CA0900534
Atomic Energy of Canada Limited
THE SUPER-CONVERTER OR VALUBREEDER
A NEAR-BREEDER URANIUM-THORIUM NUCLEAR FUEL CYCLE
DM-94
by
W. BENNETT LEWIS
Chalk River, Ontario
May, 1968 Reprinted November 1968 AECL-3081 DM-94
THE SUPER-CONVERTER OR VALUBREEDER
A NEAR-BREEDER URANIUM-THORIUM NUCLEAR FUEL CYCLE
by
W. Bennett Lewis
ABSTRACT
A special way of operating a thermal neutron near- breeder reactor with both thorium and natural uranium fuel supported by some extra neutrons produced as cheaply as possible is described and illustrated. Initially the cheapest source of the extra neutrons will be from a low enrichment of the uranium. Tie near and long term economic advantages of such a cycle promise to justify the special name of super- converter or valubreeder.
The high credit value of long irradiated thorium fuel is the key to the value gain. The high burn-up of each type of fuel keeps the cost contributions from fuel fabrication and reprocessing low.
The claim made for the valubreeder is not that its yield as a near breeder is the highest attainable but that as nuclear power develops to large units and complexes the cycle is likely soon to become, and then to remain, one of the lowest cost overall fuel cycles.
AECL-3081
Atomic Energy of Canada Limited Chalk River, Ontario May, 1968 CONTENTS
Page
1. General Characteristics 1
2. Essence of the Valubreeder cycle 3
3. Illustrative Example 4
4. Principles of Fuelling Cost Estimates 4 5. Comparison of Fuelling System in a Reference 6 Reactor
6. Standard Cost Assignments and Further Details 6 of Analysis and Results
7. Further General Discussion 12
8. Near Term Applications 15
9. Long Term Applications 16
Appendix I Fuelling Cost Evaluation
Appendix II Appropriate value of (1 + B2Mz)/f
Appendix III Effective cross-section for U-238 in BOUT program
Appendix IV Input Data for BOUT tables THE SUPER-CONVERTER OR VALUBREEDER
A NEAR-BREEDER URANIUM-THORIUM NUCLEAR FUEL CYCLE
by
W. Bennett Lewis
1. GENERAL CHARACTERISTICS One economic characteristic sought in the design of fast neutron breeder reactors is to achieve a fuel' doubling time suffi ciently short to pay for the fuel inventory and, hopefully, even for the full fuel cycle. If the value of the extra fuel bred is less than the carrying charges on the inventory the net fuelling cost would still be positive even if there were no cotts of fabrication and reprocessing. When these other costs are added in there is little real hope that the breeding gain will pay for the full fuel cycle or, in other words, yield a net negative fuel ling cost.
A special way of operating a thorium thermal neutron near-breeder offers to match or better the realistic economic characteristics of a fast breeder fuel cycle. The net fissile fuel credit, that is the credit minus the initial basic inventory value, without fabrication cost, can exceed charges on the basic inventory. Moreover the fuel turnover time can be so short that the doubling time of inventory value is only a few years. This way of operating seems to deserve a special name so will be called the super-converter or valubreeder.
It may be noted that a CANDU natural uranium reactor operating without recycle shares these economic characteristics. For example, natural uranium valued now at $16/kgU after yielding 9.5 MWd/kgU in perhaps 400 days leaves 2.73 g fissile plutonium/kg U worth, at $10/g fiss.Pu, $27.3. In such operation, however, the fuel fabrication and processing costs per megawatt-day and per kgU are quite high relative to these values. The claim to be made for the valubreeder is not that its yield as a near breeder is the highest attainable but that as nuclear power develops it is likely soon to become, and then to remain., one of the lowest cost overall fuel cycles. It has been shown1'that the neutron economy of a near breeder can be so good on a thorium cycle that adequate supplies of uranium seem assured for many centuries. Typically a kilogram of natural uranium could yield 30 to 60 thermal megawatt- days. Not only is this yield of energy so large that relatively little uranium is required, but also the cost of power generated is - 2 -
relatively insensitive to the price of uranium ($l/thermal MWd corresponds typically to 1/7 mill/ekWh or less). Since a higher price for uranium is permissible the amount available is vastly extended.
The use of reactors of poor neutron economy in the overall system, although still rapidly growing, will be limited by increasing inventory and supply costs of the fuel cycle. Although it would inherently be possible to support more exten sive use of such reactors by association with breeder reactors, it is doubtful whether they would remain economically competitive when the cost of uranium rises.
The initial valubreeder cycle, although economical in its use of uranium, is not more so than a simple natural uranium heavy water reactor but its yield of uranium-2 3 3 leads the way to a much lower total consumption of uranium when market prices make this desirable.
For a typical CANDU reactor the fuelling cost estimates shown in Table I have been derived on comparable bases.
TABLE I Fuelling Costs in Reference CANDU Reactor including Inventory and Interest Charges
Standard Std.+ $10/kgU. Std. + $10/kg. Std. + ilO/kg Fuel Cycle Costs & related U-Fabriaation U or Th charges Pvocessing
mill/kWh Natural Uranium 0. 546 0.698 0.698 no processing h=0.152 A=0.152 -
Natural Uranium 0. 376 0.453 0.528 0. 513 with Plutonium h=0.077 A=0.152 h=0.137 Credit
Enriched Uranium 0. 393 0.487 0.482 0. 471 with Plutonium h = 0.094 h> = 0.089 L=0. 078 Credit
Uranium-233 + Th. 0. 477 0.545 0. 500 with U-233 Credit L=0.068 A=0.023
Enriched Uranium 0. 296 0.367 0.345 0. 353 + Thorium (Valu h=0.071 t\=0.049 A=0.057 breeder) with Pu and U-233 Credit
NOTl 1: The table is based on 1967 U.S. dollar values and details given in Table II - 3 -
The fuel cycles selected for Table I are chosen to be both practical and close to an optimum. By adopting standard unit costs and indicating how the resulting fuelling cost changes with these values, it is possible to appreciate the advantages and limitations of the cycles and how preferences would change when, for example, processing costs fall or the price of uranium rises. For this same reason figures are given to 0.001 mill/kWh. although changes of 0.1 mill/kWh may easily be introduced by altering the circumstances.
The valubreeder fuel cycle can be applied in any of the CANDU reactors whether PHW, BHW, BLW or organic liquid cooled2. The full advantages are gained only when the neutron economy of the reactor is very good. The optimum specific power range for the valubreeder fuel appears to be 35 to 55 thermal megawatts per tonne of heavy element, uranium or thorium. This rating is higher than normally adopted in CANDU reactors and suggests an extra advantage applicable especially to the PHW that the output power of the reactor core can be very considerably increased, with no large economic penalty. Given the required pump and heat-exchanger capacity, the output from some designs could be doubled.
2. ESSENCE OF THE VALUBKEEDER CYCLE
The essence of the valubreeder is to make the fuel supply predominantly natural uranium, together with a smaller amount of plain thorium, and as a third component a small amount of the cheapest available fissile material. This small component is liable to be the most costly, it could be separated U-235, or plutonium, or it could be a slight enrichment of some or all of the natural uranium. In later years it might be U-233 recovered from the thorium. Despite these relative amounts of feed about 40% of the power comes from the fission of uranium-233 bred into the thorium and most of the fuel credit comes from the high value of the residual U-2 33.
In order to benefit quickly from the U-233 credit the thorium is operated at a considerably higher neutron flux than would be optimum for maximum breeding gain per cycle.
Having satisfied these essential conditions, there remains considerable flexibility of the fuel cycle and quite complex mixtures and fuel bundle movements may be found to give lower fuelling costs. In the face of all this permissible flexibility a simple illustrative case has been selected to describe how a valubreeder cycle operates and is evaluated. - 4 -
3. ILLUSTRATIVE EXAMPLE
Part of the merit of the valubreeder cycle lies in the economical approach over several years to the equilibrium cycle. For simplicity, however, the equilibrium condition is assumed for the description. The reactor is assumed continuously fuelled on-power with the standard CANDU 0.5 m long fuel bundles. It is therefore a permissible approximation to average the properties of the fuels charged into the reactor over a selected fairly long period of time. This will be chosen to give an average irradia tion of 6.0 n/kb (i.e. 6 x 1021 n/cm2) which at an average 13 2 8 neutron flux of 7 x 10 n/cm /sec.# takes -f x 10 seconds or 8.57 x 107 sec. = 9 92 days = 2.7 full power years. The average irradiation of the thorium when withdrawn will be set at this level,6.0 n/kb. For simplicity the extra fissile material will be assumed present in the form of uniform enrichment to the natural uranium to a level of x extra grams U-235 per kg. of nat. U. This fuel will be assumed irradiated to 2.4 n/kb before withdrawal. The costs of the.fuel cycle will be evaluated as .a function of x, and the required value of x to maintain the reactor critical will be discussed.
In the example it is supposed there are 800 g Thorium per 1000 g of Uranium in the reactor. Because of the assigned difference of irradiation level the mass feed rate of uranium
is | ^ x 8QQ = 3.125 times the feed rate of thorium.
4. PRINCIPLES OF FUELLING COST ESTIMATES The basic principles leading to the low cost estimates of Table I may be seen from the familiar type of expression 3j1 for the total fuelling cost
c = nE«v + r) Because there are two types of fuel in the cycle, namely enriched uranium and thorium, undergoing different irradiations, the expression has to be elaborated and this is done in Appendix I. c is the fuelling cost in mill/ekWh, e = net station efficiency for thermal to electrical conversion expressed as a fraction, V = value of fuel in $/kg H.E (H.E. = heavy elements, i.e. U, Th, Pu) F = fabrication cost of fuel in $/kg H.E. Cr = credit value of fuel in $/kg H.E Ex = extraction or processing cost of fuel in $/kg H.E. B is the burn-up in thermal MWdays/kg fuel H.E. - 5 - Continuous on-power fuelling is assumed and the cycle is evaluated at equilibrium and referred to the mid-time of the irradiation of the fuel. The duration of irradiation is t years. a = annual charge rate on inventory ) all expressed u = station utilization or load factor ) as i = annual interest rate applicable to credits ) fractions n is the time from the mid-irradiation to extraction in years = tx + t/2u where tx = interval from fuel removal to processing. The factor l/(l+i)n is the present worth factor referring the credit to the mid-irradiation time. Note: t a OJ/CJ> where to is the irradiation and <(J the neutron flux. The principles applied are 1. To make V as small as possible. 2. To make F small. 3. To make t short by (a) keeping to short for fuel of high V (b) making c|) as large as possible. 4. To make tx short. 5. To make u large u = 0.9. 6. To make B large. 7. To make Ex small compared with Cr. For the selected cycles of Table I and Fig. 1 a typical value for the efficiency, e, for current CANDU reactors has been taken, namely 0.30. It is expected the economic optimum effi ciency will rise, and lead to a lower fuelling cost. From previous studies of thorium fuel for CANDU reactors'11 l it was known that plain thorium oxide irradiated to 6.0 n/kb yields 35 MWd/kgTh and about 16 g U-233/kgTh with a credit value at $13/g U-233 of $208/kgTh. This makes Cr - Ex satisfactorily high and the high to is acceptable because V + F is very small and (J) is high. It appears quite practicable and safe to take ThC>2 fuel to 35 MWd/ kgTh burn-up and at this irradiation the energy yield in fissions per net neutron consumed is satisfactorily high. The next main feature of the valubreeder cycle is the supply of neutrons needed for this irradiation of thorium at as low a cost as possible. This is where the prospect is currently changing. A few years ago it appeared that apart from the few spare neutrons obtainable from natural uranium, the cheapest means of supply would be from separated fissile material in a form from which the residue would have a salvage value. Now the prospective reduction of plutonium recovery costs and the introduction of toll enrichment gives an advantage to uranium at a low enrichment. This is particularly so where the extra energy from the fission - 6 - of some plutonium is of value, as it is in a power reactor. In the valubreeder further advantage is achieved from the extra fast fission of U-238 together with an increased production of pluto nium per kgU compared with natural uranium; moreover the economic burn-up can be up to 20 MWd/kgU, so this fuel makes a very significant contribution to the total power at a reason ably low cost. In fact the limit to the enrichment level is set by the acceptable initial heat rating relative to the mean level and the extra fabrication cost of more highly subdivided fuel. The optimum appears very flat and by programming to move the fuel during irradiation to different neutron flux levels a higher enrichment and burn-up offers a further reduction in total fuelling cost. 5. COMPARISON OF FUELLING SYSTEMS IN A REFERENCE REACTOR The basis of the assessment of the fuel needed to sustain reactivity is the classical four factor relation 1 + B2M2 = nepf (1) 6 . The BOUT program is based on such a one point model for burn-up changes in thorium and uranium fuels. Here it is only necessary to note that a reference CANDU reactor is selected such that it yields 9.55 MWd/kgU when fuelled by natural uranium. The near est corresponding point in the BOUT tables (Case 5 of February 7, 1968) gives [nep]Av. = 1.0779 and a burn-up of 9.551 Mwd/kgU. By equation (1) [l+B2M2]/f = 1.0779 and this corresponds to 1+B,2M2 = 1,024 and f .= 0.95. Since the valubreeder fuel has a higher neutron absorption cross-section the appropriate value of f will be higher in the same reactor. The change is calculated by equation (2) of Appendix II and it appears that for the selected valubreeder cycle [l+B2M2J/f = 1.0593. As noted in Appendix II this value is liable to be somewhat low due to the neglect of two corrections in opposite directions. Until a fuller analysis can be carried out by a program such as LATREP this value will be taken as the required fuel reactivity [neplAv. The significance of this will appear from Fig. 1. 6. STANDARD COST ASSIGNMENTS AND FURTHER DETAILS OF ANALYSIS AND RESULTS •The standard costs of the examples in Table I and Fig.l are given in Table II together with a more detailed breakdown of the analysis and results. - 7 - 0.8 0.7 TOTAL NET FUELLING COST 0.6 mill /kWh INCLUDING INVENTORY AND INTEREST 0.5 CHARGES 0.4 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 OVERALL FUEL REACTIVITY [^eplAv. Fig, 1 CANDU fuelling cost comparisons (from Table II) _ 8 _ Attention may be directed in Table II to the inven tory and interest charges which are highest for the U-233 + Thorium cycle. If it were not for the high heat rating adopted these charges would be still larger and likely to put the cost of that cycle above that for Natural Uranium with no processing given in the footnote to Table II. It will be seen that the inventory contribution for the simple natural uranium cycle is lower than for any other but the total cost is sensitive to the price of uranium as shown in Table I and Fig. 1. The heat ratings of the fuel are given at the top of Table II and the variation with irradiation is shown in Fig. 2. The variation for natural uranium fuel is small and not illustrated. The variation of the heat rating is accommo dated by the continuous on-power fuelling with relatively small fuel bundles. Due to flux variations in the reactor it is likely to prove most satisfactory to allow most of the natural and enriched uranium bundles to occupy two positions each during irradiation. If their irradiation is to 2.4 n/kb then the thorium bundles moved with them could, if desired, be conveniently changed in position four times during the irradiation to 6.0 n/kb. It is suggested that for the first stage of their irradiation when their power output is low and the net neutron absorption high, the thorium bundles could occupy special positions from which they could be easily removed temporarily to provide the reactor with an adjustable load to override a transient excess of Xenon-135 poison brought in by a power reduction. The high heat ratings proposed make it necessary to limit the diameter of the oxide fuel rods in order to keep the / centre maximum /Xd0 to an acceptable level, that is perhaps Jsheath 50 W/cm for U02 and 60 W/cm for Th02- The following illustra- ive table,(Table III),is derived using the approximate relation d2 - 16/\de/rp where r is the heat rating in W/g (or kW/kg) and p the density 3 in g(U or T)/cm . Typically the density of U02 is 10.5 g/cm2 3 2 2 so p = 9.2 5 g/cm and for Th02 of 9.5 g/cm p = 8.35 g/cm . Also given in the table is the surface heat flux (rpd/4) at the oxide surface which is slightly higher than that of the sheath to the coolant. TABLE II COST COMPARISONS FOR FUELLING REFERENCE CANDU REACTOR • All for 7 x 1013 n/cm2/s Fuel Cycle Valubreeder Natural Uranium U-233 + Thorium Enriched Uranium BOUT reference Th Enr.U N at.U Th "U-233" Enr.U Nat.U { Case 2 Case 21 Case 5 Case 2 Case 14 Case 22 Case 5 Ratings Power rating iPeak.kW/kg 49.2 59.5 25.2 49.2 2697.0 56.0 25.2 at 7 x iol; n/cm2/s Av. kW/kg 35.93 45.76 24.07 35.93 1263.38 38 .8 23.28 Burn-up MWd/kg 35.64 18.16 9.55 35.64 626.67 23.10 13.86 Irradiation n/kb 6.0 2.4 2.4 6.0 3.0 3.6 3.6 Irradn time t,full power yr. 2.72 1.09 1.09 2.72 1.36 1.69 1.69 Init.Fissile <- x g/kgU 11 - - ,(25) 25.6 10 - Content g fiss./kg 0.0 18.11 7.11 0.0l(23) 786.6 17 .11 7.11 Fissile Value (V: $/kg 0.0 97.73 16.0 0.0 11200.0 89.54 16.0 Relative feed rate atom 1.0 3.125 - 1.0 0.031 0.3 0.7 Rel.in-reactor inv. atom 0.8 1.0 - 1.0 0.0155 0.3 0 .7 Residual recoverable fissile g/kg 16.27 3.30 2.73 16.27 115.4 3.20 2.93 Credit (Cr) $/kg 211.506 33.0 27.43 211.506 1500.56 31.98 29 .29 Credit - Value $/kg 211.506 -64.73 11.34 211.506 -9699.44 -57.56 13.29 Fabrication Cost (F) $/kg 30.0 20.0 20.0 30.0 30.0 20 20 Extraction Cost (Ex) $/kg 20.0 15.0 15.0 20.0 20.0 15 15 Burn-up total (B) MWd 92.39/kgTh 9.55/kgU 55.0 7/kgTh 16~ TvkgU $/k h $/k Fuelling Cost Components f „ mill/kWh $/kgU mill/kWh $/kgXh min/kWh ?V , mill/kWh supplied supplied supplied Fissile Value "305.4 0.459 16.0* 0.233* 347.2 0.876 38.1 0.318 Gross Credit Cr.314.5 Cr.0.473 Cr27.34 Cr.0.398 Cr258.0 Cr 0.6 51 :r.30 .1 Cr.0.251 Credit - Value Cr. 9.1 Cr,0.0136 Cell.34 Cr.0.165 89.2 0.225 8.0 0.066 Fabrication 92.5 0.139 20.0* 0.291* 30.9 0.078 20.0 0.167 Processing 66.9 0.100 15.0 0.218 20.6 0.052 15.0 0.125 Net 150.3 0.226 23.66 0.344 140.7 0.355 42.96 0. 359 Inventory Charges 19.25 0.029 1.56* 0.023* 22.2 0.056 3.78 0.032 Interest 27.2 0.041 0.71 0.010 27.0 0.068 1.17 0.010 Total 196.8 0.296 25.93 0.377 189,9 0.479 47.91 r l, r Provided 1.0594 1 .0779 1.0495 1 0735 r Required 1.0593 1 .0779 1.0488 1 0715 *ljo reprocessing $/kgU mi ll/kh'h 37. 66 0. 546 - 10 - 70 60 kW U kg 50 Th 40 30 20 0.4 0.8 1.2 1.6 2.0 2.4 n/kb U 1 2 3 4 5 6 n/kb Th Fig. 2 Variation of heat output with irradiation all for 7 x 10l3n/cm2/s -11 - TABLE III Maximum Diameter for Given Ratings Given Ratin 9 <* 1Arf e W/nm 60 60 50 50 Power r kW/kg(U,Th) 50 60 60 70 3 Density P g(U3Th) /em 8. 35 8. 35 9. 25 9. 25 Derived Oxide diameter d mm IS. 2 12. 8 12. 0 11. 1 Oxide surface z heat flux W/am 158 173 167 180 For the 103.5 mm (4.07 in) I.D. pressure tubes in the larger CANDU reactors a 37 element fuel bundle typically would have o-ide pellets of diameter 13 mm. The standard fabrication cost assignments of $20/kgU excluding the basic U cost, and of $30/kgTh including the thorium are certainly low for current practice for. rods of these limited diameters but when production is on a sufficient scale to be more fully automated these do not seem impossible tarqets m 1967 U.S. dollar values. The processing cost assignments fall in the ranges used by several estimators for operations at an optimum level. The values assigned to enriched uranium are the base costs published on 29 November 1967 in the USA Federal Register These correspond to diffusion plant tails at 0.2% U-235 and a separative work charge of $26/kg unit. $13/g U-233 is the guaranteed purchase price set by the UGAEC in November 1967. $10/g fissile Pu is slightly above the USAEC guaranteed purchase price of $9.2 8/g. The difference has some justification but should not be considered important The value is a rounded mean that simplifies arithmetic. -12 - It will be seen from Table II that the valubreeder cycle just barely justifies that name. The excess of credit over the initial value is small. The excess is, however, very sensitive to the reactor assumed as the reference. With the improvement of zirconium alloys allowing thinner tubes it is expected that in large reactors the natural uranium burn-up will exceed the assigned level of 9.55 MWd/kgU. Such an improvement in the reference reactor would result in a comfortable margin of credit over initial value. This may be verified from Table IV which presents a wider range of calculated cycles on the basis of the BOUT method of evalua tion . 7. FURTHER GENERAL DISCUSSION The choices of irradiation level, the ratio of thorium to uranium and the enrichment level were made from a preliminary investigation in which rather too high values for a ^(U-238), see Appendix III, were used. Two methods of e^-' enrichment were postulated, namely purchase of U-235 at $ll/g and toll enrichment. The effect of the lower cost of the toll enrichment was very marked as may be seen from Table IV and Figs. 3A and 3B. Note these evaluations were made omitting inven tory and interest charges. Irradiation levels of 2.0, 2.4, 2.8 and 3.2 n/kb were evaluated and it appeared that the cost reduction between 2.0 and 2.4 n/kb was significant. Beyond that, however, there was little gain and the higher enrichment needed for a given reactivity led to excessively high initial heat ratings. Previous investigations of thorium levels of 20 to 30% indicated some cost reduction for the higher levels so the 4:5 Th:U atom ratio was adopted, i.e. 44.4% Th. At an irradiation level of 2.0 n/kb for the uranium it was found that 1:1 Th:U ratio gave no significant cost change. Several cycles using enriched uranium without thorium were evaluated for comparison. It became clear that the reduced plutonium credit and increased neutron losses to fission products limited optimum irradiations to less than 4 n/kb. For such levels it was clearly possible to use a combination of natural and enriched fuel without any significant cost penalty and a practical gain from the lower fabricating cost of natural uranium not explicitly evaluated. This led to the cycles illustrated in Table I and Fig. 1 as not far from the optimum. The cycles using U-233 may be criticized for the very low fabrication and reprocessing costs assigned to the separated U-233. It seems desirable to limit the irradiation of the - 13 - 0.7 y^8.0 5 .^MWd/kgU 3 *L EACTO R tr S*9.0 0.6 3, t <_j ^ or 0.5 —TOTAL — " 11.0 UJ NET a: Z FUELLIN G 0* 12.0 COST e mill/kW h j£ —^3.0 NO INVEN TORY > 14 .0 CHARG T ^ •^Tjs^s^ 2.8 n/kb 1" ->f 0.2 - 1 VALUBREEDER r " o h- Fig. 3A CANDU fuelling cost comparisons extra U-235 toy toll enrichment 0.7 >/Vo NIUM | A^X MWdAgU < _) •PJS 0.6 — ^/-9.0 ^ _j TLR A 0.5 ._. .._ __ ' -— ._.. _ — — - FUELLIN G RF A __ COST _ 0.4 , 0 w ^< ! mill/ttWh '"' NO INVENTORY VALUBREEDER 1 u 1 CHARGE ^-"' u. ^2.8n/kb 1 0.3 ^ I i j 3.2n/kb •' or. i 1 h - ° u i < ! a: 1 REEDE R CD j 1 ! 0.1 - - -\- J ! i i | i REFEREN C FO R VAL U 1 ! .00 I -01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 OVERALL FUEL REACTIVITY [^epl Av. Fig. 3B CANDU fuelling cost comparisons extra U-235 at $ll/g. TABLE IV VALUBREEDER FUELLING COSTS WITHOUT INVENTORY CHARGES (PRELIMINARY VALUES) Fuel Costs (C) Fuel in tu 800 o 2.4 1.0416 >1.055 0,.160 2 0 .03883 0.04947 .1990 .2097 0.3288 800 10 2.4 1.0493 1.0549 0 .1897 0 .04616 0.04805 .2359 .2377 0.3579 800 1] 2.4 1.05S5 1.0544 0 .2174 0 .05307 0.04669 .2705 .2641 4340 (1.055) 0 .210 398 I 800 9 2.0 1.0560 0..240 7 0,,0589 4 0.05788 .2996 .2986 4380 800 10 2.0 1.0645 0..273 6 0.,0670 9 0.05614 .3407 .3298 4318 800 11 2.0 1.0724 0,.304 8 0,,0747 8 0.05450 .3797 .3593 0.5226 (1.055) 0..23 7 0.432 800 S 2.8 80C 10 2.8 1.0354 0 .1295 0 .0311 0.04222 .1606 .1717 0.2361 COO 11 2.8 1.0420 0,.155 0 0,,037 4 0.04107 .1924 .1961 0.3191 (1.055) 0 .207 0.330 800 10 3.2 POO 11 3.2 1.0288 0 .1075 0 .0254 0.03681 .1329 .1443 0.2545 (1.055) 0..21 0 0.3J COO JO 2.0 1.0426 0..194 5 0..047 0 0.05122 .2415 .2957 0.3844 1.1 2.0 1.0502 0 .2251 0 .0546 0.04985 .2797 .2750 0.4243 (1.055) 0..24 5 0.450 - 15 - separated U-233 because of the loss of neutrons to fission products and to any separate sheathing. On the other hand there are many reactor physics complexities in the use of separate spike fuel, some of which are advantageous. No detail scheme has been selected and the possible range of costs must be considered rather wider in this cycle. As shown in the table below, the total supply of natural uranium to the enrichment plant for the valubreeder cycle is much the same as for a CANDU natural uranium cycle with no reprocessing. This follows rather obviously from the consideration that the valubreeder cycle involves no recycle but takes credit for the spent fuel. It therefore represents a first cycle and cannot derive much more power at that stage. The U-2 33 product does, however, have higher value than plutonium for continued recycle and with such recycle the total yield of energy from a given supply of uranium is greatly increased. For the standard valu breeder case the natural uranium supply required is 3.153 kg/kg enriched U (x = llg/kg), the energy yield per kgU is from Table II 92.3907/3.125 = 29.565 MWd or 29.565/3.153 = 9.377 MWd/kg Nat.U. TABLE V Output per kg Nat-U supplied Residual Fue I Cycle Energy separable Credit fissi le MWd/kgNat.U g. fiss./kgNat. U $/kgNat. U Valubreeder ,1.045 Pu = a* = 9 . 38 $10-46}&S1 9 x 11 g; 2. 4 n/kb 1.651 U-233 Natural Uranium 9. 55 2.73 Pu . $27.3 8. NEAR TERM APPLICATIONS Any utility operating a CANDU type power reactor is likely to find in the near future that a progressive adaptation of the fuel to a valubreeder cycle would be attractive. Those with PHW coolant would especially benefit if it is practicable to allow an increase in the power rating of at least some of the fuel channels, otherwise the economic benefit will be delayed. - 16 - The change to a valubreeder cycle could be part of a program leading to a considerable stretch in the power capacity of the reactor. For the BLW coolant the main advantage would come from the improved neutron economy due to the higher effective "density" of the fuel leading to higher burn-up and longer intervals between fuelling operations. For new reactors some of the other advantages such as the possibility of the thorium fuel acting initially as a removable load deserves some consideration. The higher effec tive "density" of the fuel may also simplify the coolant circuits in the safety provisions against loss of coolant. 9. LONG TERM APPLICATIONS The valubreeder cycle appears to make possible immediately the engineering design of reactors for very large power complexes such as have been suggested for water desalina tion and agro-industrial processes. The essential character istic that makes this possible is the expectation of long term competitivity of the fuel cycle as the markets change. Such large complexes help to establish the scale of operations required to lower the fuel fabrication and reprocessing costs. Also for such large capacities the specific capital cost of heavy water reactors promises to be not significantly greater than for other types of reactor. Still further in time with more technical development it should prove practicable to retain the use of thorium and probably natural uranium but substitute for the enrichment or separate fissile material another means of providing the extra neutrons required. The incentive to do this may come from the desire to get away from problems of load-following and short shut-downs introduced by the transient xenon fission product poison. Several proposals have received some consideration exploiting the self shielding of specially compact reactor cores, or the use of small fast-fission cores or the production of neutrons by electrical means from accelerated ion beams and heavy nuclei or even possibly of a controlled nuclear fusion reaction. Neutrons produced in these ways are liable to cost more but convenience of operation of a whole complex of reactors could outweigh the extra cost of the small fraction of the neutrons produced by such means. - 17 - ACKNOWLEDGEMENTS Many colleagues have assisted in the formulation of this presentation by discussions and exchanges of memoranda. I am particularly indebted to E. Critoph and M.F. Duret. I also wish to thank M.F. Duret, M.J. Halsall and W.A. Kelly for the computations using the BOUT program. REFERENCES W.B. Lewis "How much of the Rocks and the Oceans for Power? Exploiting the Uranium-Thorium Fission Cycle" DM-72, AECL-1916, April 1964. J.L. Gray, W.B. Lewis and L.R. Haywood "CANDU Reactors to 1980 and in the Long Term" AECL-2483, Paper 34 World Power Conference, Tokyo, October 1966. W.B. Lewis "Some Economic Aspects of Nuclear Fuel Cycles" AECL-203, Paper P/4, First United Nations Conference on the Peaceful Uses of Atomic Energy, Proceedings 3_, 3, 1955 W.B. Lewis "Fuelling High Conversion Ratio Reactors" DL-58, AECL-1911, August 1963. W.B. Lewis "Outlook for Heavy Water Reactors" AECL-2947 Paper SM 9 9/3 7, IAEA Symposium on Heavy Water Power Reactors, Proceedings p.545, September 1967. M.J. Halsall,"BOUT Program for Integrating the Burn-up Equations for Thorium and Uranium Fuels,"AECL-2693, 1967. - IS - Appendix I FUELLING COST EVALUATION Starting from the familiar expression for fuelling cost for natural uranium CANDU reactors with plutonium credit (see e.g. Some Economic Aspects of Nuclear Fuel Cycles, AECL-203, Paper P/4, 1955 Geneva Conference; How much of the Rocks and the Oceans for Power? Exploiting the Uranium-Thorium Fission Cycle, AECL-1916, 1964) c = P + Pa* - Cr - Ex (1) 24Be 8766ure 24Be(l+i)n Fuel Inventory Credit Supply Charge Note the second term is correctly written for a* the effective inventory annual charge rate all u the station utilization expressed as e the efficiency of thermal to electrical conversion fractions and r the fuel rating in MW(t)/kg (U or Th) c is in mill/ekWh if P, Cr and Ex are in $/kg (U,T) and B is in MWd/kg (U,T) Because we are considering continuously fuelled reactors in an equilibrium cycle and revenue from the sale of power is also effectively continuous it is convenient to refer all costs to the mid-point of the irradiation for individual fuel bundles . (One result is that a* becomes a/2 when a is the annual charge rate on inventory, expressed as a fraction). The present worth factor l/(l+i) for the credit on the two fuels uranium H-) r.nd - 19 - Appendix I and thorium (T) is evaluated for n = 0.5 + t /2u; n = 0.75 + t_/2u years where t is the irradiation time in full-power years and the added constants are the delays before processing. The delay is longer for thorium to allow Pa-233 to decay to U-233. Because of the extra assumptions needed for the rates of interest and inventory charges it is convenient to rearrange (1) writing l/(l+i) = 1 - ni. This approximation represents a slight increase in the fuelling cost but since ni is small the increase is negligible. We then have 1 /P + Ex - Cr L Pa* , Cr - Ex .1 .„. C = 2 _ | __ + ______+ _ niJ. .... (2) Equation (2) may be further developed for the two fuels U and T with different irradiation levels w and _• n/kb. Note that P = V + F _ i.e. the cost per kg of uranium or thorium LJ^_I_ IJ/J. U/_. fuel is written as the value V per kg (U or T) and the fabrication cost F per kg (U or T). Also BTT = rTTtTT x 365.->5- B_ - r„r.r, x 365.25 (3) U U U 1 x „' Ultimately we vri.l.l express c in cerms that relate to a feed of 1 kg thorium tc the reactor but it is slightly easier at first to develop (?) in terms relating tc 1 kg uranium, either in or fed to the reactor, In the special selected cycle there are 800 g Th per kalj in the reactor, so for this case _ 20 - Appendix I 1 ((Py + EXy - C^) + 0.8 (a)u/aJir)(PT + ExT - CrT) c = 24e } B + 0.8(OJ /U) ) B, TUT v UTT' T' T (Py + 0.8PT)a* + 365.25u(rc + 0.8rT) iCCry - EXy)(0.5 + ty/2u) + 0.8(o)uA)T)i(CrT - ExT)(0.75 + tT/2u)j By + 0. 8(0^/0^) BT To simplify this expression we may use equation (3) to write 365.25 {ru + 0. 8rT) = (By + 0.8(^/^)8^,)/^ Without rewriting equation (4) we may conveniently at this point convert it to a feed of 1 kg thorium, and thus write 1 8u P + EX Cr c = .. . .a ^ R , i (V°- U^ U U " U> 24e[(o)T/0.8u)y)By + BTJ ( [(P /0.8) + P ] at + (PT + ExT - CrT) + —° ^_^ 1 + (a)T/0.8wu)i(Cru - EXy)(0.5 + ty/2u) + i(CrT - ExT)(0.75 + tT/2u)| It is this relation (5) with the further expansion of P = V + that has been used. Different irradiation levels to have been evaluated but for the finally selected example to = 2.4 n/kb, to = 6.0 n/kb so O /0.8O3 )= 3.125. - 21 - Appendix I For the interest and inventory rates the assigned values are a/u = 0.08, u = 0.9 and. i = 0.055. For the chosen neutron flux of 7 x 1013 n/cmz/sec and the assigned values of w we find .t_ = 2.1ir,D yr and trT = 1.08,c yr. and T 161B U. 6 5 • i(0.5 + t /2u) = .055(1.1036) = 0.0607 and i(0.75 + tT/2u) = .055(2.259) = 0.1242. Equation (5) becomes for this case ! c - 3 125 Ex Cr + Ex Cr 24e[3.125B0+BTJ { ' + 0.1358 (PU+0.8PT) + 0.1897 (Cr -Ex^) + 0.1242 (CrT-ExT)| - 22 - Appendix II Appropriate value of (1 + B2M2)/f In the simple one point model for the neutron balance the basic relation for criticality is 1 + B2M2 = nepf (1) The BOUT programme is based on such a one point model for burn-up changes in thorium and uranium fuels. By more elaborate programmes such as LATREP it is concluded that it is practical to achieve a burn-up of 9.5 MWd/kg, nat.U. The nearest corresponding tabulated point on the BOUT program for Nat.U. is 2.4 n/kb and 9.551 MWd/kgU. For this nep is also tabulated as 1.077886. Appropriate parameter values in eqn.(l) are 1 + B2M2 = 1.024; f = 0.95, giving [1 + B2M2]/f = 1.0779 This is taken as the reference and the value of f appropriate to valubreeder fuel is calculated assigning xz v, 4.u • n n^rr x. • TO. Z(N.INTF/W) f sheathing = 0.005 proportional to n^.TWZK/u) f structure = 0.045 proportional to y /•„ TN'TA/^) where N is the relative number of fuel atoms for which values of the integrated fissions INT.F, absorptions INT.A and excess neutrons INT(Y-A) per atom for an irradiation co appear in the BOUT tables. Z represents summation over all the fuel atoms involved. ZN.INT(Y-A) ^ . 1 + B2M2 Then ENINT A + X = n£P = f .005E (N .INT F/u>) + . 045 = 1.024 1 + Ref. 0.951 (N . INTA/o))/Re ^ when Ref. stands for the corresponding quantity in the reference design. (Appendix II) - 23 - On reduction this becomes 0.005 ^ INTF/0 ) + . j- 0.005 ""-'is + 0.045-1 1 + B2M2 = 1.024 [L + 0.95£(N.INTA/u))/9.2879lJ *•• (2) Since [I(N INT F)/u>] = -1;0! * it" ^l^16 =v 4.1500 2.4 x 0.1388 Ref. 2 73224] and [I(N INT A)/o,]^ = 2,^""L ^W " " TM = 10.2487 - 0.96079 = 9.28791 from the BOUT tables. The correction term in the last equation is applied to correct for an artificiality in the BOUT neutron balance where the absorption in natural uranium is increased about 10% to simulate the resonance absorption. The 180° C. thermal absorption cross section of U-238 is 2.73 barn. Similar 2 24 corrections have to be applied to enriched uranium absorption and to the thorium absorption (n, , = 7.5 b). r thermal 1 + B2M2 The appropriate value of •= for the valubreeder fuel is thus calculated from equation (2) from the BOUT tables. The value of 1 + B2M2 has been assumed constant although it is reduced as f increases due to the shortening of the diffusion length. The value of [1 + B2M2]/f for the valubreeder compared With natural uranium needs a further correction in the opposite direction or upward because the flux depression in the fuel is - 24 - (Appendix 133 greater and consequently the relative flux, and neutron absorption in the pressure tubes will be raised. - 25 - APPENDIX III Effective cross-section for U-238 in BOUT program The BOUT program is based essentially on a credit and debit balance of thermal neutrons. The capture of neutrons in the resonance range of energies by U-238 is simulated by assigning an augmented "effective" thermal cross-section. It is satisfactory for fuels close to natural uranium in composition because the yield of fast neutrons and therefore of resonance neutrons remains substantially constant relative to the thermal neutron density through out the irradiation. This is no longer true at the level of enrichment ~ 1.8% U-2 35 used in the valubreeder. The augmented effective cross-section has therefore been adjusted to fall with irradiation appropriately. A satisfactory fit was obtained for Cases 21, 2 2 and 2 3 by a two stage approximation to an assumption that the resonance capture and escape probabilities would remain constant throughout the irradiation. Another consequence of the changing "effective" cross- section of U-238 has already been applied in Appendix II where the estimation of an effective value of the thermal utilization f had to be made using only the true thermal cross-section, both for the natural uranium reference fuel and for the enriched uranium. For the natural uranium BOUT Case 5 of 7 February 196 8 a8 „_ = 3.70 b. For 180°C thermal neutrons, Westcott's compilation AECL-1101, Table VI, gives g(U-238) = 1.0045 and Table A III gives - 26 - (App.lII) a0 = 2.72 b. Hence g.a = 2.73 . Hence a - ga0 = 0.96776b, 1 P By the BOUT formulation f ~ )| = (ag^ - go0)u_238 hence from the initial value of the yield cross-section Y for the assigned number N of U-238 atoms from Case 5 p = 0.9138 and (1 - p)/p = 0.094291. From the two stage approximation the following values for a8 „„ were assigned for Cases 21, 22, 23 x a „, Case 21 11 5.22 - 0.40OJ b Case 22 10 5.08 - 0.355oa b Case 23 9 4.94 - 0.32OJ b where w is the irradiation in n/kb. The change in cross-section had to be made in steps at co = 0.2, 0.6, 1.0 .... 2.2, 2.6 n/kb. The values of oo _„ calculated from 8eff 9 4291 a = 2.73 + ?-°n n . ™3L1 x 1000 seff 22it 1000 - x co were then compared with the supplied values, and considered a reasonably satisfactory fit. - 27 - /APPENDIX IV BOUT INPUT DATA 1 March, 1968 Flux = 7.00000 + 13 N/Sq.CM./SEC. TN = 1.80000 + 02 deg.c. R = .070000 Westcott Epithermal Factor ALPHA = 50.000 Pu-240 Shielding Factor FFR = .05000 Fast Fission Ratio CROSS SECTIONS INPUT NO. For Case 21 TH232C 10.00 PA2 33 129.39 U2 33A 639.70 U234 153.93 U235A 654.44 18.33690 U236 39, 29 NP237 241. 27 U238C 5, 22 981.66310 NP239 65. 00 PU239A 1521 93 PU240 1150 85 PII241 A 1645.54 PU242 135.37 AM241 916. 99 AM243 220. 61 U233F 585. 06 U235F 549. 72 PU239F 1027 96 PU241F 1220 68 U8 N2N .015 TH232F .137 ADDITIONAL CROSS SECTION DATA U238F .550 F.P.I 50.00 NP238 1600.0 CM244 87.9 F.P.2 300.00 PU238 499.7 NP238F 1600.0 F.P. 3 800.00 AM242 8500.0 PU238F 19.2 XE135 3400000 CM2 42 20.0 AM242F 6800.0 RH105 21000 CM243 1400.0 CM243F 690.0 HALF-LIVES IN DAYS PA233 27.0000 NP239 2.3500 PU241 4820.0000 XE135 .3833 RH105 1.5000 CM242 163.0000 CM243 11688.0000 CM244 6611.0000 NP238 2.1000 F.P.I. F.P.2. F.P.3. SM ETC. XE135 RH105 Y3 5.0179 -01 1.5362 -01 3.1134 -03 1.1490 -02 5.9500 -02 4.8000 -03 Y5 5.5816 -01 1.6183 -01 9.1029 -04 1.4680 -02 6.4500 -02 8.5000 -03 Y9 6.5413 -01 2.4405 -01 -1.8850 -02 2.4000 -02 7.1500 -02 5.5000 -02 Yl 6.7481 -01 2.2477 -01 -4.3445 -03 2.9200 -02 7.8000 -02 6.2000 -02 Y8 6.6033 -01 2.7891 -01 -2.0085 -02 2.9520 -02 6.2000 -02 3.7000 -02 NU3 = 2.4940 NU5 = 2.4300 NU9 = 2.8710 NU1 = 2.9690 NU8 = 2.8010 E3 = 195.90 E5 = 199.10 E9 = 208.70 El = 215.20 E8 = 207.50 Additional copies of this document may be obtained from Scientific Document Distribution Office Atomic Energy of Canada Limited Chalk River, Ontario, Canada Price - $1.00 per copy 2130-68