Burnup Analysis using Euler Method in APWR 1000

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The Burn Up Analysis using Euler Method in

APWR 1000

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

Outline

1. Introduction

APWR 1000

Safety Aspect in Nuclear Reactor

Euler Method

1. Method

Burn Up Equation

Enrichment Equation

1. Results and Discussion

2. Conclusions

What is APWR Reactor ?

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

What are Nuclear Reactor Safety Aspects ?

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

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

Burn-up Equation

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

Enrichment Equation

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

Results and Discussions

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

Results and Discussions

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

Conclusions

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

References

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

Thank You

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

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