Burnup and feasibility study of low power density PWR's


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Burnup and feasibility study of low power density PWR's
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xiii, 306 leaves : ill. ; 28 cm.
Molins-Bartra, Cesar, 1953-
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Subjects / Keywords:
Pressurized water reactors   ( lcsh )
Fuel burnup (Nuclear engineering)   ( lcsh )
Nuclear Engineering Sciences thesis Ph. D   ( lcsh )
Dissertations, Academic -- Nuclear Engineering Sciences -- UF   ( lcsh )
bibliography   ( marcgt )
non-fiction   ( marcgt )


Thesis (Ph. D.)--University of Florida, 1981.
Bibliography: leaves 303-305.
General Note:
General Note:
Statement of Responsibility:
by Cesar Molins-Bartra.

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Source Institution:
University of Florida
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 028131785
oclc - 07895224
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Full Text






Tb Him who cares for all

and who gave us this world,

as an insignificant sample of my deep appreciation


The author wishes to express his sincere appreciation to the members of his supervisory committee N.J. Diaz, E.E. Carroll, E.T. Dugan, C.C. Oliver and M.L. Muga for their interest and help in preparing this dissertation. Special thanks are given to Dr. N.J. Diaz for originating the dissertation subject and providing direction of the research project. The author is deeply indebted to Dr. E.T. Dugan for providing continued technical guidance and criticism and invaluable help in obtaining necessary calculational tools, together with endless patience in correcting this report.

The author is indebted to J.A. Wethington, Jr., M.J. Ohanian, G.R. Dalton, W.H. Ellis, G.S. Roessler and W.G. Vernetson for the friendship and support given through the years of this research.

The main body of the calculations of this study were performed at Oak Ridge National Laboratory, Tennessee, where the author met a number of great friends who were instrumental in the execution of this work. Special thanks are given to J.C. Cleveland for making the necessary arrangements that made the stay at O.R.N.L. possible and for his technical advice and assistance; to Rafael Perez and iii

Pedro Otaduy (the Godfather and the executive coordinator of the Spanish colony at O.R.N.L., respectively) and to the rest of the Spanish group for their continued moral support and friendship; and to F. Clark and T. Prinm for their administrative and technical advice.

The author acknowledges that during his tenure at the

University of Florida he was financially supported by the National Science Foundation, the Hauck fund, Oak Ridge National Laboratory and two consecutive University of Florida Graduate School Fellowships.

The author keeps a special thought for Keith Johnson for his untiring help in computing matters, and to Pedro Salas for the many hours of friendship and sharing in happiness and in distress.




ACNOWLEDGEMENTS * * * * * * iii

LIST OF TABLES . .. . * * v * iii

LIST OF FIGURES ..................... ix

ABSTRACT ......................... xii

I. INTRODUCTION . . . .. . . .. . . . 1

1.1. Background . . . . ......... 1
1.2. The SHARP Concept . . . . 4
1.3. Previous Studies of Low Power Density Cores . 9
1.4. Purpose of this Study .... ... .. 10

II. SCOPING WORK . . ... . . . . . 14

2.1. Problem Framing . ... .. . .. 14
2.2. Calculational Methods for the Scoping Study . 25
2.2.1. Heat Transfer Calculations . . . 25 2.2.2. Neutron Cross Section Calculations . 31 2.2.3. Criticality and Burnup Methods . . 33
2.3. Results of Preliminary Work . . . . . 41
2.3.1. Reactivity Coefficients . . . 41 2.3.2. Neutronics and Safety Considerations 51
2.3.3. Burnup Achievements and Isotopic
Inventories . . . . . . . 63
2.4. Scoping Work Conclusions . .. . ... . 70


3.1. Burnup Calculational Methods and Present Needs 72
3.2. Method Developed for this Study . a . . 99
3.2.1. The Fuel-burning Codes . . . . 99
3.2.2. The CRIBUR Core Model a . . . 106
3.3. Benchmarking of the Burnup Calculations . 132
3.3.1. Available References for Comparison . 132 3.3.2. Criticality Benchmarking . . . 135 3.3.3. Power Distribution Benchmarking .... 140



4.1. Cases Chosen for Final Study . . . .. 143
4.2. Results of Optimization. ......... . 147
4.2.1. Neutronics and Isotopic Results . . 147
4.2.2. Plant Operational Data Variations . 160
4.2.3. Ore Usage and Enrichment Needs . . 175


5.1. Safety Related Thermal-hydraulic Considerations 179
5.1.1. Motivation .............. 179
5.1.2. Thermal-hydraulic Studies . o . 180
5.2. Economic Evaluation ............. 190
5.2.1. Introduction ............. 190
5.2.2. The Economic Comparison Studies . . 191


6.1. Introduction ...... ...... 201
6.2. Neutronics, Burnup and Ore Usage .. .... 204
6.3. Plant Operations Considerations . . . . 207
6.4. Economic Effects ..... .. 209
6.5. Suggestions for Future Rearch ........ 211


A.1. Introduction ................ 213
A.1.1. Motivation and Constraints . . 213
A.1.2. Schemes for Improving Burnup . . 215
A.2. Techniques for Improvement of Burnup o . 219'
A.2.1. Increasing Number of Batches . . 219
A.2.2. Burnable Poisons o.__ . 223
A.2.3. Low-Leakage Fuel Management . o 229
A.2.4. Alterations of Fuel-to-Water Ratio . 233
A.2.5. Low Power Density . 0 0 . 237
A.2.6. Flattening Axial Power Distribution 239
A.2.7. Increasing Enrichment . 0 . . 240
A.2.8. End of Cycle Coastdown . . . 0 242
A.2.9. Other Possibilities of Minor Importance 244

Bi. BRT CODE DESCRIPTION ............. .. 248

B2. PHRO ODE DESCRIPTION ............. 251

B3. MONA CODE DESCRIPTION .. ............. 253

B4. LEOPARD CODE DESCRIPTION ............... 255


B&. NTPUNamCOE DR IPTION . TIO9...s..*.*.* 263

B7. PDO-7 CODE DESCRIIONO... .. .. .. .. .. 265

B8. TEMPRrTCM~E DESCRIPTION. o..o... . .. 269

B9. CNCEPT,-IVCODE DESCIPTION . . .. ......4 271

B10. GEM CODE DESCRIPTION s.. *... o*. ..*.9 273

Bli. POWCx OCME DESCRIPTION . .. .. ... 275

Cl. CRIBUR COE SOUJRCELISTING . .. .. .. ... 277




2.1.1. Main Core Parameters for the Standard Reactor. . 19

2.1.2. Basic Fuel Cell of the Standard Reactor. . . . 19

2.1.3. Basic Cell Composition. Core #1 . . . . 21

2.1.4. Identification of Cases for the Scoping Study . 23

2.1.5. Tabulation of Case Number Densities Which Differ
from Those of Case #1 ............... 24
2.2.1. Basic Cell Temperatures vs. Power Level . . . 30

2.3.1. Core Reactivities at B.O.L . . . .. .... 50

2.3.2. Scoping Burnup and Isotopic Results .. ..... 65

3.3.1. CRIBUR and Batch-averaging Method Criticality Errors 137

3.3.2. Effects of Code and Data Alterations on Core K-eff. 139

4.2.1. Burnup Achievements, Fissile Isotope Usage and
Ore Usage . .. .. .. .. . . 149

4.2.2. Plant Operational Data Comparison . . . . 161

4.2.3. Ore, Enrichment and Plutonium Normalized to 1125 MWe 176

5.2.1. Capital Costs (Mills/KWh) and Percent Increases
over Standard Plant .......... ..... 193
5.2.2. Fuel Costs (Mills/KWh) and Percent Increases over
Standard Plant .................. 193
5.2.3. Generation Costs (Mills/KWh) and Percent Increases
over Standard Plant ...... ........... 199

A.2.1. Discharge Burnups of Low Power Density Cores . . 239

D.l. Cell-Homogenized Nupber Densities
(Atoms/Barn cm X 10F) ............... 301

D.2. Average Cell Neutron Velocities (eV) . . . . 302



2.2.1. Pin Cell Gemetry ................. 26

2.2.2. Geometry Used for MONA Criticality Calculations . 35 2.2.3. Code and Data Flow for Preliminary Burnup Calculation 37 2.2.4. Comparison of Boron Letdown from Leopard and Burnup. 40 2.3.1. Soluble Boron Worth at Critical vs. Burnup . . 46 2.3.2. Soluble Boron Worth at Critical. Changing Pitch . 47 2.3.3. Infinite Multiplication Factor vs. Pitch . . . 53 2.3.4. Eta and Fast Fission Factor vs. Pitch . . . 56

2.3.5. Resonance Escape Probability and Thermal Utilization 58 2.3.6. Thermal-to-Fast Flux Ratio . 0 . . 0 0 60

2.3.7. Discharge Burnup of 25% Power Density Core vs. Pitch 64 2.3.8. U-235 and Plutonium Usage vs. Pitch . . . . 69

3.1.1. Basic Steps in a Burnup Calculation . . . . 75

3.1.2. Examples of Burnup Conditions and Timestep
Specification for Fuel Cell Burnup Calculation . 78

3.1.3. Geometry and Composition Specification for a PDQ-7
1/4-assembly Burnup Calculation . . o . . 81 3.1.4. Grouping of Pin Cell Data into Core Data . . . 85

3.1.5. Constant-boron Pin Cell Burning with Boron-free
Pseudo-burnup Steps ................ 87


3.1.6. Pin Cell Burning with Soluble Boron Letdown Curve
and Power Level Following .. . . 90
3.1.7.* Effect of Time-dependent Power Level and Soluble
Boron Concentration Specification . . . . 93 3.2.1. Estimates of Boron Letdown and Relative Power ... 105

3.2.2. Flowchart of Data for a Fuel Burnup Calculation
Using PDQ-7 1/4-Assembly Geometry . . . . 107

3.2.3. Core Geometry Used in CIBUR. 109

3.2.4. Bessel-shaped Flux Distribution . . . . . 116

3.2.5. Fake-burnup Steps for Soluble Boron Worth . . 124 3.2.6. Problem of Erroneous Cycle Length . . . . 126

3.2.7. Flowchart of CR2EBUR Code . a 0 . 0 0 a 130 4.2.1. Recyclable Fissile and Net Fissile Usage vs. Pitch 155 4.2.2. Plutonium Discharge and U98 Use vs. Pitch . . 158 4.2.3. Real Cycle Length vs. Pitch . . . . . . 167

4.2.4. Total Life Refueling Time vs. Pitch . . . . 169

4.2.5. Availability and Capacity Factors vs. Pitch . . 172

5.1.1. Fuel Centerline Temperature vs. Relative
Mass Flow Rate a 6 0 0 . . 0 0 a a 183 5.1.2. Fuel Average Temperature vs. Relative Mass Flow Rate 185 5.1.3. Clad Surface Temperature vs. Relative Mass Flow Rate 185 5.1.4. DNBR-minimum vs. Relative Mass Flow Rate . . . 186

5.1.5. Percent Savings in DNBR-minimum and Fuel Temperature 188 5.2.1. Capital Cost vs. Plant Power .. . . . o . 194

5.2.2. Fuel Cycle Cost vs. Plant Power . . . . . 196

5.2.3. Total Generation Cost vs. Plant Power . . . 200


6.2.1. Discharge Burnup vs. Pitch . . . . .* . 205

A.2.1. Increase in Fuel Burnup due to Partial Refueling . 220 A.2.2. Ore Utilization vs. Enrichment and Cycle Length . 222 A.2.3. Orientations of Non-synnetric Burnable Poisons . 227 A.2.4. Batch Distribution in Core . .. . . .. 230

A.2.5. Discharge Burnup vs. Enrichment at Several
Fuel Densities ................... 235

A.2.6. Ore Utilization vs. Enrichment at Several
Fuel Densities ................... 236

A.2.7. Power Shaping Effect of Partial Length Rod . . 241 A.2.8. Ore Utilization vs. Fuel Enrichment and Burnup . 243


Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy BJNPAND FEASIBILITY STUDY OF


Cesar Molins-Bartra

June 1981

Chairman: Nils J. Diaz
Major Department: Nuclear Engineering Sciences

Operational and safety problems of current Pressurized Water Reactors are often associated with the high power density level of the cores. An alternate use of current-design cores is proposed by reducing the power density. The effects should be improved safety. improved ore utilization, and improved operational characteristics.

A scoping study is performed in order to define core parameters suitable for optimization under the low power density characteristics, while minimizing redesign requirements.

A neutronic optimization study of the reactor cores is performed by systematic changes in the fuel lattice pitch. A new core burnup computational model (CRIBUR) is developed, which allows calculation of the burnup and isotopic analysis of a multi-batch core in its equilibrium cycle with a moderate computational and human effort. CRIBtIR provides better accuracy and sensitivity than other known existing models of comparable scope. with a moderate


computational. effort. The code is benchmarked against actual core data and against multi-dimensional diffusion theory core calculations. and its sensitivity to several of the calculational parameters is also tested.

The thermal-hydraulic behavior of the low-power cores is compared to that of the standard reactors. and their enhanced safety margins are clearly demonstrated.

The low-power cores yield higher burnup, levels than the standard reactors. Ore utilization is also improved in a

once-through fuel management policy. Isotopic comparisons are

presented. Core cycles are drastically increased- Plant availability and capacity factors are also increased as a result of both the reduced impact of refueling downtimes and the reduced forced outage time resulting from the improvement of operational characteristics.

An economic comparison of the low-power cores is presented as a function of the core power level and the level of inflation. Low-power cores are at an economic disadvantage when compared to the standard reactor primarily because of the impact of the increased capital cost. The fuel cycle cost is also higher because of the long fuel core residence time. This economic disadvantage needs to be weighed against the impr oved safety and operational reliability to determine the commercial feasibility of the concept.




The most widely used reactor system for present and near future commercial production of nuclear energy is the Light Water Reactor (MR). The LWR's were developed originally as compact#, light-weight, high-power units suitable for ship propulsion and power, and they indeed performed as intended. The large research and development efforts of the U.S. military establishment for the LWR systems made them attractive for commercial power generation, and thus, they were deployed in land-based electric power plants.

LWRIs have been generating commercial electricity for a

considerable amount of time, totaling over 500 reactor-years of operation in the United States alone. However the safety systems and engineering safeguards intended to prevent or to contain and reduce the impact of accidents have become extremely sophisticated and costly. This is due to several cumulative reasons: 1) the fact that LWR's work under conditions that are close to technological limits, 2) the high power density typical of these compact reactors, 3) the fuel and coolant conditions, and 4) the inherent "core-cooling" problems in case of accidents or severe transients.


The many operational transients saiety-related incidents and the rare but significant accidents resulting in extended reactor shutdown, e.g. Three Mile Island and others, clearly substantiate this assertion.

A key dilemma appears immediately: a very high power density reactor has intrinsic serious safety problems; however, economic considerations have resulted in larger, high power density reactors working closer to their technological limits and requiring improved engineering safeguards. The industry has naturally worked towards extracting the maximum power from a given core, and also towards extending the reactor fuel cycle time in an attempt to reduce the economic impact of refueling outages and fuel carrying charges. Both these goals tend to demand performance from the reactors in a manner that is not always compatible with strict safety


Several questions need to be asked at this point. First: Is there a way of relieving the LWR's cores from these limiting situations without incurring an unacceptable economic penalty? Second: Will the new concept or approach need extensive (and thus costly and long) research and development and therefore have no impact in the short term? Third: Will the new concept be easily licensable, or will it require completely new licensing regulations and processes that would take many years to develop and create significant uncertainties for its deployment?

The first part of the first question has a relatively obvious answer from the technical point of view: reducing the power density


of the cores and making other technological fixes while maintaining the basic reactor design and technology will increase safety margins in the critical operational variables. However, the plant economics could suffer a significant penalty since a reduced power density requires a higher capital investment per unit of installed power, and this is the major part of the cost of nuclear-produced energy. On the other hand, the reduction of power density might allow a better fuel economy, reduce refueling times, reduce

personnel radiation exposures and waste handling and allow a better overall plant capacity, thus utilizing better the invested capital.

Favorable answers to the second and third questions strongly dictate that presently known and proven technology be used if the solution is to be regarded as a viable alternative by the electric power generating industry.

The Safer Highly Available Reactor Plant (SHARP) concept described below appears to be a solution meeting these overall demands. It would definitely enhance safety by improving the core power distribution, thermal-hydraulics conditions, heat removal requirements and overall plant operations. It would not require

significant new engineering and technical innovations, since minimal variations would be applied to the currently used reactor designs. These new plants will probably be easier to license than the current plants. The economic aspect is the only phase on which a conclusion is not easily forthcoming, and it requires in-depth analysis before reasonable cost comparisons can be established. The purpose of this work is to conduct an in-depth comparative and


optimization study of the fuel utilization capabilities of the Safer Highly Available Reactor Plants versus the standard MR, plants currently in operation or under construction, and concurrently, to develop calculational tools that will facilitate and enhance the accuracy of scoping-type burnup studies. The primary study must be complemented with indications of the

comparative safety and economic performance of the SHARP with respect to standard PWR plants.

1.2. The SUM Concept

The main goals pursued by the "Safer Highly Available Reactor Plantu (SHARP) are the following:

Enhance reactor safety.

Reduce the safety and operational problems caused by the operating conditions prevalent in current LWR systems.

Reduce lengthy and costly research and licensing procedures.
Offer a solution which utilizes current technology and can be implemented in a relatively short time.

Reduce economic penalties to make a commercially viable operation.

The dominant feature of the SHARP is the use of a standard PWR core, without core changes requiring technological modifications, at a reduced power density to reduce safety-related and operational problems associated with standard full power operating conditions. The single low power density core may then be employed in an essentially standard plant configuration, yielding a reduced power


rating plant. Alternatively#, it could be employed in parallel with several other low power density cores powering a single standard secondary side so as to yield a plant of normal or full power rating. This multi-core arrangement was first considered attractive to maintain the overall capital cost down and maintain large plant output. However, from the commercial point of view, it is obviously more reasonable to study the single-reactor reduced power rating plant, whose design and construction are well known. It is important to consider also that the economy of scale afforded by the present large plants lies in the reduced number of critical, expensive components used for the production of a large amount of power. The low power density concept breaks away from this constraint and attempts to demonstrate that there is no large advantage in designing large power output plants as compared to smaller sizes,, when all factors influencing plant economics are considered. Furthermore, it is frequent to find electrical demand areas where the large power rating plants are oversized and a smaller plant is better suited for such places.

A single-core SHARP, which is the main concept analyzed in this work, is a plant using a standard, full-sized reactor vessel operating at a reduced power level, with the balance of plant dimensioned according to the desired rated output power (50% of standard, 33% of standard, etc.). The use of a single full-sized core for the low power density system accomplishes the dual goal of avoiding extensive plant redesign, and operating a core at a power level clearly within its technological limits with enhanced safety

and operational characteristics. A higher plant capital cost per unit of installed power is expected (1) because of the losses associated with the economics of size, i.e. because of the additional investment in the "oversize" Nuclear Stemn Supply System (NSSS) components However, the overall cost of energy production would be competitive because of the improved operating conditions and safety.

Note that although the power density (and thus, the heat flux across the fuel elements of the core) is reduced, the thermodynamic conditions of the coolant would be maintained at the same level as in the standard plants to avoid loss of thermodynamic efficiency of the plant. This can be easily achieved by reducing the coolant flow across the core, within established heat transfer limitations. Reducing the heat flux in the fuel while maintaining standard coolant conditions reduces the temperature of the fuel,, which improves fuel/clad thermal conditions, reduces stresses in the fuel, and hopefully reduces fuel pin failures.

The advantages that can be obtained from the SHARP are:

a). From the heat transfer point of view:

Lower temperatures in th fuel pellets, due to the lower heat flux. This would imply reduced thermal-related damage to the pellets and to the cladding, and therefore, reduced pin failures.

Reduced probability of reaching critical heat transfer conditions.


-Reduced heat stored in the fuel, and increased available heat capacity, i.e., in case of an accident the core is capable of retaining more heat before suffering damages.

Milder accident conditions and emergency cooling requirements, due to the lower fuel temperature and lower power density (which means reduced decay heat generation).

b). From the neutronics point of view:

Less Doppler broadening of resonances, and therefore extra reactivity available.

Reduced xenon concentration due to the lower neutron flux, which means again some extra reactivity available.

Reduced xenon oscillation problems due to the lower, overall xenon concentration.

c0. From the fuel cycle point of view:

Longer burnup achievable from the same initial fuel, due to the extra reactivities mentioned above.

Largely increased time between refuelings due to the double effect of larger burnups achievable and the lower power generation of each core. This would reduce the impact of refueling outages on plant availability tending to increase it. The increased availability would result in proportionally increased energy generation in a given time period, thus reducing the impact of capital (which would be a basically fixed total cost) on energy generation cost.

Reduced relative activity of the fuel at discharge per MWd generated due to the largely increased residence of the


fuel in the core, which would allow more of the mid-life fission products to decay while in the reactor.

Reduced ore requirements due to the larger burnups achievable from the same initial cores.

Reduced enrichment needs.

d). Fran the operations point of view:

Increased plant availability and capacity factor due to the longer inherent fuel cycle.

Operations well within technological limits with reduced failure of components and reduced forced outage periods.

Decreased operational transients and constraints.

Better load following capability because of the large technological margins available for maneuvering.

Reduced overall personnel radiation exposure.

Reduced fuel handling cost because of less material being handled and because of its lower specific (per MWd generated) radioactivity (which results in reduced personnel radiation exposure).
Possibility of reduced spent fuel storage and

transportation requirements.

Easier inventory control and reduced risk of proliferation because of the reduction of fuel handling operations.

All these advantages appear to be qualitatively obvious, but the question remains whether or not they can outweigh the economic disadvantage mentioned before.


The present study conducted on the low power density

single-core, reduced power rating plant using essentially the standard plant configuration is also timely because of the present worldwide interest towards building new, small size plants. There are many situations where a 1000+ We plant is just too large, and so is the capital investment associated with it.

1.3. Previous Studies of Low Power Density CQres

The general trend followed by industry since the application of nuclear reactors for commercial production of energy has been to increase plant size and-power densities in an effort to reduce the capital cost per KW installed. The trend of higher power densities reduced both the materials involved in the reactor construction and the fuel inventory necessary for a given plant power rating.

A few commercial reactor concepts having significantly lower power densities than the LWR's are in operation, but they present higher capital cost and reduced operating experience. Such is the case, 'for example, of the Magnox reactors.

Lower power densities for LWR's were, thus, not considered seriously until recently under the NLW(2) project

(Nonproliferation Alternative Systems Assessment Program) where low power density cores were investigated primarily as a means for increasing the fuel utilization in a once-through fuel management scheme. This would reduce fuel handling operations, and therefore proliferation risks, while also providing additional safety



This low power density study for the NASAP project was carried out by Westinghouse Corp., and their approach to low power density was that of increasing somewhat the overall core dimensions,, while maintaining or even augmenting the output power. This approach meant only a moderate reduction in power density (about 23% as compared to the 50 to 75% reductions considered in the SHARP concept). This system was found to be advantageous from the points of view of safety and fuel utilization when compared to the standard high power plants. On the other hand, the need for redesign of the core, the pressure vessel, fuel handling mechanisms, etc., was found to require large investments both in time and in capital, and the idea was not considered practical by the private industry unless governmental support was provided.

1.4. Purpose of this Study

The main purpose of this study is to research and develop the neutronic and fuel utilization characteristics of the SHARP

concept, and for purposes of completeness, to assess its overall safety and economic capabilities in comparison with standard PWR


Several steps are necessary in order to accomplish this task:

a). Definition of what constitutes a SHARP for the purpose of this study (ranges of power densities, safety considerations and/or goals, etc.).

b). Definition of a set of possible reactor cores on which parametric studies can be effectively conducted.

c). Preliminary neutronic and fuel cycle study of the defined cores with known and reliable calculational tools in order to have a good estimate of the performance characteristics of each core. This would include obtaining first estimates of basic core

parameters (such as reactivity worth of boron, coolant temperature, Doppler reactivity coefficient, etc.) and of the expected variation of core and fuel cycle parameters (burnup, cycle length, etc.).

d). Exploration and evaluation of currently available calculational tools that may be suitable for this type of study, and development of new calculational schemes that may accomplish the established goals with the optimum cost/results ratio and serve the nuclear industry as an accurate scoping tool.

For example, this study needs a good set of calculational tools for the neutronics calculations, where power levels, fuel

temperatures, etc. can be easily specified and changed, since these are some of the main parameters that will differentiate the low-power core from the standard core. It also requires reliable and economical means of calculating core burnup distribution, core life time, etc.

e). Detailed neutronic and fuel cycle studies of the cores selected from the parametric variations performed in the preliminary study. This study must result in an optimization of the SHARP cores from fuel-cycle and plant operation points of view. The results of the SHARP study must be compared to those of

standard PWR's analyzed with the same calculational tools, in order to obtain relative figures of merit with a minimum of


methodological errors that could bias the estimates towards either


V. overview of economic evaluation of the SHARP concept as compared to the standard PWR to establish the overall economic advantages or disadvantages that may be expected from the SHARP concept. The economic evaluation must consider the variations in the costs of interest and escalation, as well as the possible size or rating variations of the plant components which depend on the plant power rating. For example, when studying a single-core SHARP for a power level of 50% that of a standard plant, the NSSS is dimensioned equal to that of the standard, full-power plant, but the BOP is dimensioned for only the new 50% power rating.

The next chapter describes the SHARP parameters and the preliminary calculations carried out in order to establish the basic expected performance of the low power cores.

Chapter III describes the burnup calculational methods used in the industry; they are compared to the needs of this study, and a new method is developed, which best suits the scope of this work and results in reduced computational effort. The new method should serve as a valuable industry-wide burnup calculational tool because of its accuracy, ease of utilization and low computational cost.

Chapter IV shows the cases chosen for in-depth study and the results obtained from the burnup calculations, plus some data referred to the expected comparative plant performance.


Chapter V is a brief description of the thermal-hydraulics safety"related aspects of the SHARP as compared to the standard

plant, and an insight into the comparative economic behavior of the SHARP.

Chapter VI contains the main conclusions of this study and recommendations for future research on the topic, considering points that have appeared as unresolved and potentially advantageous questions concerning the SHARP concept.


2-1. Problem Eraming

The purpose of this chapter is to study a sequence of different low-power cores in order to calculate first estimates of the low-power cores characteristics. A reference standard core must be defined against which one may compare the characteristics of the low-power cores. Finally, the results of the comparisons of the different reduced power density cores versus the standard one will be used to define the characteristics of selected cores that will undergo an in-depth study. The possible need for new

calculational tools to perform such in depth study will also be examined. This chapter will, therefore, study a series of low-power cores. The results of this study will be used to select the better candidate cores, and a range of their expected

characteristics, for further analysis.

The study of the SHARP requires an initial definition of the parameters of the reactor and/or of the fuel cycle that may be used as a means of comparing the SHARP with the standard PWR plant. These parameters may be classified into three main categories of interest: Safety, Neutronics, and Fuel Cycle. These are key areas of investigation which have both independent and interrelated problems.


Parameters of interest from the safety point of view would be:

a). The moderator temperature reactivity coefficient (MTrC).

b) The Doppler reactivity coefficient.

c). The fuel average temperature.

d) The power peaking factors.

e). The soluble boron reactivity worth (at the concentrations needed throughout a cycle life for each particular reactor system).

fV. Power density and linear power (KW/ft).

From the neutronics point of view, some of the more important parameters to be observed are:

a).* The changes of Doppler reactivity coefficient at the different power density levels.

b). xenon concentration.

c).* Core effective multiplication factor at beginning of life.

c). Evolution of isotopics.

d). N"-rtron energy spectrum variations.

e) Effects of varying enrichments if enrichments different from those normally used for present PWR's can be considered.

From the fuel cycle point of view, there are two main variables that have to be optimized with regard to energy

production, but which are bound by conditions like the maximum power peaking factor, fuel enrichment costs, thermal-hydraulic safety aspects, etc. These two main variables are the following:

a?). The total energy obtainable per ton of uranium ore.

b). The core cycle length.


Obviously, one is concerned with obtaining the maximum energy from "each ton of ore. In addition to this, utilities are also interested in having long core cycles. Presently there is a trend to change from a 12-month to an 18-month cycle scheme because of the reduction in refueling outage time and personnel radiation exposure, which might result in attractive savings in power generation cost.

If the currently standard core structure were maintained

(3-batch, out-in scheme) it would only take an increased fuel

enrichment and some help from burnable poisons in order to have an 18-month cycle instead of a 12-month one. By so doing, the ore

utilization is favored by the fact that the fuel is discharged at a higher burnup. A study by Combustion Engineering(3) shows that ore utilization is improved for increasing burnup levels up to about 50 GWd/MTU and fuel enrichments of about 4.5%. The problem, however, is that an 18-month cycle would yield high discharge burnup levels as compared to what is acceptable based on the present level of

fuel technology.

In order to keep the discharge burnup in an acceptable range,

given the present fuel technology, and to take advantage of the reduced refueling outages of an 18-month scheme, utilities are forced to switch to larger batch sizes. This enables the power generation cost to be reduced, but with worse ore economy than that

obtained in a 12-month core cycle. This is of some concern from a fuel resources viewpoint, mainly if reprocessing is not considered.


The optimum fuel cycle appears to be one which obtains maximum energy per ton of ore and which also has long core cycles. Discharge burnups, however, must be limited, considering present fuel technology, to somewhere between 30 and at the most 40 G~d/MTrJ. In addition, the size of the batches should be kept small (i.e. the number of batches should not be reduced) in order to maintain good ore utilization.

The reduced power density cores are expected to yield

increased burnups given a certain core management scheme, but they are not expected to vary in extremely large proportions. This would probably make the low-power cores able to comply with all the desirable conditions mentioned above: long core cycles because of the reduced power density and the associated additional burnup, and better ore utilization because of the extended burnup obtained from the same initial core load.

The comparison of the fuel cycle performance of the SHARP versus a standard PWR plant can be done from many different frames of reference, each of which would enhance the comparison of the cores in a particular aspect. However, the two most significant ones would probably be the following:

a). Maintaining feed enrichment and core structure, evaluate the differences in burnup achievable, cycle length, and ore utilization.

b). Maintaining core structure and discharge burnup, evaluate the differences in ore requirements,, enrichment needs, and cycle



Another of the other possible scenarios for canparison could be to maintain the discharge burnup constant and allow fuel enrichment, cycle length and core structure to vary. However, it is the feeling of the author that these cases would not aid significantly in demonstrating the differences of a SHARP as compared to a standard plant.

Once the main parameters of interest have been defined, it is necessary to define a reference core that represents a standard reactor plant, and whose characteristics and performance is known and usable as a frame of reference for comparison of the SHARP characteristics and as a benchmark of the calculational methods used in the study.

After the reference core is defined, it is necessary to define a basic SHARP core and a series of "variational" cores that will be used in order to obtain the coefficients, parameters, and comarative results defined above. After the main SHARP characteristics are obtained, another set of cores will be selected for the in-depth study and comparison with the standard plant. The calculational tools needed for the in-depth study will be defined based on the requirements and restrictions observed in the scoping calculations.

The core chosen for the standard reference plant is a Westinghouse four-loop, 3400 DlWth. PWR, with 17x17 pin fuel assemblies(4) whose main parameters appear on table 2.1.1. Table 2.1.2 describes the main characteristics of the basic fuel cell of this standard reactor.


Table 2.1.1. Main Core Parameters for the Standard Reactor.

Core Shape Cylindrical

Radius 168.53 cm

Active Height 365.00 cm

Reflector Thickness 34.00 cm

Active volume 3.2568 E+7 cm3

Heavy Metal Loading 94.418 rMTU

Array Geometry Rectangular

Pitch 1.2573 cm

Coolant Pressure 2250 psia

Avg. Coolant Temperature 583 K

Thermal Power 3400 Mth

Pin Average Linear Power 6 1cM/ft

Table 2.1.2. Basic Fuel Cell of the Standard Reactor.

Region Material Radius (cm) Thick. (cm) Vol. Fraction

1 Fuel 0.4096 0.4096 0.3334

2 Gap 0.4178 0.0082 0.0135

3 Clad 0.4750 0.0572 0.1015

4 Water 0.7094 0.2344 0.5516


The basic reference core used in the scoping study is described in Table 2.1.1; its fuel cell characteristics are described in Table 2.1.2. The fuel used for the reference core is uranium dioxide, enriched to 3% in U-235 isotope; the moderator is considered at standard operating pressure (2250 psia.), but at roon temperature (293 M). No soluble or lumped poisons are considered, nor are any fission products present for all the scoping beginning of life (BOL) calculations, unless otherwise specified.

Under these conditions, the composition of the basic fuel cell is as shown in Table 2.1.3. Region 1 corresponds, as in Table 2.1.2, to the fuel pellet; Region 2 is the gap between pellet and clad; Region 3 is the Zircaloy,-4 clad and Region 4 is the light water moderator-coolant. This reference core will be named

core #1.

The pin-average linear power for the standard reactor is 6 KW/ft. A pin-average linear power of 1.5 KI"/ft. is used for the scoping studies of the SHARP. This is one fourth the linear power of the standard Westinghouse core.

In an attempt to cover a wider scope and range of possible applications of low-power reactors, the scoping study includes sane exploration of a very low power, low enrichment core which could be used as a preheater in a multi-core configuration similar to the one illustrated in Figure 1.2.2. This core would have lower than standard moderator temperature and a very low power (20% that of the standard core). Such a low power density, low moderator temperature core might possibly be fueled with spent fuel


Table 2.1.3. Basic Cell Composition. Core #1.

Isotope Region Pure # Dens. (*) Cell Avg. # Dens. (*)

H 4 6.7 E-2 3.6957 E-2

O 4 3.35E-2

O 1 4.4009 E-2 3.3152 E-2

U-235 1 6.6830 E-4 2.2281 E-4

U-238 1 2.1337 E-2 7.1137 E-3

Zr 3 4.2808 E-2 4.345 E-3

Ni 3 0... E-10 0... E-10

Sn 3 4.8556 E-4 4.9285 E-5

Fe 3 1.4946 E-4 1.517 E-5

Cr 3 7.6426 E-5 7.7573 E-6

He 2 1.9 E-3 2.565 E-5

Units are atoms per barn-cm.


discharged from standard PWR plants. This core was thought of as a possibility for further use of standard plant spent fuel.

Table 2.1.4 identifies the cores used for the scoping study

with their main distinguishing characteristics. The

characteristics of these cores were selected in order to obtain indicative figures on reactivity coefficients and burnup variations. Each core has a case I.D. assigned to it, which is used for future reference. The power levels indicated are in percent relative to the standard core's full power (6 KW'/ft. or 3400 MWth. total core power).

In all cases, both the fuel and the moderator are treated as having a uniform temperature throughout their masses. In the reduced power density system, the moderator temperature is always kept at the average coolant temperature of the standard plant core, in order to maintain the thermodynamic characteristics of the steam cycle, and the thermal efficiency of the plant. The only cores with different coolant temperature are the ones intended for

preheater operation. The fuel average temperatures depend

obviously on the linear power density, and the values used for each of the scoping study cores are shown in next section.

Table 2.1.4 shows also the core effective neutron multiplication factor (K-eff.) obtained for each of the scoping

study cores in a BOL, clean, unrodded situation. The calculational procedures used for the scoping study are different than the ones used for the detailed burnup study, and they are specified later in this chapter.


Table 2.1.4. Identification of Cases for the Scoping Study.

Case # Enrich. Mod.Temp. Fuel Temp. Poisons Power K-eff(*)

1 3% 293 K 293 K 0 0 1.3532

2 3% 583 K 293 K 0 0 1.2933

3 3% 583 K 1005 K 0 100% 1.2675

3A 2.6% 583 K 1005 K 0 100% 1.233

4 3% 583 K 700 K 0 25% 1.2770

4A 2.6% 583 K 700 K 0 25% 1.242

5 2.6% 293 K 293 K 0 0 1.3184

6 3% 293 K 293 K 1300 PPM 0 1.1579

7 3% 420 K 520 K 0 20% 1.3304

8 2% 420 K 520 K 0 20% 1.2260

9 3% 583 K 1005 K 1856 PPM 100% 1.0781

* Calculated with PHROG-BRI'-MONA as shown in Sections 2.2.2 and



Table 2.1.5. Tabulation of Case Number Densities Which Differ from Those of Case #1.

Case # Isotope Region Pure #Dens(* Cell Hom. #Dens(*

2 0 4 2.346 E-2 2.76149 E-2

2 H 4 4.6926 E-2 2.58845 E-2

3 Same as core #2

4 Same as core #2

5 U-235 1 5.7924 E-4 1.9312 E-4

5 U-238 1 2.1426 E-2 7.14335 E-3

6 B 4 7.258 E-5 4.0037 E-5

7 0 4 3.0982 E-2 3.17624 E-2

7 H 4 6.1964 E-2 3.41795 E-2

8 U-235 1 4.4561 E-4 1.48565 E-4

8 U-238 1 2.1559 E-2 7.18790 E-3

8 0 4 3.0982 E-2 3.17624 E-2

8 H 4 6.1964 E-2 3.41795 E-2

9 B 4 7.258 E-5 4.0037 E-5

9 0 4 2.346 E-2 2.76149 E-2

9 H 4 4.6926 E-2 2.58845 E-2

3A U-235 1 5.7924 E-4 1.9312 E-4

3A U-238 1 2.1426 E-2 7.14335 E-3

3A 0 4 2.346 E-2 2.76149 E-2

3A H 4 4.6926 E-2 2.58845 E-2

4A Same as core #3A

*Units are atoms per barn--cm.


Same of the cores identified in Table 2.1.4 show variations in moderator temperature or fuel enrichment that imply changes in the cell number densities as compared to the reference cell. The coolant and fuel densities for the different temperature situations were calculated with the help of standard tables for each material(5,6). Table 2.1.5 shows the changed number densities for the affected isotopes and applicable cases. For the rest of the isotopes and/or cases, the reference core number densities apply.

2.2. Calculational Methods for the Scopingt Study

2.2-1. Heat Tranfer Calculations.

Some of the main differences between a standard reactor and a SHARP are related to the differences in the fuel temperature. It is therefore necessary to know the fuel temperatures that correspond to several different power-density cores before their neutronic study can be started. However, for the purpose of the present study, it is not necessary fo obtain extremely accurate results, since the data will be used for obtaining varying nuclear properties of the fuel, which are not drastically affected by a few degrees of uncertainty in the temperature.

The calculational. scheme used may be found in any complete Nuclear Heat Transfer or Reactor Analysis text (7) It is assumed that a uniform volumetric heat source exists in the fuel region; that the bulk moderator operating conditions are kept constant for all the different cores (583 K, 2250 psia.) except for the preheater cores (cases #7 and #8) which have their moderator at 420


deg. 'K but at the same 2250 psia pressure. For all the other cores, subcooled nucleate boiling has been assumed at the pin surface, while cores #7 and #8 were assumed to have subcooled

convection, due to the much lower bulk coolant temperature and to the very low heat flux rate. Figure 2.2.1 shows the geometry assumed in the pin for the heat transfer calculations.

Fuel Ga Clad Coolant


11 \I\\
.41 .008 .057 .234

(Dimensions in cm)

Figure 2.2.1. Pin Cell Geometry.

Given the heat transfer conditions found at the pin surface,

the temperature increment between the bulk coolant and the clad surface may be obtained by the Jens & Lottes expression:


Ts = Tc + 60 ( 21' 10 6 )0.25 exp ( p / 900 )

where Ts = pin surface temperature, deg. F

Tc = bulk coolant temperature, deg. F
V = surface heat flow rate, Btu/hr sq.ft

p = coolant pressure, psia

The temperature increment across the clad is given by the expression:

ATcl =' do In ( do di
2 *K S

where &Tcl = increment of temperature across the clad, deg. F

q' = linear heat flow rate, Btu/hr ft

do = clad outer diameter, ft di = clad inner diameter, ft

K = clad thermal conductivity, Btu/hr ft deg.F

S = clad surface per unit pin length, ft

Since the thickness of the gap is extremely small, the

temperature change across the gap may be obtained as A Tg =

where ATg = increment of temperature across the gap, deg. F

q' = linear heat flow rate, Btu/hr ft

K = thermal gap conductance, Btu/hr sq.ft deg.F

S = surface of heat transfer per unit pin length, ft.


With the previous expressions, it is possible to obtain the pellet surface temperature. Since the temperature of interest for nuclear calculations is the average temperature of the pellet, it is necessary to know the temperature profile in the pellet, as a function of the distance to the centerline, so that volumetric weighting of the temperature can be done.

The temperature profile inside the pellet (assuming uniform heat generation) is given by T(r) = To r2
7T Rz 4 ifwhere T(r) = temperature of the pellet at radius r deg. F

To = temperature of the pellet centerline, deg. F

qI = linear heat flow rate, Btu/hr ft

R = pellet outer radius,, ft

Kf = pellet thermal conductivity, Btu/hr ft deg. F

r = distance from centerline, ft

One more quantity is needed at this point: the pellet

centerline temperature, which is given by To = Ts + at
4 Tr Kf

where To = pellet centerline temperature, deg. F

Ts = pellet surface temperature, deg. F


With the pellet temperature profile expression in hand, the pellet average temperature may be obtained as

Tae = (2 / R2) *T(r) r dr = To (qI / 8 r, Kf) J0

For the 20% linear power, preheater cores, the calculational scheme was the same except for the temperature step from coolant to clad surface, in which case a subcooled convection heat transfer expression was used, such as the following: AT=q'' / h

where q'" = surface heat flow rate, Btu/hr sq.ft

h = forced convection coefficient, Btu/hr sq.ft deg. F

The forced convection coefficient may be calculated as

h = 0.0023 Re0"8 Pr04 (K/D)

where K = coolant thermal conductivity, Btu/hr ft deg.F
D = hydraulic diameter of the coolant channel, ft

Re = Reynolds number Pr = Prandti number

Once the thermal calculations were completed, the standard

core fuel average temperature was checked against the vendor's literature, and found to differ by a few degrees; this difference is probably due to slightly different conductivity coefficients across the core (due to temperature changes), which are not taken


Table 2.2.1. Basic Cell Temperatures vs. Power Level.

Power level % 100 50 33 25 20 (pre)

Clad surface 593.3 592.8 592.5 592.4 304.2

Clad increment 46.4 23.2 15.5 11.6 9.3

Gap increment 120.1 60.1 40.0 30.0 24.0

Fuel surface 759.9 676.1 648.1 634.0 337.5

Fuel centerline 1846.7 1219.5 1010.3 905.7 555.0

Fuel average 1303.3 947.8 829.2 769.9 446.3

Fuel average M 979.0 781.9 716.0 682.0 503.2

Vendor normalized W 1005.0 805.0 735.0 700.0 520.0

Note: Temperatures obtained from thermal calculations as described in Section 2.2.1.
Temperatures expressed in degrees Fahrenheit, unless otherwise specified as Kelvin W.
Column 20 (pre) refers to the 20% power, preheated core.


into account in the thermal calculations. Since this difference was not significant from the nuclear point of view, all the results were modified slightly to maintain consistency with the vendor's data in the neutronic calculations. T!he consistent data permit the further benchmarking of the nuclear calculations. Table 2.2.1 shows the main temperatures involved in the calculation for all the different power levels studied. All temperatures are in degrees Fahrenheit, unless otherwise specified.

2.2.2. Neutron Cross Section Calculations.

Section 1 of this Chapter described the set of cores chosen

for the scoping observation of the differences between a standard core and a low power density core. It is necessary to gather a series of codes of known reliability which can yield an accurate neutronic picture of a LWR core. Parametric studies can then be

conducted which will define significant factors differentiating a SHARP from a standard plant. In these parametric studies, the absolute accuracy of the results is not as significant as their relative values which are used to establish figures of merit.

The best neutron cross section calculationa. method available for the scoping study involved the use of several standard codes. This method allows great flexibility in specifying isotopic number densities, geometries, etc., but it requires a relatively large

amount of manual data handling from code to code. This section briefly describes these codes.


Two codes are used for the calculation of cross sections. PHROGM is used for calculation of the fast-group neutron cross sections, and the original library, consisting of a 68 energy group cross section data set is collapsed into three fast groups which are used in the core model code. A more detailed explanation of PHROG can be found in Appendix B2. As is shown in the next

section, the core criticality calculations are done with a model which defines two distinct regions: fuel and reflector. Fast cross section calculations need to be run for both of these regions. The fuel region is run first, and the group-wise fluxes and currents existing in the fuel are used as weighting functions for the ,-calculation of the reflector constants.

The thermal-group cross sections are calculated with the Battelle-Revised Thermos (BRT) code(9) using a 30-group cross section library. Thermal cross sections are collapsed into a single thermal group. it is also necessary to obtain separate

cross sections for the fuel region and for the reflector. The fuel region does not present any problem, since it can be well represented by the calculation of a unit fuel cell. However, BRT does not allow an intrinsic representation of the reflector region without an adjacent core. The reflector region is then calculated from a two-region slab reactor configuration, where one of the regions has the average core region characteristics, while the other represents the reflector. The geometry chosen was that of a slab. Because of limitations in the number of mesh spaces allowed by BRT, inaccuracies at the core-reflector boundary arise when a


cylindrical shape is considered. The basic features of M~ are described in Appendix El.

Four sets of cross sections are obtained with the calculations described above: one set with three-group fast cross sections for the core region; another set with three-group fast cross sections for the reflector; a third set with thermal cross sections for the core, and finally a set with thermal cross sections for a slab core-reflector configuration, from which only the reflector

constants are used. These cross section sets are then organized for input to the core models, which are discussed in the next section.

2.2.3. Criticality and Burnup Methods,

The first objective of the scoping study is to obtain the neutron multiplication factors of the cores described in Table 2.1.4. These multiplication factors are used to estimate the main reactivity coefficients involved in the neutronic aspects that differentiate the SHARP core from the standard core. The second goal of the scoping study is to obtain a first estimate of the burnup levels achievable by each particular core, as well as the isotopics associated with them. Following is the description of the methods used for achieving both of these purposes.

The core modeling for the criticality calculations is done with the Z4ONAMlO) code which is described in more detail in Appendix B33. MNA accepts the cross section input prepared by PHROEG and BRT~, and information about the core geometry and material region copositions. The code can perform a number of


calculations#, such as buckling searches,, poison searches, etc. In this case, a normal effective multiplication factor (K-eff.)

calculation is requested.

The code accepts a cylindrical geometry, but it is a

one-dimensional diffusion-theory code. In order to obtain accurate results for the neutron multiplication factor in one-dimensional cylindrical geometry, accurate values for the perpendicular buckling to account for perpendicular leakage are required. In

the absence of this information, it is known from previous

experience that an "equivalent" spherical system can yield accurate results for the neutron multiplication factor. For the "equivalent" spherical configuration, the core volume is kept equal to that of the cylindrical reactor, while for the reflector, the thickness is kept equal to the cylindrical reactor value. The core region has 199 mesh points allocated, and 34 mesh points are assigned to the reflector, thus assuring that the mesh spacing is smaller than the neutron diffusion length. This is necessary for these calculations if neutron diffusion theory is expected to describe the core fluxes and currents with an acceptable level of accuracy, An extrapolated zero-flux boundary condition is specified for the outer boundary. Figure 2.2.2 illustrates the geometric model used with MONA for the criticality calculations.

Two methods were used for the scoping burnup calculations. The first method involves the use of the calculational scheme already used for the criticality calculations. Once the reactor criticality status is established soluble boron is added to the


i/ Reflector


mesh: 199 pts.

HF2ogenized Fuel Mixture Cl34 uts .

Water + Structural Materials

Figure 2.2.2. Geometry Used for MONA Criticality Calculations.


mo derator in the amount necessary to force the core to be exactly critical.

With the reactor critical, the fuel-region homogenized composition that was input to MONA and the flux spectrum generated by MONA for the fuel region are input into a BURUP code, which performs the isotopic burning of the mixture to the burnup degree specified, and at the power level desired. The BUBNUP code used in this case is geometrically non-dimensional, but it allows for the specification of a number of time-steps after which the homogenized composition of the fuel region is recalculated. The flux spectrum is assumed to remain constant throughout the burnup calculation.

After the burnup calculation, the homogenized fuel-region composition is used again for a new core criticality evaluation, in the way explained above. Figure 2.2.3 shows a schematic diagram of the flow of data involved in this type of burnup calculation.

This burnup calculation scheme has some very obvious drawbacks:

a). Each burnup timestep requires an inordinate amount of


b). There is a large amount of punched card handling and typing, which largely increases the probability of human error in the calculations.

c) The BUEIUM code used has a rather low degree of sophistication, resulting in a reduced number and complexity of radioactive chains.


Cell PHROG Core
Geometry Fuel 3-group
&Compos. Cell Fast X-sect.


Reflector PHROG flector
imposition Reflector 3-group
Fast X-sec

BRT Core
Fuel Thermal
Cell X-sect.

Slab Reac BRT Reflector
Geometry Slab Thermal
& Compos. Reac, X-sect,

Sphere MONA
Geometry Spherical


< End of> New BURNUP YES K-eff .
Life ? Composition =1 ?


END )Adjust
C k / Soluble Boron

Pigure 2.2.3. Code and Data Flow for Preliminary Burnue Calculation.


This method was, however, used for some cases, but a faster and at least equally accurate method had to be obtained. The
second burnup method employed the LEOPARD program(ll). This program, which is discussed in more detail in Appendix B4, makes an automated chain of calculations involving cross sections, spectra

and burruip for an elementary fuel cell. The cross sections calculations are based on the MUFT(12) and SOFOCATE(13) codes. The geometry is always that of a fuel pin, which may be surrounded by a buffer zone simulating the structural materials present in the core but not associated with the elementary fuel cell.

LEOPARD requires an initial pin composition, a power level, a soluble boron concentration history, and a burnup timestep structure. The code calculates each isotope's cross sections

collapsed to a specified number of broad groups, performs a multiplication factor calculation, burns the fuel, recalculates the pin composition, and resumes the loop until the completion of all the burnup timesteps.

Although the cross section generation in LEOPARD is not quite as accurate as the one used for the criticality calculations, the burnup calculational structure is far superior to the one in the BURNUP code, and the automatic coupling of the calculations allows for the effortless and error free handling of a much larger number of isotopes, which definitely adds to the accuracy of the overall calculation. It is important to note the drastic reduction of effort required for similar results between the first

(PHROG-BRT-MONA-BURNOP) and the second (LEOPARD) method of burnup


calculation. Obviously, LEOPARD does not model the core and the reflector since it is just a pin cell, one-dimensional code, but neutron leakage effects are considered by means of a perpendicular buckling, which enables the code to perform rough estimates of criticality.

In an effort to compare the two burnup calculational methods, parallel calculations were run for one core representing a standard reactor's first load. Since no fuel regions were considered in the MONA core model, the fuel enrichment was specified as an average of

the concentrations of the three real batches. This was also the only way of simulating the situation in LEOPARD, because it obviously can not accept several enrichments simultaneously. Note,, however, that this is a rather crude way of representing a core, because it is very different to have three distinct regions with various enrichments or burnup levels than to have a large region with averaged characteristics. However, the procedure was deemed

adequate for a scoping comparative study.

The results from the LEOPARD and MONA-et-seq. comparison showed a discharge burnup discrepancy of about 13%. Figure 2.2.4 shows the estimated soluble boron letdown curve obtained from each calculational scheme. The agreement is very good up to about two thirds of the core life, but the separation increases thereafter. This is most probably due to the absence of proper treatment of the fission products in the MONA method, because they could not be included in the fuel pellet region, and therefore were only accounted for as a reduction of core reactivity, but their


Critical Boron Concentration ppm 2500



0 5 10 15 Burnup

Figure 2.2.4. Ccuparison of Boron Letdlown fran LEOPARD and BUPNUP.


neutronic effects on the other isotopes (due to spectral effects) could not be simulated. However, the agreement between the two methods can still be considered good, considering the different conceptual approaches, and the small amount of core information included in them. The most reassuring fact is that the quoted beginning of life (BOL) core reactivity and the quoted end of life (MOL) burnup level of the first core for the standard reactor lie just between the values obtained from the two models, with LEOPARD giving a better result for the EOL burnup.

With all these considerations in mind, LEOPARD was used with the "average fuel" enrichment for the scoping burnup, calculations. These calculations used a fuel pin with core-averaged enrichment, a perpendicular buckling corresponding to the axial leakage of a standard core, and an approximately critical boron letdown curve. Calculations were performed for the standard core, a 25% power density core using varying lattice pitches, and a 20% power density core with reduced moderator temperature (the preheater core, designated as core #8 in Table 2.1.4).* The results of the scoping calculations are shown in the next Section.

2.3. Results of Preliminary Work

2.3.1. Reactivity Coefficients.

Table 2.1.4 shows the main parameters characterizing the

different cores that were chosen for the scoping study of the SHARP. The table includes the effective multiplication factors (K-eff.) of the cores at beginning of life (B.O.L.) with no xenon


or control rods, calculated by the PHROG-BRT-MONA scheme, as explained in sections 2.2.2 and 2.2.3.

The core effective multiplication factors obtained for the different cores are used to calculate bulk reactivity coefficients. Thus, the average moderator temperature reactivity coefficient (M.T.C.) is -20.67 p.c.m./deg.K of moderator temperature variation for the temperature range between 293 K and 583 K. This rather

large reactivity coefficient would be the maln asset of a core such as core #8, which would use very low enriched fuel or even spent fuel discharged from a standard plant. A reduction of average moderator temperature of 163 Kj, as described on table 2.1.4, would provide 3.37 % of extra reactivity as compared to an identical core working with normal moderator temperature. This excess

reactivity would enable the core to work with the less reactive fuel or burn the standard fuel beyond the current discharge burnup levels. However, it should be kept in mind that these preheated cores are in some way a technical speculation, and that the real interest of this study is centered in the low-power cores with standard moderator conditions, which enables them to drive a standard balance of plant in a single-core arrangement.

As the average linear power produced by the fuel is varied according to the different power densities of the SHARP cores, so is the average fuel temperature, even though the moderator

conditions remain unchanged. This variation of fuel temperature causes a change of the absorption resonances width, due to the Doppler effect, and this causes a change of the core reactivity.


The Doppler coefficient of reactivity obtained from Table 2.1.4 is

-3.99 p.c.m./deg.K of fuel temperature change, for a variation between~ 293 K and 700 K (which correspond to 0 power and 25% power respectively). The coefficient drops to -3.12 p.c.m./deg.K for the temperature range between 700 K and 1005 K (25% power to full power range). This shows the well known behavior of saturation of the Doppler effect for increasing temperatures of the fuel. The average coefficient that applies for the total range from 0 power to full power is -3.62 p.c.m./deg.K The reduced fuel temperature is one of the main effects contributing to an increase in the reactivity of a low-power core with respect to the standard core. As was mentioned before, the moderator conditions would remain unchanged for the different power level cores for thermodynamic .reasons, and only the fuel temperature would experience a variation due to the change of the heat production rate.

Fuel enrichment obviously has an effect on core reactivity, and therefore, it is also Possible to define a reactivity coefficient for it. For enrichments between 2.6% and 3% in U-235,

the reactivity coefficient oscillates between 8.705% / 1% enrichment variation for a cold, clean reactor and 8.643% /1%

enrichment variation for a hot, clean, full power reactor. For the enrichment step between 2% and 3% of U-235, the 1/5 power, preheater core shows a reactivity coefficient of 10.44% / 1% enrichment variation. This larger magnitude may be due to the

double effect of bracketing a lower enrichment end, and having a

better moderated configuration due to the low moderator temperature


which implies higher moderator density. This rather large

reactivity coefficient associated with the fuel enrichment could be used in order to stretch burnup of the cores by increasing the fuel enrichment, which up to a certain point will result in a better ore utilization (14).

Higher fuel enrichment would, however, bring problems associated with higher power peaking requiring the permanent use of burnable poisons and the technological problem of loss of clad integrity at very high burnup levels.

The reactivity coefficient of soluble boron in the moderator is given an in-depth study for two main reasons: First, the soluble boron concentration that makes a reactor critical at the different points through the core's life is a very useful and realistic way of estimating the cycle life of the core. However, for this to be feasible, it is important to know the reactivity worth of soluble boron at all times through the core's life. This coefficient may be expected to vary, depending mainly on boron concentration and

core burnup status; these two variables are somewhat related, but they certainly don't follow any exact relationship. Second, just reducing the power density may cause the standard reactor lattice geometry not to be the optimal one from the burnup point of view, since the nuclear characteristics of the fuel are somewhat perturbed. Some changes in lattice geometry, such as fuel pitch may be required then in order to optimize the core for the new low-power situation. If this is the case, the ratio of moderator-to--fuel is likely to be changed, and then, a given


variation of soluble boron concentration would mean different total amounts of boron being added to or retrieved from the core, which implies that the soluble boron reactivity coefficient may also change for different lattice geometries.

Soluble boron worth variations are analyzed as a function of boron concentration, core burnup, core power level,, moderator density, and basic cell geometry. These calculations were based on the LEOPARD scoping core burnup calculations.

When adjusting soluble boron concentration to keep the reactor critical through life, the worth of boron decreases slightly from the B.O.L. until about 2000 or 3000 MWd/MTU and increases thereafter, with a very slowly increasing slope. This variation is shown in Figure 2.3.1. This figure shows also that the variation of power level, without variation of moderator conditions, causes practically no change in the boron reactivity coefficient. On the other hand, either a variation of pitch or a change of moderator density (temperature) cause sharp changes in boron reactivity worth. In both cases, as expected, boron reactivity worth

increases for the changes that imply a larger absolute mmunt of boron present in the core (i.e. for an increased pitch or for an increased moderator density).

Figure 2.3.2 shows more clearly the effect of lattice pitch on boron worth. It is also more evident that the variation of boron worth at critical through life is larger for larger pitches. The cause of the monotonical increase of boron worth with life is due to two adding effects: the self-shielding effect of boron itself


.Boron Worth paVppn

Data from LEOPARD Calculations.

2 Core 4A Core 3A

1.6 cm pitch, 583 K Moderator


C o re 8

.25 cm pitch, 420 K Moderator

1.25 cm pitch, Core 4A 583 K Moderator

0 5 I I I ........... .I
0 6 12 18 Burnup

Figure 2.3.1. Soluble Boron Worth at Critical vs. Burnup.


Boron Worth pcm/PPn

Data fran LEOPARD Calculations.
Pitch, cm








0 6 12 '18 Burnup
GWd/MT Figure 2.3.2. Soluble Boron Worth at Critical. Changing Pitch.


and the buildup of Pu-239 As core life advances, the boron concentration is steadily reduced;~ the boron self-shielding also decreases, causing an increase in boron worth. The contribution of Pu-239 buildup to the increase of the boron worth increases with core life. It should be noted that by the end of the core life, about 40 % of the core power is generated by Pu-239 that has been bred through parasitic captures in U-238.* Pti-239 has a higher thermal fission cross section than U-235, and it has a resonance peak in the thermal energy region (tenths of an-eV.). This causes the reactor to increase its sensitivity to the presence of a thermal poison (such as boron) that can remove neutrons from the high fission cross section energy region.

The rate of increase of boron worth with core life is faster for larger lattices, because of the effect of increased boron inventory in larger lattices.

Thus, from the point of view of the SHARP, it is possible to conclude that the reduced power density will not affect boron worth to a significant extent as long as the moderator conditions and cell geometry characteristics remain unchanged. However, if geometry changes are performed in order to optimize the cell behavior for burnup or fuel utilization, boron worth may be expected to show a significant variation, tending to increase for larger pitches and tending to increase towards E.O.L., mainly if the burnup levels achieved are high.

An important goal of the scoping study, is to make a first estimate of the burnup advantages that can be expected from the low


power cores relative to the standard core. One simple way of making such estimates is to calculate the total reactivity of the cores at B.O.L., and to assume that reactivity is lost linearly as

core burnup increases, which is a reasonable approximation for a first-estimate calculation.

The most significant parameters altering the core reactivity at B.O.L. when the fuel enrichment, core geometry and moderator conditions are fixed,, are the fuel temperature and the equilibrium xenon concentration. Fuel temperature affects the core reactivity in the amounts determined by the Doppler coefficient, explained earlier in this section. The reactivity worth of xenon in the different cores can not be obtained from the LEOPARD burnup calculations performed in the scoping study, but it can be obtained from the vendor's literature (4). Combining these xenon reactivity modifications with the core effective multiplication factors listed in Table 2.1.4, it is possible to obtain a comparison of the reactivity available at B.O.L. for each core, and therefore, an expectation of their comparative discharge burnup levels. These

figures appear on Table 2.3.1 for the standard core, the 25% power level core, and the 20% power level preheater core. Two fuel enrichments are considered for each power level.

using the linear reactivity assumption (15), Table 2.3.1 shows that a 25% power SHARP may yield a discharge burnup 10.6% above that of a standard reactor, for an average fuel enrichment of 2.6% U-235 in both cores. The burnup increase of 9% appears for a fuel enrichment of 3.1%. These burnup increases are desirable from two


main points of view: they represent additional energy obtained from the same initial ore, and they entail longer core cycles, which tends to reduce costs of refueling outages.

The expected burnups shown by the 20% power, preheater core are really surprising. The better moderation boosts reactivity in such a way that for 3% enriched fuel, a burnup increase of 32% above that of the standard core would be expected. If the preheater core is loaded with low enriched fuel, e.g. an enrichment of 2%, it would still yield 88% of the burnup expected from a standard reactor loaded with 3% enriched fuel.

However, it should be kept in mind that the burnup results obtained from these LEOPARD calculations do not take into account the significantly different neutronic situation of the various batches present in the core, which will definitely affect the isotopic dynamics, and therefore the core life. In any case, these figures give good hope for better fuel utilization by the SHARP's.

Table 2.3.1. Core Reactivities at B.O.L.

Case # ENRCH K-eff. Xe worth BOL reactivity

3 3% 1.268 -3.5% 23.3%

3A 2.6% 1.233 -3.5% 19.8%

4 3% 1.277 -2.3% 25.4%

4A 2.6% 1.242 -2.3% 21.9%

7 3% 1.330 -2.1% 30.9%

8 2% 1.226 -2.1% 20.5%


2.3,2. NeUtronics and Safety Considerations.

The reduction of power density in the cores of the SHARP causes, among other effects,, a reduction of the Doppler effect, a reduction of xenon concentration, and a reduction of fuel temperature. These changes entail unavoidable differences in the neutronic characteristics of the SHARP as compared to the standard reactor. Thus, it is necessary to check the neutronic changes associated with the power reduction, because some of their aspects are closely related to plant safety, while others are related to fuel performance or isotopic evolution.

As was pointed out in the preceding section, the neutronic differences existing between the standard reactor and the low-power reactors may result in a difference in the optimum fuel arrangement in the core. In this study, the variation of fuel arrangement is limited to the variation of fuel lattice pitch. This variation implies a change of the thermal-hydraulic characteristics of the

fuel cell, as well as a change of the fuel-to-moderator ratio, whose heavy effect on the core neutronics is well known. The pin geometry is kept constant and equal to the standard core design.

The immediate effect of changing the pitch or fuel-to-moderator ratio is a change in the neutron energy spectrum, which in turn causes a change of cell reactivity, and as fuel burnup progresses, it affects the isotopics evolution. There is an

optimum pitch which yields the maximum reactivity for a given fuel pin. However, such a configuration is not safe from the operational point of view. At the optimum point or in an


over-moderated configuration, the moderator temperature coefficient (DffC) becomes zero or positive, making the core inherently unstable. Stability and safety require a negative MflC, which means a pitch must be selected which yields an undermoderated


The scoping study included an exploration of the reactivity changes occurring in the fuel cell as pitch is varied, for some of the more representative core cases being considered. Figure 2.3.3 shows the plots of the infinite multiplication factor versus pitch for the full power standard core (core 3A), the 25% power core (core 4A) and the 20% power core with lower moderator temperature (core 8) as obtained from PH1ROG-BRP-MONA. The plots correspond to BOL, with no poisons, control rods or xenon present in the core, but with the temperatures corresponding to the assigned core power levels.

The curves show a uniform increase of reactivity between core 3A and core 4A, due to the reduced Doppler effect. Remember that no xenon effect is taken into account in these curves, since the cores are clean and with zero burnup. Curves 3A and 4A do not show, however, any visible change of shape; there is only a vertical shift due to the gained reactivity. This means that the best moderated pitch is the same independently of the power density (under equal moderator conditions). With this in mind, the

overmoderation / undermoderation safety criteria for the low-power cores would admit some relaxation as compared to the standard core, due to the inherently safer operating conditions of the SHAR.


standard. Core 4A

1.3. 583 K

420 K

1.1 I Data fran PHROG-BRT-MONA Calculations.

1.0 0.9



1.0 1.2 1.4 1.6 1.8 Pitch

Figure 2.3.3. Infinite Multiplication Factor vs. Pitch.


Figure 2.3.3 shows the pitch used by the standard reactor. Note that it complies with the safety criterion of working in an undermoderated configuration. However, it seems that the pitch could still be allowed to increase somewhat without compromising the safety, since the operation point of the standard reactor is rather far from the peak of the curve. Later in this section it is explained why the standard reactor can not take advantage of the extra reactivity achievable from a slight increase of pitch, while the low-power core can.

When examining the curve for core #8 on Figure 2.3.3, a sharp change of shape can be noticed as compared to the other curves. Reactor 8's curve has a larger curvature; its reactivity is much more sensitive to the variations of pitch. This fact is easily explainable: Reactor 8 works with reduced moderator temperature, but at the same pressure as reactors 3A and 4A. The moderator has, therefore, a higher density. This can be observed on Table 2.1.5. The higher moderator density causes a given change of pitch to represent a larger increase in moderation, i.e. there are more mean free paths or more interactions taking place in the moderator region between pins at higher moderator density. it is as if the x-axis of the curve for core #8 has been compressed as compared to the standard moderator temperature ones.

One of the consequences of the higher moderator density is a reduction of the distance between the standard reactor working pitch and the optimum moderation point. This effectively raises the multiplication factor of core 8 when using the standard pitch,


and it is one of the main factors responsible for the high reactivity found for core 8 in spite of its low fuel enrichment (see Table 2.3.1). However, it is also important to note that this same curve shift prevents considering a different pitch for core 8, because it is already working at a point much closer to the optimum moderation ratio, and any further change of pitch would bring the core too close to a possibly overmoderated configuration, which as explained above, is not acceptable from a safety point of view.

Figures 2.3.4 and 2.3.5 show the changes in the four factors of the "four-factor formula" for cores 3A, 4A and 8, as pitches are varied. These are the results of the criticality calculations performed for BOL with PHPOG-BRT-MONA. It is apparent that the neutronic effect of the higher moderator density of core 8 is far larger than the change caused by the Doppler effect difference between cores 3A and 4A. None of the four factors exhibit a difference of more than one percent in their corresponding values between cores 3A and 4A. However, the largest differences are observed in the resonance escape probability for very undermoderated lattices. This could be expected because this is the configuration and the factor that give the maximum enhancement to the Doppler effect variation.

The change of moderator density causes a sharp difference of spectra which is reflected in all the four factors. The fast fission factor, epsilon, is consistently lower for core 8 than for the other two. Note that the fast fission factor experiences a sharp rise when the lattice pitch reaches very small values and



Data frcm PHROG-BRT-MONA Calculations.

Cores 3A, 4A Core 8

Cores 3A, 4A Core 8
1. 0 1 .... ..... .
0.85 1.1 1.35 1.6 Pitch
Figure 2.3.4. Eta and Fast Fission Factor vs. Pitch.


there is almost no moderator in the cell. In the range of pitches that can be reasonably considered for practical purposes (between 1.2 and 1.4 an) the fast fission factor slowly decreases as more moderator is brought into the cell.

Eta, the number of neutrons produced per thermal neutron absorbed in the fuel#, is the least sensitive of the factors, as it remains almost flat through the whole range of lattice pitches; it only shows a fall for very tight configurations. However, it is important to note that there is still a difference between core 8 and cores 3A and 4A. This shows that more important than the

amount of moderator present in the cell is the variation of mean free path associated with the change of moderator density.

The resonance escape probability F p, shows a very predictable pattern, increasing as the amount of moderator increases, but showing a very clear saturation effect as large pitches are reached. However, in the range of practically reasonable pitches, p shows a rather steep positive slope; this factor is the one which is primarily responsible for the increase of reactivity achieved by increases of pitch in this range. Note that core 8 stays consistently above cores 3A and 4A throughout the range of pitches examined in spite of the larger relative number of resonance absorber atoms (mainly U-238) present in core 8. This is a direct effect of the different mean free path caused by the increased moderator density. If only the better moderation effect and saturation effect of p for larger pitches existed the distance between the curves for core 8 and cores 3A and 4A could be expected


f p

f Coe 3A, 4A




Data fran OHG-BRT-ON Calculations.


0.9 1.0 1.1 1.2 1.3 1.4 1.5 Pitch
Figure 2.3.5. Resonance Escape Probability and Thermal Utilization.


to decrease significantly as larger pitches are reached, but the reduction of distance is insignificant, indicating again the key role of the changed mean free path.

Finally, the thermal utilization factor, f, or ratio of thermal neutrons absorbed in the fuel to total thermal absorptions in the cell, shows a drop as pitch is increased. This effect is directly related to the amount of absorbing moderator atoms present in the fuel cell. Note that as pitch increases, the curve for core 8, which is naturally below that of cores 3A and 4A, drops faster than that of cores 3A and 4A; the reason being simply that the same increase of pitch adds more moderator atoms into core 8 than for the other cores, because of the higher moderator density of core 8.

Many of the reactivity and isotopic differences between the standard core and the low power density cores have been attributed to neutron energy spectral effects. Figure 2.3.6 illustrates some aspects of the spectral changes. The graph represents the ratio of thermal flux to first fast group (of the three fast groups used for the criticality calculations) for cores 3A, 4A and 8, and for short burnup times, up to about 50 days of equivalent full power operation of the standard reactor. These figures were obtained from short burnup calculations performed with the

PHROG-Brdl--MONA-BURNUP scheme. The effect of the increased moderator density of core 8 is much larger than all the other effects differentiating cores 3A and 4A. However, all cores show a parallel behavior as burnup increases: there is an immediate drop

of thermal flux right at the beginning of life. This may be


Data fran PHR1-BRT-MONA-B1RNUJP.Calculations.
'**- Core 8.





0 20 40 60 Time
100% Full-power Days Figure 2.3.6. Thermal-to-Fast Flux Ratio.


attributed to the appearance of xenon. Note that the cores are always burned in the critical condition, which means that at BOL there is a high concentration of soluble boron keeping the core at critical. This boron concentration is rapidly reduced as xenon builds up to an equilibrium level. It would seem then, that the core is changing one thermal poison for another, and therefore no significant change of neutron spectrum would occur, but this is not the case. The fact that the thermal poison is in the fuel (in the case of xenon) as opposed to being in the moderator (in the case of boron) has a significant effect on the neutron spectrum. This is due to the different relative changes of thermal absorption cross section occurring in the fuel and in the moderator. Thus, as

burnup increases, the thermal fraction of the neutron spectrum continues to drop slowly (the spectrum hardens) due to the

generation of fission products, which are thermal poisons located within the fuel, as is the case with xenon.

A key point in the safety of operation of a new reactor is its thermal-hydraulic behavior. It has been stated before that the low power reactors should deliver the outgoing coolant in the same thermodynamic conditions as the standard reactor, because this is a basic factor in the thermal efficiency of the plant. It is obvious that if a reactor delivers a reduced amount of power, it is also forced to deliver a reduced coolant mass flow in order to keep the thermodynamic conditions at the outlet unchanged, and this flow reduction encompasses different characteristics in the heat transfer conditions.


One of the main parameters of concern when analyzing the heat transfer conditions in a PWR is the minimum DNBR (Departure from Nucleate Boiling Ratio) existing in the core. The minimum DNBR indicates how far the core is from reaching a film boiling heat transfer condition, which would result in heavy overheating and damage of the fuel.

Mark Miller performed calculations(16) on the subject of the DNBR for several power densities and several flow rates and compared the results to the DNBR actually found in the standard reference core. A more detailed analysis of the thermal-hydraulic performance of the low-power cores is presented in Chapter V. It is, however, important to point out here that all the reduced-power cored show a higher DNBR than the standard core, under equal outlet enthalpy condition, and using the same fuel lattice geometry. For larger pitches (which may be of interest from the discharge burnup viewpoint) the low-power cores can accept some pitch increase and maintain the outlet enthalpy and still stay at a better DNBR than the standard reactor. However, the standard core can not use larger pitches without seriously reducing its thermal-hydraulic safety margins, due to the reduction of coolant velocity associated with the increase of fuel lattice pitch. This is an unequivocal and key point proving the substantially higher safety level of the low power reactors as compared to the standard ones.


2.3.3. rnup Achievments .and Isotgpic InveXntorie* As explained in Section 2.2.3, the preliminary burnup

calculations were performed with the LEOPAIRD code, using a pin enrichment equal to the average enrichment of the core, and burning it with a varying soluble boron concentration that would keep the core as close as possible to criticality. Eurnup explorations were done for the standard reference core 3A, for the 25% power density core 4A, and as a scope extension, for the 20% power density, preheater core 8. All of them were examined at the standard core's pitch of 1.2573 cn; cores 3A and 8 were also investigated at one larger pitch, and core 4IA was studied for a wide range of pitches, since it is the most representative low power density core. The multiple burnup calculations performed for core 4A have the purpose of determining the parametric effect of pitch on the discharge

burnup level, as well as giving an indication of the optimum pitch value.

Table 2.3.2 shows the main burnup and isotopic results obtained from the preliminary burnup calculations.

Reducing power density to 25% of the standard level while keeping the standard core's pitch results in an increment of burnup of 9%. However, the burnup increment can be improved to about 16% by increasing the pitch of the low power reactor to about 1.3 or 1.4 cm. Figure 2.3.7 shows the burnup levels achievable as pitch is varied on core 4IA. Note the important fact that the maximum burnup is not achieved at the pitch value having maximum BOL reactivity (shown in Figure 2.3.3) but at a smaller pitch. This


Burnup Gd/MT


21.0 Data fran LEOPARD Calculations. 20.5



]1 I i i i iii iiiii
1.25 1.35 1.45 Pitch

Figure 2.3.7. Discharge Burnup of 25% lbwer Density Core vs. Pitch.


Table 2.3.2. Scoping Burnup and Isotopic Results.

Case Pitch Energy Cycle U-235 (Kg/GWd) U-238 Fiss Pu (Kg/G~d) I.D. (cm) (Gwd) Life Fiss. Disch. (Kg/@(d) Fiss. DISCH. 3A 1.25 1737 ly 316d 0.6343 0.6319 0.0805 0.3291 0.4064

3A 1.60 1849 ly 360d 0.7073 0.4779 0.0495 0.2686 0.2726

4A 1.25 1893 8y 049d 0.6218 0.5293 0.0854 0.3519 0.3895 4A 1.30 2022 8y 252d 0.6210 0.4519 0.0787 0.3512 0.3474 4A 1.35 2033 8y 269d 0.6370 0.4307 0.0708 0.3355 0.3169 4A 1.40 2028 8y 261d 0.6518 0.4195 0.0647 0.3207 0.2969 4A 1.45 2031 8y 266d 0.6587 0.4112 0.0613 0.3127 0.2844 4A 1.60 1881 8y 031d 0.7033 0.4604 0.0499 0.2676 0.2610

8 1.25 1511 8y 043d 0.6387 0.4785 0.0707 0.3227 0.3795 8 1.40 1362 7y 116d 0.7092 0.5386 0.0545 0.2688 0.3448

Note: Ave. fuel enrichment is 2.6% for all cores except for core 8

it is 2%.

Total energy generated assumes a core with 94.42 MTU loading.

Cycle life is calculated assuming 75% availability.

For Core 3A, pitch = 1.2573 which is the Westinghouse value

for a standard core using 17X17 assemblies.

Data obtained from LEOPARD burnup calculations.

means that the isotopic and spectral effects occurring during the life of the core cause a shift of the EML reactivity, favoring less moderated configurations. The main reason for this effect is a conflict between optimum moderation and enhanced conversion ratio: Conversion ratio is enhanced when the resonance absorption in U-238 is increased, but this is obviously an effect which reduces the immediate reactivity of the core. The trade-off appears when realizing that at E.O.L., a large proportion of the power is generated by the converted plutonium. Thus, if conversion ratio is reduced in trying to optimize moderation (and thus increasing BOL reactivity), the core reaches EOL with a reduced amount ohf plutonium, and therefore becomes subcritical. at a lower burnup level.

Note on Table 2.3.2 the relatively high level of burnup achieved by core 8, in spite of being fueled with only 2% enriched fuel. The effect must be attributed primarily to the different moderator characteristics, in addition to the effect of the reduced power level.

It appears at this point that the best pitch from the burnup viewpoint is larger than the one used in the standard reactor, but smaller than the one yielding maximum reactivity at BCL. However, the model used for these scoping calculations can not be assumed to accurately represent a reactor in an equilibrium cycle since BOL compositions with no burned fuel were employed. The question is then whether the optimum burnup pitch obtained in these studies will still be the best for an "equilibrium cycle" core or if it


will be a different one. In order to answer this question it is

necessary to perform burnup calculations with a model that can reasonably represent a core in an equilibrium cycle, i.e. there must be some burned fuel present at BOL for each reload core. These scoping studies, however#, can serve as guidelines for

"equilibrium cycle" calculations.

There are a number of criteria that can be considered

important when examining the results of a burnup analysis from an isotopic or fuel utilization point of view:

a). Search for the maximum energy output from the same load of fuel.

b). Search for the minimum discharge of plutonium, for

non-proliferation purposes.

c). Search for the minimum amount of net fissile material being consumed per unit of energy produced. This would account for the fissile species being discharged with the spent fuel, and therefore would assume a spent fuel reprocessing policy.

d). In the same way as the criterion above looked for the best resource utilization, it might also be important to look for the best economical combination of resource utilization and cost of fuel cycle (including fuel enrichment, fabrication, storage, reprocessing, etc.).

Although the criteria that involve reprocessing appear more meaningful from the scientific or technological point of view than those which do not include it, the present political situation in the U.S. prevents commercial reprocessing, and this must be


considered when comparing results of burnup or uranium resources utilization.

Since the present study assumes all fresh fuel to have the same characteristics, increasing the discharge burnup implies

improving ore utilization. In this aspect, core 4A has a better fuel utilization than core 3A. Although core 8 is able to achieve a high burnup for a low-enriched fuel, the total use of U-235 per unit of energy produced appears to be somewhat worse than that of cores 3A and 4A. However, core 8 is not starting from the same type of fuel, and therefore this result should not be considered as a negative point for core 8. In addition, core 8 could be used to further burn the fuel that is ordinarily discharged from standard PWR's which would in fact represent an improvement of overall ore utilization if fuel reprocessing is still not being considered.

Figure 2.3.8 shows the use of U-235 per unit of energy produced, and the relative amounts of plutonium-to-U-235 burned for the different cores, and for some varying pitches. Note that the amount of plutonium burned is maximum for the tightest pitches, due to the better conversion ratio associated with the hard-flux, undermoderated configurations. As a logical result, U-235 consumption per unit energy produced tends to increase with pitch. It is interesting to realize that for a slight increase of pitch above the standard (from 1.25 to 1.3 an), the U-235 specific consumption actually decreases slightly. This is due to the reactivity enhancement which occurs in going to larger pitches. The poorer plutonium production quickly offsets this factor and the


0.7 0,..
Core 8 ****o
/ Core 3A Core 4A

*** U-235 Utilization

Data from LEOPARD Calculations.Core 8\ Core 3A re 4A


Relative Pu-to-U-235 Burnup Kg Pu / Kg U-235


1.3 1.4 1.5 1.6 1.7 Pitch

Figure 2.3.8. U-235 and Plutonium usage.vs. Pitch.


U-235 specific consumption begins to increase. It is thus seen that both U-235 specific usage and plutonium relative burning remain fairly close to the optimum values for the pitches that allow highest burnup and therefore longest cycle times, while worsening rapidly after the region of interest.

2.4. Scoping Work Conclusions

The scoping calculations show that there is good hope for a significant increase of discharge burnup from the same initial fuel by using low power density cores. The main effects contributing to the necessary extra reactivity are the reduced level of xenon and the reduced effect of Doppler broadening of resonances. A 9%

increase of burnup seems to be achievable by going to a 25% power density core, while up to 16% improvement appears feasible by varying the cell pitch. However, these calculations were performed with a calculational tool which is not well-suited for the burnup analysis of a core consisting of fuel of various enrichments and exposure levels. Some changes are surely to be expected when using an adequate core model for these burnup calculations. The burnup calculations made in this scoping study are indicative of a first-load core behavior rather than of an equilibrium core; the latter is the configuration of most interest for burnup or economic studies.

It has become evident that a maximum level of automatization is necessary for the calculational techniques to be used in

detailed burnup calculations. The adoption of LEOPARD to substitute the chain of PHEROG BRT MONA BURNUP proved to be


most advantageous, and a similarly automnated scheme should be used for the detailed calculations. However, a new burnup calculational scheme must be developed which allows the adequate representation of a several-batch reactor core in its equilibrium cycle.

After these scoping studies are completed, the in-depth study should be centered on the cores that can best conduce to short-term, commercially feasible low power density systems. The in-depth study is, therefore, centered on a single-core concept having a reduced power density in the 25 to 60% of the standard core. The cores selected for the in-depth study will be discussed in Chapter IV.

The safety aspects of the low power cores are extremely favorable. The fuel average temperature is drastically reduced, indicating a reduced risk of pin damage. The heat transfer conditions have their safety margins, e.g. the DNBR, significantly improved, which makes the probability of critical heat transfer conditions much lower than it is in the standard reactor.


3.1. Burnup Calculational Methods and Present Needs

Once the philosophy behind the development of the SHARP is established and a power density or a range of power densities are chosen, the key work to be done in the area of fuel utilization is the optimization of the pin-cell of the SHARP. The fuel

utilization and performance (burnup and isotopic results) are then to be compared with those obtained from a standard power density core to determine its relative merit. This optimization and

comparison require a large number of reactor life calculations, where items such as batch-wise burnup, discharge burnup and

physical cycle life, etc. are of interest among others.

Many different organizations are interested in developing and performing reactor fuel cycle and burnup calculations. The wide range of organizations and specific interests has caused the development of different calculational schemes, in order to accommodate the different cost/effort/accuracy ratios desired for each particular type of study. Some of the more important types of burnup studies are the following:

a). Vendor burnup studies and core optimization, performed as design work. These studies are most complete, and they generally include three-dimensional, pin-by-pin studies which are closely



coupled with thermo-hydraulics models. TIhese type of studies require large computational efforts and highly specialized personnel, which makes them extremely costly.

b). Burnup studies performed by utilities, either for core following or for licensing. These also have to be detailed

studies, because they require strong economical decisions affecting the core cycle, or have significant safety considerations affecting the licensing procedure. However, there is presently a trend by utilities to use more epirical codes (such as nodal codes) which run at lower costs than the fully detailed pin-by6-pin studies. Nodal codes generally need base detailed diffusion theory calculations for normalization purposes, but still result in an overall lower cost than the fine mesh neutron diffusion theory codes, while being able to maintain the information necessary for adequate core management.

c). Studies performed by engineering companies or government agencies for assessment of energy policies or new reactor concepts or fuel cycles. These studies fall in a whole new class. They are not directly concerned with the behavior of each particular pin, not even of assembly-wise details. They look at overall results of burnup, time scales, and monetary volumes. Although they need to yield reasonable results, the numerical results themselves are normally less critical, and emphasis is placed on the comparative results of two or more different concepts. These studies generally use some type of empirical formula or simplified core model which


does not require detailed specification of compositions and

geometries, as the two previous types of studies did.

d). Burnup studies performed in universities or

research-oriented organizations for developmental studies of new reactor concepts, for preliminary reactor design or fuel management. These studies may range in their specificity anywhere from the very rough empirical formulas used for fuel resources utilization and policy studies to a level close to the vendor or utility calculations. However, they tend to be more concerned with

particular theoretical details, which call for calculational methods specific to each study. These studies normally follow standard industrial calculational procedures until a certain point where the particular aspect of the study calls for a specific

calculational tool, which is often developed for the occasion.

A wide range of other types of burnup or fuel cycle studies exist, but the four categories stated above illustrate the different levels of accuracy or detail that may be sought depending

on the purpose of the study, and how they require different

calculational costs, manpower needs and calculational tools.

For every burnup study (except for the very simplest ones, where just an empirical formula is applied),two main calculational steps are performed. Each of these steps can have different levels of sophistication depending on the particular needs of the study, and in some cases one or both of the steps may need to be repeated iteratively in order to obtain the accuracy required by the study. Figure 3.1.1 shows the basic flow of data between the two steps.


-Cell Geometry Fuel Cell Burnup Code
-Power Level Generates Neutronic
-Initial Isotopics and isotopic parameters
-Operating Conditions of Fuel through Life
S-Time Steps ...._-lOptional Opional Feedback for
Coupling d- justment of
Codes Burnup Parameters

-Core Geometry M 1ELII
-Fuel Arrangement
-Control Materials Power Distributions,

-Time steps Criticality, Burnup, etc.

Figure 3.1.1. Basic Steps in a Burnup Calculation.


The first step involves using a code in which a representative unit cell of the reactor is burned. Macroscopic core geometry is avoided; the emphasis is placed in burning a unit fuel cell and surrounding it with neutronic conditions as close as possible to those to be encountered by the "average" fuel element during the real core life. The purpose of this calculational step is to obtain neutronic characteristics of the fuel as it undergoes burnup, which will then be used in the second step of the burnup calculations.

Input to these first-step codes normally includes the


a). Fuel cell geometry and initial isotopics.

b). Temperatures of fuel and moderator.

c). Power density (normally linear power density).

d).* Definition of a buffer region surrounding the fuel cell in order to modify the neutron spectrum for the presence of structural materials (guide thimtbles, fuel assembly cans, spacer grids, water holes, etc).

e). Specification of a series of burnup timesteps that will determine the points where the code has to recalculate the

neutronic status of the fuel cell, which has been modified by the burnup process.

fl. Specification of controllable poisons present in the fuel cell. This is normally specified as soluble boron concentration in the moderator, and may be specified for each of the burnurp tiuesteps defined for the calculation.


g). Some models may allow for the specification of variable power levels for the different timesteps, the specification of Dancoff factors or some geometric data that may allow the code to calculate them, the specification of a perpendicular buckling, or a buckling search in order to obtain a critical spectrum, etc.

Most of these first-step pin cell codes are self-chaining, in the sense that the user specifies the cell geometry, isotopics and

burnup history at the beginning of the code execution, and the code performs the burnup steps and the cross section evaluations after each tiniestep without user intervention. Other schemes, like the one used for some of the preliminary calculations in the SHARP study, involve several codes to perform the pin cell burnup, and they need the user to manually handle the cross section libraries and the burnup isotopics back and forth between one code and another.* The advantages and disadvantages of each method rely mainly on the flexibility and freedom of data handling and geometry specification versus convenience and man time requirements. Figure 3.1.2 shows some possible schematics of the data specification for this first step of burnup calculations.

The output of these first-step codes normally includes the

following data:

a). Microscopic cross sections for each isotope present in the fuel cell, for the number of neutron energy groups specified in the input (normally between two and five groups) and for each specified timestep.

:*:- Different Specifications

-J1 L

I I I I 1 I I I

FL0l -I---I--j.4-I-- 4-ir -ycl Timep
It I I III I I III I I I Ii I I I! 1 1 II I I I I
II I !! Ii I I I 1 I I 1
Relative 1 1 1 1 11 1 1. I I I I I
Pow r 1I I 1 I I I I I I 1 I1
1.1 II IJ .L.L.L.. 1 1 I I
1.0 j f ITime
0.9I II I I I
First clel I SJcnd CycL I_ irI Cycle +ITIe-tep

Figure 3.1.2. Examples of Burnup Conditions and Timestep
Specification for Fuel Cell Burnup Calculation.


b). Macroscopic cross sections of the fuel and the whole cell, weighted with the neutron spectrum present at each tiiestep, and with the number of energy groups requested.

c). Infinite multiplication factor of the fuel cell, and effective multiplication factor if a perpendicular buckling was specified.

6). Average neutron speed.

e). Concentration of each isotope present in the cell, regionwise and cell homogenized.

V). Cumulative burnup level since the beginning of the burnup calculation.

g). Other data depending on each particular model, such as the calculated Dancoff factors, fraction of the total core power produced by each fissile isotope, cumulative fission densities, conversion factors, etc.

The second step of the burnup calculations involves taking the data generated by the first code and using it in a core model which accepts overall core information regarding geometry and core operation in order to simulate the actual life of the reactor. This step is the one showing the widest variations from one type of burnup study to another. The most sophisticated models are able to

follow the core life without further iterations, while others need to feed their data back to step one of the burnup calculation, for a new iteration. The flow of data from step one to two and back depends on the sophistication of each of the models and the burnup data sought from the overall study.


The second step uses such a wide range of calculational approaches or methods, that it is difficult to specify the general input requirements and output data. As a general rule, the

explicit core model (in which the fuel is represented either pin by pin or in relatively small nodes, and control materials are specifically treated) needs the initial isotopics information, the microscopic cross section libraries generated by the first step of the burnup calculation, the core geometry data, the power history, the control materials history, and general editing information, while the output includes core isotopics in zone averages, pin by pin, or whatever region type is used by the code versus core history; criticality evaluations, power distributions; burnup information in average or explicit for each unit considered in the core, region averaged multigroup neutronics data, etc. Codes of this type are for example PDQ-7(17), SIMULIArEMl), etc.

Figure 3.1.3 shows the geometry and material zones specifications needed for a two-dimensional calculation of a quarter assembly of a PWR with PDQ-7. Note the extreme detail of

the geometrical description, and the relatively large number of different compositions considered. It is easy to imagine the extreme complexity of the calculation of a whole core in three dimensions, with the necessity to identify different fuel batches, control rod assemblies, burnable poison rods assemblies, assemblies with water holes, etc. Nodal codes avoid some of the complexity and reduce computational time by lumping each fuel assembly into a few nodes, but they require node-interaction parameters and albedos


*- -* --. -... ..

Diffusion Calculation Mesh a Fuel Pins
ITT Interassembly Water Gap
Water Holes (or LBP's)
Instrument Thimble

Figure 3.1.3. Geometry and Composition Specification for a PDQ-7 1/4-assembly Burnup Calculation.


which must be normalized with a detailed core calculation, as well as requiring adjustment of a large number of empirical factors.

There are other computational models which run at lower costs and may not require the technical expertise needed for running full blown PDQ-7 models or three-dimensional nodal codes. These models normally accept a lower degree of geometrical sophistication, or they may do just a part of the burnup calculation. For example, they may perform the criticality and eigenvalue calculations, but not be able to perform the actual core burning, which then has to be done by a separate code. This is the case of MONA, which was used in some of the preliminary studies of the SHARP. This type of codes are useful for criticality studies or spectral effects analysis, but they are of little use for a real life burnup, study

because of the enormous manual data handling required. However, they have the advantage of the low cost and the relatively simple input.

Other types of calculational models are often used for scoping or medium accuracy burnup, calculations. They normally are simplified codes which use part of the data obtained from the first step of the burnup. calculations, and then introduce an approximate core model, using empirical factors or formulas whenever the available data is insufficient for a rigorous treatment of the items needed for the calculation. However, these types of codes cover a wide range of sophistication and thus their accuracy and the information that can be obtained from them is largely variable. The core model used for the SHARP can be included in this


classification, evolving frau a well known calculational model. The innovative core model used for the SHARP is an improvement, on the accuracy of the results, resembling closer the real reactor life. It is achieved by the proper handling of significant core history data, which appear to have been previously neglected. An explanation of the data handling by these codes follows.

These single calculational models are normally based on a pin cell burnup calculation and often use the infinite multiplication factor calculations in order to obtain an estimate of the core criticality state or its reactivity.

In the simplest model, a pin cell would be burned for its whole life without any poisoning, and at a constant power level. The characteristics of a pin are a good representation of the fuel batch to which it belongs, since the pin is surrounded by many fuel pins alike. The only exceptions are the pins facing a fuel assembly of a different batch (and therefore having a sharply different burnup status) or facing the reflector. Then, if the fuel pin is burned for its entire life, it certainly passes through the stages corresponding to each batch in the core. This means

that it should be possible to take some of the neutronic properties of the pin being burned in the cell burnup code and obtain the characteristics of each batch present in the core at any particular time, which should allow in some way to calculate the status of the whole core. if the core contains three batches, the cell burnup calculation should be performed in such a way that the timesteps chosen would be repeated three times, and each of the three sets of


timesteps would span exactly the expected duration of one core cycle. This would allow the data from the corresponding timesteps in each cycle to be grouped into a core timestep. Figure 3.1.4 illustrates this "timestep synthesis" from a hypothetical cell burnup scheme in which five timesteps were allowed for each of the three cycles of core residence of the fuel. The data sought is the infinite multiplication factor of the core, based on the unpoisoned multiplication factor of the pin through its life. The figure shows the conceptual grouping of each timestep's data, but not the calculations involved in it, which will be dicussed later. Note that the timestep pattern is repeated in each cycle of the cell burnup scheme, in order to make the timesteps correspond to the same time of core life.

However, there are several ways of specifying the pin cell

burnup and of doing the calculations for collapsing the cell timesteps into core life timesteps. Some of the systems used for pin cell burnup specification will now be examined.

The simplest scheme, as mentioned before, burns the fuel cell without any poisoning and at the nominal power, for the length of time that is estimated that the fuel will remain in the core. Then the multiplication factors of the cell timesteps are collapsed in order to obtain the core multiplication factor through the core life. An interpolation or extrapolation of the curve of core multiplication factor as it reaches a value of unity determines the end of the core cycle. The core cycle length is then optionally used to perform new iterations of the fuel cell burnup calculation,


Pin Cell K00

1.30 FsCycle Second Cycle 1 Third Cycle


K .


1.00 LL F Tie
E Dt

Figure 3.1.4. Grouping of Pin Cell Data into Core Data.


until it agrees with the cycle length estimated by the timestep collapsing procedure.

This scheme, however, involves gross errors because the

absence of soluble boron causes variations of some percent in the cross sections of some isotopes such as U-235 and Pu-239. This entails errors in isotope concentrations and as a result, errors in the multiplication factor calculations.

Another cell burnup method, which partially solves this

problem, specifies a soluble boron concentration in the moderator with a value similar to the time-averaged boron concentration of a real core. This concentration is approximately 400 ppmo But then

the fuel cell multiplication factors can not be directly used for the calculation of the core multiplication factor, because they involve the soluble boron poisoning. The problem is solved by using a very short "pseudo-burnup" timestep, with no soluble boron, after each real burnup timestep. A "pseudo-burnup" timestep is a very short timestep which practically adds no burnup to the fuel, so that the isotopics are not altered, but still allows for the eigenvalue calculation in the boron-free configuration. This way, the fuel is always burned with a spectrum influenced by the 400 pPM of soluble boron, but the multiplication factors are obtained from the pseudo-burnup timesteps which contain no boron, and the "clean" batch reactivity can still be obtained through the fuel life.

Figure 3.1.5 illustrates this method, showing the boron specification and the multiplication factors that may be obtained through the core life.