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PER-10

1

BASIC INFORMATION RELATING TO -ENRICHMENT CALCULATIONS AND REQUIREMENTS FOR REACTORS

by

K.T. Brown

m 3

ATOMIC ENERGY BOARD Pelindaba PRETORIA Republic of South Africa February 1977

:::: : =:::""""""::::::;::: i:::""""""" :::::::::i:::::::::::::::H:::""»"""::::::::::::::::: BASIC INFORMATION RELATING TO URANIUM-ENRICHMENT CALCULATIONS AND FUEL REQUIREMENTS FOR NUCLEAR POWER REACTORS

hy

K.T. Brown

POSTAL ADDRESS: Atomic Energy Board Private Bag X256 PRETORIA 0001

PELINDABA Fi-ln liai v 1977 ISBN U 86Ü6U 654 9 Pago Page SAMEVATTING 2 ABSTRACT 2 3. REACTOR FUEL REQUIREMENTS 5 1. INTRODUCTION 3 3.1 Reactor Types 5 2. URANIUM ENRICHMENT 3 3.1.1 Pressurised-water roactor 5 2.1 Definitions 3 3.1.2 Boiling-water reactor 5 2.1.1 Natural uranium 3 3.1.3 CANDU-PHW 6 2.1.2 Fissile 3 3.1.4 High-temperature gas-cooled reactor 6 2.1.3 Fertile 3 2.1.5 Liquid-metal-cooled fast breeder reactor ... .6 2.1.4 Enrichment 3 3.2 Cycles 6 2.1.5 Product 3 3.3 Typical Fuel Requirements 6 2.1.6 Feed 3 3.3.1 Pressurised-wator reactor 7 2.1.7 Tails, or waste 3 3.3.2 Boiling-water reactor 8 2.1.8 Cascade 3 3.3.3 CANDU-PHW 9 2.1.9 Separative work 4 3.3.4 High-temperature gas-cooled reactor 9 2.1.10 Separative-work unit 4 3.3.5 Liquid-metal-cooled fast breeder reactor ... 10 2.2 Enrichment Parameters 4 3.3.6 Comparative data 10 2.3 Optimum Tails Assay 5 4. REFERENCES 10 2.4 Non-Natural Feed 5 5. APPENDIX 11

LIST OF TABLES Page Page TABLE 1 Natural feed (F) required to produce unit mass of product as a function of product TABLE 11 Model BWR : net uranium and enrichment and tails assay 18 enrichment requirements 27 TABLE 2 Separative work required lu fjiitjduce unit TABLE 12 Model CANDU-PHW : net uranium mass of product as a function ö product enrichment and tails Ossisy for requirements 28 natural-uranium feed 19 TABLE 13 Model HTGR : net uranium and enrichment requirements 28 TABLE 3 Optimum tails assay for natural-uranium feed 20 TABLE 14 Power-reactor characteristics for representative 1 000 MW (electrical) TABLE 4 1,0% feed (F) required to produce unit units 29 mass of product as a function of product enrichment and tails assay 21 LIST OF FIGURES FIGURE 1 Separative work and natural-uranium TABLE 5 Separative work required to produce unit feed required to produce unit mass of mass of product as a function of product product at various enrichments 13 enrichment and tails assay for feed at 1,0% 235U 22 FIGURE 2 Optimum tails assay as a function of the ratio of natural-uranium-feed to TABLE 6 Optimum tails assay for feed of 1,0% separative-work costs 14 235U 23 FIGURES Separative work and 1,0% assay feed TABLE 7 0,4 % feed (F) required to produce unit required to produce unit mass of product mass of product as a function of product at various enrichments 15 enrichment and tails assay 24 FIGURE 4 Separative work and 0,4% assay feed TABLE 8 Separative work required to produce unit required to produce unit mass of product of mass of product as a function of at various enrichments 16 product enrichment and tails assay for feed at 0,4 % 235U 25 FIGURE 5 Optimum tails assay as a function of the ratio of uranium-feed to separative-work TABLE 9 Optimum tails assay for feed of 0,4 % costs for feeds of 1,0%, 0,711% and 235U 26 0,4 % mass assay 17

TABLE 10 Model PWR : net uranium and FIGURE 6 Nuclear fuel flows for the most common enrichment requirements 27 reactor types 17

SAMEVATTING ABSTRACT Kwantitatiewe inligting word verstrek om nie-spesialiste op Quantitative information is provided to enable die kerngebied in staat te stel om toevoer- en non-specialists in the nuclear field to calculate feed and skeidingswerkvereistps wat by die verryking van uraan separative-work requirements involved in the enrichment of betrokke is, te bepaal. Verteenwoordigende uraan- en uranium. Representative uranium and separative-work skeidingswerkverbruikstempo's vir verskeie algemene consumption rates for various common nuclear power kernkragreaktore, word ook aangedui. reactors are also presented. PER-10-3

1. INTRODUCTION fissile isotope in nature is 235(j( although others (such as 239pu and 233ij) can be manufactured artificially from This report is intended to provide fertile material. (i) quantitative information concerning the enrichment of uranium; and 2.1.3 Fertile (ii), representative fuel requirements for three current Fertile material can be transformed into by ^ types of commercial nuclear power reactors, as well the absorption of neutrons and (in most cases) subsequent i as for two advanced types of potential interest. transformation by . The most important 238u Thfij report is aimed at persons and organisations not fertile isotopes in nature are (which yields 239pu) directly involved in nuclear energy programmes and and 232-rh (which yields 233ij). assumes that the reader has little background in such fields. 2.1.4 Enrichment t As ^ar as uranium enrichment is concerned, the information In the context of relative isotopic proportions, enrichment is limited to the relationships amongst quantities and assays means to increase the relative proportion — or assay — of a of feed, waste and product uranium in an ideal enrichment particular isotope above that of the natural or other process, together with associated quantities of separative available feed material. Enrichment of uranium in the 235(j work. Economic factors are brought into account only isotope can be accomplished by various processes, such as superficially, in order to calculate the optimum waste (or , centrifugation, aerodynamics and laser tails') assays under particular price conditions. Neither separation. The opposite of 'enrichment' is 'depletion'. In significant technical descriptions of enrichment processes the absence of a reference point, 'enriched' uranium has a nor other economic data concerning the different processes mass assay higher than 0,711 %. are included. 2.1.5 Product The section concerning reactor fuel requirements mentions The product of a uranium enrichment plant is enriched in relevant aspects of nuclear fuel cycles, but the presentation the isotope 235u. The product assay is usually relatively is (nade as simple as possible. The fuel quantities facilitate low (up to about 4 % by mass for most commercial approximate calculations of uranium and enrichment reactors), but can also be well in excess of 90 % from demands associated with nuclear power programmes, but suitable plants. no such application is attempted in the report.

2.1.6 Feed The feed to a uranium enrichment plant is usually natural 2. URANIUM ENRICHMENT uranium, but or uranium with more than 0,711 % by mass of 235u may also be used as feed. The 2.1 Definitions uranium contained in spent fuel elements from natural-uranium reactors is depleted to below 0,711% 2.1.1 Natural uranium 235u, while that from enriched-uranium reactors usually Uranium, as it occurs in nature, consists of three isotopes. (but not necessarily) has higher assays than the natural These isotopes, together with other uranium isotopes that assay. can be manufactured by artificial means, have identical chemical properties. The three isotopes in natural uranium 2.1.7 Tails or waste have the following proportions by mass: Because the product of an enrichment plant is enriched in

235u, the tails stream must contain a lower 235y assay 234u 0,000 06 (0,006 %) than the feed. There are limits to the degree to which the 235u 0,007 11 (0,711 %) tails assay can be reduced, as will be seen below. The term 238u 0,992 83 (99,283 %) 'tails' (from an enrichment plant) is not to be confused with 'tailings' (from an extraction plant). The proportions by numbers of atoms are slightly different: 2.1.8 Cascade 234(j 0,000 06 (0,006 %) An enrichment plant generally consists of many stages, each 235(j 0,007 20 (0,720 %) of which accomplishes a small amount of separation of the 238u 0,992 74 (99,274 %) isotopes. The stages arc built up into a cascade, with interconnecting piping to channel the enriched and The 234(j appears in such small quantities that its presence depleted streams from each stage to other appropriate can be ignored for practical purposes. upstream and downstream stages. An 'ideal' cascade is one in which there are no departures (as a result of mixing 2.1.2 Fissile losses, for example) from ideal theory. Although no real A fissile isotope is one which can be fissioned by the plant meets the ideal, it is common (American) practice to addition of a zero-energy neutron, and fissile isotopes are base all calculations on ideal theory except in the case of essential to self-sustaining fission chain reactions. The only very high product enrichment (> 94 %). PER-10-4 2.1.9 Separative work The separative work done by a stage or by a cascade is the increase in value of the effluent materials (enriched and F = 1 (0,03 - 0,00251/(0,00711 - 0,0025) depleted) with respect to the value of the feed material. = 5,965 kg. The term 'value' used here is a mathematical function which reflects the value of a unit mass of uranium in termValues s of F for various product and tails assays with of its assay, and must not be confused with price or cost.natural-uraniu m feed are given in Table 1 and are also The derivation and significance of 'value' and 'separative shown in Figure 1. It is worth noting that, for a particular work' are contained in the Appendix. product, the feed required increases as the tails assay Separative work is expressed in mass units, not work or increases. energy units, which may lead to confusion unless clearly kept in mind. The annual capacity of an enrichment plant,Th e following equation for separative work is derived in the expressed in (mass) units of separative work, is not the Appendix, and is reproduced here only for completeness: same quantity as the annual mass throughput of feed, product or tails material, except under very exceptional w SW= P(1 - 2xp) In 1—W(1 - 2xw) Inj * operating circumstances. xp 1 - Xf - F(1 - 2xf) In (4) 2.1.10 Separative work unit xf The term 'separative work unit', abbreviated 'SWU', is The symbols have the same meanings as before. The commonly used in the literature, and is identical to the calculation is more involved than that for feed kilogram unit of separative work. The ton unit of separativerequirements . work is acceptable, and is also commonly used because it reduces the sizes of numbers to reasonable proportions in EXAMPLE1B many cases. The ton unit of separative work must not be confused with the SWU: it is equal to 1 000 SWU. Using the same parameters as in Example 1A above, in which 5,965 kg of natural uranium were required to extract 2.2 Enrichment Parameters 1 kg of product at 3,0 % enrichment using a tails assay of 0,25%, equation (4) yields a separative-work requirement The mass balance over an enrichment cascade dictates that of 3,811 kg. all of the material that is fed into the plant appears in the tails and product, provided losses can be ignored. This leadValues s of separative-work requirements for various product to a basic equation: and tails assays with natural-uranium feed are given in Table P = F-W (1) 2, and are also shown in Figure 1. Note that, for a particular product, the separative work required decreases where P is the total mass of the product; as the tails assay increases. This is in the opposite sense to the feed requirement, and leads to the conclusion that there F is the total mass of the feed; and is a certain amount of leeway for trade-off between W is the total mass of the tails. natural-uranium supply and enrichment capacity. Under The same argument can be applied to the 235(j mass given cost conditions there exists an optimum tails assay, contents of the feed, tails and product, which leads to thwhice h is further discussed in paragraph 2.3 below. equation: EXAMPLE 2 Pxp = Fxf - Wxw (2) If an enrichment plant has an annual separative-work where xp is the mass assay of 235IJ jn the product; capacity of 10 000 t, then, using the figures of Example 1, Xf 235u is the mass assay of in the feed; and the output of 3 % enriched product will be xw is the mass assay of 235u in the tails. 10 000/3,811 =2 624 t/a. Equations (1) and (2) can be combined to yield The natural-uranium feed will be 5,965x 2 624 = 15 652 t/a. F = P(xp - xw)/(xf - xw) (3) The tails, with'an assay of 0,25 %, will amount to Equation (3) is useful for calculating the amount of feed (15 651 - 2 6241 = 13 027 t/a. required in order to obtain a given amount of product when the product, tails and feed assays are all set. The use of Figure 1 should be adequate for approximate calculations of feed and separative-work requirements. EXAMPLE1A More accurate results can be obtained by using Tables 1 and 2, using linear interpolation between columns if necessary. If a product of 1 kg of uranium enriched to 3,0 % is The greatest accuracy, of course, is obtained using required, with natural-uranium feed and 0,25 % tails assay, equations (3) and (4). then PER-10-5 2.3 Optimum Tails Assay 3. REACTOR FUEL REQUIREMENTS

The total cost of consists of two basic 3.1 Reactor Types components: uranium-feed costs and separative-work costs. There is an optimum tails assay which will minimise the The representative fuel requirements presented in this total cost of enriched product for a particular feed assay section are confined to three of the most common reactor and a particular ratio of component costs, If the feed ir. types of current commercial viability, in addition to two natural uranium, then Table 3 or Figure 2 can be used to advanced reactors which warrant consideration in the find the optimum tails assay, which is valid for any product longer term. The current commercial reactors included are assay, as a function of the ratio of component costs. the pressurised-water reactor (PWR) and boiling-water reactor (BWR), which are of US origin and are collectively EXAMPLE 3 called light-water reactors (LWR's), as well as the Canadian CANDU-PHW reactor. The advanced reactors are the U3O8 at $4G7lb is equivalent to $104/kg of uranium. If high-temperature gas-cooled reactor (HTGR) and the transport and conversion costs to UF6 are added, and these liquid-metal-cooled fast breeder reactor (LMFBR). The amount to $4/kg of uranium (including an allowance for choice of reactor types does not necessarily represent a losses), then the cost of UF5 delivered to the enrichment judgement on the relative merits of those types which have plant is $108/kg of uranium. If enrichment costs amount to been excluded. $90/kg of separative work, then the ratio of uranium to separative-work costs (i.e. the ratio of component costs) is 1,2. Table 3 indicates that the optimum tails assay at a cost 3.1.1 Pressurised-water reactor (PWR) ratio of 1,2 is 0,208 %. This is an indirect-cycle reactor, in which the cylindrical core is cooled and moderated by ordinary (light) water in a To continue the example, assume that a product of 3,25 % primary coolant circuit. The core is contained in a large assay is required, that the enrichment plant may be vertical steel pressure vessel. Heat is transferred by means of operated only to the nearest 0,01 % as regards tails assay, steam generators to a secondary circuit which includes a and that a tails assay of 0,21 % is chosen. From Table 1, steam turbine and condenser. Fuel is in the form of UO2 each kilogram of product requires 6,068 kg of uranium pellets clad in zirconium-alloy tubes which are assembled to feed, and, from Table 2, 4,735 kg of separative work. The form fuel elements. Fuel enrichments for the initial core are cost of feed is therefore $655, and the cost of enrichment typically divided into three zones in the core: less than 2 % $426, giving a total cost per kilogram of 3,25 % product of in the inner zone, between 2 and 3 % in the intermediate $1 081. zone, and slightly more than 3% in the outer zone. Replacement-fuel enrichment is generally between 3% and It may happen, because of a shortage of enrichment 3,5 %, and is contained in reload fuel elements which are capacity, for instance, that the tails assay is fixed: say at placed in the outer zone of the core. The remaining fuel is 0,25 %. In this event, one requires 6,508 kg of uranium in shuffled radially inwards, maintaining an enrichment the feed (7,3% more), costing $703, and 4,308 kg of gradient towards lower values in the centre, the lowest separative work (9,0 % less), costing $388, giving a total assay elements being unloaded. Reloading is generally cost per kilogram of 3,25% product of $1091. The carried out annually during a shutdown period of several increase above $1 081 is less than 1 %, which illustrates the weeks, and the number of reload fuel elements (ideally relative insensitivity of total cost close to the optimum tails about one third of the core) can be adjusted according to assay. The sensitivity increases progressively as one moves the plant capacity factor prior to the shutdown. The reload further from the optimum: with a tails assay of 0,35 %, the fuel enrichment can also be varied within a limited range total cost becomes $1 185 in the above example, some over a longer period to allow for capacity-factor variations. 9,6 % above the minimum. The unloaded fuel typically has a 235(j mass assay of 0,8 % to 0,9 %, and also contains approximately 0,7 % of fissile 2.4 Non-Natural Feed plutonium. Uranium recovered from irradiated fuel, as mentioned above, may be used as feed to enrichment plants. These According to IAEA world statistics, PWR's made up almost feeds may be above or below the natural assay of 0,711 %, half of the capacity of all operating reactors in mid-1976, depending upon their origins. Equations (1), (2), (3) and the largest single unit having a net electrical output of (4) are also valid in such cases, with xf as the feed assay. 1 178 MW. The world share taken up by PWR's is likely to For convenience, indicative feed and separative-work values increase. for various product and tails assays are shown in Tables 4 and 5 for 1,0 % feed, and in Tables 7 and 8 for 0,4 % feed. 3.1.2 Boiling-water reactor (BWR) These values are also represented in Figures 3 and 4. The optimum tails assays for feeds of 1,0% and 0,4% are This is a direct-cycle reactor, in which there is net steam shown in Tables 6 and 9 respectively, and in Figure 5. generation in the cylindrical core from the light-water primary coolant. The steam is passed directly from the The data sets for feeds of 0,4 %, 0,711 % and 1,0 % may be vertical steel pressure vessel housing the core to a turbine used to find intermediate values by interpolation. When in and condenser. Fuel is also in the form of UO2 pellets clad doubt, equations (3) and (4) will provide better values. in zirconium-alloy tubes. The core fuel-loading PER-10-6 arrangements are similar to the PWR, except that reload 3.1.5 Liquid-metal-cooled fast breeder reactor (LMFBR) fuel is closer to a quarter than a third of the core inventory. This type of breeder reactor is receiving more attention Graded enrichments are used within each fuel element, and worldwide than any other. Being 'fast', it has no moderator. initial core as well as reload elements may contain assays Cooling is accomplished by means of liquid sodium which from less than 2 % to more than 3% in varying amounts. passes heat to an intermediate sodium circuit, which in turn The weighted average assay is generally less than the typical passes heat to a steam-generating water circuit with turbine PWR. Reloading is also carried out annually during and condenser. The core contains Pu02, which is the fissile shutdown periods of several weeks each. The unloaded fuel 'driver' and which is surrounded by axial and radial has 235(j mass assays and fissile plutonium contents similar blankets of depleted U02- Stainless steel cladding is used. to, but generally slightly lower than, the typical PWR. As a More fissile plutonium is formed from fertile 238IJ tnan js rule, a BWR requires more UO2 in the core per unit power destroyed, so that there is a net gain of fissile fuel. Three than a PWR, whereas the average enrichment and the prototypes are in operation, in France, Britain and the energy produced per unit mass are lower. USSR, but are relatively small (250, 230 and 350 MW BWR's represented more than a quarter of world nuclear respectively) and are designed to demonstrate and develop capacity operating in mid-1976, the largest single unit technology rather than to breed. having a net electrical output of 1 065 MW. The share is likely to be maintained. 3.2 Nuclear Fuel Cycles

3.1.3 CANDU-PHW (Canadian deuterium uranium The description of the LMFBR above implies that fuel must pressurised reactor) be recycled in order to breed more fissile material than is This reactor is fuelled by natural uranium, cooled by heavy consumed: in other words, spent fuel discharged from the water in a primary coolant circuit and moderated by heavy reactors is reprocessed and the re-usable portions separated water. Fuel elements are contained in horizontal fuel out to incorporate into fresh fuel elements. Spent fuel from channels which penetrate the moderator vessel, which is LWR's also contains valuable components consisting of therefore termed a calandria. The channels are accessible slightly enriched uranium as well as plutonium. from either «nd, thus allowing fuel reloading at power in Natural-uranium-reactor spent fuel contains plutonium of two directions. Once again, fuel is in the form of UO2 value, but the residual uranium may or may not be worth pellets clad in zirconium-alloy tubes. As in the PWR, heat is re-enriching: that in CANDU fuel has too low an assay for transferred to a secondary light-water circuit in steam this purpose. Such depleted uranium, together with generators. The natural-uranium fuel is depleted to about enrichment plant tails, can be used as fertile material in 0,22 % mass assay before unloading, the discharge fuel also breeder reactors. In the case of the HTGR, the spent fuel containing approximately 0,27 % of fissile plutonium. contains fissile 233IJ 0f va|Ue, as well as 235IJ which can be recycled once. Heavy-water reactors make up about 4 % of operating, constructing and planned nuclear capacity, with the largest Figure 6 provides an overail picture of fuel flows for a operating unit having a net electrical output of 750 MW. system of the most common reactor types, on the 3.1.4 High-temperature gas-cooled reactor (HTGR) assumption that all of the processes are available. This is not the case at present, as there is a shortage of reprocessing This type of reactor holds promise for the future, primarily facilities. In addition, regulatory barriers to plutonium because of its high temperatures with the allied potential recycling have to be overcome. The HTGR and LMFBR in for direct-cycle electricity production using dry-air cooling, Figure 6 are representative of the position at some future and also for high-grade process heat applications. The US date when they have achieved significant market version of the HTGR is used in this report as typical of its penetration. In the absence of fuel recycling, 'once-through' genus working on a steam cycle. arrangements prevail, in which the spent fuel is considered Fuel is in the form of highly enriched (93,15%) uranium to be of no value. This is largely the situation commercially carbide and natural thorium oxide particles coated with at present, and spent fuel is, on the whole, stored while pyrolytic carbon and pressed into graphite moderator awaiting final decisions regarding the reprocessing and matrices to form elements. Cooling is by means of helium, recycling of plutonium. which transfers heat to steam generators. The initial core of a representative 1 000 MW unit contains 1 600 kg of 3.3 Typical Fuel Requirements 93,15% enriched uranium, together with about 321 of thorium. The highly enriched uranium is depleted to about Reactor fuel requirements as given by various references 30% in one residence period, and can be made into new differ, and the complication of fuel calculations in reactors fuel elements for a second period and then discarded. The makes checking virtually impossible. The PWR, BWR and 232Th forms fissile 233IJ which can be recycled into new HTGR examples given here are basically from fuel elements. Make-up quantities of highly enriched 235(j WASH-1348P], the CANDU-PHW from AECL-5516[2], are necessary at each (annual) refuelling, the quantity and the LMFBR from OECD/NEA-IAEA datât3!. depending upon whether recycling is possible or not. The largest operating reactor of this type is of 330 MW output, The 'model' requirements are all given for a standard size of but there are no commitments for larger units or significant 1 000 MW net electrical output - even if no reactors of HTGR expansion programmes. such a size yet exist — and the thermal power in the core PER-10-7 varies from type to type according to efficiency. In all cases First unload: 25 825 kg at 0,73 % (26,9 t U, it is assumed that the reactors operate at 40 % capacity 0,4 tSW) 124 kg fissile Pu factor during a test period of /8 of a year prior to the commercial operation date, at 65% for 17/8 years after Second unload: 25 475 kg at 0,70 % (24,9 t U, that, and subsequently at 75 %. It must be borne in mind -0,2 t SW) 157 kg fissile Pu that uranium and enrichment requirements must be met some time before fuel is loaded into the reactor, and that Third unload: 25 240 kg at 0,89 % (35,0 t U, materials in spent fuel can be obtained only some while 4,6 t SW) 175 kg fissile Pu after discharge. Fourth unload: 23 805 kg at 0,90 % (33,5 t U, In all cases the figures allow for 1 % loss prior to insertion 4,6 tSW) 165,9 kg fissile Pu into the reactors and, where applicable, 1 % loss during reprocessing. Additional losses have to be added on. If only uranium is recycled, then it is assumed here that the spent uranium from the first unload can be used to reduce 3.3.1 Pressurised-water reactor the natural-uranium requirements for the fourth reload, The 'model' PWR for post-1980 startup has a core thermal from the second unload for the fifth reload, and so on. In power of 3 019 MW to produce a net electrical output of this way the twenty-sixth unload contributes to the 1 000 MW. The initial core requires twenty-ninth (and last) reload. For simplicity, credits for the twenty-seventh, twenty-eighth and twenty-ninth 26 985 kg at 1,7 %; unloads, and for the final core discharge at the end of the 26 985 kg at 2,4 %; and life of the reactor are ignored. The total lifetime requirements for natural uranium and separative work 24 940 kg at 3,1 %. amount to 4 270 t and 3 232 t respectively, as shown in With 0,25 % enrichment-plant tails assay, the initial core Table 10. Note that the uranium savings over the therefore requires 365 t of natural uranium feed and 209 t no-recycling case are significant, but the separative-work of separative work. savings are small.

The first refuelling is assumed to take place one year after The calculation of savings as a result of plutonium recycling commercial operation, the second 2V4 years after is a more complicated exercise. Several plutonium-recycling commercial operation, and subsequent reloads on an annual schemes may be adopted, and reactor physics parameters basis. Equilibrium is reached at the fourth reload, the introduce further difficulties. The figures in Table 10 individual quantities being as follows, with corresponding assume full recycling, according to the scheme adopted in natural uranium and separative work requirements at WASH-1348. In this, the plutonium in the first unload is 0,25 % tails assay in parentheses: converted to oxide and blended with natural uranium oxide to form a mixed oxide. The fissile plutonium is taken to be First reload: 26 985 kg at 3,3 % equivalent to 0,8 times its mass of235 U, so that 3,947 t of (178,5 t U, 119tSW) mixed-oxide fuel is contained in the fourth reload, thus reducing the natural uranium and separative-work Second reload: 26 985 kg at 3,2 % requirements. The average residence time of fuel elements (172,7 t U, 114tSW) in the PWR model is 3,10 a, but it is assumed here that all of the mixed-oxide fuel in the fourth reload is discharged at Third reload: 26 985 kg at 3,2 % the seventh unload. It is assumed that the mixed-oxide fuel (172,7 t U, 114tSW) portion of the seventh unload consists of uranium of 0,288% mass assay and fissile plutonium burned down to Fourth reload: 25 475 kg at 3,2 % 58% of the amount originally loaded at the fourth reload. (163,01 U, 107 tSW) The remainder of the seventh unload is assumed to have similar characteristics to normal unloaded fuel. All of the Assuming no recycling, a nominal lifetime of thirty and a discharged fuel materials from the seventh unload are used quarter years after the commercial operation date and no in the tenth reload, the extra plutonium increasing the capacity-factor reduction in later years, the total uranium mixed-oxide mass to 6,755 t. This process is repeated to the and enrichment requirements can be expected to amount to end of the reactor life, again ignoring any credits for the 5 127 t U and 3 342 t SW respectively. last three unloads and the final core discharge. It is apparent, from Table 10 that plutonium recycling reduces The natural-uranium requirements will, of course, be both natural-uranium and separative-work requirements modified by a different tails assay and by different capacity significantly. factors through the years. Recycling may also make a significant difference. For example, the following quantities It is worth noting at this point that the model parameters of material become available from unloaded fuel after above coincide with those published in the 1975 reprocessing. The natural-uranium equivalents of the OECD/NEA-IAEA joint report on "Uranium Resources, uranium are shown in brackets. Production and Demand"!3], except insofar as the PER-10-8 treatment of plutonium recycling is concerned. The OECD First reload: 17 800 kg at 3,15 % report simply assumes fissile plutonium to be equivalent to 11 485 kg at 2,44 % 140 times its mass of natural uranium, and 140 times its 4 595 kg at 2,22 % mass of separative work, in the case of an enrichment-plant 2 300 kg at 1,80 % tails assay of 0,25 %. This may be a valid treatment when a (193,9 t U, 118,7tSW) large number of reactors are involved, but does not apply to the case of self-generated plutonium being recycled in a Second reload: 17 190 kg at 3,15 % single reactor in isolation. 11 090 kg at 2,44 % 4 440 kg at 2,22 % Another approach commonly used in the literature dealing 2,215 kg at 1,80 % superficially with plutonium recycling is to consider the (187,3 t U, 114,6tSW) amount of fissile plutonium discharged from an equilibrium unload (165,9 kg in our case) and to calculate its savings, Third reload: 13 810 kg at 3,15 % without recognising the effect plutonium recycling has on 8 915 kg at 2,44 % later-discharged fuel quantities. This tends to underestimate 3 565 kg at 2,22 % savings in comparison with full recycling, but overestimates 1 785 kg at 1,80 % savings in comparison with the situation in which (150.5 t U, 92,1 tSW) plutonium is recycled once and then discarded (to be used in fast reactors at a later stage). Fourth reload : 15 655 kg at 3,15 % 10 100 kg at 2,44 % It was established above that the equilibrium reload 4 040 kg at 2,22 % without plutonium recycling consists of 25,475 t of 3,2 % 2 020 kg at 1,80 % enriched uranium, and the equilibrium discharge consists of (170,5 t U, 104,4 t SW) 23,805 t of uranium at 0,9 % assay, together with 165,9 kg of fissile plutonium. If equilibrium plutonium recycling is Fifth reload: 14 545 kg at 3,15 % reached in which only first-generation plutonium is 9 385 kg at 2,44 % recycled, then the equilibrium reload consists of 21,110 t 3 750 kg at 2,22 % of 3,2 % enriched uranium, and mixed oxide containing 1 880 kg at 1,80 % 4,169 t of natural uranium and 196 kg of plutonium (of (158,4 t U, 97,0 tSW) which 137 kg is fissile). The equilibrium discharge contains 19,726 t of 0,9 % uranium together with 137 kg of fissile Assuming no recycling, a nominal lifetime of thirty and a plutonium, and, from the original mixed-oxide portion, half years after the commercial operation date and no 79,5 kg of second-generation fissile plutonium which is capacity factor reduction in later years, the total uranium stored along with the associated depleted natural uranium and enrichment requirements can be expected to amount to for possible later use in fast reactors. The net annual 5 096 t U and 3 076 t SW respectively. natural-uranium requirement is 111,5t, and the separative-work requirement 85,0 t. These represent savings The following quantities of materials become available from over the equilibrium uranium-recycling case shown in Table unloaded fuel after reprocessing. The natural-uranium 10, but the savings are not as great as in the case of full equivalents of the uranium are shown in brackets. plutonium recycling.

First unload: 34 725 kg at 1,05% (60,21 U, 3.3.2 Boiling-water reactor 13,3 t SW) 155 kg fissile Pu The 'model' BWR for post-1980 startup has a core thermal power of 2 940 MW to produce a net electrical output of Second unload: 33 285 kg at 0,77 % (37,5 t U, 1,8 t 1 000 MW. The initial core requires SW) 166 kg fissile Pu

56 165 kg at 2,31 % Third unload: 26 600 kg at 0,59% (19,61 U, 36 250 kg at 1,81 % -2,4 t SW) 140 kg fissile Pu 14 495 kg at 1,59% 7 250 kg at 1,40 % Fourth unload: 30 090 kg at 0,75 % (32,6 t U, 1,0 t SW) 168 kg fissile Pu With 0,25% enrichment-plant tails assay, the initial core therefore requires 433,91 of natural-uranium feed and Fifth unload: 27 815 kg at 0,83 % (35.0 t U, 3,2 t 220,7 t of separative work. The first refuelling is assumed SW) 165 kg fissile Pu to take place 18 months after commercial operation, and subsequent reloads' on an annual basis. Equilibrium is If only uranium is recycled, then it is assumed here that the reached at the fifth reload, the individual quantities being spent uranium from the first unload can be used to reduce as follows, with corresponding natural-uranium and the natural-uranium requirements for the fourth reload, separative-work requirements at 0,25 % tails assay in from the second unload for the fifth reload, and so on. In parentheses for each total reload: this way the twenty-sixth unload contributes to the PER-10-9 twenty-ninth (and last) reload. For simplicity, credits for unloaded fuel also contains plutonium, the the last three unloads and the final core discharge are fissile-plutonium quantity being approximately 348 kg per ignored. The total lifetime requirements of natural uranium annum, or about 0,27% of the discharged fuel. The and separative work amount to 41761 and 2 991 t assessment of the value of plutonium recycling in respectively, as shown in Table 11. CANDU-PHW's is difficult because of the sparsity of published information. The approach described in The calculation of savings as a result of plutonium recycling AECL-5516 is based on a reactor operating on a plutonium is complicated, as in the case of the PWR. The figures in cycle throughout its life, including the initial core. The Table 11 are for full plutonium recycling, again following plutonium is added to natural uranium, thus increasing fuel the scheme of WASH-1348. endurance from 7,5 MW.d/kg to 17,5 MW.d/kg. On this basis, at 75 % capacity factor, the initial core requires 380 Once again, the model parameters coincide with the OECD — 450 t of natural uranium (directly or indirectly) and 52 uranium report, except insofar as the treatment of — 59 t/a thereafter. plutonium recycling is concerned, and a small difference in the amount of fissile plutonium recovered from unloaded For the purposes of providing an indication of the potential fuel. The other comments made above concerning the PWR plutonium savings in a CANDU-PHW on the same basis as also apply to the BWR, except that the average fuel-element used above for the PWR and BWR, it is assumed here that residence time in the core is 3,86 a. For the purposes of the fissile plutonium is equivalent to 80 % of its mass of following mixed-oxide batches through the reactor, a 235(j. It is mixed with tails uranium from an enrichment residence time of four years is used, so that the mixed plant at 0,25 % which is available 'free': i.e. it represents no oxide loaded at the fourth reload is discharged in the eighth natural-uranium requirement. The mixed oxide is assumed unload (instead of the seventh as in the PWR case). to be equivalent to natural uranium, and therefore contains Second-generation plutonium is therefore first loaded into 0,579 % fissile plutonium. On this basis, and using the the BWR at the eleventh reload. method of WASH-1348, the figures in Table 12 result, but their approximate nature must be borne in mind, and they If equilibrium plutonium recycling is achieved in which are by no means official. The equilibrium annual only first-generation plutonium is recycled, then the natural-uranium requirement of 62 t/a in Table 12 is approximate net annual natural-uranium requirement is slightly higher than the 52 - 59 t/a in the AECL report, 108,9 t, and the separative-work requirement 79,4 t. and errs on the conservative side. The lifetime uranium required of 2 225 t is at the upper end of the lifetime 3.3.3 CANDU-PHW requirement of 1 927 - 2 222 t deduced from the AECL The fuel characteristics of this reactor as given in report. WASH-1348 appear to be out of date. The figures below have been taken from AECL-5516, which provides fewer There are no definite plans in Canada to recover plutonium details but reflects later design data. and, until such time as these have Leen made, plutonium recycling in CANDU-PHW's must be considered a The CANDU-PHW has a thermal efficiency of 29 %, so that theoretical excercise only. The economic incentive for an electrical output of 1 000 MW would require a thermal reprocessing is not as great as in the case of LWR's. power of 3 450 MW (although the largest unit in operation is 750 MW electrical).The initial core requires an inventory 3.3.4 High-temperature gas-cooled reactor of 140 t of natural uranium, which is considerably less than The 'model' HTGR has a core thermal power of 2 564 MW either the PWR or the BWR, and no separative work is to produce a net electrical output of 1 000 MW. The initial required. core requires

Reloading is carried out on-load, and equilibrium 1 616 kg at 93,15%. conditions are achieved in about one year. The annual reload requirements amount to 131 t of natural uranium, Apart from the uranium requirement, some 32 t of thorium without recycling, at 75 % capacity factor. This is is loaded into the initial core. Thorium quantities are considerably less than the LWR's without recycling, and ignored here, as the accent is on uranium-resource similar to the LWR's when they have only uranium consumption. With 0,25 % enrichment-plant tails assay, the recycling. The lifetime natural-uranium requirement over initial core therefore requires 325,7 t of natural uranium 30 years amounts to approximately 4 029t on a feed and 349,0 t of separative work. The first refuelling is once-through cycle, as shown in Table 12. The 1401 for the assumed to take place 15 months after the commercial core inventory includes an allowance for the approach to operation date, the second 15 months after that, and equilibrium, and consumption in the first two years is subsequent reloads on an annual basis. The time to reach reduced in the Table to reflect the 'standard' capacity equilibrium depends upon reprocessing facilities, and may factors. be as much as nine years. The individual quantities are as The fuel discharged from CANDU reactors contains only follows, with corresponding natural-uranium and 0,22 % 235ij, so that uranium re-enrichment is not feasible, separative-work requirements at 0,25 % tails assay in and uranium recycling does not enter the picture. The parentheses, when no recycling is carried out: PER-10-10

3.3.5 Liquid-metal-cooled fast breeder reactor

First reload: 727 kg at 93,15% (146,5t U, The breeder reactor will consume negligible quantities of 157,0 tSW) uranium in comparison with the reactors described above. By the time breeders are introduced on a significant scale,

Second reload: 727 kg at 93,15% (146,51 U, huge stocks of depleted uranium will have been built up 157,0 tSW) from enrichment-plant tails. These stocks, together with depleted uranium from other sources, are suitable for loading into breeders as fertile material. It will not be Third reload: 697 kg at 93,15% (140,51 U, necessary to obtain new natural uranium until the depleted 150,5 t SW) stocks have run out.

Fourth reload: 697 kg at 93,15% (140,51 U, 150,5tSW) The OECD model 1 000 MW(e) LMFBR requires only about 1,5 t of uranium per annum at 75% load factor, while producing a net gain in fissile plutonium of 108 kg/a. Fifth reload: 634 kg at 93,15% (127,81 136,9 t SW) The initial core requires approximately 1,53 t of fissile plutonium. The doubling time of the plutonium inventory

With no recycling, a nominal lifetime of thirty and a half in the core and in the recycling loop (which is years after the commercial operation date, and no approximately the same as that in the core) amounts to capacity-factor reduction in later years, the total uranium about thirty years. A more advanced LMFBR model given and enrichment requirements can be expected to amount to in WASH-1348, also based on oxide fuel, has a faster 4 095 t U and 4 387 t SW respectively. The total thorium doubling time of about thirteen years. This improvement requirement amounts to approximately 240 t. depends upon technological development, and can only be expected in later commercial LMFBR's.

When full recycling in HTGR's is adopted, the highly enriched uranium feed, after irradiation in the reactor, is 3.3.6 Comparative deta not re-enriched, but is recycled through the reactor once In order to provide comparative information on basic

more and then discarded. The 233ij bred from the fertile reactor characteristics. Table 14 is included, which is an thorium in the model reactor is recycled indefinitely. These adaptation from 'Estimates of Future Demand for Uranium parameters are both taken into account in the recycling and Services' by R. Krymm and G. case shown in Table 13, which indicates total lifetime Woite, published in IAEA Bulletin Volume 18, No. 5/6. No requirements of 2 519 t of natural uranium and 2 699 t of figures for the HTGR are given, neither are separative work. plutonium-recycling parameters. The Table serves to demonstrate how modei characteristics vary according to The above characteristics are derived from WASH-1348, source and time, but it is also worth noting that the and they coincide with figures given in the OECD report. differences in this case are marginal.

4. REFERENCES

[1] Snyder, A.J. Computer program NUFUEL for forecasting nuclear fuel requirements and related quantities. WASH-1348. Oct 1974. 149 p.

[2] Mooradian, A.J. CANDU fuel cycles - present and future. AECL-5516. May 1976. 20 p.

[3] OECD Nuclear Energy Agency and International Atomic Energy Agency. Uranium Resources, Production and Demand. Dec 1975. 78 p.

[4] Krymm, R.; Woite, G. Estimates of future demand for uranium and nuclear fuel cycle services. IAEA Bulletin (1976 v. 18(5/6) p. 6-15.

[5] US Atomic Energy Commission. AEC Gaseous diffusion plant operation. ORO-658. Feb 1968. 45 p. PER-10-11

5. APPENDIX

The Concept of Separative Work

This description of the concept of separative work is Assuming the existence of V(x), the value function, a value adapted from ORO-658: 'AEC Gaseous Diffusion Plant balance around the stage yields A, where A is the value Operations', published by the US Atomic Energy increment effected by that stage: Commission in February, 1968.

A=LV(x) + LV(y)-2LV(z) (6) Consider a single stage in a gaseous-diffusion enrichment plant, which has a feed of 2 L at 235IJ assay z. The stage splits the uranium up into an enriched stream at assay y and The value functions V(y) and V(z) can be expanded about a depleted stream at assay x. The stage separation factor is x in a Taylor series to obtain independent of the feed assay level, is denoted by the symbol a, and is defined as V(y) = V(x) + (y - x)V'(x) + (y " x)2 V"(x) + .... (7)

a= v 1 Vi- oi V(z) = V(x) + (z - x) V'(x) + (Z X)2 V"(x) + .... (8)

In a gaseous-diffusion process the theoretical value of a A 235(j balance yields differs very little from unity, but the difference (denoted by \p) is crucial, viz: z - x = (y - x)/2 (9) i|/ = a - 1 (2) Substituting equations (7), (8) and (9) into equation (6) and disregarding terms containing the difference (y - x) Equations (1) and (2) can be combined to yield raised to powers greater than 2, lead to the expression x(1 +j>) V = (3) 1 + y^X A= L(y- x)2v"(x)/4 (10)

As a is close to unity, t// is very much smaller than unity. The quantity (y - x) from equation (5) can be used to Equation (3) can be expanded in the form replace (y - x) in equation (10):

y = x(1 + i//) (1 - i//x + i//2x2 ) (4) A=^[x(1 -x)j2v"(x) (11)

Ignoring terms with \p raised to the power of 2 or more, Invoking the second property above, to make A equation (4) becomes independent of assay level, let y-x=i//x(1-x) (5)

Equation (5) gives the difference in 235IJ mass assay between the enriched and depleted streams leaving the stage. The separated effluents should together have a higher Equation (12) is an ordinary differential equation with the 'value' than the feed to the stage, in order to reflect the general solution work done by the stage. A 'value function' is sought to V(x) = Co + C1x + (2x-1)ln(^) (13) - reflect the 'value' of a unit of uranium as a function tcf its 235y assay. The value function should have the following properties: where Co and Ci are arbitrary constants.

1. If V(x) represents the value of one unit of uranium at A particularly convenient form of V(x) arises in the case of assay x, then MV(x) represents the value of M units. V'(0,5) = V (0,5) = 0. In this event, the value function is completely defined as 2. Since the work done by a stage on a given quantity of feed material should be independent of its assay, the V(x) = {2x-1)ln( * ) (14) value increment effected by a stage should also be independent of the feed assay level. PER-10-12

Note, once again, that V(x) should never be confused with price or cost of material.

Equation (11) now becomes

A = L1//2/4 (15)

This expression defines the 'separative work' done by a stage, i.e. the increase effected by the stage in the 'value' of the effluent streams with respect to the feed stream. The dimensions of separative work are obviously the same as those of L : mass units of uranium.

In an ideal plant there is no mismatching at any point between stages, and no mixing losses or other departures from theory. The separative work done by the plant is the sum of that done by all the individual stages. Making a value balance about the entire plant, as was done for a single stage in equation (6), provides the important result

Separative work done (SW) = PV(xp) + WV(xw) - FV(xf) (16)

This can be written out in full as

1 -X, 1 ~ xw SW= P(1 - 2xp) In fi + W(1 -2xw) In xw

1 -xf - F(1 - 2xf) In (17) Xf PER-10-13

o ' 1 1 1 1 ' 1 0,10% 0,15% 0.20% 0,25 0,30% 0,35% 0,40%

TAILS MASS ASSAY FIG. 1 SEPARATIVE WORK AND NATURAL-URANIUM FEED REQUIRED TO PRODUCE UNIT MASS OF PRODUCT AT VARIOUS ENRICHMENTS 0,35 %

0,30%

^ 0.25% < co CO < ^ 0,20% <

1 0,15% h- Q_ O

0,10%

0,05% 0 05 1,0 1,5 2,0 2,5 3,0 3,5 RATIO OF URANIUM TO SEPARATIVE WORK COST FIG. 2 OPTIMUM TAILS ASSAY AS A FUNCTION OF THE RATIO OF NATURAL-URANIUM-FEED TO SEPARATIVE-WORK COSTS °0,10% 0,15% 0,20% 0,25% 0,30% 0,35% 0,40% TAILS MASS ASSAY FIG. 3 SEPARATIVE WORK ANO 1,0 7» ASSAY FEEO REQUIRED TO PRODUCE UNIT MASS OF PRODUCT AT VARIOUS ENRICHMENTS 0,20 0,25% 0,30% TAILS MASS ASSAY PER-10-17

0,05% ' 1 1 1 1 1 1 1 0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 RATIO OF URANIUM TO SEPARATIVE WORK COST FIG. 5 OPTIMUM TAILS ASSAY AS A FUNCTION OF THE RATIO OF URANIUM -FEEO TQ SEPARATIVE-WORK COSTS FOR FEEDS OF 1,0 7., 0,711% ANO 0,47. MASS ASSAY

URANIUM ENRICHING FUEL FABRICATION REACTOR CHEMICAL REPROCESSING STORAGE

DEPLETED — — • URANIUM

F'G-6 NUCLEAR FUEL FLOWS FOR THE MOST COMMON REACTOR TYPES (ADAPTED FROM WASH-1348) m zn ATOMIC ENERGY BOARD — RA AL) ÛP AT QQMK RAG A »4»************************************»** O 00 NUCLEAR POWER STUOIES ***********************

TABLE 1 : NATURAL FEED (F) REQUIRED TO PRODUCE UNIT MASS OF PRODUCT AS A FUNCTION OF PRODUCT ENRICHMENT AND TAILS ASSAY

TAILS ASSAY *V PRODUCT (MASS X) (MASS %) * lt25 1.5 1.75 2,0 2,25 2,5 2,75 3 ,0 3,25 3,5 3,75 93, 15 o.io • * 1.E82 2.291 2.700 3. 110 3.519 3.928 4. 337 4. 746 5.155 5. 565 5. 974 152.291 0.11 1. 897 2.313 2.729 3. 145 3.5ol 3.977 4. 393 4. 809 5. 225 5. 64 1 6.057 154.809 0.12 * 1.912 2.335 2.758 3. 181 3.604 4.027 4. 450 4. 873 5.296 5.719 6. 142 157.411 0.13 * 1. 928 2.358 2.788 3.219 3.649 4.079 4.509 4. 940 5. 370 5. 800 6. 231 160.103 0.14 * 1.944 2.382 2. 820 3. 257 3.695 4.133 4. 571 5. 009 5.447 5.884 6. 322 162.890 0.15 * 1.961 2.406 2.852 3. 298 3.743 4.189 4.635 5. 080 5.52b 5. 971 6.417 165.775 0.16 * 1.978 2.432 2.886 3.339 3.793 4.247 4.701 5. 154 5. 608 6. 0b2 6. 515 168.766 0. 17 1.996 2.458 2.921 3.383 3.845 4.307 4.769 5. 231 5.693 6. 155 6.617 171.867 0.18 * 2.015 2.486 2.957 3.427 3.898 4.369 4. 840 5. 311 5.782 6.252 6.723 175.085 0.19 * 2.035 2.514 2.994 3.474 3.954 4.434 4. 914 5. 393 5. 873 6. 353 6.833 178.426 0.20 2.055 2.544 3.033 3.523 4.012 4.501 4.990 5. 479 5. 969 6. 458 6.947 181.898 0.21 2.076 2.575 3.074 3.573 4.072 4.571 5. 070 5. 569 b. 068 6.567 7.066 185.509 0.22 * 2.Ü98 2.607 3.116 3.625 -..134 4.644 5. 153 5. 662 6. 171 6. 680 7. 1B9 189.267 0.23 * 2. 121 2.640 3. 160 3. 680 4.200 4.719 5. 239 5. 759 6.279 6. 798 7. 318 193.181 0.24 * 2. 144 2,675 3.206 3. 737 4.268 4.798 5. 329 5. 860 6.391 6. 921 7.452 197.261 0.25 * 2. 169 2.711 3.254 3. 796 4.338 4.881 5.423 5. 965 6. 508 7. 050 7. 592 201.518 0.26 * 2.195 2.749 3.304 3.858 4.412 4.967 5. 521 6. 075 6.630 7. 184 7. 738 205.964 0.27 * 2.222 2.789 3. 356 3.923 4.490 5.057 5.624 6. 190 6.757 7. 324 7.891 210.612 0.28 * 2.251 2.831 3.411 3.991 4.571 5. 151 5. 731 6. 311 6. 891 7.471 8.051 215.476 0.29 * 2. 280 2.874 3.468 4.062 4.656 5.249 5.843 6. 437 7.031 7. 625 8. 219 220.570 0.30 * 2.311 2.920 3. 528 4. 136 4.745 5.353 5.961 6. 569 7. 178 7. 786 8. 394 225.912 0.31 * 2.344 2.968 3. 591 4.214 4.838 5.461 6.085 6. 708 T.332 7.955 8. 579 231.521 0.32 2.379 3.018 3. 657 4.297 4.936 5.575 6.215 6. 854 7.494 8. 133 B.772 237.417 0. 33 * 2.415 3.071 3.727 4. 383 5.039 5.696 6. 352 7. 008 7. 664 8. 320 3. 976 243.622 0.34 * 2. 453 3.127 3.801 4.474 5.148 5.822 6.496 7. 170 7.844 8. 518 9. 191 250.162 257.063 0.33 * 2.493 3.186 3.878 4.571 5.263 5.956 6. 648 7. 341 8.033 8. 726 9.413 0. 36 2.536 3.248 3.960 4.672 5. 385 6.097 6.809 7. 521 8.234 8. 94o 9. o5ô 264.359 0.37 2.581 3.314 4.047 4. 780 5.513 6.246 6. 979 7. 713 8.446 9. 179 9.912 272.082 C.3(i * 2.628 3.384 4. 139 4.894 5.650 6.405 7. 160 7. 915 8. 671 9. 42u 1U. 181 280.272 0. 39 * 2.679 3.458 4.237 5.016 5.794 6. 573 7. 352 8. 131 3.910 9. öäd 10.467 288.97* CAO * 2.733 3.537 4. 341 5. 145 5.949 6.752 7. 556 8. 360 9. 164 9. 964 10.7 72 298.231 ATOMIC ENERGY BOARD — RAAD OP ATOOHKRAG **********x**a*********-**** ***************

NUCLEAR POWER STUDIES ***********************

TABLE 2 : SEPARATIVE WORK REQUIRED TO PRODUCE UNIT HASS GF PRODUCT AS A FUNCTION OF PRODUCT ENRICHMENT AND TAILS ASSAY

FOR FEED URANIUM AT 0.711 X U235 TAILS * ASSAY * PROOUCT ASSAY IMASS X) (MASS Xt * 1.25 If 5 1.75 2,0 2f25 2,5 2,75 3,0 3,25 3,5 3,75 93,15 0.10 1.177 1.804 2.460 3.137 3.831 4.538 5.255 5.981 6.715 7.455 8.200 303.606 0.11 * 1.120 1.721 2. 350 3.001 3.669 4.349 5.040 5.740 6.447 7.160 7. 879 293.846 0.12 * 1.069 1.646 2.251 2.879 3.522 4. 179 4. 846 5. 522 6.205 6.895 7. 590 285.057 0.13 * 1.C22 1. 577 2. 162 2. 767 3.389 4.024 4. 670 5. 324 5.986 6.654 7. 328 277.076 0. 14 • 0.980 1.515 2.080 2. 666 3.268 3.883 4. 509 5. 144 5. 786 6.434 7. 088 269.779 0. 15 * C.941 1.458 2.004 2.572 3.156 3.753 4. 361 4. 978 5.602 6. 232 6. 867 263.068 0. 16 * 0.904 1.405 1.935 2.436 3.053 3.633 4. 224 4. 824 5.431 6.045 6. 663 256.862 0.17 * 0.871 1.356 1.870 2.405 2.957 3.522 4. 097 4.681 5.273 5.871 6. 474 251.098 0.18 * 0.839 1.310 1.809 2. 330 2.867 3.418 3.978 4. 548 5.125 5.708 6. 297 245.722 0.19 * 0.810 1.267 1.753 2.260 2.784 3.320 3. 867 4.423 4.987 5. 557 6. 132 240.690 0.20 0.782 1.227 1.700 2. 194 2.705 3.229 3.763 4. 306 4.857 5. 414 5. 976 235.965 0.21 * 0.757 1.189 1.650 2. 132 2.631 3. 143 3.665 4. 196 4.735 5.280 5. 830 231.515 0.22 * 0.732 i.153 1.602 2.073 2.561 3.061 3.572 4.092 4.619 5. 153 5. 692 227.313 0.23 * 0.709 1.119 1.558 2.018 2.495 2.984 3.485 3.994 4.510 5.033 5. 561 223.336 0.24 * Ù.687 1.087 1.515 1. 965 2.432 2.911 3.401 3.900 4.407 4. 919 5. 437 219.562 0.25 * 0.666 1.056 1.475 1.915 2.372 2.842 3.322 3. 811 4.308 4.811 5. 319 215.975 0.26 * 0.646 1.027 1.437 1.868 2.315 2.776 3.247 3. 727 4.214 4. 708 5. 207 212.559 0.27 0.627 0.999 1.400 1.822 2.261 2.713 3. 175 3.646 4.125 610 5. 100 209.300 0.28 * 0.609 0.972 1.365 1.779 2.209 2.653 3. 106 3. 569 4.039 4. 51t> 4. 997 206.186 0.29 0.591 Ü.947 1.331 1.737 2.160 2.595 3.041 3.495 3.957 4. 42e> 4. 899 203.205 0.30 * 0.575 0.923 1.299 1.697 2.112 2.540 2.978 3. 425 3. 879 4. 339 4. 806 200.348 0. 31 0. 559 0.899 1.269 1.659 2.066 2.486 2.917 3. 357 3. 804 4.257 4. 715 197.608 0.32 * 0.543 0.877 1.239 1.623 2.023 2.436 2. 859 3. 291 3. 731 4. 177 4. 629 194.974 0. 33 0.529 0.655 1.210 1. 587 1.980 2.387 2.803 3. 229 3. 662 4. 101 4. 546 192.441 0.34 * 0.514 0.834 1. 183 1. 553 1.940 2.339 2.749 3. 16B 3.595 «,.027 4. 465 190.001 0.35 * 0.501 0.814 1.157 1. 520 1.901 2.294 2.698 3. 110 3.530 3. 956 4. 388 187.650 0. 36 * 0.488 0.795 1. 131 1 .489 1 .863 2.250 2. 647 3.054 3. 468 3. 888 4. 313 185.381 0.37 0.475 0.776 1.106 1.458 1.826 2.207 2.599 3. 000 3.<»00 3. 82<; 24 i 183.190 0.38 0.462 0.758 1.C83 1.429 1.791 2. 166 2. 552 2. 947 3. 349 3. 758 4. 172 181.072 0. 39 0.450 0.741 1.060 1. 400 1.757 2.127 2. 507 2. 896 3.293 3. ü90 4. 10*. 179.023 U.40 * 0.439 0. 724 1.037 1. 372 1.724 2.088 2.463 2. 847 3. 239 3. 63b 4. 039 177.039 m ATOMIC ENERGY BOARD — RAAO OP ATOOHK.RAG ZD o NJ NUCLEAR POWER STUDIES O 4**4.**** ***************

TABLE 3 : OPTIMUM TAILS ASSAYtX) FOR FEED OF 0.711 X U235

PATIO CF RAT IU OF RATIO OF RATIO OF RATIO OF RATIO OF URANIUM TO TAILS URANIUM TO TAILS URANIUM TO TAILS URANIUM TO TAILS URANIUM TO TAILS URANIUM TO TAILS S.w. CUSTS ASSAY S.W. COSTS ASSAY S.W. COSTS ASSAY S.W. COSTS ASSAY S.W. COSTS ASSAY S.W. COSTS ASSAY

0.40 0.327 0.42 C. 322 0.44 0.317 0.46 0. 312 0.48 0.307 0. 50 0.303 0.52 0. 298 0.54 0.294 0.56 0.290 0.58 0. 286 0.60 0.282 0.62 0.279

0.64 0.275 0.66 0. 272 0. 68 0.268 0.70 0.265 0.72 0.262 0.74 0.259 0. 76 0.256 0.78 0.253 o.ao 0.251 0.82 0.248 0.84 0.245 0.86 0.243

0.88 0.240 0.90 0.238 0.92 0.236 0.94 0.233 0.96 0.231 0.98 0.229 1.00 0.227 1.02 0.225 1.04 0.223 1.06 0.220 1.08 0.219 1.10 0.217

1.12 0.215 1.14 0.213 1. 16 0.211 1. 18 0.209 1.20 0.20B 1.22 0.206 1. 24 0. 204 1.26 0.203 1.28 0.201 1.30 0.200 1.32 0. 198 1.34 0.197

1.36 0. 195 1.38 0.194 1.40 0. 192 1. 42 0. 191 1.44 0.189 1.46 0. 188 1.48 C. 187 1. 50 0.185 1. 52 0.184 1.54 0. 183 1. 56 0.182 1.58 0.180

1.60 0. 179 1.62 0. 178 1.64 0. 177 1. 66 0. 176 1.68 0.174 1.70 0.173 1.72 0. 172 1. 74 0. 171 1. 76 0.170 1.78 0.169 1.80 0.168 1.82 0. 167

1.84 0. 166 1.86 0. 165 1.88 0. 164 1. 90 0. 163 1.92 0.162 1.94 0.161 1.96 0. 160 1.98 0.159 2.00 0.158 2.02 0. 157 2.04 0.157 2.06 0.156

2. 08 0.155 2. 10 0.154 2.12 0.153 2. 14 0. 152 2.16 0.151 2.18 0.151 2.20 0.150 2.22 0. 149 2.24 0.148 2.26 0. 148 2.28 0.147 2.30 0. 146

2.32 0. 145 2.34 0. 144 2,36 0.144 2.38 0.143 2.40 0.142 2.42 0.142 2.44 0. 141 2.46 0. 140 2.48 0.140 2. 50 0. 139 2.52 0.138 2.54 0.137

2.56 0. 137 2.58 0.136 2.60 0.136 2.62 0.135 2.64 0.134 2.66 0.134 2.6Ö 0. 133 2. 70 0. 132 2.72 0. 132 2.74 0. 131 2.76 0.131 2.78 0.130

2.8Ü 0. 129 2.82 0. 129 2.84 0.128 2. 86 0. 128 2.88 0.127 2.90 0.127 2.92 0. 126 2.94 0. 126 2.96 0. 125 2.98 0.125 3.00 0.124 3.02 0.123

3. U4 ü. 123 3.C6 0. 122 3.08 0.122 3. 10 0. 122 3.12 0.121 3. 14 0. 121 3. 16 0. 120 3.1 8 0. 119 3.20 0. 119 3. 22 0.118 3.24 0.118 3.26 0. 118

3.28 •J. 11 7 3.^0 0. 117 3. 32 0.116 3.34 0. 116 3.36 0.115 3. 38 0. 115 3.

NUCLEAR POWER STUDIES

TABLE 4 : 1.0 X U FEED IF) REQUIRED TO PRODUCE UNIT MASS

OF PRODUCT AS A FUNCTION OF PROOUCT ENRICHMENT AND TAILS ASSAY

TAILS ASSAY PRODUCT ASSAY (MASS X) (MASS *) 1,25 1,5 1,75 2,0 2,25 2,5 2,75 3,0 3,25 3,5 3,75 93,15

0. 10 1.2 7Ö 1.55b 1.833 2. Ill 2.389 2.667 2.944 3.222 3.500 3.778 4.056 103.389 0. 11 1.28i 1.562 1.843 2.124 2.404 2.685 2.966 3.247 3.528 3.809 4.090 104.539 0.12 * 1.284 1.568 1.852 2. 136 2.420 2.705 2.989 3.273 3. 557 3.841 4.125 105.716 0. 13 1.287 1. 575 1.862 2.149 2.437 2.724 3.011 3.299 3.586 3.874 4.161 106.920 0.14 Ik 1.291 i. 581 1.072 2. 163 2.453 2.744 3.035 3.326 3.616 3.907 4.198 108.151

0.15 1.294 1.588 1.882 2. 176 2.471 2.765 3.059 3. 353 3.647 3.941 4.235 109.412 Ü.16 * 1.296 1. 595 1.893 2. 190 2.4B8 2.786 3.083 3. 381 3.679 3.976 4.274 110.702 0.17 1.301 1.602 1.904 2.205 2. 506 2.807 3. 108 3.410 3.711 4.012 4.313 112.024 * 2.220 3.439 3.744 4.049 113.378 o. la * 1. 30 5 l.tolO 1.915 2.524 2.829 3. 134 4.354 0.19 1.309 1.617 1.926 2.235 2.543 2.852 3. 160 3.469 3.778 4.086 4.395 114.765

0.20 * 1.312 1.625 1.937 2.250 2.562 2.875 3. 1B7 3.500 3.812 4. 125 4.437 116.187 0.21 * 1.31b l.b33 1.949 2. 266 2.582 2.899 3.215 3. 532 3.848 4. 165 4.481 117.646 3. 564 3.885 4.205 4.526 119.141 0.22 1.321 I. 641 1.962 2.282 2.6Û3 2.923 3. 244 0.23 1.325 1.649 1.974 2. 299 2.623 2.948 3.273 3.597 3.922 4. 247 4.571 120.67b 0.24 tr 1 . ?29 1 .658 1.987 2.316 2.645 2.974 3. 303 3.632 3.961 4.289 4.618 122.250

0.25 % 1.B33 1.667 2.000 2.333 2.667 3.000 3.333 3.667 4.000 4.333 4.667 123.867 0.2b V 1.2 38 1.676 2.014 2. 351 2.689 3.027 3.365 3.703 4. 041 4. 378 4.716 125.527 0.27 I. ?42 1.685 2.C27 2.370 2.712 3.055 3. 397 3. 740 4.082 4. 425 4. 767 127.233 Q.tB 1. 347 1.694 2.042 2. 389 2.736 3.083 3.431 3.778 4.125 4.472 4.819 128.986 0.29 * 1.352 . 1.704 2.056 2.408 2.761 3. 113 3.465 3.817 4. 169 4. 521 4.87 3 130.789

0.30 * 1.3 57 1.714 2.071 2.429 2.786 3. 143 3. 500 3.857 4.214 4. 571 4.92 9 132.643 0. 31 1. 3o2 1.725 2.087 2.449 2.812 3. 174 3. 536 3. 899 4.261 4. 623 4.986 134.551 0. 32 1.36d 1.735 2. 103 2.471 2.838 3.206 3.574 3.941 4. 309 4. 676 5.044 136.515 0.33 i.373 1. 746 2. 119 2.493 2.866 ' 3.239 3. 612 3. 985 4.358 4.731 5.104 138.537 0.34 1. 379 1.753 2.13b 2. 515 2.894 3.273 3.652 4.030 4.409 4. 788 5. 167 140.621

0.35 1. 385 1.769 2. 154 2. 538 2.923 3.308 3.692 4.077 4.462 4.846 5.231 142.769 0. 3o 1 . 391 1.781 ^.172 2.562 2.953 3.344 3. 734 4. 125 4.516 4.906 5.297 144.984 0. 37 * 1. 397 1. 794 2.190 2. 587 2.984 3.381 3. 778 4. 175 4.571 4. 968 5.365 147.270 0.33 1 . •< 0 3 i.eoo 210 2.613 3.016 3.419 3. 823 4. 226 4.629 5. 032 5.435 149.629 J. 39 - 1. <.K 1.8IJ 2 . 2 3.:• 2. 639 3.049 3.459 3.869 4.279 4.689 5. 098 5.508 152.066

0.4 0 1. «. 1 7 1. bli 2.250 2.667 3.083 3. 500 3.917 4. 333 4.750 5.167 5.583 154.583 ATOMIC ENERGY BOARD — RAAD OP ATOOMKRAG ******************************************

NUCLEAR POWER STUDIES ***********************

TABLE 5 : SEPARATIVE WORK REQUIRED TO PRODUCE UNIT MASS OF PRODUCT AS A FUNCTION OF PRODUCT ENRICHMENT AND TAILS ASSAY FOR FEED URANIUM AT 1.000 % U235

TAILS ASSAY * PRODUCT ASSAY (MASS t) (MASS 2) * 1,25 1,5 1,75 2,0 2,25 2,5 2,75 3,0 3,25 3,5 3,75 93,15 0. 10 * 0.421 0.883 1 .375 1.888 2.418 2.960 3.513 4.075 4.644 5.220 5.801 242.430 0.11 * 0.401 0.844 1.316 1.809 2.319 2.842 3.375 3.917 4,467 5.023 5.584 235.180 0.12 * 0.363 0.609 1.263 1. 736 2.230 2.735 3.251 3.775 4.307 4.845 5.389 228.635 0.13 * 0. 367 0.776 1. 214 1. 674 2.150 2.639 3.138 3.646 4. 1Ô2 4. 664 5.211 222.680 0. 14 * 0.352 0.747 1.170 1. 615 2.076 2.550 3.03* 3.528 4.029 4.536 5.048 217.224 0.15 * 0.339 0.719 1.129 1. 560 2.00/ 2.468 2. 939 3.419 3.906 4.399 4.898 212.195 0. lo * 0.326 0. 694 1.091 1. 510 1.944 2.392 2.850 3.318 3. 792 4.273 4.759 207.537 0. 17 * C.314 0.671 1.056 1. 462 1.885 2.322 2.768 3.223 3.686 4.155 4.630 203.203 0.18 * 0.30 3 Ü.649 1.023 1. 419 1.831 2.256 2.691 3. 136 3.587 4.045 4.509 199.154 0.19 * 0.293 0.628 0.992 1.377 1.779 2.194 2.619 3.053 3.495 3.942 4.396 195.357 0.20 * 0.283 0.609 0.963 1.339 1.731 2.136 2.551 2. 976 3.407 3.846 4.289 191.787 0.21 * 0.^74 0. 590 0.936 1.302 1.685 2.081 2.487 2.903 3.325 3. 754 4.189 188.419 0. 22 * 0.266 0.57 3 0.910 1.267 1.642 2.029 2.427 2.833 3. 247 3.668 4.094 185.235 0.23 * 0.257 0.557 0.885 1.235 1.601 1.980 2. 370 2.768 3. 174 3.586 4.004 182.216 0.24 * 0.250 Û.541 0.862 1.204 1.562 1.933 2.315 2.706 3.104 3. 508 3.918 179.348 0.25 * 0.242 0.526 0.840 1. 174 1.525 1.889 2. 263 2.646 3.037 3.434 3.837 176.618 0.26 * 0.235 0. 512 n.818 1.146 1.490 1.846 2.214 2.590 2.974 3.363 3.759 17*.015 0.27 * 0.228 0.499 0. 798 1. 119 1.456 1.806 2. 167 2.536 2.913 3. 296 3.685 171.529 0.2Ü * 0.222 0.486 0.779 1.093 1.424 1.767 2. 121 2.484 2.855 3.231 3.614 169.150 0.29 * 0. 216 0.473 0. 760 i. 068 1.393 1.730 2.078 2.435 2.799 3.170 3.546 166.870 oiVo 0.21C 9.462 0.742 1. 044 1.363 1.694 2.037 2.387 2.746 3. 110 3.480 164.683 U.,31 0...04 0.4 50 0. 725 1.022 1.334. 1.660 1.997 2. 342 2.694 3.053 3. HI 8 162.5B2 0.32 0. 199 0.439 0. 709 1.000 1. 307 1.627 1. 958 2. 298 2.645 2.998 3.357 160.562 0.33 * 0.193 0.429 0.693 0.979 1.261 1.596 1.921 2.256 2.598 2.946 3. 299 158.616 0.34 * 0. 188 0.419 0.678 0. 958 1.255 1.565 1. 886 2.215 2.552 2.895 3.243 156.740 0.35 * ". ! 63 0.*U9 0.663 0.939 1.231 1.536 1.851 2.176 2.508 2. 846 3. 189 154.930 0.36 * ü. 179 0.399 0.649 0.920 1.207 1.507 1.818 2. 138 2.465 2.798 3. 137 153.182 0.37 * 3.174 0.390 U.635 0.901 1.184 1.480 1. 786 2.101 2.424 2.752 3.037 151.492 0. 3 3 V 0. 17C j.381 'J.622 0. 884 1.162 1.453 1.755 2.066 2. 384 2.708 3.038 149.857 0. 39 X: 0.165 0.373 0.609 0. 866 1. 140 1.427 1.725 2.031 2.345 2.665 2.991 148.274 146.740 0.4-! .'/. i b j .). 564 0. 596 0. 850 1.120 1.402 1.696 1.998 2. 308 2. 623 2.945 ATOMIC ENERGY BOARD — RAAD OP ATOOMKRAG *****o************************************

NUCLEAR POWER STUDIES

TAELE 6 : OPTIMUM TAILS ASSAY(X) FOR FEED OF 1.000 X U235

SATIu UF r.ATIO OF PAT 10 OF RATIO OF RATIO OF RATIO OF URANIUM TU TAILS URANIUM TU TAILS UKANIUM TO TAILS URANIUM TO TAILS URANIUM TO TAILS URANIUM TO TAILS S.W. COSTS ASSAY S.W. COSTS ASSAY S.W. COSTS ASSAY S.W. COSTS ASSAY S.W. COSTS ASSAY S.W. COSTS ASSAY

C.40 0.461 0.42 C.453 0.44 0.446 0.46 0,439 0.48 0.432 0.50 0.426 O.DJ. 0.420 0.54 0.414 0.56 0.408 0.58 0.402 0.60 0.397 0.62 0.392 C. 64 «J.38 7 0.66 0.383 0.68 0.378 0.70 0.374 0.72 0.369 0.74 0.365 0.7o 0.361 0.78 0.357 0.80 0.353 0.82 0.349 0.84 0.346 0.86 0.342 o.ea u.339 0.90 0.335 0.92 0.332 0.94 0.328 0.96 0.325 0.98 0.322 1.02 0.316 1.04 0.313 1.06 0. 311 1.08 0.308 1.10 0.305 1.00 0.319 1.12 Ü.3C2 1.14 0.3C0 I.16 0.297 1.18 0.295 1.20 0.292 1.22 0.290 1.24 0.288 1.26 0.285 1.26 0.283 1.30 0. 281 1.32 0.279 1.34 0.277

1.3s- 0.27 5, 1.38 0.273 1.40 0.271 1.42 0.269 1.44 0.267 1.46 0.265 1.43 0.263 1.50 0.261 1.52 0.259 1. 54 0. 258 1.56 0.256 1.58 0.254 1.60 0.252 1. o2 C.250 L.64 0.249 1.66 0.247 1.68 0.246 1.70 0.244 i.72 0.243 1.74 0.241 1.76 0.240 1.78 0.238 1.80 0.236 1.82 0.235 1.84 0.234 1.86 0.232 1.88 0.231 1.90 0.229 1.92 0.228 1.94 0.227 l.yo 0.226 1,98 0.224 2.00 0.223 2.02 0.222 2.04 0.220 2.06 0.219

2.08 0.218 2.10 0.217 2.12 0.216 2.14 0.214 2.16 0.213 2.18 0.212 2.<:0 0.211 ^.22 0.210 2.24 0.209 2.26 0.208 2.28 0.207 2.30 0.205 2.32 0.204 2.34 0.204 2.36 0.202 2. 38 0.201 2.40 0.200 2.42 0.199 2.4A û.19Ü 2.it.- 0.197 2.48 0.196 2. 50 0. 196 2.52 0.194 2.54 0.194 2.56 0.193 2.58 0.192 2.60 0.191 2.62 0.190 2.64 0.189 2.66 0.188 2.u8 0.187 2.7' C.187 2.72 0.186 2.74 0.165 2.76 0.184 2.78 0.183 2.80 0.182 2.82 0.182 2.84 0.181 2. 86 0. 180 2.88 0.179 2.90 0.178 2.92 0. 1 78 ^.94 C.W7 2.9t> 0.176 2.98 0.175 3.00 0.175 3.02 0.174 3.04 0.173 3.0c 0.172 3.08 0.172 3.10 0.171 3.12 0.170 3,14 0.170 i. 1 o •.>. 169 3.18 • 1 6 3 ?..2C 0.168 3.22 0.167 3.24 0.166 3.26 0.166

3.2d O.lt'J. 3.30 0.lfc4 3.32 0.164 3.34 0.163 3.36 0.162 3.38 0.162 i • -^i.' 0. i 61 3.4 2 0.160 3.44 0.160 3.46 0.159 3.48 0.159 3.50 0.158 m 3}

ATOMIC ENERGY BOARD RAAD OP ATOOMKRAG » » *» I ,»*****»****»*»»** to NUCLEAR POWER STUDIES sa*********************

TABLE 7 : 0.4 % U FEEO (Fl REQUIREO TO PRODUCE UNIT HASS

OF PRODUCT AS A FUNCTION OF PRODUCT ENRICHMENT AND TAILS ASSAY

TAILS ASSAY PRODUCT ASSAY (MASS X) (MASS 35) 1.25 1.5 1.75 2,0 2,25 2,5 2,75 3,0 3,25 3,5 3,75 93,15

0. 10 3.833 4.667 5. 500 6.333 7.167 8.000 8. 833 9.667 10.500 11.333 12.167 310.167 12.552 320.827 Û. 11 * 3.V31 4. 793 5.655 6. 517 7.379 8.241 9. 103 9.966 10.828 11.690 0.12 * 4.036 4.929 5. 821 6.714 7.607 8.500 9. 393 10.286 11.179 12.071 12.964 332.250 11.556 13.407 344.518 0. 1J V 4. 146 5.074 6.000 6.926 7.852 8.778 9.704 10.630 12.461 13.885 0. 14 4. 269 5.231 6. 192 7. 154 8.115 9.077 10.038 11.000 11.962 12.923 357.730

0.15 - 4. 400 3.400 6.400 7.400 8.400 9.400 10.400 11.400 12.400 13.400 14.400 372.000 0.1b 4. 542 5.533 6.625 7.667 8.70Ö 9.7 50 10.792 11.833 12.B75 13.917 14.958 387.458 0. 17 4.696 5.783 6.870 7.957 9. 043 10.130 11.217 12.304 13.391 14.478 15.565 404.260 •f 12.818 13.955 15.091 16.227 422.591 0. 18 4. 864 6. 000 7. 136 8. 273 9.409 10.545 11.682 442.667 0. 19 5. o48 6.238 7. 429 8.619 9.810 11.000 12.190 13.381 14.571 15. 762 16.952

0. 20 5.25C 6. 500 7. 750 9. 000 10.250 11.500 12.750 14.000 15.250 16.500 17.750 464.750 0.21 5.474 6.789 8. 105 9. 421 10.737 12.053 13.368 14.684 16.000 17.316 18.632 489.158 19.611 516.277 0.22 ft 5.722 7.111 ü. 500 9. 889 11.278 12.667 14.056 15.444 16.833 18.222 16.294 17.765 19.235 20.706 546.588 0.23 6.1. uG 7.471 6.941 10.412 11.882 13.353 14.824 0.24 6.312 7. 375 9.437 11.000 12.562 14.125 15.687 17.250 18.812 20.375 21.937 580.687

U.25 6.667 8.333 10.000 11.667 13.333 15.000 16.667 18.333 20.000 21.667 23.333 619.333 0.26 . 7.07 1 8.857 10.643 12.429 14.214 16.000 17,786 19.571 21.357 23.143 24.929 663.500 0.2/ 7. 338 9.462 11.365 13.308 15.231 17.154 19.077 21.000 22.923 24.846 26.769 714.461 28.917 0. 28 •a • e.CBj io.167 12.250 14.333 16.417 18.500 20.583 22.66 7 24.750 26.833 773.916 0.29 -» 8.727 11.000 13.273 15.545 17.818 20.091 22.364 24.636 26.909 29. 182 31.455 844.181 32.000 34.500 928.499 0.3 :• *• 9.5ÜG 12.000 14.500 17.000 19.500 22.000 24.500 27.000 29.500 38.222 0. 31 * 10.444 13.2 22 16.000 10.773 21.556 24.333 27. Ill 29.889 32.667 35.444 1031.554 42.875 0. 32 * 11.625 14.750 17.875 21.000 24. 125. 27.250 30.375 33.500 36.625 39.750 1160.373 48.857 0. 32 13.143 16.714 20.286 23.357 27.429 31.000 34.571 38.143 41.714 45.286 1325.998 56.833 0. 34 r 15.167 19.333 23.300 27.667 31.833 36.000 40.167 44.333 48.500 52.667 1546.832

0.35 «• 18.C CC 23.CCJ 28.000 33.000 38.000 43.000 48.000 53.000 58.000 63.000 68.000 1855.997 0. 3o 22.25C 23. i-00 34.750 41.000 47.250 53.500 59.750 66.000 72.250 78.500 84.750 2319.745 j. 3 7 29.Jji j 7.667 46. L o'J 54.333 62.666 71.000 79.333 87.666 96.000 104.333 112.666 3092.657 C. 3d 43.5C0 56.000 60.500 81.000 93.500 105.999 118.499 130.999 143.499 155.999 168.499 4638.473 0. 3* 6t. •vss» 1 î 0. V 9 -) 1 1-3.999 16C.998 185.998 210.998 235.997 2 60.997 285.997 310.997 335.996 9275.895 ATOMIC ENERGY BOARD — RAAD OP ATOOMKRAG

NUCLEAR POWER STUDIES ***********************

TABLE 8 : SEPARATIVE WORK REQUIRED TO PRODUCE UNIT MASS

OF PRODUCT AS A FUNCTION OF PRODUCT ENRICHMENT AND TAILS ASSAY

FOR FEED URANIUM AT 0.400 X U235 TAILS * ASSAY * PROOUCT ASSAY (MASS X» (MASS XI * 1.25 1,5 1,75 2,0 2,25 2,5 2,75 3,0 3,25 3,5 3,75 93,15 0.10 * 2.809 3.791 4.802 5.834 6.883 7.944 9.017 10.098 11.186 12.281 13.361 435.681 0. 11 * 2.t65 3.604 4.573 5. 562 6.569 7.588 8.617 9.656 10.702 11.754 12.812 419.926 0.12 * 2.535 3.437 4.367 5.319 6.287 7.268 8.260 9. 260 10.268 11.282 12.302 405.800 0. 13 * 2.418 3.285 4.181 5.098 6.032 6.979 7.936 8.902 9.875 10.855 11.840 393.028 0.14 * 2.312 3.147 4.012 4. 898 5.800 6.715 7.641 8.576 9.518 10.466 11.420 381.396 0.15 * 2.214 3.021 3.857 4.714 5.587 6.474 7.371 8.277 9.190 10.110 11.035 370.737 0.16 * 2.124 2.904 3.714 4.544 5.392 6.252 7.122 8.002 8.889 9. 782 10.681 360.916 0.17 * 2.041 2.797 3.581 4.388 5.210 6.046 6.892 7. 747 8.609 9. 478 10.352 351.824 0.18 * 1.963 2.696 3.458 4. 242 5.042 5.854 6. 678 7.510 8.350 9. 196 10.047 343.372 0.19 * 1.891 2.603 3.344 4. 106 4.884 5.676 6.478 7.289 8. 107 8.932 9. 762 335.486 0.20 * 1. 823 2.515 3.236 3. 978 4.737 5.509 6.291 7. 082 7. 880 8.685 9.495 328.102 0.21 1.760 2.433 3. 135 3.859 4.599 5.352 6. 115 6. 888 7.667 8. 453 9.245 321.167 0.22 * 1.700 2.355 3.040 3. 746 4.468 5.204 5.950 6.705 7.467 8.235 9.009 314.637 0.23 * 1.643 2.282 2.950 3. 640 4. 346 5. 064 5.794 6. 532 7.277 8. 029 8.786 308.471 0.24 * 1.590 2.213 2.865 3. 539 4.229 4.932 5. 646 6. 368 7.096 7. 834 6. 576 302.63 7

0.25 1.539 2.148 2.785 3.444 4. 119 4.807 5. 506 6.213 6.928 7. 649 8. 376 297.105 0. 26 * 1.491 2.085 2.708 3. 353 4.014 4.688 5.372 6.066 6. 766 7.473 8. 186 291.849 0.27 * 1.445 2.026 2.636 3. 267 3.914 4.575 5.246 5.925 6.613 7. 306 8.005 286.846 0.28 * 1.401 1.969 2.566 3. 184 3.819 4.467 5. 125 5.792 6. 466 7. 147 7.833 282.075 0. 29 * 1. 360 1.915 2. 500 3. 106 3.728 4.363 5.009 5.664 6. 326 6. 995 7. 668 277.520

0.30 * 1. 320 1.364 2.436 3. 031 3.641 4.265 4.899 5. 542 6.192 6. 849 7. 51 1 273.163 0.31 * 1. 282 1. 814 2. 376 2.959 3.558 4.170 4. 793 5.425 6.064 6. 709 7. 360 268.991 0.32 * 1 .245 1.767 2.317 2. 890 3.478 4.080 4.692 5. 313 5.941 6. 576 7.216 264.990 0.33 * 1.210 1. 721 2.262 2.823 3.402 3.993 4. 595 5.205 5.92? 6. 447 7.077 261.149 0.34 * 1. 176 1.&77 2.208 2. 760 3. 328 3. 909 4.501 5. 102 5.710 6. 324 6.944 257.457

0.35 f 1. 143 1.635 2.156 2.698 3.257 3.829 4.411 5.002 5.600 6. 205 6.815 253.904 0. 36 A 1.112 1.595 2. 106 2. 639 3.189 3.751 4. 324 4. 906 5.495 6. 091 6. 692 250.482 0.37 V 1. 082 1.555 2.050 2.582 3.123 3.677 4. 241 4. 814 5. 394 5.981 6, 573 247.184 0. 38 * 1.053 1.518 2.012 2. 528 3.060 3. 605 4.160 4. 724 5.296 5. 874 6.458 244.000 0.39 * 1.024 1.481 1.967 2.475 2. 998 3.535 4. 082 4. 638 5. 202 ^.771 6. 34 7 240.92b ATOMIC ENERGY BOARD — RAAD DP ATDCMKRAG

NUCLEAR POWER STUDIES

TABLE 9 : OPTIMUM TAILS ASSAY(X) FOR FEEO OF 0.400 X U235

RATIO OF RATIO OF RATIO OF RATIO OF RATIO OF RATIO OF URANIUM TO TAILS URANIUM TO TAILS URANIUM TO TAILS URANIUM TO TAILS URANIUM TO TAILS URANIUM TO TAILS S.W. COSTS ASSAY S.W. COSTS ASSAY S.W. COSTS ASSAY S.W. COSTS ASSAY S.W. COSTS ASSAY S.W. COSTS ASSAY 0.40 0.184 0.42 0.181 0.44 0.178 0.46 0.175 0.48 0.1Ï3 0.50 0.170 0.52 0.168 0.54 0.165 0.56 0.163 0.58 0.161 0.60 0.159 0.62 0.156 0.64 0.155 0.66 0.153 0.68 0.151 0.70 0.149 0.72 0.147 0.74 0.146 0.76 0. 144 0.78 0.142 0.80 0.141 0.82 0.139 0.84 0.138 0.86 0.136

0.88 0. 135 0.90 0.134 0.92 0.132 0.94 0.131 0.96 0.130 0.98 0.129 1.00 0.127 1.02 0.126 1.04 0.125 1.06 0.124 1.08 0.123 1.10 0.122

1.12 0.121 1.14 0.120 1. 16 0. 119 1.18 0.118 1.20 0.117 1.22 0.116 1.24 0.115 1.26 0.114 1. 28 0.113 1.30 0.112 1.32 0.111 1.34 0.110 1.36 0.110 1.38 0.109 1. 40 0.108 1.42 0.107 1.44 0.106 1.46 0.106 1.48 0. 105 1.50 0.104 1. 52 0.103 1.54 0.103 1.56 0.102 1.58 0.101

1.60 0. 101 1.62 0.100 1. 64 0.099 1.66 0.099 1.68 0.098 1,70 0.097 1.72 0.097 1.74 0.096 1. 76 0.095 1.78 0.095 1.80 0.094 1.82 0.094

1.84 C.093 1.86 0.093 1. 38 0.092 1.90 0.091 1.92 0.091 1.94 0.090 1.96 0.090 1.98 0.089 2. CO 0.089 2.02 0.089 2.04 0.088 2.06 0.087

2.08 0.087 2.10 0.086 2. 12 0.086 2.14 0.086 2.16 0.085 2.16 0.085 2.20 Û.084 2.22 0.084 2. 24 0.083 2.26 0.083 2.23 0.032 2.30 0.082

2.32 0. 082 2.34 U.081 2. 36 0.081 2.38 0.080 2.40 0.030 2.42 0.030 2.46 0.079 *. 0.078 2. 50 0.073 2.52 0.07 8 2.54 0.077 2.44 0.079 C • 48

2. 56 0. 077 2.58 0.077 2. 60 0.076 2.62 0.076 2.64 0.075 2.66 0.075 2.68 0.075 2.70 0.075 2. 72 0.074 2. 74 0.074 2.76 0,073 2.73 0.073

2.80 0.073 2.82 0.072 2. 84 0.072 2.S6 0.072 2.85 0.071 2,90 0.. 071 2.92 0.071 2.94 0.071 2. 96 0.070 2.9S 0.070 3.00 G.07 0 3.02 0-069

3.04 0.069 3.06 C.069 3. 08 0.069 3.10 0.063 3.12 O.OoS 3,14 0,0o8 3.16 0.067 3.18 0.067 3„ 20 0.067 3. 22 0,06? 3 , 2 0,066 i.26 0 .< Q e 6

3.23 0.066 3.30 0.066 3. 32 0, 065 3.34 0.063 3*36 G. 0 6 3.40 0. 064 3. A 2 0.064 3. 4-4 0,064 3.46 0.064 PER-10-27

TABLE 10 TABLE 11 MODEL PWR : NET URANIUM AND ENRICHMENT REQUIREMENTS MODEL BWR : NET URANIUM AND ENRICHMENT REQUIREMENTS

Ult) SW(t) U(t) SWItl Ult) SW(t) Ultl SWIt) Ult) SWIt) Ult! SW(t)

NO RECYCLE U RECYCLE ONLY U 1 Pu RECYCLE NO RECYCLE U RECYCLE ONLY U + Pu RECYCLE

Initial Coie : 31)5.0 209,0 365,0 209,0 365,0 209,0 Initial Core : 433,9 220,7 433,9 220,7 433,9 220,7 Reload No : Reload No : 1 178,5 119,0 178,5 119,0 178,5 119.0 1 193.0 118,7 193,9 118,7 193.9 118,7 2 172,7 113,6 172.7 113,6 172,7 113,6 2 187,3 114,6 187,3 114,6 187,3 114,6 3 172,7 113,6 172,7 113,6 172,7 113,6 3 150,5 92,1 150,5 92,1 150.5 92.1 4 163,0 107,2 136,1 106,8 114,7 90,2 4 170,5 104,4 110,3 91,1 83,5 70,4 5 138,2 107,4 111.0 86,4 5 158,4 97,0 120,9 95,2 92,2 73.0 6 128.0 102,6 97,7 79,1 6 13B.8 99,4 114,6 80,7 7 129,5 100,8 80,3 7 125,8 95 9 96,7 73,5 8 100,8 80,3 8 123,4 93,8 94,9 71,7 9 100,8 80,3 9 94.9 71.7 10 97,7 76,7 10 94,9 71,7 11 96,8 75,7 11 91.6 66.8 12 96,4 75,1 12 91,4 66,5 13 96,6 75,4 13 91.9 67,3 14 96,6 75,4 14 91,3 66,4 15 96,6 75,4 15 91.4 66,5 16 95,5 73,9 16 .91,4 66,5 17 95,2 73,5 '7 91.4 66,5 18 95,0 73,3 18 90,2 64,5 19 95,1 73,4 19 90.1 64,4 20 95,1 73,4 20 90,3 64,7 21 95,1 73.4 21 90,1 64,4 22 94,6 72,8 22 90,1 64,4 23 94,5 72,6 23 90,1 64,4 21 94,5 72.6 24 90,1 64,4 25 94,5 72,6 25 89,7 63,7 26 94,5 72.6 26 89,6 63.6 27 94,5 72,6 27 89,7 63,7 28 F 1 p F 94,3 72,3 28 89,6 63.6 29 94,3 72,3 29 1 1 89.6 63,6

TOTAL: 5 127 3 342 4 270 3 232 3 422 2 527 TOTAL: 5 096 3 076 4 176 2 991 3 357 2 295

NOTE: U recycle lag : 3 cycles Pu recycle lag : 3 cycles 0,25 "„ TAILS ASSAY : I 000 MWtel PWR : 75 X CAPACITY FACTOR

NOTES : U recycle lag : 3 cycles Pu recycle lag : 3 cycles 0,25% TAILS ASSAY: 1 000 MWIe) DWR : 75% CAPACITY FACTOR PER-10-28

TABLE 12

MODEL CANDU-PHW : NET URANIUM REQUIREMENTS

U(t) U(t)

NO RECYCLE Pu RECYCLE

Initial Core: 140 140 Year No: 1 108 108 2 113 113 3 131 131 4 82 5 79 6 71 7 65 8 65 9 64 10 63 11 63 12 63 13 63 14 63 15 62 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 TABLE 13

TOTAL : « 4 029 2 225 MODEL HTGR : NET URANIUM AND ENRICHMENT REQUIREMENTS

NOTE : Pu recycle lag : 3 years No Recycle Full Recycle 1 000 MW(e) CANDU-PHW 75 % CAPACITY FACTOR U(t) SW(t) Ult) SW(t)

Initial Core: 325.7 349,0 325,7 349,0 Reload No. : 1 146,5 157,0 146,5 157,0 2 146,5 157,0 146,5 157,0 3 140,5 150,5 140,5 150,5 4 140,5 150,5 61,3 65,7 5 127,8 136,9 69,3 74,3 6 127,8 136,9 75,4 80,8 7 127,8 136,9 73,4 78,6 8 127,8 136,9 67,3 72,1

29 127,8 136,9 67,3 72,1

TOTAL : 4 095 4 387 2 519 2 699

NOTES: Recycle lag : 3 cycles 0,25% TAI LS ASSAY : 1000 MW(e) HTGR: 75% CAPACITY FACTOR PER-10-29

TABLE 14

POWER-REACTOR CHARACTERISTICS^) FOR REPRESENTATIVE 1 000 MW ELECTRICAL UNITS

PWR BWR CANDU-PHW LMFBR

1. Initial loading Uranium (t) 79 114 143 50 Average initial enrichment (w/o 235y) 2,38 2,03 0,711 depleted Natural uranium required (t) 372 444 145 -- Separative work required (t) 209 227 Fissile plutonium required (t) - -2,5 - - - 2. Replacement loadings Uranium (t/a) 25,4 29,6 126 15 Fresh-fuel enrichment (w/o 235y) 3,2 2,7 0,711 depleted Natural uranium requiied (t/a) 166 158 128 Separative work required (t/a) 109 97 Fissile plutonium required (t/a) - -0,90 - - - 3. Irradiated fuel Burnup (IVlW.d/kg) 32,5 27,5 7,5 2-66(2) Uranium (t/a) 24,6 28,8 124 13,5 Average enrichment (w/o 235>j) 0,90 0,83 depleted depleted Natural-uranium equivalent (t/a) 33,5 35,0 -- Separative-work equivalent (t/a) 4,7 3,2 - Fissile plutonium (t/a) 0,165 0,16 -0,32 -1,01

(1 ) Fuel amounts are in metric tonnes of heavy metal; tails assay = 0,25 %; capacity factor = 75 %. (2) Depending on position in core or blanket.

(ADAPTED FROM IAEA BULLETIN, VOL. 18, NO. 5/6, p. 8) ISBN 0 86960 654 9