REACTOR PHYSICS AND FUEL-CYCLE ANALYSES A. M. PERRY and H. F. BAUMAN Oak Ridge National Laboratory Oak Ridge, Tennessee 37830 Received August 4, 1969 Revised October 9, 1969 As presently conceived at Oak Ridge National Laboratory and described in this issue, the single- fluid Molten-Salt Breeder Reactor, operating on the “2Th-P3U fuel cycle and based on a veference design, has a breeding rvatio of ~1.06, specific fissile inventory of 1.5 kg/MW(e), a fuel doubling time of ~20 years, and fuel cycle costs of ~0.7 mill/kWh(e). Start-up may be accomplished with either enrviched uranium orv plutonium, with little effect on fuel cost; the breeding ratio, averaged over reactor life, is reduced 0.01 to 0.02 relative to the equilibrium cycle. Operated as a converter, with limited chemical processing, the veacltor may have a conversion ratio in the vange 0.8 to 0.9 with fuel cycle costs of 0.7 to 0.9 mill/kWh(e). INTRODUCTION One of the most important aspects of the Molten-Salt Reactor (MSR) concept is that it is well suited for breeding with low fuel-cycle costs, and it does so in a thermal reactor operating on the ***Th-?**U fuel cycle. This is true not primar- ily because of any unique nuclear characteristics, for the reactor is similar to other thermal reac- tors in terms of attainable fuel-moderator ratios, the unavoidable presence of certain parasitic neu- tron absorbers, and reliance on a fertile blanket to reduce neutron losses by leakage to an accept- ably low level for breeding. Indeed, the concept might be thought to have some a priori disadvan- tage, because a substantial fraction of the fissile material is invested in the heat transfer circuit and elsewhere outside the reactor core. The pe- culiar suitability of the molten-salt reactor for 208 NYJCLEAR APPLICATIONS & TECHNOLOGY KEYWORDS: molten-salt re- actors, fuels, economics, op- eration, breeding, thorium-232, uranium-233, performance MSBR, fuel cycle, cost, breed- ing ratio ’ economical thermal breeding stems rather from the practical possibility of continuous removal of fission-product wastes and ***Pa, and virtually ar- bitrary additions of uranium or thorium, without otherwise disturbing the fuel. This fundamental aspect of the molten-salt reactor, details of which are discussed in other papers of this series, has a profound effect on the relationship between neu- tron economy and fuel-cycle cost. The coinci- dence of good neutron economy with low fuel-cycle cost which characterizes the molten-salt reactor appears to be unique among thermal reactors and will be described more fully in this paper. GENERAL NUCLEAR CHARACTERISTICS The LiF/BeF; carrier salt used in the MSR concept is not by itself a very good moderator. Its moderating power is about half to two-thirds that of graphite (the exact value depending on the pro- portions of Li and Be in the salt), while its macro- scopic absorption cross section is an order of magnitude greater than that of graphite, even with the feed lithium enriched to 99.995% in the “Li isotope. (With this composition, <10% of the neu- tron absorptions in the salt occur in °Li; nearly half are in fluorine, and about a third in "Li.) It is evident, therefore, that an additional moderator is needed, and graphite is selected for this purpose because of its compatibility with the salt. There is only a weak connection between the fissile fuel concentration in the carrier salt and the heat transfer characteristics of the salt (aris- ing primarily from the influence of the thorium concentration on the physical properties of the salt), and as a consequence one has considerable latitude in selecting the uranium (and thorium) concentrations in the salt. Because the carrier salt itself constitutes a significant neutron poison, the fuel concentration in the salt must not be set VOL. 8 FEBRUARY 1970 at too low a level, but must be high enough for the fuel to compete favorably (for neutrons) with the lithium and the fluorine in the salt. On the other hand, it must not be too high, lest the inventory of fuel outside the reactor core become excessive. The optimum fuel concentration, typically ~0.2 mole% of UF, in the salt, or ~1 kg of uranium per cubic foot of salt, is interrelated with the neutron spectrum in the reactor, which is a function of the relative proportions of fuel salt and graphite mod- erator in the core. Too large a proportion of salt leads to an excessive fuel inventory and to a poorly thermalized neutron spectrum, with a re- duced neutron yield, n; too large a proportion of graphite leads to excessive neutron-absorption losses in the graphite. An optimum salt volume fraction is typically found to be ~13 to 15%. The proper balance of the above factors does, of course, depend in part on the power density in the reactor core, which may be selected almost independently of the power density in the remain- ing parts of the primary salt circuit. The maxi- mum power density in the core is limited by fast neutron damage to the graphite moderator, while the removal power density in the external power recovery circuit is limited primarily by heat transfer and pressure-drop considerations and by requirements for pipe flexibility in the piping runs between the reactor vessel and the heat exchang- ers. The necessity for maintaining a sufficiently high fuel concentration to suppress neutron losses in the carrier salt and in the moderator, together with the requirement for appreciable core size simply to generate the requisite amount of power, leads to the conclusion that thorium must be pres- ent in the core, not merely in a surrounding blan- ket. However, the question of how the thorium 1s to be incorporated in the core is crucial to the MSBR concept. One quickly recognizes several distinct possibilities, some much more desirable in principle than others, but full of implications with respect to reactor design and chemical pro- cessing. We have previously given serious consideration to a two-fluid reactor in which the fissile and fertile materials are carried in separate salt streams, the bred uranium being continuously stripped from the fertile stream by the fluoride volatility process. Blanket regions contain only the fertile salt, while the core contains both fis- sile and fertile streams; these streams must be kept separate by a material with a low-neutron cross section, that is, by the graphite moderator itself. This approach appears to yield the best nuclear performance, owing primarily to a combi- nation of maximum blanket effectiveness and min- imum fuel inventory. It also exhibits attractive NUCLEAR APPLICATIONS & TECHNOLOGY VOL. 8 Perry and Bauman FUEL-CYCLE ANALYSES safety characteristics because expansion of the fuel salt, upon heating, removes fissile material from the core while leaving the thorium concen- tration unchanged. The concept does, however, involve important questions regarding the reli- ability of the graphite ‘‘plumbing’’ in the core, the adequate proof of which may require a good deal of time and testing. The present approach employs a single salt stream which contains both the fissile and the fer- tile materials. This concept represents a modest extrapolation of the technology already demon- strated in the MSRE. A central feature of the concept is the manner in which the single salt composition can be made to function adequately both in the core and in the blanket (or outer core) regions. This is done by the simple expedient of altering the salt volume fraction, making it con- siderably larger in the blanket than in the core. This undermoderation results in enhanced reso- nance capture of neutrons by thorium in the outer region, gives rise to a negative material buckling in the outer region, and should in principle cause a fairly rapid decrease in power density in the blanket as a function of distance from the core boundary. In practice, the distinction between the core and blanket regions is not as clear cut as this argument may suggest, but the idea works reasonably well. Figure 1 illustrates the power density distribution for our present reference de- sign based on the single-fluid concept. The en- hancement of resonance neutron capture in the blanket (or outer core) region is indicated by the ratio of neutron absorptions in ?**Th to those in 2831y, this ratio is about 1.0 in the core, and 1.3 in the blanket. The salt annulus, which is required to allow the periodic replacement of the modera- tor, functions as a part of the outer core region. The principal shortcoming of the single-fluid concept, of course, is the substantial investment of fissile material in the blanket region. This re- sults in a rather different compromise between breeding gain and specific inventory than in the two-fluid concept, leading both to reduced effec- tiveness of the blanket region and to an apprecia- ble increase in fuel inventory. Fortunately, this feature of the single-fluid reactor is partly offset by a reduction in neutron captures in the carrier salt, owing to the fact that a single carrier salt contains both fissile and fertile materials. The preceding qualitative discussion is in- tended to provide a general understanding of the interplay of factors affecting the selection of MSBR design parameters. These factors are of course quite numerous. They include core size, radial and axial blanket thickness, reflector thick- ness, salt volume fractions in the core and blan- ket regions, thorium and uranium concentrations, " FEBRUARY 1970 209 Perry and Bauman FUEL-CYCLE ANALYSES 70 o 60 w it = ] o~ - L 5 N\ = & X 50 \ © 2 = | P(r) = 5 40 \ = L. — = \ = 3 AN = \\ o 20 N < Ll (e 35 6 (>50&\ \ S 10 N ) \'7 0 4 0 50 100 150 200 250 300 RADIAL DISTANCE FROM CORE CENTERLINE (cm) Fig. 1. Radial power density and fast flux distribu- tions—single-fluid MSBR. chemical processing rates, and reactor power level. Because the interaction of all these factors is rather complex, and because of the need to identify optimum values of the design variables rather closely, we have found it convenient to make use of a comprehensive, automatic reactor optimization procedure for arriving at that combi- nation of design parameters that will produce, in some sense, the best attainable performance. The Reactor Optimization and Design code (ROD) is based on a gradient projection method for locating the extreme value of a specified figure of merit, which may be any desired function of the breeding ratio, the specific fuel inventory, various ele- ments of the fuel cycle and capital costs, or any other factors important to the designer. The computational procedure comprises multigroup (synthetic), two-dimensional diffusion-theory cal- culations of the neutron flux, an equilibrium fuel- cycle calculation which determines the critical fuel concentration and nuclide composition consis- tent with processing rates and other variables, and the gradient projection calculation for moving the cluster of independent variables in the direc- tion that most rapidly improves the figure of merit. The optimization may be constrained by limiting the allowed range of the independent vari- ables, or by selecting in advance the desired value 210 NUCLEAR APPLICATIONS & TECHNOLOGY (or a limiting value) of certain derived quantities, such as the maximum power density. The figure of merit used here in determining reactor design specifications is related to the ca- pability of a reactor type to conserve fuel supply in an expanding nuclear economy. For the special case of a linear increase in power generation, the total amount of natural uranium that must be mined up to the point when the system becomes self-sufficient (i.e., independent of any external supply of fissionable material) is proportional to the product of the doubling time and the specific fuel inventory. We have chosen to optimize our MSBR design primarily on the basis of a quantity which we call the fuel ‘“‘conservation coefficient,’’ defined as the breeding gain times the square of the specific power, which is equivalent to the in- verse of the product of the doubling time and the fuel specific inventory. Therefore, a maximum value of the conservation coefficient is sought in the optimization procedure. EQUILIBRIUM FUEL-CYCLE RESULTS The result of a reactor optimization calculation is a set of specifications for the optimum reactor configuration, subject to any imposed constraints, together with a complete description of its equi- librium fuel cycle. This description includes the multigroup neutron flux distributions, the result- ing power distribution, and the consistent set of concentrations of all nuclides present in the reac- tor. We have imposed constraints on maximum power density (i.e., minimum graphite life), on overall reactor vessel dimensions, and on chem- ical processing rates which we believe will result in near-minimum power cost. Although we lack specific information as to the cost of chemical processing as a function of fuel processing rate for the liquid-metal extraction process, it appears that processing equipment sizes and operating costs will be comparable with those for the fluoride-volatility/uranium-distillation process considered for the two-fluid reactor. We have therefore fixed the processing rates, listed in Table I, at values found to be essentially optimum in studies of the two-fluid reactor, with minor ad- justments appropriate to the extraction process. While subsequent improvements in processing cost estimates may suggest some change in opti- mum processing rate and some change in fuel cost estimates, we do not expect that these will result in any major revision in performance estimates for the reactor. The reference reactor configuration which re- sults from these and other (engineering) consider- ations is described by Bettis.' A summary of its nuclear design characteristics is given in Table L VOL. 8 FEBRUARY 1970 Perry and Bauman FUEL-CYCLE ANALYSES TABLE I Characteristics of the One-Fluid MSBR Reference Design B. Performance A. Description Identification CC93 Power, MW ((e) 1000 MW (th) 2250 Plant factor 0.8 Dimensions, ft Core zone 1 Height 13.0 Diameter 14.4 Region thicknesses Axial: Core zone 2 0.75 Plenum 0.25 Reflector 2.0 Radial: Core zone 2 1.25 Annulus 0.167 Reflector 2.5 Salt fractions Core zone 1 0.132 Core zone 2 0.37 Plena 0.85 Annulus 1.0 Reflector 0.01 Salt composition, mole% UF4 0.228 ThF4 12 BeFs 16 LiF 72 Processing cycle times for removal of poisons? 1. Kr and Xe; sec 20 2. Se, Nb, Mo, Tec, Ru, Rh, Pd, Ag, Sb, Te, Zr; sec 20 3. Pa; Cd, In, Sn; days 3 4, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd; days 50 5. Sr, Rb, Cs, Ba; year 5 6. Br, I; days 5 Conservation coefficient, [MW (th)/ kg]2 14.3 Breeding ratio 1.062 Yield, % per annum 3.18 Inventory, fissile, kg 1478 Specific power, MW(th)/kg 1.52 Doubling time, system, year 22 Peak damage flux, E >50 keV, n/ (cm2 sec) Core zone 1 3.2x10™ Reflector 4.2x10" Vessel 3.7x10™ Power density, W/ cm’ Average 22.2 Peak 65.2 Ratio 2.94 Fission power fractions by zone Core zone 1 0.765 Core zone 2 0.167 Annulus and plena 0.056 Reflector 0.012 apccording to our present flow sheet, Zr, Cd, In, and Sn will be removed on a 200-day cycle, and Br and I on a 50-day cycle. The additional poisoning, however, is negligible. A neutron balance for this case is given in Table I, in which the normalization is to one neutron absorbed in ?**U plus **U. Uncertainties in Neutron Cross Sections We have estimated the effect of uncertainties in neutron cross sections on the calculated perfor- NUCLEAR APPLICATIONS & TECHNOLOGY VOL. 8 mance of the MSBR. By far the most important effect is the uncertainty in the average value of 7 of 2**U in the MSBR spectrum, which leads to an uncertainty in the breeding ratio of +0.012. Un- certainties in the cross sections of other impor- tant MSR nuclides (such as F) make a relatively small contribution to the overall uncertainty in the breeding ratio, which is estimated to be +0.016. A detailed discussion of cross-section uncertainties is given in a report by Perry.* Equilibrium Fuel-Cycle Costs As stated before, the molten-salt breeder re- | actor exhibits unusually low fuel-cycle costs in combination with good breeding performance. This results primarily from the low specific fuel in- ventory and from a small but non-negligible ex- cess production of fuel, which results from the ability to process the fuel rapidly at what appears to be a very low unit cost. The inventory of fissile material in the reactor and chemical processing plant amounts to some 1480 kg, including ~100 kg each of **U and “*Pa; when valued at $13.00/g for ?**U and **Pa and $11.20/g for 2*°*U, this material is worth $19 mil- lion. With an effective annual inventory charge rate of 10%/year and a 0.8 plant factor, the fuel inventory thus contributes 0.27 mill/kWh(e) to the FEBRUARY 1970 , 211 Perry and Bauman FUEL-CYCLE ANALYSES TABLE II Neutron Balance, Single-Fluid MSBR Absorptions Fissions 2331 0.9239 0.8239 235 0.0761 0.0619 232Th 0.9853 0.0031 234 0.0817 0.0004 2:3Pa 0.0017 ° 0.0088 23TNp 0.0061 °Li 0.0049 "Li 0.0159 'Be 0.0071 (0.0046)2 Bp 0.0205 Graphite 0.0519 Fission products 0.0196 Leakage 0.0276 ne 2.2311 a(n,2n) reaction. fuel-cycle cost. The fuel salt, with a composition LiF/BeF:/ThF4 = 72/16/12 mole%, respectively, is estimated to be worth $3 million, including the thorium. At 10%/year, this contributes 0.04 mill/ kWh(e) to the fuel cycle cost. For a conversion ratio of 1.062, fuel production results in a reduc- tion of 0.09 mill/kWh(e) in the fuel cycle cost. The cost of thorium burnup, in contrast, is negli- gible [~0.002 mill/kWh(e)]. The chemical process for removal of fission products, which is under development for use with the single-fluid MSBR, involves the accumulation of rare-earth fission products in a portion of the salt stream in the liquid bismuth extraction tower. The concentration of rare-earth trifluorides in this salt is limited by solubility to ~0.7 mole%; it is presently planned to limit this concentration by discarding ~0.5 ft°/day of carrier salt having ~100 times as high a concentration of rare earths as the salt circulating in the reactor. The makeup of carrier salt (including ThF,) required to com- pensate for this discard thus contributes ~0.5 X $1846/ft> = $932/day to the fuel cost, i.e., 0.05 mill/kWh(e) at 0.8 plant factor. The cost of processing the fuel for removal of fission products and for isolation of ***Pa from the circulating salt stream is difficult to assess pre- cisely. Our tentative estimate of these costs, in- cluding both capital and operating expense, is ~0.3 mill/kWh(e), based on the rapid processing rates indicated in Table I.° In summary, therefore, we estimate that the equilibrium fuel-cycle cost will be ~0.7 mill/kWh(e), as shown in Table III, for a single-fluid MSBR of the reference design. 212 NUCLEAR APPLICATIONS & TECHNOLOGY EFFECT OF CHANGES IN REACTOR DESIGN PARAMETERS Although our computational procedure is de- signed to lead directly to the optimum combination of reactor parameters, it is nonetheless a matter of some interest to see how deviations of these parameters from their optimum values will affect the performance of the reactor. The influence of these parameters on reactor performance may be investigated by assigning specific perturbed val- ues to each parameter in turn, the others retain- ing their reference values, and performing the flux and equilibrium fuel-cycle calculations for the perturbed cases. In some instances, a se- lected subset of the unperturbed variables may be allowed to be reoptimized, using ROD, if there is reason to suppose that such reoptimization will partially compensate for any adverse effect of the perturbation. The effect of several specific de- partures from the reference 1000 MW(e) design given in Table I is discussed in the following paragraphs. Reactor Plant Size The effectiveness of the blanket (outer core) region depends very much on its thickness. Nor- mally, the blanket will contain a larger fraction of the salt inventory for a small than for a larger reactor. Thus, both the fuel specific power and the breeding gain, for an optimized reactor, in- crease as the reactor plant size is increased, as shown in Fig. 2. This is true when the reactors are compared at equal core life (the solid curves) or at equal average core power density (the dashed curves). A brief listing of dimensions and other parameters for 500, 1000, 2000, and 4000 MW(e) reactors is given in Table IV. TABLE III Equilibrium Fuel-Cycle Cost Cost Cost Element mills/kWhe) Fuel inventory?2 0.27 Salt inventorya 0.04 Salt makeup 0.05 Moderator replacement 0.10 Processing 0.30 Subtotal 0.76 Fuel production credit -0.09 Total fuel-cycle cost 0.67 a Inventory charge 10% per annum. VOL. 8 FEBRUARY 1970 —————— CONSTANT CORE LIFE g | = —=——CONSTANT RATIO OF REACTOR 40 POWER TO CORE VOLUME ———=G x 100 comman_ — -— 30 cC 5 —v, %/year | 20 L, years 3 ! 10 ! CONSERVATION COEFFICIENT INVENTORY, GAIN, YIELD, CORE LIFE I, kg/MW(e) | O 0 ] 2 3 4 5 REACTOR POWER [103 MW(e)] Fig. 2. Effect of power level on MSBR performance. Graphite Moderator Life The useful life of the graphite moderator is limited by radiation damage effects, caused by fast neutrons. As discussed by Eatherly,” we have for the present adopted a limiting fast-neutron fluence (E > 50 keV) corresponding to zero net graphite volume change at the end of exposure. Since the fast-neutron flux is almost entirely de- termined by the local power density (per unit vol- TABLE 1V Performance of Single-Fluid MSBR’s as a Function of Plant Size Reactor Power, MW(e) 500 1000 2000 4000 Core height, ft 9.44 | 11.0 17.44 | 23.0 Core diameter, ft 10.42 | 14.4 19.36 | 25.5 Salt specific volume, ft/ MW(e) 1.75 1.68 1.62 1.55 Fuel specific inventory, kg/ MW(e) 1.65 1.47 1.36 1.28 Peak power density, W/cm? | 62.2 65.2 66.1 65.9 Peak flux (> 50 keV), 10" n/ (cm? sec) 3.04 | 3.20 | 3.25 | 3.24 Core life, years at 0.8 PF 4.3 4.1 4.0 4.0 Leakage, n/ fissile absorption x 1000 | 3.89 2.44 1.53 0.96 Breeding ratio 1.043 1.065 1.076 1.083 Annual fuel yield, %/ year 1.99 3.34 4.28 4.95 Conservation coefficient 8.0 15.1 21.0 25.9 NUCLEAR APPLICATIONS & TECHNOLOGY VOL. 8 FEBRUARY 1970 Perry and Bauman FUEL-CYCLE ANALYSES ume of salt-plus-moderator), there is a nearly unique relationship between maximum core power density, plant utilization factor, and useful core life, for a specified maximum fluence. While one expects a higher power density to be accompanied by a reduced fuel inventory, there is in fact a power density above which increased neutron leakage losses and other associated losses in breeding gain more than offset the reduced inven- tory, and the fuel yield and the conservation coef- ficient then decrease. These trends are exhibited in Fig. 3, which shows breeding gain, specific in- ventory, fuel yield, and conservation coefficient as a function of core life. In this comparison, blan- ket, reflector, and plenum thicknesses were held constant, and the core size was specified. Only the salt volume fraction was reoptimized, and it changed very little. Thorium Concentration The thorium concentration in the fuel salt pri- marily influences the uranium inventory and the breeding ratio. For a reactor configuration very similar to our present reference design (but having a slightly lower estimate of the required external salt volume) we have examined the influ- ence of thorium concentration on reactor perfor- mance over the range 10 to 14 mole% ThF4 Cross sections were carefully computed for each region in each case and iteratively adjusted to allow for resultant changes in reactor configuration. In these calculations, core size, radial and axial blanket thicknesses, and core salt volume fraction were all subject to reoptimization. 2 7 \\ y 12 Ne 10 20 | I (x 10) = X y ’.: 8 Z 185 A gl—"\ = G (x 100) 23 D o 4 14 o 3 \ O Ll — L) — - > <>(E o L) 2 S REFERENCE DESIGN ] 0 10 2 3 4 5 6 7 8 GRAPHITE CORE LIFE (year) Fig. 3. Performance of 1000 MW(e) MSBR as a func- tion of core life (at 0.8 plant factor). 213 Perry and Bauman FUEL-CYCLE ANALYSES The basic interplay, of course, is between ris- ing breeding gain and rising inventory, as thorium and uranium concentrations are increased. Both the annual fuel yield (y) and the conservation co- efficient (CC) should exhibit a peak, when plotted as a function of thorium concentration, but the peaks will occur at different places because of the difference in weight assigned to the specific power. These trends are shown in Fig. 4. It may be seen that there is quite a broad maximum in the conservation coefficient in the vicinity of 12 mole% ThF 4e Salt Volume Fractions Core. In all of our calculations, the optimum salt volume fraction in the core has fallen in the range 12 to 15 vol%, with a carbon/fissile-uranium atom ratio close to 9000. As indicated earlier, the vol- ume fraction is rather closely determined by a balance between fuel inventory, degree of neutron moderation, and neutron absorptions in the mod- erator; for the reference design, the optimum salt fraction was 0.132. ‘Blanket. The volume fraction of salt in the blan- ket (outer core) is central to the whole concept of a single-fluid, 1000 MW(e) molten-salt breeder reactor. We have tested the effect of variations in salt fraction (in the radial blanket) under the spe- cial assumptions of constant overall salt volume and constant outer diameter of the blanket region. Results of these calculations show that a broad optimum exists in the range of 0.35 to 0.6 for the salt fraction. The choice of 0.37 for the reference reactor was initially selected to permit, if de- sired, the use of a randomly packed ball bed in the blanket. 8 18 o/ Z 6 g-J @ 3 ___________________-—-———-—-""" G (x 100) = o = > g 4 14 5 - y 8% 2 __—T 1 (x10) §% > 1.2 > (o o O | = L = = = 0.8 = J — w b ) 23‘+U 0.4 T v > 2 y 241 40 | / \\\\\ 239 \\ 0 0 1 2 3 4 OPERATING TIME — EQUIVALENT FULL-POWER YEARS Fig. 10. Plutonium isotope inventories—MSBR start-up - with PWR plutonium. NUCLEAR APPLICATIONS & TECHNOLOGY VOL. 8 FEBRUARY 1970 Perry and Bauman FUEL-CYCLE ANALYSES These features of the plutonium start-up are exhibited in Figs. 10, 11, and 12. The average breeding ratio, over a 30-year plant life at 0.8 plant factor, is reduced by ~0.008 relative to the equilibrium cycle. The present value of the fuel-cycle cost is actually decreased by ~0.04 mill/kWh(e) if one assigns to the fissile plutonium a value 7 that of enriched *U. OPERATION WITH LIMITED FUEL PROCESSING The combination of good breeding performance with low fuel-cycle cost, which is associated with economical processes for the rapid removal of fission products and protactinium, is an impor- tant feature of the molten-salt reactor concept. Nevertheless, quite satisfactory fuel costs can be achieved in the absence of fuel processing for re- moval of protactinium or fission products, al- though the reactor will of course not breed when operated in this fashion. In examining this alternate mode of operation, we postulate the occasional batch discard and re- placement of the entire inventory of carrier salt, including the thorium, but not including the ura- nium; the latter is to be recovered by fluoride volatility (as was done with the MSRE fuel salt) and recycled to the reactor. The removal of noble-gas fission products from the salt by gas sparging and of noble-metal fission products by 2.0 1.6 1.2 233 0.8 SYSTEM INVENTORIES (10° kg) Pu 234 — 235 0 4 8 12 16 20 OPERATING TIME — EQUIVALENT FULL-POWER YEARS 0.4 Fig. 11. Inventories of uranium isotopes and total plu- tonium for plutonium start-up of MSBR. 217 Perry and Bauman FUEL-CYCLE ANALYSES 2.0 1.3 — o 1.2 Pu PURCHASED (239 + 241) pd 0.9 /URANIUM SOLD (233 + 235) 0 0.8 0 4 8 12 16 20 OPERATING TIME — EQUIVALENT FULL-POWER YEARS — . N — — CONVERSION RATIO I o o] 1.0 CUMULATIVE AMOUNTS (103 kg) CONVERSION RATIO o Y ‘ Fig. 12, Cumulative purchases and sales of fissile ma- terial and conversion ratio MSBR with plutoni- um start-up, deposition and by escape to the off-gas system, as observed in the MSRE, are assumed to occur. An optimum salt discard rate exists, for which the cost of replacing the salt (and recovering ura- nium) is balanced against the fuel makeup cost, which depends on the conversion ratio and hence on the level of fission-product poisoning. In addi- tion, however, there is a minimum discard rate required to limit the concentration of rare-earth trifluorides in the circulating fuel salt to an ac- ceptable level (<1 mole%). This consideration per se will place a limit of ~10 years on the salt re- placement interval. We have investigated the trend in fuel-cycle costs, as a function of the salt replacement inter- val, for a molten-salt converter reactor which is defined in terms of its general nuclear character- istics, such as neutron leakage and fuel inventory, but whose engineering design has not been speci- fied in detail. We found the fuel costs to be rather insensitive to the salt replacement interval from 3 years to 8 or 10 years, with a broad minimum at O to 6 years. The conversion ratios ranged from 0.84 for a 4-year salt-replacement interval to 0.78 for a 10-year interval. We have not yet made any detailed estimates of costs for the fluorination plant and for the chem- ical treatment plant necessary to control the com- position of the salt over long periods of time. Allowing 0.1 mill/kWh(e) for this equipment and its operation, and 0.1 mill/kWh(e) for graphite replacement in the reactor core, we estimate the 218 NUCLEAR APPLICATIONS & TECHNOLOGY VOL. 8 fuel-cycle costs for the converter reactor, with a salt discard cycle, to be 0.7 to 0.8 mill/kWh(e). Compared with the MSBR, the principal cost dif- ferences are a saving of ~0.2 mill/kWh(e) in fuel processing, an increase of 0.2 to 0.3 mill/kWh(e) for fuel burnup, and possibly some reduction of fuel and salt inventory charges [<0.1 mill/kWh(e)]. Thus, the fuel-cycle cost for the converter re- actor, without chemical processing for removal of protactinium or of fission products, appears to be within 0.1 mill/kWh(e) of the cost for the breeder reactor. TEMPERATURE COEFFICIENTS OF REACTIVITY Expansion of the single fissile-fertile salt in the one-fluid reactor reduces the density of most of the absorbing materials in the same proportion, so that one might expect a very small prompt temperature coefficient of reactivity. The density coefficient of the salt is in fact very small. In addition to this, however, there is both a positive contribution to the salt-temperature coefficient associated with the shift in thermal-neutron spec- trum with increasing salt temperature, and a neg- ative contribution associated with the Doppler broadening of resonance capture lines in thorium. The latter predominates, resulting in a prompt negative coefficient of -2.4 X 107 6k/k/°C. The graphite moderator contributes a positive component to the overall temperature coefficient, attributable to an increase in the relative cross section of ?*U with increasing neutron tempera- ture. This results in an overall coefficient which is very small, though apparently negative, i.e., -0.5 X 107°/°C. The prompt negative salt coefficient will large- ly govern the response of the reactor for tran- sients whose periods are several seconds or less. The small overall coefficient will provide little inherent system response to impressed reactivity changes, and it will consequently be necessary to provide control rods to compensate any reactivity changes of intermediate duration. Long-term re- activity effects, such as those associated with the fuel cycle, are compensated by adjustment of the fuel concentration in the salt. SUMMARY AND CONCLUSION While a full economic optimization of the single-fluid molten-salt breeder reactor has not yet been undertaken, it is apparent that good breeding performance can be achieved in conjunc- tion with unusually low fuel-cycle costs, subject to the successful completion of chemical processing | developments now under way. That is, a breeding FEBRUARY 1970 ratio of >1.06, together with a specific fuel inven- tory of <1.5 kg/MW(e), will be attainable with fuel-cycle costs of ~0.7 mill/kWh(e). The asso- ciated fuel doubling time is ~20 years. The MSBR fuel cycle may be initiated either with enriched uranium or with plutonium dis- charged from light-water reactors. The reduction in breeding ratio, averaged over the life of the re- actor, is <0.02 and 0.01, respectively, for the uranium and plutonium start-up cases relative to the equilibrium case. The present value of the fuel-cycle cost is increased, relative to that for the equilibrium cycle, by ~0.02 mill/kWh(e) for the uranium-start-up case,while for the plutonium- start-up case the cost appears to be 0.04 mill/kWh less, based on a fissile plutonium value equal to % that of **°U. Development of the technology for molten-salt reactors themselves and for the associated chem- ical processes for removal of protactinium and fission products need not necessarily be carried out on precisely the same time schedule, since an economically attractive fuel cycle may be achieved with a salt-discard cycle, resulting in a conversion ratio of 0.8 to 0.9. A given reactor, operated initially in this way, could subsequently be operated as a breeder by the addition of ap- propriate processing equipment to the reactor plant. It is thus apparent that there is considerable latitude in the mode of operation of molten-salt reactors, with only small variations in fuel-cycle cost. We believe that this can facilitate the devel- NUCLEAR APPLICATIONS & TECHNOLOGY VOL. 8 FEBRUARY 1970 Perry and Bauman FUEL-CYCLE ANALYSES opment of the molten-salt reactor and of the asso- ciated chemical-processing technology on time schedules appropriate to each, and will encourage an orderly progress toward the achievement of an economical breeder reactor. ACKNOWLEDGMENTS The authors wish to acknowledge the contributions made by many of their colleagues to the work reported here, and in particular those made by R. S. Carlsmith, W. R. Cobb, E. H. Gift, and O. L. Smith, This research was sponsored by the U.S. Atomic Energy Commission under contract with the Union Carbide Corporation. REFERENCES 1. E. S. BETTIS and R. C. ROBERTSON, ‘‘The Design and Performance of a Single-Fluid MSBR,”’ Nucl. Appl. Tech., 8, 190 (1970). 2. A. M. PERRY, ‘“Influence of Neutron Data in the Design of Other Types of Power Reactors,”” ORNL-TM- 2157, Oak Ridge National Laboratory (March 8, 1968). 3. M. E. WHATLEY, L. E. McNEESE, W. L. CARTER, L. M. FERRIS, and E. L. NICHOLSON, ‘‘Engineering Development of the MSBR Fuel Recycle,”” Nucl. Appl. Tech., 8, 170 (1970), 4, E. P. EATHERLY and D. SCOTT, ‘Graphite and Xenon Behavior and Influence on MSBR Design,”’ Nucl. Appl. Tech., 8, 179 (1970). 5. W. R. GRIMES, ‘“Molten-Salt Reactor Chemistry,”’ Nucl. Appl. Tech., 8, 137 (1970). 219