22.251 Systems Analysis of the Nuclear Fuel Cycle
Fall 2009
Laboratory Exercise #2 Solution
Using the whole-assembly CASMO-4 PWR input given in class, answer the following:
a) Calculate and plot ρ as a function of burnup up to 60 MWd/kg with and without the
burnable poison (Gd). Estimate the residual poison Δρ at high burnup (i.e. 60 MWd/kg).
0.35
No poison
0.30
With poison
0.25
0.20
0.15
ρ
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20
0
10
20
30
40
50
60
70
Burnup, MWd/kg
Residual poison reactivity
450
Residual poison reactivity penalty
400
350
Δρ, pcm
300
250
200
150
100
50
0
0
10
20
30
40
Burnup, MWd/kg
50
60
70
b) At zero burnup calculate the following reactivity feedback coefficients for gadoliniumpoisoned fuel assemblies:
1) Plot the MTC as a function of coolant temperature in the range between 400 K
and 600 K for three different boron concentrations in the coolant: 0 ppm, 1000
ppm, and 2000 ppm.
0 ppm
1000 ppm
2000 ppm
Poly. (1000 ppm)
Poly. (2000 ppm)
0.20
0.18
0.16
0.14
ρ
0.12
0.10
0.08
0.06
0.04
0.02
0.00
300
350
400
450
500
550
600
650
Coolant Temperature, K
Plot the three MTC vs. temperature curves on the same graph and qualitatively
explain the behavior of the curves.
10
0
MTC, pcm/K
-10
-20
0 ppm
-30
1000 ppm
2000 ppm
-40
-50
300
350
400
450
500
550
600
650
Coolant Temperature, K
MTC becomes positive with an increase in boron concentration because reduction in water
density with temperature also reduces absorption by the boron adding more reactivity than
reactivity reduced due to the loss of moderation.
2) Fuel Temperature Coefficient (FTC or Doppler coefficient) in units of Δρ per K
by reducing the reference average fuel temperature to 800 K.
Plot reactivity versus fuel temperature
Fit a polynomial to the calculated data
0.17
Polynomial fit
0.16
y = -1.703E-12x3 + 8.611E-09x2 - 3.581E-05x + 1.728E-01
R2 = 1.000E+00
ρ
0.16
0.15
0.15
0.14
0.14
0
200
400
600
800
1000
1200
1400
Fuel Temperature, K
Calculate the slope at 900K,
DC (900K) ≈ -2.45 pcm/K
-2.00
-2.20
DC, pcm/K
-2.40
-2.60
-2.80
-3.00
-3.20
0
200
400
600
800
Fuel Temperature, K
1000
1200
1400
3) Void Coefficient (VC) in units of Δρ per %void by reducing the moderator
density by 10%.
reactivity vs. void fraction
0.20
Polynomial fit
0.15
ρ
0.10
0.05
0.00
y = -1.1406E-05x2 - 8.4456E-04x + 1.4623E-01
R2 = 9.9993E-01
-0.05
-0.10
0
10
20
30
40
50
60
70
80
90
100
Void Fraction, %
VC ≈ 84 pcm / %void
c) Calculate the following additional effects:
Create your own “reactivity ladder” such as attached on the following page by simulating:
1) Δρ from cold zero power (CZP) to hot zero power (HZP) between 30°C and
300°C with isothermal moderator and fuel.
2) Δρ from hot zero power to hot full power (HFP)
3) Δρ due to xenon buildup at HFP by burning for 100 effective full power hours
(EFPH)
Xe
TM, K
TF, K
ρ, pcm
CZP
0
303
303
20,535
HZP
0
573
573
15,810
HFP
0
573
900
14,983
Equilibrium
573
900
12,546
Case
HFP, XE
Δρ (CZP → HZP) = 20535 – 15810 = 4725 pcm
Δρ (HZP → HFP) = 15810 – 14983 = 827 pcm
Δρ (Xe) = 14983 – 12546 = 2437 pcm
1.2E+16
Xe Concentration, at./cc
1.0E+16
8.0E+15
6.0E+15
4.0E+15
2.0E+15
0.0E+00
0
20
40
60
80
100
120
Burnup, EFPH
.
4) Calculate the control rod worth by finding the Δρ between water filled and AgIn-Cd (AIC) rod filled guide tubes. Assuming that only 53 fuel assemblies out
193 in a typical PWR core have control rods, discuss the factors that will affect
the individual control rod worth in the full core.
Δρ (CRDin → CRDout) = 14,634 – (– 16,945) = 31,579 pcm
-
-
Individual control rod worth in the full core will be lower than calculated above because
the control rods are not located in every assembly
The control rod worth depends on the local neutron importance. For example, the worth
will be higher in assemblies with high local power density or assemblies located in the
core center.
For the same reason as above, the control rod worth depends on the position (insertion
depth) of other control rods in the core.
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22.251 Systems Analysis of the Nuclear Fuel Cycle
Fall 2009
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