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David Wesley Swindle, Jr. a Thesis Submitted to The \AN OPTIMAL WITHDRAWAL POLICY FOR SPENT NUCLEAR FUEL FROM ON-SITE STORAGE, by David Wesley Swindle, Jr. A Thesis submitted to the graduate Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Nuclear Science and Engineering APPROVED: H. A. Kursted Co-Chairman a J. A. Nachlas, Co-Chairman G. H. acer August 1977 Blacksburg, Virginia ib SEs Voss 97"? S94ny C.K ' ACKNOWLEDGEMENTS The assistance of Dr. H. A. Kurstedt, Chairman, Nuclear Science and Engineering, and Dr. J. A. Nachlas, Industrial Engineering and Operations Research, in selecting and developing the technical aspects of this paper is gratefully acknowledged. A special thanks is due the author's wife Carolyn, without whom the motivation to complete this work nor the typing of this work would have been possible. Li TABLE OF CONTENTS ACKNOWLEDGEMENTS» TABLE OF CONTENTS LIST OF TABLES* »* LIST OF FIGURES e s e e ° e e » e . e e * * e e e a * INTRODUCTIONs * © * © * © © © © © © © e© © © ee ee A. Background and Motivation * * * + ** * *« se «+s B. The Problem and the Objective * *+ + + * * * « + » The Approach» e e e e e e ° e ° * e e e e ° ° e ° C. Results ee © e® ® © © e e© 8@» © @® © © e@ &#© ® © #© &© 8 @ D. DESCRIPTION OF THE SPENT+FUEL STORAGE PROBLEM «+ «+ « » 11 A. An Overview of the Nuclear Fuel Cycle * * © * » » 11 Current Uncertainties Facing the Nuclear Fuel Cycle in the United States* * © * *+ © © © © « « « 16 Reprocessing of Nuclear Fuel in the United States 19 Examination of the Role of Nuclear Energy in Meeting America's Energy Needs» » + © * + ¢ «© « « 23 DERIVATION OF THE SPENT FUEL WITHDRAWAL MODEL « « « « 27 A. Characteristics of the Spent=Fuel Withdrawal Problem- 27 B. The Dynamic Programming Formulation «+ * + «+ « » . 29 Cc. The Hitchcock Problem Formulation * * + + * «© « « 35 D. The Linear Programming Formulations * * +¢ +© + « «» 40 THE EXAMINATION AND EVALUATION OF THE COMPONENTS OF THE SPENT~FUEL WITHDRAWAL PROBLEM «+ + + « « « «© «© © « « « 46 A. Characteristics of Nuclear Reactors in Regard to Nuclear Fuel + «© « «© 2» «© © «© «© © «© © © » © «© « 46 Lii TABLE OF CONTENTS (Continued) B. Spent-Fuel Supply and Demand Projections* * * * + °« C. The Measure of Effectiveness - Profitability e e per Assembly e P e e e ° e ° ° e a e e e . e e 63 D. Storage Costs * * * * * * © © © © © © © © # © # # » 81 APPLICATION OF THE SPENT=FUEL*WITHDRAWAL MODEL* »° 85 A. Model and Data Summary’ *- * * * * * * 2 2 e+ * © © & 85 B. Implementation of the Model and Procedural Summary: 88 RESULTS © © ee ee tee we ee he he eh we te te 100 A. Optimistic Reprocessing Scenarioe* * * * * * * * & » 100 B. Realistic Reprocessing Scenario * * * * * * * © » » 106 C. Pessimistic Reprocessing Scenario a 107 CONCLUS IONS e e ° e e e e e . ° e ° e e e ® e e e e e ° 118 SUMMARY AND RECOMMENDATIONS 120 BIBLIOGRAPHY* * * * * * © © © © © © © © © © © © ¢ # « ¢ 122 10. APPENDIX ° _ @ @ @ © e@© © #@ © © © © © © © @© © #@ © © @© #© @& 2@ 125 11. VITA e e e e e e e . e e e e e e e e ® e e e e e e . ° 244 iv LIST OF TABLES Table Title Page 2.1 U.S. Electric Power Statistics 1947-1974- + >» 24 2.2 Installed Nuclear Capacity* + * + * «© © © s « « 26 3.1. Unit Measures of Profitability for the Linear Programming Problem eo © ss» © © © © © @ e@© #© © 8 @ 42 4.1 LWR Fuel and Discharge Data + * * * * + © # « « 47 4.2 Spent-Fuel Discharge Characteristics» + * « « »« 50 4.3 Average Composition of Plutonium Available for Recycle- 51 4.4 Installed Nuclear Capacity + + + + + + + e+ © ee eos 54 4.5 Discharge Quantities of Spent-—Fuel Per Gigawatt (electric) ee © e# © e © e© # @ e © © @ ee © @ @© @ @ 55 4.6 Spent-Fuel Supply Projections by Reactor Mix: »- 56 4.7 Reprocessing Plant Capacity Schedule* + * + «= » 59 4.8 Reprocessing Capability - Optimistic Scenario * 60 4.9 Reprocessing Capability - Realistic Scenarios + 61 4.10 Reprocessing Capability - Pessimistic Scenarios 62 4,11 Uranium Price Projections + + * * © «© «© #© « « « 73 4.12 Separative Work Cost Projection * * * * * * « « 75 4.13 Uranium Conversion Costs Forecast * * * * « « « > 76 4.14. Plutonium Value for Uranium Feed and Separative Work Equivalents* *© «© « «© © © «© © «© » « © © « « 83 4.15 On-Site Storage Costs Per Assembly~Year + + « » 84 5.1 Profitability Per Assembly - Westinghouse PWR > 89 5.2 Profitability Per Assembly B & W PWRe « «= « e 90 5.3 Profitability Per Assembly - Combustion Engineering 91 Cy 5.4 Profitability Per Assembly GE BWR/6 e e ° ® . e e 92 LIST OF FIGURES Figure — Title 2.1 The Light Water Reactor Fuel Cycle + * * * * * * © & 4.1 Spent-Fuel Assembly Demand Rate - Westinghouse PWR > 4.2 Spent-Fuel Assembly Demand Rate - Babcock and Wilcox PWR. ° e e ° e e e a s e s e e e e e e e e e * e * s 65 4.3 Spent-Fuel Assembly Demand Rate —- Combustion Engineering PWRe = * * © © * © © #© © #© © © #© © # © @ 66 4.4 Spent-Fuel Assembly Demand Rate - General Electric BWR/6-° s ° e e e e e e e ° . e e ° e ° e e . ° ° ° ° 67 5.1 Profitability Per Assembly - lst Discharge Westinghouse PWR * 2 e «© e@ e # @ 7. © © © 8 © @ @ @© @ | 93 5.2 Profitability Per Assembly ~ lst Discharge General Electric BWR/6 * e©= ee © © ee e@ # © @ ee ee 8 © # @ e@ © 28 94 5.3 Profitability Per Assembly - Ist Discharge No Plutonium Value; Westinghouse PWRe * * * * © » © @ » 97 5.4 Profitability Per Assembly - lst Discharge No Plutonium Value; General Electric BWR/6+ * + «© + » » 98 6.1 Optimal Selection Rule; Base Optimistic Reprocessing Scenario; Westinghouse PWR Base, +20Z SWU, +20% Storage, -20% Uranium, -20% SWU, -~20% Storage Costs + « © © © « «© «© © « © © «© # 8 © »® 101 6.2 Optimal Selection Rule; Base Optimistic Reprocessing Scenario; Westinghouse PWR +207 Uranium Coste 7 © @ e@ e © © © © 8® #© #© © e 2&© # # 102 6.3 Optimal Selection Rule; Base Optimistic Reprocessing Scenario; Westinghouse PWR No Plutonium Value; Base Cost+ *© «© © © «© «6 « « « « » 104 6.4 Optimal Selection Rule; Base Optimistic Reprocessing Scenario; Westinghouse PWR No Plutonium Value; +204 Uranium Cost+ + + « « + « « 105 6.5 Optimal Selection Rule; Base Realistic Reprocessing Scenario-Westinghouse PWR No Plutonium Value; Base Costs « «+ *© + « « «© © « « « 108 vi Figure . Title Page 6.6 Optimal Selection Rule; Base Realistic Reprocessing Scenario —- Westinghouse PWR No Plutonium Value; +20% Uranium Costs* * * + + * * © © #109 6.7 Optimal Selection Rule; Base Realistic Reprocessing Scenario —- Westinghouse PWR Base, +20% SWU, +20% Storage, ~20% Uranium, -—20% SWU, ~20% Storage Cost * * * * * « « e © © © © © © © © we hl elhlcelUC UL 6.8 Optimal Selection Rule; Base Realistic Reprocessing Scenario —- Westinghouse PWR +207 Uranium Cost * * * * © © # # # # e e e © © © © # s& ¢ 11l 6.9 Optimal Selection Rule; Base Pessimistic Reprocessing Scenario; Westinghouse PWR No Plutonium Value; Base Costs* * * * * * * * © * © © *© #113 6.10 Optimal Selection Rule; Base Pessimistic Reprocessing Scenario; Westinghouse PWR No Plutonium Value; +20% Uranium Cost * * * * * * ° © © «114 6.11 Optimal Selection Rule; Base Pessimistic Reprocessing Scenario; Westinghouse PWR Base, +20% Uranium, +20% SWU, +202Z Storage, -20% Uranium, -20% SWU, -20% Storage Costs* * * * * * * * 115 . 6.12 Optimal Selection Rule; +30% Pessimistic. Reprocessing Scneario; Westinghouse PWR +2074 Uranium Cost ee 8© © © © © © © © © © 8 ©» &© &© © © @ 116 6.13 Optimal Selection Rule; +30% Pessimistic Reprocessing Scneario; Westinghouse PWR +20% SWU Cost ° * * * © © © © © © © © © © © © © © © © © © [U7 vii 1. INTRODUCTION A. Background and Motivation In order for an industrialized country like the United States to continue to grow economically, abundant energy at a reasonable cost must be available. Otherwise, as was recently evidenced by the Arab Oil Embargo, there will be a decrease in economic growth and an in- crease in inflation. As a result of these problems, which could con- ceivably reduce the economic prosperity of this nation, the United States government has stressed energy self-reliance and conservation. To obtain this self-reliance, the energy needs of the nation must be satisfied from domestic resources. In particular, of the domestic sources of energy available, only two fuels, coal and uranium, are abundant in the sense of providing a low-cost, high-energy resource.!3 Upon examining the primary uses of these two fuels, coal and uranium are more suited for the production of electricity than for any other purpose./3 ‘However at present, when considering environmental, economic, and societal points of view, the energy obtained from uranium appears more acceptable for the generation of electricity than coal- burning and other technologies .?2 To specifically note the electrical energy picture in the United States, generation of electricity is predicted to be the fastest grow- ing area of energy use.13 Examining past history, approximately 13 per cent of the fuel utilized in the United States in 1947 was for the production of electricity. By 1970, this figure had increased to 25 per cent. By the year 2000, it is predicted that between 40 and 50 per cent of the fuel consumed in the U.S. will be for the production of electricity./3 An important fact to consider is that as demand for electrical energy increases, there will be an associated demand in the resources necessary to produce this electricity. It is evident that oil and gas will become less important as supplies diminish and prices increase. Coal will take on a much greater responsibility. However, coal will not be able to do the job alone. At least through
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