Effective delayed neutron fraction and prompt neutron lifetime of Tehran research reactor mixed-core

Highlights

► Kinetic parameters of Tehran research reactor mixed-core have been calculated. ► Burn-up effect on TRR kinetics parameters has been studied. ► Replacement of LEU-CFE with HEU-CFE in the TRR core has been investigated. ► Results of each mixed core were compared to the reference core. ► Calculation of kinetic parameters are necessary for reactivity and power excursion transient analysis.

Abstract

In this work, kinetic parameters of Tehran research reactor (TRR) mixed cores have been calculated. The mixed core configurations are made by replacement of the low enriched uranium control fuel elements with highly enriched uranium control fuel elements in the reference core. The MTR_PC package, a nuclear reactor analysis tool, is used to perform the analysis. Simulations were carried out to compute effective delayed neutron fraction and prompt neutron lifetime. Calculation of kinetic parameters is necessary for reactivity and power excursion transient analysis. The results of this research show that effective delayed neutron fraction decreases and prompt neutron lifetime increases with the fuels burn-up. Also, by increasing the number of highly enriched uranium control fuel elements in the reference core, the prompt neutron lifetime increases, but effective delayed neutron fraction does not show any considerable change.

Nomenclature

TRR

Tehran research reactor

LEU

low enriched uranium

HEU

highly enriched uranium

SFE

standard fuel element

CFE

control fuel element

LEU-CFE

low enriched uranium-control fuel element

HEU-CFE

highly enriched uranium control fuel element

BOC

begin of cycle

SAR

safety analysis report

β_eff

effective delayed neutron fraction

ι

prompt neutron life time

1. Introduction

Tehran research reactor (TRR) became critical with using highly enriched uranium (HEU), containing more than 90% enriched in ²³⁵U, in 1967. In later years, based on the International Atomic Energy Agency Non-Proliferation Treaty (IAEA-NPT), the new fuel with low enriched uranium (LEU), containing less than 20% enrichment in ²³⁵U, was used. This major alteration took place on December 1993 when TRR converted from HEU to LEU fuels with Argentina’s Applied Research Institute (INVAP). According to the history of TRR, unlike other research reactors, it has not passed the mixed-core period, in which the previous HEU fuels are gradually replaced by new LEU fuels. Due to availability of old HEU fuels with small consumption that their maximum burn-up are 20%, designing of a mixed-core for TRR is a perfect solution for optimal use of this kind of fuels. Also at the present situation, regarding that the TRR control fuel elements (CFE) are approaching the range of permissible burn-up, and some of the Shim Safety Rods (SSR) are close to saturation conditions, using old control rods (oval type) along with highly enriched uranium-control fuel elements (HEU-CFE) can be one of options for continuing TRR activity. Therefore use of HEU-CFEs instead of LEU-CFEs in a mixed core is important both economically and from the research point of view.

An elementary feasibility study of neutronic aspects of TRR mixed cores has been performed in our previous paper in which all neutronic parameters of equilibrium core and all mixed core configurations were analyzed (Lashkari et al., 2012). Analysis of the results showed that increasing the number of HEU-CFE; reduce the shutdown margin and worth of Regulating Rod (RR) and on other hand increase radial peaking factor. But all neutronic parameters were lower than the safety criteria and were far from safety margins.

The subsequent step, required for future experimental works on TRR, is calculation of kinetic parameters, which are needed for reactivity and power excursion transient analysis. Nuclear fission reactors are described, in the first approximation, by the same basic dynamic principles, whether they are thermal reactors or fast reactors, and whether the nuclear fuel is ²³⁵U, ²³⁹PU, or ²³³U. The most important difference between fast and thermal reactors is neutron lifetime and the major difference among the various fuels is delayed neutron fraction (Hetrick, 1972).

In this work MTR_PC package was used to calculate kinetic parameters of reference and TRR mixed cores. Kinetic parameters for both HEU and LEU fuels in the first TRR core have been calculated by using WIMS-D4 and CITATION (Zaker, 2003). In a new study, the results of MTR_PC for the first TRR operating core were compared with the noise analysis techniques and experimental data (Hosseini et al., 2011). The results of this study are in good agreement with the results from MTR_PC, noise analysis and experimental data. In this work, at first kinetic parameters of the reference core with average burn-up of 23% for SFEs and 44% for CFEs are calculated, then kinetic parameters of the mixed cores have been analyzed. Kinetic parameters of MTR with LEU fuel assemblies change with fuel burn-up (Muhammad, 2010). IAEAs’ documents (IAEA, 1980, IAEA, 1992) and TRR amendment ¹were used as guides in order to perform this research correctly.

1.1. Description of TRR

The TRR is pool type, heterogeneous, solid fuel, light water moderated research reactor, in which the water is also used for cooling, shielding and reflecting. The reactor is designed and licensed to operate at a maximum thermal power level of 5 MW with forced cooling mode. The reactor core assembly is located in a two-section pool and may be operated in either of two sections of the pool. One of the sections contains experimental facilities like beam tube, rabbit system, and thermal column. The other section is an open area for bulk irradiation studies. The major components of TRR are the pool (including embedment and accessories), bridge and support structure, core, cooling system, control and instrumentation, ventilation system, and the experimental facilities. Reactor general description is summarized in Table 1.

Table 1.

General description of TRR.

Reactor specifications
Thermal power	5 MW
Fuel	Low enriched U-235, MTR type, Al Clad
Ave. thermal neutron flux at 5 MW	9 × 1013 n/cm2 s
Core dimensions (first operation core)	40.5 × 38.54 × 89.7 cm
Shielding	Water, lead, barites concrete and regular concrete
Cooling system	Forced Flow Primary Loop
Primary coolant flow	500 m3/h (2200 gpm)
Secondary coolant flow	522 m3/h(2300 gpm)
Coolant inlet temperature (H.eX)in 5 MW	37.8 °C (100 °F)
Coolant outlet temperature (H.eX) in 5 MW	46.5 °C (115.7 °F) 4 Silver–Indium–Cadmium shim safety rods
Control	1 stainless steel regulating rod

Elements of the reactor core are arranged in a 9 by 6 grid plate assembly. Specifications of TRR fuel assemblies are given in Table 2² and also the cross-sectional view of LEU and HEU-CFE are given in Fig. 1. HEU-CFE is different in composition and dimension in comparison with LEU-CFE. Main differences are the enrichment, the number of fuel plates, lateral walls and the shape of absorber. To study HEU-CFE replacement in a mixed core, equilibrium core 51 was selected as a reference core which average burn-up of the standard and the control fuel elements (in percent of the initial value of ²³⁵U) are equal to 23% and 44%, respectively. The core configuration of the reference core and burn-up of the fuel elements (in percent of the initial value of ²³⁵U) at the BOC is given in Fig. 2.

Table 2.

Specifications of TRR fuel assemblies.

Parameter	Fuel assembly type
	LEU-CFE	LEU-SFE	HEU-CFE
Meat material	U3O8–Al	U3O8–Al	U–Al alloy
Enrichment	20%	20%	93.15%
Number of fuel plates	19	14	8
No of outer dummy plates	0	0	2
Meat thickness	0.07 cm	0.07 cm	0.05
Cladding thickness	0.04 cm	0.04 cm	0.038
Water channel thickness	0.27 cm	0.27 cm	0.31
Meat width	6 cm	6 cm	6.1
Meat length	61.5 cm	61.5 cm	59.9
Side wall thickness	0.45 cm	0.45 cm	0.48
Total plate width (wall to wall dist.)	6.7 cm	6.7 cm	6.6
FE dimensions	8.01 × 7.7 × 61.5 cm	8.01 × 7.71 × 89.7 cm	8 × 7.61 × 59.9 cm
Uranium per fuel plate		15.26 g	12.2 g
Weight of U-235 per fuel assembly		213.7 g	97.6
Density of total uranium in meat		3.0 gr/cc	0.69951 gr/cc
Total density of meat		4.8 gr/cc	3.16367 gr/cc
Density of U-235 in meat		0.591 gr/cc	0.6516 gr/cc

Fig. 1.

The cross-sectional view of: (a) HEU-CFE, (b) LEU-CFE of TRR (all dimensions in cm).

Fig. 2.

TRR core configuration.

2. Methodology

2.1. Simulation methodology

The MTR_PC package has been developed by INVAP in order to perform neutronic, thermal hydraulic and shielding calculations of MTR-type reactors. In this section, WIMSD-5B (NEA, 2003) BORGES (Rubio, 1993), and CITVAP v.3.1 (Villarino and Carlos, 1993) neutronic part of MTR_PC package are used to calculate kinetic parameters of TRR reference and mixed-cores.

CITVAP is a new version of the CITATION-II code. It solves 1, 2 or 3-dimensional multi-group diffusion equation in rectangular or cylindrical geometries. WIMSD with ENDF/B-IV library was employed for microscopic cross-section generation, which provides one binary file. The BORGES code prepares microscopic cross section libraries for CITVAP from WIMS output. This code homogenizes and condenses microscopic cross section in any region and energy group structures. Energy group structures used for kinetic parameters calculations are given in Table 3. Evaluation of microscopic cross section for fuel element was performed with the WIMS code, in which SFE and CFE completely simulated in slab geometry. In these simulations meat thickness has an actual size, but aluminium and water thickness were calculated according to the total aluminium and water existing in fuel element. It should be stated that two row of water are used as reflector beside graphite. All kinetic parameters calculated at the BOC situation that core configurations allow reactor operate at maximum power level (5 MW).

Table 3.

Energy group structures used in the calculations.

Energy range	Energy group
	12 groups	5 groups	3 groups
1	10–0.821 MeV	10–0.821 MeV	10–0.821 MeV
2	0.821– 0.00553 MeV	0.821– 0.00553 MeV	821000–0.625 eV
3	5530–367.262 eV	5530–0.625 eV	0.625–0.000 eV
4	367.262–48.052 eV	0.625–0.08 eV
5	48.052–15.968 eV	0.08–0.00 eV
6	15.968–4.00 eV
7	4.00–2.10 eV
8	210–1.123 eV
9	1.123–0.625 eV
10	0.625–0.280 eV
11	0.280–0.080 eV
12	0.080–0.00 eV

In MTR_PC computer code, first order perturbation theory is used to calculate kinetic parameters. The prompt neutron life time (ι) and effective delayed neutron fraction (β_eff) with regarding to the perturbation theory, was calculated from the following relations (Fowler et al., 1971):

$$\iota =\frac{{\sum }_{\text{g}}{\sum }_{\text{i}}{V}_{\text{i}}{(\frac{1}{\upsilon })}_{\text{g}}{\Phi }_{\text{i,g}}^{\ast }{\Phi }_{\text{i,g}}}{\frac{1}{K}{\sum }_{\text{i}}{V}_{\text{i}}{\sum }_{\text{g}}.X(g){\Phi }_{\text{i,g}}^{\ast }{\sum }_{{\text{g}}^{\prime }}v{\mathrm{\Sigma }}_{\text{f,}{\text{g}}^{\prime }}{\Phi }_{\text{i,}{\text{g}}^{\prime }}}$$ (1)

$${\beta }_{\text{eff}}={\displaystyle \sum _{\text{j}=1}^6}\left(\frac{{\sum }_{\text{i}}{V}_{\text{i}}{\sum }_{\text{g}}{X}^{\prime }(j\text{,}g){\Phi }_{\text{i,g}}^{\ast }{\sum }_{\text{b}}{\beta }_{\text{b,j}}{N}_{\text{b,i}}{\sum }_{{\text{g}}^{\prime }}v{\sigma }_{\text{f,}{\text{g}}^{\prime }\text{,}b\text{,}i}{\Phi }_{\text{i,}{\text{g}}^{\prime }}}{{\sum }_{\text{i}}{V}_{\text{i}}{\sum }_{\text{g}}.X(g){\Phi }_{\text{i,g}}^{\ast }{\sum }_{{\text{g}}^{\prime }}v{\mathrm{\Sigma }}_{\text{f,}{\text{g}}^{\prime }}{\Phi }_{\text{i,}{\text{g}}^{\prime }}}\right)\text{,}$$ (2)

where i refers to spatial mesh, V_i to volume of spatial mesh, υ to neutron velocity, g and g′ to energy groups, Ф to flux and Ф^∗ to the ad-joint flux, X(g) to prompt and X′(j, g) to delayed neutron distribution function, K to neutron multiplication factor, Σ_f,n to macroscopic and σ_f refer to microscopic fission cross section, ν to the average number of neutrons released per fission and β_b,j stands for the delayed neutron fraction of delayed family j for nuclide b.

2.2. Mixed-core configuration plan

Mixed core configurations of TRR, which are made from reference core (Fig. 1) is shown in Fig. 3. At the first mixed-core configuration (mixed-core1), one LEU-CFE with maximum burn-up (59.54%) replaced with one HEU-CFE 7%. At the second mixed core, two LEU-CFE with 54.77% and 59.54% of fuels burn-up are replaced with two 7% burn-up HEU-CFE. If LEU-CFE with maximum burn-up 38.06% is replaced with HEU-CFE 20% in mixed-core2, mixed-core 3 has been resulted. Finally, all LEU-CFE are replaced with HEU-CFEs in mixed-core 4 which LEU-CFE 18.40% and 47.81% was replaced by HEU-CFEs 20%. For simplicity in kinetic parameters calculations, average burn-up of 45% for LEU-CFE and 18% for HEU-CFE are considered.

Fig. 3.

TRR mixed core configurations: (a) mixed-core1, (b) mixed-core 2, (c) mixed-core 3, (d) mixed-core 4.

2.3. Validation of simulation methodology

In order to validate the simulation methodology, the LEU first core of TRR is simulated. This core contains 14 SFE, 5 CFE and water as reflector. The core configuration and specifications are given in the reference document (Zaker, 2003).³ The kinetic parameters for the first operating core are calculated and compared with the values of SAR and measurement, which is summarized in Table 4. Comparison of the results shows the good agreement between the calculated, SAR and measurement values. The error between calculated and measurement of β_eff value is 3.5%.

Table 4.

Kinetic parameters of first TRR core.

Core configuration	βeff			ι (μs)
	Calculated	Experimentala	SAR	Calculated	SAR
First operating core	0.00814	0.00786	0.00813	44.6	45.3

^aMeasurement of β_eff of Tehran research reactor, 2002.

3. Results and discussions

The kinetic parameters of all mixed and reference core configurations have been calculated at the BOC and the results are presented in Table 5. Contribution to β_eff from each fissile nuclide is shown in Table 6 and also relative abundance of β_eff for six groups of delayed neutron, for reactivity accident analysis, is given in table 7 for the first, reference and the fourth mixed core.

Table 5.

Kinetic parameters of the first, reference and mixed cores.

Core configuration	βeff	ι (μs)
First	0.00814	44.6
Reference	0.007689	55.1
Mixed 1	0.007674	56.0
Mixed 2	0.00766	57.0
Mixed 3	0.007646	57.7
Mixed 4	0.007631	58.5

Table 6.

Contribution to delayed neutron fraction from each fissile nuclide.

Nuclide	(βeff) × 105
	First core	Reference core 51	Mixed core 4
U-235	776	727	729
U-238	38	28	24
Pu-239	0	12	10
Pu-240	0	0	0
Pu-241	0	1	1
Total	814	769	763

Table 7.

Relative abundance of delayed neutron fraction.

Groups of delayed neutron	(βeff)j/(βeff)core for thermal fission
	First core	Reference core 51	Mixed core 4
1	0.032739	0.031382	0.031501
2	0.2179312	0.214710	0.214909
3	0.1955567	0.194068	0.194221
4	0.3949084	0.393296	0.393551
5	0.1164333	0.122388	0.121790
6	0.0424299	0.044172	0.043983

3.1. Burn-up effect on kinetics parameters

Investigation analysis of the results that shown in Tables 5, verify that the β_eff in the reference core is lower and ι is larger than the first core parameters. Total amount of fissile isotopes (²³⁵U and ²³⁹Pu) decreases linearly with burn-up during the reactor operation. (Fig. 4). ²³⁹Pu is produced by ²³⁸U and is consumed along ²³⁵U. According to Eq. (1), when νΣ_f decreases with burn-up, the number of fissions decreases and results in increment in neutron generation time. But in the β_eff case, νΣ_f appear in numerator and denominator of Eq. (2). Thus if there is only one fissile isotope such as ²³⁵U, β_eff should be more or less constant as a function of burn-up. The reduction of β_eff is caused by production of ²³⁹Pu from ²³⁸U. Because the neutron yield (ν) of ²³⁹Pu is larger and delayed neutron yield (ν_d) is lower than ²³⁸U (Table 8) and the fact, LEU fuels have a higher conversion to ²³⁹Pu, β_eff decreased with fuels burn-up.

Fig. 4.

Number densities of different isotopes with fuel burn-up in LEU fuel type.

Table 8.

Summary of total and delayed neutron yield values (ENDF/B-IV).

Isotope	νd	νa	βb = νd/ν (pcm)
235U	0.0167	2.437	685
238U	0.0440	2.492	1766
239Pu	0.0042	2.895	145

^aThermal yield value.

^bTotal delayed neutron fraction.

3.2. CFE replacement effect on kinetic parameters

Results of the Table 5 show that increasing the number of HEU-CFE in the mixed core configuration, results in a little reduction in β_eff and an increase in ι. Table 6 shows the contribution to delayed neutron fraction from each fissile nuclide for the first, reference and mixed core 4. As shown in Table 6, despite that the value of ²³⁵U in HEU-CFE with 18% burn-up (80.5 g) is less than LEU-CFE with 44% burns-up (117.5 g), contribution to delayed neutron fraction from ²³⁵U increases in the mixed cores. The only reason for this increment of ²³⁵U portions is increased thermalization. Ratio of N_H/N_u (ratio of hydrogen density on uranium density) in HEU-CFE is larger than LEU-CFE; thus, replacement of HEU-CFE in reference core causes dilution and increases moderation. Therefore, contribution of the thermal fission increases and the fast fission decreases with replacements. But in ²³⁸U two factors simultaneously reduce ²³⁸U contribution in β_eff, one is reduction of ²³⁸U values in HEU-CFE and others is decrease of fast fission. Because ²³⁸U has a very large delayed neutron fraction (Table 8), replacing LEU with HEU reduces the fast fission portion of ²³⁸U and results, the value of β_eff decreases. Value of ²³⁹Pu in HEU assemblies less than LEU assemblies thus with increasing the number of HEU assemblies ²³⁹Pu portion in delayed neutron decreases.

In generation time case, the increased thermalization due to HEU-CFE replacement results in decreased average neutron velocity. Also νΣ_f decreases as decrease in ²³⁵U, ²³⁸U and ²³⁹Pu values with HEU-CFE replacement. Thus according to Eq. (1), ι decreases with increasing the number of HEU-CFE in the mixed core configuration.

4. Conclusions

In this research, kinetic parameters of TRR reference and mixed cores have been calculated. The calculation methodology has been validated by performing kinetic parameters of the first TRR operating core. On the basis of this methodology, results for the first core have a good agreement with SAR but the error between calculated and measurement value of β_eff is 3.5% which is not big error. The results of this study have been summarized in two parts:

• –Comparing the results of the first core with the reference core, indicated β_eff decreased and ι increased with the fuels burn-up.
• –Kinetic parameters of all mixed core configurations with one replacement up to all CFE were analyzed. Investigation analysis of the results shows that increasing the number of HEU-CFE, increase the value of ι, but β_eff does not show any considerable change.