- e, % oa T, N » o g Ll T e T, Y . _' 3 - L. ¥ "-I. 5 B o e S BT N 3 A 3 A ¥ iy s - 5 y ‘ ' e N h.' Ry - a2 o » - "--1.',-'1 S B .\‘"!!-_-r.__h' ' ¢ % o e R R R ot s % g ot ..'.'!-‘ \ ; I I I .- e ,,-’-.-':'__:"_ Tr . vy, T | k "f ;I 5 CENTRAL RESFARCH LIBRARY ' DOCUMENT COLLECTICN AEC RESEARCH AND DEVELOPMENT REPORT ori-1s10 Reactors-Research and Power R 3 4456 0349790 1 SOME ECONOMIC ASPECTS OF THORIUM BREEDER REACTORS H. C. Claiborne M. Tobias OAK TRIOGE NATIOCNAL LARCRATORY CENTRAL RESEARCH LIBRARY DOCUMENT COLLECTION LIBRARY LOAN COPY DO NOT TRANSFER TO ANOTHER PERSON If you wish someone else to see this document, send in name with document and the library will arrange a loan. OAK RIDGE NATIONAL LABORATORY OPERATED BY ; UNION CARBIDE NUCLEAR COMPANY A Division of Union Carbide and Carbon Corporation POST OFFICE BOX P - OAK RIDGE, TENNESSEE ORNL-‘f 0 Copy No. é‘ REACTOR EXPERIMENTAL ENGINEERING DIVISION J. A. Lane Director SOME ECONCMIC ASPECTS OF THORIUM BREEDER REACTORS by H. C. 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Laboratory n Lasboratory, Berkeley Laboratory, Livermore Ce Technical Information Service, Oak Mjdge Division of Research and Medieine, AEW, ORO TABLE OF CONTENTS List of Tables and Figures Acknowledgement SUMMARY INTRODUCTION TWO-REGION REACTORS Methods and Ccnditions Processing Cycle Times and Uranium Isotopes Nuclear Calculations Cost Estimation Reactor and Turbogenerator Plant Investment f Efficiency ¢ Operation and Maintenance ¢ Inventories Chemlcal Processing Feed Costs Results Major Process Variables Effect of Group-3 Poison Cross $é;tion.Variations Effect of External Power Density Variations Accuracy of the Two-Group Model and the Calculation of Breeding Ratio Accuracy of Cost Estimate ONE -REGION REACTORS Methods and Conditions i‘.i;fi SOV ,fiwfi&fiz‘ 1k 15 15 15 16 17 17 18 20 20 23 ol 4o 43 TABLE OF CONTENTS (Contd.) Fission Product Poisgns Isotope Conéentrations and Critical Equation Cost Estimation Results NOMENCLATURE LIST OF REFERENCES APPENDIX I - Constants Used in the Nuclear Calculations Page " 46 47 51 53 54 . - LIST OF TABLES Title Page I. Nuclear Power Plant Efficiencies 15 II. Typical Cost Brcakio.m znd Heutron Balances for Two-Region Reactors 27-28 I1T. Effect of Substantial Changes in the Nuclear Constants 29-30 Iv. Cost Breakdown and Neutron Balances for Several One-Region Reactors Near Optimum Conditions 49-50 LIST OF FIGURES 1. Schematic Flowsheet for a Two-Region Thorium Breeder Reactor 31 2. Effect of Power on Cost of Two-Region Reactor Plant 32 5. Effect of Steam Conditions on Turbogénerator Plant Efficiency 33 L, Effect of Steam Conditions on Power Plant Cost for a 300 Mw Plant | h 5 Effect of Blanket Thickness on Unlt Cost 55 6 Effect of Thorium Concentration on Breeding 36 T Effect of Group-3 Poisons on Unit Cost Breeding Ratio 5T 8 Effect of Blanket Uranium Concentration on Unit Cost 38 9 Effect of Group-3 Poison Cross Section on Unit Cost 359 10. Effect of Temperature on Unit Cost 4o 11. Effect of External Power Densities on Unit Cost 41 12. Effect of Process Cycle Time on Unit Cost 51 13. Effect of Process Cycle Time on Unit Cost 52 14. Effect of Process Cycle Time on Unit Cost 23 15. Effect of Thorium Concentration on Unit Cost 54 16. Effect of Reactor Size on Unit Cost and Breeding Ratio 55 ACKNOWLEDGEMENT The authors wish to express their appreciation for the veluable advice givén in the ‘course of this work by M. C. Edlund, under whose supervision this study was performed, R. B. Briggs, and D. E. Ferguson. Grateful acknowledgément ig made to T. B. Fowler for his able and extensive efforts in coding and supervising the ORACLE calculations. SUMMARY A study of the effects of geometrical and some operational variables on the economics and characteristics of thorium breeder-power reactors has been made as an aid in the selection of design criteria for the TBR program. No original effort was made to estimate plant investmefit costs or to introduce new concepts of reactbr technology. Plant investment was assumed constant for all systems studied under equal power and temfierature conditions. The state of technology and cost factors assumed were those‘reported by -Briggs(3) and Arnold et al(l). The effect on power cost of core radius, blanket thickness, blanket uranium and thorium concentrations, chemical pro- cessing cycle times, poisons and external power density have been investigated using a consistent method of calculation with a standardized set of nuclear constants and cost factors. All results are for a 3-reactor power.station delivering 375 Mw of electricity to a power grid. For both one- and two-region reactors, the unit cost of power is - rather insensitive to fairly large changes in nuclear parameters and process variables. This is a direct consequence of plant investment and other fi;ed charges representing nearly 80% of the power cogt. The results, based on opergting and maintenance costs for conventional power and chemical plants, indicate that a two-region reactor station could produce power for 6.2 mills/kwh with a fuel cost of 1.8 mills/kwh. Applying error limits to the items comprising the total cost, a cost range of 5.5 to 8.0 mills/kwh is obtained. | The cost of power from a one-reglon reactor station was about 0.9 mills/kfih (2.6 mills/kWh fuel cost) higher than for a comparable two-region system if the plant investment and other fixed charges are considered equal —— > for the two types. It is believed that the fixed charges will be somewhat smaller for the one-region reactor because of simpler comstruction and operation. The spproximate characteristics of the reactors required for pro- ducing power for the above costs are: Two-Region | One-Region Core diameter, ft 5 12 Blanket thickness, ft 2-1/4 | -- Core power, Mw 390 fi81 Blanket powver, Mw 91 - Core povwer density, Mw 210 19 Thorium conc:, gm/kiter - . . 1000 260 Blanket uranium conc., gm/kg Th 3 . ae- Core uranium conc., gm/kg D0 8.3 4.5 Core U-235 + U-233 conc., gm/kg D0 2.8 6.7 Core Thorex cycle, days 336 450 Blanket Thorex cycle, days 140 - Hydraulic separator cycle, days 1 - Average reactor temperature, °C 280 280 A comparison of the cost items in mills/kwh for near optimum one- end two-region reactors (assumes equal fixed costs) is shown below. Two-Region One-Region Plant investment (less chem. proc.) 3.7k 3.74 Fuel inventory 0.4k 0.84 D0 inventory ' 0.52 0.66 — " Two-Region One-Region Fixed chemical processing 0.76 | 0.76 Variable chemlcal processing 0.32 0.18 Operation and maintenance 0.75 | 0.75 Feed (DEO and Th) - 0.20 0.25 Uranium (233 and 235) credit 0.49 0.05 Net unit cost of power 6.2 7.1 From these results, it is apparent that the net unit cost of pover from the two-reglon reactor 1s nearly independent of the value of uranium since the fuel inventory charge and the breeding credit are approximately equal. This is not true for the one-region reactor, however. 1In that case, the breeding credit is small compared to the fuel inventory charge, so that any variation in the latter due to a change in the value of uranium will cause a corresponding change in the cost of power which is virtually uncompensated by the breeding credit. I -5- INTRODUCTION The feasibility and the technology of aqueous homogeneous reactors have been discussed elsewhere, most recently by Briggs(j). The presgnfi work is concerned with the results of detailed calculations of the effect of the major process variables on the power cost and characteristics of thorium breeder reactors in order to help gelect design criteria for the TBR. In addition, it was desirable to estimate the possible effect of errors in the nuclear parameters on the cost of power.* The different reactor systems were coupared on the basis of a _fixed amount of electrical power (125 Mw per reactor) delivered to a power grid since power is the main product. If power output were not constant, the effect of the process variables would be masked by the effect of power level, the most important factor in unit cost calculatioms. An electrical power output of 125 Mw was chosen as standard for one reactor or 375 Mw for a 3-reactor station. This is equivalént to 480.8 Mw of heat for a net station efficiency of 26%. The parameter studies, other than temperature, were made for an average reactor temperature of 280°¢. | At the present time, it is impossible to estimate the cost of electricity from nuclear power stations without a fairly large uncertainty. Nevertheless, a study such as this, based as it is upon stated cost factors and & consistent method of calculations, can be used to determine what is, and what is not, of relative economic importance and further provides a rational basis for the selection of most design criterisa. ¥ The ORACIE was used to perform the large number of required reactor calculations. ', v Trooeat meph R . - u.‘-’.’.‘;fi?’_l by e T fiéf‘ Lo ") - S e ey Tk el This report consisgts of two principal parts. The first part is concerned with the two-region thorium breeder reactor and the second with the one-region type. Cowmparison is made on a common basis insofar as possible. TWO-REGION REACTORS A 5. TWO-REGION REACTORS Methods and Conditions The program for the study of the two-region reacto:‘has been pre- viously outlined by Briggs and Edlund(h). The data that were used to get cost_factors and process characteristics are,givén in other publications(5’lo), and are discussed in a later section of this report. A schematic flow diagram of the system studied is shown in Figure 1. The core material will be chemically procesbed by two methods. The core material is treated in a liguid-solids separation plant utilizing hydraulic separators to.remove the precipitated poisons. This érocedure is capable of removing 75% of the so-called group-3 poisons (fission product poisons affected by chemical processing). A more complete discussion of -this (1) poison removal method is given by Arnold et al Complete poison removal from the solution carrying the precipitated poisons is effected in the Thorex plant at a rate considerably less than that used for liquid- solid separation. Since the blanket materiasl is a slurry, poisons must be removed from it by the Thorex process only. In order to produce uranium of high enrichment (about 95% U-233) the blanket stream will have to be partially processed for removal of the excess U-233 (represented by breeding gain) before any mixing of the core and blanket streams in the chemical pfocessing plant. The core enrichment will be only 25-30% U-233. Byyprocessing to remove protactinium, uranium composed of nearly 100% U-233 could be produced. For these calculations, however, it was assumed that the uranium product would be that derived from the blanket with all protactinium decayed to U-233 and mixed with the uranium isotopes. S 5- The calculation procedure, which is successively described in the following sections, consists of four main parts: 1) calculation of chemical processing cycle‘times apd uranium isotope concentrations in the blanket and the core by isotope balance equations for the particular blanket power selected .(for any set of parameters, calculations were mfide for three reactor powers); | 2) two-group nuclear calculations to determine the critical con- ) centration and the neutron balance which yields in turn the core power and the ratio of resonance to thermal capture in the thorium; o 3) unit cost calcfilations ; 4) plot of unit costs versus total reactor power so that the costs at a particular total power can be used for comparison of the systems. The parameters studied were core diameter, blanket thickness, blanket U-235 concentration, thorium concentration, core poisoms, tempefature and power density of the system outside the reactor (piping and heat exchangers). Processing Cycle Times and Uranium Isotopes For purposes of chemical process calculations, the fission product poisons are considered to be composed of three groups(j). The first group consists of the noble gases, the second of the high cross-section isotopes and the third of the low cross-section isotopes which transmute by decay or neutron capture into other nuclides of approximately the same low cross section. The first two groups are virtually unaffected by chemical pro- cessing rates required for agueous homogeneous reactors and their macro- scopic cross section is approximated as 1.3% of the fission cross section (0.8% high cross section isotopes and 0.5% residual noble gases). The noble gases are continuously stripped during operation; the high cross section isotopes are rapidly destroyed by neutron capture since their cross section is around 40,000 b; The third group is, however, a function of the chemical processing cycle. For cofe processing, two modes of poison removal are employed -- poison precipitation with subsequent liquid-solid separation, followed by Thorex. The precipitation step is capable of removing only some of the atomic species comprising group-? poisons which will be called subgroup A; the remainder, subgroup B, is not removed by precipitation. Both subgroups are removed by the Thorex process. This is represented by the following equations for equilibrium conditions. - N gy [Ef(es) + Ef(ea)] e - N(A)Tlcn(o) - ,f_,:(): =0 (1) N(B) ) | (-a)y [By(25) + Bye)] o, - 22 -0 (2) and by definition _In(a) + N(B)] o (3) t; - B NI ES) | 2 o (3) N(o) | | | (4) f03 = TL(E5) + £(23) Solving for T 20’ 2c ~ 2ya (3) ¢C \1-g) _ \ 5| (5) (£5-£5z) - yo~ (3) B T ¢ 1l + 1l + T T—W N -11- CEER This equation actually defines an overall processing cycle for the core. The optimum Thorex cycle time is, of course, that determined by a balance between value of fuel recovered and inventory and chemical processing costs. Another relationship between Tlc and T2c for minimum core processing cost could be obtained by utilizing the processing cost equations. For this study, however, the precipitation cycle (T,.) was set constant at one day since the estimated cost(lo) of the precipitation process is practically independent of the processing rate for reasonable flow rates. In addition the core processing cost is very small (around 0.08 mills/kwh). Under the present state of chemical process development, only the Thorex process can be used to treat the blanket material because it is a slurry. The equation for the blanket cyclé time is simply “38 (6) T = —— B y o(3) fiB For use in the nuclear calculations, determination of the concen- trations of the wvarious isotopes in both coreiand blanket was necessary. Both core and blanket contain U-233, U-234, U-235 and U-236. In a&dition, the blanket contains Pa-233 and Th-232. Other isotopes that could be present are neglected since even very small processing losses will prevent the build- up of higher isotopes and the half-lives of Th-233 and Pa-234 are too short to permit significant concentrations to occur. For the blanket at equilibrium conditions, the following isotope balance equations apply: 2N02)(1 + B) By - A(13)N(13) - 3A13) Iy - %%”—) - 0 (7) N(13)8(13) - 5, (23) ¢ - “éf) -0 o (8 T(23) gy + 2013) gy - Do) g - 2 < o (9) S (2b) g -3, (25) ¢ - M2 Lo (10) "B T..(25) g - T(26) ¢, - Né;‘” - 0 (11) F——f,‘;) - 3(02) (14p) iy = (12) K Py ¢B = Var [ff(25) +Zf(25)] 2 and p_ x 100 Ver = Vg +~-—§-‘-T——-- (14) B vy = &%r[fifi - (a + t)%] | - (15) Similarly, for the core (neglecting chemical processing losses), VBr Ffi(ea) + N(13) | - 2. (23) =0 (16) 4 VCT | T s Zzaa. Q’C v T I | a7 E(S—“)- - Z(24) By + 24,(23) = O (17) CT I JB v [ ] a7 ML - S(25) #y + B@) 4 =0 (18) v | a E[M—%@{IB - Y(26) 8, +53,(25) ¢, = O (19) 6 0° P VCT=%E8'§+1JCC | (20) These equations hold only for a breeding ratio of one or greater, For breeding ratios slightly less than one the isotope ratios obtained are — -13- : NS . P SR o T R Oy LTI e, still approximately correct. Actually, except for one isolated case, the ,breedipg ratios were all greater than one. - The method and eese of solution for the set of equations (Eq. 7 _through 20) depend on the selection of the independent variables and the availability of automatic computing machinery. In the present study, the dimensions (R, a and t); blanket power, P,; blanket U-253 concentration, N(23); poison frattion in the core, f(3C); the thorium concentration, N(OE)} the external power density'and the o .average reactor temperature were gselected as the independent variables. The ratio resonance to thermal.cepture in thorium, B, can only be obtained from the nuclear calculation since ‘the fast flux is required to determine it. It was necessary to estimate a value for B, compute the isotppe concentrations, compute f from nuclear calculations and then compare the value so obtained with the initial guess. After a little experience, it was possible to estimate an initial wvalue of B'that required only two or three iterations. Nuclear Calculations¥* The customary two-group method was employed for obtaining the critical mass and neutron balance for the spherical two-region geometry. (6, 14) The major details of this procedure have been described elsewhere (12) The only novelty introduced was the use of a "thin shell"” approximation to account more adequately for the effect of the zirconium core tank. The nuclear constants used in the work are shown in Appendix I. These values (2, 7, 13} are based on or taken from several publications * The ORACLE was used for the large number of calculations required. That part dealing with the nu%lear calculations was based on an ORACLE code devised by Willoughby and Fowler 2) for two-region spherical reactors. Calculation, ‘tape handling and punch-out time averaged only 8 minutes for the two-region reactors and 30 seconds for the one-region reactors. If desk computers were used, about 4 to 5 men-days would be required for each case. — 2 Cost Estimation Selection of proper cost factors is the most difficult part of the evaluation of nuclear power stations. since no full-scale plant experience is available. However, reasonable values based on laboratory and pilot plant experience, coupled with normal industrial methods and practice, should produce results with at least sufficient relative accuracy to aid in the selection of design criteria and operating conditions. No new effort was made to estimate the investment cost for a réactor, (3) turbogenerator plant or chemical processing plant; the estimates by Briggs were used., Reactor and Turbogenerator Plant Investment The basis for computing the cost of the reactor with associatéd equipment and structures was $ll.65(5) per kilowatt of heat for a L50-Mw reactor considered as an integral part of a B-reactor'power station. For power levels different from 450 Mw per reactor, the unit investment cost was corrected by use of Figure 2 (reproduced from ORNL-1642). The unit investment cost for the turbogeneratorrplant, which 1s dependent on the throttle temperature, was obtained from Figure 4 (repro- duced from ORNL-164k2). The cost of boilers and coal and ash handling equipment is excluded since the reactor plant replaces these items. Since the total reactor power could not be predetermined, a quadratic equation was fitted to the points shown in Figure 2, for purposes of calculation by the ORACIE. Using a plant factor of 80% and a 15% amortization charge, the result is T .2 Investment (mills/kwh) ='%— (0.3387 - 2.828 x 10'LL P+1.873x10 ' P n +0.02140 C E,) | (21) SRR 15- where P = reactor power, Mw of heat -E, = net station efficiency E; = gross station efficiency C = turbogenerator plant cost, $/electrical kw Efficiency The efficilency of the plant is shown as a function of throttle temperature in Figure 3 (reproduced from ORNL-1642). Estimates were made for the temperature drop from the reactor to throttle. Table I below‘lists the estimates of the efficiencies used. Table 1 Nuclear Power Plant Efficiencies Av. Reactor Throttle Temp. Temp., °C O Gross Efficiency Net Efficiency 320 (608°F) 1490 0.315 X .0.281 300 (572°F) 470 0.304 0.271 280 (536°F) 450 0.292 0.260 250 (482°F) 410 0.274 ok 200 (392°%F) 340 0.240 o.211 Operation and Maintenance Operating and meintenance charges for the reactor and turbogenerator plants were taken as 3% of the total investment. Inventories A 12% charge was assessed against all non-depreciating materials. A1l fissionable materials were valued at 20/gram. Protactinium was con- sidered a fissionable material only when outside the reactor. I -16- Heavy water was valued at $40/lb. To cover the slight holdup in chemical processing and makeup invéhtory, the inventory of heavy water was taken as that required to fill the reactor system at room temperature, an amount sbout 25% greater than necessary at operating temperatures. Thorium was valued at $5/lb with no appreciable charge for making the Th0,-D0 slurry. The feed stream inventory charges were based on the following holdup times | Spent core fuel 95 days Spent blanket fuel Th + U + 75% of Pa 55 days 25% of Pa 205 days Thorium feed ' 30 days The holdup time assoclated with the poison removal by the hydraulic separator plant was considered negligible. Chemical Processing The estimated cost of the poison precipitation process and the hydraulic separator plant was $210 per day(lo) or $70 pér day per reactor. This cost was considered independent of the throughput for flow rates of the order of 25,000 liters/day per reactor. A fixed charge of § 5,500 per day(3) or $1830 per day per reactor was used for the Thorex plant. The cost includes chemical plant amortization and fixed operating costs. The estimated cost of processing thorium was $3.00 /kg and $0.50 /gram for fissionable material (U-233, U-235 and Pa con- verted to U-233). In previous studies(3) $1.00/gram was the estimate for | (10) processing fissionable uranium; the lower wvalue represents a later estimate by the Chemical Technology Division. Uranium losses were assumed to be 0.1% Y -17- of the amount processed through the Thorex plant. Prior to procéssing in the Thorex plant, heavy water must be evaporated from the feed streams. A charge of'$0.55/litef was used for the recovery of heavy watef.(lo) | Feed Costs For breeder reactors (all reactors were breeders, with one exception), only thorium is required and D2O,makéup. As is usual, 5% of D20 inventory of the reactor 'system was estimated as the annual makeup requirement. \Results The results shown in the following tables and graphs are for two-region thorifim‘reéctors delivering 125 electrical megawatts to a power grid. The power stat;on is composed of three reaétors, three turbogenerators and one chemical procéssing plant along with some accessory equipment common to the three reactors. | The major results of the study are shown in Figure 5. Results for five typiqal cases are shown in Table II. It is immedigtely apparent that the net unit cost is véry insensitive to the parameters investigated;-bnly\O,} mills/kwh separates the highest and lowest cost reactors shotm. This is a direct conseguence of piant investment aqdflother fixed éharges represent - ing n;ar%y 86% of the power cost. | The details of the effects of the individual process variables are discussed bolow under the heading Major Process Variables. Effects of external power density changes, er?ors in the group-5 poison$¢ross section and errors in the two-group constants are reported in succeeding sectionms, followed‘?y discussions of the accuracy of the two-group method and the economics calculations. E— 18- Major Process Variables 1) 2) 3) 4) Core Radius -- Variation of the core diameter from 4 to 7 feet results in a power cost change of less than 0.3 mills/kwh. The lowest cost is associated with 4-foot cores, but only a negli- gible difference of 0.0l mill/kwh exists between L- and 5-foot cores. Blanket Thickness -- For the blanket concentrations used (500 to 1500 g Th/liter), the unit cost of power varies only about 0.1 mill/kwh for a range of blanket thickness between 1-1/2 and 3 ft. The optimum thickness is about 2 feet for a six- foot core and 2-1/4 feet for a five-foot core. Thorium Concentration -- Therlowest unit cost results from using a thorium concentration of 1500 g/liter. However, the cost is only 0.02 mills/kwh less than that for 1000 g/liter. Also, the results indicate that if engineering considerations require the use of thorium concentrations as!low as 500 g/liter, the slightly increased unit coét would not preclude possible economic power generation. Fig. 6 shows the effect of thorium concentrationvon the breeding ratio and net U-233 production and again indicates that ‘use of thorium concentrations greater than 1000 g/liter leads to a rapidly diminishing improvement in the breeding ratio. Ratio of U-233 Concentration to Thorifim Concentration -- About 3 g U-233/kg thorium (see Fig. 8) produces the lowest unit cost for thorium concentrations of 1000 g Th/liter. Here aléo, only slight changes in unit cost are produced by wide variations in the ratio of U-233 to thorium. 5) ~19- Poison Concentration -- The core poisons vhich are related to the core processing cycle time have little effect on the unit cost in the range 4 - 10% (se¢ Fig. 7). The gross breeding ratio (processing losses neglected) increases almost linearly with reduction in poisons. Below 3% poisons, however, the net U-233 production and net breeding ratio decrefiselsince the highly increased chemical processing rate leads to significant uranium and protactinium losses. In similar fashion, if the blanket U-233 concentration were lowered to small values, the increased chemical procesgsing rate required would likewise cause large fissionable material losses, as well as high chemical processing costs. 6) Temperature -- Under conditions assumed, no optimum temper- ature was found for the range of average reactor temperatures congidered. Lower unit cost is obtained by increasing the temperature, but Fig. 10 indicates that little 1is to be gained by raising the average temperature appreciably over . 280°%. An average reactor temperature of 280°¢ will probably correspond to an exit temperature of about }OOOC. If engineering considerations preclude core power densities appreci- ably over 100 kw/liter, it would be necessary to increase: the core size or operate with a larger portion of the total power in the blanket. The former course appears economically preferable. The reactors with five- and six-foot cores shown in Table II where typical results for several condi- tions are shown, have power densities of 210 and 122 kw/liter, respectively. In order t6 reduce the power density of the five-foot core to 122 kw/liter, A 20- it would be necessary to operate with a U-233 concentration in the blanket of about 12 g/kg of thorium. The cost of power would rise to about 7 mills/kwh, the increase being due primarily to increased inven- tory charges. The use of a 6-foot core, on the other hand, results in a power cost of 6.45 mills/kwh. Effect of Group-3 Poison Cross Section Variations The results of reducing the group-3 poison cross section from 40 to 18 barns at 20°C are shown in Fig. 7. The higher value is a conservative one that has been used in previous studies(5); the lower value is the latest estimate(lo) for thorium-uranium reactors. In general, reducing the poison cross section by over a factor of two reduces the net unit cost by 0.1 mill/kwh and shifts the optimum core poigons from'T to &. The core cycle time is the only result appreciably affected (see Table II). A change greater than a factor of two in the group-3 poison cross section (see Fig. 9) does not appreciably affect the optimum U-233 concentration in the blanket or the optimum blanket thickness of 2 and 2-1/L feet for the 6-foot and 5-foot cores respectively. Effect of External Power Density Variations Other than plant investment the largest single cost is the inventory charge -- nearly one wmill/kwh when using values of 20 and 14 kw/liter external power densities (previously used in ORNL-1642 by Briggs) for the core and blanket systems respectively. The effect of increasing these external power densities is shown in Fig. 11. Doubling the core external power density of 20 kw/liter reduces the cost 0.25 mill/kwh, but doubling the blanket external S ;- power demsity of 14 kw/liter saves only 0.07 mills/kwh. The saving realized from further increases in power density rapidly decrease. A recent design(9) of the TBR indicates that it 1s possible to achieve external power densities as high as 61 and 55 kw/liter fqr the core and blanket systems respectively. For this condition the cost is 5.8 mills/kwh, only 0.11 mill/kwh lower than for 40 and 28 kw/liter. For these calculations, it was assumed that no change in capital or operéting expense was necessary to achieve higher power densities. Effect of Errors in the Nuclear Constants The two group nuclear constants which were estimated for use in the nuclear calculations are probably accurate to within 10-20%. The effect of such errors on the process characteristics and econ- omics was uncertain. Consequently, a study of the effect of substantial changes (* 50%) in the nuclear constants was made for a typical case¥*, Although the critical concentration and breeding ratio were changed considerably, the changes in power costs were relatively small being principally confined to altering the amount of credit obtained from excess fuel production. The largest change observgd was a difference of about 0.6 mill/kwh between two extreme cases. Where only individual constants were altered, chqngesfin the net cost were less than 0.1 mill/kwh. Considerable changes in the core uranium concentration do nqt, however, lead to proportionally large variation in fuel inventory *The single exception to this procedure was the restriction offfl(E}) to the range 2.28 to 2.36, the approximate limits of accuracy in this quantity cited in BNL 221. charges since the latter contain contributions of similar magnitude from the blanket system. Thus, for two cases where the uranium concentration differed by a factor of over 4, the fuel inventory charge differed by a factor of 1.4. The effects upon breeding gain are, on the other hand, almost directly converted into changes in credit received for excess fuel production. It seems reasonable therefore to conclude that errors in the two- group constants are of secondary economic importance since 85% of fhe power cost is tied up in factors unaffected by such errors. A summary of the results and constants used is presented in Table III. The most important cost increases were those produced by increases in the quantities TB’ 0-3‘13’ Py and decreases in ’}]23. Increasing ’I'B produces a rise in fast leakage at the expense of resonance capture in thbrium, while all other neutron losses remain practically unaffected. Raising cra.l3 causes protactinium absorpfion to rise at the expense of thorium capture, as well as a change in core isotope ratios leading to higher capture rates in U-234, 235 and 236. An increase in resonance escape probability raises blanket power, increases leakage, depresses resonance capture, and increases thermal capture. A decrease in both resonance and thermal capture in thorium is the principal result of a fall in 9{23) of 0.0k (1.T7%). The critical concentration was most strongly affected by ‘1;, D2c’ and, naturally, %) . A 50% rise in the first two produced a critical concentration increase of about 30%, while the 1.T% rise in 7(23) caused a 4.4% decrease in concentration. The breeding ratio was not significantly affected by changing either T; or Deé. | -23- None of the quantities investigated had a significant effect upon blanket processing except py, for which a decrease of 504 led to a 12% decrease in cycle time. The core thorex cycie was affected maifily by the diffusion constants and ’T;; the greatest effect obéerved, produced by lowering D2c’ was a decrease of cycle time by'about 134 days out.of 337. However, no significant changes were noted in either core or blanket chemical procéssing‘costs. | Accuracy of the Two Group Model and the Calculation of Breeding Ratio For the large reactors studied, the two group procedure Qhould provide an adequate estimate of the critical mass. The breeding ratio is, however, far more sensitive to inadequacies in the mgthod.' For example, difficulty arises in selecting a mefhod of treaping thorium resonance captures. In this fiork, fést neutrons wefe assumed to slow down without absorption, and captures due to resonance absorption were computed by multiplying the number slbwed into the thermal group by (1-p). This treatment overestimates the fast leakage by about a factor of 3. Consequentlj; the bréeding ratio as.reported in Table Ikaor a typical case may be low by about 0.02. | A wuch wmore serioué source of iné.ccuracy results from uncertainties in 'q. Errors in thé thermal value of‘q may produce an uncertainty of + 0.03 in the breeding ratio. Resonance captures in uranium may reduce the breeding ratio by 0.08 if the resonance integral of U-233 ié 1500 b and‘resonance a is as high as unitj. | | New datfi concerning the resondnde intégral bf.protactinium (650 b) and the thermal cross section (63 b) reported by R. R. Smith(ll) have only a slight effect on the breeding gain for the case of a | 1000 g Th/liter slurry; the absorptions in protactinium decrease by A -2h- only 0.002 absorptions per absorption in U-233. Uncertainties in the poison cross section may be expected to have little effect since it has been shown in a previous section that poison levels may be varied over a range of 4-10% without appreciable cost variation. To sum up, the decrease in the breeding ratio produced by the factors discussed above may be expectéd to be no greater than 0.13. While this number represents an impbrtant unce?tainty in estimated production of new material, its overall economic significance is slight. Accuracy of Cost Estimate The net unit cost of pover as determined for two-region reactors near optimum cost (6.2 mills/kwh) is a result that is based on the limited experience available. Obviously, the uncertaint& of this result is large enough to span the competitive cost range for a nuclear power industry. An estimate as to the overall accuracy is best made by assessing the accuracy of the individual cost items that comprise the net unit cost of pover. | The largest single item is the reactor and turbogenerator plant‘ investment which represents 60% of the total unit cost. Of this cost, T5% is for the turbogenerator plant and 25% is for the reactor and associated equipment. Other cost ifiems are relatively small portions of the total; the largest of these, the inventory charge, is 15% of the net unit cost. Some of the individual costs comprising the net cost of power have a fairly firm basis and error limits based on experience can be assigned with a fair degree of confidencé. These items are capital investument, maintenance and operation for'the turbogenerator plant; capital invest- ment for the reactor plant and associated equipment; inventory and L -25- feed costs. Other charges which cannot be assigned error limits with any degree of certainty are maintenance and operation of the reactor plant and chemical processing. Fortunately, the individual costs that rest on a falrly firm basis comprise approximately 80% (based on the total cost without breeding credit) of the cost of power. The accuracy of the turbogenerator plant investment cost 1is estimated at +15%. For such a plant, based on vast industrial experience, the error limit could be narrowed with a definite site selection and the establish- ment of detailed design criteria (for example, nearly &% cost reduction could (3) be achieved by installing the turbogenerators outdoors). Briggs sets an error range of O to +30% on the estimated cost of the reactor plant since the figures used do not allow for construction contingencies. For mainten- ance and operation of the turbogenerator plant, a fairly well known quantity, a +15% assessment of the accuracy should be adequate. It is difficult to estimate an error limit for the maintenance and operating cost assumed for the reactor plant since a design in which these costs are under control has not yet been visualized. Ultimately, they might be expected to approach the costs for modern, conventional plants. An error of O to +100% is assumed because of the unknown factors involved. The error limits for the fixed chemical processing costs (investment, operation and maintenance) also are difficult to estimate. A wvalue of +25% is assumed here. Based on various designs and limited data, arguments could be advanced for either raising or lowering the cost used. It is felt that the part of the process{ng cost that is a function of the through- put is as low as can be expected in the near future; consequently, a 0 to +100% limit is assumed. A _26- The nuclear and isotope calculations are probably accurate to within +15%. Consequently, cost items (uranium inventory, thorium feed, breeding gains, and, to some extent, prdcessing rates) based on these results have about the. same degree of uncertainty if the external power density 1is assigned approximately the same error range. - Applying the estimated limits of accuracy to the cost items comprising the 6.2 mills/kwh for a near optimum reactor, a cost range of 5.3 to 8.0 mills/kvh is obtained. The cost of D,0 and the inventory charge (12% and $40/1b used in this study) for non-depreciating items is Subjeét to government control and at present it is difficult to predict the changes in the future. The latest proposed pricing policy by the Atomic Energy Commission lists the cost of D0 as $28/1b and requires only a 4% inventory or rental charge for non-depreciating items. Applying these proposed costs, the unit cost of power will be in the range of 4.6 to 7.2 mills/kwh. -27- Table II1 Typical Cost Breakdown and Neutron Balances For Two-Region Reactors Process Characteristics and Costs r Core diameter, ft 5 Thorium concentration, g thorium/liter 1000 U235 concentration in in blanket,.g/liter 3 Blanket thickness, ft 2-1/k4 Core external power density, kw/liter 20 Blanket external power density, kw/liter 14 Group-3 poison cross section at 200C, b 40 Core poisons, % 7.0 Blanket poisons, % 4.33 Blanket power, Mw 89 Core power, Mw 202 Net unit cost of power, mills/kwh 6.32 Plant investment (less chemi- cal processing) mills/kwh 3.7k Fuel inventory, mills/kwh 0.48 D20 inventory, mills/kwh 0.52 Fixed chemical processing mills/kwh 0.76 Blanket processing, mills/kwh 0.26 Core processing, mills/kwh 0.09 Operation and maintenance, mills/lcwh 0.75 Feed cost (DoO and thorium), mills/kwh 0.20 Uranium (233 & 235) credit, mills/kwh S 0.Lh Gross breeding ratio 1.110 Net breeding ratio 1.109 Net U233 produced, g/day 59 U235 in product, wt. fraction 0.001k4 U233 in product, wt. fraction 0.959 Core system volume, liters 21,400 Blanket system volume,liters 17,100 Core concentration, g u233/ kg D20 2.55 Core. concentratlon, g U255/ \ kg D20 0.34 Core concentration, g uranium/ kg D20 9.21 > 1000 3 2-1/h4 20 1k 18 6.0 2.67 91 590 6.22 3. Th O.Lh 0.52 0.76 0.25 0.07 0.75 0.20 0.49 1.121 1.119 65 - 0.0013 0.961 21,400 17,200 2 .48 0.30 8.30 2 1000 Z-l/h Lo 28 18 6.0 2.7k .~90 591 5.91 3. Th 0.35 0.3 0.76 0.24 0.06 0.75 0.13 0.46 1.115 1.11k 61 0.C01l4 0.958 11,600 14,000 2.49 0.31 8.49 500 20 14 40 7.0 5.50 392 6.53 3.74 0.37 0.49 0.76 0.20 0.09 0.75 0.19 0.050 1.013 1.012 0.0026 0.937 21,400 15,200 2.44 0.38 9.90 1000 20 1h 18 6.0 2.72 92 38 6.32 3.Th 0.40 0.5k 0.76 0.24 0.07 0.75 0.20 0.%8 1.096 1.095 51 0.001k4 0.960 22,600 18,100 1.59 0.19 5.3k — 26- Table II (Contd) Reactor (internal & external) inventories, kg Thorium 17,100 17,200 14,000 U233 97.1 96.2 66.3 y23> 6.3 5.5 3.2 Pa22> 18.6 19.0 18.2 Feed stream inventories, kg Thorium 6,500 6,800 6,400 U235(includes Pa23d) 5%,1 45,4 45.9 . U255 3.0 1.5 1.6 Core thorex cycle, days 198 336 182 Blanket thorex cycle, days 146 140 120 Net thorium feed, g/day Flux at core wall, n/cm® sec Absorptions in fuel 557 625 1.06x1015 1.10x1015 1.08x1015 621 Neutron Balance U233 (core) 0.7957 0.7941 0.7950 U253 (blanket) 0.2043 0.2059 0.2050 U255 (core) 0.1164 0.103%5 0.1066 U222 (blanket) 0.0004 0.000L 0.0005 Neutron losses (other than fuel) Core Poisons 0.0576 0.0486 0.0487 y23h 0.1153 0.1024 0.1054 U236 0.018%4 0.0163 0.0168 Sulfur 0.002k 0.0021 0.0022 Core tank 0.0%05 0.0309 0.0308 D20 0.0169 0.0172 0.0172 Blanket Thorium (thermal) 0.8114 0.8171 0.8143 Thorium (resonance) 0.3297 0.3351 0.3351 Protactinium 0.0188 0.0192 0.0226 Poisons 0.0080 0.0050 0.0051 y23h 0.0018 0.0017 0.0019 y236 3%10-T 35x10-T bx10-T D20 0.0027 0.0028 0.0027 Fast leakage 0.0265 0.0264 0.0264 Slow leakage 0.0075 0.0075 0.007h Total absorptions and losses 2.56U43 2.5362 2.5437 Neutrons produced from U223 2.3200 2.3200 2,%200 Neutrons produced from U235 0.24hl 0.2172 0.2238 Total neutrons 2.5641 2.5372 2.5438 0.7928 0.2072 0.1350 0.0010 0.0584 0.1328 0.0214 0.0026 0.0396 0.017k4 0.8230 0.2264 0.0358 0.0104 0.00%2 8x10-7 0.0059 0.0508 0.0423 2.6040 2.3200 0.28L2 2.6042 5 1.36x1015 18,100 84.3 3.8 18.8 6,600 L4 .0 1.5 208 150 610 0.84x1015 L7508 .2102 .1039 .000k O OO0 OO OO0 Q |_I () \N Extrapolation distance, in. 15.24 of U235 vé.}e (13) K !OD TB 212.4 Effect of Substantial Changes T.62 15.24¢ 22.86 2.28 2.36 h8.4 145.2 106.2 191 .2 233.6 318.6 109.0 196.2 239.8 327.0 0.T745 2.24 0.5865 1.76 0.835 2.505 0.6152 1.8L46 0028 0.84 Comblnation case 1 (D's, T's, p high; extrapolation dis- tance low) Combination case 2 (D's, T's, p low; extrapolation dis- tance high) 6.257 6.229 6.219 6.354 6.109 6.158 6.299 6.136 6.210 6.248 6.324 6€.217 6.227 6.2354 6.259 6.223 6.238 6.224 6.256 6.224 6.2%6 6.214 6.255 6.181 6.308 6.692 6 .080L ~29- Table III 0.3879 0.4173 0.429k 0.2896 0.5546 0.4965 0.3262 0.5288 0.4400 0.3943 0.3062 0.3956 0.4130 0.4210 0.435h 0.4048 0.4235 0.42k4kg 0.3952 0.4332 0.4097 0.3797 0.4300 0.4913% 0.3262 0.0102 0.5131 in the Nuclear Constantsa 097 .10k 107 073 1355 1.124 1.086 HFHEFHH RFHEPPF o 151 .110 .098 077 -099 .103 .105 .109 .101 .106 .101 -099 .107 10k -095 107 122 .082 .00k .128 B(G) G(U) 51.7 8.4 55.5 8.4 59.0 8.4 38.6 8.8 T2.6 8.1 66.3 7.8 L5.7 9.0 70.5 8.8 58.6 8.5 52.6 8.4 40.8 8.2 52.8 6.7 55.1 8.0 56.1 8.8 58.0 10.8 54.0 7.5 56.4 9.0 5T7.0 7.5 52.7 8.9 57.1 9.5 50.2 7.8 50.6 5.1 57.4 10.8 65.4 8.3 43.5 8.6 1.2 15.4 68.42 3.5 o — -30- ?" ?(‘y-,‘ *zi‘*w-{l Table III (contd) & The following properties were common to all the calculations performed: Temperature L LI I B "« % v 0 & 8 0 & s a8 &S 88 s 28000 Grams of U233 per kilogram of thorium. 3 Grams of thorium per llter...........,... 1000 Poison fraction in core.....ceceoeseceees 0.06 REBCEOT POWET +eravevearenerronaspeaccasss U480.8 Mw (125 Mw elect. output ) Core aiametertl..t!‘._...lIC.I.OU“I.IOCD. Sft Pressure vessel diametereceecersssesnsssas 9 TL External power densities, kw/liter Core Systemil..i..tl..'....l........ 20 Blanket SYSteM.eeceesssacecasassesss 1h The symbolg in column headings are defined as follows: Cp = total power cost, mills/kilowatt-hour CX = credit for excess fissionable material produced, mills/kilowatt-hour BR = breeding ratio, atoms of fissionable material produced per atom of fuel burned B(G) = net grams of fissionable material produced per day G¢(U) = uranium concentration in core, grams of uranium per kilogram of heavy water c This row gives results for standard case. Underlined numbers are values chosen for parameters in standard case. CORE _3]_ ORNL-LR-DWG 4084A ThO, SLURRY MAKEUP LIQUIDS —SOLIDS SEPARATION ThO, RECYCLE Y EXTRA U2 THOREX PLANT et~ BLANKET FISSION PRODUCTS Fig. 1. Schematic Flow Sheet for a Two Region Thorium Breeder Reactor. REACTOR PLANT COST PER Mw OF HEAT RELATIVE TO THAT OF 1350 Mw-1000 psia STATION 3.0 1.0 O 300° C-2000 psia PLANT ° o . ! ] T 250° C-1000 psia PLANT AND 300° C—1600 psia PLANT WITH HOMOGENEQUS CATALYSTS 400 800 1200 1600 2000 2400 2800 3200 PLANT POWER (Mw heat) Fig. 2. Effect of Power on Cost of Two—Région Reactor Plant. THERMAL EFFICIENCY (%) 40 38 36 34 32 30 28 26 24 22 e S DWG. 23095 | | THERMAL EFFICIENCIES BASED UPON: 1. SATURATED STEAM REHEATED TO LIMIT | MOISTURE IN EXHAUST TO 12% AT t%in. Hg 2. THREE STAGES OF FEEDWATER HEATING _ 3.125-Mw, 1800-rpm TURBOGENERATORS — 600 psia P ~ , X " 4OODSIO\ ??\GV 350 400 450 500 THROTTLE TEMPERATURE (°F) Fig. 3. Effect of Steam Conditions on Turbogenerator Plant Efficiency. INVESTMENT COSTS (DOLLARS PER kw CAPABILITY) 90 80 70 60 50 40 30 20 _34_ DWG. 23096 DATA FOR SATURATED-VAPOR PLANT BASED UPON THREE STAGES OF FEEDWATER HEATING, 1%, in. Hg EXHAUST PRESSURE, STEAM REHEATING TO LIMIT MOISTURE IN EXHAUST TO 12% DATA FOR SUPERHEATED-VAPOR PLANT BASED UPON THREE STAGES OF FEEDWATER HEATING, 1V, in. Hg EXHAUST PRESSURE, SUPERHEATING TO LIMIT MOISTURE IN EXHAUST TO 12 % TOTAL =3 w & B m —— 400 —— 600 — 850 S op SATURAT 140 - 100 psia —f—— 215 psia - . ] 0 FPC ACCOUNT No. 314 TURBOGENER CONDENSERS ATORS, , etc “ 30 o R 46 [ T m L I m 5 m o = T 66 960 1465 120 100 80 / No. 311 BUILDI NGS AND GRO UNDS \ No. 312 FEEDWATER EQUIPMENT | Nos. 342 TRANSMISSION PLANT 343 Na. 315 MISC. | No. 316 ACCESSORY ELECTRICAL EQUIPMENT No. 340 T 200 400 600 800 THROTTLE TEMPERATURE (°F) 1000 1200 Fig. 4. Effect of Steam Conditions on Power—Plant Cost for 300 ~Mw Plant. TOTAL INVESTMENT (DOLLARS PER kw CAPABILITY) NET UNIT COST (mills/kwhr) 7.0 6.9 6.8 6.7 6.6 6.5 6.4 6.3 6.2 O!!L- Ll-!l! ll!l\ 3gOFU TEMPERATURE, 280°C 233 PER kg OF Th CORE POISONS, 7% 125 Mw OF ELECTRICITY 480.8 Mw OF HEAT GROUP 3 POISON CROSS—-SECTION, 40 b AT 20°C N\ /?ft', {000 g OF Th/liter N\ \ 5-ft CORE DIA, 500 g OF Th/liter -6 ft; {000 g OF Th/liter / = _-6ft; 1500 g OF Th/liter / - 5ft; 750 g OF Th/liter 5 ft; 1000 g OF Th/liter § Feed gtream inventories,kg Thorium _ U233 (includes Pa) U235 U235 in product, wt. fraction U232 in product, wt. fraction Thorium feed, g/day U230 feed, g/day Reector poisons, -49- Table IV Process Characteristics afid Costs 10 300 450 2.00 0 0.17 0.40 0.52 0.92 38,900 32.4 0.957 0.956 7.99 1.18 26.08 11 300 400 1.92 0.0L 0.20 0.22 0.58 0.96 43,800 4.1 1,011 1.009 5.T9 7.62 0.71 17.60 13,100 270.9 25.% 19.8 1,800 41.8 345 0.433 0.038 560 4.93 12 250 400 1.88 0.057 '0.18 0.25 0.66 0.84 49,700 18.8 1.012 1.010 6.3 5.82 0.56 13.4k2 12,400 236.0 22.5 19.9 1,700 37.0 3.1 0.434 0.038 561 5.46 13 250 500 1.93 0.15 0.16 0.28 0.75 0.89 56,600 14.8 1.035 1.03L4 20.4 5.60 0.46 10.68 14,200 258.8 21,2 20.9 1,600 324 2.3 0.52k4 0.040 580 6.10 1L 200 450 2.01 - 0.11 0.16 0.52. 0.86 0.7T" 64,700 11.8 1.025 1.02%4 14 .3 4,15 0.37 8.50 12,900 220.4 19.7 20.4 Absorptions and losses -50- Table IV (Contd) Neutron Balances pa23>3 0.0191 0.0186 0.021L 0.0206 0.0235 ~yadd 1.0000 1.0000 1.0000 1.0000 1.0000 y23h 0.1090 1.1019 0.1040 0.0910 0.0986 U255 0.1599 0.1009 0.1029 0..0883 0.0966 236 0.0235 0.0095 0.0095 0.00L4 0.0061 D0 0.0070 0.0073 0.0095 0.0099 0.0133 Poisons 0.0573 0.0491 0.0545 0.0601 0.0629 Th232 (thermal) 0.5516 0.5775 0.6269 0.6516 0.6998 Th222 (resonance) 0.4687 0.4520 0.4063 0.4043 0.3488 Fast leakage . .0.1873 0.1518 0.1309 0.1123 0.0993 Slow leakage 0.07081 0.062% 0.0694 0.0622 0.0730 Total neutrons absorbed and lost 2.6541 2.5309 2.5351 2.5046 2.5218 Production Neutrons from Ued2 2.3200 2.32000 2.3200 2.,3200 2.3200 Neutrons from U235 0.3341 0.2109 0.2151 0.1846 0.2018 Total neutrons produced 2.6541 2.5309 2.5351 2.5046 2.5218 * 125 Mw of electricity, 480.8 Mw of heat. Average temperature 280°C, external power density, 20 kw/liter. PARTIAL NET UNIT COST OF POWER (mills/kwh) _5].. ORNL-LR-DWG 8576 2.6 | 125 Mw OF EL!IECTRICITY 480.8 Mw OF HEAT AVERAGE TEMPERATURE; 280°C ONE REGION; ThO2—UO3z— D0 SLURRY 2.5 \ \ \\2509 OF Th/liter N 2.4 200 150 REACTOR DIAMETER 46 ft | 175 [/ 2.3 2.2 \ / | 175 > REACTOR DIAIMETER 15 ft A 2.2 \\ \ 300 150 / 2.4 [ ——— REACTOR DIAMETER {4 ff 200 2.0 100 200 300 400 500 600 700 CHEMICAL PROCESS CYCLE TIME (days) Fig. 12. Effect of Process Cycle Time on Unit Cost. 24 2.0 N - n w PARTIAL NET UNIT COST OF POWER (mills/kwh) N 2.0 1.9 1.8 ORNL-LR-DWG 8577 \ /4509 OF Th/liter <" 175 REACTOR DIAMETER, 13 ft - ¢]0) - 250 125 Mw OF ELECTRICITY 480.8 Mw OF HEAT AVERAGE TEMPE RATURE: 280°C ONE REGION; ThO,-U0O3-D,0 SLURRY W OF Th/liter O~ 300 REACTOR DIAMETER, 42 ft {00 200 300 400 500 CHEMICAL PROCESS CYCLE TIME (days) 600 Fig. 43. Effect of Process Cycle Time on Unit Cost. 700 PARTIAL NET UNIT COST OF POWER (mills/kwh) _53_ ORNL-LR-DWG 8578 2.3 T T 125 Mw OF ELECTRICITY 480.8 Mw OF HEAT 150 g OF Th/ liter AVERAGE TEMPERATURE; 280°C \ ONE REGION; ThO,—UO3z—D,0 SLURRY 2.2 ' ' 175 \. / 200\ REACTOR DIAMETER {4 ft 21 ‘K 250\ / 300 _/ Xa 1.9 2.3 — 150 175 200 2.2 \ / REACTOR DIAMETER 10 ft 21 \——._ 300 250 2.0 100 200 300 400 500 600 700 CHEMICAL PROCESS CYCLE TIME (days) Fig. 14. Effect of Process Cycle Time on Unit Cost. PARTIAL NET UNIT COST OF POWER (mills /kwh) -54- ORNL-LR-DWG 8579 | | 125 Mw OF ELECTRICITY 480.8 Mw OF HEAT AVERAGE TEMPERATURE; 280°C ONE REGION; ThO,~UO3—D,0 SLURRY 2.5 OPTIMUM PROCESS CYCLE REACTOR DIAMETER 16 ft / N W 15 ft / 14 ft Z i\ 7 N 2.0 \ {3 ft 11 ft 1.9 - N 1.8 100 150 200 250 300 350 THORIUM CONGCENTRATION (g/ liter) Fig. 15. Effect of Thorium Concentration on Unit Cost. 400 PARTIAL NET UNIT COST OF POWER (mills /kwh) 2.5 2.4 2.3 2.2 21 2.0 _55_ ORNL-LR-DWG 8!80 125 Mw OF ELECTRICITY 1 480.8 Mw OF HEAT AVERAGE TEMPERATURE: 280°C | ONE REGION; ThO,—U03—D,0 SLURRY 1.06 OPTIMUM PROCESS GYCLE AND Th CONCENTRATION 1.04 // —— ' .02 / 1.00 ——gl— / / 0.98 . 0.94 10 1 12 13 14 15 16 REACTOR DIAMETER (ft) Fig. 16. Effect of Reactor Size on Unit Cost and Breeding Ratio. GROSS BREEDING RATIO -56- NOMENCLATURE Core radius, cm Breeding gain, atoms of fissionable material produced per atom of fuel burned Reactor buckling, cmm2 Net grams of fissionable material produced per day Turbogenerator plant investment, $/kw Totél power cost, mills/kwh Credit for excess fissionable material produced, mills/kwh D, diffusion constant, cm-l, for fast and slow groups, respectively 2 Gross efficiency of power plant Net efficiency of power plant Poison fraction Net feed to reactor, atoms/sec Core uranium concentration grams of uranium per kg of heavy water Fraction of group-3 poisons that can be precipitated External power density, kw/liter 16 Power constant, 3.38 x 10 fissions/Mw sec Concentration, atoms/cm3 Resonance escape probability Reactor power, Mw Fraction of material processedignd returned to reactor Inside Radius of pressure véssel, cm Thickness of core vessel, cm t=1.39R x lOfe Chemical process cycle time, sec Reactor or system volume, cm5 Yield of group-3 fission products, 1.31 atoms/fission AR -57- B Ratlc of resonance to thermal absorption o liicroscopic cross section, cm2 I Mecroscopic cross section, cm ¢ Average neutron flux of system, neutrons/cme-sec A Decay constant, sec T Fermi age, cu’ Subscripts: a Total capture B | Blanket C | .Core f Fission captfire T Radiative capture T Total system 1 Hydraulic separator processing 2 Thorex processing . 3 Group-3 poisons Parenthetical Symbols (used to identify N, A, o=, andL): A Group-5 poilson subgroup.A B Group—finpoison subgroup B 0 Precipitated poisons not removed in hydraulic separators 5 Group-3 poisons 25 U-233 2k U-234 25 U-235 26 U-236 13 Pa-23%3% 02 Th-252 E— 2- (1) (2) (3) (4) (5) (6) (7) (8) (10) (11) (12) (13) (14) Y - & £5 d & REFERENCES Arnold, E. D, Gresky, R. J., Klotzbach, R. J., and Irvine, A. R., "Preliminary Cost Estimation: Chemical Processing and Fuel Costs for a Thermal Breeder Reactor Power Station", ORNL-1761, Jan. 27, 1955. AEC Neutron Cross Section Advisory Group, Neutron Cross Sections, BNL-170, -170A, -170B, -221, (1952-1953). Briggs, R. B., "Aqueous Homogeneous Reactors for Producing Central-Station Power", ORNL-1642, May 13, 195k. Briggs, R. B., and Edlund, M. C., "A Preliminary Program for the Conceptual Design of the TBR", ORNL-CI-54-8-89, August 13, 195k. Fowler, T. B., and Willoughby, R. A., "ORACLE Code for the Two-Group, Two- Region Homogeneous Reactor Calculation", ORNL-CF-54-7-38, July 7, 195k. Glasstone, S., and Edlund, M. C., Elements of Nuclear Reactor Theory, Chapter XIII, (1953). Halperin, J., et al, "Capture Cross Sectlion of Pa-2335 for Thermal Reactor Neutrons", Reactor Science and Technology, p. 108, Vol. 3, TID-2010, (sept., 1953). HRP Quarterly Progress Report, ORNL-181%, October 31, 195k. HRP Quarterly Progress Report, ORNL-1853, January 3, 1955. Klotzbach, R. J., "Comments on Proposed Power Breeder Design Calculations”, ORNL-CF-54-8-78, August 10, 195L. Smith, R. R., Letter to J. Halperin, RRS-14-55A, March 28, 1955. Tobias, M., "A Thin Shell Approximation for Two-Group, Two-Region Spherical Reactor Calculations", ORNL-CF-54-6-135, June 16, 195k. Tobias, M., "Calculation of Fermi Ages for ThOo-Heavy Water Slurries”, ORNL-CF-54-9-97, September 14, 195h4. Visner, S., "Nuclear Calculations for Homogeneous Reactors Producing U-233", ORNL-CF-51-10-110, October 22, 1951. oy o -50- APPENDIYX T Constants Used in the Nuclear Calculations 1. Thermal Microscopic Cross Sections at 28000, barns. (Corrected for a Maxwell Boltzmenn Distribution) ' Absorption Cross - Radiative Capture Fission Cross Substance Section, og Cross Section, oF Section, 6Ff Th-232 L.52 -- -- Pa-~233 96.8 | -- o -- U-233 | 380.7 B 3h.3 ‘ 346.4 U-23h 57.4 -- -- U-235 41k.0 65.1 348.9 U-236 5.81 - - Dp0 1.76 x 1077 -= -- S L 0.316 \ - -- Group j poisons 13.1 - -~ . S T | 2. Macroscopic Absorption Cross Section of Zircalloy at 280°% = 5.897 x 10 > emt. e s 0 5. Diffusion Constants, Ages, and Resonance Escape Probabilities at 280°C for Various Thoria-Heavy Water Slurries. Concefitration of Fast Diffusion Slow Diffusion Fermi Age Resonance Escape Slurry, g Th/l Constant, D1B, cm Constant, D2B, cm Ty, cm@ Probability,ps - 200 1.73 1.19 21k 0.728 750 1.53 1.18 212 0.638 1000 1.49 1.17 P12 0.560 1500 1.47 1.17 207 0.435 4. Diffusion Constants, Ages, and Resonance Escape Probabilitiles at Various Temperatures for a Thoria-Heavy Water Slurry containing 1000 g‘Th/l. Temp. Fast Diffusion Slow Diffusion Fermi Age Resonance Escape °C Constant, DiB, ecm Constant, Dop, cm Tg, cm Probability 200 -1.34 0.998 168 0.590 250 1.42 1.09 190 0.575 280 1.49 1.17 212 0.560 300 1.56 1.24 23k 0.547 320 “1.62 1.34 260 0.530 el -60- ¥ et 5. Diffusion Constants and Ages for Uranyl Sulfate-Heavy Water Solutions at Various Temperatures. Resonance Escape Probability Taken as Unity for all Cases. Temp. Fast Diffusion Slow Diffusion Fermi Age oc Constant, Dic, cm Constant, Doc, cm T, em 200 1.46 1.05 167 250 1.57 1.1k 193 280 1.67 1.25 218 300 1.76 1.30 2LL 320 1.87 1.40 276 6. Density of Heavy Wéter; Zircalloy and Thoria at Various Temperature, g/cme. Temp. Heavy Water, 99.8L¢ Do0 oC Thoria Zircalloy at 2000 psi 200 | 9.69 | 6.55 0.959k4 250 (a1l temperatures) (all temperatures) 0.8935 280 0.8395 300 i 0.7959 320 0.7480