Wolsong Nuclear Power Plant 2

NUCLEAR SCIENCE AND ENGINEERING: 150, 37–55 ~2005!

Benchmarking MCNP and WIMS/RFSP Against Measurement Data—II: Wolsong Nuclear Power Plant 2 Hangbok Choi* and Gyuhong Roh Korea Atomic Energy Research Institute P.O. Box 105, Yusong, Taejon, Korea

and Donghwan Park Gnest Inc. Munji-dong 103-16, Yusong, Taejon, Korea Received June 18, 2003 Accepted June 24, 2004 Abstract – Benchmark calculations of the Canada deuterium uranium reactor design and analysis codes were performed for the Monte Carlo and conventional methods using Phase-B measurement data of the Wolsong Nuclear Power Plant 2. In this study, the benchmark calculations were done for the criticality, boron worth, reactivity device worth, and flux scan. For the benchmark calculation of the Monte Carlo method by MCNP-4B, the criticality was estimated within 4 mk. The reactivity worth of the control devices was consistent with the measurement data within 15%. For the benchmark calculation of the conventional method composed of WIMS-AECL, SHETAN, and RFSP, the criticality was also predicted within 4 mk. The reactivity device worth was generally consistent with the measured data except for the strong absorbers such as shutoff rods and mechanical control absorbers. The results of the flux distribution calculations were also satisfactory for both code systems.

I. INTRODUCTION

opment of the direct use of spent pressurized water reactor ~PWR! fuel in CANDU ~DUPIC! reactors.5,6 The Phase-B measurement data were also used for the benchmark calculation of the MCNP-4B code,7 which is widely used as an alternative benchmark tool because of its superiority in the solution method. In the case of new fuel or new reactor development such as DUPIC, the criticality experimental data were not available, and it is also difficult to perform the criticality measurement because of radiation emission and the complexity of the fuel composition. Therefore, the MCNP has been used as a computational benchmark tool at the developmental stage.8 Nonetheless, it is still required to validate the MCNP code using measurement data of the system that is closest to the reactor of interest. Though the Phase-B measurement data were produced for natural uranium fuel, the results can be used for the validation of crosssection generation and the core analysis model of the MCNP code.

It is essential to validate the reactor physics codes in order to ensure the credibility of the reactor design and analysis. This study performs benchmark calculations using the physics measurement data 1 of the Wolsong Nuclear Power Plant 2 ~Wolsong-2!, which were obtained from the Phase-B test performed in 1997. The Phase-B test is a part of the overall commissioning program of Canada deuterium uranium ~CANDU! reactors and conducted to verify and analyze the physics design of the CANDU reactor. Specifically, this study assesses the performance of the conventional physics design and analysis method of a CANDU reactor based on WIMSAECL ~Ref. 2!, SHETAN ~Ref. 3!, and RFSP ~Ref. 4! ~WIMS0RFSP!, which are currently used for the devel*E-mail: [email protected] 37

38

CHOI, ROH, and PARK

This study presents the benchmark calculation results of the WIMS0RFSP and MCNP codes against the physics measurement data of Wolsong-2 for the criticality, boron worth, device reactivity worth, and flux scan. Section II explains the general characteristics of the CANDU reactor. Section III describes the computer code and analysis model used for the benchmark calculations. Section IV provides the validation results of the conventional and Monte Carlo methods. Finally, the summary and conclusions are given in Sec. V.

II. DESCRIPTION OF A CANDU REACTOR

In the CANDU reactor, heavy water is used as both the coolant and moderator. The lower absorption cross section of D2O allows natural uranium to be used as fuel. However, because the fissile content of the natural uranium is very low, only a limited burnup can be achieved and frequent refueling is required, which is accomplished by the “on-power” refueling capability of the CANDU reactor. At the equilibrium state, the power distribution of the CANDU reactor is flattened by a combination of adjuster ~ADJ! ~absorber! rods and the higher fuel burnup of the central core region. In the initial core with completely fresh fuels, however, the central region power is suppressed by placing two depleted fuel bundles in each channel in the central core region. Based on a series of parametric simulations, it was decided to place two depleted fuel bundles at bundle positions 8 and 9 in the 80 central channels.9 Because of the bidirectional fueling scheme, the distribution of the depleted fuel bundles is actually symmetrical about the axial midplane of the core. II.A. CANDU Fuel Bundle The standard CANDU fuel lattice has 37 natural uranium fuel rods as shown in Fig. 1. The fuel bundle is loaded in a fuel channel ~or pressure tube!, and the calandria tube surrounds the pressure tube, which physically separates the moderator from the coolant. The fuel pellet is 1.22 cm in diameter and stacked at 48.2 cm, resulting in a total uranium mass of 19.1 kg0bundle. The atomic contents of 235 U are 0.72 and 0.52% for the standard and depleted uranium fuels, respectively. II.B. CANDU-6 Reactor Core The design data of the standard CANDU-6 core are given in Table I. Figures 2 and 3 show the layout of 380 fuel channels and the principal calandria dimensions of the core. Each fuel channel contains 12 fuel bundles. Figure 3 also shows the layout of four major reactivity devices: the liquid zone controller unit ~ZCU!, ADJ, me-

Fig. 1. Configuration of natural uranium fuel lattice.

chanical control absorber ~MCA!, and shutoff rod ~SOR!. The reactivity devices ~28 SORs, 21 ADJs, 6 ZCUs, and 4 MCAs! are placed symmetrically about the vertical midplanes ~both axial and radial!. The ZCU is filled with light water and used to provide a continuous fine control of the reactivity and hence the reactor power level. This system is also designed to accomplish spatial control of the power distribution, which prevents xenon-induced power oscillations. The locations

TABLE I Design Data of the CANDU-6 Reactor Number of fuel channels Lattice pitch Inner radius of main calandria Inner radius of subcalandria Length of calandria notch Length of fuel channel ~12 fuel bundles! Extrapolated length of fuel channel Extrapolated reactor radius Reactor core radius Reflector thickness

380 28.575 cm 379.7 cm 337.8 cm 96.52 cm 594.4 cm 606.0 cm 384.7 cm 314.3 cm 65.6 cm

Moderator0reflector volumetric average temperature Moderator0reflector D2O purity

698C 99.85 wt%

Number of ADJs Number of light water ZCUs Number of MCAs ~cadmium! Number of SORs ~cadmium!

21 6 4 28

Total fission power Total reactor power Total electrical power

NUCLEAR SCIENCE AND ENGINEERING

2158.5 MW 2061.4 MW~thermal! 713 MW~electric!

VOL. 150

MAY 2005

BENCHMARKING MCNP AND WIMS0RFSP

39

Fig. 2. Face view of reactor showing fuel channels and calandria shell.

of the ZCU and ADJ inside the core in the vertical direction are shown schematically in Fig. 4. The ADJ is a group of absorber rods fully inserted in the reactor during normal full-power operation. This system of rods consists of 21 stainless steel tubes. The ADJ system is used to extend the range of the reactor regulating system in the positive direction beyond that available from the ZCU system. If more positive reactivity is required than the ZCU system can provide, these rods are withdrawn in groups as necessary. The MCA system consists of four control absorber devices, which are physically the same as the SOR, but they do not form a part of the shutdown system. The MCA is normally fully withdrawn from the reactor when the reactor is operating under normal steady-state fullpower conditions. When the reactor regulating system requires more reactivity than the ZCU system can provide ~the ZCU is normally designed to provide a reactivity control capability of about 60.3 mk!, the MCA system NUCLEAR SCIENCE AND ENGINEERING

VOL. 150

MAY 2005

is used to expand the range of the control in the negative direction. The SOR is a tube made of a cadmium sheet sandwiched between two concentric steel cylinders and inserted into perforated circular guide tubes, which are permanently fixed in the core. The rods are normally fully withdrawn from the core and held in position by an electromagnetic clutch.

III. COMPUTER CODE AND ANALYSIS MODEL

The design and analysis of the natural uranium CANDU reactor are typically performed by the POWDERPUFS-V lattice code 10 in conjunction with a MULTICELL supercell code 11 and an RFSP core analysis code. The POWDERPUFS-V was developed based

40

CHOI, ROH, and PARK

Fig. 3. Plan view of reactor showing layout of reactivity devices.

on a series of physics measurements, but the application is limited to the natural uranium fuel because of the empirical correlations implemented. Therefore, for the advanced CANDU fuel ~e.g., DUPIC! design and analysis, a WIMS-AECL transport code is widely used owing to its capability of two-dimensional modeling and the diverse isotopic data of the cross-section library. In addition, instead of MULTICELL, a SHETAN threedimensional transport code is used for the generation of the incremental cross sections of reactivity devices for the DUPIC fuel CANDU core analysis in order to maintain the consistency of the solution method with the lattice calculation. This section describes the conventional and the Monte Carlo methods used for CANDU physics calculations. The CANDU core design and analysis is typically performed by the RFSP code. The RFSP has been benchmarked for various reactor conditions, which are described in Refs. 12 through 16. However, these benchmark calculations have been done with the POWDERPUFS-V lattice code and the MULTICELL supercell code. For the DUPIC fuel core analysis, the RFSP code is used,

too; however, the lattice parameters and incremental cross sections are generated by the WIMS-AECL and SHETAN, respectively. III.A. Conventional CANDU Core Analysis The conventional CANDU core analysis procedure includes three steps: the lattice parameter generation, the incremental cross-section generation for reactivity devices and structural material, and the core simulation. This section describes the computer code and analysis model of each step. III.A.1. Lattice Calculation The lattice parameters are generated by the WIMSAECL, which is a multigroup transport code for the fuel lattice and depletion calculations. It performs a detailed calculation for a single lattice cell, providing flux distributions, eigenvalues, and reaction rates, as well as the usual lattice parameters. For the CANDU fuel lattice calculation, the collision probability ~PIJ! method was NUCLEAR SCIENCE AND ENGINEERING

VOL. 150

MAY 2005


41

Fig. 4. Face view of reactor showing zone controllers and ADJs.

chosen to analyze the two-dimensional geometry exactly. The cross-section library used in this study is an 89-group ENDF0B-V that has 147 nuclides. The multigroup burnup-dependent cell average cross sections are collapsed into two-group lattice parameters to be used for the RFSP code. Because the fast fission and upscattering are not explicitly treated in the RFSP version used in this study, the effective fission and moderation cross sections are obtained as follows: nS f 5 nS f 2 2 nS f 1 and S m 5 S s12 2 S s21

S D f1 f2

S D f2 f1

,

where the notations are conventional. NUCLEAR SCIENCE AND ENGINEERING

VOL. 150

MAY 2005

III.A.2. Reactivity Device Model The incremental cross sections for all the reactivity devices are calculated by the SHETAN, which is a computer code that solves the three-dimensional neutron transport equation in a few neutron energy groups using collision probability techniques. The input cross sections of a supercell ~composed of fuel, tubes, coolant, moderator, and reactivity device! are provided by the WIMS-AECL. There are many reactivity devices deployed in the CANDU reactor core, and therefore, they are generally not represented discretely in the core analysis model. In the RFSP core model, the properties of a given device are smeared over a fairly large region along the entire length of the device. The choice of the size of this region is arbitrary but is typically a one lattice pitch ~LP! ~LP 5 28.575 cm! by one bundle length ~BL! ~BL 5 49.53 cm!. The properties of this smeared region are usually obtained by what is known as a supercell calculation, which

42

CHOI, ROH, and PARK

must be done for the ZCU, ADJ, MCA, SOR, and other structural components. The final products of the supercell calculations are a set of incremental cross sections for an individual device to be added to the standard cell cross sections in the regions of the core over which the device has been smeared. The reactivity devices and some of the structural materials ~guide tube, support bar, support cable, liquid poison injection tube, and zone controller tube! are located vertically between the two fuel channels. Considering the symmetry, one-eighth of a one lattice bundle is modeled by the SHETAN as shown in Figs. 5 and 6. The cross sections of the device material are obtained from the WIMS-AECL by putting an equivalent amount of device material in the boundary of the lattice model. In the SHETAN, it is possible to model the reactivity devices exactly using the cylindrical coordinates. Then, the incremental cross section is written as DS 5 S 3D ' 2 S 3D ,

Fig. 6. SHETAN model for reactivity device.

where S 3D ' and S 3D are the macroscopic cross section of a three-dimensional lattice with and without the reactivity device. Therefore, in the core calculation, the reactivity device is represented by adding DS to the standard cell cross sections. Some of the structural materials ~tension spring, locator, and bracket! are located near the calandria tank. Since there is no fuel material nearby, a fixed-source problem is solved for these materials using the surface condition obtained by the WIMS-AECL. In the WIMSAECL, the structural materials are modeled in a slab geometry between the outermost fuel channel and the calandria tank. Seven regions are modeled as shown in Fig. 7. In this model, a thin fuel source is located in the

left boundary, and regions 1 to 6 are filled with D2O. The material cross sections of INCONELt ~tension spring!, Zircaloy ~coupling rod and guide tube!, and stainless steel ~coupling nut, locator, and bracket! are generated by putting thin layers of these materials in the center region ~region 4!. Region 7 is the stainless steel calandria tank with a free boundary condition. For the nonfuel region, the material cross sections are collapsed into two energy groups and used by the SHETAN. The SHETAN solves for the fluxes in regions 3 to 7 with the currentto-flux ratio obtained for the interface of regions 2 and 3 by the WIMS-AECL.

Fig. 5. SHETAN model for fuel channel.

III.A.3. Core Calculation Once the cell average and incremental cross sections are prepared, core calculations can be carried out. The diffusion calculations are performed by the RFSP, which is a computer code used for fuel management calculations of a CANDU reactor. Its main function is to calculate neutron flux and power distributions based on the two-group three-dimensional neutron diffusion theory. In the RFSP code, the finite difference model is used to divide the reactor core, including the reflector region, into rectangular parallelepipeds ~nodes!. The basic mesh structure is 1 LP 3 1 LP in the XY plane and 1 BL in the axial direction, respectively. At present, the number of meshes used for the core simulation has already been optimized to 44 3 36 3 22 through various numerical tests.17 The typical CANDU core mesh structure is illustrated in Figs. 8 and 9. In Fig. 8, the cylindrical boundary of the calandria is represented by a series of steps. In the X direction, one LP is typically divided into two numerical meshes in the core center region. In the Y and Z directions, the meshes have been set to describe the reactivity devices and the fuel bundle correctly. NUCLEAR SCIENCE AND ENGINEERING

VOL. 150

MAY 2005


43

Fig. 7. WIMS-AECL slab model for structural materials.

III.B. Monte Carlo CANDU Core Analysis The MCNP is a general-purpose Monte Carlo transport code that is capable of generalized geometry modeling, time-dependent calculations, and coupled neutron-photon-electron calculations. Because the public MCNP cross-section libraries have a limited number of isotopes and temperature data, this study uses the crosssection libraries generated in the previous study.8 These cross-section libraries were generated based on ENDF0 B-VI release 3 by the NJOY nuclear data processing system.18 The fractional tolerance used in the NJOY input parameter was 0.1%. The neutron S~a, b! thermal crosssection data were used for the light water and heavy water medium to take account of the thermal motion of the target molecules. Because the CANDU core geometry is not symmetric, a full core model is necessary for the MCNP calcuNUCLEAR SCIENCE AND ENGINEERING

VOL. 150

MAY 2005

lation. Though the computing time is tremendous, a threedimensional full core model including reactivity devices was developed to eliminate the modeling uncertainties associated with the homogenization process, which is typically adopted in the conventional design and analysis code system. In order to facilitate the explicit modeling of the fuel bundles in the core, a repeated structure option of the MCNP was used. Three input cards are used to expand the lattice model in the core including all the fuel pins: The lattice card ~LAT! is used to define an infinite array of all the hexahedra or hexagonal prisms, the universe card ~U! is used to specify a universe to which a cell belongs, and the fill card ~FILL! is used to specify a universe with which a cell is filled. This option makes it possible to describe a cell and its surfaces, to model their distribution in a core, and therefore, the input description and calculation memory can be saved appreciably.

44

CHOI, ROH, and PARK

Fig. 8. Typical RFSP nodal model for XY plane.

In this study, a total of 4560 bundles in the CANDU core were fully modeled including the fuel pellet, cladding, pressure tube, and calandria tube except for the fuel gap, end cap, and end plate. All reactivity devices were explicitly modeled except for the structural material such as the tension spring, locator, bracket, etc., which are used to fix reactivity devices to the calandria tank. The end shield materials were simplified as concentric annuli at each end of the fuel channel. Figure 10 is a side view of the CANDU reactor showing the calandria shell, fuel channels, and built-in reactivity devices. Figure 11 is the plan view of the CANDU reactor showing the

layout of reactivity devices. Figures 10 and 11 were generated by the plotting module of the MCNP code. For the criticality calculation, the KCODE option of the MCNP code is used, in which a fission generation is computationally equivalent to a k eff cycle. Each k eff cycle consists of an inactive cycle, which is to be skipped before beginning the tally accumulation to obtain the appropriate spatial fission source distribution, and an active cycle, which is the cycle to be done before the problem ends. Because of the statistical nature of the Monte Carlo calculation, the accuracy of the result depends on the statistical variance of the computed k eff . Therefore, NUCLEAR SCIENCE AND ENGINEERING

VOL. 150

MAY 2005


Fig. 9. Typical RFSP nodal model for XZ plane.

each simulation was allowed to run for a sufficient number of cycles with a sufficient number of source histories per cycle. All MCNP calculations were performed with 50 000 particles0cycle and 3000 active cycles after 100 inactive cycles.

IV. VALIDATION OF CORE ANALYSIS CODE

For the validation of the WIMS0RFSP system and the MCNP code, benchmark calculations were performed using the Phase-B physics measurement data of Wolsong-2. The Phase-B test includes the first approach for criticality and low-power tests necessary to verify the physics design and to evaluate the performance of the control and protective systems. Most tests were performed at ,0.1% of full power.19 The benchmark calculations were performed for the following cases: 1. approach to the first criticality Fig. 10. Side view of CANDU core ~MCNP model!.

2. calibration of the ZCU reactivity worth NUCLEAR SCIENCE AND ENGINEERING

VOL. 150

MAY 2005

45

46

CHOI, ROH, and PARK

2. The average ZCU water level is 16.94%. 3. The purity of the coolant and moderator are 99.63 and 99.84 wt%, respectively. 4. The MCA is inserted by 55%. 5. The critical boron concentration is 9.0 6 0.5 ppm.

Fig. 11. Top view of CANDU core ~MCNP model!.

3. reactivity calibration of devices ~ADJ, MCA, and SOR! 4. neutron flux distributions. For all the cases, the coolant and the moderator are assumed to be uniformly distributed inside the core. Then, the reactivity worth was calculated by changing the core condition from the nominal case to the perturbed one as follows: a ~mk! 5 1000 3

S

1 1 2 k nominal k perturbed

D

.

IV.A. Criticality Calculation The criticality calculation was performed by the WIMS0RFSP and MCNP codes. The critical operating conditions of the Phase-B measurements are as follows: 1. The average temperatures of the coolant and moderator are 308.12 and 302.16 K, respectively, for the initial core condition.

For the WIMS0RFSP and MCNP, the simulated effective multiplication factors at the critical operating condition are 0.99648 and 0.99622 6 0.00005, respectively. The discrepancies from the measured criticality are 3.78 and 3.52 mk for the WIMS0RFSP and MCNP, respectively. For the critical boron concentration, the criticality was achieved by slowly removing the poison from the moderator. The critical boron concentrations were estimated to be 8.55 and 8.50 ppm for the WIMS0RFSP and MCNP, respectively, which are within the uncertainty level of the critical boron concentration. It was also found that the prediction of the effective multiplication factor by the WIMS0RFSP agreed well with that of the MCNP within 0.3 mk. IV.B. Reactivity Device Worth During the Phase-B test, the calibration of the ZCU was performed by dissolving the boron batch in the moderator, which corresponds to a reactivity worth of ;0.45 mk. After a boron batch was added, the average ZCU water level was adjusted to maintain core criticality. The reactivity worth of the ZCU was calculated for the initial core condition, in which the reactivity worth of the ZCUs was obtained by directly changing the ZCU water level. The simulation results of the average ZCU worth are given in Table II. Compared to the measurement results of the typical operating range ~20 to 60%!, the maximum difference between the measurement and calculation is ,2.8% for both code systems. For the extended operating range ~20 to 80%!, the simulation results match the measured values within 2.5% for both code systems, which is much smaller than the allowed uncertainty of 610%.

TABLE II Comparison of Average Zone Level* Worth WIMS0RFSP

MCNP-4B

AVZL ~%!

Measured ~mk 0%AVZL!

Calculated ~mk 0%AVZL!

Difference ~%!

Calculated ~mk 0%AVZL!

Difference ~%!

20 to 60 20 to 80

0.07166 0.06769

0.07368 0.06938

2.8 2.5

0.07047 0.06667

21.7 21.5

*AVZL 5 average zone level. NUCLEAR SCIENCE AND ENGINEERING

VOL. 150

MAY 2005


47

TABLE III Reactivity Worth of the ADJ Bank WIMS0RFSP

MCNP-4B

ADJ Bank Number

ADJ Rod Number

Measured ~mk!

Calculated ~mk!

Difference ~%!

Calculated ~mk!

Difference ~%!

1 2 3 4 5 6 7

1, 7, 11, 15, 21 2, 6, 18 4, 16, 20 8, 9, 13, 14 3, 19 5, 17 10, 12

1.36 1.53 1.51 2.33 1.77 1.79 3.37

1.236 1.399 1.387 2.021 1.500 1.524 2.703

29.1 28.6 28.2 213.3 215.3 214.9 219.8

1.118 6 0.056 1.494 6 0.056 1.341 6 0.056 2.227 6 0.056 1.420 6 0.056 1.426 6 0.056 2.624 6 0.055

217.8 22.4 211.2 24.4 219.8 220.4 222.1

13.66

11.770

213.8

11.649 6 0.257

214.7

Total

The reactivity worth of the ADJ bank was calculated by the RFSP and MCNP codes, and the results are given in Table III. For the WIMS0RFSP calculation, the maximum error was 19.8%, and the total reactivity worth was underpredicted by 13.8%. For the MCNP, the magnitude of error is similar to that estimated by the WIMS0 RFSP. It is worth noting that the allowed uncertainty of

the reactivity device worth ~ADJ, MCA, and SOR! is reported to be 615% in average. The individual and bank reactivity worth of the MCA were calculated by the RFSP and the MCNP codes, and the results are given in Tables IV and V, respectively. For the WIMS0RFSP calculation, the maximum differences of the individual and bank reactivity worth of the MCA

TABLE IV Reactivity Worth of the Individual MCA WIMS0RFSP

MCNP-4B

MCA Rod Number

Measured ~mk!

Calculated ~mk!

Difference ~%!

Calculated ~mk!

Difference ~%!

1 2 3 4

1.885 1.944 1.876 2.009

2.070 2.068 2.097 2.092

9.8 6.4 11.8 4.1

1.833 6 0.057 1.843 6 0.057 1.873 6 0.057 1.963 6 0.057

22.8 25.2 20.2 22.2

Total

7.713

8.327

8.0

7.512 6 0.213

22.6

TABLE V Reactivity Worth of the MCA Bank WIMS0RFSP

MCNP-4B

MCA Bank Number

Measured ~mk!

Calculated ~mk!

Difference ~%!

Calculated ~mk!

Difference ~%!

1 ~MCA#1, #4! 2 ~MCA#2, #3!

4.85 4.73

5.60 5.60

15.4 18.4

4.862 6 0.057 4.802 6 0.057

0.3 1.5

Total

9.58

11.20

16.9

9.664 6 0.388

0.9


VOL. 150

MAY 2005

48

CHOI, ROH, and PARK

are 11.8 and 18.4%, respectively. Unlike the ADJ case, the reactivity worth of the MCA is overestimated by the WIMS0RFSP. This could be due to the imperfect homogenization of a strong absorber contained in a relatively large numerical volume so that the thermal flux depression is not well described by the coarse-mesh calculation. The simulation results of the MCNP code are consistent with the measurement data, and the maximum differences are 5.2 and 1.5% for the individual MCA and MCA bank, respectively. The reactivity worth of the SOR simulated by the RFSP and MCNP codes is given in Table VI. For the WIMS0RFSP calculation, the maximum and root-meansquare ~rms! errors of the individual SOR worth are 25.5 and 12.4%, respectively. As was the case for the MCA worth calculation, the reactivity worth of the SOR is overestimated by the WIMS0RFSP. The MCNP results for the SOR reactivity worth are generally consistent with the measurement data with a maximum error of

17.9%. As a whole, the reactivity worth of the SOR is underpredicted by the MCNP; the error of the total SOR reactivity worth is 26.6%. IV.C. Flux Distribution During the Phase-B test, thermal flux scans were performed several times for various reactor configurations. The flux measurement confirms the physics design of the core and, in particular, the effects of various reactivity devices and depleted fuel on the neutron flux distribution. The flux scans along a chord of the reactor core are made with a fission chamber. Vertical fission chamber scans are performed along 26 vertical flux detector ~VFD! assemblies, while the horizontal fission chamber scans are carried out along the horizontal flux detector ~HFD! tubes. Flux scan calculations have been performed for the following cases:

TABLE VI Reactivity Worth of the Individual SOR WIMS0RFSP

MCNP-4B

SOR Number

Measured ~mk!

Calculated ~mk!

Difference ~%!

Calculated ~mk!

Difference ~%!

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

1.292 1.601 1.598 1.310 0.913 1.891 1.957 0.980 1.313 2.266 2.398 2.321 1.395 1.314 1.421 1.573 2.210 2.363 2.334 1.382 0.906 1.846 1.946 1.008 1.264 1.593 1.630 1.351

1.328 1.645 1.64 1.323 1.043 2.206 2.213 1.042 1.533 2.456 2.563 2.448 1.527 1.601 1.596 1.549 2.498 2.612 2.494 1.549 1.095 2.317 2.312 1.100 1.430 1.795 1.788 1.427

2.8 2.8 2.6 1.0 14.2 16.6 13.1 6.4 16.8 8.4 6.9 5.5 9.4 21.8 12.3 21.5 13.0 10.5 6.9 12.1 20.9 25.5 18.8 9.1 13.1 12.7 9.6 5.6

1.181 6 0.064 1.602 6 0.064 1.452 6 0.064 1.141 6 0.064 0.931 6 0.064 1.743 6 0.064 1.793 6 0.064 0.931 6 0.064 1.201 6 0.064 2.204 6 0.064 2.335 6 0.064 2.174 6 0.064 1.171 6 0.064 1.301 6 0.064 1.261 6 0.064 1.291 6 0.064 2.204 6 0.064 2.224 6 0.064 2.094 6 0.064 1.151 6 0.064 0.921 6 0.064 1.823 6 0.064 1.783 6 0.064 0.991 6 0.064 1.211 6 0.064 1.452 6 0.064 1.602 6 0.064 1.211 6 0.064

28.6 0.1 29.2 213.0 1.9 27.9 28.4 25.0 28.5 22.7 22.6 26.3 216.1 21.0 211.3 217.9 20.3 25.9 210.3 216.7 1.6 21.3 28.4 21.8 24.2 28.9 21.8 210.4

Total

45.378

10.5

42.377 6 0.535

26.6

50.13


VOL. 150

MAY 2005


TABLE VII

1. case 1: nominal case

RMS Error of Flux Scan

2. case 2: MCA bank 1 is inserted by 50% with all ADJs

WIMS0RFSP

3. case 3: all MCAs inserted with all ADJs 4. case 4: without ADJ banks 1, 2, 3, and 4 5. case 5: without all ADJs. The RFSP and MCNP calculations were performed for HFD 1 and VFD 19 for the horizontal and vertical fluxes, respectively. During the RFSP simulation, the average ZCU water level was fixed at 34.469%, and the moderator boron concentration was 8.5 ppm. The RFSP calculations were performed utilizing the INTREP module to estimate the neutron flux at the detector position. For the MCNP simulation, the flux distribution was calculated using the cell detector tally ~F4!. The cell detector is a sphere with a radius of 0.938 cm, which is located in the VFD 19 and HFD 1 guide tubes. During the MCNP simulation, the average ZCU level was fixed at 40.0%, and the moderator boron concentration was 9.0 ppm. In order to reduce the error to the level of 65%, the MCNP calculation was performed with 100 000 particles0cycle and 2000 active cycles after 100 inactive cycles. For all the cases, the horizontal and vertical thermal flux distributions are shown in Figs. 12 through 21. The

Case 1 Case 2 Case 3 Case 4 Case 5

VOL. 150

MAY 2005

MCNP-4B

Vertical ~%!

Horizontal ~%!

Vertical ~%!

Horizontal ~%!

12.9 4.0 4.2 4.1 1.7

11.8 10.0 20.7 11.6 8.6

6.6 4.1 5.4 5.0 4.0

6.6 6.8 6.9 1.5 4.2

rms errors of the horizontal and vertical flux calculations are summarized in Table VII. For the WIMS0RFSP calculations, it should be noted that the calculated flux was interpolated among the smooth node average fluxes. Therefore, if the interference of the fuel to the node average flux is considered, the error of the WIMS0RFSP calculation will be reduced. For the MCNP calculation, the flux distribution was, in general, well predicted for all the cases within 7%. The allowed uncertainty of neutron flux estimation is 15% rms.

Fig. 12. Vertical flux scan for case 1. NUCLEAR SCIENCE AND ENGINEERING

49

50

CHOI, ROH, and PARK

Fig. 13. Horizontal flux scan for case 1.


VOL. 150

MAY 2005




VOL. 150

MAY 2005

51

52

CHOI, ROH, and PARK



VOL. 150

MAY 2005




VOL. 150

MAY 2005

53

54

CHOI, ROH, and PARK


V. CONCLUSION AND RECOMMENDATION

The results of the conventional CANDU physics and the Monte Carlo calculations were benchmarked against the measured data of the Phase-B tests conducted in Wolsong-2. The benchmark calculation results have shown that both calculations predict the criticality and power distribution with good accuracy. Though both calculations estimate the reactivity device worth within the allowed uncertainty, on average, the predictions of individual rod worth still have relatively large errors, especially for the diffusion calculation done by the RFSP. Therefore, it is recommended that a super homogenization methodology, which considers the strong heterogeneity effect of the reactivity device, be introduced to the conventional CANDU physics analysis method to improve the calculation results. It is also recommended to perform further calculations on the temperature reactivity coefficients and the trip transient to complete the benchmark calculation of the physics design code system.

ACKNOWLEDGMENT This work has been carried out under the nuclear research and development program of Korea Ministry of Science and Technology.

2. J. V. DONNELLY, “WIMS-CRNL: A User’s Manual for the Chalk River Version of WIMS,” AECL-8955, Atomic Energy of Canada Limited ~1986!. 3. H. CHOW and M. H. M. ROSHD, “SHETAN—A ThreeDimensional Integral Transport Code for Reactor Analysis,” AECL-6787, Atomic Energy of Canada Limited ~1980!. 4. D. A. JENKINS and B. ROUBEN, “Reactor Fuelling Simulation Program—RFSP: User’s Manual for Microcomputer Version,” TTR-321, Atomic Energy of Canada Limited ~1993!. 5. J. S. LEE et al., “Research and Development Program of KAERI for DUPIC ~Direct Use of Spent PWR Fuel in CANDU Reactors!,” Proc. Int. Conf. Technol. Exhibition Future Nuclear Systems: Emerging Fuel Cycles and Waste Disposal Options (GLOBAL ’93), Seattle, Washington, September 12–17, 1993, American Nuclear Society ~1993!. 6. H. B. CHOI, B. W. RHEE, and H. S. PARK, “ Physics Study on Direct Use of Spent Pressurized Water Reactor Fuel in CANDU ~DUPIC!,” Nucl. Sci. Eng., 126, 80 ~1997!. 7. “MCNP—A General Monte Carlo N-Particle Transport Code, Version 4B,” LA-12625-M, J. F. BRIESMEISTER, Ed., Los Alamos National Laboratory ~1997!. 8. G. H. ROH and H. B. CHOI, “Benchmark Calculations for Standard and DUPIC CANDU Fuel Lattices Compared with the MCNP-4B Code,” Nucl. Technol., 132, 128 ~2000!.

REFERENCES 1. S. M. KIM, “ Physics Post Simulation of Wolsong Nuclear Power Plant 2,” Wolsong Nuclear Power Plant 1 ~1997!.

9. “Design Manual: CANDU 6 Generating Station Physics Design Manual,” Wolsong Nuclear Power Plant 234, 86-03310DM-000, Rev. 1, Atomic Energy of Canada Limited ~June 1995!. NUCLEAR SCIENCE AND ENGINEERING

VOL. 150

MAY 2005


10. E. S. Y. TIN and P. C. LOKEN, “ POWDERPUFS-V Physics Manual,” TDAI-31, Part 1, Atomic Energy of Canada Limited ~1979!. 11. A. R. DASTUR et al., “MULTICELL User’s Manual,” TDAI-208, Atomic Energy of Canada Limited ~1979!. 12. D. A. JENKINS, “Comparison of RFSP with HBAL and with Phase ‘B’ Experiments at Point Lepreau,” Appendix D of Addendum to TDAI-440, Part I, Atomic Energy of Canada Limited ~1991!. 13. M. A. SHAD and A. C. MAO, “Comparison of HistoryBased Core Tracking and Powermap Simulations with Conventional Production Runs for Point Lepreau,” TTR-486, Atomic Energy of Canada Limited ~1994!. 14. H. C. CHOW, “ Post-Simulation of 1992 Point Lepreau Restart Physics Tests,” TTR-480, Atomic Energy of Canada Limited ~1994!.


VOL. 150

MAY 2005

55

15. D. A. JENKINS, “Simulation of 1992 SDS1 Trip Test at Point Lepreau,” TTR-532, Atomic Energy of Canada Limited ~1994!. 16. H. C. CHOW and D. A. JENKINS, “RFSP Simulation of Point Lepreau Derating Events,” TTR-544, Atomic Energy of Canada Limited ~1994!. 17. D. JENKINS et al., “AMAD for Physics Simulations,” Addendum to TDAI-440, Part I, Atomic Energy of Canada Limited ~1991!. 18. R. E. MACFARLANE and D. W. MUIR, “The NJOY Data Processing System Version 91,” LA-12740-M, Los Alamos National Laboratory ~1994!. 19. B. G. KIM, “ Phase-B Physics Tests Report,” 86-03310AR-001, Korea Atomic Energy Research Institute ~1997!.