Monograph of Department of Nuclear Energy

Faculty of Energy and Fuels

AGH University of Science and Technology

Advanced fuel burnup assessments in

prismatic HTR for Pu/MA/Th utilization

using MCB system

Jerzy Cetnar1, Mariusz Kopeć

1, Mikołaj Oettingen

1

1AGH University of Science and Technology

Al. Mickiewicza 30, 30-059 Krakow, Poland

KRAKOW 2013

2

STUDY for the PUMA project of EUROPEAN Union’s 6th

FP EUROATOM

AGH WEIP KEJ/2013/2

This monograph is peer reviewed

ISBN 978-83-911589-2-0

Editor : Mariusz Kopeć

Copyright by

Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

Wydział Energetyki i Paliw, Katedra Energetyki Jądrowej

Al. A. Mickiewicza 30, 30-059 Kraków

3

Assessment of Pu and MA utilisation in deep burn Prismatic HTR by Monte Carlo Method -

MCB

Appendix A

Deliverable 124

Work Package 1

Project PUMA

Jerzy Cetnar

Mariusz Kopeć

Mikołaj Oettingen

AGH-University of Science and Technology, Krakow, Poland

4

Contents

Contents ................................................................................................ 4

List of figures ......................................................................................... 5

List of tables .......................................................................................... 6

Scope ..................................................................................................... 7

1. Introduction ................................................................................. 7

2. Monte Carlo burnup code system – MCB ....................................... 8

2.1. General features of MCB ................................................................ 9

2.2. Solution of Bateman equations ..................................................... 10

2.2.1 Transmutation Trajectory Analysis ............................................... 11

2.2.2 Fission product transmutation modelling ...................................... 14

2.3 MCB added values in applications for HTR analysis ..................... 14

2.3.1 Thermal-hydraulic coupling with POKE ......................................... 15

2.3.2 Bridge scheme for burnup step ..................................................... 16

3. HTR reactor calculation model .................................................... 17

4. Reactor physics calculations for deep burn of Pu/MA .................. 21

4.1. Transmutation analysis ............................................................... 22

4.2. Power distribution in equilibrium cycle in 4-batch shuffling ........... 24

4.2.1 Reduction of power spatial oscillations ......................................... 25

4.2.2 Influence of CR operation on power distribution ............................ 26

4.2.3 Distribution of discharge burnup .................................................. 30

4.2.4 Thermal-hydraulic assessment .................................................... 31

4.3. Reactivity control in equilibrium cycle in 4-batch shuffling ............. 32

5. Core characteristics in Pu/MA fuel cycle ..................................... 34

5.1. Case identification and description .............................................. 34

5.2. General fuel/reactor/system specifications .................................. 34

5.3. Rating and power density ............................................................ 35

5.4. Core inventory ............................................................................. 36

5.5. Fuel ............................................................................................ 38

5.6. Temperature at nominal conditions .............................................. 41

5.7. Temperature reactivity coefficients ............................................... 42

5.8. Control rod worth ........................................................................ 43

6. Conclusions ................................................................................ 44

References ........................................................................................... 45

ANNEX: Auxiliary tables and figures.................................................... 46

5

List of Figures

Fig. 1 Diagram of bridge scheme of burnup step ................................ 17

Fig. 2 Radial division of active core .................................................... 18

Fig. 3 Core regions with fuel rods and CR/RS holes .......................... 19

Fig. 4 Details of the fuel block structure ............................................ 19

Fig. 5 Scheme of 4-batch axial-only block shuffling ........................... 20

Fig. 6 Fuel temperature distr. in uniformly loaded PUMA core ........... 25

Fig. 7 Power spatial distr. in the bridge scheme of burnup step ......... 26

Fig. 8 Power profile in cycle with CR operation modelled .................... 28

Fig. 9 Axially integrated power profile with CR operation modelled..... 30

Fig. 10 Distr. of burnup on discharge with effect of CR operation ........ 31

Fig. 11 Burnable poison mass (Eu151) evolution in 4-batch shuffling .. 33

Fig. 12 Criticality evolution with stepwise operation of CR ................... 34

Fig. 13 Temperature distr. with CR operation simulated stepwise ........ 52

6

List of Tables

Tab. 1 Reference fuel compositions .................................................. 21

Tab. 2 Reaction branching dependence on location; 2nd ref. fuel ....... 23

Tab. 3 Core parameters related to the power at three time points ..... 29

Tab. 4 Distribution of discharge burnup in 4-batch 350-day cycle .... 30

Tab. 5 Thermal-hydraulic parameters in 4-batch 350-day cycle ....... 32

Tab. 6 Reactivity change versus control margin; 2nd ref. fuel ............ 32

Tab. 7 Power density and ratings for case G1 (2nd fuel vector) ........... 36

Tab. 8 Amount of the heavy metal isotopes; case E12 (1st fuel vec.) .. 36

Tab. 9 Amount of the heavy metal isotopes; case G1 (2nd fuel vec.) ... 37

Tab. 10 Amount of the FP isotopes; case E12 (1st fuel vec.) ................. 37

Tab. 11 Amount of the FP isotopes; case G1 (2nd fuel vec.) .................. 38

Tab. 12 Amount of the BP; case E12 (1st fuel vec.) .............................. 38

Tab. 13 Amount of the BP; case G1 (2nd fuel vec.) ............................... 38

Tab. 14 Fuel and BP loaded, discharged and consumed ..................... 39

Tab. 15 Fuel and BP loaded and discharged per one cycle .................. 40

Tab. 16 Max. temp. [K] in 4-batch 350-day cycle with 2nd ref. fuel ...... 41

Tab. 17 Reactivity coefficients at BOC in 4-batch 350-day cycle ......... 42

Tab. 18 Fuel kernel power density [kW/cm3] after 5 FPD .................... 46

Tab. 19 Fuel kernel power density [kW/cm3] after 150 FPD ................ 47

Tab. 20 Fuel kernel power density [kW/cm3] after 350 FPD ................ 48

Tab. 21 Zone average fuel temperature [ºC] after 5 FPD ...................... 49

Tab. 22 Zone average fuel temperature [ºC] after 150 FPD .................. 50

Tab. 23 Zone average fuel temperature [ºC] after 350 FPD .................. 51

7

Scope

This report describes the work done under the scope of deliverable 124

for the PuMA project, which is part of the European Commission’s 6th

framework program. It is concern with application of Monte Carlo

burnup calculation system – MCB for analysis of reactor physics and

core design of prismatic HTR for plutonium and MA utilisation in deep

burn mode.

1. Introduction

As some features of various nuclear reactors are similar, the other

differs thus requiring an additional attention. The core of an HTR reactor

is characterized by specific features, which imposes particular

requirements on analytical tools and models that are to be used for

analysis of its physics and safety along with fuel cycle analysis. The

major differences, as compared to other systems like LWR or FBR, that

need to be taken into consideration in analysis of nuclear transmutation

in deep burn mode are concerned with high temperature of the fuel,

different fuel form and different moderator. These specific features are:

high operational temperature of the fuel and graphite, which

necessitates the thermal-hydraulic and neutronic coupling;

high level of core heterogeneity caused by a fine structure of fuel

compacts filled with TRISO particles, for which a highly

structured geometrical model is needed in order to account for

neutron spectra effects that occur in the fuel due to resonant

cross sections;

deep neutron thermalisation, which imposes few important

neutronic effects like: shortening free path length, higher flux

gradients, stronger influence of reflectors, and as a consequence

needed attention for spatial effects particularly in the vicinity of

control rods or reflectors;

large core size in terms of free path length as well as of the core

fine structure length (i.e. TRISSO kernel size), which is primarily

caused by relatively low average power density.

Due to the existing complexity of burnup process, it is effective to

apply an integrated calculation system, which will allow the user taking

into consideration the spatial effects of full heterogeneous reactor model

with continuous energy representation of cross section and the thermo-

hydraulic coupling. For this purpose, an integrated Monte Carlo burnup

8

calculation code MCB is very suitable. However, statistical fluctuations,

which are intrinsically present in Monte Carlo methods, need to be

discriminate from an expected real solution. In case of HTR Monte Carlo

modelling, flux oscillations and convergence problems with fission source

may be brought about.

The MCB methodology in application for HTR core analysis is

described in Chapter 2, while in the next Chapter 3 we present prepared

high fidelity models of PUMA reactor used in our analysis. Chapter 4

contains analysis of physical conditions of an HTR in deep burn mode

with plutonium and MA utilization, where influence of local conditions on

nuclide time evolutions are assessed. The initial analysis of physical

properties of HTR in deep burn is also presented there. Detailed core

characteristics are described in Chapter 5, for both reference fuel

options, with the chosen shuffling scheme adopted. We also investigated

the CR operation concerning its influence on the local power deposition.

Finally, the conclusions are presented in Chapter 6.

2. Monte Carlo burnup code system - MCB

The Monte Carlo Continuous Energy Burn-up Code (MCB) is a general-

purpose code used to calculate a nuclide density evolution with time

(after burn-up or decay). The code performs eigenvalue calculations of

critical and sub-critical systems as well as neutron transport calculations

in fixed source mode to obtain reaction rates and energy deposition that

are necessary for evaluation of the burn-up. MCB internally integrates

the well-known MCNP code (currently - version 5 [1]), which is used for

neutron transport calculation, and a novel Transmutation Trajectory

Analysis code (TTA) [2], which calculates density evolution, including on-

line formation and analysis of transmutation chains. The code version

MCB1C [3] became available to the scientific community on a freeware

basis though Nuclear Energy Agency Data Bank, Package-ID: NEA-1643

since 2002. The MCB code has been developed recently and applied to

neutronics and fuel cycle analysis of helium cooled reactor system in

frame of EU FP5 project “PDS-XADS” [4]. Recent development of the code

was directed towards advanced description of modern reactors, including

double heterogeneity structures that exist in HTR-s. Current version

allows users to define models that are more detailed, with larger number

of universe levels, as well as to consider statistical fluctuation effects on

Monte Carlo modelling of nuclear reactors. Below the methodology of

core design and fuel cycle analysis using MCB is briefly described. The

code is still under development; recently added features concern

9

statistical analysis of burnup, emitted particle collection, thermal-

hydraulic coupling, automatic power profile calculations, advanced

procedure of burnup step normalization – so called “bridge scheme”, and

others.

2.1. General features of MCB

The main goal of a burnup code is to calculate the evolution of material

densities. It concerns all possible nuclides that may emerge in the

system after nuclides decays, transmutations, or particles emissions.

Transmutation process includes fission product breakdown into nuclides

as well as helium and hydrogen atoms formed from emitted α particles

and protons respectively. There is no required predefined list of nuclides

under consideration since all transmutation chains are being formed

automatically on-line basing on physical conditions that constrain the

system under the control of user-defined thresholds. These thresholds

concern contribution to the nuclide mass change from constructed

transmutation trajectories. In a real system under irradiation or decay,

the nuclide composition undergoes evolution that generally can be

described with a continuous function of time. An approximation of this

function is obtained in MCB throughout time the step procedure which

starts from assessing reaction and decay probabilities of every possible

channel by means of stationary neutron transport calculations. In the

next step, the transmutation chain is formed and then solved to produce

nuclide density table in required time points. The main features of the

code can be outlined as follows below.

The decay schemes of all possible nuclides and their isomeric states

are formed and analysed on the basis of the decay data taken from two

sources. The first one – TOI.LIB, which is based on Table of Isotopes

[5], describes decay schemes for over 2400 nuclides including

formation of nuclides in the excited states.

Numerous cross-section libraries and data sets can be loaded into

computer memory to calculate adequately reaction rates and nuclide

formation probabilities. It includes possibility of separate treatment of

cross section for different burnable zones, to account for thermal

effects, employment of energy dependent distribution of fission

product formation, and energy dependent formation of isomer

nuclides.

Thermal-hydraulic coupling with POKE [6] is available for prismatic

HTR.

10

Reaction rates are calculated exclusively by continuous energy method

with the usage of the point-wise transport cross-section libraries and,

in case of lack of proper library, by using the dosimetry cross section

library. The contributions to reaction rates are being scored at every

instant of neutron collision occurring in cells filled with burnable

material by using the track length estimator of neutron flux.

Fission product yield is calculated from incident energy dependent

distributions of fission products prepared separately for every

fissionable nuclide.

Heating is automatically calculated in a similar way as the reaction

rates during neutron transport simulation by using heating cross

sections, which are KERMA factors included in standard cross section

tables. The code calculates automatically also the heating from

natural decay of nuclides, what allows for consideration of afterheat

effects. The energies of decays are taken from the ORIGEN library [7].

Time evolutions of nuclide densities are calculated with the complete

set of linear transmutation chains that is prepared for every zone and

time step so it is being automatically adjusted to the transmutation

conditions evolving with time.

The code uses extended linear chain method, which is based on the

Bateman approach, to solve prepared-on-line a set of linear chains

that noticeably contribute to nuclide formation.

Detailed analysis of transmutation transitions from nuclide to nuclide

is performed. The transmutation chains that are formed by the code

can be printed for nuclides of interest.

Material processing is available along with material allocations to

geometry cells during the burnup. Using this feature the user can

simulate the fuel shuffling or CR operation.

2.2. Solution of Bateman equations

MCB adopts general solution of Bateman equations derived from linear

chain method. The general transmutation chain, which is nonlinear, is

resolved into series of linear chains using methodology of transmutation

trajectory analysis. MCB is free from producing and using one-group

neutron cross section. It uses transmutation probabilities instead, which

are assessed directly in the process of neutron transport calculation

executed independently for every transmutation zone and every time

step.

11

Transmutation constants can be expressed as follows:

,,

,,, )()(pnx

x

ji

xd

j

d

jiji dEEEb (1)

where the symbols denote:

dj - decay constant of j-th nuclide,

,

d

jib - branching ratio of j-th nuclide decay into i-th nuclide,

x - particle flux (x = neutrons, protons, pions +,0,-), x

ji, -cross section for production of i-th nuclide by particles x

during interaction with j-th nuclides.

The transmutation constants appear as the coefficients of the Bateman

equations describing the general, non-linear transmutation chain for w

nuclides as follows:

)1,=( d

d

,1, wiN

t

Nj

wjji

i

. (2)

2.2.1. Transmutation Trajectory Analysis

Usually, in the commonly applied numerical methods the set of linear

chains is prepared arbitrarily, which is sufficient for well-defined cases.

However, for a more general case the application of procedure that

resolves the non-linear chain into a set of linear chains is necessary to

assure the mass flow balance and the numerical solution stability.

In order to derive the solution of a general case basing on the known

solution of a linear decay case, it is convenient to focus on the

transmutation transition from one nuclide to the other one after elapsing

time t. The transmutation transitions can lead through many paths,

which possibly branch, forming a non-linear chain. Now, let us define a

transmutation trajectory as a sequence of direct nuclide-to-nuclide

transitions, starting from the first nuclide and ending at the last, n-th

nuclide. The transmutation trajectory is almost equivalent to a decay

chain, but due to an occurrence of branching in the non-linear chain, the

mass flow is not preserved on a single trajectory level. It is preserved,

however, over all the trajectories that can be extracted from the non-

linear chain. The Bateman equations for transmutation trajectory

representing a linear chain will have the following form:

12

)2,=( - d

d

d

d

11

111

niNNbt

N

Nt

N

iiii i

i

(3)

where

i

ii

i

wj

ij

jii

b 1,

,

(i = 1,n) (4)

The solution is following:

exp)0(

)(1

1

n

i

iii

n

n tN

tN

(5)

where

1 )(

n

ijj ij

j

i

(6)

In a general case when certain transition can appear in the chain mk

times the solution takes more complicated form:

mi

m

m

in

i

iii i

i

m

ttt

,

01n

1n

! exp

)0(N)(N (7)

where

,1

ijnj

m

ij

j

i

j

and 1 kk

m (8)

The omegas for ni ,1 and ij ,0 take the following forms:

j

h

j

h

j

h

n

ikk

n

ill

l

h

ki

i

k

kk

ji

n

k

hjh

0 0 0 1 0

,

1 2

,

(9)

The concentration of the last trajectory nuclide due to the trajectory

transition can be written as:

13

)()0()( tAB

NtNn

nn

(10)

where

1,1

nk

kbB (11)

is the total trajectory branching rate. The disintegration or removal rate

of the last trajectory nuclide can be expressed as follows:

)()0()( tABNtA nn (12)

It can be thought of as generalized activity. The time integral of the

removal rate (19) leads to the following function:

)()0( )()( ,

0

,1

t

0

tfBNdttAtI mi

m

min

i

i

(13)

where

m

k

k

iimi

k

tttf

0

,!

exp1)(

(14)

The above stands for the sum of the nuclides concentrations of formed in

the disintegration process of the n-th nuclide or their daughters after

being produced from the transition along considered trajectory. For given

time t, every transmutation trajectory can be characterized by two

quantities: the trajectory transition

)0(/)( )( 1NtNtT n (15)

and the trajectory passage

)0(/)( )( 1NtItP (16)

The transition and passage functions are important for the mass balance

of transmutations, which is an ultimate parameter for checking

correctness and convergence of any numerical algorithm for calculation

of time evolutions of concentrations in a transmutation system. They are

used to control the numerical algorithm of breaking down a non-linear

transmutation chain into a series of transmutation trajectories for which

the concentration can be calculated.

14

2.2.2. Fission product transmutation modelling

The equations derived can be also adapted for the case of continuously

supplied nuclides such as nuclides yielding form the fission product. In

this case, the concentration of nuclide that starts a transmutation

trajectory is described as follows:

d

d 111

1 sNt

N (17)

where s1 is the nuclide production rate. The production rate, s1, can be

represented by the decay of an artificial nuclide N0 that is characterized

by decay constant 0 and branching ratio b0, which need to be set to

satisfy the following conditions:

1 where1

ln1

and

0 when0)0( and )0(

00

00

10

bb

b

t

iNtsN i

(18)

As b0 is set arbitrarily as a large number, the 0 constant results from

equation (18) for a given value of the required production rate s1. The

case of continuously supplied nuclides takes places when fission

products are produced with assumed constant rate of the actinides

fissioning.

2.3. MCB added values in applications for HTR analysis

Due to existing complexity of burnup process and reactor physics itself

in an HTR, in order to ensure high quality of design, particularly with its

safety features, it is reasonable to apply few different tools of reactor core

analysis. This can bring about results obtained from few different

perspectives. Here, the Monte Carlo methods, although demanding more

computer power, are characterised by higher level of model complexity

and fidelity, thus the results can be obtained in an integrated way,

possibly displaying important effect that can be hidden or neglected in

another approach. For this purpose, an integrated Monte Carlo burnup

calculation code MCB is very suitable. It is fully integrated calculation

system, which allows the user taking into consideration of spatial effects

of full heterogeneous reactor model with continuous energy

representation of cross section and the thermo-hydraulic coupling. Here,

a particular importance lays in a proper assessment of the power

distribution, but not merely at BOL but as a function of burnup with

consideration of the CR operation. The power distribution affect many

15

core safety features, therefore a simplified approach can lead to biased

conclusions. As Monte Carlo approach presents some benefits, it is not

free from their intrinsic problems, which need to be treated accurately.

Namely, statistical fluctuations, which are intrinsically present in Monte

Carlo methods, need to be discriminate from an expected real solution.

In case of HTR Monte Carlo modelling, flux oscillations and convergence

problems with fission source may be brought about.

2.3.1. Thermal-hydraulic coupling with POKE

Introduction of thermal hydraulic calculations into Monte Carlo

simulations was done by coupling MCB with the POKE code [6]. The

POKE code was written in GA; its original version was designed for the

geometry and parameters of Ft. St. Vrain reactor, and later it was used

for GT-MHR analysis as well. POKE determines fuel and coolant

temperature distributions as well as coolant mass flow in the steady

state. The reactor configuration consists of a number of parallel coolant

channels connected to common inlet and outlet plenums. The reactor

between the inlet and outlet plenums is divided into inlet reflector, core

and outlet reflector. All heat is assumed to be generated in the core. For

calculational purposes the reactor is divided into a number of cylindrical

regions, which extend from the inlet to the outlet plenum. The POKE

code iteratively solves three one-dimensional equations that express the

conservation of mass, momentum and energy for each channel modelled.

The coolant mass flow rate results from balancing the pressure drop from

the inlet to the outlet plenum.

The code coupling was done on the level of source code, where the

modified version of POKE has been incorporated into the MCB code, but

all the data exchange between codes has been left on external files, in

order to allow the user to recalculate. The thermal-hydraulic

specification is read in from the POKE input file, which describes the

reactor geometry and other parameters, whereas MCB delivers only the

power distribution profile. The temperature profile at BOL is to be

defined by the user after arbitrary assumptions or using the results

obtained in earlier calculations. Invoked POKE calculates the required

thermal hydraulic parameters as well as the new temperature profiles.

On that basis the new temperatures of all regions together with the cross

sections adjusted to the temperature are used for new power profile

iteration, and the subsequent burnup calculations provides more

realistic isotope production results.

16

2.3.2. Bridge scheme of burnup step

Statistical fluctuation in Monte Carlo modelling should in general

follow the law of large numbers of the probability theory. On this

assumption, the standard formulations of statistical measures of

probability distribution are used in Monte Carlo neutron transport

calculations. However, in some nuclear reactor systems like HTR, the

fluctuation of the calculated power distribution contains a systematic

term, which is propagated in consecutive neutron generations through

the fission source distribution. In burnup calculations scheme the

process of source normalization to the constrained power is done usually

using the neutron heating rate as evaluated at the beginning of step. In

this treatment, the systematic term (in the fluctuation of power

distribution) tends to conserve itself or to form increasing oscillations.

This process of creating oscillations is linked with production and

depletion of Xe135 in a deeply moderated HTR core. Here we do not

mean the real physical oscillations, which can be created also, but the

numerical oscillations in the calculated density distribution. Another

source of systematic term is related directly to the neutron source

convergence problem, which occurs when the fundamental distribution of

the source is difficult to achieve, even if the reactivity converges early.

This behaviour occurs in large HTR cores, which was studied in more

details in KTH work [8].

The magnitude of both effects can be reduced when the source

normalization procedure is improved. This is done in so-called bridge

scheme of burnup step, in which the normalization is done using the

step average functions. This procedure involves repeated calculation of

the neutron heating rates and reaction rates at both step ends –

beginning of step (BOS) and end of step (EOS) as shown in Figure 1. In

the first approximation the number density at EOS is calculated with

assumption of constant heating and reaction rates over the entire step.

This may result in biasing of the burnup if reaction or heating rates

change with time. A correct calculation of final number density requires

the average values of the neutron source strength and reaction rates.

The process of averaging uses a simple average of two values: at BOS and

at EOS after correction. The EOS correction in done in a step predictor

module, in which the reaction rates and source strength of the first

approximation are scaled by the ratio of the burnup constrained to its

first approximation.

17

Figure 1. Diagram of bridge scheme of burnup step

3. HTR reactor calculation model

The PUMA prismatic core model for MCNP/MCB calculations was

prepared according to the reference specification from Deliverable 121

(D121) [9], with recommended design option concerning axial-only fuel

shuffling and 4-batch refuelling scheme. The major objective of our

Monte Carlo study is to understand deeply the neutronic and burnup

characteristic of the deep burn core in the reference configuration by

consideration of that core features in the models that were neglected so

far, or are difficult to be considered using other methods. We pay a

particular attention to the modelling of CR operation as the CR insertion

level is adjusted along with the reactivity loss during burnup. The

reference PUMA reactor core comprises five radial rows of fuel blocks in

eight axial block layers. For the power distribution analysis and burnup

calculations, the active core is divided into burnup zones. Every fuel

block row is divided radially into two halves, while axially every block

layer is divided into three regions, which altogether constitute 240 fuel

zones. The core was filled with fuel compacts containing TRISO in 18%

18

volume fraction. The exact locations of the radial regions used in thermal

hydraulic calculations and fuel burnup are shown also in Figure 2. The

active core is model with high level of fidelity with full description of

details including the fuel double heterogeneity. The fragment of the core

model is shown in Figure 3, where different colours denote different

zones with their materials and corresponding temperatures. It can be

observed that the core structure is already very complicated, but in fact

each fuel rods has its own internal structure shown in Figure 4, where

the fragment of hexagonal spheres) can be seen. In the applied model,

apart from the fuel, also burnable poison rods constitute burnable zones

in number of 80; 10 radial regions times 8 axial zones. The CR channels

are also axially divided in order to allow for modelling of CR operation,

which follows the reactivity loss with burnup. Concerning the fuel

shuffling, we have applied recommended axial- only shuffling scheme

with the mirror symmetry in respect to the core middle plane, as is

shown in Figure 5. This is one of the simplest schemes, which reduces

the space of an operator error and shortens the outage time required for

shuffling, as compared with radial or mixed axial-with-radial shuffling

schemes.

Figure 2. Radial division of active core

19

Figure 3. Core regions with fuel rods and CR/RS holes

Figure 4. Details of the fuel block structure

20

Figure 5. Scheme of 4-batch axial-only block shuffling

The adopted core design features are summarised below.

The eight fuel-block layers design has been applied.

The four-batch axial only shuffling scheme has been chosen.

The core has been divided into burnup zones in 10 radial regions

and 24 axial segments, which makes 240 fuel burnable zones.

Control rods operation has been modelled with insertion level

adjustment of 50 cm bins.

Reserve shutdown channels have been modelled and filled by

helium.

Burnable poisons rods have been applied only in the inner region

(inner half of the 4-th block row). Eu2O3 rods with density of 7.4

g/cm3 have been used. Remaining burnable poison holes have

been filled with helium.

All coolant holes have been modelled in the blocks of active core

and axial reflectors.

Reduced height of the channels located under dowels has been modelled.

The fuel handling holes have been modelled.

21

The second reference fuel composition with MA content, as

shown in Table 1 is our primary choice, while the first vector is

an option used in comparative analysis.

In the course of the study, the cycle lengths have been adjusted,

according to the manageable reactivity margin, to 420 days for

the “first reference fuel composition” and to 350 days for the

“second reference fuel composition”.

Table 1. Reference fuel compositions [9].

Fraction, wt%

Nuclide First vector Second vector

Np-237 - 6.8

Pu-238 2.59 2.9

Pu-239 53.85 49.5

Pu-240 23.66 23.0

Pu-241 13.13 8.8

Pu-242 6.78 4.9

Am-241 - 2.8

Am-242m - 0.02

Am-243 - 1.4

4. Reactor physics calculations for deep burn of Pu/MA

Since the PUMA core in deep burn design has to achieve as high

burnup as possible, we need to understand which physical processes

play the major role in transmutation and burnup. We also need to know

what the dependences on the local conditions occurring in the core are.

This knowledge is vital in order to make proper design decisions that will

bring about an effective and safe design. Concerning the safety aspects,

not only reactivity control is important, but also an acceptable power

distribution. This concerns not only power generated during operations

but also the afterheat distribution, which should be manageable during

possible LOCA accidents. Although the analysis of LOCA accident is

beyond the scope of this project, a neutronic analysis can identify safety

threats possibly implied in incorrect designs. In this chapter, we present

reactor physics analysis of deep burn design comprising of transmutation

analysis, power distributions during operation and the impact of

reactivity control on power and temperature distributions.

22

4.1. Transmutation analysis

In a deep burn design, the process of transmutations is a primary

driver of power distribution in that the heavy metal nuclides can fission

out early or contribute to the transmutation chains that are leading to

either non-fissile or fissionable nuclides. In the first case this can

increase afterheat globally or locally in the long term, whereas in the

second - contrary case, reduce the reactivity loss. Since the neutronic

conditions in HTRs differ strongly depending on the location within the

core due to the local temperature and the reflector distance, we have

analysed what is the characteristics of transmutation process in the

PUMA core. The transmutation chain distribution depends on the

reaction branching, which is presented in Table 2. This analysis has

been performed in the static burnup conditions of the PUMA core entirely

filled with the fresh fuel. This model would reflect reality only in the real

case single-batch refuelling scheme where the power peaks in the vicinity

of inner reflector as a result of unacceptable power distribution.

What is important here, the burnup rate varies depending on local

position by factor of four, which can have an adverse effect on the power

distribution. Leaving aside the question whether this power distribution

can be levelled out by burnable poison, let us focus on transmutation

analysis. As fission reaction contributes the most significantly to the

burnup, the fission rate serves here as a point of reference. The product

of reaction branching and destruction rate is a good measure of the

respective reaction rate. Reaction branching to fission is responsible for

the ultimate heavy metal nuclide destruction, which terminates the

possibility of further transmutation. If a heavy metal nuclide avoids

fission it can become an active actinide contributing to afterheat, mostly

in alpha decay. The fissionable nuclides under considerations are

Pu239, Pu241, Am242m, Cm243 and Cm245. All plutonium isotopes

have substantial probabilities of fission avoidance, higher than 1/3;

therefore significant fraction of them can be transmuted into non-fissile

ones. We observe significant dependence on location of the branching in

case of three nuclides: Pu238, Pu241 and Am241. The formation of

Am241 from Pu241 strongly depends on the location, mostly due to

different burnup rates. Similar case occurs with direct alpha decay,

which contributes stronger in locations with lower burnup rate. Ratios of

neuron capture to fission shown in the bottom of Table 2 indicate an

increase of neutron capture with lower burnup in case of Pu238 but a

decrease in the case of Pu241. The effect of cross section dependence on

fuel temperatures plays here some role.

23

Table 2. Reaction branching dependence on location; second ref. fuel case

Location:

Description Inner column

(4th block row’s inner half)

Middle row column

(6th block row’s outer half)

Radial region 1 1 1 6 6 6

Axial segment 1 15 24 1 15 24

Conditions

Flux 1014 n/cm2s 1.75 2.25 1.27 1.20 1.33 8.03

50 day step burnup MWd/kgHM

72.97 84.77 55.04 32.63 28.62 23.20

Neutron capture branching

Pu238→Pu239 88.42% 86.90% 85.01% 79.89% 75.63% 74.70%

Pu239→Pu240 37.04% 37.60% 37.51% 37.58% 38.45% 37.76%

Pu240→Pu241 99.51% 99.57% 99.53% 99.47% 99.57% 99.48%

Pu241→Pu242 23.66% 23.95% 23.49% 21.74% 20.95% 20.52%

Pu244→Pu245 99.92% 99.94% 99.92% 99.94% 99.96% 99.94%

Am241 (n.γ) 98.89% 98.91% 98.80% 98.58% 98.62% 98.36%

Am241→Am242 78.40% 78.60% 78.30% 78.12% 78.60% 78.03%

Am241→Am242m 20.49% 20.31% 20.50% 20.46% 20.02% 20.33%

Am242m→Am243 18.54% 18.26% 18.43% 17.80% 17.25% 18.20%

Am243→Am244 99.59% 99.63% 99.58% 99.60% 99.68% 99.58%

Decay branching

Pu238→(α)U234 4.54% 4.58% 7.14% 10.31% 12.05% 15.29%

Am241→(α)Np237 0.22% 0.19% 0.31% 0.45% 0.44% 0.69%

Pu241→(β)Am241 5.31% 5.14% 7.72% 12.35% 14.45% 17.71%

Fission branching

Pu238→FP 7.04% 8.52% 7.85% 9.79% 12.32% 10.00%

Pu239→FP 62.96% 62.40% 62.49% 62.41% 61.54% 62.23%

Pu241→FP 71.04% 70.91% 68.79% 65.90% 64.60% 61.77%

Am241→FP 0.89% 0.90% 0.89% 0.97% 0.94% 0.95%

Am242m→FP 81.46% 81.74% 81.57% 81.88% 82.75% 81.80%

Ratio: (n.γ)/fission

Pu238 12.56 10.20 10.84 8.16 6.14 7.47

Pu239 0.588 0.603 0.600 0.602 0.625 0.607

Pu241 0.075 0.072 0.112 0.187 0.224 0.287

Am241 112 110 111 102 105 103

Am242m 0.228 0.223 0.226 0.217 0.208 0.222

The lower temperature in the upper locations enhances neutron

capture of Pu238 while suppresses its fission. Other effects also occur

but on lower amplitude. Nevertheless, they lead to different nuclide

24

evolution patterns depending on the locations. General conclusions of

this study are as follows:

Local conditions in uniform core are causing non-uniform burnup

distribution.

Non-uniform burnup distribution results mostly form variation of

fission to capture ratio depending on locations.

In the locations with low burnup rate, increased fissile destruction by

neutron capture occurs, which leads to a steeper reactivity swing,

thus lowering achievable burnup on discharge.

The axial buckling of the neutron flux needs a correction, particularly

in the inner column, which might be obtained with introduction of

axial shuffling.

4.2. Power distribution in equilibrium cycle in 4-batch shuffling scheme

Power distribution in an HTR with prismatic core uniformly loaded

with fuel is characterised by power peaks near reflectors that might lead

to unacceptable temperature level. This is presented in Figurte 5, where

the temperature peaks at the level of 1300°C, exceeding its acceptable

limit. It should be noted that within the hottest fuel block the

temperature could differ by about 300 degrees. This observation

necessitates the usage of a model with radial segments thinner than a

block row; otherwise, the results of temperature calculation will be biased

and too optimistic Distributed burnable poison introduction to the core

can effectively lower power peaks. One can expect similar influence on

the core power distribution from the fuel axial shuffling.

For the assessment of power distribution, we have performed

calculations in the full core burnup model with four-batch axial-only

block shuffling, according to the recommendation from D121. Applied

scheme of fuel shuffling is presented in Figure 5. Burnable poison rods

have been applied only in the first radial region, i.e. the inner half of the

first fuel block row. We have applied both reference fuel vectors in order

to reach the equilibrium cycle. The current Monte Carlo analysis has

shown that with the first reference fuel, which is without minor actinide

content, it is possible to achieve an equilibrium cycle of 420 days in four

reloading batches, which sums up to 1680 full power days of irradiation.

For the second case of fuel, with minor actinides content, the cycle length

is shorter due to the lower amount of fissionable nuclides and equals 350

days summing up to 1400 full power days.

25

Figure 6. Fuel temperature distribution in uniformly loaded PUMA core.

4.2.1. Reduction of power spatial oscillations

Applied burnup calculation model includes the bridge scheme of

burnup in order to account for numerical oscillation of the neutron flux,

as well as to adjust the power normalization to the heating rates,

calculated as step average values instead of BOC values. The flux

oscillations that occur in the thermalized neutron spectra originate from

two sources: Xe135 unsteadiness and fission source convergence. The

real concentration of Xe135 can have spatial oscillations caused by a

local tilt in neutron flux, which changes the balance between its

production and destruction rates. A global reduction or increase in

neutron flux can also lead to the global oscillations of Xe135, which in

return directly affects the neutron flux. A phenomenon of similar nature

occurs in Monte Carlo calculations of the neutron flux in such a system.

Here, calculated local flux oscillations at BOS change their distribution at

EOS due to a feedback effect; flux oscillation vector changes its phase

angle by 180°. This effect is presented in Figure 7. The occurring power

oscillations have a collective nature; areas of power oscillations in the

same direction exceed the fuel block dimensions. Since the average

values have been used for the burnup step, these power oscillations have

been reduced in our results of power distribution.

26

Figure 7. Power spatial distributions in the bridge scheme of burnup step

4.2.2. Influence of CR operation on power distribution

Modelling of CR operations is not often being included in core

performance assessments, due to complexity it involves. However,

locations of power peaks and assessments of power and temperature

peak values can be strongly affected by the CR operations, particularly in

PUMA - like systems, due to the short neutron transport length.

Moreover, the influence of CR operation on the power distribution might

be stronger in fuel batch reloading schemes. Therefore, before any

optimization of fuel refuelling and shuffling can be undertaken, the

assessment of CR operation needs to be accomplished. As the axial only

shuffling scheme has positive influence on the power distribution by

leading to reduction on power peaking near reflectors, we need to assess

how the CR operation influences it. This analysis has been carried out,

where CR operation were modelled by changing the CR insertion level

stepwise linearly in 100 cm bins along with the fuel burnup. The time

evolution of power profile is depicted in Figure 8, which concerns

equilibrium cycle of 350 days with the second reference fuel. The graphs

apart from the first one on the figure show the step average distributions,

where the basic step duration of 50 days has been used. At the cycle

beginning, two shorter steps were applied in order to stabilise Xe135.

The power ratings for three characteristic points: after 5, 150 and 350

days are presented in the Annex appended to this report. At BOC the

27

operational CR were fully inserted while the start-up CR were fully

withdrawn. The power distribution then was quite well balanced; the

BPR suppressed power peaking close to the inner reflector while in the

central location of axial direction the power peak is reduced due to the

fuel partially burned. The power generated in the upper core half is

greater than in the lower. This results from lower temperature in the

upper part, which negatively changes the reactivity. The power ratings in

radial outer regions are generally lower than the average, due to CR

influence, which reduced the reflector significance. In the next steps the

CR have been gradually shifted, which brings about a significant change

in the axial power profile.

28

Figure 8. Power profile in cycle with CR operation modelled; Pu+MA fuel,

350- day 4-batch equilibrium cycle in axial only shuffling.

When the insertion level of CR became smaller than 600 cm, the 7-th

block layer, with the fresh fuel became uncovered by CR, thus allowing

the power to grow there, which should be expected generally. The second

quarter of the cycle presents the highest power factors, exceeding four,

which is more than twice bigger than at BOC. During that time, the most

of the power was generated in the lower half of the core. The range of

changes in parameters related to the power distribution is significant,

which is shown in Table 3. The power profiles reach their maximum

after about 150 days due axial profile change; the radial profile gets lower

with burnup slightly.

29

Table 3. Core parameters related to the power at three characteristic time points of 350-day cycle.

Parameter 5 Days 150 Days 350 Days

Fuel kernel average power density [kW/cm3] 3.56

Fuel kernel maximum power density [kW/cm3] 7.33 16.87 12.90

Maximum axial form factor 1.768 4.056 3.113

Average radial form factor 1.264 1.169 1.162

Total form factor 2.056 4.739 3.618

It is worth noting that the power peaks at the outer radius, whereas the

radial profile is not a matter of concern as is shown in Figure 9 and there

is no need for an additional power profile tailoring with burnable poison

in regard to the radial power distribution. The observed increased power

generation in outer regions during the second half of the cycle is caused

primarily by its suppression early in the cycle. The CR operation

increases the contribution to the total power from the lower half of the

core. This is reflected in the distribution of the discharge burnup, which

is presented in Table 4 and Figure 10. Since the burnup is not linear in

time and its highest rate occurs during the first cycle, the fuel loaded into

the lower layer undergoes a deeper burnup. The shuffling cannot

compensate the difference in achieved burnup, which spreads up to 12%

concerning the fuel loaded in upper and lower layers. Radially the

burnup spread is about 22 %. Probably, there is room for improvements

concerning burnup distribution by optimization of burnable poison

distribution, or implementation of an asymmetric shuffling scheme. The

obtained results concerning axial profile bring in a safety concern in

relation to afterheat. During a certain period in the middle of cycle, the

power is concentrated in 7th block layer and potentially high afterheat in

case of a LOCA will need to be diffused. This problem needs to be

investigated since it can be the source of a possible serious safety threat.

30

Figure 9. Axially integrated power profile with CR operation modelled;

Pu+MA fuel, 350-day 4-batch equilibrium cycle in axial only shuffling.

4.2.3. Distribution of discharge burnup

Table 4. Distribution of discharge burnup in 4-batch 350-day cycle with 2nd reference fuel.

Location Radial region

1 2 3 4 5 6 7 8 9 10 Average

Burnup MWd/HMt

2nd

layer 448.2 455.8 493.0 527.4 547.7 531.5 489.4 467.4 425.0 458.3 485.2

7th layer 465.2 473.6 521.1 557.0 575.6 567.8 534.1 527.5 481.2 524.7 527.4

Ratio of local to average Total average 506.3

2nd

layer 0.89 0.90 0.97 1.04 1.08 1.05 0.97 0.92 0.84 0.91

7th layer 0.92 0.94 1.03 1.10 1.14 1.12 1.05 1.04 0.95 1.04

The results presented above show that the CR operation reverses the

axial power distribution, as compared to the results obtained in models

without CR operation modelling. Therefore, neglecting of this modelling

will result in biased distributions and should be avoided. In reality, the

temperature distribution effect on the power distribution is overshadowed

by a counter effect resulting from the CR operation.

31

Figure 10. Distribution of burnup on discharge with effect of CR

operation

4.2.4. Thermal-hydraulic assessment

The thermal hydraulic calculations for the analysed cycle were performed

using POKE, which was invoked at the beginning of every step, with the

power distribution assessed with MCB. The results obtained in the three

characteristic points of the cycle are shown in Table 5 below. Two first

points are more representative than BOC and MOC respectively, since

after 5 days the Xe135 mass is stabilised while 150-day point is the point

of maximum of temperature. Detailed temperature distributions at these

points are presented in the Annex appended to this report. The thermal-

hydraulic parameters are under constraints during all the cycle. The fuel

temperature at its maximum occurs at the middle point, due to the effect

of CR withdrawal above the 7th layer, where the fresh fuel was loaded.

32

Table 5. Thermal-hydraulic parameters in 4-batch 350-day cycle; 2nd ref. fuel.

5 day 150 day 350 day Limit

Power (total core) 600.0 MWth

Coolant inlet temperature 491.0 °C

Average coolant outlet temperature 851.6 851.6 °C

Maximum coolant outlet temperature 919.4 934.2 931.2 1021.0 °C

Coolant flow rate (total core) 320.0 320.0 kg/s

Bypass flow fraction 0.2

Maximum fuel temperature 1023.4 1187.5 1076.4 1218.0 °C

Average fuel temperature 893.6 735.9 759.1 891.0 °C

Maximum graphite temperature 973.8 1055.3 1022.4 1142.0 °C

Average graphite temperature 766.6 706.8 729.9 770.0 °C

Core inlet pressure 7.067 7.100 MPa

Core pressure drop 0.040 0.037 0.038 0.050 MPa

4.3. Reactivity control in equilibrium cycle in 4-batch shuffling

The length of equilibrium cycle in our reference case (G1) been

evaluated as 350 full power days, where the main limiting factor was the

criticality level at EOC.

Table 6. Reactivity change versus control margin; 2nd reference fuel

Reactivity change / reactivity margin [pcm]

CZP to HZP -2020

HZP to HFP – Xe135 buildup on power -2430

CZP to HFP – startup reactivity change -4450

Startup CR worth 8400

Cycle reactivity loss (350 fpd) -4580

Margin for Xe135 buildup after shutdown -1000

Required operational reactivity -5580

Operational CR worth 6550

33

The reactivity change during the cycle is manageable by set of

operational CR even with a margin of 980 [pcm] as is shown in Table 6

along with other reactivity changes and the control margins. The cycle

length is shorter than desirable 420 days, which was possible to obtain

with 1st reference fuel. There is a room for increasing the cycle length by

a better burnable poison implementation, which m reduce the level of

criticality. As it is shown in Figure 11, the applied amount of burnable

poison, which primarily has been adopted in order to reduce the power

peaking in fresh fuel, actively consumes neutrons for all four cycles.

Applied burnable poison in form of rods probably can be improved in

order to reduce its inventory.

The fuel cycle in our studies has been analysed with simulation of CR

operation, which is presented in Figure 12. In the applied scheme, the

CR operation has been simulated in equal shifts, which does not

represent the reality, and requires a better adjustment to the actual

reactivity swing rate. In the simulation, the start-up CR-s haven’t took

part, therefore the initial drop of reactivity due to Xe135 build-up occurs.

Later, the simulated CR movement is too slow, and then too fast, which

is the effect of the fresh fuel uncovering by CR-s and Xe135 balance.

Figure 11. Burnable poison mass (Eu151) evolution in 4-batch shuffling

scheme.

0 200 400 600 800 1000 1200 1400 16000

500

1000

1500

2000

2500

3000

Burnable Poison Evolution in PuMA

Second reference fuel4-batch shuffling scheme

Eu

15

1 m

ass [g

]

Time [days]

Upper core batch load

Lower core batch load

34

Figure 12. Criticality evolution with stepwise operation of CR.

5. Core characteristics in Pu/MA fuel cycle

5.1. Case identification and description

5.1.1. Origin: Jerzy Cetnar

5.1.2. Organisation: AGH

5.1.3. Case identifier: Pu-Cycle-D124-E12 (E12); MA-Cycle-D124-G1 (G1)

5.1.4. Date: 30.08.2009

5.1.5. Applied code system: MCB; see Chapter 2.

5.2. General fuel/reactor/system specifications

5.2.1. Main system dimensions: as D121 8-block-layers;

5.2.2. Coated particle dimensions: as D121

5.2.3. Initial coated particle composition: as D121

- E12 - 2nd reference fuel; - G1 - 2nd reference fuel;

- see Table 1

0 200 400 600 800 1000 1200 1400 16000.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

PuMA criticality in 4-batch refuelling

Second reference fuel4-batch shuffling schemeStep-wise CR withdrawal

Xe135 buildup

Reload, CR reposition, Xe135 decay out

K-e

ff

Time [days]

35

5.2.4. Compact and block dimensions: as D121 8-block-layers

5.2.5. Number of compacts and blocks in the core: 4 393 728 compacts, 768 full fuel blocks, 384 fuel blocks with holes for CR/RCS, altogether 1152 fuel blocks

5.2.6. Fuel composition per nuclide: (outside coated particles; including impurities, burnable poison, etc.; units: (barn cm)-1) – as D121, outside TRISO none

5.2.7. Block composition per nuclide (outside fuel compacts; including impurities, burnable poison, etc ; units: (barn cm)-1) – as D121, no homogenization applied

5.2.8. Number of coated particles per compact: 9054

5.2.9. Operating cycle length (units: full power days) E12 – 420 ; G1 – 350;

5.2.10. Reload stop duration: 50 days

5.2.11. Nominal reactor power: 600 MWth

5.2.12. Capacity factor (units: %): 100%

5.2.13. Number of fuel batches: 4

5.2.14. Nominal coolant inlet temperature: 746.15 K

5.2.15. Nominal coolant inlet pressure: 7.067 MPa

5.2.16. Nominal coolant outlet temperature at nominal HFP conditions:1124.75K

5.2.17. Nominal coolant outlet pressure at nominal HFP conditions: 7.027MPa

5.2.18. Nominal coolant mass flow: 320 kg/s

5.2.19. Control rod positions: see [9].

5.2.20. Description of fuel cycle strategy and other relevant information on the specific case: see Chapter 3

5.3. Rating and power density

See Chapter 3 and Annex

36

Table 7. Power density and ratings for case G1 (2nd fuel vector);

for calculation of power density the volume of active

core of 128.85 m3 has been used.

Parameter BOL

0 days HFP

5 Days Maximum 150 Days

MOL 175 days

EOL 350 Days

Power produced per compact [W] 136.56

Maximum compact power [W] 282.54 280.76 647.15 504.45 494.07

Power produced per block [kW] 520.83

Maximum block power [kW] 1077.60 1070.83 2468.23 1923.96 1884.38

Power density in the core [W/cm3] 4.66

Maximum power density [W/cm3] 9.63 9.57 22.07 17.20 16.85

5.4. Core inventory

5.4.1. Amount of each of the heavy metal isotopes present in the core

Table 8. Amount of the heavy metal isotopes [g]; case E12 (1st fuel vector)

Actinides BOC EOC (420 fpd)

U234 U235 U236 U238 Np237 Np238 Np239 Pu238

Pu239 Pu240 Pu241 Pu242 Pu243 Pu244 Am241 Am242m Am243 Cm242 Cm243 Cm244 Cm245 Cm246 Cm247 Cm248

427 95.9 57.5

0.457 31.2

0 0.025

35 102

396 570 249 270 209 710 138 960

0 3.88

10 041 280

29 195 1 873

60 14 517 1 147

184 2.76 0.206

671 150 88.9

0.798 54.3

0.084 0.037

31 950

191 900 175 730 180 750 155 920

19.6 5.86

15 135 358

42 868 2 377

93.5 23 860 1 770

404 6.53 0.585

Sum 1 087 528 824 113

37

Table 9. Amount of the heavy metal isotopes [g]; case G1 (2nd fuel vector);

Actinides BOC EOC (350 fpd)

U234 U235 U236 U238 Np237 Np238 Np239 Pu238 Pu239 Pu240 Pu241 Pu242 Pu243 Pu244 Am241 Am242m Am243 Cm242 Cm243 Cm244 Cm245 Cm246 Cm247 Cm248

707 120.7 54.8

0.307 82 738

0 0

68 209 417 660 267 910 176 590 105 320

0 2.56

33 126 741

34 494 4 133

156 14 879 1 185

178 2.59 0.184

1 121 204.5 83.8

0.509 67 876

124.9 0.171

75 648 239 380 206 040 172 250 121 520

16.6 3.99

26 095 783

41 179 5 953

218 23 645 1 806

372 6.14 0.497

Sum 1 208 207 984 327

5.4.2. Amount of each of the fission product isotopes present in the core

Table 10. Amount of the FP isotopes [g]; case E12 (1st fuel vector)

F.P. BOC EOC (420 fpd)

Se79 Rb87 Sr90 Zr93 Nb95 Tc99 Pd107 Sn126 I129 Cs135 Cs137 Sm147 Sm151 Eu154

34.4 2 035 4 674 8 675

477 12 533 5 869

564 4 120 9 342

19 713 1 353

303 4 417

50.7 2 999 6 808

12 815 513

18 253 8 835

832 6 047

14 042 28 976 2 278

354 6 381

38

Table 11. Amount of the FP isotopes [g]; case G1 (2nd fuel vector)

F.P. BOC EOC (350 fpd)

Se79 Rb87 Sr90 Zr93 Nb95 Tc99 Pd107 Sn126 I129 Cs135 Cs137 Sm147 Sm151 Eu154

27.7 1 613 3 718 6 822

519 10 018 4 488

446 3 277 6 975

15 449 979 266

3 610

41.9 2 444 5 600

10 364 618

14 296 6 961

677 4 931

10 589 23 482 1 612

321 5 368

5.4.3. Amount of possible extra nuclides, such as burnable poisons (units: kg) at BOL, MOL, EOL (different values if applicable)

Table 12. Amount of the burnable poison [kg]; case E12 (1st fuel vector)

BP BOC MOC EOC (420 fpd)

Eu151 8.93 5.85 3.78

Table 13. Amount of the burnable poison [kg]; case G1 (2nd fuel vector)

BP BOC MOC EOC (350 fpd)

Eu151 10.39 7.81 5.43

5.5. Fuel

Fuel (actinide) consumption, actinide and fission product production

and discharge burnup at nominal conditions. This includes extra

nuclides, such as burnable poison:

5.5.1. Amount and composition of fresh fuel loaded into the system for one operating cycle, preferably per fuel type

5.5.2. Amount and composition of fuel discharged from (and not reloaded into) the system for one operating cycle, preferably per fuel type (per heavy metal and fission product nuclide;

Directly after final discharge from the reactor

After 100 years of decay after final discharge from the reactor

39

Table 14. Fuel and burnable poison loaded, discharged and consumed

in one operating 4-batch cycle [g]; E12 case (1st fuel vector)

Actinides Load Discharge (1680 fpd)

Consumption After 100 y.

of decay

U234

U235

U236

U238

Np237

Np238

Np239

Pu238

Pu239

Pu240

Pu241

Pu242

Pu243

Pu244

Am241

Am242m

Am243

Cm242

Cm243

Cm244

Cm245

Cm246

Cm247

Cm248

0

0

0

0

0

0

0

10 553

219 412

96 403

53 498

27 625

0

0

0

0

0

0

0

0

0

0

0

0

244

54

31

0

23

0

0

7 401

14 742

22 863

24 538

44 585

20

2

5 094

78

13 673

504

34

9 343

623

220

4

0

-244

-54.1

-31.4

-0.34

-23.1

-0.08

-0.01

3 152

204 670

73 540

28 960

-16 960

-19.6

-1.98

-5 094

-78

-13 673

-504

-33.5

-9 343

-623

-220

-3.77

-0.38

4 491

95.97

339.4

8.42

3 642

0

0

3 600

14 860

31 540

200

44 580

0

1.98

25 760

49.44

13 560

0.12

2.94

203

618

217

3.77

0.38

All 407 450 144 035 263 415 143 773

Se79

Rb87

Sr90

Zr93

Nb95

Tc99

Pd107

Sn126

I129

Cs135

Cs137

Sm147

Sm151

Eu154

0

0

0

0

0

0

0

0

0

0

0

0

0

0

16.3

964

2 134

4 140

36

5 720

2 966

268

1 927

4 700

9 263

925

51

1 964

-16.3

-964

-2 134

-4 140

-36

-5 720

-2 966

-268

-1 927

-4 700

-9 263

-925

-51

-1 964

16.3

964

197

4 143

0

5 745

2 966

268

1 941

4 706

919

3 104

23.9

0.75

Selected FP 0 35 074 -35 074 24 994

Eu151 (BP) 5 228 85 5 143 85

40

Table 15. Fuel and burnable poison loaded and discharged per one

operating cycle [g]; case G1 (2nd fuel vector);

Actinides Load Discharge (1400 fpd)

Consumption After 100 y.

of decay

U234

U235

U236

U238

Np237

Np238

Np239

Pu238

Pu239

Pu240

Pu241

Pu242

Pu243

Pu244

Am241

Am242m

Am243

Cm242

Cm243

Cm244

Cm245

Cm246

Cm247

Cm248

0

0

0

0

27 707

0

0

11 816

201 688

93 714

35 856

19 965

0

0

11 409

81

5 704

0

0

0

0

0

0

0

414

83.8

29

0.2

12 844

124.9

0.17

19 255

23 408

31 844

31 516

36 165

16.6

1.43

4 378

123.5

12 389

1 820

62

8 766

621

194

3.55

0.31

-414

-83.8

-29

-0.2

14 862

-124.9

-0.17

-7 439

178 280

61 870

4 340

-16 200

-16.6

-1.43

7 031

-42

-6 685

-1 820

-62

-8 766

-621

-194

-3.55

-0.31

11 790

150.2

425.7

6.76

17 180

0

0

9 634

23 510

39 870

257

36 170

0

1.43

31 240

78.27

12 290

0.19

5.45

190

616

191

3.55

0.31

All 407 450 184 059 223 880 183 610

Se79

Rb87

Sr90

Zr93

Nb95

Tc99

Pd107

Sn126

I129

Cs135

Cs137

Sm147

Sm151

Eu154

0

0

0

0

0

0

0

0

0

0

0

0

0

0

14.2

831

1 882

3 542

2 230

4 278

2 473

231

1 654

3 614

8 033

633

55

1 758

-14.2

-831

-1 882

-3 542

-2 230

-4 278

-2 473

-231

-1 654

-3 614

-8 033

-633

-55

-1 758

14.19

831

174

3 544

0

4 297

2 473

231

1 666

3 619

797

2 124

25.8

0.67

Selected FP 0 31 228 31 228 19 796

Eu151 (BP) 5 228 267 4 960 267

41

5.5.3. Attained discharge burn-up of the fuel (units: MWd/kg)

Case G1:

Minimum value 425.0

Average value 506.3

Maximum value 575.6

Average FIMA: 55%

Case E12:

Minimum value 576.0

Average value 642.7

Maximum value 694.0

Average FIMA 65%

The quoted numbers concern burnup on zone level (1/6 of one block row

and layer). The differences on smaller scale are estimated below 2%.

See Chapter 4.2.3.

5.6. Temperature at nominal conditions

5.6.1. Coated particle temperature (units: K):

Maximum value occurring anywhere in the core at BOL, MOL,

EOL (different values if applicable)

Maximum value occurring anywhere in the core at BOL, MOL,

EOL (different values if applicable)

Maximum value occurring anywhere in the core at any time

during the operating cycle

5.6.2. Block surface temperature (units: K):

Results for case G1:

Table 16. Maximum temperature [K] in 4-batch 350-day cycle with 2nd

ref. fuel

Element BOL

0 days Max.

150 days MOL

175 days EOL

350 days

Coated particle 1296 1461 1335 1349

Block surface 1128 1274 1237 1273

42

5.7. Temperature reactivity coefficients

The temperature reactivity Doppler constant coefficient αT is

subsequently calculated as shown in equations 19, 20 and 21 below. In

case of LWR reactors with uranium or mixed uranium plutonium oxide

fuel, the Doppler constant D (for the fuel)

dT

dT

(19)

)ln(

11

)ln(

REF

DELTA

DELTAREF

REF

DELTA

REFDELTA

T

T

kk

T

TdT

dTD

(20)

T

DT (21)

is independent of temperature. However, that is not granted in HTR

cores. In Table 17 shown below presented are results of reactivity

coefficient assessment obtained with JEFF3.1 library in BOC with all

control rods out. In Cold Zero Power (CZP), zero xenon conditions the

reactivity change is calculated for 300K and 400 K, whereas in Hot Zero

Power (HZP) and Hot Full Power (HFP) – for 1000K and 1200K.

Uncertainties of the summary results are about 5% for CZP and 3% for

HZP and HFP.

Table 17. Reactivity coeff. at BOC in 4-batch 350-day cycle; 2nd ref. fuel

Varied core element/state D [pcm]

[pcm]

αT [pcm/K]

[pcm/K] Fuel /CZP -1010 -2.905

Moderator /CZP 200 0.574

Reflector /CZP 720 2.073

Sum /CZP -90 -0.258

Fuel /HZP -2250 -2.050

Moderator /HZP -7630 -6.952

Reflector /HZP 180 0.163

Sum /HZP -9700 -8.839

Fuel /HFP -2515 -2.294

Moderator / HFP -6820 -6.215

Reflector / HFP 55 0.048

Sum /HFP -9280 -8.461

43

5.7.1. Calculated at BOC with the start-up CR being withdrawn while the operational CR being inserted, the differences in reactivity between:

CZP (zero xenon) state and HZP (zero xenon) state: -2020

[pcm]

HZP (zero xenon) state and HFP (equilibrium xenon) state: -2430

[pcm]

CZP (zero xenon) state and HFP (equilibrium xenon) state: -4450

[pcm]

The uncertainties are about 3%.

5.8. Control rod worth

The perturbed states have “frozen” thermal hydraulics and the same

nuclide concentrations as the reference state anywhere in the system.

The following items have been calculated at BOL:

5.8.1. Control rod worth at CZP:

All Start-up CR worth: 8 200 [pcm]

All Operational CR worth: 6 300 [pcm]

All CR worth: 14 500 [pcm]

5.8.2. Control rod worth at HZP:

All Start-up CR worth: 8 410 [pcm]

All Operational CR worth: 6 570 [pcm]

All CR worth: 14 980 [pcm]

5.8.3. Control rod worth at HFP:

All Start-up CR worth: 8 390 [pcm]

All Operational CR worth: 6 480 [pcm]

All CR worth: 14 870 [pcm]

44

6. Conclusions

In the course of presented study, we have been investigating the

physics of the PUMA core in the deep burn conditions using Monte Carlo

methodology. Few novel features of Monte Carlo burnup modelling were

applied in order to analyse the core features deeply. The most important

findings are summarised below.

Power profile peaking in the reflector vicinities need to be assessed in

a finer radial mesh than the thickness of one block, in order to avoid

power peaking underestimation.

Power peaking can be controlled effectively with axial-only shuffling

scheme, with additional power suppression in fresh fuel block by

burnable poison.

Operation of CR significantly influences axial distribution of power

and burnup and reverses the effect of the temperature impact on the

power profile.

The modelling of CR operation is necessary for a proper evaluation of

axial power profile and power peaks.

Power peaks during fuel cycle occur when operational CR insertion

level is raised above the block layer with fresh fuel.

Statistical oscillations in Monte Carlo solution of transport equations

in PUMA fuel cycle have been reduced by “bridge scheme” of burnup

step.

Temperature reactivity coefficients are negative in all conditions, but

in CZP the graphite coefficient is positive, with no safety threat

however.

Achievable burnup of 65% FIMA for 1st reference fuel and 55% for 2nd

reference fuel was found in our Monte Carlo model.

45

References

[1] X-5 Monte Carlo Team, “MCNP — A General Monte Carlo N-Particle

Transport Code, Version 5”, LA-UR-03-1987, Los Alamos National

Laboratory, 2003

[2] J. Cetnar “General solution of Bateman equations for nuclear

transmutations” Annals of Nuclear Energy Volume: 33, Issue 7, May

2006, pp. 640-645

[3] J. Cetnar, W. Gudowski and J. Wallenius "MCB: A continuous

energy Monte Carlo Burnup simulation code", In "Actinide and

Fission Product Partitioning and Transmutation", EUR 18898 EN,

OECD/NEA (1999) 523.

[4] J. Cetnar, et al. ”Reference Core Design for a European Gas Cooled

Experimental ADS AccApp’03 Conference, San Diego June 2003, p.

772

[5] Firestone, R., B., et al.: ”Table of Isotopes, 8E” John Wiley & Sons,

Inc.(1996)

[6] W. Pfeiffer et al. “POKE A Gas-Cooled Reactor Flow and Thermal

Analysis Code” GA-10226 Gulf General Atomic Incorporated, 1970

[7] A. G. Croff: “A User’s Manual for the ORIGEN2 Computer Code”,

ORNL /TM-7157 (Oct. 1980)

[8] J. Zakowa “MCNP/MCB analysis of GT-MHR” Deliverable D124, EU

FP6 project PUMA

[9] J. Kuijper et al. ”Selected Reference HTGR Designs and Fuel Cycle

Data” Deliverable D121 EU FP6 project PUMA

46

ANNEX: Auxiliary tables and figures

Table 18. Fuel kernel power density [kW/cm3] after 5 full power days

in 350-day equilibrium cycle with 2nd reference fuel.

Row #4 Row #5 Row #6 Row #7 Row #8

Layer #1

0.80 0.92 0.98 1.09 0.77 0.58 0.47 0.49 0.29 0.17

1.19 0.90 1.06 1.00 1.06 0.76 0.75 0.65 0.53 0.29

1.38 1.48 1.39 1.36 1.34 1.16 1.14 1.17 0.75 0.60

Layer #2

3.43 2.31 3.47 3.86 3.79 3.26 2.89 2.67 2.08 2.07

3.41 3.25 4.30 4.80 4.57 4.11 3.23 2.89 2.55 3.20

4.41 4.21 4.68 4.55 5.05 4.74 4.22 3.70 3.37 3.52

Layer #3

3.00 3.29 3.29 4.30 4.33 3.73 3.31 2.96 2.88 2.61

2.91 2.95 3.59 3.98 3.69 4.77 3.07 3.32 3.02 2.64

3.60 3.80 3.84 3.67 4.51 4.41 3.26 3.04 3.03 2.87

Layer #4

4.72 4.35 4.34 5.14 5.87 4.79 3.96 3.59 3.24 2.90

4.51 4.16 5.05 4.97 5.79 4.91 3.91 3.87 3.59 3.34

4.84 4.09 5.07 5.56 5.54 5.07 4.77 4.43 3.80 3.59

Layer #5

6.08 5.89 4.94 6.11 6.68 6.49 4.60 4.98 4.45 4.28

5.09 4.67 5.27 6.24 5.50 5.52 4.59 3.40 3.66 3.97

6.50 5.28 5.48 6.29 6.86 6.86 5.26 4.12 3.13 3.50

Layer #6

3.90 4.49 4.63 5.01 5.30 3.93 3.68 2.92 2.48 1.99

3.57 3.33 4.79 5.19 5.15 5.08 3.74 3.54 2.86 2.06

3.73 4.21 4.96 5.02 4.63 3.96 3.32 3.51 2.87 2.27

Layer #7

5.24 6.51 6.68 6.34 7.33 6.06 4.92 4.93 4.31 4.45

5.13 4.86 6.08 5.15 5.33 5.52 4.25 3.85 3.31 3.58

4.81 4.97 4.82 5.97 6.20 5.97 4.77 4.19 3.69 3.46

Layer #8

2.92 3.30 4.19 3.63 3.18 3.65 3.46 2.91 2.47 2.35

2.42 2.89 2.97 2.78 3.16 2.73 2.70 2.19 1.58 1.40

1.76 2.27 2.72 3.02 2.60 2.44 2.20 1.85 1.57 1.20

47

Table 19. Fuel kernel power density [kW/cm3] after 150 full power days

in 350-day equilibrium cycle with 2nd reference fuel.

Row #4 Row #5 Row #6 Row #7 Row #8

Layer #1

0.09 0.16 0.13 0.10 0.10 0.08 0.11 0.13 0.09 0.09

0.22 0.20 0.32 0.22 0.19 0.18 0.16 0.14 0.16 0.12

0.39 0.34 0.46 0.47 0.38 0.37 0.28 0.16 0.21 0.23

Layer #2

0.87 0.82 0.82 1.46 0.91 1.53 0.78 0.75 0.89 1.10

1.87 1.37 1.40 1.42 1.50 1.07 0.95 0.85 0.91 0.84

2.01 2.09 2.18 2.87 1.97 1.83 1.36 1.06 1.11 1.03

Layer #3

1.49 1.82 1.70 2.16 1.99 1.60 1.50 1.46 1.01 0.90

1.47 1.79 1.82 2.20 2.10 1.93 1.44 1.42 1.46 0.99

1.95 1.69 2.11 2.00 2.03 1.92 1.59 1.75 1.27 1.28

Layer #4

2.66 2.50 2.93 3.48 2.92 2.30 1.99 1.38 1.64 1.13

2.56 2.53 2.81 2.44 2.12 2.35 1.96 1.52 1.50 1.16

2.31 3.15 3.18 2.64 2.51 2.52 2.45 2.06 1.79 1.64

Layer #5

3.52 2.84 2.68 3.89 3.76 3.59 2.66 2.51 2.33 2.83

2.74 3.02 3.28 3.99 3.88 3.47 3.35 3.17 2.36 2.97

3.41 3.90 4.61 4.50 4.77 4.99 4.07 4.39 3.47 4.78

Layer #6

2.19 3.75 3.96 4.18 4.69 4.67 4.69 4.27 4.01 4.10

3.16 3.45 4.31 4.81 5.15 5.59 6.31 5.58 5.57 5.18

3.52 4.37 5.06 4.73 5.45 5.48 6.37 6.34 6.64 6.95

Layer #7

7.32 7.34 7.82 8.29 10.00 10.07 9.47 11.39 10.93 16.87

7.47 6.92 7.70 8.84 8.62 9.02 9.61 10.85 10.63 14.84

6.47 6.92 7.83 8.18 9.91 9.95 10.19 10.57 10.69 15.15

Layer #8

3.62 4.56 4.78 5.07 4.79 5.58 6.25 6.85 6.80 6.70

2.24 3.19 2.93 3.57 4.30 4.65 4.64 4.75 4.83 5.15

1.87 2.48 3.31 2.99 3.20 4.13 3.86 3.40 4.09 3.82

48

Table 20. Fuel kernel power density [kW/cm3] after 350 full power days

in 350-day equilibrium cycle with 2nd reference fuel.

Row #4 Row #5 Row #6 Row #7 Row #8

Layer #1

0.45 0.60 0.47 0.35 0.41 0.38 0.30 0.33 0.30 0.13

0.30 0.49 0.48 0.53 0.50 0.40 0.47 0.36 0.33 0.20

0.71 0.85 0.81 0.61 0.54 0.48 0.54 0.56 0.55 0.32

Layer #2

1.98 1.49 1.78 1.67 1.99 1.55 1.55 1.25 1.18 1.48

2.34 2.64 2.05 2.14 2.27 2.05 2.07 1.67 1.53 1.58

3.21 2.58 2.70 2.75 2.95 2.87 2.52 1.87 2.02 1.61

Layer #3

2.21 2.47 2.48 2.52 2.28 2.51 2.27 2.20 1.85 1.54

2.54 2.93 2.98 3.41 2.76 2.38 2.43 2.38 2.10 2.09

3.48 3.14 3.42 3.58 3.84 3.51 3.40 3.72 2.75 2.65

Layer #4

3.88 4.00 4.69 4.49 4.84 4.76 5.57 5.55 4.78 5.33

4.79 4.97 5.32 5.13 5.99 6.36 6.14 6.15 6.23 7.07

3.95 4.65 5.30 5.60 6.32 7.05 7.80 8.29 8.07 9.84

Layer #5

4.45 6.14 6.18 7.63 8.10 8.94 9.50 9.19 9.38 12.88

5.83 5.14 5.56 7.03 8.20 8.31 7.81 8.38 7.63 11.01

5.86 4.43 6.02 6.63 8.11 7.46 7.44 7.40 7.05 9.29

Layer #6

3.15 3.78 4.21 4.31 4.62 4.43 4.95 4.99 5.12 4.82

2.98 3.21 3.30 3.72 3.88 4.16 4.41 4.84 4.38 4.35

2.50 2.97 2.71 2.73 3.02 3.35 3.42 3.73 3.61 3.22

Layer #7

3.98 3.30 3.33 4.02 3.99 5.29 4.68 4.57 4.59 5.79

3.38 3.03 2.73 3.97 3.52 3.64 3.89 3.83 3.61 5.15

2.87 2.25 3.51 3.24 3.66 3.47 3.66 3.93 3.72 4.80

Layer #8

1.17 1.48 1.70 1.33 1.79 1.77 2.07 2.20 2.17 1.99

1.12 0.90 0.96 1.16 1.11 1.37 1.98 1.44 1.47 1.24

0.91 1.08 1.18 0.87 0.87 1.13 1.26 1.18 1.01 0.89

49

Table 21. Zone average fuel temperature [ºC] after 5 full power days

in 350-day equilibrium cycle with 2nd reference fuel.

Row #4 Row #5 Row #6 Row #7 Row #8

Layer #1

526.4 523.9 527.7 527.8 520.8 512.7 512.1 511.8 507.2 499.4

539.5 535.6 537.2 535.2 532.0 523.5 525.0 525.2 517.4 508.2

571.9 559.1 567.1 566.7 564.7 554.9 556.7 557.6 543.3 536.2

Layer #2

620.5 596.4 621.9 628.3 622.2 609.5 605.4 604.0 586.8 592.2

661.8 641.1 670.9 676.7 672.1 659.8 650.6 644.6 632.1 650.9

683.8 673.5 689.5 695.2 697.1 685.7 680.3 672.2 666.3 680.1

Layer #3

683.7 679.5 688.7 703.3 701.2 700.2 688.5 687.1 685.8 684.8

690.9 688.7 699.6 709.9 707.3 723.2 694.2 701.5 703.0 696.5

726.7 720.8 725.5 729.4 741.4 746.6 717.4 722.3 725.6 719.7

Layer #4

767.4 753.3 758.0 764.8 786.4 769.0 748.4 750.7 753.2 746.3

796.4 773.2 792.0 796.5 813.9 794.3 780.5 785.7 785.3 779.1

832.3 804.9 816.5 828.5 839.1 829.0 814.2 825.4 822.0 818.2

Layer #5

871.0 845.4 837.6 863.8 867.3 867.0 840.7 850.1 854.2 856.1

901.9 868.3 864.5 893.2 890.7 897.0 867.8 856.7 865.4 878.1

921.1 884.9 885.4 908.7 913.3 911.3 888.9 866.3 863.5 875.4

Layer #6

911.0 889.1 895.8 913.5 921.4 907.5 890.2 876.3 868.4 861.4

905.5 890.1 912.7 925.8 924.1 913.4 893.7 894.5 886.6 865.5

935.6 932.4 950.0 954.2 954.5 939.8 918.8 931.3 922.6 907.4

Layer #7

980.2 985.6 995.6 984.7 996.6 979.3 956.1 968.7 962.3 963.8

1010.6 1003.1 1014.6 1004.7 1016.0 1012.6 984.4 988.7 984.0 991.3

1012.0 1001.6 1009.4 1011.8 1013.9 1020.2 998.8 996.5 992.4 993.8

Layer #8

994.2 992.4 1000.5 995.9 994.6 1001.5 995.5 990.5 983.9 981.7

979.6 983.3 991.0 982.5 982.3 982.8 984.7 979.3 970.4 964.9

975.9 983.6 987.0 987.5 987.4 980.3 982.3 977.2 968.6 958.0

50

Table 22. Zone average fuel temperature [ºC] after 150 full power days

in 350-day equilibrium cycle with 2nd reference fuel.

Row #4 Row #5 Row #6 Row #7 Row #8

Layer #1

496.8 498.0 499.2 495.8 495.3 494.6 495.1 496.5 496.2 494.4

502.6 502.0 505.4 501.9 500.1 499.2 498.3 497.7 498.5 496.2

515.2 512.1 515.8 519.5 511.5 516.3 507.3 504.8 507.5 506.6

Layer #2

543.0 532.8 533.7 545.1 532.1 539.4 522.3 518.9 523.5 522.7

578.9 563.2 562.2 575.0 557.6 554.5 538.0 531.7 536.3 530.9

597.6 590.6 587.4 605.5 579.6 568.8 553.8 544.9 543.9 534.3

Layer #3

599.2 603.3 597.3 618.0 594.7 582.5 566.0 559.4 553.1 537.9

608.8 609.7 607.8 621.6 606.1 594.8 574.7 572.0 565.0 544.7

637.5 626.4 633.0 643.0 624.1 610.2 588.4 581.5 575.8 553.3

Layer #4

670.2 654.4 663.4 672.0 643.8 627.4 605.3 586.6 586.5 558.1

688.7 684.3 687.6 682.6 652.8 643.9 622.2 598.2 597.3 566.0

711.3 710.7 704.5 701.8 675.7 668.6 643.3 621.3 614.3 589.6

Layer #5

743.3 730.1 720.2 742.5 716.6 701.5 669.8 650.1 636.5 622.2

766.0 757.3 756.2 778.5 754.9 737.7 704.2 689.5 663.1 659.2

778.7 794.5 800.3 806.1 790.5 778.9 745.2 731.9 701.8 696.8

Layer #6

788.9 818.9 825.9 831.9 822.7 815.9 796.5 771.2 752.2 724.7

817.9 842.8 855.9 861.9 855.6 851.3 854.3 821.2 814.5 767.5

893.7 909.6 922.6 921.0 928.1 921.3 924.0 913.6 909.7 899.1

Layer #7

1003.2 1000.8 1008.8 1015.4 1026.9 1019.4 1011.7 1033.9 1024.6 1078.1

1074.3 1059.5 1070.5 1087.0 1092.3 1086.9 1085.4 1109.4 1101.6 1172.2

1073.1 1075.0 1085.6 1095.6 1103.0 1100.9 1108.5 1118.7 1117.2 1154.9

Layer #8

1031.3 1054.7 1052.8 1060.7 1063.3 1068.7 1076.6 1081.6 1081.7 1068.1

997.0 1028.2 1022.7 1030.1 1031.2 1042.8 1042.0 1038.3 1044.5 1003.3

986.4 1018.9 1022.0 1022.3 1030.9 1047.0 1034.6 1018.5 1034.9 990.2

51

Table 23. Zone average fuel temperature [ºC] after 350 full power days in 350-day equilibrium cycle with 2nd reference fuel.

Row #4 Row #5 Row #6 Row #7 Row #8

Layer #1

496.9 591.4 580.3 609.6 592.8 609.0 603.4 609.8 624.3 607.0

502.8 576.0 570.5 586.5 574.8 586.6 586.4 600.2 604.3 590.1

515.8 563.4 560.3 565.8 558.5 563.1 569.7 588.0 581.8 569.3

Layer #2

544.3 561.9 557.5 560.5 551.8 553.0 559.9 572.6 568.2 553.1

581.1 557.2 551.9 552.7 544.5 545.4 547.6 553.6 553.6 537.8

600.5 559.3 553.3 551.9 545.1 544.0 546.1 550.1 550.6 533.8

Layer #3

602.4 576.9 574.5 568.5 563.8 557.7 560.9 563.0 563.6 548.0

612.4 612.9 607.4 599.5 600.2 587.5 589.4 585.3 584.6 573.4

641.9 653.5 639.8 632.9 634.9 621.7 619.9 607.1 607.7 590.8

Layer #4

652.3 677.3 666.7 658.2 655.9 648.0 640.7 625.3 626.6 597.4

621.8 694.7 688.7 681.4 667.1 659.7 652.6 644.0 639.4 607.6

604.3 721.4 716.7 712.2 692.9 676.5 673.1 673.1 658.0 628.4

Layer #5

629.4 756.9 760.7 748.7 741.2 719.8 724.1 728.0 701.8 674.0

673.1 806.7 818.1 791.8 798.4 783.3 793.4 795.2 773.0 751.1

716.4 856.6 869.2 838.2 854.7 850.8 860.3 863.7 855.7 844.1

Layer #6

744.6 902.7 913.2 896.0 914.8 920.3 936.8 942.1 941.6 953.7

754.1 949.6 955.7 960.7 981.8 985.9 1000.0 1004.0 1001.6 1045.1

777.5 970.9 989.8 999.0 1034.6 1021.5 1021.3 1028.9 1017.9 1070.4

Layer #7

823.7 972.0 1008.9 1001.6 1042.9 1014.2 1016.8 1022.9 1014.1 1037.8

874.2 973.5 1001.8 982.7 1010.6 985.4 998.9 1004.8 1001.8 985.2

915.4 976.8 987.5 967.0 985.8 972.1 985.6 998.2 991.7 956.7

Layer #8

941.3 989.9 993.5 974.4 991.8 991.5 994.9 1006.5 1001.4 972.0

985.5 1010.8 1012.0 1004.8 1014.3 1022.4 1019.7 1024.2 1022.9 1015.2

1045.4 1031.3 1030.5 1039.6 1038.9 1046.6 1044.9 1044.3 1042.7 1057.8

52

BOC 100 days

200 days 350 days (EOC)

Figure 13. Temperature distribution with CR operation simulated stepwise; 350-day equilibrium cycle; 2nd reference fuel; CR-s shifted

100 cm every 50 days.

Assessment of Th/Pu Fuel Cycle in Prismatic HTR by Monte Carlo Method - MCB

Appendix B

Deliverable 125

Work Package 1

Project PUMA

Jerzy Cetnar

Mariusz Kopeć

AGH-University of Science and Technology, Krakow, Poland

54

Contents

Contents ......................................................................................................... 4

List of figures .................................................................................................. 5

List of tables ................................................................................................... 7

Scope .............................................................................................................. 8

1. Introduction .......................................................................................... 8

2. Simulations ........................................................................................... 9

3. Uniform thorium distribution ............................................................... 11

3.1. Pu/Th fuel ............................................................................................ 11

3.2. Results for the Pu/Th fuel ..................................................................... 12

3.3. U/Th fuel ............................................................................................. 24

3.4. Results for U/Th fuel ............................................................................ 24

3.5. U+Pu/Th fuel ....................................................................................... 29

3.6. Results for U+Pu/Th fuel ...................................................................... 29

3.7. Power profiles ...................................................................................... 38

4. Non-uniform thorium distribution ........................................................ 41

4.1. Axial Th distribution ............................................................................. 41

4.2. Radial Th distribution ........................................................................... 43

4.3. Selected results .................................................................................... 44

5. Conclusions ......................................................................................... 47

References .................................................................................................... 48

55

List of figures

Fig. 1 Radial Th distribution ...................................................................... 59

Fig. 2 Axial Th distribution ......................................................................... 59

Fig. 3 4-batch axial fuel shuffling scheme (reference) .................................. 60

Fig. 4 3-batch axial fuel shuffling scheme for axial Th distribution ............. 61

Fig. 5 Keff in a 5 years once-through cycle for 3.0%Pu fuel ......................... 66

Fig. 6 Production of U233 in 3.0%Pu fuel ................................................... 67

Fig. 7 Evolution of U and Pu masses in 3.0%Pu fuel ................................... 67

Fig. 8 Keff in a 5 years once-through cycle for 5.0%Pu fuel ......................... 68

Fig. 9 Production of U233 in 5.0%Pu fuel ................................................... 68

Fig. 10 Evolution of U and Pu masses in 5.0%Pu fuel ................................... 69

Fig. 11 Keff in a 5 years once-through cycle for 10%Pu fuel .......................... 69

Fig. 12 Production of U233 in 10%Pu fuel .................................................... 70

Fig. 13 Evolution of U and Pu masses in 10%Pu fuel .................................... 70

Fig. 14 Keff in a 5 years once-through cycle for 25%Pu fuel .......................... 71

Fig. 15 Production of U233 in 25%Pu fuel .................................................... 71

Fig. 16 Evolution of U and Pu masses in 25%Pu fuel .................................... 72

Fig. 17 Keff in a 5 years once-through cycle for 50%Pu fuel .......................... 72

Fig. 18 Production of U233 in 50%Pu fuel .................................................... 73

Fig. 19 Evolution of U and Pu masses in 50%Pu fuel .................................... 73

Fig. 20 Keff in a 5 years once-through cycle for 2.5%U fuel .......................... 76

Fig. 21 Production of U233 in 2.5%U fuel ..................................................... 77

Fig. 22 Evolution of U and Pu masses in 2.5%U fuel .................................... 77

Fig. 23 Keff in a 5 years once-through cycle for 3.0%U fuel .......................... 78

Fig. 24 Production of U233 in 3.0%U fuel ..................................................... 78

Fig. 25 Evolution of U and Pu masses in 3.0%U fuel .................................... 79

Fig. 26 Keff in a 5 years once-through cycle for 4.0%U+1.0%Pu fuel ............. 82

Fig. 27 Production of U233 in 4.0% U+1.0%Pu fuel ...................................... 83

Fig. 28 Evolution of U and Pu masses in 4.0%U+1.0%Pu fuel ....................... 83

Fig. 29 Keff in a 5 years once-through cycle for 2.8%U+0.7%Pu fuel ............. 84

Fig. 30 Production of U233 in 2.8%U+0.7%Pu fuel ....................................... 84

Fig. 31 Evolution of U and Pu masses in 2.8%U+0.7%Pu fuel ....................... 85

Fig. 32 Keff in a 5 years once-through cycle for 2.4%U+0.6%Pu fuel ............. 85

56

Fig. 33 Production of U233 in 2.4%U+0.6%Pu fuel ....................................... 86

Fig. 34 Evolution of U and Pu masses in 2.4%U+0.6%Pu fuel ...................... 86

Fig. 35 Keff in a 5 years once-through cycle for 2.0%U+0.5%Pu fuel ............ 87

Fig. 36 Production of U233 in 2.0%U+0.5%Pu fuel ....................................... 87

Fig. 37 Evolution of U and Pu masses in 2.0%U+0.5%Pu fuel ...................... 88

Fig. 38 Power profile – control rods fully inserted ......................................... 89

Fig. 39 Power profile – control rods withdrawn by 25% ................................. 89

Fig. 40 Power profile – control rods withdrawn by 50% ................................. 90

Fig. 41 Power profile – control rods withdrawn by 75% ................................. 90

Fig. 42 Power profile – control rods fully withdrawn ..................................... 91

Fig. 43 Keff in core with ThO2 in bottom and top blocks (axial) ..................... 92

Fig. 44 Production of U233 (axial Th distribution) ........................................ 93

Fig. 45 Keff in core with ThO2 in inner two rings (radial) .............................. 94

Fig. 46 Production of U233 (radial Th distribution) ...................................... 94

57

List of tables

Tab. 1 Masses at BOC and EOC for 3% Pu fuel................................. 63

Tab. 2 Masses at BOC and EOC for 5% Pu fuel................................. 63

Tab. 3 Masses at BOC and EOC for 10% Pu fuel ............................... 64

Tab. 4 Masses at BOC and EOC for 25% Pu fuel ............................... 64

Tab. 5 Masses at BOC and EOC for 50% Pu fuel ............................... 65

Tab. 6 Masses at BOC and EOC for 5% Pu fuel (small kernels) ......... 65

Tab. 7 Breeding rates for Pu/Th fuels (uniform Th distr.) .................. 66

Tab. 8 Masses at BOC and EOC for 2.5% U fuel ............................... 75

Tab. 9 Masses at BOC and EOC for 3.0% U fuel ............................... 75

Tab. 10 Breeding rates for U/Th fuels (uniform Th distr.) ................... 76

Tab. 11 Masses at BOC and EOC for 4.0%U+1.0%Pu fuel ................... 80

Tab. 12 Masses at BOC and EOC for 2.8%U+0.7%Pu fuel ................... 80

Tab. 13 Masses at BOC and EOC for 2.6%U+0.4%Pu fuel ................... 81

Tab. 14 Masses at BOC and EOC for 2.0%U+0.5%Pu ......................... 81

Tab. 15 Breeding rates for U+Pu/Th fuels (uniform Th distr.) ............. 82

Tab. 16 Breeding rates in subsequent periods (axial Th distr.) ............ 92

Tab. 17 Breeding rates in subsequent periods (radial Th distr.) .......... 93

Tab. 18 Temperature reactivity coefficients at CZP (300K) ................... 95

Tab. 19 Temperature reactivity coefficients at HZP (800K) .................. 95

Tab. 20 Control rod worth values ....................................................... 95

Tab. 21 Masses of selected actinides at BOC and EOC ....................... 96

Tab. 22 Masses of selected fission products at BOC and EOC ............. 97

58

Scope

This report describes the work done in AGH as a contribution to the

deliverable 125 of PuMA project, which is part of the European

Commission’s 6th framework program.

1. Introduction

The objective of this task was to investigate the feasibility of the Th/Pu

cycle in a prismatic HTR reactor. The primary goal is to find design

configuration with high conversion ratio, which would allow to burn Pu

efficiently in conjunction with high Th-conversion and U233-burning

rate. It should be noted that Th and Pu belong to different fuel cycles

and the combination of them creates many physical and technical

problems, burden of which need to be paid off by gained profits. First of

all, plutonium is generated in existing LWRs but cannot be completely

burnt in these due to reactor physics limitations. In order to utilise

plutonium as a fuel one can apply a fast reactor or HTR in an burner or

breeder option. As for breeder options there are advantages and

disadvantages of both Th-U and U-Pu cycles we should focus on. The

biggest disadvantages of Th-U cycle is the lack of the driver fuel - fissile

U233 in nature, and high radioactivity due to U232 that complicates

reprocessing which obviously works against this cycle. As advantages

there is about three orders lower final waste repository radiotoxicity as

compared to U-Pu cycle and potential feasibility to design a breeder in

thermal neutron spectrum which is physically impossible in U-Pu cycle.

Possible realization of mixed or cross progeny cycle – Pu-Th-U depends

on the U233 load availability. In case of existence of an external supply

of U233 one can consider core design with overwhelming fuel load of

Th232 and U233, where Pu plays a supplementary role to compensate for

fuel breeding below one. In other case, which is an actual one, without

initial U233 load the core design should aim in net generation of U233 to

be used inside or outside the current system. Outside usage would be

justifiable in other breeder reactors of Th-U cycle. As the first case is

more futuristic and depends upon development of U233 production

technology, in the current study we focus on the second case that is

design of U233 net production system.

It should be noted that, there is no strong incentive to replace U238

with Th232 just for reduction of consumed plutonium, since its breeding

from U238 can be efficient and fully feasible in fast reactors. Being

aware of existing problems and challenges there are still existing

incentives to combine Th with Pu in HTR which are possibilities of net

59

breeding U233 with limited fraction of U232 due to thermalized neutron

spectra.

In the current report we present the results of feasibility study of few

design strategies concerning core composition and fuel reloading and

shuffling. Several design parameters (fuel kernel diameter, fuel

composition, Th fraction in fuel, Th distribution in core) and fuel cycles

strategies (once-through cycle, 3 and 4-batch cycle with axial shuffling),

have been assessed.

2. Simulations

Two general solutions have been investigated. In the first one, referred

to later as “Uniform thorium distribution” Th was located in fuel kernels

uniformly in the whole core. For this case once-through cycle was

applied. In the second one, referred to later as “Non-uniform thorium

distribution” Th was either in two inner rings (radial Th distribution –

Figure 1) or in bottom and top core blocks (axial Th distribution –

Figure 2). In simulations with radial Th distribution the 4-batch axial

fuel shuffling scheme (reference) was used (Figure 3). In the case of axial

Th distribution the 3-batch axial fuel shuffling scheme was used

(Figure 4).

Figure 1 Radial Th distribution Figure 2 Axial Th distribution

Th

Fuel

Th

60

The results of simulations have been analysed from the point of view of

effective multiplication factor and its evolution, U233 production,

breeding rates and power profiles. The breeding rate BR was calculated

as follows:

tmaf

fissBR

1 (1)

where:

Δfiss – change of mass of fissionable materials (over some period of

time)

tmaf – fission product total mass (i.e. mass of burned fuel)

It may be observed that results given by this formula are

underestimated especially when destruction of fissionable nuclides

caused by non-fission processes becomes important (eg. for Pu). In a

such case it would be better to use more precise definition:

ndestructio

fissBR

1 (2)

where:

destruction is a total destruction of fissionable materials (over

some period of time).

Figure 3 4-batch axial fuel shuffling scheme (reference) used for radial

Th distribution

8

1

2

3

4

6

5

7

8

1

2

3

4

6

5

7

8

1

2

3

4

6

5

7

8

1

2

3

4

6

5

7

61

Figure 4 3-batch axial fuel shuffling scheme used for axial Th distribution

Within this work the thermal hydraulics calculations were done by

means of code POKE written in GA which determines the steady-state

coolant mass flow, coolant and fuel temperature distributions in a gas-

cooled reactor. The modified version of POKE has been incorporated into

MCB code. The initial power profile was determined for arbitrary

assumed core region temperatures. Then, POKE calculated the required

thermal hydraulic parameters as well as the new temperature profiles.

On this base the new MCB input was generated, where the new

temperatures of all regions together with better temperature fitted cross

sections were used, and the subsequent burnup calculations provided

more realistic isotope production results.

3. Uniform thorium distribution

3.1. Pu/Th fuel

The basic problem investigated in this point was whether it is possible

to design the core filled initially with the same type of fuel (with Th),

which could operate without reload for a reasonable time, providing

appropriate keff evolution, U233 production rate and smoothed power

profiles. In this case the fuel was a mixture of ThO2 and PuO2 (in various

proportions). Thorium was contained only in fuel kernels and its

distribution in reactor core was almost uniform. Comparing to the

reference PUMA specifications, higher fuel packing fraction (36%) was

8

1

2

3

4

6

5

7

8

1

2

3

4

6

5

7

8

1

2

3

4

6

5

7

62

used, just to provide appropriate amount of Pu in core. Simulations were

done assuming a 5 years once-through cycle, for two fuel kernel

diameters:

0.3 mm

0.6 mm

and for the following fuel compositions:

3% Pu + 97% Th

5% Pu + 95% Th

10% Pu + 90% Th

25% Pu + 75% Th

50% Pu + 50% Th

The calculations were done for 3 different control rod positions: CR

withdrawn, CR inserted to ½ core length and CR fully inserted. The

resulting keff evolutions (limited to ‘withdrawn’ and ‘inserted’ positions)

are presented in figures 5,8,11,14 and 17. The figures 6,9,12,15 and 18

show the total mass of U233 produced in core for appropriate fuel

compositions (only production without destruction). The evolutions of U

and Pu masses in core are shown in figures 7,10,13,16 and 19. As these

data do not depend significantly on CR locations, only the results for

withdrawn CR are shown.

Results of calculations in terms of masses of selected nuclides at BOC

and EOC for all fuel compositions are stored in tables 1-5. Also here only

data obtained for withdrawn CR is presented. The influence of CR

positions on the final fuel composition can be observed in table 6 which

compares the results obtained for all three CR positions. The appropriate

breeding rates BR1 and BR2 calculated according to formulae (1) and (2)

respectively are collected in Table 7.

3.2. Results for Pu/Th fuel

The highest BR values (greater than 1.0) have been obtained for the

large kernels and fuel with 3% Pu. However these results seem to be

interesting, the appropriate keff evolutions (fig. 5) show that such a

system is practically all the time subcritical with keff slightly above 0.8.

With the smaller kernels the system starts operating with keff>1 but gets

subcritical after 1 month and finally stabilizes between 0.6-0.7. The

similar situation can be observed in Figures 8 and 11 for 5% Pu and 10%

Pu fuels respectively. The initial Pu load is too small to allow for the

stabilization of keff on some reasonable level. It can be found in tables 1-

3 that for these fuels Pu at EOC almost completely disappears. It is

interesting that for the smaller kernels the final mass of fissionable

nuclides is almost the same for all these 3 fuels. By the larger kernels

63

the initial Pu mass is greater and due to that the keff changes are slower

– it seems to stabilize between 0.85 and 0.90. These values are however

still too low. Since the CR were already withdrawn, there left no room for

compensation.

Table 1 Masses of nuclides (kg) at BOC and EOC of 5 years once-

through cycle for 3% Pu fuel with CR withdrawn

Mass

(kg)

kernel 0.3 mm kernel 0.6 mm

BOC EOC BOC EOC

HM 5714.00 4579.40 15880.00 14700.00

Th232 5554.80 4383.40 15437.00 14174.00

U232 0.0 0.05 0.0 0.22

Pa233 0.0 23.25 0.0 26.64

U233 0.0 73.86 0.0 300.57

U233prod 0.0 1171.40 0.0 1263.00

U233dest 0.0 1097.55 0.0 962.43

Ufiss 0.0 83.90 0.0 318.17

Pufiss 106.65 0.13 296.39 2.23

Fissionable 106.65 84.43 296.39 322.10

Table 2 Masses of nuclides (kg) at BOC and EOC of 5 years once-

through cycle for 5% Pu fuel with CR withdrawn

Mass

(kg)

kernel 0.3 mm kernel 0.6 mm

BOC EOC BOC EOC

HM 5725.60 4594.70 15912.00 14737.00

Th232 5458.60 4383.60 15170.00 14132.00

U232 0.0 0.05 0.0 0.24

Pa233 0.0 23.30 0.0 25.42

U233 0.0 74.10 0.0 317.12

U233prod 0.0 1075.00 0.0 1038.00

U233dest 0.0 1000.90 0.0 720.88

Ufiss 0.0 83.69 0.0 331.06

Pufiss 178.80 0.16 496.90 9.34

Fissionable 178.80 84.50 496.90 342.84

64

Table 3 Masses of nuclides (kg) at BOC and EOC of 5 years once-

through cycle for 10% Pu fuel with CR withdrawn

Mass

(kg)

kernel 0.3 mm kernel 0.6 mm

BOC EOC BOC EOC

HM 5754.70 4624.80 15993.00 14818.00

Th232 5216.50 4365.10 14497.00 13750.00

U232 0.0 0.05 0.0 0.20

Pa233 0.0 23.02 0.0 17.12

U233 0.0 75.79 0.0 380.33

U233prod 0.0 851.40 0.0 747.00

U233dest 0.0 775.61 0.0 366.67

Ufiss 0.0 84.77 0.0 389.47

Pufiss 360.46 0.27 1001.76 230.81

Fissionable 360.46 86.35 1001.76 625.75

Table 4 Masses of nuclides (kg) at BOC and EOC of 5 years once-through cycle for 25% Pu fuel with CR withdrawn

Mass

(kg)

kernel 0.3 mm kernel 0.6 mm

BOC EOC BOC EOC

HM 5843.90 4684.40 16241.00 15068.00

Th232 4462.80 4130.50 12403.00 11869.00

U232 0.0 0.07 0.0 0.10

Pa233 0.0 10.00 0.0 11.62

U233 0.0 122.31 0.0 376.51

U233prod 0.0 332.30 0.0 534.00

U233dest 0.0 209.99 0.0 157.49

Ufiss 0.0 126.73 0.0 380.91

Pufiss 924.98 55.55 2570.62 1583.96

Fissionable 924.98 185.74 2570.62 1974.82

65

Table 5 Masses of nuclides (kg) at BOC and EOC of 5 years once-

through cycle for 50% Pu fuel with CR withdrawn

Mass

(kg)

kernel 0.3 mm kernel 0.6 mm

BOC EOC BOC EOC

HM 5999.70 4827.40 16674.00 15503.00

Th232 3111.20 2913.80 8646.30 8319.80

U232 0.0 0.03 0.0 0.04

Pa233 0.0 4.50 0.0 7.34

U233 0.0 125.75 0.0 262.10

U233prod 0.0 197.40 0.0 326.50

U233dest 0.0 71.65 0.0 64.40

Ufiss 0.0 128.28 0.0 264.50

Pufiss 1934.52 942.20 5376.10 4071.01

Fissionable 1934.52 1080.42 5376.10 4345.15

Table 6 Masses of nuclides (kg) at EOC of 5 years once-through cycle for 5% Pu fuel (small kernels) for different CR positions

Mass

(kg)

5% Pu fuel, small kernel, EOC

CR out CR half CR in

HM 4594.70 4630.40 4612.50

Th232 4383.60 4418.90 4399.70

U232 0.05 0.05 0.05

Pa233 23.30 22.49 22.71

U233 74.10 76.35 77.68

U233prod 1075.00 1039.70 1058.90

U233dest 1000.90 963.35 981.22

Ufiss 83.69 85.86 87.31

Pufiss 0.16 0.17 0.20

Fissionable 84.50 86.70 88.18

66

Table 7 Breeding rates for Pu/Th fuels in uniform Th distribution case

(CR withdrawn)

Fuel composition

Kernel diameter

0.3 mm 0.6 mm

BR1 BR2 BR1 BR2

3% Pu + 97% Th 0.98 0.98 1.02 1.02

5% Pu + 95% Th 0.92 0.93 0.87 0.90

10% Pu + 90% Th 0.76 0.82 0.68 0.79

25% Pu + 75% Th 0.36 0.59 0.49 0.68

50% Pu + 50% Th 0.27 0.56 0.12 0.48

Figure 5 Keff evolution in a 5 years once-through cycle for fuel with 3% Pu and 97% Th

67

Figure 6 Production of U233 in fuel with 3% Pu and 97% Th

(CR withdrawn)

Figure 7 Evolution of U and Pu masses in fuel with 3% Pu and 97% Th

(CR withdrawn)

68

Figure 8 Keff evolution in a 5 years once-through cycle for fuel

with 5% Pu and 95% Th

Figure 9 Production of U233 in fuel with 5% Pu and 95% Th

(CR withdrawn)

69

Figure 10 Evolution of U and Pu masses in fuel with 5% Pu and 95% Th

(CR withdrawn)

Figure 11 Keff evolution in a 5 years once-through cycle for fuel

with 10% Pu and 90% Th

70

Figure 12 Production of U233 in fuel with 10% Pu and 90% Th

(CR withdrawn)

Figure 13 Evolution of U and Pu masses in fuel with 10% Pu and 90% Th (CR withdrawn)

71

Figure 14 Keff evolution in a 5 years once-through cycle for fuel with 25% Pu and 75% Th

Figure 15 Production of U233 in fuel with 25% Pu and 75% Th

(CR withdrawn)

72

Figure 16 Evolution of U and Pu masses in fuel with 25% Pu and

75% Th (CR withdrawn)

Figure 17 Keff evolution in a 5 years once-through cycle for fuel with 50% Pu and 50% Th

73

Figure 18 Production of U233 in fuel with 50% Pu and 50% Th

(CR withdrawn)

Figure 19 Evolution of U and Pu masses in fuel with 50% Pu and 50% Th (CR withdrawn)

74

The 25% Pu fuel (with small kernels) allows for stabilization of keff

above 1 up to 3 years (Fig. 14), but the BR=0.59 is below assumed target

value (0.80). The higher value BR=0.69 can be obtained with larger

kernels, but the system remains subcritical even by withdrawn CR.

For all fuels with Pu fraction greater than 10% the BR values are lower

than 0.80. It can be observed however that results of formula (2) are

significantly higher than the ones obtained from (1) and this difference

increases with increasing fraction of Pu. The amounts of U233 produced

presented in Fig. 6,9,12,15 and 18 reflect the fact that for the larger

kernels there was more Th in the core. Increasing the Pu fraction in fuel

allows generally for higher keff values (Fig. 5,8,11,14 and 17) but

simultaneously the Th fraction, the U233 production and BR decrease.

Probably the best results could be obtained for kernels even larger than

0.6 mm and fuel with relatively low Pu concentration but external limits

on kernel dimensions will be imposed by technology or heat transport

requirements.

The amount of Ufis in system after 5 years (taken together with Pa233)

reaches the highest value 406 kg for 10%Pu fuel in large kernels.

Simultaneously the U232 fraction (U232/Ufis) is as high as 0.049%.

3.3. U/Th fuel

For comparison purposes, additional simulations were done for U233-

based fuel, assuming once-through cycle, two fuel kernel diameters:

0.3 mm

0.6 mm

and two fuel compositions:

2.5% U + 97.5% Th

3.0% U + 97.0% Th

3.4. Results for U/Th fuel

Results of calculations in terms of masses of nuclides at BOC and EOC

for both fuel compositions are presented in Tables 8 and 9. The

appropriate breeding rates BR1 and BR2 calculated according to formulae

(1) and (2) are collected in Table 10.

The evolutions of effective multiplication factors are shown on figures

20 and 23. The U233 production (without destruction) is shown on

figures 21 and 24. The changes of U and Pu masses in the core are

presented on figures 22 and 25.

75

According to these results, the uranium-based fuel seems to behave

similar to the plutonium-based one: it is impossible to get such a system

working for a time longer than one year (fig. 20 and 23). Comparing the

3%Pu fuel with 3%U fuel one can find almost the same BR values (tabl. 7

and 10) and almost the same final composition (tabl. 1 and 9). In fact,

after some time the Pu/Th fuel with low Pu fraction becomes the U/Th

fuel.

Table 8 Masses of nuclides (kg) at BOC and EOC for 2.5% U fuel

Mass

(kg)

kernel 0.3 mm kernel 0.6 mm

BOC EOC BOC EOC

HM 5709.50 4574.20 15867.00 14686.00

Th232 5578.70 4402.60 15504.00 14230.00

U232 0.0 0.04 0.0 0.18

Pa233 0.0 23.28 0.0 26.31

U233 130.73 73.60 363.30 303.69

U233prod 0.0 1176.10 0.0 1274.00

U233dest 0.0 1233.23 0.0 1333.61

Ufiss 130.73 83.60 363.30 325.92

Pufiss 0.0 0.13 0.0 0.03

Fissionable 130.73 84.43 363.30 325.95

Table 9 Masses of nuclides (kg) at BOC and EOC of 5 years once-

through cycle for 3.0% U fuel

Mass

(kg)

kernel 0.3 mm kernel 0.6 mm

BOC EOC BOC EOC

HM 5712.00 4575.00 15874.00 14693.00

Th232 5554.90 4403.00 15437.00 14234.00

U232 0.0 0.04 0.0 0.18

Pa233 0.0 23.46 0.0 26.18

U233 157.17 73.67 436.78 307.23

U233prod 0.0 1151.90 0.0 1203.00

U233dest 0.0 1235.40 0.0 1332.55

Ufiss 157.17 83.74 436.78 329.46

Pufiss 0.0 0.09 0.0 0.02

Fissionable 157.17 83.82 436.78 329.49

76

Table 10 Breeding rates for U/Th fuels in uniform Th distribution case

Fuel composition

Kernel diameter

0.3 mm 0.6 mm

BR1 BR2 BR1 BR2

2.5% U + 97.5% Th 0.96 0.96 0.97 0.97

3.0% U + 97.0% Th 0.94 0.94 0.91 0.92

Figure 20 Keff evolution in a 5 years once-through cycle for fuel with 2.5% U and 97.5% Th

77

Figure 21 Production of U233 in fuel with 2.5% U and

97.5% Th (CR withdrawn)

Figure 22 Evolution of U and Pu masses in fuel with 2.5% U and 97.5% Th (CR withdrawn)

78

Figure 23 Keff evolution in a 5 years once-through cycle for fuel

with 3.0% U and 97.0% Th

Figure 24 Production of U233 in fuel with 3.0% U and 97.0% Th (CR withdrawn)

79

Figure 25 Evolution of U and Pu masses in fuel with 3.0% U and 97.0% Th (CR withdrawn)

3.5. U+Pu/Th fuel

Another set of simulations was done for a U+Pu+Th fuel in a 5 years

long once-through cycle. Two fuel geometries were considered:

0.4 mm diameter and compact packing fraction 0.3709 – further referred to as core 6

0.5 mm diameter and compact packing fraction 0.4018 – further referred to as core 7,

and 4 fuel compositions:

Fuel 1: 4.0% U + 1.0% Pu + 95.0% Th

Fuel 2: 2.8% U + 0.7% Pu + 96.5% Th

Fuel 3: 2.4% U + 0.6% Pu + 97.0% Th

Fuel 4: 2.0% U + 0.5% Pu + 97.5% Th.

3.6. Results for U+Pu/Th fuel

Results of calculations in terms of masses of nuclides at BOC and EOC

for all fuel compositions are presented in Tables 11-14. The appropriate

breeding rates calculated according to formulae (1) and (2) are collected

in Table 15. The evolutions of effective multiplication factors are shown

80

on Figures 26, 29, 32 and 35, the U233 production on Figures 27, 30, 33

and 36. The changes of U and Pu masses in the core are presented on

Figures 28, 31, 34 and 37.

Table 11 Masses of nuclides (kg) at BOC and EOC in a 5 years once-through cycle for 4.0% U + 1.0% Pu + 95.0% Th fuel

Mass

(kg)

core 6 core 7

BOC EOC BOC EOC

HM 9389.70 8231.70 14017.00 12844.00

Th232 8957.40 7942.90 13372.00 12396.00

U232 0.0 0.09 0.0 0.15

Pa233 0.0 24.68 0.0 24.40

U233 344.99 150.56 515.00 280.12

U233prod 0.0 1014.50 0.0 976.00

U233dest 0.0 1208.93 0.0 1210.88

Ufiss 344.99 166.00 515.00 300.10

Pufiss 58.45 0.12 87.25 0.47

Fissionable 403.44 166.39 602.25 300.99

Table 12 Masses of nuclides (kg) at BOC and EOC in a 5 years once-

through cycle for 2.8% U + 0.7% Pu + 96.5% Th fuel

Mass

(kg)

core 6 core 7

BOC EOC BOC EOC

HM 9376.80 8214.40 13998.00 12825.00

Th232 9074.80 7932.70 13547.00 12404.00

U232 0.0 0.09 0.0 0.16

Pa233 0.0 25.01 0.0 25.77

U233 241.01 148.10 359.78 261.44

U233prod 0.0 1142.10 0.0 1143.00

U233dest 0.0 1235.01 0.0 1241.34

Ufiss 241.01 163.47 359.78 281.33

Pufiss 40.86 0.10 61.00 0.24

Fissionable 281.87 163.77 420.78 281.90

81

Table 13 Masses of nuclides (kg) at BOC and EOC in a 5 years once-

through cycle for 2.6% U + 0.4% Pu + 97.0% Th fuel

Mass

(kg)

core 6 core 7

BOC EOC BOC EOC

HM 9372.50 8211.80 13991.00 12815.00

Th232 9114.20 7931.50 13606.00 12398.00

U232 0.0 0.09 0.0 0.16

Pa233 0.0 25.02 0.0 25.95

U233 206.09 148.38 307.65 258.33

U233prod 0.0 1182.70 0.0 1208.00

U233dest 0.0 1240.41 0.0 1257.32

Ufiss 206.09 163.71 307.65 278.31

Pufiss 35.01 0.10 52.26 0.19

Fissionable 241.10 163.98 359.91 278.79

Table 14 Masses of nuclides (kg) at BOC and EOC in a 5 years once-through cycle for 2.0% U + 0.5% Pu + 97.5% Th fuel

Mass

(kg)

core 6 core 7

BOC EOC BOC EOC

HM 9368.20 8204.50 13985.00 12805.00

Th232 9152.50 7926.70 13663.00 12393.00

U232 0.0 0.09 0.0 0.16

Pa233 0.0 25.10 0.0 26.19

U233 172.14 147.30 256.97 256.71

U233prod 0.0 1225.80 0.0 1270.00

U233dest 0.0 1250.64 0.0 1270.26

Ufiss 172.14 162.56 256.97 276.86

Pufiss 29.16 0.10 43.53 0.15

Fissionable 201.30 162.80 300.50 277.27

82

Table 15 Breeding rates for U+Pu/Th fuels in uniform Th distribution case

Fuel composition

Fuel geometry

core 6 core 7

BR1 BR2 BR1 BR2

4.0% U + 1.0% Pu + 95.0% Th 0.80 0.82 0.74 0.78

2.8% U + 0.7% Pu + 96.5% Th 0.90 0.91 0.88 0.90

2.4% U + 0.6% Pu + 97.0% Th 0.93 0.94 0.93 0.94

2.0% U + 0.5% Pu + 97.5% Th 0.97 0.97 0.98 0.98

Figure 26 Keff evolution in a 5 years once-through cycle for fuel

with 4.0% U, 1.0% Pu and 95.0% Th

83

Figure 27 Production of U233 in fuel with 4.0% U, 1.0% Pu and 95.0% Th (CR withdrawn)

Figure 28 Evolution of U and Pu masses in fuel with 4.0% U, 1.0% Pu

and 95.0% Th (CR withdrawn)

84

Figure 29 Keff evolution in a 5 years once-through cycle for fuel

with 2.8% U, 0.7% Pu and 96.5% Th

Figure 30 Production of U233 in fuel with 2.8% U, 0.7% Pu and

96.5% Th (CR withdrawn)

85

Figure 31 Evolution of U and Pu masses in fuel with 2.8% U, 0.7% Pu and 96.5% Th

Figure 32 Keff evolution in a 5 years once-through cycle for fuel

with 2.4% U, 0.6% Pu and 97.0% Th

86

Figure 33 Production of U233 in fuel with 2.4% U, 0.6% Pu and

97.0% Th (CR withdrawn)

Figure 34 Evolution of U and Pu masses in fuel with 2.4% U, 0.6% Pu and 97.0% Th (CR withdrawn)

87

Figure 35 Keff evolution in a 5 years once-through cycle for fuel with 2.0% U, 0.5% Pu and 97.5% Th

Figure 36 Production of U233 in fuel with 2.0% U, 0.5% Pu and

97.5% Th (CR withdrawn)

88

Figure 37 Evolution of U and Pu masses in fuel with 2.0% U, 0.5% Pu and 97.5% Th (CR withdrawn)

The obtained results are generally similar to the ones from calculations

done for Pu/Th and U/Th fuels. The initial mass of fissionable nuclides

is too low to keep keff>1.0 for a reasonable long time. But assuming that

such a system is working for 5 years, the final fuel composition (table 13)

is almost the same as for Pu/Th or U/Th fuel (Table 1 or 9) taking into

account the correction due to difference in initial HM masses (different

kernel radius and packing factor).

3.7. Power profiles

In the case of uniform Th distribution a few additional simulations

were done to investigate the generated power profiles and their changes

due to movement of control rods. In the optimal situation the power

profiles should be smooth, without any rapid changes between adjacent

blocks or regions. The results of simulations presented on figures 38-42

show that it is not easy to satisfy these expectations. With control rods

fully inserted (fig. 38) the power produced in outer regions (radial

segments) of the core is low. It is obvious, as the CR are located in these

regions and in external reflector. Withdrawal of CR leads to an increase

of power generated in lower blocks (in axial position) of outer regions (fig.

39-41). Finally, the profile gets best equalized when the CR are fully

89

removed (fig. 42). As the power profiles so strongly depend on positions

of control rods, the power profile management in such a system would be

complicated, and requires special attention concerning the control rod

arrangement.

Figure 38 Power profile – control rods fully inserted

Figure 39 Power profile – control rods withdrawn by 25%

90

Figure 40 Power profile – control rods withdrawn by 50%

Figure 41 Power profile – control rods withdrawn by 75%

91

Figure 42 Power profile – control rods fully withdrawn

4. Non-uniform thorium distribution

In this section an alternative to the uniform thorium distribution was

investigated. Instead of mixing ThO2 with fuel, it was separately located

in TRISO-like particles either in two inner rings of core (radial Th

distribution – figure 1) or in bottom and top core blocks (axial Th

distribution – figure 2). The fuel and Th particles had the following

parameters:

PuO2 - driver fuel - 0.2 mm kernel diameter, 18% packing fraction

ThO2 - fertile fuel - 0.6 mm kernel diameter, 36% packing fraction.

For both types of Th distribution the reactor operated for 4 sub-cycles

in the same sequence: 370 full power days (f.p.d.) at 450 MW + 30 days

of cooling. During the simulated period of 4 sub-cycles the blocks with

Th were left in their initial positions and only the plutonium fuel blocks

were shuffled/reloaded axial only reloading scheme in 3 batch scheme for

the axial distribution of Th, and in 4 batch scheme for the radial Th

distribution. As the axial only shuffling was applied, it was necessary to

use non-reference shuffling scheme when Th was in top and bottom

blocks (axial Th distribution). The details of shuffling schemes applied

are shown on Figures 3 and 4.

92

During MCB calculations thermal-hydraulic module was activated

providing appropriate core temperature distributions. This allowed for

using temperature dependent cross sections data.

4.1. Axial Th distribution

The results of simulations in terms of evolution of effective

multiplication factor as well as U233 production are presented on figures

22 and 23. The values of breeding rates, calculated according to the

formula (1) separately for each period, have been collected in Table 16.

Table 16 Breeding rates in subsequent periods in axial Th distr. case

Period no. Breeding rate

1 0.14

2 0.15

3 0.15

4 0.15

Figure 43 Keff evolution in core with ThO2 kernels in bottom and top blocks (axial Th distribution)

93

Figure 44 Production of U233 in blocks with ThO2 (axial Th distribution)

Applying the appropriate axial shuffling scheme it is possible to keep

effective multiplication factor above 1.0 over the whole cycle (fig. 43). The

production of U233 is almost linear in time (fig. 44), but the final amount

of 34 kg is not impressive. The values of breeding rate are low and

doesn’t change much in subsequent periods: 0.12 to 0.15. It is worth

noting that in the same time only 0.347 g of 232U has been produced

and U232/Ufis ratio is as low as 0.001% making U233 extraction

relatively easy.

4.2. Radial Th distribution

The obtained results analogical to the ones from the previous

subchapter are shown on figures 24 and 25 as well as in Table 17.

Table 17 Breeding rates in subsequent periods in radial Th distr. case

Period no. Breeding rate

1 0.26

2 0.28

3 0.29

4 0.29

94

Figure 45 Keff evolution in core with ThO2 kernels in inner two rings

(radial Th distribution)

Figure 46 Production of U233 in blocks with ThO2 (radial Th distribution)

95

The average value of effective multiplication factor is here lower than it

was in the axial Th distribution case (fig. 45), but such effect could be

expected: this time there is no fuel in the inner rings where usually the

power profiles reach maximum values. These keff values were obtained

with fully inserted control rods so there is still a room for compensation.

From the other hand, due to the same reasons, the production of U233 is

almost 3 times higher as in the previous case (fig. 46), reaching 105 kg.

Also the values of breeding rate are higher: they vary between 0.24 and

0.75 for the last period. It is interesting that the production of 232U,

3.21 g, is almost 10 times higher than in the previous case resulting in

U232/Ufis ratio = 0.003%. This still allows however for relatively easy

U233 extraction.

4.3. Selected results

The values of temperature reactivity coefficients obtained for the Radial

Th distribution case are shown in Tables 18 and 19. The appropriate

control rod worth values are show in Table 20.

Table 18 Temperature reactivity coefficients at CZP (300K) conditions

Condition CZP (300K), control rods out (pcm/K)

fuel temperature increase by 100K -3.456

moderator temperature increase by 100K -0.640

reflector temperature increase by 100K 3.631

Table 19 Temperature reactivity coefficients at HZP (800K) conditions

Condition HZP (800K), control rods out (pcm/K)

fuel temperature increase by 100K -2.146

moderator temperature increase by 100K 1.480

reflector temperature increase by 100K 2.906

Table 20 Control rod worth values

Control rod position keff

CZP HZP

all rods in 0.96053 0.9553

startup rods out 1.02290 1.02664

all rods out 1.11104 1.10197

96

Tables 21 and 22 present the amount of selected actinides and fission

products respectively at BOC and EOC in 4 batch reloading scheme as

plutonium zones are concerned, where sub-cycle duration is 370 f.p.d. It

must be, however, taken into account that during the simulated case the

fuel reloading occurs in the radial zones filled with plutonium fuel,

whereas the inside radial zone initially filled with Th without U233 are

not reloaded. Therefore the presented values for nuclides transmuted

from Th232 (i.e. Th230, Pa231, Pa232, U232, U233, U234) at BOC

concern beginning of 4th batch cycle of 370 f.p.d. that is 1110 f.p.d form

thorium loading and EOC concerns time after 1480 f.p.d. The plutonium

zones are in the equilibrium state.

Table 21 Masses of selected actinides in core (g) at BOC and EOC

Actinides BOC EOC

Th230 0.00e+0 2.29e-1

Th232 4.69e+6 4.54e+6 Pa231 1.33e+1 1.33e+1

Pa233 4.03e+3 1.87e+3 U232 1.50e+1 1.50e+1 U233 6.72e+4 6.94e+4

U234 8.24e+3 8.09e+3 U235 1.09e+3 1.06e+3

U236 1.46e+2 1.29e+2 U238 4.33e-1 2.69e-1 Np237 2.90e+1 3.03e+1

Np238 5.22e-2 6.55e-5 Np239 2.08e-2 2.09e-2 Pu238 2.48e+4 2.50e+4

Pu239 1.35e+5 1.35e+5 Pu240 1.33e+5 1.33e+5

Pu241 1.41e+5 1.40e+5 Pu242 9.85e+4 9.85e+4 Pu243 1.19e+1 0.00e+0

Pu244 2.82e+0 2.82e+0 Am241 8.70e+3 6.55e+3 Am242m 3.63e+2 2.59e+2

Am243 2.42e+4 1.60e+4 Cm242 2.00e+3 1.32e+3

Cm243 5.52e+1 3.30e+1 Cm244 1.31e+4 7.82e+3 Cm245 1.13e+3 6.49e+2

97

Table 22 Masses of selected fission products in core (g) at BOC and EOC

FP BOC EOC

Se79 0.00e+0 6.06e+1 Rb87 1.23e+3 3.13e+3 Sr90 3.81e+3 5.74e+3

Zr93 5.96e+3 8.95e+3 Nb94 1.17e-3 1.79e-3 Tc99 8.06e+3 1.18e+4

Pd107 3.35e+3 5.04e+3 Sn126 4.09e+2 6.17e+2

I129 2.87e+3 4.28e+3 Cs135 8.17e+3 1.21e+4 Cs137 1.27e+4 1.88e+4

Sm147 8.20e+2 1.38e+3 Sm151 3.85e+2 4.88e+2

Eu154 2.96e+2 4.99e+2

5. Conclusions

The presented results of our calculations indicate that assuming

uniform Th distribution concept it would be difficult to design the HTR

core which could operate in a once-through cycle for a time longer than

one year. All the analyzed fuels, i.e. Pu/Th, U/Th and U/Pu/Th give

comparable results in terms of keff evolution, BR values and final

composition (which actually becomes U/Th). The last effect can be

expected since in Pu/Th fuel the Pu mass decreases due to burning and

the U233 mass increases (at least initially) due to production from Th.

Especially in case of fuels with higher Th fractions the initial amount of

fissionable nuclides is not sufficient for operation with keff>1 for a longer

time. The effective multiplication factor cannot stabilize falling

significantly below 1.0. From the other hand, increasing the fraction of

fissionable nuclides in fuel leads to decrease of Th mass in core and

lowers U233 production as well as BR values. Our results show that the

optimal situation would be for fuels with high Th fraction and,

simultaneously, with sufficient Pu or U load. Probably much better

results require kernel radii few times bigger than in the reference design

in order to accommodate larger load of Th.

The promising results were obtained for non-uniform Th distribution –

especially when Th was in 2 inner rings of core. Probably with further

optimizations it would be possible to get BR0.8 and keff 1.0 in the

98

whole cycle. Due to small amount of 232U produced and the fact that

U233 is to be extracted from blocks with no fuel, reprocessing of the Th

kernels would be relatively easy and may be profitable despite of lower

production than obtained in the uniform Th distribution cases.

99

References

[1] J. Cetnar, et al. ”Reference Core Design for a European Gas Cooled

Experimental ADS AccApp’03 Conference, San Diego June 2003, p.

772

[2] J. Cetnar, W. Gudowski and J. Wallenius "MCB: A continuous

energy Monte Carlo Burnup simulation code", In "Actinide and

Fission Product Partitioning and Transmutation", EUR 18898 EN,

OECD/NEA (1999) 523.

[3] Waters L. S. et al., (editors), “MCNPXTM User’s Manual Version

2.3.0”, LA-UR-02-2607, Los Alamos National Laboratory, 2002

[4] J. Kuijper et al. ”Selected Reference HTGR Designs and Fuel Cycle

Data” Deliverable D121 EU FP6 project PUMA

[5] W. Pfeiffer et al. “POKE A Gas-Cooled Reactor Flow and Thermal

Analysis Code” GA-10226 Gulf General Atomic Incorporated, 1970