Sensitivity Study of Fuel Cost in Extended Burnup BWR Core

Transcription

1 Journal of Nuclear Science and Technology ISSN: (Print) (Online) Journal homepage: Sensitivity Study of Fuel Cost in Extended Burnup BWR Core Yasuhiro KOBAYASHI & Kikuo UMEGAKI To cite this article: Yasuhiro KOBAYASHI & Kikuo UMEGAKI (1984) Sensitivity Study of Fuel Cost in Extended Burnup BWR Core, Journal of Nuclear Science and Technology, 21:9, , DOI: 1.18/ To link to this article: Published online: 15 Mar 212. Submit your article to this journal Article views: 85 View related articles Full Terms & Conditions of access and use can be found at Download by: [ ] Date: 16 December 217, At: 13:42

2 journal of NucLEAR SCIENCE and TECHNOLOGY, 21[9J, pp (September 1984). TECHNICAL REPORT Sensitivity Study of Fuel Cost in Extended Burnup BWR Core Yasuhiro KOBAYASHI and Kikuo UMEGAKI Energy Research Laboratory, Hitachi Ltd.* Received February 12, 1983 Revised june 26, Downloaded by [ ] at 13:43 16 December 217 A sensitivity study on the fuel cost of an extended burnup BWR core has been carried out on the basis of a realistic model of discharge burnup extension. Full power operating length in months in a refueling cycle and the number of refueling batches are chosen as independent variables in the model to describe extended burnup cores of various types. The reference core for the sensitivity study adopts 9-month full power operation and 4-batch refueling scheme. The difference in the plant cost between the extended burnup core and the reference core, which is referred to as plant capacity factor (PCF) credit, is estimated and combined with the fuel cost to calculate the fuel cost with PCF credit. The results show that the fuel cost with PCF credit decreases for the extended burnup core with stretched operating length as the burnup extends in cases of constant non-operating length in a cycle, and that it may increase for the extended burnup core with decreased batch number in cases of constant plant capacity factor. It is also suggested that the cost minimum combination of the independent variables can be found to a given discharge burnup for the extended burnup core with decreased batch number in an intermediate case between these two extreme cases. Extended burnup cores with fixed batch number tend to have a lower natural uranium requirement, but larger separative work requirement. The economic break-even condition for the extended burnup core with decreased batch number is discussed based on the fraction of fixed part in the non-operating length, which is insensitive to the cycle length stretch-out. KEYWORDS: fuel co8t, plant co8t, power co8t, nuclear power plant8, fuel cycle, dibcharge burnup extenbion, uranium requirement, Beparative work requirement, plant capacity factor, BWR type reactor8 I. INTRODUCTION This report describes a sensitivity study of the fuel cost in an extended burnup BWR core. The objective of this study is to clarify the effect of discharge burnup extension on the core economic performance on the basis of a realistic cost estimation model for an extended burnup core. The extension of discharge burnup in light water reactor cores has been intensively studied by others to improve characteristics in fuel cycle and core design. The effect of modest burnup extension on uranium saving and fuel cost was studied for typical PWR once-through fuel cycle '. Economic benefit was also discussed on the cycle stretch-out using normal power coastdown and feedwater-pressure augmentation operation< >. Recently, parametric analysis on the fuel cost of extended discharge burnup was made considering increased cycle length operation in PWR's<s>-«>. These studies were made based on some * Moriyama-cho, Hitachi-ski

3 Vol. 21, No. 9 (Sep. 1984) TECHNICAL REPORT (Y. Kobayashi, K. Umegaki) 73 Downloaded by [ ] at 13:43 16 December 217 reference data of core design at relatively mature phases. Studies have been also directed to the methodology of fuel cost evaluation for elaborated cost analyses. An economic model was, for example, proposed to evaluate the fuel cost for a sequence of a number of non-equilibrium cycles(5). Methods used in these papers, however, need reference design parameters which are supposed to be supplied from detailed core design calculations and, therefore, are restricted in pursuing the global view of the effect of discharge burnup extension in fuel cycle and core design considerations. The number of refueling batches is one of the design variables which are important from the viewpoint of core design but few previous works dealt with the effect of fuel batch size variation on the extended burnup cores. The present study attempts to cover wider parametric range for design variables including the number of refueling batches in discharge burnup stretch-out and to survey the characteristics of extended burnup BWR cores through sensitivity analysis using a numerical tool for fuel cost estimation. Since the power cost is a measure of economic performance of nuclear plants, designers frequently face with decision problems to select promising design concepts out of a range of design alternatives in the course of design study. Detailed design data are not necessarily available to them at the conceptual design stage. Core designers attempt to optimize their design through the cost comparison among a number of design alternatives. For the purpose of this study, a cost estimation tool has been developed to deal with realistic discharge burnup extension process and to identify the difference in potential economic capability of the design alternatives with limited design information available at an early design stage. In this report, the power cost is divided into two components ; the plant cost and fuel cost, for simplicity. As the extended cycle operating length may cause the plant cost reduction through improved plant capacity factor (PCF), the plant cost credit due to this potential increase in PCF should be evaluated to grasp the total economic performance of the power plant with the extended burnup core. The difference in the plant cost between the extended burnup core and the reference core, which is referred to as PCF credit, is estimated and combined with the fuel cost to calculate the fuel cost with PCF credit. Two types of fuel cost are, hence, employed in subsequent chapter to evaluate the economic performance of extended burnup cores; the fuel cost with and without plant capacity factor credit. II. METHOD OF FUEL COST ESTIMATION 1. Fuel Cost Estimation A numerical tool for fuel cost estimation has been developed and applied to this study. It is important and frequently necessary to evaluate the economic capability of a design concept in terms of the fuel cost at this design phase when detailed fuel management schemes have not been established. The numerical tool for this purpose is supposed to deal with the fuel cost estimation at the early phase of core design, when new core design concepts are proposed and the viability of them are to be evaluated. Two major requirements to the tool with this purpose is itemized as follows; (a) to be accurate and consistent enough to treat realistic discharge burnup extension process, and (b) to be flexible and handy enough to be applied to frequent fuel cost analyses at an early design phase

4 74 TECHNICAL REPORT (Y. Kobayashi, K. Umegaki) ]. Nucl. Sci. Techno!.. Downloaded by [ ] at 13:43 16 December 217 The concept of an equilibrium cycle is very useful for defining one representive value of fuel cost throughout the plant life. The fuel cost to be obtained is defined at the beginning of the in-core residence period in an equilibrium cycle core. The fuel cost calculation method adopted in this study is based on one of the wellestablished methods c J csj ' 7 l. A few of the special features of numerical tool are outlined in the subsequent section. 2. Characteristics of Cost Estimation Tool The numerical tool employed in this study is characterized by three functions outlined in the following. ( 1 ) Linear Fuel Depletion Model A simple model to estimate nuclear core design parameters is incorporated into the numerical tool for cases where key dependent variables are not given. If the core discharge burnup and the number of refueling batches are specified, for example, this model consistently guesses the average fissile enrichment of fuel using a linear depletion assumption. The linear depletion model gives clean-cut relations among key design variables, together with an empirical correlation of fissile enrichment's). A brief description about the fuel depletion model is given in APPENDIX. ( 2 ) Cost Components Three cost components are defined for the following time domains : Upstream fuel cycle before the in-core residence of fuel In-core residence period Downstream fuel cycle after the in-core residence of fuel. Fuel cost components for these domains are referred to as the cycle upstream cost, Table 1 Cost data for sample calculations in-core residence cost and cycle downstream cost. The in-core residence cost is estimated from the economic worth of fuel at the beginning of cycle and that at the end of Item Value Yellow cake Conversion Enrichment cycle. It is convenient to divide fuel cost Fabrication Transportation of fresh fuel into these three components to treat various Storage and transportation of spent fuel types of fuel cycles in a flexible fashion in Reprocessing the cost computation. Reconversion The cost data employed here are based Credit for fissile Pu in spent fuel 4$/g Pu on references'") ' 7 J ' 9 J being updated where Exchange rate 25 yen=l $ necessary. The main cost data are summarized Interest rate 8%/yr. in Table 1. ( 3 ) Plant Capacity Factor (PCF) Effect The increased cycle operating length in the extended burnup core has a critical influence on the plant operation scheme and, therefore, a potential impact on the plant cost, as well as the fuel cost, through variation in PCF. The plant cost is, in general, inversely 5$/lb U 8s 1$/kg u 8$/kg u swu 32 $/kg u 5$/kg u 2$/kg u 4$/kg u 2 $/kg u proportional to PCF, which is determined by two factors; full power operating length and non-operating length in a cycle. In this study, the effect of discharge burnup extension on the plant cost is evaluated in the form of the difference in the plant cost between the extended burnup core and a reference core. This incremental plant cost due to PCF variation is referred to as PCF credit. The fuel cost with PCF credit is obtained simply by adding this plant cost credit -58-

5 Vol. 21, No. 9 (Sep. 1984) TECHNICAL REPORT (Y. Kobayashi, K. Umegaki) 75 Downloaded by [ ] at 13:43 16 December 217 m. SENSITIVITY STUDY FOR EXTENDED CORE BURNUP A sensitivity study on the burnup extension of a BWR core is carried out on the basis of the cost estimation tool outlined in the previous chapter. Both natural uranium and separative work requirement, as well as economic performance, in extended burnup cores are discussed in the following. to the fuel cost. The PCF credit is zero Table 2 Refueling parameters for reference core for the reference core. Item Value 3. Extension of Discharge Burnup Discharge burnup 28GWd/t A typical combination of refueling parameters is selected to define a reference core Operating length in a Number of refueling batches 4 concept for this study as shown in Table 2. refueling cycle 9 months Non-operating length in a Some assumptions are made for an analytical basis to evaluate the core performance Plant capacity factor 75% refueling cycle 3 months Type of refueling scheme consistently. employed Pu recycle The extension of discharge burnup can be realized in two ways in refueling schemes ; stretching the refueling cycle length and increasing the refueling batch number. The extended burnup core is described by two independent design variables ; operating length in a refueling cycle and the number of refueling batches. Four types of extended burnup cores are covered in this study ; Type I core with increased COL and fixed NOB Type II core with increased NOB and fixed COL Type III core with increased COL and increased NOB Type IV core with increased COL and decreased NOB, where COL and NOB stand for cycle operating length and the number of batches respectively. As mentioned in the previous section, PCF may be changed to produce a significant difference in the plant cost as well as in the fuel cost. The incremental plant cost due to the plant capacity factor variation from that of the reference core is calculated to survey the effect of extended burnup on the plant cost under a wide range of plant operation condition; however, a detailed analysis of the plant cost is not within the scope of this study. Three typical cases are picked up to describe the relationship between the operating and non-operating lengths. Case A : The non-operating length is constant. The PCF is improved to produce plant cost credit. Case B : The ratio of non-operating length to the operating length is constant. The PCF is insensitive to the burnup extension. Case C : Half of the non-operating length is proportional to the operating length, while the other half is constant. This gives an intermediate case between A and B. The ratio of the plant cost to fuel cost is 3 in the reference core. This value is used to estimate the incremental plant cost, which is added to the fuel cost to give the fuel cost with PCF credit. -59-

6 76 TECHNICAL REPORT (Y. Kobayashi, K. Umegaki) ]. Nucl. Sci. Techno!., Downloaded by [ ] at 13:43 16 December Fuel Cost The fuel cost is estimated for various combinations of two design variables described in the previous chapter The fuel cost given in Fig. 1 represents the economic performance of each core design concept for different cycle operating lengths and refueling batch numbers. For the extended burnup core spedfied by the combination of these two variables, the fissile enrichment of fresh reload fuel can be calculated on the basis of the linear depletion model to obtain the fuel cost, natural uranium requirement, and separative work requirement. From core design consideration, including power flattening easiness, 2 :2 the cycle operating length might not be " Q) c changed continuously, since the number of... Ul No. of batches refueling batches is usually selected to be a 8 2 value close to an integer such as 2, 3, 4, 5 etc. <D :::! lj.. 3 As shown in the figure, the fuel cost 4 decreases as the average discharge burnup 5 extends for the core with stretched operating Const.ant length and fixed batch number (Type I core), discharge burn up the core with increased batch number and fixed operating length (Type II core) and the core with increased operating length and Fig. 1 Relation between original fuel cost and increased batch number (Type III core). The cycle operating length (The fuel cost in fuel cost in this figure corresponds to the this figure corresponds to the fuel cost with PCF credit in Case B.) fuel cost with PCF credit in Case B. The curves for constant discharge burnup show that the fuel cost is improved in cores with shorter cycle operating length and/or bigger refueling batch number. This suggests that the fuel cost does not necessarily decrease for the core with decreased batch number and stretched operating length (Type IV core) as the burnup extends. For example, the core with the discharge burn up of 3 GW d/t and 4-batch refueling is slightly lower in the fuel cost than the core with the burnup of 4 GWd/t and 3-batch refueling. The linearity of constant discharge burnup curves is one of the most dominant characteristics of the fuel cost. The slope for the constant discharge burn up of 4 GW d/t suggests that about.3 yen/kwh in fuel cost reduction can be expected for each month eliminated. Presumably, the extended burnup core with decreased refueling batch number (Type IV core) is less favorable from the viewpoint of the fuel cost. 2. Fuel Cost with PCF Credit As mentioned in the previous chapter, stretching the operating length portion in a cycle offers some credit in the plant cost due to improved PCF. For extended burnup cores with stretched operating length (Type I, III and IV cores) the amount of this credit was evaluated and incorporated into the fuel cost. Since the plant cost is, in general, inversely proportional to PCF, the fuel cost with PCF credit can be estimated for Cases A, B and C, once a reference value for the plant cost is given. The fuel cost with PCF credit is shown in Fig. 2 for a constant discharge burnup case of 4 GWd/t in Fig. 1. Case B in Fig. 2 is the same as the constant burnup line of -6-

7 Vol. 21, No. 9 (Sep. 1984). TECHNICAL REPORT (Y. Kobayashi, K. Umegaki) 77 Downloaded by [ ] at 13:43 16 December GW d/t in Fig. 1. The PCF credit is significant in Case A (constant non-operating length), while no PCF credit is obtained in Case B (constant PCF). In Case A, longer operating length contributes to increased PCF credit. Since the operating length is longer for the core with less number of refueling batches to attain Discharge burnup the same discharge burnup, the extended 4GWd/t burnup core with decreased batch number (Type IV core) is most favorable from the viewpoint of PCF credit. The graph suggests that the dependence of the fuel cost with PCF credit on the operating length is reversed by the overwhelming effect of the capacity factor improvement in Case A. As is expected, results in Case B correspond to only the fuel cost portion. In the intermediate Case C, the minimum cost is observed at an operating length between 12 and 21 months, though the cost is rather insensitive to the operating length in this range. The minium cost can be given to the core concept with 18-month cycle operating length and 3-batch refueling scheme, if the number of refueling batches is supposed to an integer. :2 '2 '"' '6 Q) '- ll. u a...s: - '"' '"' Qi ::J ll 2 Discharge burnup 3GWd/t case B I }_ : :-----! case C I ----:.. f.-- 1 I I 3 case A I I I 2 No. of batches :2 '2 '6 '"' 2 ll CL {; '"' Qi ::J ll :2 '2 '"' '6 (': case B! _-i :--! :::-+--_ I I case C ; -t-- J -! case A r No. of batches. Fig. 2. Relation between fuel cost with PCF credit and cycle operating length (Discharge burnup 4 GWd/t) 3 Discharge burnup 5GWd/t.L I case B ll u I I a J_Case C.s: I I I '"' I '"' Qi ::J ll. case A 4 No. of batches (a) 3 GWd/t (b) 5GWd/t Fig. 3(a),(b) Relation bt::tween fuel cost with PCF credit and cycle operating length (Discharge burnup 3 and 5 GWd/t) -61-

8 78 TECHNICAL REPORT (Y. Kobayashi K. Umegaki) ]. Nucl. Sci. Techno!., Downloaded by [ ] at 13:43 16 December 217 Similar kind of figures for cases of constant discharge burnup of 3 and 5 GWd/t are provided in Fig. 3(a) and (b), respectively. The common characteristics of the variation of fuel cost with full PCF credit (Case A) as a function of cycle operating length is that relatively drastic cost reduction can be 1.6 expected for initial two or three months extended but that beyond such cycle operating No. of batches length the decreasing trend in the cost... c <lj curves tends to be mitigated. E e :; 3. Natural Uranium Requirement rr e The amount of natural uranium requirement is also evaluated. As shown in Fig. 4, the natural uranium required to generate unit integrated power of 1 MWd decreases with extended cycle operating length or/and increased number of refueling batches. The extended operating length tends to cancel the improvement of natural uranium requirement due to burnup extension, because the fissile inventory in the core increases as the cycle length extends. Constant discharge burnup curves in the figure show relatively large difference in natural uranium requirement observed in cores of equivalent discharge burnup extension. The result in Fig. 4 clearly shows that less natural uranium is required in the extended burnup core with fixed or increased batch number (Type I, II and III cores) and that natural uranium saving is not efficient in the extended burnup core with decreased batch number (Type IV core). 4. Separative Work Requirement The effect of discharge burnup variation on the separative work requirement is also determined by a delicate balance between the fissile inventory and the fuel discharge burnup. Relative separative work units required to generate unit integrated power is shown in Fig. 5. Stretching the operating cycle length causes a remarkable SWU requirement increase, though increasing the refueling batch number slightly decreases it. This result suggests that separative work requirement may be increased in the extended burnup core with fixed or decreased batch number (Type I, III and IV cores) for E :J c: e ::J -e :J... c "' <lj.-:; > a; "' :: Cons!ant discharge burnup.6 l L jl jl jc --,1---l Fig. 4 Relative natural uranium requirement in extended burnup cores 1.3,--,------,----r , No. of batches Constant discharge burnup 9L ;! : :':15: ,1:': ::'2':-1...J Fig. 5 Relative separative work requirement in extended burnup cores -62-

9 Vol. 21, No. 9 (Sep. 1984) TECHNICAL REPORT (Y. Kobayashi, K. Umegaki) 79 Downloaded by [ ] at 13:43 16 December 217 the range of discharge burnup 3"'5GWd/t. As shown in Fig. 4, for the extended burnup core with 4-batch refueling the separative work requirement tends to increase as the cycle operating length extends. It is because the increase in SWU value, to which separative work requirement is proportional, due to extended burnup is larger than that in the integrated power, as shown in Fig. 6. This figure also shows that the increase in feed component, to which natural uranium requirement is proportional, due to burnup extension is milder than that in the integrated power. Natural uranium saving is, therefore, realized for the extended burnup core with 4-batch refueling as the cycle operating length is stretched. IV. DISCUSSION OJ :::J 2 1. Fuel Cost with PCF Credit Fig. 6 The cost depends strongly on the cycle operating length, as well as on the discharge burnup, in Cases A and C, since the combination of operating length determines the discharge burnup. OJ.2:,.. til a; a: Natural uranium requirement Feed cc component Separative work cc SWU requirement Dependence of SWU, integrated power and feed component on cycle operating length for 4-batch refueling refueling batch number and cycle A longer operating length is favored for the PCF credit in Case A, while a shorter length is favored for the cost in Case B, where no such plant cost credit is expected. In the intermediate Case C, the cost is not so sensitive to the cycle operating length between 15 and 21 months. Numerical results in three cases show that the economic performance of extended burnup cores depends on the sensitivity of discharge burnup to PCF increase as well as discharge burnup extended. Results obtained in this study suggest that the extension of cycle operating length by a few months has straightforward impact on the cost because of PCF credit. 2. Optimum Cycle Operating Length In intermediate cases the minimum cost values are obtained for fuel costs with PCF credit in the range of cycle operating length, as shown in Figs. 2 and 3(a), (b). The fuel cost itself increases with approximately constant slope, though the fuel cost with PCF credit decreases with a slope steeper than the fuel cost slope for the initial 2 or 3 months extended and then turns its slope to be more gentle than the fuel cost slope later. These two characteristics are combined to produce the broad minimum in the cost of intermediate cases. The optimum cycle operating length and refueling batch number can be determined to a given goal discharge burnup in these cases. 3. Break-even Condition for Discharge Burnup Extension Two choices are available to improve the economic performance of extended burnup cores ; one is to increase the number of batches for the decrease in the fuel cost and the

10 71 TECHNICAL REPORT (Y. Kobayashi, K. Umegaki) ]. Nucl. Sci. Techno!., Downloaded by [ ] at 13:43 16 December 217 other is to decrease it and to increase efficiently the operating length for the increase in the plant cost credit. The discharge burnup extension is desirable from economic viewpoint for the core with decreased batch number (Type IV core), if the PCF credit exceeds the fuel cost increment. It is useful to introduce a gross parameter indicating the economic break-even condition for burnup extension. Case C is employed to represent intermediate cases between the two extreme Cases A and B in this study. It can be interpreted that Case C is based on two assumptions; (1) the non-operating length can be approximately divided into two parts ; one is the fixed part which is insensitive to cycle operating length and the other is the variable part which is proportional to the cycle operating length and (2) the fraction of the fixed part is 5%. This fraction of the part insensitive to the operating length in the nonoperating length can be treated as a parameter to describe the condition that potential fuel cost increase is equal to the PCF credit in the extended burnup core with stretched operating length. It is convenient to define a break-even condition for discharge burnup extension with this parameter from economic viewpoint. The break-even fraction is intuitively understood as the fraction of the fixed part of non c operating length that assures that the cost -u ttl... of an extended burnup core is comparable - c with that of the reference core. Break-even.5 fractions are plotted in Fig. 7 for three discharge burnup values. The PCF credit is more than the fuel cost increment in the region above curves in this figure. It is, for example, economically meaningful to extend the discharge burnup to 4 GWd/t and the cycle operating length to 15 months, when at least 25% of non-operating length is insensitive to operating length. Cl> I re PCFcredit >fuel cost mcrement o/"-,r::.g ;..No/" G... Ill 5. Fuel cost PCFcred1t <increment QL Fig. 7 Break.even fraction of plant cost which is insensitive to cycle ope rating length extension 4. Natural Uranium and Separative Work Requirement Stretching the cycle operating length increases the natural uranium amount required to produce unit integrated power, as shown by the constant discharge burnup curves in Fig. 4. The extended burnup, in general, tends to reduce the natural uranium requirement, since the effect of increased fissile nventory is dominated by the effect of extended discharge burnup. The proper choice of cycle operating length, presumably, improves the utilization of natural uranium in various types of extended burnup core. The increase in the number of batch is the most effective way of discharge burnup extension to suppress natural uranium requirement. The separative work required to produce unit integrated power tends to increase as the cycle operating length increases in months, as shown in Fig. 5. This result suggests that the SWU requirement may increase in the course of burnup extension unless the extension is eventually realized by increasing refueling batch number and keeping the cycle operating length constant. -64-

11 Vol. 21, No. 9 (Sep. 1984) TECHNICAL REPORT (Y. Kobayashi, K. Umegaki) Core Design Consideration Some class of extended burnup cores are not necessarily acceptable, since an improper choice of refueling batch number spoils the core performance. Current BWR cores are designed and operated on the basis of 4-batch refueling. The number of batches should be carefully selected from the viewpoint of design feasibility and ease of realization of core thermal performance comparable with current BWR's. The discharge burnup extension is, therefore, best done by combining cost optimality with design feasibility. At more mature phase of core design a more detailed fuel and core analysis should be pursued on the basis of cost sensitivity results, as well as of the present status of technical feasibility. Downloaded by [ ] at 13:43 16 December 217 V. CONCLUSIONS A sensitivity study on fuel cost of extended burnup BWR core has been carried out on the basis of a realistic model of discharge burnup extension. In this study, full power operating length in months in a refueling cycle and the number of refueling batches are chosen as independent variables in the model to facilitate the evaluation of the economic performance of conceptual core design. The results of cost calculations have clarified the sensitivity of extended burnup to the fuel cost, the fuel cost with plant capacity factor (PCF) credit, natural uranium requirement, and separative work requirement as a function of both cycle operating length and the number of refueling batches. (1) Three cases are picked up to represent situations in which extended burnup operations take place ; Case A of constant non-operating length, Case B of constant PCF and Case C which is an intermediate case between these two extreme cases. The results showed that the fuel cost with PCF credit decreases for the extended burnup core with decreased batch number as the discharge burnup extends in cases of constant non-operating length in a cycle, and that it may increase in cases of constant PCF. The cost minimum combination of two independent variables can be found for a given discharge burnup for intermediate Case C. Results obtained in Cases A and C suggested that the stretch-out of cycle operating length by a few months has straightforward impact on the cost because of improved PCF. (2) The stretch-out of discharge burnup causes lower natural uranium requirement, but larger separative work requirement in the cores with fixed batch number. The increase in the number of batches is the most effective way of discharge burnup extension to minimize natural uranium requirement and to avoid increased separative work requirement. (3) The discharge burnup extension is desirable for the core with decreased batch number from the economic viewpoint, if PCF credit exceeds the fuel cost increment. The economic break-even condition for discharge burnup extension was evaluated and discussed on the basis of the fraction of the fixed part of non-operating length which is insensitive to the cycle operating length stretch-out. (4) Fuel cost estimation tool has been developer and applied to this sensitivity study. The tool is able to deal with the realistic discharge burnup extension and useful in an early phase of conceptual design evaluation. ACKNOWLEDGMENT The authors would like to express their thanks to Drs. K. Taniguchi, S. Yamada, S. Kobayashi and R. Takeda of Energy Research Laboratory, Hitachi Ltd., for their guidance -65-

12 712 TECHNICAL REPORT (Y. Kobayashi, K. Umegaki) ]. Nucl. Sci. Techno!., and encouragement during the course of this work. --REFERENCES-- Downloaded by [ ] at 13:43 16 December 217 (1) MACNABB, M. V.: Two near-term alternatives for improved nuclear fuel utilization, Nucl. Technot., 49, 435 (198). (2) MATZIE, R. A., et al.: The benefits of cycle stretchout in pressurized water reactor extendedburnup fuel cycles, ibid., 52, 189 (1981). (3) ScHERPEREEL, L. R., FRANK, F. J. : Fuel cycle cost considerations of increased discharge burn up, ibid., 56, 16 (1982). (4) FRANK, F. J.: A new assesment of LWR recycle, Paper presented before AIChE 74th Annu. Mtg., (1981). (5) ABou-GHANTOUS, C.: An economic model for fuel cycle cost, Nucl. Techno!., 52, 57 (1981). (6) FuJI, H. : "Economic Analysis of Nuclear Power Generation and Prediction of Nuclear Fuel Industry in Future", (in Japanese), (1973), Fuji-International. (7) NIWA, K. : "Nuclear Power Cost", (in Japanese), (1976), JAIF. (8) SPECKER, S. R.: Private communication, (1977). (9) GRAVES, H. W.: "Nuclear Fuel Management", (1979), John Wiley & Sons. [APPENDIX] Fuel Linear Depletion Model ( 1 ) Integrated Power Balance in Equilibrium Cycles F Bd=3.45 Ls, L=JT, M=T-L, where F: Fractional refueling batch size Ed: Average discharge burnup f: Plant capacity factor (PCF) T: Total length of refueling cycle L : Full power operating length in a cycle M: Non-operating length in a cycle s: Core specific power (MW /t). ( 2 ) Linear Depletion Equation (a) Linear depletion of core (Al) (A2) (A3) (A4) (b) where R: Reactivity at core average burnup of E Ro: Reactivity at E = E : Core average burnup E : Core average burnup at R=O. Linear depletion of refueling batch Rk=Ro(l-Bk! Eo), k-l Boc=---Bd' n where Rk: Reactivity at k-th batch at average burnup of E E k: Average burn up of k-th batch Ezoc: E k at the beginning of cycle -66- (A5) (A6) U\7)

13 Vol. 21, No. 9 (Sep. 1984) TECHNICAL REPORT (Y. Kobayashi, K. Umegaki) 713 (c) Boc : B k at the end of cycle n : Number of refueling batches (n = 1/ F) Core reactivity at the end of cycle (EOC) 1 n R=- Roc=O. n kl This leads to the relation between Bo and Bd; Bo=!!zl Bd=J1F Bd. (AS) (A9) Downloaded by [ ] at 13:43 16 December 217 ( 3 ) Correlation of Average Fissile Enrichment The fissile enrichment can be empirically correlated to B where e: Average fissile enrichment a, b: Empirical coefficients. e=a+bbo, (AlO) Coefficients a and b can be empirically determined from results of design calculations. One example correlation for a typical BWR is shown in Fig. Al. This linear correlation is combined with Eq. (A9) to give the relation among discharge burnup, number of refueling batches and fissile enrichment. 4..., c.c tl 'i: c <ll 3..!!! u;.!!2 LL. (All) 2 1';;------L------;2-----_l _j3 Core average burnup at EOC CGWd/t) Fig. Al Linear correlation between fissile enrichment and core average burnup -67-