Arung Bahari Muslim / 10215063
Bilal El Bari / 10215009
M.Iqbal Mauludi / 10215095
Vicqy Bayu Putrama V/10215004
Physics Department
Faculty of Mathematics and Science
Institut Teknologi Bandung
2018

1. Introduction
APWR 1000
Safety Aspect in Nuclear Reactor
Euler Method
1. Method
Burn Up Equation
Enrichment Equation
1. Results and Discussion
2. Conclusions

APWR reactor is the fourth generation reactor with better safety and economically aspects than the previous generation reactor
1
APWR1000 reactor has 3 benefits than the previous generation reactor, these benefits are
1. The safety aspect hasn’t been competed by other generations
2. More efficient in economic aspect
3. The efficiency of the operation is better than the previous generation
APWR1000 reactor has been developed by Westinghouse, the component which has been developed are
1. Steam Generator
2. Instrument and digital control
3. Fuel rod
4. Reactor core

Nuclear Reactor Safety Aspects are categorized into three different physical properties which are
1. Neutron Distribution
2. Thermal Hydraulics
3. Burnup Analysis
2
Neutron Distribution will calculate the energy produced by the generator
Thermal Hydraulics will analyse how heat distributed inside the reactor axially and radially.
Burnup Analysis is an analysis that involves chain reaction from actinide to product of fuel reactor. Fuel enrichment is an important factor in burnup analysis.

Euler Method is one of numerical method to solve ordinary differential equation (ODE) also in the most basic explicit method for numerical integration of ODE. Euler method has the 3 type equations, these equation are :
3
1.Explicit
2.Implicit
3.Semi Implicit
Determined by
Euler Method can solved burn up equation
α

𝑑𝑁
𝑃𝑢1 𝑑𝑡 𝑑𝑁 𝑢9 𝑑𝑡 𝑑𝑁
𝑁𝑝9
= 𝜎 𝑐𝑈8 𝑑𝑡 𝑑𝑁
𝑃𝑢9 𝑑𝑁 𝑢8 𝑑𝑡
= 𝜆 𝑢9
= 𝜆
= −𝜎
𝑁𝑝9
𝑁
ΦN
𝑁 𝑢9
𝑁𝑝9 𝑎𝑈8 u8
ΦN
− λ
− 𝜆
− 𝜎 u8 u9
𝑁𝑝9
𝑁 𝑎𝑃𝑢9
1
N u9
𝑁𝑝9
ΦN
Pu0 𝑑𝑡 𝑑𝑁
𝑃𝑢0
2
3 𝑑𝑡
= 𝜎 𝑐𝑃𝑢9
ΦN
Pu0
− 𝜎 𝑎𝑃𝑢0
ΦN
Pu0
= 𝜎 𝑐𝑃𝑢0 𝑑𝑁
𝑃𝑢2
ΦN
Pu0
− 𝜆
𝑃𝑢1
𝑁
𝑃𝑢1
4
5
− 𝜎 𝑎𝑃𝑢1
ΦN
Pu1 𝑑𝑡
= 𝜎 𝑐𝑃𝑢1
ΦN
Pu1
− 𝜎 𝑎𝑃𝑢2
ΦN
Pu2
7 𝑑𝑁
𝐴𝑚1 𝑑𝑡
= 𝜆
𝑃𝑢1
𝑁
𝑃𝑢1
− 𝜎 𝑎𝐴𝑚1
ΦN
Am1
− 𝜆
𝐴𝑚1
𝑁
𝐴𝑚1
8
6
4

𝑁 𝑢8
=
% 𝑢
8
𝑁
𝐴
𝑀 𝑢
8 𝜌 𝑢𝑜
2
𝑀 𝑢𝑜
2
𝑀 𝑢
1
𝑀 𝑢
=
% 𝑢
5
𝑀 𝑢
5
+
% 𝑢
8
𝑀 𝑢
8
10 .
9 .
5

Figure 1 Atom Density of Isotope U
8 vs Time (second).
Figure 2 Atom Density of Isotope U
9 vs Time (second).
Figure 3 Atom Density of Isotope Np
9 vs Time (second).
Figure 4 Atom Density of Isotope Pu
9 vs Time (second).
6

Figure 5 Atom Density of Isotope Pu
0 vs Time (second).
Figure 6 Atom Density of Isotope Pu
1 vs Time (second).
Figure 7 Atom Density of Isotope Pu
2 vs Time (second).
Figure 8 Atom Density of Isotope Am
1 vs Time (second).
7

The process Burn-up which some nuclides undergo can be classified into :
1. Tend to diminished by the time
2. Increased so fast in a brief time, and decreased so fast too
3. Enlarge (not relatively fast) and fall off by the time
4. From zero, rising for a moment, and tend to be stagnant
The results of calculation cannot representing the actual process that happened in reactor APWR-1000, however the results can be reconstructing the process that happened
8

1. Schulz, T. L. (2006). Westinghouse AP1000 advanced passive plant. Nuclear
Engineering and Design, 236(14-16), 1547-1557.
2. Abram, T., & Ion, S. (2008). Generation-IV nuclear power: A review of the state of the science. Energy Policy, 36(12), 4323-4330.
3. Dufek, J., Kotlyar, D., & Shwageraus, E. (2013). The stochastic implicit Euler method–A stable coupling scheme for Monte Carlo burnup calculations. Annals of Nuclear
Energy, 60, 295-300.
4. Kim, T. K., Taiwo, T. A., & Szakaly, F. (2005). Evaluation of the high temperature engineering test reactor (HTTR) start-up experiments. Argonne National Laboratory,
Nuclear Engineering Division. ANL-GenIV-059
9

Arung Bahari Muslim / 10215063
Bilal El Bari / 10215009
M. Iqbal Mauladi / 10215095
Vicqy Bayu Putratama V / 10215004
Physics Department
Faculty of Mathematic and Science
Institut Teknologi Bandung
2018