) and 1000 segments connecting those nodes (figure 2). The incidence matrix is thus composed of 300,000 entries, most of which are empty or zero since the network is sparse, as is the case with most networks normally encountered. To represent this matrix on a computer would require 0.6 megabytes of memory for integer values or at least 1.2 megabytes of memory for real numbers. This limits the usefulness of the matrix method in dealing with real network problems. A second method of dealing with transportation networks is through linear programming (LP). A special class of problems commonly referred to as transportation problems can be solved by linear programming. Hillier and Lieberman [30] provide examples of the transportation problem and solution techniques in their text. Generally, the solution concerns the distribution of a commodity from a set of origins to a set of destinations so as to minimize the distribution cost. Since the emphasis of the analysis is on origin-destination pairs, network-level detail on a segment by segment basis is lost. So, linear programming is not well suited for selecting. from among a variety of alternative paths between an origin and destination. A third technique for analyzing networks is through dynamic pro- gramming. In his text, Dane [16] describes dynamic programming as a proce- dure in which a complex problem is decomposed into a series of subproblems, 14 MN WI MI IA IN OH MO 27 Figure 2. Transportation Network for the MILLRWC 15 each involving fewer variables. The solutions to the subproblems are com- bined to obtain a solution to the original problem. He also presents an exam- ple of dynamic programming applied to the problem of solving the shortest path between two nodes on a network. This is accomplished through back- ward recursion, that is, tracing the shortest path back from the destination to the origin. A similar method (with the exception that it operates in the forward direction) is described in Price [55]. This approach is in the form of an algo- rithm attributed to Dijkstra [17] which will calculate the shortest path on a network possessing nonnegative weights. In this technique, a label is assigned to each node representing the distance (or some other weight mea- sure) from the origin at each stage of the analysis. A node is considered permanently labelled if no shorter path from the origin exists, otherwise the label is referred to as temporary. The permanent label for each node is the distance along the shortest path to the origin. Also recorded is the pre- decessor node for each permanently labelled node. This node represents the first connection along the path between any permanently labelled node and the origin. Tracing along the path from one predecessor node to the next generates the shortest path from the origin. Initially all nodes are temporarily given a label of co with the exception of the origin, S, which is assigned a permanent weight of zero (0). The nodes connected to the origin are then given labels equal to their weight from the origin. The node with the smallest temporary label is assigned that label permanently. So at this time there are two nodes with permanent labels, the origin, S, and the node nearest to it (call this node A). The process continues by examining those nodes with temporary labels which are connected to A. The weight from A to each of these nodes is added to the label of A (which is 16 the weight between A and S). If this new weight value is less than the tem- porary label for any node connected to A, the new value becomes the tempo- rary label. If the new weight value is not less than the previous temporary label, then the weight from the origin to that node is less than the weight by way of A, and the temporary label is not replaced. Again the node with the lowest temporary label is given that label permanently. The process conti- nues recalculating the temporary labels and assigning permanent labels until either the desired destination is reached or the entire network is assigned permanent labels. Converting the Dijkstra algorithm into a computer program results in a procedure which makes efficient use of both computer time and memory. The efficiency of this algorithm is documented in a text by Syslo, Deo and Kowalik [71]. Also included is an implementation of the algorithm in Pascal. The listing requires only 50 lines of computer code excluding input and output statements. Unlike the matrix method of analyzing networks, the Dijkstra algorithm can take advantage of the sparse nature of the data and make use of more compact data structures such as lists linking adjacent nodes. As an example, the network previously mentioned as requiring 0.6 megabytes to describe with a matrix could be described in 0.01 megabytes using a linked adjacency list. The Dijkstra algorithm appears to be the best method available for determining the shortest path in a network. Application of Network Models to Hazardous Materials In general, all of the methods of network analysis have been applied to the study of transportation systems, the method of analysis chosen depending upon the objective of the particular study. Recent applications have 17 examined the shipment of hazardous or radioactive materials using both linear programming and dynamic programming as optimization techniques. Hasit and Warner [28] describe a linear programming model used in the regional planning of solid waste management. This model, the Waste Resource Allocation Program (WRAP), optimizes an objective function which is the sum of the transportation costs for waste shipment, the capital and operating costs of disposal or waste processing sites and the site prepa- ration costs minus any revenues generated from the waste. The decision variables are the shipment and processing activities, that is, the amount of waste to be shipped from a region to specified facilities for disposal or pro- cessing. Emphasis has been placed on incorporating realistic values for the costs used in the objective function. Hasit and Warner report that the model has been successfully used to reduce regional waste disposal costs by provid- ing a basis for integrated long range planning of waste disposal facilities. Note that since thismodel is an LP, it does not determine the best routes for ship- ment based upon transportation costs but instead has as input the distances along chosen routes between all source and disposal site pairs. The WRAP model was used by Jennings and Sholar [41] to study the shipment of hazardous waste in Kentucky. They added the element of risk estimation to the network analysis performed by WRAP. Their estimates of the risks involved in transporting, treating and disposing of the hazardous material were of a relative nature, that is, Jennings and Sholar provided a cardinal ranking of risks for various hazardous materials and treatment or disposal processes. They then optimized the network with and without using the risk estimates. They concluded that WRAP is useful in weighing waste management policies whether risk is a consideration or not. In terms of calculated risk, the optimal solution they obtained ignoring risk did not differ 18 significantly from the solution in which risk was minimized, but the treatment and disposal practices did vary significantly. Calculation of relative risk values also pointed out inconsistencies in proposed regulatory policies, in one case a proposed regulation resulted in an increase in both cost and risk over the status quo. Jennings and Sholar noted that their method of esti- mating relative risks was only a surrogate for more thorough risk evaluation techniques. Application of Network Models to Radioactive Materials Transportation of radioactive material has been studied primarily at the national laboratories, especially Sandia National Laboratories (SNL) and Oak Ridge National Laboratory (ORNL). Joy, Johnson and their collaborators at ORNL have produced a number of papers on transporting radioactive material, two of which are relevant to this research. Reference 45 is a review of four U. S. Department of Energy computer programs maintained at ORNL. One is a routing model for rail shipments, another routes highway ship- ments. Two other programs provide a data base for use in transporting radioactive material, AIRPORT contains information on 800 airports in the continental U. S., and the LEGISLATIVE AND REGULATORY INFORMA- TION SYSTEM acts as network for gathering and disseminating information affecting the transportation of radioactive or hazardous materials. The rail shipment model is called INTERLINE and is composed of 17,000 links on the nation’s rail system. Transfer points are defined so as to reflect the tendency of traffic to remain on a single railroad’s line as long as possible. The route is determined by the minimum impedance path between origin and destination. The second routing model, HIGHWAY, is a comput- erized road atlas of the U. S. describing 240,000 miles of road. The complete 19 Interstate system and U. S. system (except for those links closely paralleling an Interstate route) are included as well as most principal state routes and a number of county and local roads. Again, routes are determined by mini- mizing impedance values where impedance is a function of distance and driving time on any given road segment. Certain routing constraints can be imposed on the model, such as avoiding high population areas. In reference 44, Joy, et al. used HIGHWAY to route shipments of spent fuel between Richland, Washington and Barnwell, South Carolina. Three different routing criteria are used to test HIGHWAY: 1. No special constraints, 2. Avoidance of high population density areas, 3. Maximize the use of the Interstate system. The routes were chosen to minimize an impedance function based on the distance and estimated driving speed of each segment, subject to the relevant constraint. Avoiding high population density areas resulted in a 5% distance increase, a 12% driving time increase and a decrease in the use of Interstate routes by 38%. Maximizing Interstate use resulted in a 6% distance increase, a 3% driving time increase and an increase in the use of Interstate routes by 7%. The authors note that population density information was to be added to the data base to allow the calculation of radiation exposure to the public from radioactive material shipments. Brogan and Cashwell [2] note that the coarseness of the data used by the routing algorithm in HIGHWAY limits the usefulness of this program for intrastate levels of analysis. They call for additional parameters to be used for routing at this higher level of detail. Geometric considerations, roadway capacities and land use data are among the parameters they recommend. 20 Cox [13], in his dissertation prepared for Cornell University, examines the transportation of spent nuclear fuel. In doing so, he modifies Dijkstra’s algorithm so that more than one parameter can be evaluated to determine the shortest path in a network. The values of the decision parameters are represented as the components of a vector. The vector components are assumed to be linearly independent. Each link on the network is defined by its endpoints and parameter vector. In determining a path, the vectors are added component-wise to produce a resultant vector which is compared to the best or ”dominant” vectors recorded for each node. A dominant vector is one in which every component is less than or equal to the respective compo- nents of all other vectors. That is, vector 32 dominates vector 3? if and only if Xi S Yi for all components i. The result of Cox’s modified algorithm is a set of paths with final vectors that dominate all other paths. An example he pro- vides has three paths in the solution set with final vectors of (4,6), (5,5) and (6,4). The method cannot choose from among these solutions. because of its assumption that the parameters should not be combined into a unified measurement during the routing analysis but should rather be left for ”the political decisionmakers." [14] Still, this begs the question, ”Which route should be used?” since surely at least one route will be used. Cox proceeds to apply his algorithm to a case study [15] in which spent nuclear fuel is shipped by truck on Interstate routes from Maine to Louisiana. Two parameters are used by the decision-making algorithm, shipping cost and risk exposure. Actually surrogates for these parameters are used in the analysis because of difficulty in measuring the variables of interest. Travel time was taken as an approximation of the shipping cost and the population within 0.5 miles of each network link replaced the risk exposure. No attempt 21 was made to quantify the magnitude of the risk or to estimate the health effects caused by the postulated exposure. The end product is a set of six paths, each with a final vector of (total travel time, total number of persons ”exposed”). The parameter values for the paths range from (35 hours, 810,000 people exposed) to (40 hours, 475,000 people exposed). Weighing the results is left to the decisionmakers. Risk of Transporting Materials Risk of Shipping Hazardous Materials A discussion of risk, consequences and risk assessment will be deferred until chapter 3 but some applications of risk assessment to transportation will be reviewed here. Wright and Glickman [87] have surveyed research performed between 1978 and 1984 outside the United States and Canada on hazardous materials transportation. Included in the survey is a section on risk assessment. All of the papers dealt with non-radioactive hazardous materials. The nine papers discussed fall into three categories: public perception, emergency planning and risk analysis. The emphasis was on the modelling of risks, seven papers dealt with risk analysis and quantification with application to specific cases or materials. One paper dealt with the public perception and acceptance of risk while the final paper dealt with familiarizing emergency response personnel and transportation workers with the risks involved in transporting hazard- ous materials. The current use of risk assessment is reviewed by Rowe [58] for the National Cooperative Highway Research Program. Three categories of risk assessment are described: enumerative indices, regression models and proba- bilistic risk assessment models. An enumerative index develops a rating or 22 score for risks. Typically, parameters relevant to the hazardous activity are counted. Weights are assigned to each parameter based on empirical evi- dence or some other rationalized criterion. The weighted counts are then combined mathematically. The resulting score can be ranked against other comparable activities. Regression models use measurable parameters to estimate the proba- bility of an accident per vehicle mile. Parameters such as average daily traffic (ADT), number of signals, type of road and condition of road are used. A consequence estimate is determined through the population density of those at risk. The probability and consequence are combined to arrive at risk. The models are route and site specific because they are calibrated to actual conditions or data. Probabilistic risk assessment models also make use of accident proba- bility and consequence magnitude. The models currently in use differ in their definition of risk, their level of detail and their methods for generating data. One model defines risk as the conditional probability of an accident causing some loss, while three other models examined define risk as the product of the conditional probability and consequence magnitude. The level of detail covered ranges from analysis of specific materials and routes to the use of aggregated data for risk estimates. Probability data is generated in some cases by fault-tree analysis while other models use average accident rates. The magnitude of consequences are estimated by dispersion models, simulations and other techniques. An example of a risk assessment model for hazardous materials trans- portation is presented by Scanlon and Cantilli [62]. Their approach is to esti- mate a risk level index for a community. A linear model is used to calculate the risk level index: 23 RLmvi = Ltv . (Ni + th + ch + Cp + Cm +N,h + th) RLhmi = RLmvi . (5.5Pex + 2.5Pfl + 40ch + 1.0Pc + 1.0Pp) . Lv . Ld CR = RLhmi . (Dp + Na + V55 + N5) Where: CR= Community Risk RLmvi = Risk Level of Motor Vehicle Incident Ltv = Traffic Volume Level index (from 1 to 10) based on ADT N i = Number of Intersections per mile th = Number of Horizontal Curves per mile ch = Number of Vertical Curves per mile CI) = Condition of Pavement index Cm = Condition of Median index (from 1 to 10) N ,h = Number of Roadside Hazards per mile index (1 to 10) Cm = Condition of Traffic Control devices index (from 1 to 10) RLhmi = Risk Level of Hazardous Material Incident Pex’fllcglcip = Proportion of ADT of Explosives vehicles, Flammable Liquids vehicles, Compressed Gas vehicles, Corrosives vehicles and Poisons vehicles respectively. Multipliers are empirical comparisons of impact of incidents involving such vehicles. Lv = Vehicle Level index Ld = Driver Level index Dp = Population Density index (scaled from rural to heavily urbanized) N a = Number of hazardous materials Actors (generators, etc.) V5 = Dollar Value of property affected NS = Number of Sensitive facilities (schools, hospitals, etc.). 24 This model incorporates data of interest to the traffic engineer such as L“, and th as well as data used by an emergency planner such as DI) and N s but the result cannot be a true measure of risk because it does not incorporate accident rates in the equation. Its value in assessing relative risk is also questionable because of inconsistencies in units of measurement used, such as the addition of dollars, V3 and number of buildings, N 5° Pijawka, et al. [54] assessed the risk of transporting hazardous materials in Arizona. Hazardous material types, volumes and flows were identified. Exposure-miles, defined as the annual mileage traversed by vehicles carrying hazardous materials on a route by route basis, were estimated for each of the major routes in the state. The prevailing accident rate per vehicle mile on each route was estimated and multiplied by the exposure-miles to determine the number of hazardous material carrier accidents per year. Pijawka states that 5% of these accidents result in a release of material (note that others cite values as high as 40% [1]), so the probability of a hazardous materials release is: Pr = .05 . (accident rate/vehicle-mile) . (exposure-miles). A population risk factor was then calculated by multiplying the release probability, P,, with the population at risk, defined as the population within 3 miles of a route. Note that the population risk factor does not consider the health effects of different materials, a uniform health impact is assumed. Clearly this is an area of future refinement, a chlorine release has a much greater impact than a release of the same volume of diesel fuel. Another refinement might be to calculate Pr based on a unit of measurement smaller than an entire route. An attempt was made in the article to correct this shortcoming by introducing a Potential Hazard Rating (PHR) into the equation. PHR is a 25 measure of relative hazard of classes of materials, combining the volume of material shipped in each hazard class and the average evacuation distance for each hazard class. This distance depends upon the physical characteristics of the class of materials. So, some degree of incident severity is taken into account, but since PHR is an index rather than an actual measurement of risk, the results are useful only for comparing the rank order of hazards. Rowe [58] discusses the difficulties inherent in determining ”absolute” risk assessments and the resulting reliance upon ”relative” risk estimates by many models currently in use. He divides the search for absolute risk into two approaches: bottom-up estimates and top-down estimates. In the bottom-up approach, the analyst begins at the finest detail available, looking at the risks of a given shipment of a particular material on one mode along a specific route segment. The accident probabilities are added for each segment along the route until the desired destination is reached. Rowe’s quarrel with this approach is the propagation of errors through the process which can lead to error ranges of orders of magnitude, especially for rare events. In his view, these ruinous errors are introduced through the multiplicative nature of accident probability calculations: risk is usually modeled as the product of a number of factors, each contributing substantial error. For example, risk might be defined as: R=Pi-PS-Ph-Pm-Pe Where: Pi = the probability of an incident occurring P8 = the probability of a particular accident severity class Ph = the probability of release of hazardous material Pml = the probability of specific meteorological conditions Pe = the probability of exposure resulting in damage. 26 Top-down risk estimates use aggregate historic data as the basis for analysis. If data does not exist, models are used to explain causality between accidents and consequences. The major problems with this approach accord- ing to Rowe is that either the data is extremely difficult to obtain or the mod- els used as a substitute are not directly testable. Again, this is especially the case for rare events. Rowe’s conclusion is that, ”More practical analyses have then focused on relative risk estimates for specific situations.” [59] Rowe is disingenuous in his labelling of risk assessment methods as either absolute or relative. Rowe’s definition of ”absolute” risk is actually a definition of relative risk, that is, a method of measuring risk relative to the conditions present. Altering conditions results in different risk values, intro- ducing a new variable into the equation above results in a new risk measure- ment. Risk can only be measured in context, it exists only as a relative value. Rather than absolute risk, this category could be better named true risk or actual risk or real risk (or estimated or approximate ). Rowe’s category of ”relative” risk could more properly be called ordinal risk or risk indices or normative risk since the best that can be obtained from such analyses are rankings of risks (as with Pijawka’s PHR index). Risk of ShippinLRadioactive Material As noted earlier, the risks associated with transporting radioactive materials have long been recognized if not fully understood. One indication of this was the decision to locate radioactive materials processing facilities, utilization facilities and waste sites near each other. While security was of paramount importance, especially at military sites, eliminating transportation risks was a secondary concern. Still, in 1983, Zeigler, Johnson and Brunn [88] 27 noted that, ”The risks of radioactive waste transportation have yet to be adequately assessed, however.” An early study performed by Goodridge [27] summarized transpor- tation accidents involving radioactive materials over a period of fifteen years through 1964 in the United States and the United Kingdom. Two noteworthy observations are made by Goodridge: the first is that during the study period about 1 in 15,000 shipments was involved in an accident, the second is that 28% of these accidents resulted in release of radioactive material and subse- quent contamination of surrounding areas. Also noted in the paper is that while there were 27 serious injuries and 10 fatalities in the 153 accidents examined, none of the personal injury was due to the radioactive properties of the materials carried. Shappert [63] reports 30 incidents involving radioactive materials in transit during the 1968-1970 period in the United States. Half of these acci— dents resulted in the breach of package integrity, 10 of which involved the release of radioactivity. During this time period there were approximately 900,000 shipments of radioactive materials per year in the U. S. More recent information on transportation accidents involving radio- active materials in the United States is summarized by Wolff [85]. This report compiles the results of three accident surveys performed by various research- ers in 1975, 1980 and 1982 as well as incorporating later accident reports. The time frame covered is from 1971 through 1982. 123 transportation accidents were reported. Of these, 12 accidents or 10% resulted in the release of radio- activity due to failure of the packaging. Seven other accidents resulted in packaging failure but radioactivity was not released. The rate of accidents involving radioactive material was quite low since by 1982, 2 million ship- ments occurred annually. All packages that failed were classified as DOT Type 28 A packages or lower. (DOT Type A packaging is not required to withstand accident conditions.) The potential for and the occurrence of this type of incident led to regulations for the packaging of radioactive materials for shipment, the placarding of vehicles and shipment documentation. The International Atomic Energy Agency prepared guidelines for standardized regulations in these areas [35] which were adopted by many member nations. Further experience with shipping incidents such as those related to the 1979 closure of waste disposal sites and concern for the potential consequences of catastrophic accidents caused regulations to be adopted in the U. S. controlling the physical form of the material shipped [74] and suggesting preferred routes for shipment [76]. Are these regulations warranted? Are more stringent requirements needed? Do the existing regulations address the goal of safely transporting radioactive materials? A computer code designed at Sandia National Laboratories (SNL) has proven useful in answering questions such as these. RADTRAN (version 111 is the most current) was written by Taylor and Daniel [72] to examine the environmental impact of transporting radioactive materials by air. It has since been used to model consequences for the ship- ment of materials ranging from spent fuel to radiopharmaceutical sources over a variety of transportation modes. RADTRAN provides estimates for the expected radiological conse- quences due to incident-free transportation and accidents [33]. For accident scenarios, order-of-magnitude estimates of decontamination costs are calcu- lated. The approach used is probabilistic. For example, a shipment may or may not be involved in an accident as determined by an imputed accident rate. In the case of no accident, (the most likely occurrence), the radioactive 29 properties of the material being shipped are used to calculate the dose received by the population surrounding the transportation route. A health effects model estimates the latent cancer fatalities caused by the postulated whole body dose, based on the probability of occurrence of such effects. The consequences of an accident are determined by a given distribution of accident severity, the probability of the shipping container being breached, the fractions of material released and aerosolized, the dispersion of the aerosol based on a distribution of meteorological conditions and finally the health effects model to calculate the uptake of the contaminants by the surrounding population and the health effects experienced. An interesting application of RADTRAN is described by McClure [35]. In this paper, McClure first chooses categories of LLW to ship, then uses RADTRAN to calculate constant unit consequence and unit risk factors for each shipment type. He chose a population distribution of 90% rural, 5% suburban and 5% urban for analysis. The unit consequence factor (UCF) is the exposure received during incident-free transportation of the chosen waste group over the distance of 1 kilometer. Similarly, the unit risk factor (URF) is the exposure per kilometer assuming an accident rate for the transport link. These factors have units of person-rem/ kilometer, so multiplying by the distance shipped gives the expected population dose. In this way routes differing in length can be compared on a radiological basis. It seems that a useful extension to this method is to apply it to a detailed network, with measured input parameters of material shipped, accident rates, population density and segment length. This simulation of the flow of radioactive materials could then be used to route the shipments so that potential impacts are lessened. 30 Integrating Distinct Models or Methods The goal of this research is to integrate disparate methods of analysis in areas such as routing algorithms, health physics, traffic safety and risk assess- ment to provide a basis for the selection of a low-level radioactive waste disposal site. While this has not yet been attempted, some examples of inte- grating analysis methods do exist. In his overview of the transportation of radioactive materials, Wolff [36] provides values for unit risk and unit consequence factors for the radiological and nonradiological impacts of shipping radioactive waste. The set of radiological factors were calculated with RADTRAN, the nonradio~ logical factors were calculated using a line source pollutant dispersal model and a health effects model. Cashwell, Joy and McGuire [40] combine the routing models HIGH- WAY and INTERLINE with a logistics model. The Nuclear Materials Trans- portation Logistics Model schedules shipments, optimizes destinations and packaging choices and calculates capital and operating costs. The combined models are used to generate spent fuel flow density maps of the United States under varying assumptions. The transport of high-level waste (HLW) as studied by Neuhauser, et al. [41] provides an opportunity similar to LLW transportation for the inte- gration of analytical methods. Again, HIGHWAY and INTERLINE were used to route HLW shipments based on minimized travel times. The demand for HLW shipments was calculated using a simulation model, WASTES. Capital and operating costs were modeled for both truck and rail transport modes. Finally, RADTRAN was used to provide unit risk and unit consequence factors for risk analysis. This analysis was performed after the shipping routes had been determined with the routing algorithms. 31 Voth [42] prepared a dissertation combining existing models to deter- mine optimum LLW disposal site and technology combinations. In this research, candidate disposal sites were chosen throughout Pennsylvania. The environmental impact of each site was modeled with the EPA-PRESTO com- puter code. Transportation impacts were estimated by first categorizing waste shipments, using RADTRAN to determine unit risk and unit consequence factors for each category and then multiplying the unit factors by the distance between the appropriate generators and disposal site. The distances were esti- mated by the Pythagorean theorem applied to a Cartesian coordinate system. Finally, Saccomanno and Chan [43] have studied alternative routing strategies for hazardous materials in Toronto. Three strategies were exam- ined: minimize truck operating cost, minimize accident likelihood and min- imize objective risk exposure. The operating costs included only the salaries and out-of-pocket expenses borne by the truck operator. Accident costs were ignored since they rarely occur and so are usually not part of the route decision process. The routes selected to minimize costs were those that would exist in an unregulated environment. They were used as bases for comparison. Minimizing accident likelihood called for the consideration of two influences upon accident rates: deterministic effects and stochastic effects. The deterministic influences were mainly the geometric design characteristics of a given roadway link. The stochastic influences dealt principally in wea- ther and visibility conditions. It was assumed that these influences were independent and that the probability of truck accident occurrence could be expressed as the joint probability of a truck accident for a given set of deter- ministic and stochastic influences. The accident probability for a route is the sum of the link probabilities. 32 The objective risk exposure, or absolute risk exposure, was defined as the product of the accident likelihood and the consequences of an accident. The consequences were determined by an airborne dispersion model for toxic materials, by the size of a flammable vapor cloud for flammable material and the blast effects of explosive material. The risk exposure was estimated for all possible stochastic conditions and the results summed for each route. The city of Toronto was divided into eleven zones and the minimum path between each zone centroid was generated for each of the routing stra- tegies. Minimizing operating costs resulted in the largest use of arterial roads at the expense of increased risk. Minimizing risk caused the central business district to be avoided and increased the use of expressways. Higher operating costs also resulted. Minimizing accident likelihood resulted in both increased costs and increased risk exposure in almost all cases. Support for the Current Research This literature review has shown that: 1. Routing algorithms exist, 2. These algorithms have been applied to shipment of hazardous materials with distance or travel time as the decision variable, 3. Attempts have been made at quantifying transportation risk through either relative or indexed measurements, 4. Some studies have combined routing hazardous or radioactive shipments and risk assessment, 5. No attempt has yet been made to use risk estimates as the decision variable in routing radioactive shipments. Chapter 3 RISK and PHILOSOPHY What is risk? Can it be measured? Is a certain level of risk acceptable or tolerable? Who is to bear the risks in life? These questions must be answered (or the attempt made) before proceeding. Defining Risk The common meaning of risk is exposure to danger or loss. Webster [82] defines risk as, ”the chance of injury, damage, or loss; dangerous chance; hazard,” injecting the element of probability into the formal definition. The magnitudes of the chance and the loss are left open for argument. Few of us have an intuitive feel for probabilities, instead events are viewed as black or white, if a risk is accepted we ”expect” something to interfere with our plans or conversely we ”expect” to succeed completely with the loss confined to ”the other guy.” 33 34 Statisticians have taken risk to a more neutral ground: they define risk as the expected value of all possible outcomes of an event [57]. The risk function is: R=2m'0i where: pi = the probability of occurrence of outcome i Oi = the magnitude of the consequences of outcome i. The summation is performed over all possible outcomes i. This definition includes both positive and negative outcomes, that is, the expected value of a wager would include possible gains as well as losses. The definition of risk used in the literature dealing with the risk of technology ranges from the popular to the statistical, depending upon the author’s point of view and purpose. Langdon Winner [83,84] chooses to view risk strictly in terms of hazards. Nicholas Rescher [57] uses the expected value of all outcomes to define risk. William Lowrance [50] falls in the middle, believing that risk is best defined as a measurement of the probability and severity of the negative or adverse outcomes. How can the literature hold such a broad definition of risk? The answer appears to be two-fold: 1. The definition of risk is limited by the perception of risk. 2. The definition of risk chosen is the one which best supports the author’s argument or purpose. Perceived Risk Perceiving is Understanding Decisions are made by weighing alternatives with knowledge and experience as bases. A decision to take a risk is no different. Even impulsive 35 decisions involving risk-taking are based on what we have learned. Darting across a busy street to buy a lottery ticket is not a random, baseless action. Senseless perhaps, but we knew that we would not find a parking spot across the street, we knew that we would not be struck by a car and though we knew we would not win the lottery, ”Where else can I turn a buck into 40 million?" The gestalt of this situation is so strong that we recognize it immediately. No overt cognitive process need have taken place and yet, at some level, risks were weighed and a decision made. Imprinted upon our memory is that which we have learned, providing a basis for future behavior. In response to a stimulus, we sift through the memories, searching for a similar situation. More often than not, the decision reached will be based on the analogous experience. The decision-making process is colored by the stimulus received and the image retrieved, that is, our perception of the situation. Judgments about possible outcomes of a situation are biased by exper- ience. Lack of experience can cloud judgment. Still, experience remains the basis and so a memory may be stimulated which has no actual relation to the perceived situation. An extraordinary event like the explosion of the space shuttle Challenger might later be associated with an impending airplane flight, even though the two have almost nothing in common. The lingering image of the fireball hanging in the sky may cause an individual boarding a plane to perceive the risk of flying as much higher than it actually is. Perceived risk may significantly differ from the ”true” risk. Distortion may occur by assigning high probabilities to extremely rare events. Potential loss may be judged as severe when in fact, little is at risk. Any distortion in the perceived risk can lead to behavior which might be called irrational by an observer with a different perspective. (An omniscient observer would of course recognize the limits of human perception.) Whether irrational or not, 36 the behavior follows from the perception of risk and so is justified teleologically if not morally. If there is disagreement between observers, it is the perception of risk and the knowledge base that should be examined for differences rather than the action taken as a result of the risk. Perception versus reality of risk (defined as hazards of technology) is g g discussed by Zeigler, Johnson and E; 2 Brunn [89]. They present a graph sim- f1; ilar to figure 3, relating the perception g of a hazard to the reality of the situ- g 8 ation. In an ideal world, we would all 2623 None D Severe live within the shaded squares along Reality of the Hazard the diagonal, assigning to each risk Figure 3. Perception vs. Reality encountered its ”true” value. Of course this is not how the universe operates, some of us exist off the diagonal. Furthermore, the ”true” risk may not be objectively knowable, in other words, the perception is the reality. The subjectivity inherent in perceiving, that is sensing and interpreting events, colors the reality of the situation even as the reality shapes the perception. Perhaps the graph would better reflect the situation if reality and perception were not depicted as independent (orthogonal) variables. Nevertheless, instances of perception not matching ”reality” do exist. Zeigler, et al. give examples. For the case in which the perception of risk was higher than necessary they mention the supersonic transport (SST) debate: The SST’s impact on the earth’s ozone layer was perceived in the early 1970’s to be so severe that the technology was rejected by the U. S. Congress. Some recent evidence suggests, however, that high-flying SSTs may actually encourage the formation of ozone rather than breaking it down. 37 At the opposite extreme, in which the actual hazard is much worse than perceived, they cite the health effects of the Rocky Flats nuclear weapons plant: Johnson [42] used the plutonium content of the soil around the nuclear installation-as a measure of cumulative exposure, 1953-1971. ...Exhaust from the plant’s smokestack was the primary source of plutonium so that the configuration of the hazard zone is a function of wind direction and distance from the source. ...Johnson calculated the percentage of excess cancer deaths, 1969-1971. He found a higher incidence of all cancers near the plant and a decided distance decay effect with decreasing concentrations of plutonium. ...Had the residents around Rocky Flats recognized the true configuration of the contoured risk surface, measures might have been taken to further reduce the release of radionuclides from the smokestack The authors conclude that public policy should be formulated first to draw risk perception versus reality to the diagonal of their diagram and second to reduce the zones along the diagonal toward the origin. In other words, policy initiatives should align the perception of risk with the actual risk and then the risks of technological ventures should be driven to zero. My conclusions from this figure deal not with future policy initiatives but with the errors made in current policy decisions due to differences in perception and reality. If the reality of the risk is large where none is seen, the error is that a dangerous venture may be accepted resulting in unwarranted exposure to risk. On the other hand, if a risk is perceived as large when actually it is trivial, the error is that a worthwhile venture might be rejected or that effort is made to reduce an already minute risk. Alternatively, concentration on an overestimated risk can cause us to ignore issues with large inherent risk, especially those existing below the diagonal in Zeigler’s diagram. Figure 4 summarizes the conclusions I have drawn from the work of Zeigler, Johnson and Brunn. In either case the perception of risk has led to an error in judgment. Which area represents the worse error? What is risked by the faulty 38 perception of risk? It seems that being below the diagonal might be a more immediate and perhaps fatal error. Erring above the diagonal appears to result in only economic consequences, but being above the diagonal may also lead to stagnation and stultification which, in terms of the human race, may be the more grievous error. Perceiving is Sensing To perceive also has the denotation of becoming aware through the senses and the ability or inability to detect a hazard with the senses certainly affects the perception 0.) 8'3 Worthwhile > . 3 technologies ' ed ,3 ‘ reject :3 t6 :1: . q) Reduction of '5 non-existent H- o a Dangerous .9 technologies % accepted 8 Q) a. Q Unwarranted g risks taken 2 5 Severe Reality of the Hazard Figure 4. Errors Resulting from Incorrect Evaluation of Risk of risk. This is one factor keeping any activity involving radiation in the realm of perceived risk exceeding real risk. Because we cannot directly sense the products of radioactive decay, we must rely on technology to provide the senses. The proper tool, properly used, will detect radiation, but are the tool 39 and the technician to be trusted? This is the argument put forth by those perceiving the risk to be great, at least greater than that perceived by the tech- nician. The perceptions here are still marked by experience, the technician deals with radiation and instruments daily and so is familiar if not comfort- able with the risk. The nuclear opponent is dealing with a rare event or an abstraction, the only references available are Chernobyl and Three Mile Island. Radiation is not the only subject leading to distorted perceptions of risk. Each year a number of welders or construction workers die because they entered an area with an oxygen-poor atmosphere. Their senses could not warn them that the oxygen had been displaced by argon (to prevent oxidation during tungsten inert gas welding), incapable of supporting life. Their sensory perceptions had skewed their perception of risk in the opposite direction, the perceived risk was much lower than the actual risk. (It is this type of error in perception, thinking risk is lower than it really is, that provides the driving force for those who see risks as being greater than they actually are. In reaction to the fear of erring on the side of accepting more risk than originally thought, some individuals will give an event a large risk value where little risk is present. We fear too much the unfamiliar, we fear too little the familiar.) Culture and Beliefs Determine Risk To this point I have explained the nebulous nature of risk, how the concept varies with the definition used and the perception experienced. Next we will see how a person’s beliefs and role within society form the basis for deciding what is a risk and what is not. 40 Cultural Perception Douglas and Wildavsky, in their essay entitled Risk and Culture [18], repeatedly make the point that, ”T he perception of risk is a social process.” They state that certain types of social structures stress particular types of fears or risks. Their argument is that society is formed through the organization of social relations. Organization implies choosing. Choice implies prioritiza- tion and ordering. Some things are of high rank and stressed, others are ignored because of their unimportance. This applies to all decisions made by a society, including the decision as to what should be considered risky. That is, a society selects the activities to be viewed with collective fear, it chooses its risks. Douglas and Wildavsky give examples of cultures selecting their risks. For instance, they describe the Lele of Zaire. Although these people were often inflicted with terrible tropical diseases, they focused on the risks of being struck by lightning, suffering from infertility and being afflicted with bronchitis. Illnesses more severe than bronchitis and more likely to occur than lightning strikes are nevertheless regarded with less fear. Cultures choose their demons. Relativism The idea that risk or perception of risk depends on one’s point of view is, of course, a relativistic approach. Relativism is apparent not only between cultures but also within a culture. To see this, we can employ one of Einstein’s favorite techniques when dealing with relativity, the thought experiment. Within our society, a person’s economic or social condition may affect the perception of risk and the likelihood of accepting a risk. Someone living 41 in poverty might accept a risk that would be unthinkable for a person of wealth, even if the two individuals have fundamentally the same beliefs and values. The difference in risk acceptance originates with the viewpoint. Suppose, for example, that an unemployed father of four is offered a job as a coal miner. He accepts the position to provide for his family. Suppose however that the position was first offered to the Chairman of the Board of General Motors. Does he accept the new challenge? Not likely. Inter- changing the individuals, however, results in a swapping of risk acceptance behavior. Acceptance is relative to the situation. The viewpoint also changes according to differences between value systems within a single culture. Douglas and Wildavsky [20] identify two distinct approaches to Western culture: the market and the bureaucracy. The first is populated by individualists, the second by those who are comfortable in a hierarchy. Risk acceptance again flows from the conditions. The bureau- crat’s opinion of risk in a given situation may be very different from that of the small businessman. If any risk acceptance behavior can be rationalized by calling upon relativism, is it possible to set aside a group of activities that may be considered ”safe”? Or must we accept the lowest common denominator, that is, no activity is safe if any one person says it is not? Cultural Consensus Within a culture it is possible and necessary for a consensus to be reached. Agreement is needed on, at the very least, a range of acceptable risk- bearing activities. This returns us to the process of social organization proposed by Douglas and Wildavsky. Just as a culture can agree on what is to be feared, it can agree on which activities are acceptable. If an individual or ”AH“ ”.ydb A .5“ a“ As-oI\“ Conse M““ .‘I \r’ byohya 42 group engages in activities excessively risky, then those involved can be removed from the culture in one way or another. In The Calculus of Consent, Buchanan and Tullock [3] show the mechanisms by which a society of diverse individuals can reach a consensus. They show that unanimous consent need not be reached as long as rules exist which allow social groups to bargain over ”externalities” such as risk. Thus risk can be traded against insurance costs or another external cost to allow for agreement. That agreement can be reached is empirically evident. Both the Lele and our own culture have been able to come to broad agreement within themselves as to the risks to be accepted and those to be avoided. To reach agreement, a wide range of viewpoints (economic, philosophic, social, reli- gious, scientific, politic) need to be accommodated. Choices must be made. Lovborg: ”. . . and this book deals with the future.” Tesman: ”With the future. But, good heavens, we know nothing of the future!” Levborg: ”No; but there is a thing or two to be said about it just the same.” Henrik Ibsen. Hedda Gabler. 1890, Act II. Choice and the future are inescapably linked, to choose is to decide along which path the future lies. Each of us has a view of the future colored by our beliefs and views. That is why a workable consensus on any topic including risk can follow only from consideration of the viewpoints men- tioned above. To ignore any of these viewpoints is to ignore the picture of the future held by part of society, with a resulting lack of support for any decision made. The need to consider a society’s collective view of the future before choosing its course may help explain the differences between cultures, our view of the future differs from that of the Lele, and so the risks we choose to worry about differ. hu' vmu lull I A (‘1.- ‘ o-I ukd V hnl bucl v i« -l “4.: . .\ m4 N 1.. 7.)“ my 1} i‘ur ‘k u " 43 Cultural Issues to Resolve A number of issues recur in our intracultural negotiations on risk. These issues spring from the perspective each discipline brings to the negotiation. Control over the acceptance of a risk, distribution of the risk imposed, measurement of risk, the desired socio—political structure and decision-making process, the value of a life, the value of a species, the role of technology in our lives; these are some of the recurring issues to be argued and negotiated. These issues are intricately entwined, woven into a fabric of cultural transactions. The control over risk acceptance, the equity of risk distribution and the role of technology are tied in with the type of socio—political structure employed. The decision—making process influences how risk is measured and what value is to be placed on the outcomes of an activity. The interactions involved are complex and cannot be severed. Control and Voluntary/ Involuntary Risk The issue of control over the acceptance of a risk follows from the argument that some risks are imposed involuntarily and that these risks are inherently different from those freely accepted. Evidence exists showing that the sense of control over a situation or choice influences the magnitude of risk accepted [61,69,70]. The risk of death or injury due to voluntary activities (smoking, occupation, driving, etc.) are an order of magnitude or more greater than the risks due to involuntary hazards (floods, volcanoes, lightning, etc.). Control of the decision, that is, conscious consent to an activity apparently causes us to be more receptive to risks than if the risk is imposed by an outside force. Seemingly, accepting the authority of the decision leads to acceptance of the responsibility for the outcome. Does this mean that if we were in control of floods and tornadoes we would accept ‘A". T”. Um.» inih‘ hiw‘: .VV‘ 6". 1;. .sn', v v... “If“: 44 greater risk from them? Do we actually accept the possibility of a hazardous outcome from a decision we make? I do not think this is the case. I believe instead that each of us truly feels that no harm will come to us due to our decisions. Only favorable outcomes are acceptable to us, even if we are fully aware of the hazards before we decide. Unfavorable outcomes are unac- ceptable and are the responsibility of others (e.g. government, a corporation, another individual). Judith Jarvis Thomson [73] supports this argument through an exam- ple she gives in ”Imposing Risks.” Imagine there are two routes home from work. One is a long, safe walk through a brightly lit middle-class shopping area. The other is a short walk along Unpleasant Way, through a poorly lit warehouse district known to be infested with muggers and other assorted reprobates. Thomson places herself in the example and knowing the risks involved, decides to walk through the warehouses because the longer walk would be too tiring. No duress, compulsion or coercion is felt while deciding. Of course, upon entering Unpleasant Way she is immediately mugged. She asks if she should not have grounds for complaint if not against the city then at least against the mugger. She holds that she did not consent to being mugged by an individual or to the imposition of risk of mugging by such a person. She contends that she did not consent to the dangerous nature of Unpleasant Way at night nor did she consent to the case that if she walks Unpleasant Way at night she is placed in risk of being mugged. Thomson instead says that she consented only to walking Unpleasant Way at night, even though she knew its danger. In other words, she is willing to accept the responsibility for the outcome only if it is favorable, if she gets mugged then it is proper to blame the mugger or the city. 45 This is precisely the behavior I referred to earlier, denial of respon- sibility if the untoward happens, acceptance of responsibility if and only if the outcome is what we wanted. This behavior is exhibited by both individuals and bureaucracies. A cigarette smoker wonders, ”Why me?” when the diagnosis is terminal lung cancer. A gambler asks why he wasn’t stopped by management before losing his life savings at the Las Vegas craps table. A speeding driver spends the rest of his life in a wheelchair because the road commission did not install a guard rail to keep him from hitting the bridge at 90 miles per hour. This type of behavior is not rare and isolated, it is the order of the day. In Catch-22, Yossarian vowed to live forever or die trying [29]. It is all any of us can hope to do. None of us truly accept our mortality, a few perhaps are resigned to it. The issues of control, voluntary risk or involuntary risk are merely constructs enabling us to rationalize away our own responsibility for our losses. My conclusion is that the debate over control, voluntary versus involuntary only touches the surface and draws attention away from deeper, more productive discussion. Douglas and Wildavsky [19] also regard the debate over control as specious: ”Voluntary/ involuntary is a movable boundary, capable of turning every constraint on choice into injustice.” That is, the person, the culture and the person’s situation within the culture determine what is regarded as a voluntary or involuntary risk. The rich might consider air pollution an involuntary risk but the poor may find industrial pollution more acceptable than being unemployed. Douglas and Wildavsky find that, ”Either invol- untary risk is an empty logical category, or it has to be a complaint against the particular social system which gives some people a harder life.” Douglas and Wildavsky hold that the distinction between voluntary and involuntary risk can be made only if the cultural structure is stagnant, 46 frozen for all time. If that is the case then all activities, risk-generating or not, are predetermined by the structure and so every activity is involuntary. Douglas and Wildavsky reduce this argument to its absurd conclusion using a society modeled after ours, but possessing a petrified social system. Any risk that is involuntary and unjust would be relieved by law. Because all risks could be regarded as involuntary, all responsibility would be treated this way until all losses are compensated by the society’ 5 institutions. The culture is responsible for all actions, the individuals are not. I disagree with Douglas and Wildavsky’s interpretation that all risk is voluntary within a culture’s set of rules in only one particular case. Hazards that are greatly displaced in time from the initiating event seem to fall into the involuntary category whether or not society tries to represent the views of future generations in social transactions. Recall Lovborg’s statement in Hedda Gabler bear in mind however that the future cannot disagree with what we say about it. The decisions of today present future generations with a fait accompli and we have no way of knowing whether our interpretation of their wants and needs is correct. Will they judge as we do conditions that we believe are acceptable? Or will they find our decisions to be totally wrong? Future generations cannot represent themselves today in our cultural negotiations and have no way of correcting our mistakes. As an example, perhaps we should have taken the opportunity presented by OPEC to eliminate the use of petroleum products as fuel, reserving those products for petrochemical production now and in the future. Not doing this may place future generations at risk with respect to materials necessary to support their lives in exchange for an economical means of supporting our lives. - t I.“ Ms“ A ‘1 it)». ”I n. l u in. .3 U 47 Distribution of Risk The distribution of risk is closely tied to both the social structure and the chosen boundary between voluntary and involuntary risks. Zeigler, et al. [90] show the geographical distributions of some risk—bearing activities. One set of maps show that hazardous material incidents are highly correlated (r = 0.83) with population distribution on national and state levels. On the surface this appears to be an equitable distribution of ”involuntary” risk. An individual’s exposure to this risk is roughly uniform, independent of location. Categorizing the incidents by type reveals another factor for consid- eration, low population areas were more likely to see transportation incidents while high population areas were exposed to a higher rate of handling and processing incidents. So, policies designed to lower the rate of industrial inci- dents while ignoring transportation would cause the distribution of risk to skew to lower population areas. Public policy affects the distribution of risk. At the local level, the incidents were strongly correlated (r = 0.73) with the location of industry. The risk passes from involuntary to voluntary at this level of detail, industrial workers ”choose” to accept the risk as part of the job whereas a member of the general populace probably did not choose to live near a hazardous stretch of railroad track involved in a derailment of chlo- rine tank cars. Working at the local level, it might be decided that nothing should be done to reduce the number of incidents because the risk is borne by those gaining the benefits of the associated activities. Another map reproduced by Zeigler, et al. projects the distribution of fallout in the United States following a nuclear war. The low population density region of the Plains States is subjected to a disproportionate risk of fallout because of the prevailing winds and the concentration of strategic military bases in the region, that is to say, targets. The ultimate price of 48 defense appears not to fall equally upon the citizens of this country. The socio-political structure has placed the residents of the Plains States at risk in return for greater security for the country. A final diagram illustrates how technological hazards can be displaced in time as well as space. Figure 5 is derived from Zeigler, et al. [91]. Tech- nology A is displaced in both time and space from the hazard it generates. Technology B is displaced in time only, while technology C is displaced in space only from its hazards. Technology D exhibits displacement in time and space by varying degrees. The hazard associated with technology E is exper- ienced at the same place and time occupied by that technology. Displacements of either type can lead to conflict. As mentioned earlier, temporal dislocation can place unwarranted burdens on future generations. Spatial displacement leads to the issue of risk distribution. §@ 6 o ©——>© 9 ° 150 0 SPACE ® =Technology ()9 = Hazard Figure 5. Displacement of Hazards in Space and Time 49 These examples show the interaction among the various disciplines (political science, engineering, philosophy, ...) needed to resolve the issue of risk distribution. The social imperative draws people together into com- munities. Economics causes industries to be clustered near the population served, just as those industries act as magnets drawing people to them. Science gives us the techniques to build the industries and mitigate accidents. Politics and economics close some paths opened by science while allowing others to remain open. Political pressure places hazardous activities in areas of low population because they are far removed from the coasts or simply because the population is low or to attract industry and population to the area. Enumerating the interactions might take forever and still leave the questions of how, why and to whom risk is distributed unanswered. To deal with these questions it is necessary to place them in a cultural context. Just as voluntary/involuntary is a movable boundary, the equity/ inequity boundary varies with the circumstances. In fact the question of equal distribution of risk depends upon the boundary set for voluntary/ involuntary risk. It makes no sense to speak of the equal distri- bution of voluntary risk, equity presupposes involuntary risk. An individual exposed to what he would consider an involuntary risk does not want to be singled out for exposure. Better still would be no exposure, whether his neighbor’s exposure is relieved or not. (In other words, he would like to be a ”free rider” and not be exposed to the risk while still gaining any benefits associated with the risk-generating activity. ”Not in my back yard!” is the slogan of the free rider.) As an example, a wealthy individual might find a vacation home on Florida’s Gulf coast enjoyable, that is until a hurricane destroys it. Not as enjoyable would be rebuilding it with his own funds, federal disaster relief would be a much better system of paying for repairs. Of 50 course, if his investment position allowed him to escape taxes, then so much the better, as long as the factory line—workers in the north continue to pay theirs. Clearly the situation is asymmetric, the vacationer’s judgment on equity of risk distribution would undoubtedly reverse if the situation was reversed and it is unlikely that the northern factory worker would ever say that the risk was distributed equally if any relief program is established. Once again, the culture, the person and the person’s status within the culture determine what is or is not an equitable distribution of risk. The Desire to Shape Society Arguments over the voluntary versus involuntary nature of risk or over the distribution of risk throughout society are merely smoke screens. The real issue is this: who decides; who shapes the future; who wins. Behind every risk debate, on any side of the debate, is a hidden agenda. The argu- ments put forth by each side of the debate are molded by the beliefs of that side, by their desire to see society fit those beliefs and by their vision of the path leading them to this promised land. Are there no neutral observers of life? No dispassionate jurors waiting to decide our fate? No indifferent and aloof navigators charting the course to the future? Quite simply, there are not. As Wordsworth [86] said, ”The Child is father of the Man,” and so each of us brings to the debate on risk our acquired learnings and beliefs. The arguments we put forth reflect these beliefs, the decisions we make support our beliefs. Like Heisenberg, we are forced to realize that no neutral observer exists, the very act of observing affects the system being observed. Societal values and our own values for society affect our perception of risk which, in turn, affects societal values. How risk is to be measured and the units of measurement to be used are also 51 affected. The viewpoints taken in the risk debate are not pure and absolute, instead they are infected by the debators’ beliefs about the past and their desires for the future. The desire to create a society attuned with our beliefs fixes the stand each of us takes in the debate on risk. Vivid examples of this assertion exist. During the 1970’s, in the midst of the energy crisis, a vituperative debate on the future of energy sources ran between proponents of coal and nuclear power and proponents of renewable energy sources. Lovins [48,49] coined the term ”soft energy” for renewable energy sources, painting the technology as warm and cuddly, easy to build, use and maintain. His future world was decentralized, with people living near their food supplies and jobs, using little energy, staying at home and being perfectly happy. In his analysis of the risks of this lifestyle he not surprisingly found the major risks to be from the technologies and lifestyles currently practiced. In his studies however, Lovins chose to ignore some sources of risk and uncertainty, such as the use of toxic materials in photoelectric cells or the risk due to frequent interruption of power, issues that would not support his claims. Coal and nuclear proponents were quick to pick up the gauntlet, Inhaber [33,34] recalculated the risks of renewable and conventional energy sources and found that renewable energy sources had risks that were orders of magnitude greater than almost all conventional sources. Inhaber reached this conclusion by including in his analysis the materials used for construction of energy sources, labor and transportation accidents and an allowance for the loss of power due to the intermittent nature of renewable sources. Inhaber, then an employee of the Atomic Energy Control Board of Canada and later with Oak Ridge National Laboratory, concluded that centralized energy production and distribution systems were to be favored. Holdren et al. [31,32] responded by claiming that 52 Inhaber placed too much emphasis on the risk of losing power and that Inhaber’s solution of having coal backup systems for the renewable sources created most of the risk due to renewables. The debate continued with both sides choosing to ignore risks or methods injurious to their cause. No one ever suggested that perhaps a combination of technologies would produce both lowered energy use and reduced risk. Such an idea would have been antithetical to both sides, a hybrid social and technological structure was unacceptable. . Winner [83] would have advised Lovins and Holdren, ”. . . to think twice before allowing the concept [of risk assessment] to play an important role in their positions on public issues.” Winner prefers to speak in terms of hazards rather than risks since hazards can be agreed upon [84]. By way of example, he states that New Englanders, ”are under no obligation to begin analyzing the risks of acid rain; they might . . . confound the experts by talking about ’that destructive acid rain’ and what’s to be done about it.” Since his beliefs do not support the type of risk analysis performed by Lovins, Inhaber and Holdren, that is the weighing of costs versus benefits of an activity, Winner is able to eliminate an entire side of an issue. In Winner’s version of the world, the hazard of unemployment for people in the Ohio Valley is not an issue of concern to New Englanders being rained upon. Lowrance [50], Rescher [57], Shrader—Frechette [64] and Fischhoff, et al. [25] all believe that risk assessment in one form or another is useful. The form of risk assessment generally supported in the literature is cost-benefit analysis or risk-benefit analysis. As alluded to earlier, this formal analysis weighs the benefits of an activity against the costs of that activity. The sources of conflict are immediately apparent, the benefits and costs must be defined, units of. measurement agreed upon, weighting factors determined, 53 methodologies confirmed, models calibrated and on and on. The scope of this task is an endorsement for Winner’s argument, for the sake of simplicity if for no other reason. Furthermore, no amount of calculation will assuage the anxieties of those biased against the questioned activity in the first place. Another bias which can not be overcome is that held against the group performing the assessment, whether that group is a bureaucracy or a business. Yet, for all of this, risk assessment has become widely accepted and practiced within our technological culture. This is because risk assessment as practiced today tends to support the status quo, just as Winner states [83]. The hand sculpting society seeks tools which will complete the work as envisioned by the sculptor, not as envisioned by the critic. Is it possible for risk assessment (or any technical method) to be neutral and objective? Invoking Einstein and Heisenberg again, we realize that just as there are no neutral observers, there are no neutral analysts. Fischhoff, Lichtenstein and Slovic [24] address this question indirectly while searching for ”acceptable” risk: That choice depends upon the alternatives, values, and beliefs that are considered. As a result, there is no single all-purpose number that expresses ”acceptable risk” for a society. Values and uncertainties are an integral part of every acceptable risk problem. As a result, there are no value—free processes for choosing between risky alternatives. The search for an ”objective method” is doomed to failure and may blind the searchers to the value-laden assumptions they are making Not only does each approach fail to give a definitive answer, but it is predisposed to representing particular interests and recommending particular solutions. Hence, choice of a method is a political decision with a distinct message about who should rule and what should matter. Shrader-Frechette [65] examines the ethical and philosophical aspects of positivism (i.e. complete objectivity and neutrality) and concludes that such behavior is not only impossible but that it is not desirable in risk assessment and so should not even be attempted. 54 Where Does All of This Lead? If objectivity and neutrality do not exist, if the definition of risk depends on who is doing the defining, if our beliefs and desires shape our evaluation of risk, is there any point in dealing with risk and risk assessment as research methods? Can meaningful research be performed with risk assessment as its basis? I think the answer to both questions is yes. To clarify the issues surrounding the use of risk and risk assessment, Shrader-Frechette [65] recommends that four elements be added to risk or technology assessment methods: 1. Explicit admission of the methodological, ethical, factual, and theoretical assumptions upon which the technology assessment (TA) or environmental- impact analysis (EIA) conclusions are contingent; Use of much broader and much more varied social indices; Employment of an adversary system of TA and EIA; Evaluation of alternative philosophical positions on various policy options. 9‘9“!" When dealing with risk and risk assessment, the basis for decision must be kept in mind. Following Shrader-Frechette’s first recommendation, this basis should be stated directly, as with any other assumptions affecting the results of an analysis. No apologies need be made for the basis used. When confronted with work in the area of risk in which assumptions are not explicitly stated, it is not unreasonable to be skeptical, to search for the hidden agenda behind the results. This is not to say that such results should be ignored or discounted, only that the path leading to the results may be as important as the results themselves. Guidance concerning the use of risk assessment may be obtained from Douglas and Wildavsky [18]. They view risk as the ”joint product of knowledge about the future and consent about the most desired prospects." (Italics in original.) From this they derive a matrix (figure 6) outlining four problems associated with risk and the avenues to solving the problems. ““915: a iia': r _) .‘r. r.- n ('w 55 KNOWLEDGE Certain Uncertain Problem: Problem: {3 Technical Information '5. CE, Solution: Solution: U E— Calculation Research 2 m an 2 8 Problem: Problem: '8 Disagreement Knowledge and 2m: Consent :3 Solution: Solution: U Coercion or ? Discussion Figure 6. Four Problems of Risk If consent exists, then risk assessment appears to be a viable and appro- priate tool, within the limits of knowledge. It is when consent does not exist that risk assessment fails as a tool and instead becomes an issue of debate, part of the problem rather than part of the solution. Following the course set by Shrader—Frechette and Douglas and Wildavsky, the use of risk assessment techniques to site LLW repositories is appropriate. The final section of this chapter lists the basis for this conclusion. Basis for the Current Research This research is based on the premise that consent has been reached concerning both the need to dispose of LLW and the need to maintain industries and facilities that generate the waste. This consent springs from the Congress of the United States as seen in the Atomic Energy Act of 1954 56 and the Low Level Waste Policy Act of 1980. Consent has also been reached on the risks of radioactivity. The International Commission on Radiological Protection and the National Academy of Sciences provide methods for assessing those risks [12,26,35,36,37,38,39,40,66,79]. The assumption is made that the risks due to contact with radioactive material and the costs of transporting such material can be stated in terms that will allow the risks and costs to be combined. Finally, the philosophical framework for this research is utilitarianism-to seek and choose the course of action that promises the greatest good for the greatest number. Chapter 4 RESEARCH METHODS Overview The method to be used in assessing the risks and costs of transporting LLW consists of four major subcomponents: a LLW shipment inventory, a transportation network description, a radiological risk assessment model and the optimization algorithm. The first two subcomponents are data sets. This chapter gives in general terms the parameters needed to describe the LLW shipment inventory and the transportation network. Data specific to the Midwest Interstate Low Level Radioactive Waste Compact (MILLRWC) are contained in appendices. The second pair of subcomponents are analytical methods, using the data contained in the LLW inventory and the transporta- tion network. The risk assessment model and optimization algorithm are described in detail in this chapter. 57 58 Low-Level Waste Shipment Inventory The parameters needed to describe LLW shipments in a region are largely dictated by the requirements of the risk assessment model and the optimization algorithm. These parameters are: 1. Generator Location: The geographical location of the LLW gener- ators in the region. 2. Waste Form: The form of the waste generated at each site (e.g. irradiated reactor components, immobilized scintillation liquid, compactible waste, etc.) and shipped for disposal. The packaging requirements are useful for distinguishing between waste forms (e.g. shielded cask, LSA box, etc.). 3. Isotopes Shipped: The isotopes contained in each waste form listed above. 4. Volume Shipped: The volume of each waste form shipped annually. 5. Annual Shipments: The number of annual shipments of each type of waste form or package. 6. Curie Content: The quantity of Curies of each isotope per shipment by waste form. This data can best be obtained through a survey of the generators in a region. Some broad surveys have been performed in the past by various federal or state government agencies, but generally these do not provide the level of detail needed. These surveys also do not usually reflect the volume reduc- tion programs implemented or planned by many generators. Surveys per- formed by the regional compacts will be more likely to contain current data and the level of detail needed by the optimization method described in this chapter. Some of the necessary waste shipment parameters may be derived from others. The number of annual shipments may be obtained from the annual volume by using the average truckload for each shipment type. The 59 Curie content per shipment may be estimated by the average shipment con- tent of each waste form, or perhaps based on another factor, such as the great- est quantity expected to be in a single shipment. The risk analysis model requires the identification of the waste forms (package types) and isotopes shipped. The optimization algorithm uses the results of the risk assessment model in conjunction with the generator loca- tion, the Curies shipped and the number of annual shipments in the routing of shipments. Appendix A presents the LLW shipment inventory for the MILLRWC as obtained through a survey conducted by ERM-Midwest, Inc. Transportation Network As with the shipment inventory, the parameters necessary to describe the transportation network are primarily dictated by the risk assessment model or the optimization algorithm. The network parameters required are: 1. Node Identification: Identify and geographically locate each node on the network. 2. Link Identification: Identify connections between nodes. 3. Link Length: Distance between linked nodes. 4. Population Density: The population density surrounding each link. The area within 5 kilometers of each link is used to calculate the density. 5. Population Density Classification: Classify link as urban, suburban or rural. The risk assessment model makes use of this system of classification as well as requiring a representative value of population density (mean, mode, etc.) for each class. 6. Commercial Vehicle Accident Rate: The rate of accidents involving commercial vehicles on each link expressed as number per commercial vehicle per unit length. 60 Nodes, links and link lengths can be obtained from maps. The most likely source for the remaining information is the Department of Transportation in each of the states spanned by the network. If necessary, commercial vehicle accident rates can be estimated using average daily traffic counts, total accident rate and the percentage of commercial vehicles on each link. Population density can be obtained through the Census if it is not avail- able from the state department of transportation although some interpreta- tion of the data may be needed since Census tracts as a rule do not match the 5 kilometer boundary around the routes. All of these parameters are used by the route optimization algorithm. The values for population density in the three classifications are used by the risk assessment model as is the commercial vehicle accident rate. The data used to model the MILLRWC are contained in appendices B and C; appendix B holds the node data, appendix C the link data. Radiological Risk Assessment Model The model used in this research to assess radiological risk is derived in large measure from RADTRAN III [51] which has been developed over the last decade by Sandia National Laboratories. Some of the techniques used in RADTRAN III are duplicated in the following model while other of RADTRAN’s methods have been rejected in favor of alternatives. Tech- niques developed elsewhere are appropriately referenced. To accurately model radiological risk requires detailed knowledge about specific situations and exposures, a condition that is impractical if not impossible to deal with on even a limited basis. Accordingly, a number of assumptions have beenmade to simplify the risk assessment problem, these are noted as they occur. These simplifications cause an increase in the '0“)- WI»! Ind: id‘s H‘AiS- wk“ fist 61 uncertainty of risk magnitudes but the basis for comparison between risk measurements remains. Risk Modeled by Exposure The assessment of radiological risk is based upon the exposure of indi- viduals in a population to a radiation source. The source may be outside the body resulting in an external dose (in the case of gamma radiation this is called the whole-body dose) or the radiation source may be ingested or inhaled resulting in an internal exposure. The frequency of health effects (somatic or genetic) caused by either type of exposure is generally accepted to be proportional to the dose received [12], that is, the probability of a particular health effect is a linear function of the exposure. The precise relationship depends on the source and type of exposure and the particular health effect to be measured, but in general, the risk of incurring an undesirable health effect due to radiation can be estimated by knowing the radiation dose received. Dose or exposure is a surrogate measure for risk when dealing with the health effects of radiation. Risk as measured by exposure can be applied on an individual or population basis. Individual response to a given exposure varies, there is a distribution of responses if the same dose is received by a number of persons, especially if each exposure is small. As a result, dealing with individual exposures leads to significant risk uncertainties. The population dose response (the sum of the individual doses) is less subject to these uncer- tainties, even when the individual exposures are small. So, population dose (in units of person-rem) will be the parameter used to model radiological risk in this method. 62 Overview of the Radiation Exposure Model To estimate the population exposure and thus the risk due to the transportation of LLW, unit risk factors (URF) will be developed for each of the isotopes noted in the LLW shipment inventory as described above. The dimensions of URF are person-rem per unit distance. Only the isotopes shipped in large quantities need be considered and of those, only the strong gamma emitters (> 10 KeV per disintegration), the internal-dose-significant beta emitters (90Sr), and the alpha emitters will produce significant exposures. As in RADTRAN, two transportation situations will be modeled, accident- free transportation and shipment involving an accident. To simplify the process, only three shipment package types (casks, drums and boxes) will be modeled. Each shipment will be assumed to consist of one truckload of the particular package type. The volumes per truckload are: cask, 5 m3; 55 gallon drums, 16 m3 and LSA boxes, 27.5 m3. Constant and uniform population densities will be assumed for each of the three types of population zones. As seen in figure 7, Isotope each combination of isotope, . Accident-Free packa e r 8 Accident package type and population [ Exposures H 8 YPe Exposures density will be analyzed by Population two exposure models: Density 'd nt-free e osures and acc1 e xp Figure 7. Model Outline accident exposures. The accident-free portion will examine the exposure to three population segments: persons along the shipment path, the vehicle crew and those persons sharing the transportation link with the shipment. Figure 8 1 provides a summary of the accident-free model. . 63 The accident exposure Dose Along section calculates the expo- Path sure for two cases: accidents Acadent-Free Dose to Crew in which the radioactive Exposures Same material is contained within ~ DlreChO" Dose to Perso its T e B acka e and acci- Sharing Link YP P g Opposite dents in which the contain- Directlon ment provided by a Type A Figure 8. Accident-Free Exposures package fails and the mate— rial is dispersed to the atmosphere (figure 9). Dose to Surrounding Non-Dispersal Population Accidents: Type B Packages Dose to Work Crew I Dose to Traffic Accident Exposures Immersion Dose Accidents Involving Atmospheric Dispersal ‘ Dose to Surrounding ‘ Ground shin e Dose of Material: Population Type A Packages Direct Inhalation and Resuspension Dose Figure 9. Accident Exposures For the non-dispersal accident, the dose is calculated for the surrounding population, the recovery crew and persons in vehicles passing the accident scene. In the case of an accident involving dispersal of material, the dose to the downwind population is estimated by modeling the whole body dose due to immersion in a radioactive cloud, the whole body dose 64 caused by radioactivity deposited from the cloud onto the ground and the internal dose from inhaling the material in the initial cloud and the material resuspended by wind or other means. Since the material is assumed to be completely dispersed and only relatively small quantities of LLW will be modeled, the dose to a recovery or decontamination crew has been neglected in the dispersal accident dose estimation. Both models will be described in detail in the following sections. Accident-Free Esture As in RADTRAN, accident-free exposure will be estimated by repre- senting each shipment as a point source. All exposures in the accident-free case will be external, so only gamma emitting isotopes are studied. The dose rate at distance r from a point gamma source is given by the inverse-square law: 5 1 DR(r) = 3&2. e-ur - B(ur) - I; (1) Where: DR(r) = Dose Rate at distance r from source Sp = Source photon emission rate Sp/41tr2 = Flux at distance r u = Attenuation coefficient for intervening medium edit = Attenuation factor for thickness r of medium B(ur) = Dose-rate buildup factor in medium at distance r (pg = Flux to dose rate conversion factor for 7 energy E. The product of the attenuation and buildup factors, e‘l1r . B(ur), is a function of the energy of the photon, the medium through which the photon passes and the distance to the receptor. In this research, the intervening medium will be limited to air. Appendix D shows that in air, e't" . B(ur) is 65 approximately 1 to a distance of 50 m for 0.5 MeV and 1 MeV photons. These factors can be ignored when calculating dose rates at distances of 50 meters or less. At distances greater than 50 m, the effect of attenuation and buildup can be represented by KE(r), defined as the ratio of the dose rate with attenuation and buildup to the dose rate neglecting these factors. KE(r) values are cal- culated in appendix D for distances from 100 to 800 meters at 0.5 and 1.0 MeV. The dose calculations in this research fall into two categories: receptors less than 50 m from the source for which KE(r) = 1 and receptors out to a distance of 800 m. Since r = 800 meters, it will be unambiguous to refer to the attenuation and buildup factor as simply KB. From appendix D, K3075 = 0.21, KE20.75 = 0.30. With this simplification equation (1) becomes: S K}; DR(r) — 4an (PE (1a) or, letting the constant k = SpKE/41tcp5: DR(r) = k / r7- (1b) Dose Along Path The dose to persons along the transportation path is modeled by the point source traveling at a speed v by a person located at a perpendicular distance x from the path. References 51 and 78 give the dose at distance x along the path as: 2k D =7 - mo (2) Where: k = SPKE/4mpg W dr 1t I(x) = fr , (r2 - x2)0.5 = 2x- X 66 I(x) is integrated from the shortest perpendicular distance to the source, x, to the longest, co, representing the dose received at x during the approach of the source. The factor of 2 accounts for the source returning to an infinite distance. Substituting for I(x) equation (2) becomes: k . It _ Sp . KE V°xu4o(pEovox D(x) = (2a) The total dose along the path is calculated by integrating D(x) over the range of distances of concern, that is from a distance to be considered the minimum reasonable value for x to that distance at which the inverse-square law causes the dose rate to become negligible. The minimum distance dmin, from a roadway at which an individual might be found probably depends on the population density classification; in an urban area, 5 meters seems reasonable while in rural areas 50 meters may be a better estimate. Since the method will be used for all population zones, I will use the smaller value, 5 meters, for dmin- The maximum distance dmax, will be 800 meters (0.5 miles) at which the dose rate is about 10'6 times its value at 1 meter. The definite integral then must be multiplied by a factor of 2 to account for both sides of the road, by the population density PDi, of the area sur— rounding the link and by a units conversion factor Z. The total dose along the path is expressed as: dmax Dpath = 2 . z - PD; - jtxx) dx (3) dmin 800m S - K dx Dpath=2-z-PDi-—E——E- — (4) o- X 4MP}: VI5m ZOPD'.S OKE 800m DPath= l p 'h‘( 5m ) (5) 2'¢E°W 67 2.54-Z-PDi-Sp-KE (PE'Vi Dpath = (6) Note that the shipment velocity has been given the subscript i to allow the speed to vary with population density class i. (Three types of population density zones are used: urban, suburban and rural.) To complete the derivation, the conversion constant Z needs to be defined by unit analysis. Dpath will actually be used to estimate unit risk factors and so the desired units are person-rem/km. PDi has units of persons/kmz. Sp is given in photons/ second. (pg has units of rem/ hr per photon/sec-cmz. The shipment velocity v, is in km/ hr. Combining these factors results in: persons . hotons . rem person-rem km2 sec hr km = km photons hr . sec 0 m2 0 Z (7) Z must have units of km2/ cm2, and so Z = 10‘10 kmz/ cmz. Since URF’s are being estimated, it seems reasonable to assume that the source Sp has a strength of 1 Curie = 3.7 x 1010 disintegrations/ second. By also assuming that the energy of decay for the isotopes in question can be represented by 1 photon of the appropriate energy per disintegration then Sp = 3.7 x 1010 photons/ sec. The energy E, used to look up the flux to dose rate conversion factor (pg, is the total energy per disintegration. Dpath for a URF simplifies to: 2.54 . 10'10 . PD: . 3.7 . 1010 . KE Dpath = (8) (PE ' Vi PD' 0 K Dpath = 9.4 . _l__—§- (9) (PE ' Vi Finally, a correction factor needs to be applied to Dpath to account for the differences in shielding and source geometryiamong the types of packages modeled. For example, the dose rate due to 1 Curie of a 1 MeV-photon 68 emitting isotope at a given distance from the source would depend on whether the package is a steel box, a drum of asphalt-solidified material or a lead-shielded cask. The shielding provided by the cask and the self-shielding provided by a large, solid source must be considered. Also to be considered is the energy dependence of the shielding correction factor. As seen earlier, the attenuation and buildup factors are energy dependent. These arguments lead to a correction factor, CEh, that varies with isotope energy E and package type h. Table 1 lists the correction factors CEh for LSA boxes, 55 gallon drums filled with solidified waste and shielded casks over photon energies ranging from 0.1 MeV to 1 MeV and greater. The final form of Dpath is: C . PD- . K Dpath = 9.4 - Eh ‘ E (10) ve-w This is the first component of the total accident-free exposure model. Table 1. Values of CEh Energy(MeV) LSA Box 55 gal Drum Cask 0.1 1 0.05 0.001 0.5 1 0.1 0.005 21.0 1 0.5 0.01 Table 2 lists the values for the parameters speed (vi), population density (PD;) and traffic count (TCi) (which will be encountered in a later section) by the population density class i. Table 2. Parameters Specific to Population Density Class i Classification v (km/hr) PD (persons/kmz) TC (vehicles/hr) 1 Rural 88 50 470 2 Suburban 88 1000 1200 3 Urban 64 3500 2800 69 Dose to Crew The vehicle’s crew compartment must have a dose rate less than 2 mrem/ hr by Federal law (49 CFR 173.441b(2)). Assuming a crew of two and a dose rate (DR) in the cab of 1 mrem/ hr = 0.001 rem/ hr, the dose to the crew while travelling at speed vi is: _2-DR_0.002 crew- Vi - Vi (11) Dose to Those Sharing Transportation Link Vehicles Travelling in the Opposite Direction Dose models for persons sharing the transportation link have been derived from RADTRAN III [51]. The dose model for persons travelling in the direction opposite the LLW shipment is similar to the model for dose received along the path. Some changes are in order though. The speed of passage is 2 . vi since each vehicle has speed vi. dmin and dmax must cover the opposing lanes of traffic, so dmin = 3m and dmax = 10m. The final difference is that the population density is the product of the vehicle density and the number of persons per vehicle (PPV). The vehicle density in units of vehicles/ km can be calculated by dividing the traffic count in the population density zone i, TCi (units of vehicles/ hr), by the vehicular speed in zone i, vi (units of km/ hr). PPV is assumed to be 2 persons per vehicle for all PD classes. Sp is again assumed to be 3.7 x 1010 photons / sec and Z is again 10'10 kmz/ cmz. Correction factor CEh remains applicable. Dopp is: z - s1D . CE}. PPV . TCi 10m = O O 1 — 12 DOW 2° Having the values of x, the amount of material deposited on the ground can be calculated as well as the depleted concentration XD. The average depleted concentration XD will also prove useful. These calculations and results are presented in appendix E. Whole Body Dose The exposure resulting from atmospheric dispersal accidents can be divided into three components as shown by figure 9. Whole body dose is the exposure received by being immersed in a cloud of radioactive material. Meteorology and Atomic Energy 1968 [68] gives the dose rate in rad/ sec (z rem/ sec for 7 radiation) for the case of a receptor at ground level in an infinite cloud of 'yemitting isotopes as: DR(x,y,0,t) = 0.25 . E - x(x,y,0,t) (39) E is the average gamma energy of the cloud components. By previous d“afiIIition, a URF will be defined for each isotope shipped, so DR and E are SpeCific to a particular isotope. Since isopleths of concentration have been defiI‘ted and deposition has been considered in appendix E, the dose rate Within an elliptical area n, can be estimated using the X9 for the nth area: 79 DRn(t) = 0.25 - E - tuna) (40) The population dose in elliptical area n can be calculated by multi- plying DRn(t) by the area of the nth ellipse An, the zonal population density PDi, the exposure time t, and a conversion factor of 10‘6 km2/ m2 correcting the unit differences between An and PD. To simplify, assume that t = 8 hr = 2.88 x 104 seconds and that PDi does not vary within the downwind area, that is, the subscript i is constant over the area affected by the release. The total population exposure is the summation of the area doses over all 11 ellipses: 11 DWB = 2 DRn(t) - t - An - PDi - 10-6 (41) n=1 11 DWB = t - PDi . 10-6 - ZDRnu) . An (42) n=1 11 Dwg = 2.88 x 10-2 . PDi - 2 DRn(t) - An (43) n=1 Inhalation Dose The second dose component is the internal dose which results from inhaling the radioactive material suspended in the air. There are two sources 01’ suspended material, the original release and material which is initially deposited on the ground and then resuspended by wind or other mechanical means. The total inhalation dose Dinh is the sum of the initial release dose D init and the dose resulting from resuspension of the material Dres! lDinh = Dinit + Dres (44) D Dinh = Dinit ° (1 + fi) (45) Dinh = Dinit '- RDF (46) 80 D Where: RDF = 1 + DT—e? (47) imt The resuspension dose factor or RDF for an individual isotope as given in RADTRAN III [51] was originally derived in the Reactor Safety Study [79]: -5 - 0 10 RDF = 1 + vd - 8.6 x 104 0 Cl] 0 (1-e'18250n)+ . (1-9-1 825071.) ) (48) Where: vd = Deposition velocity (assumed to be 0.005 m/ sec) _ ._1_ 1 n _ 0.693 - (Rn/2 + j (49) FE 0.693 . . = T/Z— : Rad1oact1ve decay constant RT1/2 = Resuspension half-life (assumed to be 365 days) t1 /2 = Radioactive half-life in days 8.6 x 104 = Seconds per day 18250 = Days in 50 years The deposition velocity (0.005 m/ sec) used to calculate RDF and Ito is a value representative of field test results on fission product particulates as reported in reference 67. As defined by equation (48), RDF typically has values in the range of 1.5 to 3. With RDF quantified, only Dinit remains to be defined in order to cal- culate the inhalation dose. The formulation of Dinit used here will be adapt- ed from that used in RADTRAN III [51]. The RADTRAN model gives the dose for an individual within elliptical area An as a function of a number of factors which have been assumed to be unity for the case of a URF. These fac- tors include the Curies per package, the packages per shipment, the fraction of material released, the fraction of material which becomes airborne and the fraction of airborne material of respirable size. Eliminating these factors lea"es: 81 IDinit’mJ‘IO = RPCm,O . an . BR (50) Where: ID = Individual dose RPCmp = Radiotoxicity factor for material m, organ 0 an = Depleted concentration of airborne material BR = Breathing rate For use in this research the subscript m can be eliminated since URF’s are isotope specific. Radiotoxicity factors have been estimated for individual isotopes by the International Commission on Radiological Protection and can be calculated from data presented in Permissible Dose for Internal Radiation, Table 1 [36]. These factors have units of rem per Curie inhaled. Rather than use the organ specific values used by RADTRAN, the model employed in this research will use the values for the total body found in reference 36. The breathing rate used is found in Report of the Task Group on Reference Man [39] and has a value of 3.3 x 10‘4 m3/ sec. The population dose in area It is found by multiplying equation (50) by the population density PD, and the area An. This introduces a unit conversion factor of 10'6 kmz/ m2. Summing over all areas it gives the complete initial dose: D,,,,,,n = 1016 - RPC - 56D“ - BR . An - PD, (51) 11 Dinit = z iDn 0 An 0 RFC 0 PDi 0 BR 0 10'6 (52) n=1 ll Dinit = RPC 0 PD, 0 3.3 x 10‘4 o 10‘6 0 2 TD“ 0 An (53) n=1 ll Din“ = 3.3 x 10‘10 - RPC 0 PD, 0 z iDn 0 An (54) n=1 The total inhalation dose due to initial release and resuspension is fluls: 82 11 Dmh = RDF - 3.3 x 10-10 - RPC - PD, - z in, - An (55) n=1 Groundshine Dose The final component of dose due to atmospheric dispersal accidents is that caused by radioactive material deposited on the ground by the initial release plume. The deposited material creates a plane source of exposure to persons entering the area. Within each elliptical isodose area the source can be regarded as an infinite plane. This is the model used by RADTRAN III [51] to estimate groundshine exposure and will also be used here. The dose rate from an infinite plane source depends on the surface density of the contaminant (Curie/ area) and the decay energy of the contam- inant. The contamination level can be determined if the undepleted x/Q values and the depleted XD/QD values are known. Appendix B provides estimates for XD/QD taken from reference 68, the incremental and cumu- lative amounts deposited in each ellipse and the surface density of the depo- sition. The equation for the population dose rate due to the deposition of a given isotope within area It is: De DRgnd,n(t) = 22 . j?- . Ey . Pop, - e'M - (0.63e':0031t + 0.37e'-00002“) (56) rem-m2 Where: 22 = 3.04 x 10‘4 day-Ci-MeV = conversion constant Depn = Material deposited in elliptical area It (Ci) km2 . . . Pop, = An - PD, . 10'6 F2- : Population in PD zone 1 E, = Gamma decay energy (MeV) 0.693 A = TU;- = Radioactive decay constant t = time since release (days) 83 The first exponential term decreases the source strength through radioactive decay. The exponential terms in parentheses decrease the source strength via soil uptake, wind dispersion, weathering or other processes. Combining the constants and exponential terms leaves: DRgnd, “(0 = Z3 0 Depn 0 BY 0 FBI 0 (0.63e'(.003I+A)I + 0_37e'(.000021+7\.)t) (57) erson-rem Where: Z3 = 3.04 x 10‘10 gay-Ci-MeV = conversion constant At this point the method to be used departs from that used in RADTRAN III. Where RADTRAN continued by determining if the contamination level was high enough to require interdiction of the land of decontamination, the method used here will assume that the contamination levels are of a magnitude which would not require decontamination or interdiction. So the resident population would receive a low intensity yet chronic exposure during the remainder of their lives. That exposure is quantified by the definite integral of DRn(t) from the release at t = 0 through t= lifetime. Assume the average life after exposure is 50 years and set K = 0.0031 + A. and a) = 0.000021 + )c. Integrating equation (57) results in: 50y Dgnd, n = Z3 - Depn . EY - PD, ooj (0.63e-Kt + 0.37e-wt) dt (58) -0.63 -0.37 Dgndm = Z3 ' Depn ' E7 ' PDi '( K ' (e'KT- 1) + - (62'0”T - 1)) (59) 0.63 0.37 D :2 .D .E.pD-.—.1-e-KT+ gnd,n 3 epn y 1 (K ( ) - (1 - €90) (60) Where: K = 0.0031 + it (o = 0.000021 + 71. T = 50 years = 18250 days With the exception of Depn, all the terms in equation (60) are 84 independent of the elliptical area n. The total groundshine exposure is simply the summation over n of Depn multiplied by the remaining terms, which are specific to the isotOpe in question or the population density class: 0.63 0.37 11 Dgnd=z3o EY-PD, ( K . (1 -e-KT)+ m - (1 -e'°°T))- 21Depn (61) 11: Total Dose (URF’S) due to an Atmospheric Dispersal Accident The total dose from an accident involving dispersal of radioactive material is the sum of the whole body or cloudshine dose, the inhalation dose and the groundshine dose. This again is the consequence of an assumed accident so the unit risk factor is the total dose multiplied by the base probability of 1 x 10'7 accidents per kilometer per year: ADADTotal = DWB + Dinh + Dgnd (62) URFEhi = (ADADTotal)Ehi - 10‘7 (63) Table 4 gives examples of the dose components for accident-free as well as non-dispersal and atmospheric dispersal accident situations, appendix F presents the complete list of estimates of dose components for the isotopes shipped in quantity in the MILLRWC. Appendix G gives the Unit Risk Factors for those same isotopes. N e tWOI’k Optimization Model Three components make up the network optimization computer moClel: input and initialization module, weight or optimization function and optimization algorithm, and output module. The input and initializa- t‘on module loads network and shipment data into memory, allows the user 85 Table 4. Dose Component Examples Accident-Free Dose Components I sotope 8: Package Dpath Dcrew lDopp Dsame AFDTotal RURAL 60C0 Cask 1.98E-07 2.27E-05 5.01E-09 5.36E-11 2.29E-05 60C0 LSA 1.98E-05 2.27E-05 5.01E-07 5.36E-09 4.30E-05 2 26Ra LSA 1.41E-05 2.27E-05 3.56E-07 3.81E-09 3.71E-05 SUBURBAN 60C0 Cask 3.96E-06 2.27E-05 1.28E-08 1.37E-10 2.67E-05 6C)Co LSA 3.96E-04 2.27E-05 1.28E-06 1.37E-08 4.20E-04 2 26Ra LSA 2.81E-04 2.27E-05 9.09E-07 9.73E-09 3.05E-04 URBAN 60CO Cask 1.90E-05 3.13E-05 5.65E-08 8.31 E-IO 5.03E-05 6(3C0 LSA 1.90E-03 3.13E-05 5.65E-06 8.31E-08 1.94E-03 2 26Ra LSA 1.35E-03 3.13E-05 4.01E-06 5.90E-08 1.39E-03 Non-Dispersal Accident Dose Components (Cask Shipments) Isotope Dareal Dveh Dwork NDADT Prob-NDADT RURAL 60Co 1.20E-04 1.95E-04 4.37E-03 4.69E-03 4.69E-10 SUBURBAN 60Co 2.40E-03 4.98E-04 4.37E-03 7.27E-03 7.27E-10 URBAN 60Co 8.41E-03 1.60E-03 4.37E-03 1.44E-02 1.44E-09 Dispersal Accident Dose Components (LSA 8: Drum Shipments) Isotope DWB Din}, Dgnd ADAD-r Prob-ADADT RURAL 60Co 7.64E+01 1.92E-02 2.90E-05 7.64E+01 7.64E-06 226Ra 4.71E+01 1.751~:+02 8.94E-05 2.22E+02 2.22E-05 SUBURBAN 60Co 1.53E+03 3.85E-01 5.79E-04 1.53E+03 1.53E-04 226Ra 9.41E+02 3.50E+03 1.79E-03 4.44E+03 4.44E-04 URBAN 60Co 5.35E+03 1.35E+00 - 2.03E-03 5.35E+03 5.35E-04 226Ra 3.30E+03 1.23E+04 6.26E-03 1 .56E +04 1.56E-03 86 to choose the destination point for the shipments, permits the user to choose the desired optimization function (minimize cost or risk) and allows the user to specify the output mode. The output module displays or prints the opti- mal route for each shipment and the cost (or total weight) of each shipment. Alternatively, the routing information can be suppressed and only the cost results displayed. The heart of the program is the analysis module containing the optimization algorithm and the weight function. Cg timization Algorithm The optimization algorithm is an adaptation of the Dijkstra algorithm found on pages 234-5 of Discrete Optimization Algorithms with Pascal P 1' Ograms by Syslo, Deo and Kowalik [71]. This algorithm solves for the Shortest path between two nodes on a network with links having nonneg- ative weights. The algorithm fails if any segment is negatively weighted but this constraint should not pose a problem for a transportation network where Wei ghts always parameters possess positive values such as distance, travel time or economic cost. The algorithm works by first naming an origin node, S, and a destina- tion node, T. All nodes on the network are initially given a temporary label of °<>, with the exception of node S which is given a permanent label of 0. The adgorithm then searches for all nodes with temporary labels connected to S (at this stage all nodes connected to S have temporary labels). Each node CotInected to S is given a new temporary label equal to the sum of the Pel‘manent label of S (0) and the weight to the connecting node, in other W0rds, the new temporary label for each node connected to S is the weight of the connecting link. Also recorded is the designation of the preceding node, in this case node S. Next, the smallest temporary label is found. This will be 87 a node adjacent to S since all other nodes are labelled 00. This node, call it A, is permanently assigned a label equal to the weight of its link with S. If A is the destination node T, then the algorithm stops and the final weight total is the value of the permanent label. If A is not T, then the algorithm continues by searching through all temporarily labelled nodes for those connected to A. N ew temporary labels are calculated for these nodes by adding the weights of their links to A with the permanent label for A. The new set of temporary labels are compared with the existing temporary labels for these nodes, if the new value for a node is less than the previous value, the new value becomes the temporary label otherwise the previous value is retained. If a new temporary label is installed, A is recorded as the predecessor node. Once the new set of temporary labels is in place, the smallest label is found and made Permanent for that node. If the last permanently labelled node is not the C198 tination node T then the process of: 1 - Searching for connections to the node most recently given a perma- nent label, 2- Determining new temporary labels, and 3- Selecting the smallest temporary label and making it permanent, Con tinues until T is assigned a permanent label. Once this happens, the label Of T equals the total weight from S to T. (The weight parameter can of course be any variable associated with network links such as cost or distance.) The path from S to T can be traced back from T by looking at the predecessor I\Odes. The predecessor of T leads to another node and so on until eventually the path leads to a node with A as its predecessor which in turn has the origin 3 as its predecessor. As noted in chapter 2, this algorithm is considered efficient by Syslo, Deo and Kowalik for solving the path between two points. For the type of 88 problem addressed here however (that is, a large number of origins and one destination), the algorithm becomes even more efficient if it is run from the destination to each origin under certain conditions. Two network conditions are possible, one is a network in which the link weights are independent of the choice of endpoints, the other is a network in which the endpoints chosen affect the weight calculations. For the case of weights independent of the choice of endpoints, if the permanent labels established for the first des tination-origin pair are not reset to 00, then all origins having weight less than the first origin have already been solved and the algorithm only need refer to the permanent label to report the solution. If the second origin chosen has a weight greater than the first, the algorithm can proceed from the firs l: origin, building the network outward from the destination. The expected $01 ution time for an origin becomes less as more of the network is solved because it becomes more and more likely that any particular node has been permanently labelled. In the case where link weights are dependent upon the CIIOice of endpoints, the permanent labels must be reset for each origin- degtination pair and the calculational savings are not realized. Figure 12 is a flow diagram of the optimization algorithm, graphically depicting the steps deSCribed in this section for the case of endpoint-independent link weights. Verification of Algrithm The operation and accuracy of the optimization algorithm was verified using a simple network. This verification process is described in appendix H. vEght Functions The function used to determine the weight of each link on the network is critical to the selection of succeeding nodes by the optimization algorithm 89 Initialize Variables . and Network: Choose Destination, —> DeSignate Node T a;| Temporary Labels Node T: RECENT. are set equal to co, . Set Permanent Label Predecessors equal to to 0. ficticious node. Choose Origin, S. Let NEWLABEL = Look at Nodes with Weight from Temporary Labels, RECENT + Find all Nodes Permanent Label ‘ connected to Is NEWLABEL < | (for each Node I emporary Label connected to f of Node X? RECENT). ~ Yes NEWLABEL becomes the Temporary Label Temporary Label of remains unchanged. -— Node X. . * ‘ ‘ Predecessor remains Set Predecessor of X unchanged. If RECESS at S, eel Dal to RECENT. Continue to Solve Network. Choose Smallest Temporary Label: *5 Designate this Node Make Label as RECENT Permanent. If RECENT = S, then Permanent Label = Total Weight from T Path can be traced through Predecessors. l . . . . _ . . C ti e 'th net Figure 12. Optimization Algorithm Flow Diagram on 25%;; x 90 since the choice is made by adding the weight of each link to the permanent label (or total weight from the initial node) of the predecessor node. A link Wei ght may be an easily measured physical property such as distance or travel time or it may be an economic function based on such properties, as in the cos 1: per mile multiplied by the distance. The weight function need not be dependent upon obvious geometric properties like distance. For example, the ra tio of flow volume on a link to the flow capacity of that link might be used to examine the best paths for an additional increment of flow. This is analogous to the resistance offered by a component in a circuit. The weight function used to model the economic cost of transporting LLW in this research is a straightforward function of link length while the function used to model risk is only partially dependent upon the network’s geometry. Cost Function The function used to estimate the economic cost of shipping LLW is based on the commodity rates charged by Tri-State Motor Transit Company [77] of Joplin, Missouri, a major carrier of LLW shipments in the Midwest. The rates in cents per mile are given in table 5. Using regression analysis, analytical models of these rates (in cents per II‘il‘e) can be determined: Round Trip: One Way Mileage < 100 miles: Rate = 338 100 miles < One Way Mileage < 600 miles: Rate = 3140 . (One Way Mileage)'0-484 r2 = 0.98 (64) One Way Mileage > 600 miles: Rate = 142 91 One Way Trip: One Way Mileage < 100 miles: Rate = 471 100 miles < One Way Mileage < 1000 miles: Rate = 4290 . (One Way Mileage)‘0~4799 r2 = 0.99 (65) One Way Mileage > 1000 miles: Rate = 156 Table 5. LLW Rates in Cents per Mile One Way Mileage One Way Round Trip One Way Mileage One Way Round Trip 100 471 338 450 207 158 125 433 313 475 202 155 150 396 289 500 194 152 175 362 268 550 190 149 200 313 245 600 185 142 225 296 233 650 179 142 250 284 217 700 176 142 275 271 204 750 173 142 300 259 194 800 165 142 325 252 183 850 164 142 350 244 177 900 162 142 375 235 171 950 159 142 400 224 165 21000 156 142 425 217 162 MO t Os: 1. For a rate to apply, mileage cannot exceed one way mileage value. 2. Trips less than 100 miles are charged 100 mile rate. The round trip rate equation is used to calculate the cost of cask ship- I1‘91‘1 ts since the shielding casks are returned and reused rather than disposed after each trip. Shipments of 55 gallon drums or LSA boxes use the one way trip rate equation since the empty vehicle may be used for other commodities after unloading the LLW. Since both rate functions monotonically decrease as total mileage in- Cl‘Eases, the length of each link can be used as the link weights. This reduces the number of calculations performed by the algorithm since link lengths are part of the data describing the network. Thus the labels and weights 92 calculated by the algorithm represent the distances from the destination, the economic cost is computed after the optimal path and weight are determined ra ther than during each iteration of the algorithm. So in the case of economic cos t, the weight function is the link length. Since the length of a link is inde- pendent of the origin-destination pair, the form of the algorithm may be used which does not require resetting the permanent labels after each solution. After the distance between the destination and an origin is optimized, the shippingrates are calculated using equations (64) and (65), then the annual cos 1' (in cents) of shipment from the origin is calculated with the following cos 1: functions: Cask shipments: Cost = (# of annual shipments) - [(Rate . 2 . distance) + 200000 + (100000 . 2 . distance/ 500)] (66) Drum or Box shipments: Cost = (# of annual shipments) . Rate - distance (67) The factors of (2 - distance) in the cask function reflect the round trips nee(:led to return the cask. The cask function also includes two factors 1.91) resenting the cask rental fee charged by the operator of the LLW repository. The fees used are representative of those charged by Chem-Nuclear Systems Incorporated [6], which operates the LLW repository site at Barnwell, South Car()lina. The fees include a flat rental charge of $2,000 for use of the Sl‘tielding cask plus an additional $1,000 per day, with the assumption that 500 miles are travelled each day. Risk Function The risk function uses link statistics, shipment data and URF information to assess the risk of shipment from the generating sites to the 93 destination. The risk function produces a weight specific to each link for each ori gin. This means that the weights must be reset after each origin- des tination solution. As the algorithm proceeds after initialization, an origin is designated for evaluation. A reference is established to the shipment data for that origin. The data required for the risk function are the waste forms (package types), the isotopes shipped, the Curie content of each isotope per shipment and the annual number of shipments. The next step, weighing links connected to the des tination node T, requires the use of link data such as population density, accident rate and length. Two components of risk are calculated for each link, the accident-free consequence and the accident consequence. The probability Of a commercial vehicle accident normalizes these two factors. The weight functions used to estimate risk are: Accident-Free Consequence: AFConseq = 2 2 [Clij 0 NURijl 0 Ln 0 Sij 0 (1-Pn)] (68) k i Accident Consequence: AccConseq = z 2 [Ciii - AURijl . Ln . Sij - Pn] (69) k 1 Total Consequence : Conseq = AFConseq + AccConseq (70) Where: Cij = Curies from origin i in package type j shipped annually N URijl = Non—accident Unit Risk Factor for isotope k in package type j in population density zone 1 (person-rem per mile) AURijl = Accident Unit Risk Factor for isotope k in package type j in population density zone 1 (person-rem per mile) Ln = Length of link n 94 Sii = Number of annual shipments from origin i of package WPel Pn = Accident rate for commercial vehicles per mile per year on link n. Combining Cost and Risk To this point cost and risk have been dealt with independently, the algorithm minimizes cost exclusive of the risk imparted upon the populace While risk is minimized without thought of the expense imposed on the waste generators. Policy based on either case alone suffers from lack of perspective. The goal of this research is to shed light on the issue, not cast it i n to shadow, so a way to combine cost and risk is needed. One approach to combining cost and risk is to define a common unit of measurement. The two parameters could then be combined prior to optimi- Za tion resulting in a solution which minimizes the combination. For exam- PIE, shipment distance is the cost measurement which is minimized while risk is minimized through an estimate of radiological exposure. As noted earlier, distance is easily converted to an economic unit such as dollars giving an estimate of the minimum economic cost in units dealt with on an everyday basis. If risk can be expressed in terms of dollars then it can be easily CoInbined with cost. While the conversion of exposure to dollars is possible, the procedure is not as straight-forward as with distance and raises additional Complications for policy makers. The units of exposure are person-rem. Title 10, Code of Federal Ragulation states that if exposure can be reduced by one person-rem at a cost 0f $1,000 or less, then it must be done. This provides a basis for equivalency between risk and dollars: 1 person-rem = $1,000 (71) 95 With this equation and equations (66) and (67) cost and risk estimates can be combined for each shipment and link during the optimization process to produce a solution which minimizes the combination. If a great deal of confidence is placed in the cost and risk estimates then the optimization of the network with respect to the combined parameters is the preferred method of evaluation. From a practical point of view though such a method forces the algorithm to perform a large number of calculations at each step and so slows the algorithm considerably. The extra time needed to optimize the network may not be warranted if low levels of confidence exist for either the cost or risk estimates. Alternatively, equation (71) is a basis for trading risk against cost. If the cost and risk of shipping LLW to a number of potential repository sites are known a graph can be generated showing the relationship between the two parameters. If a correlation between the variables exists, equation (71) sug- gests that a potential repository should be rejected if an alternative exists which would reduce risk at a cost less than or equal to $1,000 per person-rem. (Should is used rather than must because of the uncertainty inherent in the risk estimates.) So, if the relationship between risk and cost is such that risk can be reduced at a cost of $500 per person-rem for all sites then the most expensive site is acceptable and should probably be recommended as the repository. If on the other hand the cost of risk reduction is greater than $1,000 per person-rem then the lowest cost site may be justified. On the surface either method seems reasonable, the equivalence between risk and economic value is mandated by the federal government (Nuclear Regulatory Commission) which is a persuasive argument for both methods. Taking the equivalence a step further though brings some incon- sistencies to light. Previously it was noted that the radiological risk has been 96 quantified by the Committee on the Biological Effects of Ionizing Radiation [12]. One of the primary conclusions of their studies is that a population exposure of 8225 person-rem can be expected to generate 1 excess cancer fatality in the exposed population. In other words, 1 life equals 8225 person- rem. Since by law 1 person-rem equals $1,000 then it follows that: $1000 ' — - . = 6 1 life saved — 8225 person rem p er s o n-r em $8.2 x 10 (72) The act of equating risk and dollars places a dollar value on a life. There is nothing inherently wrong with placing a value on a life, it is done daily in decisions made deliberately or instantaneously (compare the values weighed in deciding to run a yellow light and in deciding which hospital receives the latest diagnostic tool). The problem arises in trying to choose a value to place on a life. Clearly the NRC equates one life with about $8 million. The value endorsed by the Federal Highway Administration in weighing alternative highway improvement projects is about $250,000 per life saved. Here is a second unit of the federal government using a value for a life 1/32 of that used by the first. Which is right? A traffic fatality is immediate and the average life expectancy lost is on the order of decades. A cancer generated by exposure to radioactivity has a latency period of about 5 years for leukemia to nearly 30 years for lung cancer. As a result the average life expectancy lost is more likely on the order of years rather than decades yet the value of a life saved from radiation induced cancer is held to be 32 times as valuable as a life saved from a highway accident. The question is further complicated by the subject of this research. If an accident occurs which results in one highway fatality and a substantial release of radioactive material causing one excess cancer fatality, are the two lives to be valued differently by society and policy makers? 97 To sidestep conflict or controversy over the monetary value of life the measures of both risk and cost can be normalized to produce risk and cost indices for potential repository sites. The values obtained for risk and cost through the optimization algorithm may be normalized to any standard but perhaps the most easily interpreted standard of comparison is the minimum value for each parameter. An index can thus be produced by simply taking the ratio of a risk or cost value at a site to the lowest value obtained for the network. Since the indices are dimensionless indicators of rank, they can be combined into a composite index. The composite can be calculated in any manner deemed reasonable by policy makers, for example the two indices may be weighted equally or cost may represent 90% of the final composite or perhaps the cube of the risk index is to be added to cost index. In any event the lowest composite index will represent the choice within the imposed framework. This will be the method used to evaluate the MILLRWC. Model Implementation The four components of the model are brought together in a computer program listed in appendix I. This program, written in ZBasic (a compiled Basic language with versions available for many different types of personal computers), contains the shipment data for the MILLRWC and the URF data for isotopes shipped within the MILLRWC. It accesses a file containing the network data for the Midwest. Two network analysis options are provided based upon the weight functions defined in the previous section: minimize cost or minimize risk. The program was verified with the simple network used in appendix H before it was applied to the MILLRWC data. The results from the network analysis of the MILLRWC will be discussed in Chapter 5. Chapter 5 MODELLING THE MILLRWC Results The Midwest Interstate Low-Level Radioactive Waste Compact was modeled using the data contained in appendices A, B, C and G. A number of nodes were tested as potential repository sites by simulating the shipment of waste to those nodes and estimating the cost and risk of the shipments. The most illustrative way to display the results is to place the cost (or risk or combined) estimate for each node on a map of the region and then connect the points of equal cost. The resulting iso-cost (iso-risk, etc.) map shows at a glance the area of lowest cost and the variation in cost with respect to location. This technique will be used to examine cost and risk separately and also the combination of the two parameters. All values used to generate the maps are contained in appendix 1. 98 99 Annual costs of waste shipment in millions of dollars are shown in figure 13. The cost at each site is based on the shortest distance between each waste generator and that site. As seen by the map, shipment cost is relatively insensitive to location in the region. The lowest annual shipment cost is $860,000 to Gary, IN, the highest is to the Minnesota border near Fargo, ND at $1,500,000 or about 1.8 times the lowest cost. Note that the center-of-mass of LLW shipments as calculated by the MILLRWC is designated C on the map. The lowest cost site does not coincide with the center-of-mass because Lake Michigan prevents straight-line shipments from generators in Michigan and Ohio to the center-of—mass. The displacement of the lowest cost repository site from the center-of-mass in southeastern Wisconsin to north-central Indiana is due to the higher connectivity of the network in the three eastern states relative to the four western states. This is especially true with regard to the major generators, that is nuclear power plants, in Michigan and Ohio which are located very close to the I-80 corridor across northern Indiana and Ohio. These power plants, representing the three largest volume generators in Michigan and the two largest in Ohio, are all within 40 miles of I-80 which in turn provides direct east-west access across the entire region. In contrast, the power plants in the four western states, with the exception of the plant located near Cedar Rapids, Iowa, are situated 200 miles or more off the I-80 axis. The importance of I-80 to minimal distance transportation routes in the region is seen in figure 13. The iso-cost lines form concentric ellipses with major axes along the I-80 corridor. The cost gradient perpendicular to I-80 is much steeper than along I-80 so that locating a site anywhere between Gary, IN and Toledo, OH, a distance of 200 miles, does not change the transporta- tion cost while the cost at Grayling, MI, 200 miles north of I-80, is 20% higher. 100 ‘44. 5.. V K 1.0 C 0.9 j 1.0 1.2 F 1-1 :3 1.4 Figure 13. Iso-Cost Lines (in Millions of Dollars per Year) 25! (n 7r The risk of shipping LLW in thousands of person-rem per year (calculated using the assumptions stated in Chapter 4) is shown in figure 14. Risk is somewhat more sensitive than cost, ranging from a low of 5500 person-rem near Iowa City, IA to 12,100 person-rem at Sault Ste. Marie, MI, a factor of 2.2 larger. Since risk is primarily determined by the population exposed and the distance travelled, the point of lowest risk occurs in a low 101 10 if 12 Figure 14. Iso-Risk Lines (in Thousands of Person-Rem per Year) population density area within the I-80 corridor. The region of low risk extends along I-80 and I-35 forming a boomerang shaped area in Iowa. Metropolitan areas such as Minneapolis—St. Paul, MN and St. Louis, MO form local maxima within regions of lower risk. High population density along the Lake Erie shore in Ohio and along I-94 in Michigan cause the risk gradient to steepen in these areas. Some aberrations in the results such as high values for St. Joseph, MO and Akron, OH and the low value for Springfield, OH may be caused by abnormal accident rates assigned to links in 102 these areas. In general, areas of low risk are areas with low population density and good accessibility along I-80 and I-35. -‘ fife .j\ \ C / :> 2.25 25 2.75 2.75 3.1 O \ Figure 15. Normalized Cost + Normalized Risk (Arbitrary Units) Combined Cost and Risk To produce figure 15, the cost estimates were normalized to the minimum value of $860,000 at Gary, IN while the risk estimates were normalized to the minimum value of 5500 person-rem at Tiffin, IA. The 103 resulting cost and risk indices were then added to create the combined index displayed in figure 15. This map is a superposition of the two previous maps and reflects its origin. The area of lowest combined cost and risk is confined to a narrow ellipse along I-80 from Iowa City, IA to the Illinois-Indiana border. Regions of successively higher cost and risk are bounded by ellipses with major axes skewed off the I-80 axis reflecting the influence of low risk values along I-35 in Iowa and Minnesota. The combined index ranges from 2.2 at Tiffin, IA to 3.7 at Sault Ste. Marie, MI, 1.7 times greater than the low value. This is a smaller range than either cost or risk alone because the low cost values for sites in the eastern states are balanced by higher risk estimates while the opposite situation prevails in the western group of states. As a result, the profile of the combined cost and risk index is relatively flat across the entire region. Figure 15 assumes equal weight is given to the cost and risk indices. Other linear combinations are of course possible, however, all other such combinations will be bounded by figures 13 and 14. Figure 15 represents a transition state in passing from a condition in which all weight is on cost and none on risk (figure 13) to the opposite condition where risk receives 100% of the weight and cost none (figure 14). Cost—Risk Correlations The relationship between cost and risk for the nodes tested as potential repositories is exhibited in figure 16. Evidently there is no correlation when the data is taken over the whole region, the F ratio of 0.123 indicates that the null hypothesis of slope equal to 0 cannot be rejected. 104 14 E, 12.. + ' o- § l' + ##4- " x- 'l' + 43' + 8. 10-- * r t “5 f 41" P' :4' ‘I- + + 1- ‘” fi ti "' It + + " r'" 45" “U 2: L —;.L "' 5 8-- "' " + * t 1' 1' 't ‘3 *4- " + " “'4' + «l- 6- .2 + t + + + H- ‘- 3 t + + 4: .3.“ 6-. + + as + + s, * Risk = 8140 + (3.4 54 .. Cost) 52 + Correlation Coefficient = 0.033 F Ratio = 0.12 4 : i : : : : : 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Stratifying the data by geographical region highlights a relationship between cost and risk which was not apparent for the entire region. This correlation is interesting in that it is positive in both geographical regions, that is, increasing the transportation cost to reach a non-optimal site will Cost (millions of $) Figure 16. Regression of All Data Points generally be associated with an increase in the population risk. 13 ’5 12-- 9.3 G 8 11 -- 8 3, 10-- 'U 8 3 Risk = 633 + (0.0088 .. Cost) ..‘2 8-- "' «t- Correlation Coefficient = 0.672 m " + + F Ratio = 46.9 ‘- 7 i ‘r* : z 0.8 0.9 1. 1.1 1.2 Cost (millions of $) Figure 17. Regression of Eastern Data Points 1.3 105 In the eastern group of states (Indiana, Michigan and Ohio) this rela- tionship is somewhat stronger than in the western group (Iowa, Minnesota, Missouri and Wisconsin). The correlation coefficient for the eastern group is 0.67, for the western group it is 0.57. In both cases though the F ratios suggest that the slope is not equal to 0 at the 0.01 confidence level. Figures 17 and 18 contain the graphs of cost versus risk for the eastern and western groups of states. 10 Risk (thousands of person-rem) + "' Risk = 1051 + (0.0055 * Cost) 6'" .- 4. + M Correlation Coefficient = 0.572 + F Ratio = 19.9 5 i i i i i i 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Cost (millions of $) Figure 18. Regression of Western Data Points Sensitivity Analyses Four sensitivity analyses were performed on the model to test its behavior under extreme conditions. The first analysis tested the effects of withdrawal of one state from the MILLRWC. The three states producing the largest volumes of LLW, Michigan, Minnesota and Ohio were removed in turn from the model. Subsequent analyses examined the effects of accident rates, shipment volume and packaging type. Each analysis was performed for 106 five nodes, the four nodes with the largest or smallest estimates for cost or risk, and one node with average cost and risk estimates. (In the analysis of a state removed from the Compact, nodes within that state were not tested.) Comparisons are provided between the results of each sensitivity analysis and the base results presented earlier. One State Withdraws from MILLRWC To test the effect of a state withdrawing from the Compact, all ship- ments generated in one state were set to zero and estimates made of the cost and risk of shipments from the remaining six states. Michigan, Minnesota and Ohio were individually removed from the model. These three states produce the largest volumes of LLW in the Compact and represent the geographical extremes. Withdrawal of a state from the Compact reduces the total number of shipments and so results in lower transportation cost and risk. To place the results of the sensitivity analysis in the proper context for comparison with the results from the complete Compact, the cost and risk estimates are normalized within this analysis. These normalized values are then com- pared to the normalized base values obtained in the analysis of the complete MILLRWC. The cost values are normalized to Gary, IN and the risk values are normalized to Tiffin, IA. Table 6. Michigan Withdraws Normalized Cost Normalized Risk Node Base Test Base Test Tiffin, IA 1.19 1.06 1.00 1.00 Gary, IN 1.00 1.00 1.32 2.00 Moorhead, MN 1.77 1.52 1.70 1.67 Normalized Cost Table 7. Minnesota Withdraws Normalized Risk Node Base Test Base Test Tiffin, IA 1.19 1.25 1.00 1.00 Sault Ste. Marie, MI 1.49 1.47 2.18 1.67 Gary, IN 1.00 1.00 1.32 0.99 East Lansing, MI 1.07 1.04 1.62 1.15 Table 8. Ohio Withdraws Normalized Cost Normalized Risk Node Base Test Base Test Tiffin, IA 1.19 1.15 1.00 1.00 Sault Ste. Marie, MI 1.49 1.54 2.18 2.54 Gary, IN 1.00 1.00 1.32 1.51 Moorhead, MN 1.77 1.69 1.70 1.72 East Lansing, MI 1.07 1.12 1.62 1.90 The results of this test are as expected, removal of Michigan lowers the relative cost at western sites in the Compact region and increases the relative risk at eastern sites. Similar results are shown when Ohio is removed from the model. This behavior flows from the relative redistribution of LLW generators within the region. In both of these cases, shipments from the western states take on a greater role in determining the cost and risk relative to the base case. These shipments travel short distances to repository sites in the west, lowering the relative cost. Shipments to eastern sites have greater relative risk because of the greater weight given to the long distances trav- elled by shipments from the western generators. Conversely, removing Minnesota from the model produces lower cost and risk for eastern sites and higher cost and risk for western sites. 108 Accident Rate Reduction Accident rates and population density are two important parameters in the estimation of exposures. To test the effect of accident rates on the risk estimates, the accident rates were reduced by a factor of 10 for three cases: rural links only, urban links only and all links. The results are presented in tables 9 and 10: Table 9. Risk Estimates (person-rem) with Accidents Reduced by a Factor of 10 Node Base Data Rural Only Urban Only All Links Tiffin, IA 5517 5516 4176 3499 Sault Ste. Marie, MI 12050 12050 9786 8500 Gary, IN 7302 7302 5292 4216 Moorhead, MN 9354 9353 7161 6128 East Lansing, MI 8964 8963 6973 5754 Table 10. Fraction of Base Node Rural Only Urban Only All Links Tiffin, IA 1.0 0.76 0.63 Sault Ste. Marie, MI 1.0 0.81 0.71 Gary, IN 1.0 0.72 0.58 Moorhead, MN 1.0 0.77 0.66 East Lansing, MI 1.0 0.78 0.64 Mean 1.0 0.77 0.64 Standard Deviation 0.0 0.03 0.05 Reducing accident rates in rural areas has little effect because the popu- lation density and accident rates are already low in rural areas (relative to urban areas) and so the dose component along the rural section of a route is small relative to the urban component. A ten-fold decrease in the urban acci- dent rates returns a decrease in the population exposure of nearly 1/ 4. If the preventive measures were extended to suburban areas, the dose reduction is more than 1/ 3. Policies intended to reduce risk through reduction of accident rates should recognize that risk will be reduced only by a factor 1 / 6 to 1 / 8 the 109 magnitude of the reduction in accident rates. Volume Reduction Many generators are practicing or planning waste volume reduction measures to reduce waste shipping and disposal costs. All such procedures do not reduce the amount of radioactivity in the waste but in fact may increase the concentration of the radioactivity. To examine the effect of volume reduction and increased concentration on transportation cost and risk, the volume shipped by each generator was halved except for those generators currently requiring only one truckload per year. It was assumed that concen- trating the waste in this manner would not result in the requirement of shielding casks for shipments currently unshielded. Tables 11 and 12 contain the results: Table 11. Cost and Risk with Volume Reduced 50% Base Base Node $ (millions) $ (millions) Person-rem Person-rem Tiffin, IA 1.02 0.56 5517 5721 Sault Ste. Marie, MI 1.28 0.70 12050 12450 Gary, IN 0.86 0.47 7302 7581 Moorhead, MN 1.52 0.82 9354 9801 East Lansing, MI 0.92 0.51 8964 9262 Table 12. Fraction of Base Node Cost Risk Tiffin, IA 0.54 1.04 Sault Ste. Marie, MI 0.55 1.03 Gary, IN 0.54 1.04 Moorhead, MN 0.54 1.05 East Lansing, MI 0.55 1.03 Mean 0.54 1.04 Standard Deviation 0.003 0.007 110 As expected, the cost is nearly halved since the number of shipments is nearly halved. The risk increases, also as expected since the concentration of radioactivity in each shipment has increased. The interesting point is the trade-off between cost and risk, risk increases by 4% while cost decreases by 50%. This indicates that an effective volume reduction program could save a substantial fraction of the annual shipping costs at the expense of only a minor increase in the risk. Improved Package Integrity The atmospheric dispersal accident dose (ADADTotal) is a major con- tributor to population exposures in the model. Elimination of this compo- nent would reduce the expected health effects due to radiation exposure. Noting that a cask or Type B container has never been breached in an acci- dent, the dispersal accident component could effectively be removed by requiring all shipments to be in Type B or similar high integrity containers. This scenario was tested by assuming that: 1. Present cask shipments remain the same, 2. Material currently shipped in drums, barrels or boxes will be shipped in ”casks” of 10 m3 capacity. Since current drum shipments are assumed to be 16 m3 and LSA box shipments are assumed to be 27.5 m3, the new containers will require more shipments, those shipments will be two-way to return the cask and a cask rental fee will be charged. 3. Accident consequence factors can be neglected since they are approximately 1 x 10‘5 the magnitude of the accident-free conse- quence factors which are in person-rem per mile: 111 Rural zones = 3.65 x 10'5 Suburban zones = 3.73 x 10'5 Urban zones = 5.45 x 10’5 As shown in tables 13 and 14, requiring casks for all shipments would triple the annual costs while reducing the exposures by a factor of 3. Table 13. Cost and Risk if Casks are Required Node $ (millions) Person-rem Tiffin, IA 3.14 2044 Sault Ste. Marie, MI 4.00 5181 Gary, IN 2.62 2438 Moorhead, MN 4.56 3643 East Lansing, MI 2.87 3352 Table 14. Fraction of Base Node Cost Risk Tiffin, IA 3.08 0.37 Sault Ste. Marie, MI 3.13 0.43 Gary, IN 3.05 0.33 Moorhead, MN 3.00 0.39 East Lansing, MI 3.12 0.37 Mean 3.08 0.38 Standard Deviation 0.05 0.04 Model Applied to Single State The final exercise performed with the model was to apply it to a single state, representing the case in which a state chooses to dispose of its waste independently. This tested the effect of reducing the scale of the network. Michigan was chosen for this test, all generators located outside of Michigan were eliminated from the data set. The cost and risk of shipping LLW within Michigan was estimated by the model. The results were then normalized and combined. 112 .. 3‘ r“ 2.4 2.3 Figure 19. Iso-Cost Lines if Michigan Goes Alone (in Hundred Thousand Dollars per Year) Figure 19 shows the cost of shipping LLW generated within Michigan to repository sites in Michigan. The site with the lowest transportation cost ($216,000 per year) is near Marshall, MI. The variation in cost is small, the highest cost node on the network, Sault Ste. Marie, is only 1.6 times as costly as the least expensive site. These costs are about 25% of the costs incurred when the MILLRWC is modeled. Interestingly, modelling the MILLRWC produces a transportation cost ratio between Sault Ste. Marie and Marshall of 1.4 : 1. This is approximately the same as when Michigan is modeled alone. This can be explained by the geography of the state, shipments originating outside of Michigan have a limited number of routes to any site within the 113 state due to the peninsulas defined by the Great Lakes. Thus shipments origi- nating outside of Michigan will take roughly the same route to any potential repository site within Michigan when the object is to minimize distance. The risk of shipping LLW in Michigan is shown in figure 20. The sites with the lowest risk are along I-275 between I-94 and I-75, close to the Fermi II nuclear power plant. Risk increases slowly westward along I-94 due to the influence of the Palisades and Cook nuclear power plants. Northeast of the area of lowest risk, risk increases rapidly as a result of the high population density and accident rates encountered in the Detroit metropolitan area. J4~ ~ ' 7.0 @ 5‘ 12.0 Figure 20. Iso-Risk Lines if Michigan Goes Alone (in Hundreds of Person-Rem per Year) 114 Risk values range by a factor of 2.6 from lowest to highest. These areas are adjacent to one another, unlike the other analyses performed thus far which generally show a smooth transition from minima to maxima. Where the cost results were a factor of four lower for Michigan alone versus the entire MILLRWC, risk estimated by analyzing Michigan separately is lower by a factor of 10 to 20. 3.0 Figure 21. Normalized Cost + Normalized Risk if Michigan Goes Alone (Arbitrary Units) Figure 21 shows the results of normalizing the cost and risk values to their respective minima and then combining the normalized values. Equal weight was given to both the cost and risk components. Figure 21 reflects the 115 structural relief imposed by the risk estimates smoothed by the slowly varying cost estimates. The maximum value is approximately twice the minimum. A broad region of the Lower Peninsula varies by less than 20% from the I-275 corridor containing the area of lowest cost and risk. A final note to these analyses is that St. Ignace, MI was the westernmost site tested in the Upper Peninsula. Sites west of St. Ignace can be expected to have cost and risk values greater than those at St. Ignace or Sault Ste. Marie because the western Upper Peninsula is further removed from the LLW gen- erators in the state which are concentrated in the southern Lower Peninsula. This application of the model shows that it works well with small or large networks. In terms of computation time a small network is desirable since the time needed to calculate the shortest path increases by the square of the number of nodes. To be weighed against the computation time is the level of detail required for confidence in the conclusions. The level of detail increases with the number of nodes on the network, a large number of nodes produces fine structural details. The model is capable of providing reliable cost and risk estimates for the shipment of LLW and by judicious choice of nodes, can do so in a reasonable amount of time. Appendix K contains the complete results of modelling Michigan alone. 116 Summary Applying the model and assumptions to the Midwest Low-Level Radioactive Waste Compact produces these results: 1. The region of lowest shipping cost is northern Indiana and Ohio and southern Michigan. This region is centered by I—80 and extends approximately 30 miles on either side of this route. The highest cost in the MILLRWC is 1.8 times greater than the lowest cost. 2. The region of lowest radiological consequence is in Iowa along the axes formed by I-80 and I-35. The greatest consequence is 2.2 times larger than the lowest consequence. 3. Combining normalized cost and risk values on an equal basis produces minimum values in a narrow region along I-80 in eastern Iowa. The largest value of the combined index is 1.7 times greater than the smallest. 4. Locating a repository in a region with higher cost will tend to increase the risk. Similarly, locating in areas of higher risk will typically result in increased costs. 5. Withdrawal of a state from the compact tends to shift the regions of low cost and risk away from that state. 6. Reducing urban accidents by a factor of 10 reduces the radiological consequences by nearly 25%. Reducing all accidents by a factor of 10 reduces the consequences by 35%. 7. Volume reduction (or shipment reduction) of 50% results in a 50% cost reduction and a 5% increase in risk. 8. Requiring Type B containers for all shipments will triple the cost while reducing the risk by a factor of three. 9. The model is effective in analyzing single states if the network is defined to the appropriate level of detail. 10. 11. 12. 13. 14. 117 Applying the model to Michigan alone results in: The region of lowest transportation cost is in the south central Lower Peninsula. Of the sites tested, the highest cost is in the eastern Upper Peninsula, 160% greater than the lowest cost. The transportation cost to a repository site when Michigan is modeled separately is about 25% of the cost to that site if the entire MILLRWC is modeled. The area of lowest risk is the I-275 corridor between I-94 and I-75 in southeastern Michigan. The highest risk estimated is in down- town Detroit, 2.6 times greater than the lowest risk. The consequence of shipping LLW to a site in Michigan is 10 to 20 times less if Michigan is modeled alone than if the MILLRWC is modeled. The region of lowest combined cost and risk is in the I-275 corridor between I-94 and I-75. The region of highest combined cost and risk is in the Upper Peninsula, Sault Ste. Marie has a combined index about twice the minimum index. Chapter 6 CONCLUSION Some broad conclusions may be drawn from this research in addition to the results specific to the Midwest region given inChapter 5. Some of the conclusions are applicable in general to the topics of risk and transportation while the remaining conclusions are specific to the model developed for this research. Before stating these conclusions however, the assumptions critical to the conclusions will be restated. Assumptions Upon Which the Results Are Based The assumptions used in each of the four components of the model will be listed in turn. Low-Level Waste Shipment Inventory 1. Full truckloads are shipped whenever possible. 2. Packaging is one of three types: casks for high-activity wastes, 55 118 119 gallon drums for immobilized reactor wastes and LSA boxes for other waste. Packaging is assigned to waste based on the isotope and quantity of radioactivity. 3. Shipments are modeled as the annual averages of each of the three package types from each generator. Transportation Network 1. The population density for each link in Michigan was calculated as the weighted average of the population density within 5 kilometers of each link. The values fell within three ranges: rural (0-600 per- sons per kmz), suburban (601-1600 persons per km2) and urban (>1600 persons per kmz). Segments outside Michigan were assigned population density categories based on their geographic location and then randomly assigned a population density from the ranges defined above. 2. Commercial vehicle accident rates were calculated for each link in Michigan using 1983 and 1984 traffic volumes (including percentage of commercial vehicles) and the commercial vehicle accident re- cords from the same years. When grouped by the population density category of the link, these accident rates have a log-normal distribution. Segments outside Michigan were randomly assigned an accident rate based on the population density category of the link and the accident rate distribution for that category. Raditfligical Risk Assessment Model 1. Radiological risk is estimated by external and internal exposure models. 2. Unit risk factors can be defined for a unit distance and unit quantity of material (1 Curie) based on the isotope, the package type, the pop- ulation density and the presence or absence of an accident. A base accident rate of 1 x 10 '7 per kilometer per year is assumed. 120 Accident-Free Exposure 1. A point source model, modified by attenuation and buildup in air and package shielding is used as the basis for estimating exposure in accident-free situations. The dose to the population along the path is calculated from a min- imum distance of 5 meters to a maximum distance of 800 meters. The dose to the crew is based on a dose rate in the crew compart- ment of 1 millirem per hour. The dose to vehicles travelling in the direction opposite the ship- ment’s direction is calculated between 3 meters and 10 meters. The dose to vehicles travelling in the same direction as the ship- ment is based on a minimum distance of approach equal to the distance travelled by the vehicles in 2 seconds. Non-Dispersal Accident Exposure 1. All accidents involving casks (Type B containers) are non-dispersal accidents. A point source model is used for non-dispersal accident situations. Exposure time is assumed to be 8 hours except for the work crew which is exposed for 4 hours. The dose to the surrounding population is calculated from 10 meters to 800 meters. The population density is assumed to be constant over this area. Vehicles are assumed to pass no closer than 30 meters from the accident site. The dose to the work crew is calculated based on an average distance of 10 meters from the source over a period of 4 hours. The work crew consists of 10 people. Atmospheric Dispersal Accident Exposure 1. All accidents involving packages other than casks are atmospheric dispersal accidents. In an atmospheric dispersal accident, the assumptions are that all material shipped is released to the atmosphere and all material 121 released is respirable. 3. Meteorological conditions typical of the Great Lakes region are assumed. 4. The deposition velocity of all material is assumed to be 0.005 m / sec. 5. Radiotoxicity factors are calculated from the MPC values for total body as presented in Permissible Dose for Internal Radiation [36]. 6. The breathing rate for internal exposure is 3.3 x 10'4 m3/ sec as found in Report of the Task Group on Reference Man [39]. Network Optimization Model 1. Cask rental charges are a flat fee of $2,000 plus $1,000 per day. 2. For a given repository site, the risk estimates are linearly additive for all shipments from all generators. The conclusions which follow are based upon these assumptions as they were applied in their respective model components. Conclusions Applicable to Risk and Transportation The first broad conclusion is that it is possible to estimate and quantify the risk of shipping radioactive material. Although this has been demon- strated previously by RADTRAN and other models, the method used in this research, derived in large measure independent of RADTRAN, serves to confirm the ability to estimate risk. The methods to estimate risk used in this research may be more accessible than mainframe models such as RADTRAN because they can be easily adapted to any spreadsheet program available for personal computers. The ability to estimate transportation risk is now in the hands of transportation and emergency response planners or policy makers rather than confined to federal research laboratories. Furthermore, the pro- cess used here should be useful as guidance for methods of estimating risk in transporting other hazardous materials. 122 Another conclusion to be drawn is that risk can be used as the criterion for selecting routes. Minimizing risk will not, in general, produce the same routes as minimizing distance. It is therefore appropriate to consider risk as a route selection parameter when analyzing or establishing public policy affect- ing the transportation of hazardous materials. It can also be concluded that parameters with quite different units of measurement such as cost and risk may be combined through the use of indices. The resultant index describes the value of a chosen point relative to others within the framework of the combination. In other words, indices provide both a means to combine dissimilar parameters and a basis for com- parison among the results of the combination. A benefit of this method is that issues such as the monetary value of a life can be avoided because all comparisons are on relative terms. So any value for a life can be used as long as it is consistent within the calculations for each parameter. Finally, the overall method used in this research should be applicable to the shipment of materials other than LLW. Hazardous material such as gasoline, explosives or chemicals are candidates for further examination. Application of the method to these materials is dependent upon formulating a risk model for the material in question. Choosing the proper network will allow routing shipments within a city or in multi-state regions. While some work has been done in the. past [60] on minimizing the risk of hazardous material shipments, the body of knowledge is by no means complete. Use of a method such as the one presented here makes risk assessment accessible to anyone with a personal computer and the expertise necessary to design a risk model. 123 Conclusions Specific to the Model Used in this Research The conclusion which stands out is that the radiological risk of ship- ping LLW as calculated by this model is small compared with other transpor- tation risks. With the heroic assumptions that all accidents are of the most severe type resulting in release of all material from Type A shipments and that all of the material is respirable produces Unit Consequence Factors on the order of 1 x 10'4 person-rem per Curie per kilometer in urban areas if the accident rate is 1 x 10'7 per kilometer per year. At the rate of about 1 latent cancer fatality per 8200 person-rem, the average UCF represents 1 x 10‘8 fatal- ities per Curie per kilometer. Trucks cause about 3 x 10'8 fatalities per kilo- meter directly and another 10 x 10“8 fatalities per kilometer due to environ- mental pollution [85]. The radiological risk per Curie is an order of magni- tude less than the non-radiological risk without taking the assumptions into consideration. Doing so further reduces the magnitude of the radiological risk. For example, about 60% of the shipments in the MILLRWC carry less than 1 Curie. Another consideration is that less than 1% of all truck accidents exceed the conditions established as design specifications for Type B packages [85]. These factors as well as others cause the radiological risk of transporting LLW to be much less than other risks involved in truck transportation. A further conclusion drawn from this research is that the dose consequences of shipping LLW is sensitive to the population density along the route. The region of lowest risk (figure 14) falls in the region of lowest population density nearest the center of the region. In selecting routes to all sites, the model chose routes through rural areas almost exclusively, entering urban areas only if no alternative routes'existed. Because the population density assumed for urban areas was 70 times greater than rural areas, the model was willing to trade substantial distances through rural areas to avoid 124 exposing urban populations. Increasing the requirements for packaging LLW to the level of Type B containers for all shipments is an effective way to reduce the risk due to transportation but at a substantial cost. With the assumptions made in Chapter 5, this policy would reduce the consequences by a factor of 3 while increasing the costs by a factor of 3. Reducing the accident rates for LLW shipments will result in lowered consequences but this appears to be an inefficient method of reducing risks. Lowering accident rates by a factor of 10 on all links lowers the risks by about 1/ 3. Accident rates would have to be lowered by a factor of 100 to approach the risk reduction resulting from the use of Type B containers on all ship- ments. No attempt has been made to estimate the cost required to reduce the accident rates for LLW shipments. Finally, waste volume reduction appears to be a useful practice in low- ering the costs of transporting LLW. Reducing the volume by half reduces the shipments by half while doubling the Curie content of each shipment. The result is to cut shipping costs by 50% in exchange for increasing the risk by about 5%. ”Wisdom is the goal of knowledge.” I. D. Salinger. Franny and Zooey. 1961. APPENDICES Appendix A ANNUAL INVENTORY OF LOW-LEVEL WASTE SHIPMENTS IN THE MILLRWC Appendix A Annual Inventory of Low-Level Waste Shipments in the MILLRWC Volume (£13) Annual Shipments Location Generator Type Two Rivers, WI PWR Total Volume = 9993 cu. ft. 371 3513 Curie Total = 7.5 6109 3 8 7 Cs-137 H-3 I-129 N i-59 Ni-63 Pu-241 Sr-90 C-14 Co-60 Cs-137 H-3 l-129 Ni-59 Ni-63 Pu-241 Sr-90 Genoa, WI BWR Total Volume = 953 cu. ft. 339 219 Curie Total = 6.9 395 3 1 1 GM Co-60 Cs-137 H-3 l-129 Ni-63 Pu-241 Sr-90 North Perry, OH BWR Total Volume = 30261 cu. ft. 2719 24011 Curie Total = 1269 3531 28 34 4 GM Co-60 Cs-137 H-3 I-129 N b-94 N i-59 Ni-63 Pu-241 Sr-90 194 480 Curie Total = 4023 Kewaunee, WI PWR 953 2 2 2 Total Volume = 1628 cu. ft. Co~60 Cs-134 Cs-137 Ni-63 742 2987 0 5 7 0 Curie Total = 191 Oak Harbor, OH PWR Total Volume = 3729 cu. ft. 125 Cask Drum LSA Box Cask Drum LSA Box Isotope Curies C-14 5.2E-2 Co-60 5.1E 1 1.2E 1 1.4E 0 1.3E-3 3.1E-2 9.7E 0 1.1E 0 1.0E-1 1.9E-2 3.5E 1 3.3E 1 1.5E-1 3.3E-3 2.1E-2 4.7E—l 1.3E-1 5.9E-2 3.0E-1 7.313 2 5.2E 2 3.6E 0 5.2E—2 9.9E 0 4.5E 0 9313-1 2.7E—1 1.6E 3 1.8E 0 2.2E—1 3.3E-3 8.4E-3 1.4E 0 2.1E 2 1.7E-1 1.6E-2 8.9E 0 4.313 1 1.3E 2 9.1E 0 126 Volume (ft3) Location Generator Type Cask Drum LSA Box Cask Drum LSA Box Isotope Curies Charlevoix, MI BWR Total Volume = 5120 cu. ft. 1236 2648 1236 Curie Total = 223 Fulton, MO PWR Total Volume = 7027 cu. ft. 3496 3037 494 Curie Total = 30 Palo, IA BWR 1624 15289 2966 Total Volume = 19880 cu. ft. Curie Total = 12937 Bridgman, MI PWR Total Volume = 26977 cu. ft. 1342 22598 3037 Curie Total = 1044 Annual Shipments 7 5 2 20 6 1 17 23 4 8 44 4 G14 Co-60 Cs-137 H-3 I-129 Nb-94 N i-59 Ni-63 Pu-241 Sr-90 C-14 Co-60 Cs-137 H-3 N i-59 Ni-63 Pu-241 Sr-90 C-14 Co-60 Cs-137 Fe-55 H-3 I-129 Nb—94 N i-59 Ni-63 Pu-241 Sr-90 C-14 Co-58 Co—60 Cs-134 Cs-137 H-3 l-129 Ni-59 Ni-63 Pu-241 Sr-90 6.6E-2 1.1E 2 1.1E 2 4.5E-l 1.1E-2 2.2E-3 7.0E-2 1.5E 0 4.1 E-l 2.0E-1 1.4E-2 2.2E 1 3.2E O 3.9E-1 1.3E-2 4.1E 0 4.2E-1 2.9E-2 9.7E-1 5.3E 3 3.3E 2 6.7E 3 2.3E 0 3.3E-2 3.4E-2 4.4E 0 6.413 2 2.1E 0 5813-1 8013-2 7.5E 1 2.9E 1 4.0E 2 5.0E 2 3.0E 1 2.0E-3 2.8E-2 8.7E 0 1.2E 0 1613-1 127 Volume (ft3) Annual Shipments Location Generator Type Cask Drum LSA Box Cask Drum LSA Box Newport, MI BWR 3213 12464 4237 33 11 5 Total Volume = 19915 cu. ft. Curie Total = 1524 Covert, MI PWR 547 5296 11299 4 10 13 Total Volume = 17143 cu. ft. Curie Total = 2136 Monticello, MN BWR 777 6003 3143 8 10 4 Total Volume = 9922 cu. ft. Curie Total = 8004 Red Wing, MN PWR 530 671 3037 4 1 4 Total Volume = 4237 cu. ft. Curie Total = 40 Charlotte, Ml Medical 0 0 35 0 0 1 Total Volume = 35 cu. ft. Curie Total = 0.008 Canton, OH Medical 35 0 ‘ 0 2 0 0 Total Volume = 35 cu. ft. Curie Total = 70.5 Isotope C-14 Co-60 Cs-137 H-3 I-129 Nb-94 Ni-59 Ni-63 Pu-241 Sr-90 C-14 Co-60 Cs-137 Fe-55 H-3 I-129 Nb-94 Ni-59 Ni-63 Pu-241 Sr-90 C-14 Co-60 Cs—137 Fe-SS H-3 I-129 Nb—94 Ni—59 Ni-63 Pu—241 Sr-90 C-14 Co-60 Cs-137 H-3 N i-59 Ni-63 Pu-241 Sr—90 S-35 Co—60 Ir-192 Curies 3.6E-1 8.8E 2 6.2E 2 4.3E 0 6.2E-2 1.7E-2 5.5E-1 1.2E 1 5.4E 0 1.1E 0 2.2E-1 8.9E 2 2.1E 1 1.1E 3 2.5E 0 2.3E-3 5.9E-3 7.6E-1 1.2E 2 2.0E 0 1.9E-l 1.113 0 6.8E 3 2.0E 2 1.7E 2 1.6E 0 2.0E-2 3.8E-2 5.8E 0 8.4E 2 1.6E 0 3.5E-1 2613-2 2813 1 5.813 0 7.1 E-l 1.7E-2 5.3E 0 5.6E-1 5.2E-2 8.0E-3 7.0E 1 5.0E-1 128 Volume (ft3) Annual Shipments Location Generator Type Cask Drum LSA Box Cask Drum LSA Box Isotope Curies Cleveland, OH Medical 0 0 632 C-14 2.0E-3 Total Volume = 632 cu. ft. Curie Total = 0.179 Cr-51 5.4E-2 H-3 5.6E-2 I-125 3.4E-2 P-32 1.4E-2 S-35 4.5E—3 River Falls, WI Medical 0 0 21 H-3 2.6E-2 Total Volume = 21 cu. ft. Curie Total = 0.043 P-32 7.2E-3 S-35 9.6E-3 Iowa City, IA Medical 0 0 300 C-14 2.0E-1 Total Volume = 300 cu. ft. Curie Total = 0.44 H-3 2.0E-1 I-125 4.0E-2 Toledo, OH Medical 0 0 388 GM 3.6E-1 Total Volume = 388 cu. ft. Curie Total = 1.67 H-3 1.0E-2 I-125 1.3E 0 Kansas City, MO Medical 0 0 88 Cr-51 58136 Total Volume = 88 cu. ft. Curie Total = 3.2E-5 H-3 2.6E-5 Stillwater, MN Medical 0 0 124 CM 1.0E-3 Total Volume = 124 cu. ft. Curie Total = 0.044 Cr-51 4.4E-4 H-3 5.7E-3 I-125 9.3E-4 S-35 2.3E-2 Appleton, WI Medical 0 0 56 H-3 3.3E-3 Total Volume = 56 cu. ft. Curie Total = 0.003 Rochester, MN Medical 0 0 272 CM 3.8E-5 Total Volume = 272 cu. ft. Curie Total = 0.03 Cr-51 1.3E-4 H-3 3.2E-3 I-125 2.2E-2 P-32 4.2E-3 S-35 1.3E-5 Detroit, MI Medical 0 0 1222 GM 3.0E-2 Total Volume = 1222 cu. ft. Curie Total = 3.76 Cl-36 8.7E-4 Cr-51 8.1E-2 H-3 2.3E 0 I-125 2.6E-1 P-32 7.9E-1 S-35 2.8E-1 Lacrosse, WI Medical 0 0 39 C-14 1.3E-4 Total Volume = 39 cu. ft. Curie Total = 0.008 Cr-51 2.4E-3 H-3 4.8E-3 I-125 1.1E-3 129 Volume (ft-3) Annual Shipments Location Generator Type Cask Drum LSA Box Cask Drum LSA Box Isotope Curies Milwaukee, WI University 163 0 402 1 0 1 C-14 1.1E 0 Total Volume = 565 cu. ft. Curie Total = 519 Cl-36 9.5E 0 H-3 6.3E 1 I-125 3.5E 0 P-32 4.1E 2 S-35 3.0E 1 Sr-85 1.7E 0 Cincinnati, OH University 0 0 1543 0 0 3 C-14 6.7E-2 Total Volume = 1543 cu. ft. Curie Total = 0.887 Co-60 1.3E-3 Cr-51 5.2E-1 Cs-137 1.1E-3 H-3 2.8E-1 I-125 7.3E-3 Ni-63 3.8E-5 P-32 4.1E 2 St. Louis, MO University 163 0 7641 1 0 14 C-14 1.1E 0 Total Volume = 7804 cu. ft. Curie Total = 24.8 C060 2.5E 0 Cs-137 1.2E 0 H-3 1.913 1 Sr-90 9.6E-1 W. Lafayette, IN University 0 0 191 0 0 1 GM 5.2E-2 Total Volume = 191 cu. ft. Curie Total = 1.28 Cl-36 1.7E-4 H-3 1.2E 0 I-125 1.7E-2 P-32 1.6E-3 S-35 9.5E-3 Madison, WI University 0 0 148 0 0 1 014 1.1E—2 Total Volume = 148 cu. ft. Curie Total = 0.076 Cl-36 2.8E-5 Cs-137 6.0E-6 H-3 6.5E-2 Stevens Point, WI University 0 0 4 0 0 1 GM 1.0E-4 Total Volume = 4 cu. ft. Curie Total = 1.0E-4 Ames, IA University 0 0 134 0 0 1 GM 3.8E-3 Total Volume = 134 cu. ft. Curie Total = 0.305 Co—60 5.0E-6 Cs-137 2.05-4 Fe-55 4.0E-2 H-3 2.6E-1 Ra-226 7.0E-5 Th-232 9E-6 Bloomington, IN University 0 0 343 0 0 1 CM 9.5E-2 Total Volume = 343 cu. ft. Curie Total = 1.92 Co-60 8.5E-2 H-3 1.6E 0 Sr-90 7.4E-2 130 Volume (£13) Annual Shipments Location Generator Type Cask Drum LSA Box Cask Drum LSA Box Isotope Curies Duluth, MN Total Volume = 388 cu. ft. University Curie Total = 0.486 Columbus, OH University Total Volume = 1306 cu. ft. Curie Total = 0.875 Columbia, MO University Total Volume = 343 cu. ft. Curie Total = 19.2 Ann Arbor, MI Total Volume = 989 cu. ft. University Curie Total = 0.435 Minneapolis, MN University Total Volume = 7133 cu. ft. Curie Total = 7.98 E. Lansing, MI Total Volume = 3513 cu. ft. University Curie Total = 1.52 Dayton, OH Total Volume = 148 cu. ft. University Curie Total = 0.875 C-14 H-3 C-14 Cr-51 H-3 I-125 P-32 S-35 C-14 Co-60 Cs-137 H-3 I-129 Nb-94 Ni-59 Ni-63 Pu-241 Sr-90 C-14 Cr-Sl H-3 I-125 P-32 S-35 C-14 Cr-51 H-3 I-125 P-32 S-35 C-14 H-3 I-125 P-32 S-35 Sr-85 C-14 Cl-36 Co-60 Cs—137 Fe-55 H-3 Kr-85 S-35 U-238 2.6E-2 4.6E-1 8.5E-2 1 .4E-1 3.9E-1 2.4E-1 1 .1 E-2 9.2E-3 1.6E-2 5.3E 0 3.8E 0 1.0E 1 3.8E-4 1.0E-4 3.3E-3 7.2E-2 3.2E-2 1.8E-2 5.6E-2 1 .5E-3 2.2E-1 1.2E-1 5.3E-3 4.8E-3 2.0E-1 1.5E 0 2.6E 0 9.5E-1 2.0E 0 8.0E-1 1.0E-1 8.6E-1 2.0E-1 3.4E-1 1.6E-3 1.8E-4 1 .1 E-l 7.8E-4 3.1E-2 2.3E-5 2.4E-2 8.6E-2 3.9E-4 3.4E-4 1.1E-5 131 Volume (ft3) Annual Shipments Location Generator Type Cask Drum LSA Box Cask Drum LSA Box Isotope Curies Muskegon, MI Industrial 0 0 300 0 0 1 C-14 3.8E-2 Total Volume = 300 cu. ft. Curie Total = 0.113 Cr-51 2.3E-5 H-3 4.5E-2 I-125 9.0E-3 P-32 2.1E-3 Centerville, OH Industrial 0 0 148 0 0 1 CM 4.0E-3 Total Volume = 148 cu. ft. Curie Total = 0.004 Mattawan, MI Industrial 99 0 0 3 0 0 Am-241 4.1E 1 Total Volume = 99 cu. ft. Curie Total = 92.0 Cs—137 2.05 1 Pu-239 3.1E 1 Ra-226 1.2E-2 South Bend, IN Industrial 0 0 501 0 0 1 Co-60 1.0E-3 Total Volume = 501 cu. ft. Curie Total = 0.645 Cs-137 1.2E-3 H-3 4.0E-1 Ra-226 5.0E-4 Th-232 2.3E-1 U-235 1.2E-2 Elkhart, IN Industrial 0 0 71 0 0 1 GM 1.6E 0 Total Volume = 71 cu. ft. Curie Total = 1.6 Minneapolis, MN Industrial 681 0 5650 5 0 11 C-14 1.0E-1 Total Volume = 6331 cu. ft. Curie Total = 1620 Cs-137 1.015 3 l-125 2.5E 1 Kr-85 1.013 1 Pm—147 5.0E 0 Po-210 6.0E 2 Ra-226 2.0E 0 Sr-90 4.0E-1 Athens, OH Industrial 0 0 399 0 0 1 GM 1.1E-2 Total Volume = 399 cu.ft. Curie Total = 0.202 H-3 8.1E-2 I-125 1.1E-1 Warren, MI Industrial 150 0 58 4 0 1 Am-241 4.4E 0 Total Volume = 208 cu.ft. Curie Total = 94.7 Co-60 4.0E 0 Cs-137 8.013 1 Fe-55 8.0E-2 Kr-85 6.0E 0 Ra-226 8.0E-3 Sr-90 1.6E-1 Minneapolis, MN Industrial 0 0 9357 0 0 17 Am—24l 3.3E-2 Total Volume = 9357 cu. ft. Curie Total = 5.23 H-3 2.0E-1 U-238 5.0E 0 132 Volume (ft3) Annual Shipments Location Generator Type Cask Drum LSA Box Cask Drum LSA Box Isotope Curies Indianapolis, IN Industrial 0 0 2984 C-14 1.1E 0 Total Volume = 2984 cu. ft. Curie Total = 13.8 Cl-36 1.6E-3 Cr-Sl 1.3E-1 H-3 8.0E 0 I-125 4.013 0 P-32 5.3E-1 S-35 1.9E-2 Sr-85 1.6E-3 Akron, OH Industrial 0 0 201 I-125 3.3E-1 Total Volume = 201 cu. ft. Curie Total = 0.33 Des Moines, IA Industrial 109 0 0 Co-60 2.1E 2 Total Volume = 109 cu. ft. Curie Total = 210 Clinton, IA Industrial 0 0 14 Sr-90 6.1E 0 Total Volume 2 14 cu. ft. Curie Total = 6.1 Atlantic, IA Industrial 0 0 4 GM 5.0E-6 Total Volume = 4 cu. ft. Curie Total = 5.0E-6 Chaska, MN Industrial 0 0 56 C-14 1.5E-3 Total Volume = 56 cu. ft. Curie Total = 0.266 H-3 2.6E-1 I-125 39134 N i-63 3.1E-3 P-32 5.5E-5 S-35 7.7E-4 Southfield, MI Industrial 0 0 60 C-14 1.0E-5 Total Volume = 60 cu. ft. Curie Total = 1.0E-5 Indianapolis, IN Industrial 0 0 900 C-14 7.8E-1 Total Volume = 900 cu. ft. Curie Total = 1.04 H-3 2.3E-1 I-125 3.3E-2 P-32 5.9E-4 Mt. Vernon, IA Industrial 0 0 11 C-14 5.0E-4 Total Volume = 11 cu. ft. Curie Total = 7.5E-4 Kalamazoo, MI Industrial 0 0 7 GM 2.5E-2 Total Volume = 7 cu. ft. Curie Total = 0.084 Cs-137 1.0E—3 H-3 5.6E-2 N i-63 5.0E-4 Solon, OH Government 0 0 39 C-14 4.3E-3 Total Volume = 39 cu. ft. Curie Total = 0.016 H-3 1.1E-2 Ni-63 2.4E-4 Sr-90 1.2E-6 133 Volume (ft3) Annual Shipments Location Generator Type Cask Drum LSA Box Cask Drum LSA Box Isotope Curies Yellow Springs, OH Government 0 0 11 0 0 1 C-14 1.8E-1 Total Volume = 11 cu. ft. Curie Total = 0.18 Charles City, IA Government 0 0 60 0 0 1 G14 1.0E-4 Total Volume = 60 cu. ft. Curie Total = 4.8E-4 H-3 3.8E-4 Appendix B NODE DATA FOR THE MILLRWC TRANSPORTATION NETWORK Node 3 12 14 15 16 17 24 25 26 27 28 29 30 31 Appendix B Node Data for the MILLRWC Transportation Network Location Intersection Fargo, ND I—29, 194 E Sioux Falls, SD I-90, I-229 Sioux City, IA I-29, US-75 Missouri Valley, IA I-680, I-29 N Council Bluffs, IA I-680, I-29 Council Bluffs, IA I-80, I-29 Neola, IA I-80, I-680 St. Joseph, MO I-29, US-36 N Kansas City, MO I-29, I-635 N Kansas City, MO I-29, I-35 N Kansas City, MO I-35, I-435 Kansas City, MO I-70, 1-435 Node Kansas City, MO I-435, I-70, US-71 Kansas City, MO I-29, I-35, I-70 48 NW Minneapolis, MN I-94, 1494 49 50 51 52 53 54 55 56 57 58 59 61 62 63 66 67 69 70 71 72 73 74 75 76 78 79 SW Minneapolis, MN I-494, US-169 Bloomington, MN I-35, I-494 S St. Paul, MN 1494, MN-3 SE St. Paul, MN 1494, US-lO N Minneapolis, MN I-694, I-35W N St. Paul, MN I-694, I-35E NE St. Paul, MN 1694, MN-36 Hastings, MN US-61, MN-SS Lino Lakes, MN l-35, I-35E, I-35W Barnum, MN l-35, Co-5 Duluth, MN I-35, I-535 E St. Paul, MN I-94, 1-494, 1694 Albert Lea, MN I-35, I-90 Dexter, MN I-90, MN-16 Marion, MN I—90, US-52 La Crescent, lvfl\l I-90, US-61 Minneapolis, MN I-94, I-35W St. Paul, MN I-35E, I-94 Ames, IA l-35, US-30 NE Des Moines, IA I-35, [80 SE Des Moines, IA I-235, US-65 NW Des Moines, IA 180, IA-141 SW Des Moines, IA I—35, I-80 Tiffin, IA I-80, l-380 N Davenport, IA I-80, l-280 Bettendorf, IA I-80, I-74 W Davenport, IA I-280, U961 Rock Island, IL I-74, I-80, I-280 Moline, IL I-74, I-80, l-280 Harrisonville, MO US-71, MO-13 Joplin, MO I-44, US-166 134 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 Location Fidelity, MO Springfield, MO Kirkwood, MO Mehlville, MO Crystal City, MO Cape Girardeau, MO Miner, MO Hayti, MO Cooter, MO Caruthersville, MO Charlestown, MO Bridgeton, MO St. Louis, MO Columbia, MO Elk Mound, WI Rice Lake, WI Chippewa Falls, WI Eau Claire, WI East St. Louis, IL Tomah, WI Portage, WI Merrill, WI Madison, WI Beloit, WI Green Bay, WI Oshkosh, WI Bayside, WI Intersection I-44, U971 1-44, US-65 I-44, I-270 I-55, I-270 I-55, US-67 I-SS, MO-146 I-55, I-57 I-55, I-155 I-55, US-61 I-155, Co-J I-57, US.60 I-70, I-270 I-55, I-70 I-70, USo63 I-94, WI-29 US-53, WI-48 US-53, WI-29 I-94, US-53 I-55, I-64 I-90, I-94 l-90, I-94, US—51 US-51, WI-17 I-90, I-94 I-90, WI-15 I-43, Wl-54 U541, WI-21 I-43, WI-100 Menomonee Falls, WI US-41, WI-100 West Allis, WI SW Milwaukee, WI Milwaukee, WI S Milwaukee, WI Rockford, IL Arlington Hts., IL Northbrook, IL Highland Park, IL Buffalo Grove, IL Rosemont, IL NW Chicago, IL Elmhurst, IL Chicago Loop, IL Burr Ridge, IL S Chicago, IL Plainfield, IL Joliet, IL Tinley Park, IL US-45, 1-94, I-894 I-894, WI-15 1-43, I-94 I-94, I-894 I-90, USoZO I-90, I-290 I-94, I-294, IL-68 l-94, US-41 I-290, IL-68 I-90, I-294 I-90, I-94 I-290, I-294 I-90, I-94, I-290 I-55, I-294 I-90, I-94 I-55 I-55, [~80 I-57, I-80 Node 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 135 Location Intersection S Chicago, IL I-57, I-94 Hazel Crest, IL I-80, I-294 South Holland, IL I-80, I-94, I-294 Barstow, IL I-80, IL-5 Dixon, IL IL-5, US-52 Galesburg, IL I-74, US-34 NW Bloomington, IL I-55, I-74 S Bloomington, IL I-55, I-74, US-57 Springfield, IL I-55, I-72, IL-54 W Decatur, IL I-72, US-51 N Decatur, IL I-72, US-51 Farmer City, IL I-74, IL-54 Champaign, IL I-57, I-72, I-74 Effingham, IL I-57, I-70 S Springfield, IL I-55, US-36 Troy, IL I-55, I-70, I-270 Salem, IL 1-57, US-50 Mt. Vernon, IL I-57, I-64 Pulleys Mill, IL I-57, I-24 S Gary, IN I-65, I-80, l-94 E Gary, IN I-80, I-90, I-94 Paducah, KY l—24, US-45 Chicago, IL I-55, I-90, I-94 W Peoria, IL I-74, I-474 Bartonville, IL 1474, US-24 E Peoria, IL I-74, I-474 Sault Ste. Marie, MI I-75 St. Ignace, MI I-75, USoZ Grayling, MI I-75, US—27 Clare, MI US-10, US-27 Bay City, MI I-75, US—10 East Lansing, MI I-69,I-496,US-127 S Lansing, MI I-96, US-127 Jackson, MI I-94, US-127 SW Lansing, MI I-69, I-96 W Lansing, MI I-96, I-496 E Grand Rapids, MI I-96, I-196 N Grand Rapids, MI I-96, US-131 Grand Rapids, MI I-196, US-131 Reed City, MI US—131, US-10 Muskegon,MI I-96, US-31 Ludington, Ml US-31, US-10 Holland, MI I-196, USo31 Benton Harbor, MI I-94, l-96 Kalamazoo, MI I-94, US-131 Marshall, MI I-69, I-94 NW Flint, MI I-75, I-475 - NE Flint, MI I-475, MI-54 Flint, MI I-69, I-475 Lapeer, MI 1-69, MI-24 W Flint, MI I-69, l-75 SW Flint, MI I-75, U523 Brighton, MI I—96, US-23 Node Location Intersection 180 N Ann Arbor, MI US-23, MI-14 181 AnnArbor, MI I-94, MI-14 182 NE Ann Arbor, MI US-23, MI-14 183 SE Ann Arbor, MI I-94, US-23 184 Farmington, MI I-96, I-275, I-696 185 Livonia, MI I-96, I-275, MI-14 186 Wayne, MI I-94, I-275 187 Southfield, MI I-696,US-10,MI-39 188 W Detroit, MI I-96, MI-39 189 Dearborn, MI I-94, MI-39 190 Detroit, MI I-75, I-94, I-96 191 Sylvania, OH 1475, US-23 192 Toledo, OH I-75, I-280 193 Port Huron, MI I-69, I-94 194 Fremont, IN I-69, I-80, I-90 195 Muncie, IN I—69, IN-32 196 NE Indianapolis,IN I-69, I-465 197 Royalton, IN I-65, I-465 198 NW Indianapolis, IN 1465 199 W Indianapolis, IN I-65, I-465 200 Indy Speedway, IN I-74, I-465 201 Veedersburg, IN I-74, US-41 202 E Indianapolis, IN I-70, I-465 203 Indianapolis, IN I-65, I-70 204 SW Indianapolis, IN I-70, I465 205 S Indianapolis, IN I-65, I-465 206 SE Indianapolis, IN l-74, 1-465 207 New Albany, IN I-64, I65 208 W New Albany, IN I-64, US-150 209 Ottawa Hills, OH 1-475, I-75 210 Maumee, OH I-80, I-90, I-475 211 Perrysburg, OH I-75, I-475 212 Lemoyne, OH I-80, I-90, I-280 213 Amherst, OH I-80, I-90 214 Elyria, OH I-80, I-480 215 Strongsville, OH I-71, I-80 216 Brook Park, OH I-71, 1480 217 Cleveland, OH I-77, I-90, I-480 218 Euclid, OH I-90, OH-2 219 Willoughby Hills, OH I-90, 1-271 220 Grand River, OH OH-2, OH-44 221 Mentor, OH I-90, OH-44 222 Ashtabula, OH I—90, 01-1-11 23 Parma, OH I-77, 1480 224 Shaker Heights, OH I-271, I-480 225 Northfield, OH I-271, I-480 226 Streetsboro, OH I-80, 1480 227 Richfield, OH I-77, I-271 228 West Austintown, OH I-76, I-80 229 Girard, OH 180, OH-11 230 Austintown, OH 180, OH-ll 231 Youngstown, OH I-680, US-422 232 North Lima, OH I-76, I—680 136 Node Location Intersection 233 Bridgeport, OH I-70, OH-7 234 Akron, OH I-76, I-77 235 W Akron, OH I-76, I-77 236 SW Akron, OH I-76, 1-277 237 S Akron, OH I-77, 1-277 238 Weymouth, OH I-71, I-271 239 Seville, OH I-71, I-76 240 NE Columbus, OH I-71, I-270 241 Dublin, OH I—270, US-33 242 Lincoln Village, OH 1-70, 1-270 243 Columbus, OH I-70, I-71 244 SW Columbus, OH I-71, I-270 245 Whitehall, OH I-70, I-270 246 Murlin Heights, OH I-70, I-75 247 Cambridge, OH I-70, I-77 248 Marietta, OH I-77, OH-7 249 Findlay, OH I-75, US-23 250 N Columbus, OH I-270, US—23 251 Hamilton Meadows,OH I-270, US—23 252 Portsmouth, OH US-23, US-52 253 Dayton, OH I-75, US-35 254 Glendale, OH I-75, I-275 255 Cincinnati, OH I-71, I-75 256 Taylors Creek, OH I-74, I-275 257 Miamitown, OH I-74, l-275 258 Petersburg, KY 1-275, KY-338 259 Covington, KY I-71, I-75, I-275 260 Highland Heights, KY I-275, I-471 261 262 263 264 265 266 267 268 269 270 272 273 274 278 279 280 282 Withamsville, OH I-275, OH-125 Brecon, OH I-71, I-275 NW Akron, OH I-77, OH-21 Norton, OH I-76, OH-21 Warrenton, IN I-64, US-41 Fulton, KY US-51, Pur Pkwy Mayfield, KY US-45, Pur Pkwy Gilbertsville, KY Eddyville, KY I-24, Pur Pkwy I-24, W KY Pkwy Mortons Gap, KY US-41,W KY Pkwy Henderson, KY US-41, Aud Pkwy Owensboro, KY Aud Pky, GR Pky Beaver Dam, KY W KY Pky,GR Pky Elizabethtown, KY I—65, W KY Pkwy NW Louisville, KY I-64, I-264 SW Louisville, KY I-264, US-60 Louisville, KY I-64, I-65 Node 283 284 285 286 287 288 289 290 291 294 295 296 297 301 302 303 304 305 306 307 308 309 310 31 1 312 313 314 315 316 317 318 334 335 336 337 338 339 340 348 350 351 352 354 355 Location Intersection S Louisville, KY I-65, I-264 NE Louisville, KY I-71, I—624 E Louisville, KY I-64, I-264 Walton, KY I-71, I-75 N Lexington, KY I-64, I-75, US-25 W Lexington, KY US-60, KY-4 Lexington, KY US-25, US-60 5 Lexington, KY US-25,US-27,KY-4 E Lexington, KY I-64, I-75, US-60 Winchester, KY I-64, BC Pkwy Kenova, KY I-64, US-23 Charleston, WV I-64, I-77, I-79 Ravenswood, WV I-77, WV-2 Rochelle, IL US-51, IL-5 Dyersburg, TN I—155, US-51 N Lansing, MI I-69,US-27,US-127 NW Lansing, MI I-69, I-96 Charlotte, MI 169, US-27 Canton, OH I-77, US-62 River Falls, WI I-94, WI-65 W Lafayette, IN I-65, US-52 Stevens Point, WI US-51, US-10 Bloomington, IN IN-37, IN-46 South Bend, IN Elkhart, IN I-80,90, US-31 I-80,90, IN-l9 Athens, OH US-33, US-50 Clinton, IA US-67, US-30 Le Claire, IA [80, US-67 Atlantic, IA I-80, US-6 Springfield, OH I-70, US-68 Mason City, IA I-35, US-18 Monticello, MN I—94, MN-25 Red Wing, MN US-61, US-63 Cedar Rapids, IA I-380, lA-94 Fulton, MO I-70, US-54 Genoa, WI I-90, US-53 Manitowoc, WI 1-43, W142 Manitowoc, WI I-43, WI-42 Indian River, MI I-75, MI-68 Covert, Ml I-196 Bridgman, MI I-94 Newport, MI I-75, I-275 Oak Harbor, OH I-80,90, OH-53 North Perry, OH I-90, US-20 Appendix C LINK DATA FOR THE MILLRWC TRANSPORTATION NETWORK 137 gm .om .mm .mm conga—95m owe m m onD ow m-ZS_ val mm 3 mm 3 .am .3“ .3 .mm .vm :mQLD GEN pm 0 3% 0w «.3..— >>mm-_ mo om mm 0v .9. .mm .mm .3 .N 35% won w mm 9‘0-— Q «.31 mm; 3 cm 8 am .wm RN .8 .vm 53.59% own m m m-ZE um 26m-— vaul 5 cm mu AN .8 .mm .5 55596 omma m e >>mm% 0w $7m3 val cm a. 3 mm Am J 3.5% may Ow mm «.31— ...w mN-Z$_ «$-— vmm wv mm em .mm .mm .mm .5 53.59% cm»: ms 3 3mm; ow «.31 wow; .34 mm we NN em .mm .NN :Bhfism emu“ on 2 $Tm3 ow 3% «3..- av wv pm me .2 .2 3.5% gm w Mm 5.02 ...w mmwl gm: mm on ow mm .3 .2 .9 3.5% 3N m 3% mom: on mmvé on; mm am an my .5 ...: .3 53.5 comm mm m mm-_.mm-_ 0» mmvé E-— ~m mm m: cm .2 .3 .3 .N~ 53.5 co? : u KmD Q on; mmul om mm 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R... 3.8 3...). mF.m3 ow om-m3 8&3 ow mm-— ©.m3 % mm-— cw. ow omm-m3 .we-m3 on ma: .8053— mm. on.— ow-— N©-m3 ow-— 2:3— me uFm oFm mFm mFm no 3N Fm va oN F m; an OFF. m; v: «“52 FF 352 < :5.— Appendix D MASS ATTENUATION AND DOSE BUILDUP FACTORS Appendix D Mass Attenuation and Dose Buildup Factors The attenuation of gamma photons in a medium is a function of the mass attenuation coefficient p. for that medium and the distance r travelled through the medium. The atten- uation function exponentially decreases over distance: Attenuation = e’tu' (D1) 11 in turn is dependent on the energy of the photon. In air the mass attenuation coefficients are: E = 0.5 MeV: u = 1.15 E-Z m-1 E = 1.0 MeV: u = 8.20 E-3 m-1 Dose buildup factors 8011') are empirical corrections which account for measured dose rates being greater than predicted by theories that incorporate only the inverse-square law and mass attenuation. The dose rate (and integrated dose) at a point r from the source is larger than predicted due to scattering of the photons from the surrounding medium to the reception point. Analytical models have been fit to the empirical data, Lamarsh [46] favors the Berger form: Bun) = 1 + cure-Bur (D2) Substituting the values given in [46] for the parameters gives the following buildup functions: E = 0.5 MeV: Bum) = 1 + 1.5411ure'0-099l-u' (D3) E = 1.0 MeV: B(ur) = 1 + 1.1305me-0-057ur (D4) Using the values given above, the product of the attenuation and buildup factors, e4” - B(ur), is found in the following tables for photon energies of 0.5 MeV and 1.0 MeV. Distances range from 1 to 800 meters. Also calculated for each 100 meter band is an average value for the product over the band. This value is the geometric mean of the endpoint values. If attenuation and buildup are insignificant, the product would equal 1 at all distances and the mean over any range of distances would also equal 1. The sum of the mean values for each 100 meter band from 0 to 800 meters is thus 8. Taking the ratio of the cumulative mean product with attenuation to the cumulative mean product without attenuation (= 8) gives K3, the attenuation and buildup factor used in Chapter 4. Table D-l. e‘w 80.11) at 0.5 MeV Mean Cum. Value Cum. Value Distance (111) e'lu’ Bun) e4” B(p.r) e1“ B011) w/Atten. w/o Atten. 1 0.99 1.01 1.00 5 0.94 1.06 1.01 10 0.89 1.13 1.01 50 0.56 1.63 0.92 100 0.32 2.22 0.70 0.84 0.84 1.00 200 0.10 3.28 0.33 0.48 1 .32 2.00 300 0.03 4.20 0.13 0.21 1.53 3.00 400 0.01 5.00 0.05 0.08 1.61 4.00 500 3.18E—03 5.68 0.02 0.03 1.64 5.00 150 151 Table D-1. (continued) Mean Cum. Value Cum. Value Distance (m) e4" 8011:) e'l'“ Butt) e'lu’ Bun) w/Atten. w/o Atten. 600 1.01E-03 6.26 0.01 0.01 1.65 6.00 700 3.19E-04 6.75 2.15E-03 3.69E-03 1.66 7.00 800 1.01E-04 7.16 7.23E-04 1.25E-03 1.66 8.00 Table D-2. e-U-l' 30.1!) at 1.0 MeV Mean Cum. Value Cum. Value Distance (m) e'l” B(|.u') e'w' B(ur) e'ur B(p.r) w/Atten. w/o Atten. 1 0.99 1.01 1.00 5 0.96 1.05 1.00 10 0.92 1.09 1.01 50 0.66 1.45 0.96 100 0.44 1.88 0.83 0.91 0.91 1.00 200 0.19 2.69 0.52 0.66 1.57 2.00 300 0.09 3.42 0.29 0.39 1.96 3.00 400 0.04 4.08 0.15 0.21 2.17 4.00 500 0.02 4.67 0.08 0.11 2.28 5.00 600 0.01 5.20 0.04 0.05 2.33 6.00 700 3.21E-03 5.68 1.83802 2.63E-02 2.36 7.00 800 1.42E-03 6.10 8.64E—03 1.26E-02 2.37 8.00 From the data above: K05 = —1§6 = 0.207 2.37 K1 .0 = —8_ = 0.297 To simplify matters, assume that K05 applies to all energies less than 0.75 MeV and K10 applies to all energies greater than 0.75 MeV, in other words: K05 = KE<0.75 Kw = 19520.75 Appendix E CALCULATION OF ATMOSPHERIC DISPERSION AND DEPOSITION Appendix E Calculation of Atmospheric Dispersion and Deposition The airborne concentration x can be calculated downwind from an emission source. The concentration will depend on the strength of the source, the distance downwind, the wind speed and the turbulence or mixing characteristics of the atmosphere. Meteorology and Atomic Energy 1968 [66] is a collection of methods for calculating the downwind concentration. To remove the effects of source strength from the process, the calculations are based on the concentration normalized to the source amount Q (if the data is time averaged) or the rate of release Q’ (if instantaneous data is being used). The resulting quantity, x/ Q, (pronounced ki over Q) has the units of seconds per cubic meter or Curie-seconds per cubic meter per Cuire released. To account for differing wind speeds, the x/ Q values are often reported for a wind speed of 1 m/ sec. The wind speed is represented by the variable u and the reported values are designated xu/ Q (ki u over Q). These values are corrected for the appropriate wind speed when used in calculations. The general release model is a plume originating at the release point and travelling downwind. The axis of the wind direction is designated x. The horizontal radius of the plume is designated y and the vertical radius is designated 2. The concentration within the plume at any downwind location x is described by a Gaussian distribution about the centerline in both the y and 2 directions. Reference 66 provides results of xu/ Q calculations in graphical form for continuous distances downwind up to 100,000 meters in some cases. Turbulence in the atmosphere can be caused by mechanical processes such as the flow of air over the topography or by thermal gradients. Atmospheric turbulence is classified by a number of methods, the most frequently used measure is the Pasquill stability categories. These categories range from A which denotes unstable conditions (usually low-speed, meandering winds) to G which signifies extremely stable conditions (usually low-speed, constant direction winds). A plume produced under class A conditions would be broad and widely dispersed, a plume formed in class C conditions would be narrow and concentrated. Deposition of material from the plume onto the ground is also dependent on the concentration of material in the plume. Meteorology and Atomic Energy 1968 [67] shows that the rate of depositon is proportional to the concentration x. The proportionality constant is called the deposition velocity. The experimental values of depositon velocity for fission products reported in [67] range from 0.057 m/ sec for Nb-95 over water to 0.0004 m/ sec for Cs-137 over soil. Accordingly, a deposition velocity of 0.005 m/ sec will be used for all deposition calculations. The graphical method presented in [67] will be used, corrected to a deposition velocity = 0.005 m/ sec. RADTRAN [51] has adapted the methods used in Meteorology and Atomic Energy 1968 [66] for calcu- lation of x/ Q. Rather than determine the concentration downwind and off axis from the plume centerline, RADTRAN assumes that the plume can be modeled as a 0 set of nested ellipses originating at the release point (figure E-l). The ellipses connect points of constant x or x/ Q (or quantities proportional to x). The ellipses are referred to as iso-dose lines. RADTRAN gives the values for the area enclosed by each ellipse and time- Figure E-l. Nested Ellipses integrated x/ Q at the boundary of each ellipse.- 152 153 Also given in Reference 51 are values of wind speed typical of the Pasquill categories A through F. (Category C is not used in [51].) With these numbers, X/ Q can be calculated for each stability class at each iso-dose line. At this point, the method which follows departs from that used in RADTRAN III. Examining the exposure equations derived in Chapter 4 reveals that the parameters critical to the calculations are the amount of material deposited on the ground and the airborne concentration which has taken such deposition into consideration. This concentration is the Depleted x/ Q and can be calculated from the values of x/ Q at each iso-dose line using the method presented in Meteorology and Atomic Energy 1968 [66] and the boundary condition that the amount of material entering Area(n) is equal to the amount of material leaving Area(n-l). The amount deposited within Area(n) is the difference between that entering and that leaving the area. The first step in calculating Depleted x/ Q for a particular Pasquill stability class is to convert the area used by RADTRAN into a downwind distance on which the graphs in Reference 67 are based. This was done by referring to the xu/ Q versus distance graphs in Meteorology and Atomic Energy 1968 [66]. The downwind distance can be read from these graphs by multiplying the x/ Q value at the area boundary by the wind speed u for the Pasquill category. The depletion fraction Qx/Qo at the downwind distance is estimated from the appropriate graph on page 205 of Meteorology and Atomic Energy 1968 [67] and corrected for the assumed deposition velocity of 0.005 m/ sec using the formula given on page 206 of [67]. Multiplying x/ Q by the depletion fraction produces the Depleted x/ Q value at the iso-dose line. The following tables present the x/ Q, the depletion fraction and Depleted x/ Q values for each Pasquill category. The units of the parameters are: Area in square meters, x / Q and Depleted x/ Q in seconds per cubic meter, Length and width in meters. Table E-l. Plume Depletion Calculation Pasquill Category A wind speed = 1 m/s P(A) = 0.10 Area x/Q Plume Length Plume Width Qx/Qo Depleted x/Q 4.59E+02 6.00E-03 4.00E+01 3.65E+00 9.10E-01 5.46E-03 1.53E+03 1.70E-03 7.50E+01 6.49E+00 8.90E-01 1.51E-03 3.94E+03 8.40E-04 1.IOE+02 1.14E+01 8.90E-01 7.48E-04 1.25E+04 1.70E-04 2.20E+02 1.81E+01 8.80E-01 1.50E-04 3.04E+04 7.80E-05 3.00E+02 3.23E+01 8.80E-01 6.86E-05 6.85E+04 2.80E-05 4.50E+02 4.85E+01 8.6OE-01 2.41E-05 1.76E+05 8.00E-06 8.00E+02 7.00E+01 8.60E-01 6.88E-06 4.46E+05 2.20E-06 1.30E+03 1.09E+02 8.50E-01 1.87E-06 8.59E+05 9.00E-07 1.70E+03 1.61E+02 8.40E-01 7.56E-07 2.55E+06 1.40E-07 2.ZOE+03 3.69E+02 8.40E-01 1.18E-07 4.45E+06 7.00E-08 3.20E+03 4.43E+02 8.4OE-01 5.88E—08 154 Table E—l. (continued) Pasquill Category B wind speed = 2 m/s P(B) = 0.05 Area x/Q Plume Length Plume Width Qx/Qo Depleted x/Q 4.59E+02 4.00E-03 5.00E+01 2.92E+00 9.50E~01 3.80E-O3 1535-1-03 1.30E-03 9.00E+01 5.41 E+00 9.40E-01 1.22E—03 3.94E+03 5.50E-04 1.40E+02 8.96E+00 9.40E-01 5.17E-04 1.25E+04 1.30E-04 2.50E+02 1.59E+01 9.30E-01 1.21E-04 3.04E+04 6.00E—05 3.80E+02 2.55E+01 9.20E-01 5.52E-05 6.85E+04 2.70E-05 5.50E+02 3.96E+01 9.10E-01 2.46E-05 1.76E+05 1.00E-05 9.00E+02 6.23E+01 9.10E-01 9.10E—06 4.46E+05 3.50E-06 1.50E+03 9.46E+01 9.00E-01 3.15E-06 8.59E+05 1.60E-06 2.05E+03 1.33E+02 8.90E-01 1.42E-06 255134-06 4.10E-07 3.10E+03 2.62E+02 8.80E-01 3.61 E07 4.45E+06 2.20E-07 4.00E+03 3.54E+02 8.80E—01 1.94E-07 Pasquill Category C wind speed: 3 m/s P(C) = 0.10 Area x/Q Plume Length Plume Width Qx/Qo Depleted x/Q 4.59E+02 4.00E-03 6.00E+01 2.44E+00 9.60E-01 3.84E-03 1.53E+03 1.10E-03 1.10E+02 4.43E+00 9.40E-01 1.03E—03 3.94E+03 5.70E-04 1.80E+02 6.97E+00 9.40E-01 5.36E—04 1.25E+04 1 .30E-04 3.10E+02 1.28E+01 9.20E-01 1.20E-04 3.04E+04 6.70E-05 4.70E+02 2.06E+01 9.20E-01 6.16E—05 6.85E+04 3.00E-05 7.00E+02 3.12E+01 9.20E-01 2.76E-05 1 .76E+05 1 .00E-05 1.20E+03 4.67E+01 9.10E-01 9.10E-06 4.46E+05 5.00E-06 2.00E+03 7.10E+01 9.00E-01 4.50E—06 8.59E+05 2.80E-06 3.00E+03 9.11E+01 8.90E—01 2.49E-06 2.55E+06 1.005-06 5.00E+03 1.62E+02 8.80E-01 8.80E-07 4.45E+06 6.00E-07 6.20E+03 2.28E+02 8.80E-01 5.28E-07 Pasquill Category D wind speed = 4 m/s P(D) = 0.40 Area x/Q Plume Length Plume Width Qx/Qo Depleted x/Q 4.59E+02 4.30E-03 7.00E+01 2.09E+00 9.60E-01 4.13E-03 1.53E+03 1.30E-03 1.30E+02 3.75E+00 9.40E-01 1.22E-03 3.94E+03 6.50E-04 2.10E+02 5.97E+00 9.30E-01 6.05E-04 1.25E+04 1 8013-04 4.00E+02 9.95E+00 9.20E-01 1.66E-04 3.04E+04 9.50E-05 5.SOE+02 1.76E+01 9.10E-01 8.65E-05 6.85E+04 4.30E-05 9.00E+02 2.42E+01 8.90E-01 3.83E-05 1.76E+05 1 .80E-05 1.60E+03 3.50E+01 8.80E-01 1.58E-05 4.46E+05 8.50E-06 2.50E+03 5.68E+01 8.60E-01 7.31E-06 8.59E+05 5.00E-06 4.00E+03 6.84E+01 8.40E-01 4.20E-06 2.SSE+06 1.9OE-06 7.00E+03 1.16E+02 8.10E-01 1.54E-06 4.45E+06 1.30E-06 9.00E+03 1 .57E+02 8.00E-01 1.04E-06 155 Table E-l. (continued) Pasquill Category E wind speed = 2.5 m/s P(E) = 0.25 Area x/Q Plume Length Plume Width Qx/Qo Depleted x/Q 4.59E+02 9.60E-03 9.00E+01 1.62E+00 9.00E-01 8.64E-03 1.53E+03 3.20E-03 1.60E+02 3.04E+00 8.70E—01 2.78E-03 3.94E+03 1.60E-03 2.20E+02 5.70E+00 8.60E-01 1.38E-03 1.25E+04 4.00E-04 4.80E+02 8.29E+00 8.30E-01 3.32E-04 3.04E+04 2.10E-04 7.00E+02 1.38E+01 8.00E-01 1.68E-04 6.85E+04 1.40E-04 1.10E+03 1.98E+01 7.70E-01 1 .08E-O4 1.76E+05 4.40E-05 1.90E+03 2.95E+01 7.50E-01 3.30E-05 4.46E+05. 2.10E-05 3.00E+03 4.73E+01 7.20E-01 1.51E-05 859134-05 1.20E-05 5.00E+03 5.47E+01 6.70E-01 8.04E-06 2.55E+06 4.80E-06 8.00E+03 1.01E+02 6.20E-01 2.98E-06 4.45E+06 3.60E-06 1.10E+04 1.29E+02 5.70E-01 2.05E—06 Pasquill Category P wind speed = 1 m/s P(F) = 0.10 Area x/Q Plume Length Plume Width Qx/Qo Depleted x/Q 4.59E+02 6.20E-02 9.50E+01 1.54E+00 7.10E-01 4.40E-02 1.53E+03 1.80E-02 1 .80E+02 2.71 13400 6301501 1 .13E-02 3.94E+03 8.40E-03 2.40E+02 5.23E+00 5.70E-01 4.79E-03 1.25E+04 2.00E-03 5.50E+02 7.23E+00 4.60E—01 9.20E-04 3.04E+04 9.205-04 8.00E+02 1.21E+01 4.20E-01 3.86E-04 6.85E+04 4.40E-04 1.30E+03 1.68E+01 3.50E-01 1.54E-04 1.76E+05 2.00E-04 2.20E+03 2.55E+01 2.80E-01 5.60E-05 4.46E+05 1.00E-04 3.70E+03 3.84E+01 2.20E-01 2.20E-05 8.59E+05 6.20E-05 5.50E+03 4.97E+01 1.80E-01 1.12E-05 2.55E+06 2.60E-05 1.00E+04 8.12E+01 1.30E-01 3.38E-06 4.45E+06 1.90E-05 1.6OE+04 8.85E+01 8.00E-02 1.52E-06 The probability of occurrence for each Pasquill category is typical of the Great Lakes region. x/ Q and Depleted x/ Q can be weighted using these probabilities to produce expected values at each area boundary or iso-dose line. The weighted values can now be applied to the estimation of exposure and unit risk factors required by this research. Since the URF’s are calculated assuming a release of 1 Curie, the weighted values for x/ Q and Depleted x/ Q actually represent weighted x and Depleted x in this case. The exposure equations derived in Chapter 4 calculate the dose to populations within an area, so an average value for Depleted x has been calculated equal to the geometric mean of the concentrations at the inner and outer boundaries. This average is designated Depleted X- The amount deposited within each area is calculated through conservation of mass considerations. The amount of material leaving an area must be equal to the amount entering the area minus the amount deposited. The ratio of the the undepleted quantity Qo to x/ Q 15 equal to the ratio of the depleted quantity Qo- Qdep to the Depleted x/ Q QO _ QO'Qdep (E1) x/Q Depleted x/ Q Since Q0 = 1 Curie, it follows that the amount deposited in the first area is: Depleted x/ Q (E2) = 1 - Qdep X/Q 156 This formula is recursive since the amount entering the second area is 1 - Qdep which replaces the value of 1 in equation (E2). The following table presents the weighted parameters discussed above for the eleven elliptical areas. Depleted X has units of Ci per cubic meter. Table E-2. X and Deposition Values Weighted Weighted Cumulative Area x/Q Depleted x/Q Depleted X Ci Deposited Ci Deposited 4.59E+02 1.15E-02 9.33E-03 9.66E-02 1.90E-01 1.90E-01 1.53E+03 3.47E-03 2.63E—03 4.96E-03 4.98E-02 2.40E-01 3.94E+03 1.67E-03 1.22E-03 1.79E-03 2.99E-02 2.70E-01 1.25E+04 4.09E-04 2.74E-04 5.78E-04 5.921302 3.29E-01 3.04E+04 2.00E-04 1.31 E-04 1.90E-04 1.62E-02 3.45E-01 6.85E+04 1 0313-04 6.41E—05 9.16E~05 3.53E-02 3.80E-01 1.76E+05 4.05E-05 2.22E-05 3.77E-05 7.07E-02 4.51E-01 4.46E+05 1.95E-05 9.70E-06 1 .47E-05 5.29E-02 5.04E-01 8.59E+05 1.17E-05 5.20E-06 7.10E-06 4.97E-02 5.53E-01 2.55E+06 4.69E-06 1.82E-06 3.07E-06 5.98E-02 6.13E-01 4.45E+06 3.40E-06 1.15E-06 1.44E-06 4.85E-02 6.62E-01 Appendix F RISK FACTOR COMPONENTS Appendix F Risk Factor Components Table F-l contains data which are specific to the three population density classifications: Table F-l. Population Zone Parameters v (km/hr) TC(veh/hr) PD(p/km2) Rural 88 470 50 Suburban 88 1200 1000 Urban 64 2800 3500 Data specific to the isotopes shipped in quantity in the MILLRWC are contained in Table F-2. Energy is given in MeV, half-life in days and the photon fluence to dose rate conversion factor 4) is in units of photons/cmZ-sec per R/ hr (which is approximately equal to rem/ hr for gamma radiation) [26,47,81]. Rem per Curie inhaled values were calculated from maximum permissible concentration (MPC) values in Table 1 of Permissible Dose for Internal Radiation [36]. Those MPC values are expressed in terms of Ci/ cubic meter in air or water which if ingested result during the course of a 40-hour work week in an exposure of 0.1 rem. (MPC values for 168 hours per week of environmental exposure are also given but the occupational exposure values were used because they result in a greater dose per Curie inhaled.) Since airborne contaminants are being modeled, the airborne factors for the total body, (MPC)a, are used in the calculation. Breathing in an atmosphere containing 1 (MPC)a for 40 hours results in a whole body dose of 0.1 rem, therefore a 10 (MPC)a atmosphere for 40 hours yields and exposure of 1 rem. To calculate the rem per Curie inhaled from this information, all that is needed is the breating rate. The standard breathing rate of the reference man at light activity is 3.3 E-4 cubic meters per second as given by Reference 39. The calculation becomes: Rem 1 . . = (F1) C1 inhaled Ci-wk m3 sec hr 10 ' ((MPC)a m) 0 3.3E-4 E 0 3600 T1? 0 40 :v-k- Table F-2. Isotope Data Isotope Energy Half-life ¢ Rem/Ci inhaled Am241 0.022 1.67E+05 1.80E+06 1.00E+08 C136 0.015 1.13E+08 8.00E+05 5.20E+03 C058 0.977 7.08E+01 S.60E+05 2.10E+03 C060 2.505 1.92E+03 2.70E+05 S.20E+O3 Cr51 0.029 2.78E+01 3.50E+06 2.10E+02 Cs134 1.591 7.53E+02 3.70E+05 5.20E+04 C5137 0.563 1.10E+04 9.00E+05 3.50E+04 Ir192 0.779 7.42E+01 7.80E+06 5.20E+03 Nb94 1.573 7.30EI+06 3.70E+05 4.20E+03 Ni59 1.060 2.92E+07 5.20E+05 2.10E+03 P32 0.000 1.43E+01 0.00E+00 5.20E+03 Pu241 0.022 4.82E+03 1.80E+06 2.60E+06 Ra226 1.544 5.85E+05 3.80E+05 4.20E+07 157 Isotope S35 Sr90 T11232 U238 Misc Isotope 8: Package Am241 Cask Am241 LSA C136 LSA C058 Cask C060 Cask C060 Drum 158 Table F-2. (continued) Energy Half-life 0 Rem/Ci inhaled 0.000 8.79E+01 0.00E+00 2.10E+03 0.000 1.06E+04 0.00E+00 2.30E+06 0.001 5.11E+12 0.00E+00 2.10E+08 0.014 1.65E+12 6.80E+05 1.00E+06 0.511 7.30E+02 7.60E+06 2.10E+03 Table F-3. Package Shielding Factor Isotope 8: Package Energy Cjk Am241 Cask 0.022 0.001 Am241 LSA 0.022 1 C136 LSA 0.015 1 C058 Cask 0.977 0.01 C060 Cask 2.505 0.01 C060 Drum 2.505 0.5 C060 LSA 2.505 1 Cr51 LSA 0.029 1 C5134 Cask 1.591 0.01 C5137 Cask 0.563 0.005 C5137 Drum 0.563 0.1 C5137 LSA 0.563 1 Ir192 Cask 0.779 0.01 Nb94 Cask 1.573 0.01 Nb94 Drum 1.573 0.5 Nb94 LSA 1.573 1 N159 Cask 1.06 0.01 Ni59 Drum 1.06 0.5 Ni59 LSA 1.06 1 Pu241 Drum 0.022 0.05 Pu241 LSA 0.022 1 Ra226 Cask 1.544 0.01 Ra226 LSA 1.544 1 U238 LSA 0.014 1 Misc Drum 0.511 0.1 Misc LSA 0.511 1 Table F-4. Accident-Free Dose Components RURAL Dpath Dcrew Dopp Dsame AFDTotal 6.14E-10 2.27E-05 7.52E-11 1.67E-13 2.27E-05 6.14E-07 2.27E-05 - 7.52E-08 1.67E-10 2.34E-05 1.38E—06 2.27E-05 1.69E-07 3.75E-10 2.43E-05 2831-3-08 2.27E-05 2.42E-09 7.68E-12 2.28E-05 5.88E-08 2.271505 5.01 E-O9 1.59E-11 2.28E-05 2.94E-06 2.27E-05 2.51E-07 7.97E-10 2.59E-05 Isotope 8: Package C060 LSA Cr51 LSA C5134 Cask C5137 Cask C5137 Drum C5137 LSA Ir192 Cask Nb94 Cask Nb94 Drum Nb94 LSA Ni59 Cask Ni59 Drum Ni59 LSA Pu241 Drum Pu241 LSA Ra226 Cask Ra226 LSA U238 LSA Misc Drum Misc LSA Isotope 8: Package Am241 Cask Am241 LSA C136 LSA C058 Cask C060 Cask C060 Drum C060 LSA Cr51 LSA C5134 Cask C5137 Cask C5137 Drum C5137 LSA Ir192 Cask Nb94 Cask Nb94 Drum Nb94 LSA Ni59 Cask Ni59 Drum Ni59 LSA Pu241 Drum Pu241 LSA Dpath 5.88E-06 3.16E-07 4.29E-08 6.14E-09 1 .23E-07 1 .23E-06 2.03E—09 4.29E-08 2.14E-06 4.29E-06 3.05E-08 1.53E-06 3.05E-06 3.07E—08 6.14E-07 4.1 7E-08 4.1 7E-06 1.63E-06 1.45E-08 1 .45E-07 Dpath 1 2313-08 1.23E-05 2.76E-05 5.67E-07 1.18E-06 5.88E-05 1 .1 8E-04 6.32E-06 8.57E-07 1.23E-07 2.46E-06 2.46E-05 4.07E-08 8.57E-07 4.29E-05 8.57E-05 6.1OE-07 3.05E-05 6.105-05 6.14E-07 1 .23E-05 159 Table F-4. (continued) RURAL Dcrew Dopp 2.27E-05 5.01E-07 2.27E-05 3.87E-08 2.27E-05 3.66E-09 2.27E-05 7.52E-10 2.27E-05 1 5013-08 2.27E-05 1.50E-07 2.27E-05 1.74E-10 2.27E-05 3.66E-09 2.27E-05 1.83E-07 2.27E-05 3.66E-07 2.27305 2.60E-09 2.27E-05 1 .30E-07 2.27E-05 2.60E-07 2.27E-05 3.76E-09 2.27E-05 7.52E-08 2.27E-05 3.561309 2.27E-05 3.56E-07 2.27E—05 1.99E-07 2.27E-05 1.78E-09 2.27E—05 1 .78E-08 SUBURBAN Dcrew Dopp 2.27E-05 1.92E-10 2.27E-05 1.92E-07 2.27E-05 4.32E-07 2.27E-05 6.17E-09 2.27E-05 1285-08 2.27E-05 6.40E-07 2.27E-05 1.285-06 2.27E-05 9.87E-08 2.27E-05 9.34E-09 2.27E-05 1 .925—09 22713-05 3.84E-08 2.27E-05 3.84E-07 2.27E-05 4.43E-10 2.27E-05 9.34E-09 2.27E-05 4.67E-07 2.27E-05 9.34E-07 2275-05 6655-09 2.27E-05 3.32E-07 2.27E-05 6.65E-07 2.27E-05 9.60E-09 2.27E-05 1.92E-07 Dsame 1.59E-09 8.57E-11 1.16E-1 1 1.67E-12 3.33E-1 ‘l 3.33E-10 5.51E-13 1.16E-11 5.81E-10 1.16E~09 8.27E-12 4.14E-10 8.27E-10 8.33E-12 1.67E—10 1.1313-1 1 1.13E-09 4.41E-10 3.94E-12 3.94E-11 Dsame 4.25E-13 4.25E-10 9.57E-10 1965-1 1 4.07E-11 2.03E—09 4.07E-09 2.19E-10 2.97E-1 1 4.25E-12 8.51E-11 8.51 E-lO 1.41E-12 2.97E-11 1.48E-09 2.97E-09 2.11E-11 1.06E-09 2.1 115-09 2.13E-11 4.25E-10 AFDTotal 2.91E-05 2.31E-05 2.28E-05 2.27E-05 2.29E-05 2.41E-05 2.27E-05 2.28E-05 2.51E-05 2.74E—05 2.28E-05 2.44E-05 2.60E-05 2.28E-05 2.34E-05 2.28E-05 2.73E-05 2.46E-05 2.27E-05 2.29E-05 AFDTotal 2.27E-05 3.52E-05 5.08E-05 2.33E-05 2.39E-05 8.21E-05 1.42E-04 2.91E-05 2.36E-05 2.29E-05 2.52E-05 4.77E-05 2.28E-05 2.36E-05 6.61E-05 1.09E-04 2.33E-05 5.36E-05 8.44E-05 2.34E-05 3.52E-05 Isotope 8: Package Ra226 Cask R3226 LSA U238 LSA Misc Drum Misc LSA Isotope 8: Package Am241 Cask Am241 LSA C136 LSA C058 Cask C060 Cask C060 Drum C060 LSA Cr51 LSA C5134 Cask C5137 Cask C5137 Drum C5137 LSA Ir192 Cask Nb94 Cask Nb94 Drum Nb94 LSA Ni59 Cask Ni59 Drum Ni59 LSA Pu241 Drum Pu241 LSA Ra226 Cask Ra226 LSA U238 LSA Misc Drum Misc LSA Dpath 8.35307 8.35305 3.25305 2.91307 2.91306 Dpath 5.91308 5.91305 1.33304 2.73306 5.65306 2.83304 5.65304 3.04305 4.13306 5.91307 1.18305 1.18304 1 .96307 4.13306 2.06304 4.13304 2.94306 1.47304 2.94304 2.96306 5.91305 4.02306 4.02304 1.56304 1.40306 1 .40305 160 Table F-4. (continued) SUBURBAN Daew Dopp 2.27505 9.09509 2.27505 9.09507 2.27505 5.08507 2.27505 4.55509 2.27505 4.55508 URBAN Denew Dopp 3.13505 8.47510 3.13505 8.47507 3.13505 1.91506 3.13505 2.72508 3.13505 5.65508 3.13505 2.82506 3.13505 5.65506 3.13505 4.36507 3.13505 4.12508 3.13505 8.47509 3.13505 1.69507 3.13505 1.69506 3.13505 1.95509 3.13505 4.12508 3.13505 2.06506 3.13505 4.12506 3.13505 2.93508 3.13505 1.47506 3.13505 2.93506 3.13505 4.23508 3.13505 8.47507 3.13505 4.01508 3.13505 4.01506 3.13505 2.24506 3.13505 2.01508 3.13505 2.01507 Dsame 2.89511 2.89509 1.13509 1015-11 1015-10 Dsame 2.58312 2.58309 5.80309 1.19310 2.47310 1.23308 2.47308 1.33309 1.80310 2.58311 5.16310 5.16309 8.54312 1.80310 9.00309 1.80308 1.28310 6.41309 1.28308 1.29310 2.58309 1.75310 1.75308 6.83309 6.1 1311 6.11310 AFDTotal 2.36305 1.07304 5.58305 2.30305 2.57305 AFDTotal 3.13305 9.12305 1.66304 3.40305 3.70305 3.17304 6.02304 6.21305 3.54305 3.18305 4.32305 1 .51304 3.14305 3.54305 2.40304 4.48304 3.42305 1.80304 3.28304 3.42305 9.12305 3.53305 4.37304 1.90304 3.27305 4.55305 Table 35. Non-Dispersal Accident Risk Components (Cask Shipments) Isotope Am241 Cask C058 Cask C060 Cask C5134 Cask C5137 Cask Darea 3.73307 1.72305 3.57305 2.60305 3.73306 RURAL Dveh Dwork 2.93306 6.56305 9.41305 2.11E-03 1.95E-04 4.37303 1.42E-04 3.19E—03 2.935-05 6.56E—04 6.89305 2.22303 4.60303 3.36303 6.89304 NDADTml Prob . NDADT 6.89312 2.22310 4.60310 3.36310 6.89311 RURAL Isotope Darea Dveh Dwork NDADToml Prob - NDAD]~ Ir192 Cask 1.24306 6.76306 1.51304 1.59304 1.59311 Nb94 Cask 2.60305 1.42304 3.19303 3.36303 3.36310 Ni59 Cask 1.85305 1.01304 2.27303 2.39303 2.39310 Ra226 Cask 2.54305 1.39304 3.11303 3.27303 3.27310 SUBURBAN Isotope Dare; Dveh Dwork NDADTom Prob - NDADT Am241 Cask 7.46306 7.48306 6.56305 8.05305 8.05312 C058 Cask 3.44304 2.40304 2.11303 2.69303 2.69310 C060 Cask 7.14304 4.98304 4.37303 5.58303 5.58310 C5134 Cask 5.21304 3.64304 3.19303 4.07303 4.07310 C5137 Cask 7.46305 7.48305 6.56304 8.05304 8.0531 1 Ir192 Cask 2.47305 1.73305 1.51304 1.93304 1.93311 Nb94 Cask 5.21304 3.64304 3.19303 4.07303 4.07310 Ni59 Cask 3.71304 2.59304 2.27303 2.90303 2.90310 Ra226 Cask 5.07304 3.54304 3.11303 3.97303 3.97310 URBAN Isotope Dam Dveh Dwork NDADToml Prob 0 NDADT Am241 Cask 2.61305 2.40305 6.56305 1.16304 1.16311 C058 Cask 1.20303 7.71304 2.11303 4.08303 4.08310 C060 Cask 2.50303 1.60303 4.37303 8.47303 8.47310 C5134 Cask 1.82303 1.17303 3.19303 6.18303 6.18310 C5137 Cask 2.61304 2.40304 6.56304 1.16303 1.16310 Ir192 Cask 8.65305 5.54305 1.51304 2.93304 2.93311 Nb94 Cask 1.82303 1.17303 3.19303 6.18303 6.18310 Ni59 Cask 1.30303 8.30304 2.27303 4.40303 4.40310 Ra226 Cask 1.78303 1.14303 3.11303 6.02303 6.02310 Table 36. Atmospheric Dispersion Data Ellipse # Total Area A Area X ACi Deposited AA 0 X 1 4.59E+02 4.59E+02 9.66302 1.90301 4.43301 2 1.53E+03 1.07E+03 4.96303 4.98302 5.31E+00 3 3.94E+03 2.41E+03 1.79303 2.99302 4.31 E+00 4 1.25E+04 8.56E+03 5.78304 5.92302 4.95E+OO 5 3.04E+04 1.79E+04 1.90304 1.62302 3.40E+00 6 6853-04 3.81E+04 9.16305 3.53302 3.49E+00 7 1.76E+05 1.08E+05 3.77305 7.07302 4.05E+00 8 4.46E+05 2.70E+05 1.47305 5.29302 3.97E+00 9 8.59E+05 4.13E+05 7.10306 4.97302 2.93E+00 10 2.55E+06 1.693106 3.07306 5.98302 5.19E+00 11 4.45E+06 1.90E+06 1.44306 4.85302 2.74E+00 Totals 4.45E+06 1.04301 6.62301 8.47E+01 161 Table 35. (continued) Isotope Am241 C136 C060 C151 Cs137 Nb94 Ni59 P32 Pu241 Ra226 S35 5190 Th232 U238 Misc 71 1 .90303 1.90303 2.26303 2.68302 1.96303 1.90303 1.90303 5.04302 2.04303 1 .90303 9.78303 1 .96303 1 .90303 1.90303 2.85303 162 Table 37. Resuspension Dose Factors 71. 4.14306 6.16309 3.61304 2.49302 6.32305 9.49308 2.37308 4.85302 1.44304 1.18306 7.88303 6.54305 1 .36313 4.20313 9.49304 RDF 3.28E+00 3.28E+00 2.91E+00 1.163100 3.21 E+00 3.28E+00 3.283100 1.093100 3.12E+00 3.28E+00 1.44E+00 3.20E+00 3.28E+00 3.28E+00 2.52E+00 Table 38. Dispersal Accident Risk Components (LSA 8: Drum Shipments) Isotope Am241 C136 C060 Cr51 C5137 Nb94 Ni59 P32 Pu241 Ra226 $35 $190 Th232 U238 Misc Isotope Am241 C136 C060 C151 C5137 Nb94 N i59 P32 Pu241 Ra226 $35 DWB 6.71301 4.57301 7.64301 8.78301 1.725+01 4.803101 3.23E+01 0.00E+00 6.71501 4.715+01 0.00E+00 0.005+00 3.05502 4.33301 1.56E+01 DWB 1.34E+01 9.15E+00 1.53E+03 1.76E+01 3.43E+02 9.59E+02 6.46E+02 0.0031-00 1.34E+01 9.41E+02 0.00E+00 RURAL Dinh Dgnd 4.16E+02 1.24306 2.17302 8.77307 1.92302 2.90305 3.10304 1.08308 1.43301 2.07305 1.75302 9.19305 8.76303 6.20305 7.17303 0.00E+00 1.03301 5.16307 1.753102 8.94305 3.85303 0.00E+00 9.36E+00 0.00E+00 8.76302 5.85308 4.17E+00 8.31307 6.72303 2.76306 SUBURBAN Dinh Dgnd 8.33303 2.49305 4.34301 1.75305 3.85301 5.79304 6.19303 2.16307 2.85E+00 4.13304 3.50301 1.84303 1.75301 1.24303 1.43301 0.00E+00 2.06E+02 1.03305 3.50E+03 1.79303 7.69302 0.00E+00 ADADTotal 4.173102 4.79301 7.64E+01 8.78301 1.73E+01 4.80E+01 3.233101 7.17303 1.10E+01 2.2213+02 3.85303 9.36E+00 8.76E+02 4.60E+00 1.56E+01 8.343103 9.58E+00 1.53E+03 1.76E+01 3.46E+02 9.59E+02 6.46E+02 1 .43301 2.19E+02 4.44E+03 7.69302 Prob ' ADADr 4.17305 4.79308 7.64306 8.78308 1 .73306 4.80306 3.23306 7.17310 1.10306 2.22305 3.85310 9.36307 8.76305 4.60307 1.56306 Prob ' ADADT 8.34304 9.58307 1.53304 1.76306 3.46305 9.59305 6.46305 1.43308 2.19305 4.44304 7.69309 Isotope Sr90 Th232 U238 Misc Isotope Am241 C136 C060 Cr51 C5137 Nb94 Ni59 P32 Pu241 Ra226 S35 Sr90 Th232 U238 Misc DWB 0.0013100 6.10301 8.663100 3.1213102 DWB 4.69E+01 3.20E+01 5.353103 6.15E+01 1.20E+03 3.36E+03 2.26E+03 0.00E+00 4.69E+01 3.30E103 0.003100 0.00E+00 2.1313100 3.0313101 1.09E+03 163 Table 38. (continued) SUBURBAN Dinh Dgnd 1.873102 0.0013100 1.75E+04 1.17306 8.343101 1 .66305 1.34301 5.52305 URBAN Dinh Dgnd 2.913104 8.71305 1.523100 6.14305 1.35E+00 2.03303 2.17302 7.57307 9.983100 1.45303 1.23E+00 6.43303 6.13301 4.34303 5.02301 0.00E+00 7.213102 3.61305 1.233104 6.26303 2.69301 0.0013100 6.5513102 0.00E+00 6.1315104 4.09306 2.923102 5.81305 4.70301 1.93304 ADADTotal 1.87E+02 1.75E104 9.21 E101 3.12E+02 2.92E+04 3.3515101 5.35E+03 6.15E+01 1.21 E103 3.363103 2.2613103 5.02301 7.6815102 1.56E+04 2.69301 6.5515102 6.1313104 3.223102 1.09E+03 Prob ' ADADr 1.87305 1.75303 9.21306 3.12305 Prob ' ADADT 2.92303 3.35306 5.35304 6.15306 1.21304 3.36304 2.26304 5.02308 7.68305 1.56303 2.69308 6.55305 6.13303 3.22305 1 .09304 . Appendix G UNIT RISK FACTORS Appendix G Unit Risk Factors Table G-l. Risk Factors: Person-Rem per Kilometer 164 ACCIDENT-FREE ACCIDENT RISK FACTORS RISK FACTORS Isotope Package Rural Suburban Urban Rural Suburban Urban Am241 Cask 2.27305 2.27305 3.13305 6.89312 8.05312 1.1631 1 Am241 LSA 2.34305 3.52305 9.12305 4.17305 8.34304 2.92303 C136. LSA 2.43305 5.08305 1.66304 4.79308 9.58307 3.35306 C058 Cask 2.28305 2.33305 3.40305 2.22310 2.69310 4.08310 C060 Cask 2.28305 2.39305 3.70305 4.60310 5.58310 8.47310 C060 Drum 2.59305 8.21305 3.17304 7.64306 1 .53304 5.35304 C060 LSA 2.91305 1.42304 6.02304 7.64306 1.53304 5.35304 Cr51 LSA 2.31305 2.91305 6.21305 8.78308 1 .76306 6.15306 Cs134 Cask 2.28305 2.36305 3.54305 3.36310 4.07310 6.18310 C5137 Cask 2.27305 2.29305 3.18305 6.89311 8.05311 1 .16310 C5137 Drum 2.29305 2.52305 4.32305 1.73306 3.46305 1.21 304 C5137 LSA 2.41305 4.77305 1.51304 1.73306 3.46305 1 .21 304 Ir192 Cask 2.27305 2.28305 3.14305 1.5931 1 1.93311 2.9331 1 Nb94 Cask 2.28305 2.36305 3.54305 3.36310 4.07310 6.18310 Nb94 Drum 2.51305 6.61305 2.40304 4.80306 9.59305 3.36304 Nb94 LSA 2.74305 1.09304 4.48304 4.80306 9.59305 3.36304 Ni59 Cask 2.28305 2.33305 3.42305 2.39310 2.90310 4.40310 N i59 Drum 2.44305 5.36305 1.80304 3.23306 6.46305 2.26304 Ni59 LSA 2.60305 8.44305 3.28304 3.23306 6.46305 2.26304 P32 LSA 0.00E+00 0.00E+00 0.00E+00 7.17310 1.43308 5.02308 Pu241 Drum 2.28305 2.34305 3.42305 1.10306 2.19305 7.68305 Pu241 LSA 2.34305 3.52305 9.12305 1.10306 2.19305 7.68305 Ra226 Cask 2.28305 2.36305 3.53305 3.27310 3.97310 6.02310 Ra226 LSA 2.73305 1.07304 4.37304 2.22305 4.44304 1.56303 535 LSA 0.00E+00 0.00E+00 0.003100 3.85 310 7.69309 2.69308 Sr90 LSA 0.003100 0.00E+00 0.003100 9.36307 1.87305 6.55305 Th232 LSA 0.003100 0.00E+00 0.00E+00 8.76305 1.75303 6.13303 U238 LSA 2.46305 5.58305 1 .90304 4.60307 9.21306 3.22305 Misc Drum 2.27305 2.30305 3.27305 1.56306 3.12305 1.09304 Misc LSA 2.29305 2.57305 4.55305 1.56306 3.12305 1.09304 165 Table G-2. Risk Factors: Person-Rem per Mile ACCIDENT-FREE ACCIDENT RISK FACTORS RISK FACTORS Isotope Package Rural Suburban Urban Rural Suburban Urban Am241 Cask 3.65305 3.65305 5.04305 1 .1 1 31 1 1.30311 1.87311 Am241 LSA 3.77305 5.66305 1.47304 6.71305 1 .34303 4.70303 C136 LSA 3.91305 8.18305 2.67304 7.71 308 1.54306 5.39306 C058 Cask 3.67305 3.75305 5.47305 3.57310 4.33310 6.57310 C060 Cask 3.67305 3.85305 5.95305 7.40310 8.98310 1.36309 C060 Drum 4.1 7305 1.32304 5.10304 1.23305 2.46304 8.61304 C060 LSA 4.68305 2.29304 9.69304 1 .23305 2.46304 8.61304 Cr51 LSA 3.72305 4.68305 9.99305 1.41 307 2.83306 9.90306 C5134 Cask 3.67305 3.80305 5.70305 5.41310 6.55310 9.95310 C5137 Cask 3.65305 3.69305 5.12305 1.1 1 310 1.30310 1.87310 C5137 Drum 3.69305 4.06305 6.95305 2.78306 5.57305 1.95304 C5137 LSA 3.88305 7.68305 2.43304 2.78 306 5.57305 1 .95304 Ir192 Cask 3.65305 3.67305 5.05305 2.56311 3.11311 4.72311 Nb94 Cask 3.67305 3.80305 5.70305 5.41 310 6.55310 9.95310 Nb94 Drum 4.04305 1.06304 3.86304 7.72306 1.54304 5.41304 Nb94 LSA 4.41305 1.75304 7.21304 7.72306 1.54304 5.41 304 N i59 Cask 3.67305 3.75305 5.50305 3.85310 4.67310 7.08310 N i59 Drum 3.93305 8.63305 2.90304 5.20306 1.04304 3.64304 N i59 LSA 4.18305 1.36304 5.28304 5.20306 1.04304 3.64304 P32 LSA 0.00E+00 0.0013100 0.003100 1.15309 2.30308 8.08308 Pu241 Drum 3.67305 3.77305 5.50305 1 .77306 3.52305 1.24304 Pu241 LSA 3.77305 5.66305 1.47304 1.77306 3.52305 1.24304 Ra226 Cask 3.67305 3.80305 5.68305 5.26310 6.39310 9.69310 Ra226 LSA 4.39305 1.72304 7.03304 3.57305 7.15304 2.51303 S35 LSA 0.003100 0.00E+00 0.00E+00 6.20310 1.24308 4.33308 Sr90 LSA 0.00E100 0.0015100 0.00E+00 1.51306 3.01 305 1.05304 Th232 LSA 0.003100 0.0013100 0.003100 1.41304 2.82303 9.87303 U238 LSA 3.96305 8.98305 3.06304 7.40307 1.48305 5.18305 Misc Drum 3.65305 3.70305 5.26305 2.51306 5.02305 1.75304 Misc LSA 3.69305 4.14305 7.32305 2.51 306 5.02305 1.75304 Appendix H VERIFICATION OF THE NETWORK OPTIMIZATION ALGORITHM Appendix H Verification of the Network Optimization Algorithm To verify its accuracy, the algorithm was tested with a simple network (figure PM). The link weights shown are assumed to be independent of the nodes chosen as origin or desti- nation. The destination is node T, S] and 52 are source nodes. Figure H—l. Test Network Stepping through the algorithm, the network is initialized by setting the temporary labels to 0°. The destination node is given the permanent label 0 and all nodes connected to it are found, receiving temporary labels equal to their weight plus the permanent label of T. C has the smallest temporary label, so it is made permanent. Listed below are the labels and predecessors for all nodes to this point in the process. Table H-l. Test of Algorithm Temp. Penn. Temp. Perm. Node Label Label Predecessor Node Label Label Predecessor T oo - - T - 0 - 51 oo - - SI oo - - 82 oo - - 52 co - - A oo - - A oo - - B on - - B oo - - C 00 - - C 00 - - D co - - D co - - E co - - E oo - - F oo - - F on - - G 00 - - G on - - T - 0 - T - 0 - 51 oo - - S1 00 - - 52 co - - 82 oo - - A 8 - T A 8 - T B 7 - T B 7 - T C 4 - T C - 4 T D co - - D 00 - - 1:; co - - E 66 - - F 00 - - F 00 - - G «>0 - - G 0° - - 166 167 Since C is not 51, the origin desired, the algorithm continues by calculating new tempo- rary labels for those nodes connected to C. Notice that node B has a new temporary label of 6, less than the value of the direct link to T. Next, the entire list of temporarily labeled nodes is scanned for the smallest value. In this case it is node B, which becomes permanently labeled. Since no temporarily labeled nodes are connected to B, the lists do not change and node A becomes permanently labeled. Table I-I-1. (continued) Temp. Perm. Temp. Perm. Node Label Label Predecessor Node Label Label Predecessor T - 0 - T - 0 — Sl co - - 51 oo - - 52 12 - ' C S2 12 - C A 8 - T A 8 - T B 6 - C B - 6 C C - T C - 4 T D co - - D co - - E 11 - C E 11 - C F oo - - F on - - G co - - C 00 - - T - 0 - T - 0 - 51 oo - - 51 oo - - $2 12 - C 82 12 - C A 8 - T A - 8 T B - 6 C B - 6 C C - 4 T C - 4 T D co - - D - - E 11 - C E 1 1 - C F on - - F co - - C 0° - - G 9° - - T - 0 - T - O - 51 co - - S] on - - $2 12 - C 52 12 - C A - 8 T A - 8 T B - 6 C B - 6 C C - 4 T C - 4 T D co - - D co - - E 11 - C E - 11 C F 00 - - F on - - c .. - - c .. - - The only node with a temporary label connected to A is 82 but its weight through A is greater than through C so its temporary label does not change. E has the lowest temporary label so it becomes a permanent label. Connected to E are D and G which have their temporary labels lowered to 17 and 20 respectively. 52 now is permanently labeled, resulting in a new weight of 15 for D. This is the smallest value on the list of temporary labels, so it is made permanent. 168 Table H-l. (continued) Temp. Perm. Temp. Perm. Node Label Label Predecessor Node Label Label Predecessor T - 0 - T - 0 - 51 oo - - 51 oo - - $2 12 - C 82 - 12 C A - 8 T A - 8 T B - 6 C B - 6 C C - 4 T C - 4 T D 17 - E D 17 - E E - 11 C E - 11 C F oo - - F oo - - G 20 - E G 20 - E T - 0 - T - 0 - 51 oo - - 51 oo - - $2 - 1 2 C 52 - 12 C A - 8 T A - 8 T B - 6 C B - 6 C C - 4 T C - 4 T D 15 - 52 D - 15 52 E - 11 C E - 11 C F oo - - F co - - G 20 - E G 20 - E T - 0 - T - 0 - SI 00 - - 51 oo - - $2 - 1 2 C 82 - 12 C A - 8 T A - 8 T B - 6 C B - 6 C C - 4 T C - 4 T D - 15 52 D - 15 52 E - 11 C E - 1 1 C F 24 - D F 24 - D G 19 - D G - 19 D With D permanently labeled, F becomes accessible and its label is reduced to 24. G has weight 19 through D and retains that value for its permanent label. This leads to the labeling of S] with a value of 23. Since this is the smaller of the two remaining temporary labels, it becomes a permanent label and the algorithm ends. The result for 31 then is a final weight of 23. The path to T can be traced by the predecessors: 51, G, D, 52, C, and finally, T. 169 Table H-l. (continued) Temp. Perm. Node Label Label Predecessor Node T - 0 - T 51 23 - G 51 52 - 12 C 32 A - 8 T A B - 6 C B C - 4 T C D - 15 82 D E - 11 C E F 24 - D F G - 19 D (3 Temp. Label Perm. Label Predecessor 0 - 23 G 12 C 8 T 6 C 4 T 15 52 1 1 C - D 19 D To complete the test, the algorithm needs to solve the path from 52. S2 is found on the list of permanent labels and so the algorithm does not solve the network again but merely reports the value of 12 and the path 52, C, T. If F were to be designated an origin, the algo- rithm proceeds from the temporary list above rather than reinitializing the network. Figure H-2 shows the permanent labels assigned to each node and the paths from each node to the destination. F is not included since the algorithm stopped before it was made permanent. The solution is verified by enumerating all possible paths between $1 and T. Certain paths can be eliminated by inspection because of domination by alternative paths. For example, C-T will always be better than C—B-T and Sl-F—D is always dominated by Sl-G-D. Figure H-Z. Solution Eliminating any path passing through nodes B or F leaves six possible paths: Sl-G-D-SZ-A-T 4 + 4 +3 + 7 + 8 Sl-G-D-SZ-C-T 4 + 4 «1 3 + 8 + 4 Sl-C-D-E-C—T 4 + 4 + 6 + 7 + 4 Sl-G-E-D-SZ-A-T 4 + 9 + 6 + 3 + 7 + 8 Sl-G-E-D-SZ-C-T 4 -1 9 -1- 6 + 3 + 8 + 4 Sl-G-E-C-T 4 + 9 + 7 -1 4 =26 =23 =25 =37 =34 =24 So, the path chosen by the algorithm is the optimal solution. Enumeration is only practical with small networks, for the network modelling the MILLRWC, enumeration is not feasible and the algorithm quickly proves its worth. Appendix I RISK AND COST OPTIMIZATION PROGRAM REM GOSUB TEXT Appendix I Risk and Cost Optimization Program "Carrick 4.0" Programmed by James T. Carrick This software was created using the ZBasicm‘Cbmpiler. Portions of this code are Copyrighted CM 1985 by Zedcor Inc. This is a modification of the Dijkstra algorithm found on page 235 of DISCRETE OPTIMIZATION ALGORITHMS by Syslo, Dec and Kowalik, as translated from their Pascal listing. One modification is in the data structure. Syslo, et. al. used a segment weight matrix requiring N x N entries where N = number of nodes. This new structure is a linked adjacency list. For each node a list of connecting nodes and segment weights is maintained. Associated with each node & weight is a link code, pointing to the next entry in the list for the originating node. A second list is maintained containing the starting point in the adjacency list of each node. These two lists require only N + (5 x M) memory locations where M = the number of segments. So a network of 300 nodes and 450 links will need only (300 x 2b)+(450 x 10b) = 5.1 Kb of memory as opposed to 300 x 300 x 4 bytes = 360 Kb for the weight matrix format. Note that most of the weight matrix is composed of null entries, that is, representing no connection between nodes. The random file containing the list of pointers for each node is called "Pointers." Its format is 2 bytes for each pointer indexed by node number. The random file containing the connecting nodes, weights and links is called "MidW Len, PopD, TrAcc." Its format is 2 bytes for the connecting node number, 2 bytes for the weight, 2 bytes for the population density, 2 bytes for the truck accident rate and 2 bytes for the link number. An arbitrary index is assigned to each entry. The index of the first entry for a particular node equals the value stored in “Pointers" for that node. The value of LINKER equals the index of the following entry in the list. If there are no other entries, LINKER = 0. The second alteration is that the search algorithm has changed. When looking for the nodes adjacent to RECENT (the node most recently given a permanent label), this program only looks at the nodes linked to RECENT rather than looking at all the nodes or all the segments. This is a result of the structure of the data (adjacency list). The search proceeds much faster, reducing the search by a factor of 15. "Initialize" 170 pfip -" 171 "Opening" PRINT: PRINT: PRINT PRINT " This program analyzes the shipment of Low-Level Radioactive" PRINT " Waste in the Midwest Compact Region. The annual shipments" PRINT " from all waste generators in the region to a specified repository" PRINT " site are simulated. 2 alternative methods of evaluating the" PRINT " transportation of LLW are provided. They are:" PRINT PRINT " 1. Minimize the transportation cost," PRINT " 2. Minimize the radiological risk," PRINT PRINT " Please enterthe number of the option you wish to use. ".- INPUT Option% "Decision" WHILE (Option% < 1) OR (Option% > 2) PRINT PRINT " Only alternatives 1 or 2 are available." PRINT " N. I Please enter the number of your selection again. INPUT Option% WEND " OK" ON Op PRINT PRINT INPUT RRRS tion% GOSUB "Cost", "Risk" : PRINT " Would you like to use a different method of analysis"; RespondS = LEFT$(Respond$,1) IF (RRRS = "Y") OR (RRRS = fly") THEN "Opening" "Comp END "Init REM REM REM CLS DIM Origin(62), letion" ialize" Initialization of variables ShipType(3), 7ShipType$(3), PopDens(3), 9PopDens$(3) DIM AnnualShip(62,3) i 1 DO READ Origin(i) i: i+1 UNTIL i > 62 DATA DATA DATA DATA DATA DATA DATA k DO 1 READ ShipType(k), k = UNTIL DATA FOR i FOR READ AnnualShip(i, 31,49,55,59,63,65,65,65,67,69 72,92,93,102,105,110,158,l67,171,171 180,187,187,l90,203,203,209,217,224,234 243,253,253,255,305,306,307,308,309,310 311,312,313,314,316,317,318,334,335,336 336,337,338,338,339,339,348,350,351,352 354,355 ShipType$(k), PopDens(k), PopDens$(k) k+l k > 3 1, Cask, 200, - 1 TO 62 k = 1 TO 3 Rural, 2, LSA, 1000, Suburban, 3, Barrel, 3500, Urban k) DATA 5,0, DIM AS(3) DIM AccUnitRisk#(30,3), AFUnitConseq#(30,3), Offset(62,3) DIM Attach(267), Ci!(267), Isotope(267) REM Origin(i) - Node number of generator site. 62 sites REM Offset 30 b = b + 1 UNTIL b > 3 DATA 1.13E-1l, 6.71E-5, 7.71E-8, 3.64E-10, 7.55E-10 DATA 1.23E-5, 1.23E-5, 1.4lE-7, 5.5E-10, 1.13E-10 DATA 2.78E-6, 2.78E-6, 2.61E-11, 5.5E-10, 7.728-6 DATA 7.72E-6, 3.91E-10, 5.2E-6, 5.2E-6, 1.15E-9 DATA 1.77E-6, 1.77E-6, 5.36E-10, 3.57E-5, 6.2E-10 DATA 1.51E-6, 1.41E-4, 7.4E-7, 2.51E-6, 2.51E-6 DATA 1.75E-11, 1.34E-3, 1.54E-6, 5.65E-10, 1.17E-9 173 DATA 2.46E-4, 2.46E-4, 2.83E-6, 8.55E-10, 1.75E-10 DATA 5.57E-5, 5.57E-5, 4.06E-11, 8.55E-10, 1.54E-4 DATA 1.54E-4, 6.08E-10, 1.04E-4, 1.04E-4, 2.3E-8 DATA 3.52E-5, 3.52E-5, 8.32E-10, 7.15E-4, 1.24E-8 DATA 3.01E-5, 2.82E-3, 1.48E-5, 5.02E-5, 5.02E-5 DATA 3.48E-11, 4.7E-3, 5.39E~6, 1.12E-9, 2.32E-9 DATA 8.61E-4, 8.61E—4, 9.9E-6, 1.69E-9, 3.48E—10 DATA 1.95E-4, 1.95E-4, 8.01E-11, 1.69E-9, 5.41E-4 DATA 5.41E-4, 1.2E-9, 3.64E—4, 3.64E-4, 8.08E-8 DATA 1.24E-4, 1.24E-4, 1.64E-9, 2.51E-3, 4.33E-8 DATA 1.05E-4, 9.87E-3, 5.183-5, 1.75E-4, 1.75E-4 b = 1 DO a = 1 DO READ AFUnitConseq#(a,b) a = a + 1 UNTIL a > 30 b = b + l UNTIL b > 3 DATA 3.658-5, 4.22E-5, 4.91E-5, 3.67E-5, 3.7E-5 DATA 5.5E-5, 7.35E-5, 3.94E-5, 3.69E-S, 3.67E-5 DATA 3.77E-5, 4.76E-5, 3.658-5, 3.69E-5, 5E-5 DATA 6.36E-5, 3.67E-5, 4.62E-5, 5.58E-S, 0 DATA 3.69E-5, 4.22E-5, 3.69E-5, 6.29E-5, 0 DATA 0, 0, 5.13E-5, 3.67E-5, 5.97E-5 DATA 3.67E-5, 1.34E-4, 2.56E-4, 3.97E-5, 4.31E—5 DATA 3.62E-4, 6.87E-4, 8.67E-5, 4.14E-5, 3.75E-5 DATA 5.6E-5, 2.32E-4, 3.69E-5, 4.14E-5, 2.74E-4 DATA 5.1E-4, 3.99E-5, 2.06E-4, 3.73E-4, 0 DATA 4.158-5, 1.34E-4, 4.12E-5, 4.99E-4, 0 DATA 0, 0, 2.95E-4, 3.89E-5, 5.97E-5 DATA 5.07E-5, 5.21E-4, 1.11E-3, 6.55E-5, 8.18E-S DATA 1.63E-3, 3.19E-3, 2.93E-4, 7.32E-5, 5.5E-5 DATA 1.45E-4, 9.93E-4, 5.13E-5, 7.32E-5, 1.2E-3 DATA 2.35E-3, 6.66E-5, 8.66E-4, 1.67E-3, 0 DATA 7.39E-5, 5.21E-4, 7.26E-5, 2.29E-3, 0 DATA 0, 0, 1.3E-3, 6.15E-5, 1.63E-4 b = 1 DO a = 1 DO READ Offset(a,b) a = a + 1 UNTIL a > 62 b = b + l UNTIL b > 3 DATA 0,0,0,0,0,0,10,0,0,16,0,18,21,0,0,0,0,0,35,0 DATA 0,0,43,0,0,0,0,0,0,0,0,0,0,0,0,71,0,0,0,0 DATA 0,0,0,0,0,0,0,88,104,117,0,134,147,0,163,176,190,205,219,234 DATA 251,256 DATA 1,0,3,0,6,7,11,13,15,0,0,20,23,26,0,28,32,0,0,38 DATA 40,0,46,49,53,0,0,58,59,0,61,62,0,66,0,0,0,0,0,76 DATA 78,0,0,84,0,0,0,92,107,121,0,137,150,162,166,180,193,209,224,237 DATA 0,258 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 DATA 0,0,0,0,0,0,0,98,112,127,0,142,156,0,171,185,199,214,229,244 DATA a a 1 DO 174 254,263 READ Attach(a) a - a + l UNTIL a > 267 DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA a = 1 DO 0,0,4,0,0,0,8,9,0,0,12,0,14,0,0,0,0,19,0,0 22,0,24,25,0,0,0,29,30,31,0,33,0,0,36,37,0,39,0,41 0,0,44,45,0,47,48,0,50,51,52,0,54,55,0,0,0,0,0,0 0,63,64,0,0,67,68,69,0,0,72,0,0,0,0,77,0,79,80,81 0,0,0,0,0,0,0,89,90,91,0,93,94,95,96,97,0,99,100,101 102,103,0,105,106,0,108,109,110,111 0,113,114,115,116,0,118,119,120,0 122,123,124,125,126,0,128,129,130,131 132,0,0,135,136,0,138,139,140,141 0,143,144,145,146,0,148,149,0,151 152,153,154,155,0,157,158,159,160,161 0,0,164,165,0,167,168,169,170,0,172,173,174,175,0,177,178,179,0,181 182,183,184,0,186,187,188,189,0,191 192,0,194,195,196,197,198,0,200,201 202,203,204,0,206,207,208,0,210,211 212,213,0,215,216,217,218,0,220,221 222,223,0,225,226,227,228,0,230,231 232,233,0,235,236,0,238,239,240,241 242,243,0,245,246,247,248,249,250,0 252,253,0,255,0,257,0,259,260,261 262,0,264,265,266,267,0 READ Ci! (a) a: a + 1 UNTIL a > 267 DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA .001,0,.001,.012,0,.001,.ll4,.150,.062,200 .181,.036,.002,.294,.001,210,0,2.5,1.2,.069 5.3,3.8,.003,.032,.018,.001,0,9.5,410,30 .018,.049,.003,0,13.67,6.667,.004,.001,.001, .13,0,1.1,1,20,.008,.16,.012,.027,.026 .093,.007,.022,.088,.003,0,0,.027,.001,0 .047,.001,.031,.032,0,.001,.173,.001,.003,0 35,.25,0,0,0,.085,.074,.001,.001,.001 .23,0,0,6.1,0,0,0,830,12.5,.004 .7,10,7.143,.001,.012,.114,.025,10,7.143,.001 .012,.264,.114,3.5,.725,.002,2.8,.580,.002,.112 .01,2.8,.58,.002,.112,.01,295.9,9.706,.001,.247 8.519,6.111,.01,.008,.021,.001,8.519,6.1ll,.01,.008 .021,.001,0,.55,.08,.001,1.57l,.229,.001,.6 .004,1.571,.229,.001,.06,.004,5.833,5.5,.004,8.75 8.25,.005,.065,.03,.001,8.75,8.25,.005,.O65,.03 .001,.002,8.5,2,.005,1.7,.4,.001,.073,.007 1.7,.4,.001,.073,.007,802,.45,.004,.7,1.013 .225,.001,.042,.004,1.013,.225,.001,.042,.004,7.857 7.857,.005,7.857,7.857,.005,.059,.029,.001,7.857,7.857 .005,.059,.029,.001,211.5,2.625,.001,.175,2,.456 .002,.087,.008,2,.456,.002,.087,.008,9.375,1.813 50,31.25,.002,.302,5.208,.025,.001,.001,.302,5.208 .025,.001,.001,20,l4.09,.008,13.75,9.688,.001,.017 .338,.069,.001,13.75,9.688,.001,.017,.338,.069,.001 .89,8.6,13,.636,.929,13.04,9.286,9.605,6.842,.118 .001 DATA 175 .024,.001,9.605,6.842,.118,.024,.001 a = 1 DO READ Isotope(a) a a + 1 UNTIL a > 267 DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA REM REM REM DIM FINAL%(355), DIM NODE%(836), 30,0,8,30,0,30,8,20,25,10,24,26,2,28,30,5,0,5,10,26 5,10,19,22,26,30,0,3,20,25,30,20,30,0,1,10,23,12,30,8 30,0,1,5,10,24,26,30,8,20,25,30,8,20,30,0,0,8,30,0 8,3,7,30,0,7,8,12,30,0,5,13,0,0,0,7,26,7,12,24 27,0,0,26,0,0,0,5,10,14,17,7,12,16,19,22,26,6,11,15 18,21,26,5,10,17,7,12,l9,22,26,6,11,18,21,26,5,10,14,17 7,12,19,22,26,30,6,11,18,21,26,29,0,5,10,17,7,12,19,22 26,6,11,18,21,26,5,10,17,7,12,19,22,26,30,6,11,18,21,26 29,8,5,10,17,7,12,19,22,26,6,11,18,21,26,5,10,14,17,7 12,19,22,26,6,11,18,21,26,S,10,17,7,12,19,22,26,30,6,11 18,21,26,29,5,10,14,17,7,12,19,22,26,6,11,18,21,26,4,5 9,10,17,7,12,22,26,30,6,11,21,26,29,5,10,17,7,12,16,l9 22,26,30,6,11,15,18,21,26,29,5,9,10,6,11,5,10,7,12,22 26,30,6,11,21,26,29 Read files "Pointers" and "MidW Len, PopD, TrAcc" PRED%(355), Length%(836), Pointer%(355), H%(355) PopD%(836), TrAccRate%(836), LINKER%(836) PRINT OPEN OPEN N% = NUM% DO - REC READ #2, LET P% IF WHI RECORD #1, READ #1, LET NODE%(P%) LET Length%(P%) LET PopD%(P%) LET TrAccRate%(P%) LET LINKER%(P%) P% 2 PopD, TrAcc", "R", "R", 355 = 1 #2, #1, "Pointers", "Midw Len, 10 ORD #2, NUM% Pointer$;2 Pointer%(NUM%) - Pointer%(NUM%) P% 1000 THEN "Null.Node" LE P% <> 0 P% Connector$;2, = CVI(PointerS) Length$;2, TrAccRate$;2, LINKER$;2 CVI(ConnectorS) CVI(LengthS) CVI(PopD$) CVI(TrAccRate$) CVI(LINKERs) POPDSIZI LINKER%(P%) WEND "Nu H%( ll.Node" NUM%) = NUM% NUM% = NUM% + 1 UNTIL NUM% > N% CLOSE #1,#2 Saver% 8 0 C% 1 WHILE C% < N% - Saver% IF WHI Pointer%(C%) <> 1000 THEN "Ignore" LE Pointer%(N% - Saver%) 1000 Saver% = Saver% + 1 WEND 176 H%(C%) = H%(N% - Saver%) Saver% = Saver% + l "Ignore" C% - C% + 1 WEND REM REM REM RETURN Initialization process completed. "Cost" DIM DIST(355) "NewSitel" V% = 1 DO DIST(V%) a 9999 FINAL%(V%) = 0 PRED%(V%) = -1 V% = V% + 1 UNTIL V% > N% TotalCost! = 0 TotalDist! = 0 PRINT: PRINT: PRINT INPUT " Which node is to be the location of the repository? "; DIST(S%) = 0 FINAL%(S%) = -1 Recent% = 8% PRINT PRINT " Would you like the results for each generation sitez" PRINT PRINT " PRINT " PRINT " PRINT PRINT " Please enterthe number of your selection. " ,- INPUT ReportOut% PRINT IF ReportOut% = 3 THEN PRINT " FOR ii% = 1 TO 62 CaskCost! = 0 BarrelCost! = 0 TransCost! - 0 CaskTariff! = 0 BarrelTariff! = 0 Decide = 2 T% = Origin(ii%) REM 1. Not reported," 2. Displayed on the screen," 3. Printed on the line printer." 8% Please insure that the printer is turned on." REM REM REM REM WHILE FINAL%(T%) = 0 REM REM REM REM REM REM The next statement creates a loop which causes the problem to be solved for all nodes until the destination node is solved. The solution for the remainder of the network is not completed. The following FOR loop finds all nodes connected to the current node (designated as RECENT). For all nodes connected to RECENT and not yet permanently labelled, the total distance from the source is calculated and temporarily stored for comparison. 177 Z = Pointer%(Recent%) WHILE Z <> 0 IF FINAL%(NODE%(Z)) <> 0 THEN "UPWARDl" NEWLABEL = DIST(Recent%) + Length%(Z) IF NEWLABEL >= DIST(NODE%(Z)) THEN "UPWARDl" DIST(NODE%(Z)) = NEWLABEL PRED%(NODE%(Z)) = Recent% "UPWARDl" Z = LINKER%(Z) REM The next DO loop sorts through the nodes adjacent to RECENT and REM chooses the node nearest RECENT (the node currently being REM examined.) REM TEMP = 9999 U% = 1 DO IF ((FINAL%(H%(U%))=O) AND (DIST(H%(U%)) (N% - Saver%) REM Once the node closest to RECENT is determined, it is made part REM of the set of permanently labelled nodes by giving it a FINAL REM value of -1 and it is assigned the temporary title of RECENT. REM The process continuesby solving for the node nearest the newly REM crowned RECENT. IF TEMP > 9998 THEN "FINISl" FINAL%(Y%) = -1 Recent% = Y% "FINISl" WEND IF DIST(T%) < 100 THEN Decide = 1 ON Decide GOSUB "ShortDist", "LongDist" TransCost! = CaskCostl/IOO + BarrelCostE/IOO TotalCost! = TotalCost! + TransCost! TotalDist!=TotalDist!+(DIST(T%)*(AnnualShip(ii%,1)+AnnualShip(ii%,2) +Annua1$hip(ii%,3))) ON ReportOut%-l GOSUB "Displayed", "Printed" NEXT ii% PRINT " The TOTAL COSTof shipping LLW to"; 3%.- "is: $"; TotalCost! PRINT PRINT USING " #.### “‘2“ "; TotalDistl; PRINT "vehicle-miles are required for annual shipments to"; 3% PRINT: PRINT INPUT " Would you like to examine another repository site? "; Replys AA$ = LEET$ 600 THEN CaskTariff! = 142 CaskCost! = AnnualShip(ii%,l) * ((CaskTariff! * 2 * DIST(T%)) + (100000 * INT((2 * DIST(T%)/500))+.5) + 200000) "Barrelsl" BarrelTariff! = INT((4290 * DIST(T%)“(-.4799)) + .5) IF DIST(T%) > 1000 THEN BarrelTariff! = 156 BarrelCost! = (AnnualShip(ii%,2) + AnnualShip(ii%,3)) * BarrelTariff! * DIST(T%) RETURN "ShortDist" REM REM Distances less than 100 miles are charged for 100 miles of REM shipping. REM CaskTariff! = 338 BarrelTariff! = 471 CaskCost! = AnnualShip 5% PRINT PRED%(X%), x% = PRED%(X%) WEND PRINT PRINT "The distance between nodes"; T%; "and"; 5%; "is:"; DIST(T%) PRINT "Soon" PRINT "Thecostoftransporting LLWbetween"; T%,- "and"; 5%; "is: $"; TransCost! PRINT: PRINT TEXT 3,12,o,1 RETURN "Printed" TEXT 4,9,0,1 IF 5% = T% THEN "Goon" LPRINT LPRINT "The path between node"; T%; "and node"; 5%; "is:" LPRINT T%, LPRINT PRED%(T%), X% = PRED%(T%) WHILE X% <> 5% LPRINT PRED%(X%), x% = PRED%(X%) WEND LPRINT TV“- LPRINT "The distance between nodes"; 179 T%; "and"; 5%,- "is:"; DIST(T%) LPRINT "Goon" LPRINT LPRINT: "Thecostoftransporting LLWbetween"; T%; "and"; 5%; "is: $"; TransCost! LPRINT TEXT 3,12,o,1 RETURN "Risk" DIM Risk#(355),RDist(355),RFinal(355),RPred(355),DDist(355) "NewSiteZ" TotalRi5k# = 0 TotalDist! = 0 V = 1 DO RDist(V) = RFinal(V) RPred(V) 9999 =0 =-1 V = V + l UNTIL PRINT: INPUT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT INPUT PRINT IF ReportOut% = v > N% PRINT: PRINT " Which node is to be the location of the repository? "; T% " Would you like the results for each generation sitez" " 1. Not reported," " 2. Displayed on the screen," " 3. Printed on the line printer." " Please enterthe number of your selection. " ,- ReportOut% 3 THEN PRINT " Please insure that the printer isturned on." RDist(T%) = 0 RFinal(T%) = -1 RRecent = T% FOR ii% = 1 TO 62 As(1) = AnnualShip(ii%,l) As(2) = AnnualShip(ii%,2) As(3) = AnnualShip(ii%,3) Chooser = 1 IF (Offset(ii%,1)=0 AND Offset(ii%,2)=0 AND Offset(ii%,3)=0) THEN Chooser=2 REM REM If the shipment being modelled has risk factor equal to 0, then REM the route selected will be the shortest distance route. RRisk REM optimizes risk while RDistance optimizes distance REM ON Chooser GOSUB "RRisk", "RDistance" TotalRisk# = TotalRisk# + Risk# TotalDist! = TotalDist! + (RLength * (As(1) + As(2) + As(3))) ON ((Chooser+1)*(ReportOut%-1)-1) GOSUB "DisplayedZ","Disp2a","PrintedZ","zip","Prin2a" NEXT ii% PRINT " The DOSE CONSEQUENCE of shipping LLW to"; T% ; "is ".- PRINT USING "#.### ““2“ "; TotalRisk#; PRINT "person-rem." PRINT 180 PRINT USING " #.### "*““ "; TotalDistl; PRINT "vehicle-miles are required for annual shipments to"; T% PRINT: PRINT INPUT " Would you like to examine another repository site? "; Replys AAS = LEFT$(Reply$,1) IF (AA$ = "Y" OR AA$ = "y") THEN "NewSiteZ" RETURN "RRiSk" V% = 1 DO Risk#(v%) = 9E6 FINAL%(V%) = 0 DDist(V%) = 0 PRED%(V%) = -1 V% = V% + 1 UNTIL V% > N% 5% = Origin(ii%) Risk#(S%) = 0 FINAL%(S%) = -1 Recent% - 8% WHILE FINAL%(T%) = 0 Z = Pointer%(Recent%) WHILE Z <> 0 IF FINAL%(NODE%(Z)) <> 0 THEN "UPWARDZ" AccConseq# = 0 AFConseq# = 0 Conseq# = 0 ST% = 1 DO REM REM Risk is calculated for each link (population density zone) REM all shipment types. REM PP% = Offset(ii%,ST%) WHILE PP% <> 0 AccConseq# = AccConseq# + Ci!(PP%) * (AccUnitRisk#(Isotope(PP%),PopD%(Z)) * TrAccRate%(Z) * Length%(Z) * As(ST%)) AFConseq# = AFConseq# + Ci!(PP%) * (AFUnitConseq#(Isotope(PP%),PopD%(Z)) * Length%(Z) * As(ST%)) Conseq# = Conseq# + AccConseq# + AFConseq# PP% = Attach(PP%) WEND ST% = ST% + 1 UNTIL ST% > 3 NEWLABEL# = Risk#(Recent%) + Conseq# IF NEWLABEL# >= Risk#(NODE%(Z)) THEN "UPWARDZ" Risk#(NODE%(Z)) = NEWLABEL# PRED%(NODE%(Z)) = Recent% DDist(NODE%(Z)) DDist(Recent%) + Length%(Z) "UPWARDZ" Z = LINKER%(Z) WEND TEMP# = 9E6 U% = 1 DO for IF ((FINAL%(H%(U%))=0) AND (Risk#(H%(U%)) (N% - Saver%) IF TEMP# >= 9E6 THEN "FINISZ" FINAL%(Y%) t -1 Recent% = Y% "FINISZ" WEND Risk# = Risk#(T%) RLength = DDist(T%) RETURN "RDistance" S% = Origin(ii%) WHILE RFinal(S%) = 0 R2 = Pointer%(RRecent) WHILE Rz <> 0 IF RFinal(NODE%(RZ)) <> 0 THEN "RUPWARD" RNEWLABEL a RDist(RRecent) + Length%(RZ) IF RNEWLABEL >a RDist(NODE%(RZ)) THEN "RUPWARD" RDist(NODE%(RZ)) = RNEWLABEL RPred(NODE%(RZ)) = RRecent "RUPWARD" R2 = LINKER%(RZ) WEND RTEMP = 9999 U = 1 DO IF ((RFinal(H%(U))=0 AND RDist(H%(U)) (N% - Saver%) IF RTEMP > 9998 THEN "RFinis" RFinal(RY) = -l RRecent = RY "RFinis" WEND Risk# = 0 RLength = RDist(S%) RETURN "Displayed2" WIDTH 7o DEF TAB = 7 TEXT 4,9,o,1 IF 5% = T% THEN "Soon2" PRINT PRINT "The path between node"; 5%; "and node"; T%,- "is:" PRINT T%, PRINT PRED%(T%), 182 X% = PRED%(T%) WHILE X% <> 8% PRINT PRED%(X%), x% = PRED%(X%) WEND PRINT "Soon2" PRINT " The consequence of transporting LLW between"; 5%; "and"; T%; "is" PRINT USING " #.### “AA“ "; Risk#; PRINT "person-rem." PRINT PRINT USING " #.### “‘9“ "; (RLength * (As(1) + As(2) + As(3))); PRINT "vehicle-miles are required for annual shipments to"; T% PRINT: PRINT TEXT 3,12,0,1 RETURN "Disp2a" WIDTH 70 DEF TAB = 7 TEXT 4,9,o,1 IF 5% = T% THEN "Soon2a" PRINT PRINT "The path between node".- 5% .- "and node" ,- T%; "is:" PRINT 5%, PRINT RPred(5%), X% = RPred(S%) WHILE X% <> T% PRINT RPred(X%), X% = RPred(X%) WEND PRINT "Soon2a" PRINT " The consequence of transporting LLW between"; 5%; "and"; T%; "is" PRINT USING " #.### “2‘“ "; Risk#; PRINT "person-rem." PRINT PRINT USING " #.### “A“? "; (RLength * (As(1) + As(2) + As(3))); PRINT "vehicle-miles are required for annual shipments to"; T% PRINT: PRINT TEXT 3,12,0,1 RETURN "zip" RETURN "Printed2" TEXT 4,9,o,1 IF 8% = T% THEN "Goon2" LPRINT LPRINT "The path between node"; 5%; "and node"; T% ; "is:" LPRINT T%, LPRINT PRED%(T%), X% = PRED%(T%) WHILE X% <> 8% LPRINT PRED%(X%), X% = PRED%(X%) WEND LPRINT "Goon2" 183 LPRINT " The consequence of transporting LLW between",- 5%,- "and"; T%,- "is" LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT: USING " #.### “A?“ "; "person-rem." USING " #.### M“ ".- "vehicle-miles are required for annual shipments to"; T% LPRINT TEXT 3,12,0,1 RETURN "Prin2a" TEXT 4,9,0,1 IF 5% = T% THEN LPRINT LPRINT "The path between node"; LPRINT 5%, LPRINT RPred(S%), X% = RPred(S%) WHILE X% <> T% LPRINT RPred(X%), RPred(X%) X% = WEND LPRINT "Goon2a" Risk#(T%); (RLength * (As(1) + As(2) + As(3))); S %; "and node"; T%; u iSZ" LPRINT " The consequence of transporting LLW between"; 5%; "and",- T%; "is" LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT: USING " #.### 9““ "; "person-rem." USING " #.### MM ": "vehicle-miles are required for annual shipments to"; T% LPRINT TEXT 3,12,0,1 RETURN Risk#(T%): (RLength * (As(1) + As(2) + As(3))); ‘ 1 Appendix J COST, RISK AND INDEX RESULTS: MODELLING THE MILLRWC Appendix I Cost, Risk and Index Results: Modelling the MILLRWC Cost Risk Cost Risk Combined Node Location (9136) (P-rem’E3) Norm. Norm. Index 3 Fargo, ND 1.52 9.35 1.77 1.70 3.46 12 E Sioux Falls, SD 1.40 8.02 1.63 1.45 3.08 14 Sioux City, IA 1.36 8.24 1.58 1.49 3.07 17 Council Bluffs, IA 1.26 7.53 1 .47 1.37 2.83 25 St. Joseph, MO 1.34 8.87 1.56 1.61 3.17 31 Kansas City, MO 1.30 8.22 1.51 1.49 3.00 49 SW Minneapolis, MN 1.21 6.31 1.41 1.14 2.55 55 NE St. Paul, MN 1.20 6.69 1.40 1.21 2.61 58 Barnum, MN 1.34 8.48 1.56 154 3.10 59 Duluth, MN 1.38 8.80 1.60 1.59 3.20 61 Albert Lea, MN 1.17 6.02 1.36 1.09 2.45 63 Marion, MN 1.13 6.51 1.31 1.18 2.49 65 Minneapolis, MN 1.21 7.36 1.41 1.33 2.74 67 Ames, IA 1 .09 5.84 1 .27 1.06 2.33 69 SE Des Moines, IA 1.09 5.89 1 .27 1.07 2.34 72 Tiffin, IA 1.02 5.52 1.19 1.00 2.19 79 JOpIin, MO 1.40 9.29 1.63 1.68 3.31 81 Springfield, MO 1.35 9.16 1.57 1.66 3.23 85 Cape Girardeau, MO 1.25 9.11 1.45 1.65 3.10 87 Hayti, MO 1.31 9.52 1.52 1.72 3.25 90 Charlestown, MO 1.24 8.92 1.44 1.62 3.06 92 St. Louis, MO 1.14 8.72 1.33 - 1.58 2.91 93 Columbia, MO 1.19 8.06 1.38 1.46 2.85 95 Rice Lake, WI 1.19 7.94 1.38 1.44 2.82 97 Eau Claire, WI 1.13 7.26 1.31 1.32 2.63 99 Tomah, WI 1.08 7.13 1.26 1.29 2.55 100 Portage, WI 1.02 7.59 1.19 1.38 2.56 101 Merrill, WI 1.18 9.01 1.37 1.63 3.01 102 Madison, WI 1.01 7.80 1.17 1.41 2.59 103 Beloit, WI 0.91 7.77 1.06 1.41 2.47 104 Green Bay, WI 1.10 9.15 1.28 1.66 2.94 105 Oshkosh, WI 1.07 8.67 1.24 1.57 2.82 110 Milwaukee, WI 0.95 8.12 1.10 1.47 2.58 112 Rockford, IL 0.90 6.87 1.05 1.24 2.29 120 Chicago Loop, IL 0.89 7.51 1.03 1.36 2.40 124 Ioliet, IL 0.89 6.30 1.03 1.14 2.18 131 Galesburg, IL 1.01 6.08 1.17 1.10 2.28 133 S Bloomington, IL 0.97 6.43 1.13 1.17 2.29 134 Springfield, IL 1.05 7.10 1.22 1.29 2.51 138 Champaign, IL 0.97 6.68 1.13 1.21 2.34 139 Effingham, IL 1.01 7.24 1.17 1.31 2.49 144 Mt. Vernon, IL 1.09 8.06 1.27 1.46 2.73 145 Pulleys Mill, IL 1.18 8.59 1.37 1.56 2.93 147 E Gary, IN 0.86 7.30 1.00 1.32 2.32 153 Sault Ste. Marie, MI 1.28 12.05 1.49 2.18 3.67 184 185 Cost Risk Cost Risk Combined Node Location (5’56) (P-rem‘E3) Norm. Norm. Index 154 St. Ignace, MI 1.21 11.40 1.41 2.07 3.47 156 Clare, MI 1.00 9.82 1.16 1.78 2.94 157 Bay City, MI 1.01 10.32 1.17 1.87 3.05 158 East Lansing, MI 0.92 8.96 1.07 1.62 2.69 160 Jackson, MI 0.88 8.54 1.02 1.55 2.57 163 E Grand Rapids, MI 0.92 8.94 1.07 1.62 2.69 166 Reed City, MI 0.98 9.69 1.14 1.76 2.90 167 Muskegon, NH 0.95 8.71 1 .10 1 .58 2.68 168 Ludington, MI 1.03 9.53 1.20 1.73 2.92 169 Holland, MI 0.93 8.56 1.08 1.55 2.63 170 Benton Harbor, MI 0.89 8.15 1.03 1.48 2.51 171 Kalamazoo, MI 0.91 8.49 1.06 154 2.60 172 Marshall, MI 0.90 8.27 1.05 1.50 2.54 175 Flint, MI 0.97 9.80 1.13 1.78 2.90 176 Lapeer, MI 0.98 10.70 1.14 1.94 3.08 179 Brighton, MI 0.91 9.13 1.06 1.65 2.71 180 N Ann Arbor, MI 0.90 9.27 1.05 1.68 2.73 186 Wayne, MI 0.91 9.28 1.06 1.68 2.74 187 Southfield, MI 0.94 9.63 1.09 1.75 2.84 190 Detroit, MI 0.94 11.24 1.09 2.04 3.13 191 Sylvania, OH 0.90 8.54 1.05 1.55 2.59 193 Port Huron, MI 1.03 11.22 1.20 2.03 3.23 195 Muncie, IN 0.95 7.50 1.10 1.36 2.46 201 Veedersburg, IN 1.01 7.05 1.17 1.28 2.45 203 Indianapolis, IN 0.97 8.07 1.13 1.46 2.59 207 New Albany, IN 1.06 8.60 1.23 1.56 2.79 209 Ottawa Hills, OH 0.90 8.74 1.05 1.58 2.63 213 Amherst, OH 0.97 9.42 1.13 1.71 2.84 217 Cleveland, OH 1.00 10.48 1.16 1.90 3.06 222 Ashtabula, OH 1.05 10.94 1.22 1.98 3.20 224 Shaker Heights, OH 1.01 10.08 1.17 1.83 3.00 226 Streetsboro, OH 1.01 10.17 1.17 1.84 3.02 232 North Lima, OH 1.04 11.20 1.21 2.03 3.24 233 Bridgeport, OH 1.13 10.44 1.31 1.89 3.21 234 Akron, OH 1.02 11.08 1.19 2.01 3.19 239 Seville, OH 1.00 9.74 1.16 1.77 2.93 243 Columbus, OH 1.01 9.56 1 .17 1.73 2.91 247 Cambridge, OH 1.07 10.12 1.24 1.83 3.08 248 Marietta, OH 1.14 10.62 1.33 1.92 3.25 249 Findlay, OH 0.94 8.67 1.09 1.57 2.66 252 Portsmouth, OH 1.17 10.26 1.36 1.86 3.22 253 Dayton, OH 0.97 9.59 1.13 1.74 2.87 255 Cincinnati, OH 1.00 9.32 1.16 1.69 2.85 265 Warrenton, IN 1.12 8.82 1.30 1.60 2.90 305 Charlotte, MI 0.92 8.54 1.07 1.55 2.62 306 Canton, OH 1.03 10.50 1.20 1.90 3.10 307 River Falls, WI 1.16 6.96 1.35 1.26 2.61 308 W Lafayette, IN 0.97 7.68 1.13 1.39 2.52 309 Stevens Point, WI 1.14 8.46 1.33 1.53 2.86 310 Bloomington, IN 1.03 7.94 1.20 1.44 2.64 311 South Bend, IN 0.88 7.72 1.02 1.40 2.42 312 Elkhart, IN 0.88 7.73 1.02 1.40 2.42 Node 313 314 315 316 317 318 334 335 336 337 338 339 340 348 350 351 352 354 355 Location Athens, OH Clinton, IA Le Claire, IA Atlantic, IA Springfield, OH Mason City, IA Monticello, MN Red Wing, MN Cedar Rapids, IA Fulton, MO Genoa, WI Manitowoc, WI Manitowoc, WI Indian River, MI Covert, MI Bridgman, MI Newport, MI Oak Harbor, OH North Perry, OH Cost ($136) 1.12 1.01 0.99 1.20 0.99 1.18 1.24 1.15 1.07 1.19 1.11 1.07 1.07 1.18 0.89 0.88 0.93 0.91 1.02 186 Risk (P-rem*E3) 10.17 6.17 5.86 6.83 8.93 5.98 6.98 6.91 5.88 8.14 6.83 8.72 8.72 1 1 .09 8.23 7.69 9.43 8.92 10.89 Cost Norm. 1.30 1.17 1.15 1.40 1.15 1 .37 1.44 1.34 1 .24 1 .38 1.29 1.24 1.24 1 .37 1.03 1.02 1.08 1.06 1.19 Risk Norm. 1 .84 1 .1 2 1.06 1 .24 1.62 1.08 1 .27 1.25 1.07 1.48 1 .24 1 .58 1 .58 2.01 1.49 1.39 1 .71 1 .62 1 .97 Combined Index 3.15 2.29 2.21 2.63 2.77 2.46 2.71 2.59 2.31 2.86 2.53 2.82 2.82 3.38 2.53 2.42 2.79 2.68 3.16 Appendix K COST, RISK AND INDEX RESULTS: MODELLING MICHIGAN Node 147 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 209 210 Appendix K Cost, Risk and Index Results: Modelling Michigan Location F Gary, IN Sault Ste. Marie, MI St. Ignace, MI Grayling, MI Clare, MI Bay City, MI East Lansing, MI 5 Lansing, MI Jackson, MI SW Lansing, MI W Lansing, MI E Grand Rapids, MI N Grand Rapids, MI Grand Rapids, MI Reed City, MI Muskegon, MI Ludington, MI Holland, MI Benton Harbor, MI Kalamazoo, MI Marshall, MI NW Flint, MI NE Flint, MI Flint, MI Lapeer, MI W Flint, MI SW Flint, MI Brighton, MI N Ann Arbor, MI Ann Arbor, MI NE Ann Arbor, MI SE Ann Arbor, MI Farmington, MI Livonia, MI Wayne, MI Southfield, MI W Detroit, MI Dearborn, MI Detroit, MI Sylvania, OH Toledo, OH Port Huron, MI Fremont, IN Ottawa Hills, OH Maumee, OH Cost (S‘ES) 2.46 3.45 3.32 2.63 2.40 2.40 2.21 2.21 2.19 2.19 2.21 2.25 2.25 2.25 2.40 2.38 2.82 2.38 2.36 2.29 2.16 2.31 2.31 2.30 2.36 2.29 2.30 2.28 2.26 2.26 2.27 2.34 2.31 2.37 2.38 2.39 2.38 2.40 2.40 2.42 2.44 2.57 2.32 2.43 2.42 Risk (P-rem’EZ) 7.56 11.33 10.22 8.45 7.39 8.28 6.24 5.70 5.87 6.18 6.28 6.43 6.68 8.81 7.73 6.77 8.29 6.97 7.18 7.57 5.78 9.78 9.88 7.27 10.33 7.39 6.39 5.70 5.70 6.59 5.54 5.48 5.68 5.52 4.62 6.47 9.91 11.73 12.13 5.50 5.14 11.16 5.54 6.08 5.58 187 Cost Norm. 1.14 1.60 1.54 1.22 1.11 1.11 1.02 1.02 1.01 1.02 1.02 1.04 1.04 1.04 1.11 1.10 1.31 1.10 1.09 1.06 1.00 1.07 1.07 1.07 1.09 1.06 1.06 1.06 1.05 1.05 1.05 1.09 1.07 1.10 1.10 1.11 1.10 1.11 1.11 1.12 1.13 1.19 1.07 1.13 1.12 Risk Norm. 1.64 2.45 2.21 1.83 1.60 1.79 1.35 1.23 1.27 1.34 1.36 1.39 1.45 1.91 1.67 1.47 1.79 151 1.55 1.64 1.25 2.12 2.14 1.57 2.24 1.60 1.38 1.23 1.23 1.43 1.20 1.19 1.23 1.19 1.00 1.40 2.15 2.54 2.63 1.19 1.11 2.42 1.20 1.32 1.21 Combined Index 2.78 4.05 3.75 3.05 2.71 2.90 2.38 2.26 2.28 2.35 2.38 2.43 2.49 2.95 2.79 2.57 3.10 2.61 2.65 2.70 2.25 3.19 3.21 2.64 3.33 2.66 2.45 2.29 2.28 2.47 2.25 2.27 2.30 2.29 2.10 2.51 3.25 3.65 3.74 2.31 2.24 3.61 2.27 2.45 2.33 Node 303 304 305 311 312 348 350 351 352 Location N Lansing, MI NW Lansing, MI Charlotte, MI South Bend, IN Elkhart, IN Indian River, MI Covert, MI Bridgman, MI Newport, MI Cost ($‘E5) 2.22 2.21 2.19 2.41 2.41 3.24 2.38 2.40 2.41 188 Risk (P-rem‘EZ) 6.41 6.28 6.31 7.41 6.19 9.54 7.04 7.52 4.62 Cost Norm. 1.03 1.03 1.02 1.12 1.12 1.50 1.10 1.11 1.12 Risk Norm. 1 .39 1 .36 1 .37 1.60 1 .34 2.06 1 .52 1.63 1.00 Combined Index 2.42 2.38 2.38 2.72 2.46 3.57 2.63 2.74 2.12 LIST OF REFERENCES 10. 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