Analysis Of Doppler Reactivity Coefficient On The Typical Pwr-1000 Reactor With Mox Fuel

Rokh madi

Introduction

Mixed oxide fuel, composing MOX, PUO₂ and UO₂ [1], is a mixture of plutonium and natural uranium or depleted uranium, which is almost similar with the enrichment of uranium used in the most of nuclear reactors. MOX fuel can be an alternative uranium fuel with low enrichment in light water reactors (LWRs). Most commercial nuclear power plants (NPPs) are of LWR type. In NPPs, about 10% of the used fuel are produced and can be used as a large number of MOX source in the world [2]. During operation, an increase in fuel temperature will cause a decrease in thermal conductivity of the fuel pellets [3–5], causing a slow down of heat flow due to fission reactions. That will result in change of absorption cross section of U-233, U-235 and Pu-239, so that at the end the reactivity will change following the temperature change. Due to the smaller thermal conductivity of MOX fuel than the UO₂ fuel, a same temperature change will result in a different Doppler reactivity coefficient among those fuels.

Fuel temperature reactivity coefficient, or better known as the Doppler reactivity coefficient, is an important parameter and a dominant factor to achieve the safe operation of the reactor by controlling the reactivity transients. The Doppler reactivity coefficient is part of the coefficient reactivity feedback, together with the moderator temperature and density coefficient, which are designed to be negative for reactor control purpose. When the fuel or moderator temperature increase due to the increase in reactor power, the negative feedback will decrease the reactivity automatically, so that the reactor is still in safe condition. This characteristic is known as the reactor inherent safety.

The Doppler effect and the isotope U-238 ensure the negative reactivity coefficient at the beginning of the cycle (BOC) of the reactor. However, the accumulation of P-239 due to the burn up can lead to the positive reactivity or an increase in the Doppler reactivity. The existence of plutonium in the MOX fuel needs a special attention because of the shifting towards a broader spectrum of the core and the possibility of the positive reactivity coefficient [6]. The Doppler reactivity coefficient is defined as fractional change in reactivity caused by changes in fuel temperature. This coefficient is considered more important than the moderator reactivity coefficient because an increased fuel temperature is followed immediately by an increase in reactor power. The main effect is due to the Doppler reactivity resonance capture of U-238 fission and absorption ratio changes due to changes in fuel temperature [7, 8].

This paper presents the effect of the MOX fuel in a typical PWR-1000. The typical PWR-1000 is a pressurized water reactor (PWR) reactor type similar to the AP-1000 without the use of 104 Integrated Fuel Burnable Absorber (IFBA) and pyrex. The purpose of the research is to determine the effect of MOX fuel to the Doppler reactivity coefficient of the typical PWR-1000 reactor core. The research was performed using the Monte Carlo MCNPX transport program [9] to calculate the MOX fuel assemblies in the typical PWR-1000 reactor core. During that process, a Nuclear Data Library continuous energy dependent temperature of ENDF/B-VII [10] files was generated using NJOY99 code for the whole calculation. The results of the MOX fuel has been compared with the calculation of a standard UO₂ fuel also loaded in the typical PWR-1000.

Description of the Typical PWR-1000 Reactor

The PWR-1000 typical reactor core is designed to produce power output of 1000 MWe or 3400 MWth from the 157 UO₂ fuel assemblies. Each fuel assembly is arranged by 17ձ7 elements, consisting of 264 fuels rod and 25 guide tubes. The number of control rod assemblies in the core are 69 pieces consisting of 53 pieces of rod cluster control assembly (RCCA) and 16 pieces of gray rod control assembly (GRCA) [11]. Table 1 shows the design parameters and the description of the reactor core.

Table 1

Desain parameters of typical PWR-1000 reactor [12]

Parameter	Value
Parameter	Power of reactor:
Thermal power, MWth	3400
Electric power, MWe	1117
Active core:
High of fuel achtive on first core, cm	426,7
Equivalen diameter, cm	304
Fuel assembly (FA):
arrangement one perangkat	17×17
Number of FA on core	157
Fuel material	UO₂ (sintered)
Enrichment of ²³⁵U,w%	2,35; 3,40 dan 4,45
Enrichment of MOX, w%	2
Number of fuel rod	264
Number of guide tube/instrument guide thimbles	24/1
Structure of core:
Material of core barrel	SS304
Diameter of core barrel, ID/OD, cm	339,72 / 349,88
Material of baffle	SS304
Thickness of baffle, cm	2,2
Fuel UO₂: rod (pitch), cm	0,81915
Pelet diameter,cm	0,01645
Gap thickness,cm	0,0572
Clading material	Zirlo
Guide tube:	1,123/1,224
Inner/outer diameter, cm	ZIRLO
Tube material	1,260

The core as shown in Figure 1 is surrounded by a single row of reflector assemblies of the same width as the fuel assembly containing 2.50 cm thick baffle (Fe-Cr-Ni-Mn). The outer radial boundary condition is vacuum. Each fuel assembly consists of 17×17 square pin cell lattice as shown in Figure 2. The pin cell pitch equals to 1.26 corresponding to an assembly width of 21.42 cm, which is located at the highest worth regions in the vicinity of the guide tube. Their purpose is to compensate excess reactivity of the fresh fuel.

Figure 1

Typical of PWR-1000 core using VISED code

Figure 2

Fuel assembly cross section of typical PWR-1000 core (green: fuel element, yellow: guide tube)

I. Design of the MOX core :

The MOX core of the typical PWR-1000 is designed from the original UO₂ core of AP 1000 [12] by replacing the UO₂ fuel with 2.35 % enrichment with the MOX fuel, as shown in Figure 3.

Figure 3

Design of the MOX core in the typical PWR-1000

Based on Figure 3, the number of fuel assemblies with different fuel type and enrichment are listed in Table 2.

Table 2

Number of fuel assemblies in the MOX core

Number of Fuel Assemblies
MOX (2%)*	UO₂ (3.40%)*	UO₂ (4.45%)*
53	52	52

[i] * in parenthesis is enrichment

Referring to the data from Table 1 and 2, the calculated atomic density of UO₂ and MOX fuel are shown in Table 3 and 4.

Table 3

Atomic Density of MOX with 2% enrichment [13–15]

No.	Nuclide	Atomic density (10²⁴ atom/cm³)
1.	U-235	3.8879e-5
2.	U-235	1.9159e-2
3.	Pu-238	8.3986e-5
4.	Pu-239	2.1706e-3
5.	Pu-240	9.9154e-4
6.	Pu-241	3.6732e-4
7.	Pu-242	2.5174e-4
8.	Am-241	1.0664e-4
9.	O-16	4.6330e-2

Table 4

Atomic Density of UO₂ fuel with various enrichment

			Atomic Density
	Nuclide	(10²⁴atom/cm³),		enrich. (%)
		2.35%	3.4%	4.45%
1.	U-235	1.02668e-3	1.92585e-3	1.00572e-3
2.	U-238	2.23265e-2	2.12877e-2	1.111691e-2
3.	O-16	4.67064e-2	4.64272e-2	2.42453e-2

II. Core calculation

The calculation of Doppler reactivity coefficient using MCNPX is performed step by step as follow :

Generation of continuous nuclear data cross section taken from ENDF/B-VII file as a function of temperature (300 K, 400 K, 500 K, 600 K, 700 K, 800 K, 900 K and 1000 K) using NJOY99 code.
Calculation of fuel atomic density on for UO₂ fuel with 3.40% and 5.45% enrichment and MOX fuel with 2% enrichment using the ENDF/B-VII nuclear data generated on step 1.
All calculation on step 1 and 2 are performed with temperature of 300 K, 400 K, 500 K, 600 K, 700 K, 800 K, 900 K and 1000 K respectively
Calculation of k_eff
Calculation of Doppler reactivity coefficient.

The Doppler reactivity coefficient is expressed as amount of reactivity change for a parameter change in the reactor, and defined in the following equation (1) [16]:

(1)

αT=(keff[n]−keff[n−1])(keff[n]×keff[n−1])×100%

α_T:

Doppler reactivity coefficient

k_{eff [n]}:

k_effon T temperature

k_{eff [n-1]}:

k_effon preceding T temperature

Results and Discussion

The core reactivity can be direct calculated after determining k_eff. The k_eff. is calculated on the UO₂ and MOX core as a function of temperature respectively. The fuel temperature as the basis of calculation starts from 300 K up to 1000 K, with 100 K variation. The resulted k_eff calculation for UO₂ and MOX core are shown in Table 5 and depicted in Figure 3.

Table 5

k_eff calculation for UO₂ and MOX fuel

No.	Temperature (K)	k_eff
		UO₂	MOX
1.	300	1.41547 ± 0.00751	1.28357 ± 0.00621
2.	400	1.41206 ± 0.00643	1.28314 ± 0.00829
3.	500	1.40067 ± 0.00828	1.27857 ± 0.00702
4.	600	1.37780 ± 0.00737	1.26473 ± 0.00779
5.	700	1.37466 ± 0.00712	1.26254 ± 0.00795
6.	800	1.37286 ± 0.00743	1.26135 ± 0.00764
7.	900	1.37168 ± 0.00690	1.26074 ± 0.00692
8.	1000	1.37021 ± 0.00601	1.25443 ± 0.00802

From Figure 4, the k_eff will decrease as the fuel temperature increases for the UO₂ and MOX core. In general, the k_eff of MOX core is lower than UO₂ core for all temperature. The results of this calculation are in good agreement with the other calculation, showing that the presence of MOX in the core will lower the k_eff[14]. The decrease of k_eff for MOX core is mainly caused by the effect of Pu-239 and Pu-241 having higher neutron absorption macroscopic (1011.3 and 1377 barn) compared to U-235 (680 barn)[2,18].

Figure 4

Relation between fuel temperature and k_eff in the the UO₂ and MOX core

The effect of fuel temperature increase to decrease the k_eff is also caused by the increase of resonance absorption and fission capture. By referring the k_eff values in Table 5, the Doppler reactivity coefficient (α_T) can be determined using equation (1) as shown in Table 6 and depicted in Figure 5.

Table 6

Doppler reactivity coefficient α_T for UO₂ and MOX fuel

No.	Temperature (K)	α_T(pcm/K)×10⁻²
		UO₂	MOX
1.	300 – 400	−1.71	−0.26
2.	400 – 500	−5.76	−2.79
3.	500 – 600	−11.90	−8.56
4.	600 – 700	−1.66	−1.37
5.	700 – 800	−0.95	−0.75
6.	800 – 900	−0.63	−0.38
7.	900 – 1000	−0.78	−3.99

Looking at Figure 5, the Doppler reactivity coefficient of the MOX and UO₂ core show a same characteristic as it decreases at temperature of 300 K – 400 K, then increases at temperatures up to 700 K, and drops again at 1000 K temperature. In overall, the Doppler reactivity coefficient of UO₂ fuels is smaller than the Doppler reactivity coefficient of MOX fuels. This phenomenon is again influenced by the presence of plutonium having a larger absorption cross section (Pu-239 =1029 barn, Pu-241= 1377 barn) than of uranium (U-235=681 barn, U-238=2.70 barn)[19].

Figure 5

Relation between fuel temperature and Doppler reactivity coeficient in the the UO₂ and MOX core

Conclusions

The Doppler reactivity coefficient with MOX fuel in the typical PWR-1000 reactor core has been calculated using the Monte Carlo MCNPX transport program. The results show that the Doppler reactivity coefficient decreased to a critical value as the fuel temperature increased. This is because the presence of Pu-239 and Pu-24. Since the absorption cross section of MOX fuel is much bigger than the absorption cross section of uranium, the Doppler reactivity coefficent become negative, so that the core of typical PWR-1000 reactor core with MOX fuel is considered to be safe to be operated

Acknowledgements

The authors would like to express many thanks to Division Head of Physics and Reactor Technology (BFTR) for valuable support to the writing of this paper. Moral supports from colleagues on BFTR-PTKRN are greatly appreciated.

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