Argonne National Laboratory
RERTR
Reduced Enrichment for Research and Test Reactors
Nuclear Engineering Division at Argonne
U.S. Department of Energy

RERTR Publications:
Analysis Methods for Thermal Research and Test Reactors

ANL/RERTR/TM-29

COMPUTING CONTROL ROD WORTHS
IN THERMAL RESEARCH REACTORS

4. CONTROL ROD WORTH EVALUATIONS

Because of their strong neutron-absorbing character, special methods are needed to determine control rod worths in diffusion theory calculations. As discussed in the above paragraphs, one such method is to determine a pair of group- and mesh-dependent effective diffusion parameters for the absorber rod. An alternate method is to isolate the absorber material from the diffusion calculation by applying a group-dependent set of internal boundary conditions (current-to-flux ratios) at the absorber surface. Using these methods, control rod worths have been calculated for several control rod materials.

4.1 Cadmium Control Elements

Control elements used in the Oak Ridge Research Reactor (ORR) and the Swedish R2 Reactor have the same design. The poison section consists of a water-filled square cadmium annulus 2.345 in. (5.956 cm) on a side, 30.5 in. (77.47 cm) long, and 0.040 in. (0.1016 cm) thick. Since the width-to-thickness ratio is very large, effective diffusion parameters obtained earlier for a cadmium slab of this thickness (see Table 1) are applicable. For the reasons given earlier, effective diffusion parameters are needed only for the group 5 thermal neutrons (En < 0.625 eV). Table 1 shows that for this group the cadmium thickness in absorption mean free paths is greater than 5. Therefore, the cadmium sheet is effectively black to group 5 neutrons with a corresponding current-to-flux ratio equal to 0.4692. It was shown in Ref. 3 that the worth of a cadmium slab of this thickness calculated with effective diffusion parameters obtained from the spectrum-weighted P5 blackness coefficients (<a(P5)> and <b(P5)> and calculated using the group-5 black internal boundary condition gave nearly identical results both of which agreed with the result of a Monte Carlo calculation within 1s statistics. Therefore, control rod worths for the ORR and R2 reactors were calculated using the black internal boundary condition for group 5 neutrons incident on the cadmium absorber and normal diffusion theory for all the other groups.

Table 6 summarizes 3D calculations for control rod worths in the R2 reactor. Note that all the diffusion-theory worth calculations agree within 1s of the corresponding VIM9-Monte Carlo results. These values are taken from Ref. 3, which includes a description of the R2 reactor core configuration.

The ORR 179-AX5 core10 was water-reflected with all-fresh U3Si2 (4.8 gU/cm3) LEU fuel. It contained 14 standard (19-plate) fuel elements and 4 shim rods each with an upper cadmium poison section and a lower 15-plate fuel follower section. Differential rod worths were measured by the positive period method. The integral rod worth was obtained by integrating the differential measurements from the lower to the upper limit of the shim rod displacement.

Measured and calculated integral worths for the D6 shim rod in ORR Core 179-AX5 are compared in Table 7. As with the Swedish R2 reactor, the black internal boundary condition (J/f = 0.4692) was applied at the surface of the cadmium absorber for the thermal group (En <0.625 eV) in the diffusion-theory calculations. Table 7 also shows that the DIF3D-diffusion and the VIM-Monte Carlo total worth calculations are in good agreement, but are about 5.6% larger than the measured value. This difference is typical of ORR worth measurements discussed in Ref. 10 and is partly the result of approximate corrections to the experimental data for delayed photoneutrons and temperature feedback effects. Note that the integrated worth and the total worth, based on rod-in and rod-out eigenvalue calculations, agree to within less that 1%. However, these integral and total

TABLE 6

EIGENVALUES AND CADMIUM CONTROL ROD WORTHS FOR THE SWEDISH R2 REACTOR

Fuela

Rod Config.

Keff -DIF3Db

Drc-%dk/k

keff -VIM

Drc-%dk/k

HEU 25019

All Out

1.1602

1.16620.0025

"

All In

0.9654

17.39

0.97000.0022

17.340.30

"

At 50%

1.0826

6.18

1.08620.0024

6.320.27

"

Only G3 Out

1.0233

11.53

1.02660.0024

11.660.29

LEU 32616

All Out

1.1562

1.15370.0020

"

All In

0.9655

17.09

0.96560.0025

16.890.31

"

At 50%

1.0816

5.97

1.07900.0026

6.000.27

"

Only G3 Out

1.0184

11.70

1.01910.0025

11.450.28


aThe HEU 25019 notation stands for HEU fuel with 250 g 235U per 19-plate element.

bThe DIF3D calculations were done for group 5 of cadmium made black.

cDr = (kout - kin)/koutkin.

TABLE 7

D6 INTEGRAL ROD WORTH FOR ORR CORE 179AX5

Integration Limits, In.a

Integral worth, % dk/k

LL = 0.0

UL = 26.56

Calc.

Exp.

C/E

7.239

6.855

1.056

Total Worth

Code

R-out, In.

R-in, In.

R-bank, In.

k-out

k-in

% dk/k

VIM

26.56

0.0

17.72

1.04000.0018

0.96660.0020

7.2990.273

DIF3D

26.56

0.0

17.72

1.0371

0.9641

7.309


aIntegration of the differential rod worth from the lower to the upper limit gives the total rod worth.

ORR WATER-REFLECTED LEU CRITICAL 179AX5

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

FE

FE

FE

H2O

H2O

H2O

H2O

H2O

FE

FFD4

FE

FFD6

FE

H2O

H2O

H2O

H2O

FE

FE

FE

FE

FE

H2O

H2O

H2O

H2O

FE

FFF4

FE

FFF6

FE

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

FE = 19-plate standard fuel element

FF = 15-plate fuel follower element

worths are not expected to be exactly the same because of differences in the rod bank elevations.

4.2 Ag-In-Cd Control Elements

Some research reactors use control elements consisting of flat forked blades composed of the Ag-In-Cd alloy described earlier. For this alloy and for a thickness t = 0.310 cm, Table 2 gives the effective diffusion parameters based on the flux-weighted P5 blackness coefficients, <a(P5)> and <b(P5)>, for mesh intervals of h = t and h = t/2. These blackness-modified diffusion parameters were used in 3D diffusion-theory calculations to determine control rod worths in the 10-MW IAEA Generic Reactor11. For this reactor the 23-plate fuel elements use fresh LEU U3Si2 - Al dispersion fuel with a 235U loading of
390 g per fuel element.

DIF3D-diffusion and VIM-Monte Carlo results for eigenvalues and reactivities are compared in Table 8. They all agree within the 1s Monte Carlo statistics. Based on effective diffusion parameters calculated from the Ag-In-Cd blackness coefficients, the worth of Rod 3 was determined for mesh intervals of h = t, t/2, t/3, and t/4. Table 8 shows that the calculated rod worth is nearly independent of the mesh interval size. However, the results suggest a maximum value of h=t/2 be used for determining the effective diffusion parameters from the blackness coefficients.

4.3 Hafnium Control Elements

Control elements for the Japanese 20-MW JRR-3 reactor12 consist of square water-filled natural hafnium boxes 6.36 cm on a side and 0.50 cm thick. Using the methods described earlier, Table 3 shows the evaluated blackness coefficients for a hafnium slab of this thickness and a density of 13.3 g/cm3. The effective diffusion parameters were evaluated using the spectrum-averaged P5 blackness coefficients.

Three-dimensional DIF3D diffusion and VIM Monte Carlo calculations were used to calculate control rod worths in the JRR-3 reactor. The standard fuel element has 20 plates whereas the control rod follower element has 16 plates of fresh LEU fuel. Using effective diffusion parameters corresponding to a mesh interval h = t/2, Table 9 compares DIF3D and VIM eigenvalues and control rod worths for the JRR-3 reactor.

TABLE 8

XYZ CALCULATIONS FOR THE 10-MW IAEA GENERIC REACTOR

FOR FRESH LEU U3Si2 FUEL WITH Ag-In-Cd CONTROL BLADES

Rod Configuration

Code

h-cm

keff

Dra-% dk/k

All Out

VIM

1.19220.0031

All Out

DIF3D

1.1903

All In

VIM

1.02960.0031

13.250.36

All In

DIF3Db

h = t/2

1.0309

12.99

Rod 3 Out

VIM

1.08380.0033

8.390.36

Rod 3 Out

DIF3Db

h = t

1.0790

8.66

Rod 3 Out

DIF3Db

h = t/2

1.0813

8.47

Rod 3 Out

DIF3Db

h = t/3

1.0818

8.43

Rod 3 Out

DIF3Db

h = t/4

1.0816

8.44


aBased on the Ag-In-Cd blackness-modified diffusion parameters.

bDr = (kout - kin)/koutkin.

LOCATIONS of the Ag-In-Cd CONTROL BLADES in the 10-MW IAEA GENERIC REACTOR

C

C

C

C

C

C

SFE

SFE

CFE-1

SFE

SFE

SFE

SFE

SFE

SFE

SFE

CFE-2

SFE

SFE

CFE-3

SFE

Irr. Pos.

SFE

SFE

SFE

SFE

SFE

SFE

CFE-4

SFE

Irr Pos.

SFE

CFE-5

SFE

SFE

SFE

C

C

C

C

C

C

SFE = 23-plate standard fuel element

CFE = 17-plate control fuel element

TABLE 9

EIGENVALUES AND HAFNIUM CONTROL ROD WORTHS FOR THE JRR-3 REACTOR

Rod Config.

Keff -DIF3D

Dra-% dk/k

keff -VIM

Dra-% dk/k

All Out

1.2291

1.22270.0023

At 50%

1.1224

7.74

1.11430.0024

7.960.25

All In

0.8689

33.74

0.87630.0028

32.330.39


aDr = (kout - k)kout k.

Ford Nuclear Reactor Core Congiguration With Fresh LEU Fuel

D2O TANK

H2O

H2O

SFE

SFE

SFE

SFE

SFE

H2O

H2O

H2O

SFE

CFE-A

SFE

CFE-C

SFE

H2O

H2O

H2O

SFE

SFE

SFE

SFE

SFE

H2O

H2O

H2O

SFE

CFE-B

SFE

CFE-RR

SFE

H2O

H2O

H2O

SFE

SFE

SFE

SFE

SFE

H2O

H2O

H2O

H2O

SFE

SFE

H2O

H2O

H2O

SFE = 18-plate standard fuel element

CFE = 9-plate control fuel element

Figure 2. FNR 27-Element Water-Reflected LEU Core

4.4 Borated Stainless Steel Control Elements

Shortly after the conversion of the Ford Nuclear Reactor (FNR) from HEU to LEU fuel, full-length rod worth measurements were made in the 27-element fresh LEU core (Fig. 2) in December 1981. Total rod worths were obtained by integrating incremental worths, measured by the positive period technique, from the lower to the upper limit of rod movement. The results of these measurements are reported in Ref. 13.

The shape and composition of the borated stainless steel shim-safety rods used in this UAlx-Al core are described in Table 4. This table shows that the FNR shim-safety rods cannot be approximated by a thin slab treatment and so blackness theory cannot be used to evaluate their worth. However, rod worths were evaluated for this 27-element core configuration using the MCNP Monte Carlo code14, the DIF3D code with internal boundary conditions (IBC's) for groups 3 and 4 (see Table 5), and the DIF3D code with effective diffusion parameters (EDP's) obtained by matching reaction rate ratios15.
Table 10 compares measured and calculated rod worths and includes the University of Michigan results based on their two-group reaction rate matching process described in Ref. 5. For all these calculations the rod worth was determined by computing the reactivity difference between rod-in and rod-out cases with the regulating rod (RR) fully withdrawn. The Monte Carlo and diffusion calculations with IBC's are three-dimensional whereas the diffusion calculations with EDP's are two-dimensional XY calculations. None of the calculations account for the beam tubes associated with the D2O tank on the north side of the core, nor do the calculations account for the rod bank and regulating rod elevations corresponding to the differential worth measurements, since this data is unavailable. Nevertheless, Table 10 shows very acceptable agreement among the measured and calculated rod worth values. Note that the rod worths are increased by about 7% when they are evaluated for the case where the regulating rod is withdrawn 50% and the rod bank is withdrawn 67%.


4.5 Titanium Diboride Aluminum Control Elements

In October 1995 the FNR borated stainless steel shim-safety rods were replaced with borated aluminum rods composed of an alloy of titanium diboride in 6351 aluminum. The boron in the TiB2 has a 10B enrichment > 95%. Table 4 compares the geometry and compositions of the TiB2(95%10B)-Al6351 shim-safety rods with the former borated stainless steel ones while Table 5 compares the internal boundary conditions. These IBC's were used in 3-dimensional DIF3D calculations to determine the worths of the borated aluminum rods in the 27-element FNR core (Fig. 2). These rod-out and rod-in calculations were done with the rod bank and the regulating rod fully withdrawn.
Table 11 summarizes the results and compares the rod worths with those obtained earlier

TABLE 10

FNR EIGENVALUES AND SHIM-SAFETY ROD WORTHS

FOR THE 27-ELEMENT FRESH UAlX LEU CORE

% Rod Withdrawal

Code

Geom.

Eigenvalue

Rod Worth, % dk/k

Reg. Rod

Bank

Rod

Meas

Calculated

100.0

100.0

A: 100.0

MCNP

XYZ

1.032340.00070

DIF3D: IBC's

XYZ

1.03632

DIF3D: EDP's

XY

1.02208

100.0

100.0

A: 0.0

MCNP

XYZ

1.009990.00074

2.220

2.1440.098

DIF3D: IBC's

XYZ

1.0145

2.109

DIF3D: EDP's

XY

0.99910

2.250

UM-2DB: EDP's

XY

2.279

50.0

66.7

A: 100.0

DIF3D: IBC's

XYZ

1.02035

A: 0.0

DIF3D: IBC's

XYZ

0.99751

2.244

100.0

100.0

B: 0.0

MCNP

XYZ

1.009380.00070

2.320

2.2030.095

DIF3D: IBC's

XYZ

1.01176

2.342

DIF3D: EDP's

XY

0.99782

2.379

UM-2DB: EDP's

XY

2.648

50.0

66.7

B: 100.0

DIF3D: IBC's

XYZ

1.02106

B: 0.0

DIF3D: IBC's

XYZ

0.99529

2.535

100.0

100.0

C: 0.0

MCNP

XYZ

1.010840.00073

2.283

2.0600.097

DIF3D: IBC's

XYZ

1.01450

2.075

DIF3D: EDP's

XY

0.99944

2.216

UM2DB: EDP's

XY

2.247

50.0

66.7

C: 100.0

DIF3D: IBC's

XYZ

1.02040

C: 0.0

DIF3D: IBC's

XYZ

0.99778

.

2.222


TABLE 11

COMPARISON OF THE BORATED STAINLESS STEEL AND THE TiB2-Al

SHIM-SAFETY ROD WORTHS IN THE FNR 27-ELEMENT CORE

Rod

Withdrawala

Code

Eigenvalue

Rod Worth % dk/k

Ratio

%

(TiB2-Al)

TiB2-Al

B-SS

Calc'd

Meas.b

A

A

B

C

100.0

0.0

0.0

0.0

DIF3D: IBC's

DIF3D: IBC's

DIF3D: IBC's

DIF3D: IBC's

1.03568

1.01074

1.00801

1.01113

2.383

2.650

2.345

2.109

2.342

2.075

1.130

1.131

1.130

1.148

1.095

1.096


aFor these calculations the regulating rod (RR) and the other shim-safety rods were fully withdrawn.

bThe TiB2-Al/B-SS rod worth ratio was calculated for the 27-element core (Fig. 2). However, the measured ratio is based on rod calibrations made in the October 1995 core when the borated stainless steel shim-safety rods were replaced with TiB2(95%10B)-Al6351.


(Table 10) for the borated stainless steel material. The worth of the newer rods is about 13% larger than that of the original rods. This increase in rod worth is the result of the larger circumference (6.8%) and the larger 10B concentration (42%) of the TiB2-Al6351 shim-safety rods relative to the borated stainless steel ones (see Table 4). Although both shim rod materials are black to thermal neutrons (En<0.625 eV), the higher 10B concentration results in greater epithermal absorption in the TiB2-Al6351 (compare the group-3 IBC's in Table 5). Shim-safety rod worths for both materials were measured in the FNR October 1995 core16. Table 11 compares the measured TiB2-Al/B-SS worth ratios in this core with the values calculated for the 27-element core configuration. The average calculated and measured ratios are 1.13 and 1.11, respectively. Different core configurations and core burnup may be responsible for the somewhat different worth ratios.

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Last modified on July 29, 2008 11:33 +0200