Depletion Code System
1
Depletion Code System
Yunlin Xu
T.K. Kim T.J. Downar
School of Nuclear Engineering
Purdue University
March 28, 2001
2
Content
Motivation
What is Depletion?
Depletion code system
Verification
Further improvements
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Motivation
Why do we need depletion code system?
Basic tool for Nuclear Reactor fuel cycle analysis
NERI/DOE projects at Purdue
SBWR
HCBWR
Nuclear Power Reactor Analysis
– Economics
– Safety (throughout core life)
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What is Depletion?
Nuclide density change in nuclear reactor core when operated at
power
Related changes
Cross Section
Nuclide density
(Heavy metal,
Cross Section
feedback
Fission products)
Decay Heat
Reactivity
economic
safety
Depletion code system must solve coupled nuclide/neutron and
temperature/fluid field equations
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Cm246
Heavy Metal Chains
Cm245
Pu243
Am244
Cm244
Am243
Cm243
m
Pu242 Am242 Am242 Cm242
Pu241
Np240
Pu240
U239
Np239
Pu239
U238
Np238
Pu238
U237
U236
α
Am241
α
Np237
Np236
Pu236
U235
α
Pa234
Th233
U234
(n,3n)
Pa233
U233
Th232
Pa232
U232
Th231
Pa231
U231
(n,3n)
Th230
α
(n,3n)
Arrow up
Arrow down
Arrow left
Arrow right
:neutron capture
:(n,2n) reaction
:electron capture
: decay or
 decay for Am242m
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Equations for Depletion
Nuclide depletion equation (Bateman)
dN A (t )
 ( Aa   A ) N A (t )   C N c (t )  B N B (t )
dt
Absorb netron
B
β
β
A
n,γ
C
Neutron Transport Equation (Boltzmann)
1 
1
    (r , E , , t )  t (r , E ) (r , E , , t ) 
S f (r , E , t )
v t
4
    s (r , E '  E , '  ) (r , E ' , ' , t )dE ' d'
' E '
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Micro vs Macroscopic Depletion
   N i i
Microscopic
Lattice code provide σ
Solve for Nuclide Field
from the Bateman equation
Σ
change depend on Ni and σ
i
Macroscopic
Lattice code provide Σ
N/A (Nuclide density and micro changes
are combined)
Σ
change depend on Burnup
Complicated
Easy to implement
Smaller history effect
Larger history effect
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Basic Depletion code system
Lattice Code
(HELIOS)
Neutron Flux
Solver
(PARCS)
Σ
Cross Section
Library
(PMAX)
T/H code
(RELAP
/TRAC)
Φ
Depletion Code
(DEPLETOR)
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HELIOS and PMAX
HELIOS is a comercial (Studsvik
Scandpower) lattice physics code for
solving Boltzmann equation with fine
energy group, heterogeneous, twoDimensional models of the fuel lattice
Gadolinium
pin
BP1
BP2
HELIOS uses consistent fuel assembly
homogenization and energy group
collapsing methods to produce few group
cross sections at all fuel assembly
conditions throughout the burnup cycle.
PMAX tabulates the XS’s of the base state
and the derivatives or difference of XS of
the branches
The octant of fuel assembly
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Base state and Branches
Base state
0GWD/T
Branches
Fuel temp.
mod temp.
Mod. den.
Soluble B.
Control
Tf1, Tf2…
Tm1, Tm2…
Dm1, Dm2…
ppm1, …
rod …
Fuel temp.
mod temp.
Mod. den.
Soluble B.
Control
Tf1, Tf2…
Tm1, Tm2…
Dm1, Dm2…
ppm1, …
rod …
1GWD/T
2GWD/T
3GWD/T
4GWD/T
5GWD/T
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Reactor Core Configuration
Characteristics of Configuration
Heterogeneous in Radial Direction
- Fuel Assemblies
- Fissionable Absorbers
- Control Banks
- Reflectors
•Homogeneous / Heterogeneous in Axial
Direction
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PARCS
Purdue Advanced Reactor Core Simulator
A Multidimensional Multigroup Reactor Kinetics Code
Based on the Nonlinear Nodal Method
Under NRC Contract
Thomas J. Downar
Han Gyu Joo
Douglas A. Barber
Matt Miller
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PARCS Validation
Pressurized Water Reactor:
– Reactivity Initiated Transients (CEA, etc.)
– OECD TMI Main Steam Line Break (PARCS coupled
to RELAP5 and TRAC-M)
Boiling Water Reactor
– OECD Peach Bottom Turbine Trip Benchmark
– OECD Ringhalls Stability Benchmark (Ongoing)
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PARCS
The Cross Section representation used in PARCS




1  2
( ppm, Tf , Tm, D)   
ppm 
 Tf 
Tm 
D 
(D) 2
2
ppm
Tm
D
2 D
 Tf
r
Where
Σr: XS at reference state
ppm: soluble boron concentration (ppm)
Tf: fuel temperature (k)
Tm: moderator temperature (k)
D: moderator density (g/cc)
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Coupling
Coupling of
of PARCS
PARCS to
to TRAC-M/RELAP5
DEPLETOR
Thermal
Depletor
Hydraulics
Input
Input
Tf
Tfcl
Tfsf
v
l

P
B
Tm

Neutronics
Input
Depl.
Side
T/H Side
Interface
Input
T/H
P2DIR
Data
Map

(A)  (AB)
Q fp
Q ac
Memory
Structure
(A)

Tf
 v
Tm
Thermal
DEPLETOR
Hydraulics
Qf
Neut. Side
Interface
Input
General
Interface
Neut.
Data
Map
(AB)  (B)
Memory
Structure
(AB)

Tfcl
l

Tfsf

P
B

Neutronics
Qf
 Q
Qfp
ac
Memory
Structure
(B)
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Depletion code system based on PARCS
In order to minimize the changes to PARCS, A separate
code DEPLETOR was developed
The general interface used to couple TH (RELAP5) and
PARCS was used to coupled DEPLETOR to PARCS
The message transfer between PARCS and
DEPLETOR is performed using the standard message
passing interface software PVM.
P2DIR, a module to communicate with DEPLETOR,
was created in PARCS (only 5 entry points in PARCS)
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Algorithm for Depletion code system
PARCS
DEPLETOR
Read inputs
Read inputs
Exchange ID
Initialize PVM
Initialize PVM
Nodalization
Calculate XS
Receive XS
XS &
Derivatives
Send XS
Neutron Flux Calc
Send Fluxes
Burnup Clac
Flux & XS
Receive Fluxes
EOC
EOC
END
END
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Coupling PARCS/DEPLETOR to TH
RELAP/TRAC
PARCS
PREPROC
DEPLETOR
SCANINPUT
depl
INPUTD
READINP
CHANGEDIM
y
depl
CHANGECOMI
n
P2DIR(1)
D2NIR(1)
P2DIR(2)
D2NIR(2)
INITIAL
XSB
INIT
R(T)DMR(1)
PDMR(1)
PDMR(2)
y
extth
n
y
depl
n
P2DIR(4)
P2DIR(2)
R(T)DMR(2)
PDMR(2)
R(T)DMR(3)
PDMR(3)
done
y
End
Thconv
y
D2NIR(2)
XSB
SSEIG
y
End
n
D2NIR(4)
n
EOC
DEPLETION
n
n
n
depl
y
P2DIR(3)
D2NIR(3)
EOC
y
End
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Cross Section Model used in Depletor
Interpolating XS for a Specified burnup Using a Tabular XS Set
( Bi )  ( Bn )
Bn1  Bi
B  Bn
 ( Bn1 ) i
Bn1  Bn
Bn1  Bn
Bn1  Bi  Bn
Calculating the Burnup Distribution.
B(i )  Bc
P(i ) Pc
/
G (i ) Gc
ΔB(i): burnup increment of ith region
ΔBc: Core average burnup increment
G(i): the heavy metal loading in ith region Gc: total heavy metal loading in the core
Pc: Total power in core.
P(i): Power in ith region
P(i )  V ( j )( [(ig , j )   f (ig , j )])
ji
ig
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Cross Section Model used in Depletor
Calculating XS and Derivatives at Reference States

1  2
( x )   
x 
(x) 2
2
x
2 x
r
No Branch State Case
 1  2 

0
x 2 x 2
 r   0  ( x0 )
One Branch State Case
 r   0  ( xr  x0 )d1

 d1
x
1  2
0
2 x 2
Two Branch States Case
 r   0  ( x0  xr )
d1  ( x2  xr )  d 2  ( x1  xr )
x2  x1
 d1  ( x2  x0  2 xr )  d 2  ( x1  x0  2 xr )

x
x2  x1
1  2  d 2  d1

2 x 2 x2  x1
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Verification
Problem 1: Single Assembly with reflective B.C.
Comparison with HELIOS
PARCS/HELIOS
PARCS/HELIOScomparison
comparison with 500ppm
1.10
1.10
Gadolinium
HELIOS
HELIOS
PARCS
PARCS
pin
1.05
1.05
Kinf
Kinf
BP1
1.00
1.00
0.95
0.95
BP2
0.90
0.90
00
10
10
20
20
30
40
30
40
Burnup(GWD/T)
50
60
Maximum Difference 2×10-5
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50
60
Burnup(GWD/T)
The octant of fuel assembly
Verification
Problem 2 Checkerboard small core with vaccum B.C.
Compared with MASTER (KEARI)
PARCS/MASTER Comparison
1.20
Vacuum
Vacuum
1.18
R3
R3
R3
R3
R3
R3
A
A
A
R3
R2
MASTER
PARCS
30
R2
21.607
R2
1.16
C
A
R3
R3
A
A
A
R3
Keff
A
R3
R3
R3
R3
R3
1.10
1.08
200.0
R3
1.12
Vacuum
Vacuum
1.14
R3
R3
1.06
1.04
Vacuum
1.02
1.00
0
2
4
6
8
10
12
14
16
Burnup(GWD/T)
R2
R2
R2
Maximum Difference 0.3%
Vacuum
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BWR model
Mapping between Neutronic and T/H model
SINK
401
Upper Plenum: 400
301
A
B
302
303
B
A
201
101
Neutronic model
TANK
099
202
102
203
103
Lower Plenum: 100
Plenum to Plenum T/H model
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Comparison between RELAP and VIPRE
RELAP and TRAC are transient codes and do not solve the steady-state
thermal-hydraulics equations
We therefore examined another T/H code, VIPRE (EPRI), which has a steady
state option
There are three models in VIPRE:
HEM, Drift Flux Model, and Two Fluid Model
Drift Flux Model was used for preliminary comparison
RELAP
VIPRE
DIFFERENCE
TH steps per depletion step
1123
75
-93.3%
keff
1.0816502
1.0816311
-1.9pcm
fxy
1.0897
1.0878
-0.17%
fz
1.8066
1.8200
0.74%
Exit void
Fraction
Chan-1
0.6572
0.6578
0.06%
Chan-2
0.7150
0.7172
0.22%
Maximum fuel
Temperature (K)
Chan-1
2144.4
2153.9
9.5
Chan-2
1847.3
1844.8
-2.5
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Comparison between RELAP and VIPRE
1
2
0.9
1.8
1.6
0.7
1.4
0.6
relative power
void fraction
Active Core
0.8
0.5
RELAP
0.4
Vipre
Relap
1.2
1
0.8
0.3
VIPRE
0.6
0.2
0.4
0.1
0.2
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
0
0
axial node
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
564
2200
562
2000
RELAP
VIPRE
560
558
556
554
Fuel centerline temperature (K)
Liquid Temperature (K)
axial node
1800
RELAP
VIPRE
1600
1400
1200
1000
552
800
550
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
axial node
600
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
axial node
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Comparison between RELAP and VIPRE
There is generally good agreement between RELAP and VIPRE
The only visible difference is the fluid temperature which may be
due to the sub-cooled void model. VIPRE provides LEVY and
EPRI models (The EPRI model is used in this comparison)
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Further improvements
VIPRE Two Fluid Model
History effects in Macroscopic X-sections
Predictor-corrector Time integration method
Microscopic depletion?
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Thank You !
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