Optimal timing of the US breeder

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<ul><li><p>Optimal timing of the US breeder </p><p>Richard G. Richeis and James L. Plummer </p><p>Optimal timing of the introduction of the FBR is very sensitive to factors such as the availability of l ow-cost u ran ium, fu ture energy demands and the possibility of the introduction of yet more advanced technology. To a lesser extent i t is also sensitive to the relative cap i ta l costs of fast breeder and thermal nuclear plants. The relationship between R &amp; D costs and the programme t im ing is a lso cruc ia l in deciding opt imisat ion . </p><p>Richard G. Richels is a member of the technical staff, Electric Power Research Institute, and James L. P lummer is Ch ie f Corporate Economist, Occidental Petro leum Corporat ion, USA. </p><p>This study was completed while the authors were affiliated, respectively, to Harvard University and the National Science Foundation. The views expressed in this paper do not necessarily reflect the positions of either of those institutions or the organisations to which the authors are currently affiliated. </p><p>The authors wish to thank Alan Manne for making the ETA model available to this study, and for his helpful comments on an earlier version of this paper. </p><p>'General Accounting Office, Costs and Schedule Estimates for the Nation's First Liquid Metal Fast Breeder Reactor Demonstration Power Plant, RED-75- 358, May, 1975. 2 Atomic Energy Commission, Liquid Metal Fast Breeder Reactor, Proposed Final Environmental Statement, WASH- 1535, US Government Printing Office, Washington, DC, December, 1974. </p><p>In the mid-1960s, the Atomic Energy Commission (AEC) selected the liquid metal fast breeder reactor (LMFBR) as its highest priority reactor development programme. In January 1975, the Energy Research and Development Administration (ERDA) came into being, and assumed responsibility for the AEC's former research and development functions, including those associated with the LMFBR programme. After reviewing the AEC's position, the Administrator of ERDA committed that agency to continuing the research, development and demonstration of the LMFBR concept. Despite large increases in federal spending on coal, geothermal, solar, and fusion R &amp; D, roughly one-third of the ERDA budget for FY 1976 went to the LMFBR. The $492 million allocated to the LMFBR represents the largest expenditure for any single civilian R &amp; D project. Moreover, according to a GAO report, more than $10 billion will be needed to carry the programme through to planned completion in 2020. j </p><p>Proponents point to the LMFBR's potential for extending the supply of low-cost uranium. Today, oil and gas furnish nearly 80% of our energy needs. If we are to free ourselves from dependence on insecure and expensive foreign sources of energy, it will be necessary to reduce our dependence on oil and gas by conservation and by shifting to coal and nuclear fuels. </p><p>The long-term advantages of nuclear fission may be severely constrained, however, unless improvements can be made in the efficiency of uranium use. With currently available nuclear reactors, we are able to take advantage of only 1-2% of the energy potential of uranium. This is because the light water reactor (LWR) only uses the relatively scarce uranium-235 isotope present in natural uranium. If LWRs were the only type of reactors available in the future, they could possibly use all our currently estimated low-cost uranium resources within the next 30-50 years. </p><p>Breeder reactors offer .the largest opportunity for uranium conservation. When breeder reactors convert the abundantly available uranium-238 to plutonium-239, more plutonium is created than is fissioned. In this way breeders would be able to utilise more than 60% of the thermal energy available in uranium. No other nuclear alternative can have such an impact on long-term uranium availability. </p><p>Among the various breeder concepts, the AEC chose the LMFBR for priority treatment because of 'its predicted performance, existing industrial support, established base of technological experience, and proven basic feasibility'. 2 The LMFBR is also being developed on this </p><p>106 ENERGY POLICY June 1977 </p></li><li><p>3 The model used in this study differs from ETA as described in A.S. Manne, 'ETA: A model for energy technology assessment,' Bell Journal of Economics and Management Science, Autumn, 1976, in that it provides the following additional options: LMFBR availability in the year 2005; ERDA's optimistic and pessimistic uranium supply curves; $50/kW and $150/kW capital cost differentials between the LWR and LMFBR; and an exogenous demand component. The model differs from ETA in that: the ADV becomes available in 2015; we assume a breeding gain of 8% per year (consistent with an advanced oxide fuel); and the marginal cost of coal remains constant at $1 per million BTU for the first 25 quads (1 quad - 1015BTU) consumed annually and then rises linearly to $1.5 at 50 quads, $2 at 75 quads, etc. Note that this assumption is intermediate between the case of 'rising costs' and 'constant costs' in the original ETA model. </p><p>Optimal timing of the US breeder </p><p>basis in the UK, France, West Germany, Japan and the USSR. Although a number of benefit--cost analyses have economically </p><p>justified a breeder research and development programme, the issue of optimal breeder timing has received surprisingly little attention. In its proposed-final environment statement for the LMFBR programme (WASH-1535), 2 the AEC did measure the impact of a delay in breeder availability. However, this was measured primarily in terms of a decline in gross breeder benefits. Although the shape of the gross benefits function is an important determinant of optimal timing, it is misleading to discuss breeder timing solely in those terms. Attention must also be given to the shape of the R &amp; D cost-time function. Only then can it be determi~ned how net benefits change with the breeder's availability date. </p><p>In this study, a programming model is used to calculate LMFBR gross benefits. Our results indicate that if optimal timing depended solely on the shape of the gross benefits function, early availability would always be at least as preferable as later availability. However, our R &amp; D cost analysis shows that with a declining discounted R &amp; D cost-time function, later availability is often preferalSle. </p><p>The model </p><p>A non-linear programming model is used to calculate LMFBR gross benefits. The model, called ETA (for energy technology assessment), was developed by Alan Manne and first used in his work on the interdependence between benefits from the fast breeder and from synthetic fuels. 3 </p><p>ETA differs from the WASH-1535 model (the model used by the AEC for its breeder benefits calculations) in two fundamental ways. First, the AEC model focused exclusively on the supply and demand for electric energy. The electric and non-electric energy sectors were completely decoupled. Such a formulation tends to underestimate breeder benefits. Coal, for example, is used in coal-fired fossil plants to produce electricity, but could also be used for coal-based synthetic liquids and gases. </p><p>If the breeder technology decreases our dependence on coal for electric power, then the marginal costs of coal production could be affected - and hence the cost of coal-based synthetics. A model that looks only at electric energy will fail to capture these benefits. ETA, by contrast, covers the entire energy sector. </p><p>Similarly, by concentrating on the electric energy sector, the WASH-1535 model is unable to capture the effects of breeder availability on inter-fuel substitution. For example, rising oil prices may make hydrogen via electrolysis an attractive source of non- electric energy. The competitiveness of this option, however, will depend upon the price of electricity, but this in turn depends on breeder availability. A model that decouples electric and non-electric energy will ignore this interdependence when calculating breeder benefits. </p><p>A second distinguishing feature of ETA is the effect of own- and cross-price elasticities. In the WASH-1535 model, as in many other energy models, the demand for electricity is specified exogenously, and the optimisation is performed so as to meet these demands at minimum cost. ETA, on the other hand, incorporates both own- and cross-priced elasticities for electric and non-electric energy, and it </p><p>ENERGY POLICY June 1977 107 </p></li><li><p>OptOnal thning of the US breeder </p><p>4 1Q unit ((luad) 1 0 TM British Thermal U~lits ~,~ 10 TM joules. </p><p>calculates a market equilibrium for the whole energy sector. In this way, rising prices for one energy form can be offset by conservation of that fuel - and also through substitution of other fuels whose prices have risen less rapidly. </p><p>Principal assumptions </p><p>In a deterministic analysis, it is necessary to act as though all parameters are known with certainty. The following assumptions define our 'reference case'. Later we will determine how the results vary with different sets of values for the key parameters. </p><p>Planning horizon ETA employs a 75-year timespan, and covers 15 sub-intervals, each 5 years long. A planning horizon of this length is required to analyse the exhaustion of limited natural resources (oil, natural gas, and low-cost uranium) and the introduction of new technologies (eg, the breeder, solar, and/or fusion). Unless otherwise indicated, the analysis employs a discount rate of 10% - as is recommended by the Office of Management and Budget for federal benefit-cost calculations. The discount rate and all costs are stated in terms of 'real' 1975 dollars, relative to the GNP deflater for that year. </p><p>Demand assumptions Demand projections are based upon the following assumptions: </p><p> GNP will grow at 3.5% per year from 1970 to 2000 and eventually slow down to 2.5% towards the end of the 75-year planning horizon; </p><p> Total energy demands would have grown at the same rate as the GNP if prices had remained at their 1970 levels; </p><p> Price elasticities for energy are as follows: </p><p>Own price Cross price elasticity elasticity </p><p>Electric energy -0.75 0.50 Non-electric energy -0 .50 0.25 Total energy -0.25 </p><p>Our initial set of assumptions leads to electrical energy demands of 6 trillion kWh in the year 2000. </p><p>Resource availabilities and costs Oil and gas. It is assumed that a total of 2Q units 4 of oil and gas are available domestically at 1975 import prices - $12/bbl (or $2/million BTU). Approximately IQ falls into the highly speculative 'undiscovered recoverable resources' category (eg, outer continental shelf). As for imports, it is supposed that for political reasons - as well as because of limited foreign supplies - US dependence on oil and gas imports will be limited to its current level of 7 million bbl/d. </p><p>Coal. It is assumed that diseconomies of scale appear when the annual consumption rate exceeds 25 quads (twice the 1970 level). Heavy dependence on coal, for example, will probably result in a further tightening of primary air quality standards, as well as </p><p>108 ENERGY POLICY June 1977 </p></li><li><p>Figure 1. U3 08 cost versus supply est imates. </p><p>Source. ERDA, Reference 9, p 111, F-51. </p><p>Note: The U 3 08 costs used in this study refer to production costs and are substantially less than current market prices. </p><p>5 In 1970, hydroelectric and geothermal accounted for 16% of the electricity generated. It is assumed that these sources will expand at the annual rate of 2% in the future. </p><p>200 </p><p>Optimal timing of the US breeder </p><p>180 </p><p>16C </p><p>14C </p><p>120 el) </p><p>0 </p><p>,.- I00 0 </p><p>_o </p><p>0 C) </p><p>6O </p><p>4O </p><p>2O </p><p>I I 1 1 1 0 2 4 6 8 I0 </p><p>Qu0ntify of U308 (million tons) </p><p>, Pessimistic supply </p><p>Opt imis t i c supply </p><p>I I 12 14 </p><p>increased environmental costs from surface mining as we are forced to become less selective in our choice of sites. Moreover, sharp increases in demand will most likely result in spiralling labour costs, particularly in the case of labour-intensive underground mines. Therefore, it is assumed that marginal coal costs remain constant at the 1975 price level of approximately $1 per million BTU for the first 25 quads and then rise linearly to $1.5 at 50 quads, $2 at 75 quads, etc. </p><p>Uranium. The reference case adopts ERDA's most recent 'pessimistic' uranium supply curve (see Figure 1). Here, only 3 million short tons of U3 08 are available at $100/lb. Later we shall explore the effect of switching to ERDA's 'optimistic' supply curve. </p><p>Electric energy supply options Except for limited amounts from hydroelectric, geothermal and the remaining initial oil- and gas-fired units, future electricity demands will be satisfied by the following four sources: coal-fired fossil plants; LWRs; LMFBRs; and ADVs (an acronym for an advanced technology, eg, fusion, solar, or perhaps the breeder)P The cost assumptions for each technology are summarised in Figure 2. The </p><p>ENERGY POL ICY June 1977 109 </p></li><li><p>Optimal timing of the US breeder </p><p>Figure 2. Electric energy costs. </p><p>6 The model also allows for fixed rates of shale oil production: 1 million bbl/d in 1990, 2 million bbl/d in 1995, 3 million bbl/d in 2000, etc. We assume that shale oil development will be severely limited by the availability of water and the problems of disposal of spent shale waste. 7 The model has 300 rows, 700 columns and 2500 non-zero matrix elements. It is solved by a reduced gradient algorithm written by B.A. Murtagh and M.A. Saunders of the Systems Optimization Laboratory at Stanford University. </p><p>20 </p><p>r - </p><p>o~ </p><p>15- </p><p>I0 - </p><p>5- </p><p>/ / / / / / / / / / / , </p><p>Fossil </p><p>( Coal at </p><p>$ I /mi l l i on BTU) </p><p>/Uran ium at </p><p>r" d" </p><p>Uranium , / </p><p>/ / / / </p><p>/ / / / / / / / </p><p>, t / / i / / / / / / / / </p><p>1/ / / / / / / </p><p>2;;; LWR FBR </p><p>$ lO011b </p><p>at $1511b </p><p>/ / ' J r </p><p>//.// 1/ / I / / / I I I I L </p><p>x / i v </p><p>/ / / / / / / / 1 / / ) / / / / </p><p>Y// / / / / / / / / </p><p>ADV </p><p>following constraints are placed on the rates of introduction of new capacity. </p><p>Coal-fired fossil plants. It is supposed that these constitute at least 40% of all new electric energy output added up to the year 2000. The reason for this restrictive ordering policy is that coal-fired plants are likely to be the least expensive means of satisfying demands outside the baseload portion of the load duration curve. Eventually, it should be possible to develop low-cost storage technologies, or to use LWRs for cycling duty. Hence, this constraint is gradually relaxed between the years 2000 and 2020. </p><p>LMFBR. For the reference case, the first commercial breeder reactor (CBR-I) becomes available in 1995. The LMFBR is then limited to 20% of new electric energy capacity added in the year 2000, 40% in 2005, 80% in 2010, and unlimited thereafter. These ceilings on the rate of commercialisation are intended to reflect the reluctance of utility executives to invest massively in new technologies before they are thoroughly tested. </p><p>ADV. For the reference case, the ADV becomes available in 2015 and is limited to 20% of new capacity in that year; 40% in 2020, etc. Thus, it follows the same timetable as the LMFBR except for a...</p></li></ul>