CRITICALITY EXCURSION ANALYSIS - Nuclear Energy · PDF fileCRITICALITY EXCURSION ANALYSIS TRACY Benchmark I ... they have different configuration of thermocouples to each other. Type-1

CRITICALITY EXCURSION ANALYSIS

TRACY Benchmark I IDENTIFICATION NUMBER: TRACY-LEU-SOL-STEP-001, 002, 003, 004, 005 KEY WORDS: Low enrichment, Solution, Step reactivity insertion 1.0 DETAILED DESCRIPTION

Many experiments1-7) have been performed to study criticality accident with solution fuel, however, obtained data have been not available in useful form for long time. TRACY Benchmark problem was made to provide experimental condition and obtained data of fission yield, power, temperature and pressure in organized form, which should be useful for the calculation by various criticality accident evaluation codes. The benchmark is expected to be beneficial to evaluate and/or improve such numerical codes through its analysis and to give the basis of the common knowledge of criticality accident.

The feature of TRACY benchmark problem is as follows; - Low enriched uranyl nitrate solution, - Co-axial double cylinders tank, - Three methods of reactivity insertion.

In this benchmark, the experiments of pulse reactivity insertion are provided, that is the simplest method of reactivity insertion for TRACY experiments. The selected experiment and its ID number are tabulated in Table 1.1.

Table 1.1 Benchmark case and its excess reactivity. ID number Run number Excess reactivity ($)

001 100 0.30 002 143 0.70 003 72 1.10 004 196 2.00 005 203 2.97

1.1 Overview of Experiment

Low enriched Uranyl nitrate aqueous solution is contained in a cylindrical core tank made of SUS304L stainless steel. There is a guide tube in its vertical center line for a transient rod, Tr-rod, which contains B4C inside it. After pumping fuel solution into the core tank, the transient rod is withdrawn from the core in order to insert reactivity. Desired reactivity is achieved by tuning the height of fuel solution. During free excursion, power, temperature and core pressure are measured. At the end, Tr-rod was inserted to shutdown. 1.2 Description of Experimental Configuration

The core tank has an annular shape with 52cm outer and 7.6cm inner diameter. The effective cross section area for solution fuel is 1918 cm2. For more information, see Fig.1.1, 1.2 and 1.3. In Fig.1.3, the position 0.0mm of the Tr-rod means that the bottom of B4C inside the Tr-rod is 90mm below of the bottom of the fuel solution. The solution height is measured a needle type level gauge with accuracy of ±0.25mm.

700

550

80

1875

150

25

20

Core bottom

250

10t

3.5t

38.15

405520

Figure 1.1: Schematic view of TRACY core tank.

76.3

3.5

10

50

36

15028

80

15

550

500

150

130

75

Core thermometer

Fuel feed/drain lineSUS304LOD34.0/ID28.0

Pressure gauge

Core tank

(Unit : mm)

14080

195

Thermocouples (Type-1)Guide tube：SUS304LOD25.2/ID19.4 mm

Microwave level gaugeGuide tube：ZircaloyOD22.94/ t 2.34

100

30° Neutron source guide tubeSUS304TPOD89.1/ t 4.0

10

Core tank support

42.7

Pressure gauge

100

Polyethylene moderator for Fission chamberOD47.0/ID7.0 mmLength = 100mmAt 250mm from core bottom(to the center)

Figure 1.2: Schematic view of TRACY core tank cross section (detail).

0.0(Core bottom)

-80.0-90.0-100.0

Hc (Critical solutionlevel)

260.0250.0

38.1534.65

30.9527.45

18.00[13.40]

16.00[9.90]

15.50

0.0

B4CSUS304(Cladding for Tr-rod) SUS304L (Core tank)

[9.40] Unit：mm

The numbers in the bracket [ ] show the size for Rod I.

Figure 1.3: Schematic view of cross section of TRACY core tank and Tr-rod.

1.3 Description of Material Data

The fuel solution is uranyl nitrate solution, which consists of uranyl nitrate [UO2(NO3)2], free nitric acid [HNO3], and water [H2O]. The enrichment of 235U is 9.98 wt.%. Tables 1.2 through 1.6 give standard value of composition and atomic number density of materials.

Table 1.2: Solution fuel conditions at 25°C.

ID Run NO. I.R.($) U Conc.(gU/L) Acidity(N)001 100 0.30 392.9 0.66002 143 0.70 375.9 0.64003 72 1.10 393.5 0.74004 196 2.00 385.5 0.58005 203 2.97 388.2 0.58

Table 1.3: Fuel conditions and kinetic parameters at 25.5°C. U-235 enrichment (%) 9.98Uranium concentration (gU/L) 390Acid morality (mol/L) 0.77Solution height (cm) 50.88Neutron multiplication factor[keff] 1.0111Effective delayed neutron fraction[βeff] 7.5x10-3

Prompt neutron life time [Λ](sec) 4.6x10-5

Table 1.4: Atom number densities of the fuel solution with the concentration of 390 gU/L at 25.5°C.

Nucleus Number density (atoms/barn.cm)H 5.7292x10-2

N 2.4394x10-3

O 3.7708x10-2

U235 9.9622x10-5

U238 8.8823x10-4

Table 1.5: Atom number densities of SUS304L at 25.5°C. Nucleus Number density (atoms/barn.cm)

C 1.1939x10-4

Si 1.7004x10-3

Cr 1.7450x10-2

Mn 1.7385x10-3

Fe 5.7180x10-2

Ni 8.9482x10-3

Si 4.4682x10-5

Table 1.6: Atom number densities of air at 25.5°C. Nucleus Number density (atoms/barn.cm)

O16 1.8789x10-6

N14 5.7238x10-6

1.4 Description of External Neutron Source No external neutron source was used for each experiment. 1.5 Description of Initial States In each experiment, the reactivity is inserted by pulse withdrawal of the transient rod, and there was no external neutron source. Initial conditions are tabulated in Table 1.7.

Table 1.7: Selected experiments and their initial states.

Criticality(Power)

Sol.Level(mm)

Fuel Temp.(°C)

Tr-rodposition

(mm)001 100 0.30 Cri. (1W) 508.52 26.2 471.7002 143 0.70 Sub 551.83 24.8 0.0003 72 1.10 Sub 537.05 26.2 0.0004 196 2.00 Sub 582.50 25.9 0.0005 203 2.97 Cri. (1W) 623.76 26.1 0.0

Run NO.

Initial stateInserted

Reactivity($)ID

1.6 Description of Reactivity Insertion

In each experiment, a transient rod (Tr-rod) was fully inserted initially and was fully withdrawn within 0.2 seconds. Desired reactivity was achieved by following procedure; 1) The criticality solution height for which Tr-rod was fully withdrawn, Hc1, is measured. 2) The solution level, h, corresponding to desired reactivity for the experiment was determined by solving

following formula;

( ) ( ) ⎭⎬⎫

⎩⎨⎧

+−

+−= 2

12

112 λλ

ρc

I HhC

where ρI is desired reactivity, Hcl: critical level of solution, C: constant; , and λ: extrapolation length

)/(1067.7 28 mmcentC ×=)(102 mm=λ .

3) Solution level was tuned to the level h with Tr-rod fully inserted. 4) Tr-rod was withdrawn pneumatically at the time 0. 1.7 Description of the Detector or Measurement Systems and Measured Results Reactor power, fuel solution temperature and core pressure were measured.

1.7.1 Measurement of Power Levels – There were three neutron detectors. Two were linear channels and one was log channel. They were on ceiling of the core room right above the core tank as shown in Fig. 4. As the log detector, a cadmium covered 235U fission chamber was employed, which was covered with 10mm-thick polyethylene and 1mm-thick cadmium in order to detect epi-thermal neutrons. It was placed in a lead shielding of 10cm-thick to reduce the noise due to gamma rays, which was about 2.5m far from the core. 1.7.2 Measurement of Temperature Levels and Distributions – Almel-chromel thermocouples were used to measure the temperature distribution in fuel solution. There were two types of thermocouple groups, they have different configuration of thermocouples to each other. Type-1 group was used for all experiments. Type-2 was used for R196 and R203 experiments. Type-1 has response time of about 1s and type-2, 0.1s.

1.7.3 Measurement of Pressure Levels – Core pressure was measured with a pressure gauge installed to the side wall of the core tank. The pressure was observed for more than 1.5$ of reactivity insertion.

2.0 EVALUATION OF DATA 2.1 Evaluation of Power Levels and Distributions

There is a difference in measured values between linear channel and log channel. Such difference is less than 5% for reactivity lower than 1.5$. However, it increases as inserted reactivity increases. The difference is about 17% for R196(2.0$), about 48% for R203(2.97$). 2.2 Evaluation of Temperature Levels and Distributions

Thermocouples have response of 0.1 to 1 second. The accuracy is ±1.5°C. 2.3 Evaluation of Pressure Levels and Distributions

The base line of the pressure decreases after the first peak power. That may be due to temperature change of solution fuel and the noises due to radiation. Amount of uncertainty is unknown.

3.0 CALCULATION MODEL OF KINETICS CODES

Four kinetics codes, AGNES8), CRITEX9), INCTAC10), TRACE11) were used for sample calculations of the benchmark problems. AGNES, CRITEX and TRACE are based on one-point approximation and INCTAC solves neutron transportation equation by the finite element method. Brief summary of those codes are described hereinafter.

3.1 AGNES

This code models the transient criticality of a fissile solution contained in a cylindrical vessel with vertical walls. Temperature, radiolytic gas void and boiling void feedback are taken into account. Cooling by natural convection of air outside of core or forced cooling by water can be calculated. Total number of fission is calculated based on the power profile.

3.1.1 Neutronics – One-point kinetics equation is solved. The calculation geometry consists of three regions such as fuel, container and coolant. The

calculation regarding neutron is done in fuel region only. The basic equation of AGNES2 is the one-point kinetics equation as follows;

.,6

1

iiii

i

ii CPdt

dCSCPdtdP λβλβρ

−Λ

=++Λ−

= ∑=

Nuclear solution fuel region is assumed to be homogeneous and only cylindrical shape can be calculated by using R-Z coordinate.

As temperature reactivity feed back, many effects such as Doppler effect, scattering cross section effect, density effect, and volume expansion effect can be taken into account, if the reactivity coefficients of those are evaluated beforehand.

3.1.2 Thermodynamics –Average temperature is considered in fuel, container and coolant region.

The fuel and coolant regions connect each only to the container region, and the energy released by fission in the fuel region goes to the coolant region through the container region. The temperatures denoted by Ti are calculated as follows;

),()()()()( 111 +−− −−−+=∂

∂iiiiiiii

iipi TThATThAPV

tT

CV γρ

where i denotes region number; 1 for fuel, 2 for container and 3 for coolant region. The first term of the right hand side is the energy released in the region i, and the second and third are the energy transferred from or to the adjacent regions. The heat transfer from the container region to the structural materials connected directly to the container and to the natural convection of air can be calculated.

3.1.3 Radiolysis –Modified energy model is adopted. It assumes followings; 1) Radiolytic gas is created in proportion to the power. 2) Concentration of radiolytic gas beyond a threshold gives rise to void which gives reactivity

feedback. 3) Growth rate of gas void is proportional to the power and excess radiolytic gas concentration. 4) Gas void moves to the solution surface and disappears.

Main parameters are Ci,j ; the mol density of radiolytic gas, the gas void fraction Fij in a mesh (i,j) , νt ; void-energy transfer coefficient, C0, the saturation mol density of dissociation gas, G ; gas production rate.

3.1.4 Calculation Procedure – The atomic number densities calculated using SST12) formula are shown in Table 3.1. Using those values, kinetics parameters shown in Table 3.2, (βeff = 0.0076, Λ = 0.00004864s) and reactivity temperature effect (ρt(cent) = -3.7578∆T - 0.00544∆T2) and its void effect (ρv(cent) = -43.7%V - 0.946%V2) are estimated using SRAC13) and TWODANT14) codes with JENDL-3.215) library. The reactivity insertion time was assumed to be 0.15s, which is almost the same as the time for the transient rod passes through the full height of the fuel solution. The initial power density was assumed to be 1x10-5W/m3, which is based on a

measurement by neutron detectors for start up with no external neutron source condition. In each simulation, the temperature and void feedback reactivity coefficients were used with a weight which denotes the effect of the no-uniform distribution of the temperature and the void, and its value was 1.6 at the first. It changed to be unity exponentially with a time constant, TCT, which denotes the effect of convection driven by buoyancy or void. TCT was determined to be the same order as the peak power profile for each case, and TCT = 500s for R100, 80s for R143, 30s for R72 and 5s for R196 and R203. For the parameters which affect the creation of radiolysis dissociation gas void, the saturated concentration of dissociation gas, CD, was 15 mol/m3. The generation rate of dissociation gas, G, was 6x10-7 mol/J for the case with less than 1$ and 3x10-7 mol/J for the case greater than 1$. Those values are determined so that the power profile is reproduced for the best. The energy-void transfer coefficient, ν, was determined so that the experimental data could be reproduced for the best and was 1x10-7 m6/J/mol through all cases.

Table 3.1: Atom number density of the fuel solution with the concentration of 390 gU/L at 25.5°C.

Nucleus Number density (atoms/barn.cm)H 5.7292x10-2

N 2.4394x10-3

O 3.7708x10-2

U235 9.9622x10-5

U238 8.8823x10-4

Table 3.2: Delayed neutron fraction and decay constant with the concentration of 390 gU/L at 25.5°C.

Delayed Neutron Fraction Decay Constant [1/s]

β1 2.5490E-04 1.2703E-02 β2 1.6521E-03 3.1704E-02 β3 1.4940E-03 1.1525E-01 β4 3.0053E-03 3.1161E-01 β5 8.9084E-04 1.4003E+00 β6 3.2420E-04 3.8740E+00 βeff (total) 7.6213E-03 ---

3.2 CRITEX This code models the transient criticality of a fissile solution contained in an open cylindrical vessel with

vertical walls, so that the solution is able to expand vertically (thermal dilatation, production of radiolytic gas bubble). The solution vertical extent is divided with axial meshes into a number of volumes that allows to calculate the axial movement of the solution and the following reactivity effect. The energy deposited in the volumes is calculated based on the power profile (assuming fundamental neutronic mode), coupled with the central power calculated with the point kinetic equation.

3.2.1 Neutronics – One-point kinetics equation is solved.

3.2.2 Thermal – hydraulics – Heat conduction and natural convection are considered.

3.2.3 Radiolysis – Radiolytic gas bubble migration is modeled by means of a conservation equation

with bubble migration velocity and a source term.

3.2.4 Calculation procedure – Kinetics parameters such as neutron life time, delayed neutron constants, Doppler coefficients and etc. are tabulated as internal data, they have been evaluated with WIMS or APOLLO deterministic neutronics code.

3.3 INCTAC

INCTAC is applicable to the analysis of criticality accident of aqueous homogeneous fuel solution system. Neutronic transient model is composed of equations for the kinetics and for the spatial distributions, which are deduced from the time dependent multi-group transport equations with the quasi steady state assumption.Thermo-hydraulic transient model is composed of complete set of the mass, momentum and energy equations together with the two-phase flow assumptions.

3.3.1 Neutronics – Quasi-steady state approximation or transport theory is used. 3.3.2 Thermal – hydraulics – Heat conduction is solved with pseudo 3 dimensional calculation.

Two phase flow model with liquid and gas is adapted. 3.3.3 Radiolysis – Gas concentration is calculated as follows;

( ) GNCvtC

moll =Γ=⋅∇+∂∂ : before saturation ( C < C0 )

lv : liquid flow velocity [m/s]

GNmol =Γ : radiolysis gas generation rate [(mol/m3 )/s] C < C0 : after the saturation ( C ≥ C0 ) and gas (void) generation rate is GNM a=Γ

where, Γ: radiolysis gas (void) generation rate [(kg/ m3)/s] Ma: molecular weight of radiolysis gas [kg/mol] G: energy to generate radiolysis gas [mol/J] N: power density [watt/ m3] C: radiolysis gas concentration [mol/ m3] C0: radiolysis gas saturation (threshold) concentration[mol/ m3]

Mass conservation of non-condensable gas (void) is denoted as follows;

( ) 0=⋅∇+∂

∂ga

a

tυαραρ

α : void fraction [-] ρg : density of void [kg/m 3 ] νg: void flow velocity [m/s]

3.3.4 Calculation procedure– The atomic number densities calculated using SST12) formula are

shown in Table 3.3. Based on those values, evaluated kinetics parameters are tabulated in Table 3.4. Neutron cross sections used are based on SCALE-4.4 44 group library. Delayed neutrons are evaluated using SRAC9513) with JENDL-3.214) library.

Table 3.3: Atom number density of the fuel solution with the concentration of 390 gU/L at 20°C.

H 5.7917E-02 N 2.3371E-03 O 3.7765E-02 U-235 9.9723E-05 U-238 8.8814E-04 At base state: 20 deg-C and no void.

Table 3.4: Delayed neutron fraction and decay constant with the concentration of 390 gU/L at 20°C.

Delayed Neutron

Fraction Decay Constant

[1/s] β1 2.5084E-04 1.2710E-02 β2 1.6285E-03 3.1704E-02 β3 1.4697E-03 1.1525E-01 β4 2.9606E-03 3.1162E-01 β5 8.7734E-04 1.4003E+00 β6 3.1936E-04 3.8740E+00 βeff (total) 7.5064E-03 ---

3.4 TRACE

3.4.1 Neutronics – TRACE code adopts the point kinetics approximation with 6 group neutron precursors. The code assumes that calculations begin when the system attains delayed criticality (keff=1) at time zero. The spatial power distribution is assumed constant during transients. Fuel solution temperature feedback and void feedback reactivities were taken into account. The fuel solution region is divided into coarse meshes in 2-D cylindrical geometry. The feedback reactivity induced by fuel solution temperature change and void generation are calculated by using a spatial weighting function. For the present benchmark calculations the power weighting function was adopted, i.e. cosine and Jo Bessel functions for axial and radial dimensions, respectively.

3.4.2 Thermal – hydraulics – The heat transfer model in the fuel solution is treated by a transient

heat conduction model in 2-D cylindrical coordinates. The spatial distribution of the heat generation from neutron fission reactions is assumed constant during simulation (represented by cosine and Jo Bessel function in axial and radial dimensions, respectively). The effect of complex fluid motion on the distribution of solution temperature is modeled by a temperature mixing parameter. The vessel is divided only into two lumped regions, i.e. the side wall and the bottom wall. The heat transfer from the vessel walls to the surrounding air is also approximated by air natural convection. The natural heat transfer coefficients (at the inner and outer sides of the vessel walls) are calculated inside the code. Different coefficients are used for horizontal and vertical walls.

3.4.3 Radiolysis – The radiolytic gas modeling of TRACE code mainly consists of two models, one

for the radiolytic gas bubble nucleation formation and another for the gas bubble velocity. The main parameters for this model are the G value (proportional to the number of product molecules formed for each 100 eV of energy absorbed by the system; input in mol/J) and the critical number of moles of radiolytic gas per unit void volume (mol/m3). It should be noted here, although the fuel solution region is divided into coarse meshes in 2-D cylindrical geometry, the bubble movement is treated in the axial direction only (no bubble movement in the radial direction). For gas bubble velocity a model which is originally based on the CRITEX code empirical model is adopted, where a continuous function of bubble velocity is developed based on the absolute value and the sign of the inverse period. The absolute value of the inverse period is a measure of how fast the power changing and the sign of the inverse period is set to -1, 0, and 1 for negative (decreasing power), zero (local minima or maxima) and positive inverse period (increasing power), respectively.

3.4.4 Calculation Procedure – For TRACY benchmark calculations, atomic number density of fuel solution, TRACY vessel (SUS-304L), and the surrounding air were taken from Tables 4, 5, 6, and 7 of the Specification of TRACY Benchmark I. The kinetic parameters (delayed neutron fractions, prompt neutron lifetime, neutron generation time, temperature coefficients and void coefficients) were determined by using SRAC code system and JENDL-3.2 library and shown in Table 3.5 and 3.6. First, using SRAC’s PIJ module (1-D collision probabilistic method) transport group constants were prepared in 107 neutron energy group for each region, i.e. the fuel, vessel and the surrounding air. Second, using SRAC’s ANISN module (1-D neutron transport approximation, S8 P1, cylindrical geometry) 16 group diffusion constants were prepared. SRAC’s CITATION module (neutron diffusion approximation, cylindrical geometry) was then used for estimating the delayed neutron fractions, prompt neutron lifetime and neutron generation time. The temperature coefficients were calculated using SRAC’s TWOTRAN module by varying the fuel solution temperature (adjusting also its density; 5 temperature points; maximum temperature 100°C) and 2-nd order polynomial fitting was applied to obtain the coefficients. Similarly, the void coefficients were calculated by varying the fuel density (but keeping the fuel solution temperature constant, i.e. fixed at the room temperature) (4 points; maximum void ratio 60 %) and 2-nd order polynomial fitting was applied to obtain the coefficients.

Table 3.5 Kinetic parameters for TRACY benchmark calculations by TRACE code

Parameter TRACY experiments 2.5140E-04 1.6199E-03 1.4689E-03 2.9505E-03 8.7515E-04

Delayed neutron fractions

3.1892E-04 1.2703E-02 3.1704E-02 1.1524E-01 3.1160E-01 1.4003E+00

Precursor decay constant (s)

3.8739E+00 Generation time (s) 4.8585E-05

Prompt neutron lifetime (s) 4.7624E-05

Table 3.6 Temperature and void reactivity coefficients for TRACY benchmark calculations by TRACE code

Feedback reactivity

TRACY experiments

Temperature (T, Kelvin)

5 2( ) 6.0 10 0.0335T Tρ − T∆ ∆ = × ∆ − ∆

Void (V, % volume)

2( ) 0.0015 0.4715V Vρ∆ = − − V

Note: Reactivity is given in $ unit.

4.0 RESULTS OF SAMPLE CALCULATIONS A summary of sample calculations by using four kinetics codes explained section 3 is described in this section. 4.1 ID001 -R100(0.3$)

This is the case for which the excess reactivity is very low so that no radiolytic gas void was observed. As shown in Figures 4.1 to 4.4, the power increases gradually with the course of time to reach the peak at about 190s, then decreases in the rather gradual manner.

Table 4.1 summaries the calculation results. Each code reproduced the whole power profile well and for maximum inverse period, experimental value was reproduced within 3 to 16%. However, it is seen that calculated power runs late to the experiment in some cases and the delay time of the 1st peak time is up to 30s. Temperature reactivity feedback was well evaluated and calculated, and most of the codes reproduced the peak power within 6 to 19% and the released energy to the 1st peak is within 12 to 15%.

The total energy was reproduced within 5 to 19% by most of the codes. Because the whole power profile was reproduced very well, calculated value of the final solution temperature was almost the same as the experimental value.

Core pressure due to radiolytic gas void was not observed.

Table 4.1 Summary of calculation results for R100. Items B. MARK AGNES CRITEX INCTAC TRACE

Max. Inverse Period (s-1) 6.51E-02 6.34E-02 5.5E-02 5.7E-02 5.70E-02

Time to 1st Peak (s) 189.39 184.29 223 206.55 204.1 Power @ 1st Peak (w) 3.16E+04 3.34E+04 3.75E+04 2.99E+04 4.53E+04 Energy to 1st Peak (J) 1.47E+06 1.28E+06 1.69E+06 1.29E+06 1.94E+06 Fissions to 1st Peak 4.58E+16 4.00E+16 5.28E+16 4.03E+16 6.06E+16 Time to 1st Minimum (s) - - - - - Power @ 1st Minimum (w) - - - - - Energy to 1st Minimum (J) - - - - - Fissions to 1st Minimum - - - - -

Total Energy (J) 4.20E+06 3.99E+06 5.00E+06 3.85E+06 6.45E+06 Total Fissions 1.31E+17 1.25E+17 1.56E+17 1.20E+17 2.02E+17

Temperature Initial Temperature (°C) 26.2 26.2 26.2 26.2 26.2 Max. Temperature (°C) - - - - - Min. Temperature (°C) - - - - - Final Temperature (°C) 36.2 35.6 37.3 35.5 42.7

Pressure Maximum Pressure (MPa) - - - - 3.53E-03

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

0 100 200 300 400 500 600

Time(s)

Power(W)

Experiment

Analysis

Fig.4.1 AGNES calculation -R100(0.3$).

1.E+10

1.E+11

1.E+12

1.E+13

1.E+14

1.E+15

1.E+16

0 100 200 300 400 500 600

Time (s)

Pow

er (f

issi

ons/

s)

Calculations

Experiment

Fig.4.2 CRITEX calculation -R100(0.3$).

101

102

103

104

105

106

0 100 200 300 400 500 600

0 100 200 300 400 500 600

RUN100measuredcomputed

reactor power [W]

measured time [sec]

computed time [sec]

PEAK POWER 2.99E+4[W] computed 3.42E+4[W] measured

Fig.4.3 INCTAC calculation -R100(0.3$).

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

0 100 200 300 400 500 600

Time (s)

Pow

er (

W)

Experiment

TRACE

Fig.4.4 TRACE calculation -R100(0.3$).

4.2 ID002 -R143(0.7$)

This is the case for which the excess reactivity is lower than 1$. As shown in Figures 4.5 to 4.8, the power increases gradually with the course of time to reach the peak at about 39s, then decreases about one decade.

Table 4.2 summaries the calculated results. Calculated power profile is slightly different from the experiment in some cases; experimental value was reproduced within 8 to 19% for maximum inverse period and the time to 1st power peak is in the range between 20 and 44s. Temperature reactivity feedback was well evaluated and calculated, and most of the codes reproduced the peak power within 8 to 14% and the released energy to the 1st peak is within 1 to 9%.

Most of the codes estimated power higher than experiment and the total energy was over estimated up to 49%. One of the reasons may be that a small power dip after the peak could not be simulated well. Due to the over estimation of the total energy, the final solution temperature was also overestimated several degrees by most of the codes.


Table 4.2 Summary of calculation results for R143.

Items B. MARK AGNES CRITEX INCTAC TRACE Max. Inverse Period (s-1) 6.29E-01 6.93E-01 5.1E-01 6.9E-01 5.80E-01

Time to 1st Peak (s) 39.313 39.021 28.4 19.841 44.1 Power @ 1st Peak (w) 3.72E+05 3.41E+05 4.23E+05 4.49E+05 4.01E+05 Energy to 1st Peak (J) 1.78E+06 1.79E+06 2.50E+06 1.94E+06 1.84E+06 Fissions to 1st Peak 5.55E+16 5.58E+16 7.81E+16 6.06E+16 5.75E+16 Time to 1st Minimum (s) - - - - - Power @ 1st Minimum (w) - - - - - Energy to 1st Minimum (J) - - - - - Fissions to 1st Minimum - - - - -




1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0 20 40 60 80

Time (s)

Pow

er

(W)

Experiment

Analysis


1.E+10

1.E+11

1.E+12

1.E+13

1.E+14

1.E+15

1.E+16

1.E+17

0 10 20 30 40 50 60 70

Time (s)

Pow

er (f

issi

ons)

80

Calculations

Experiment


100

101

102

103

104

105

106

107

20 30 40 50 60 70 80

0 10 20 30 40 50

RUN143

60

measuredcomputed

reactor power [W]

measured time [sec]

computed time [sec]



1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

0 10 20 30 40 50 60 70 80

Time (s)

Pow

er

(W)

Experiment

TRACE

Fig.4.8 TRACE calculation -R143(0.7$). 4.3 ID003 -R72(1.1$)

This is the case for which the excess reactivity is slightly beyond 1$. As shown in Figures 4.9 to 14, the power increases rapidly to reach the peak at about 1.6s, then decreases about two decades.

Table 4.3 summaries the calculation results. Each code reproduced power profile well. Experimental value was reproduced within 9 to 31% for maximum inverse period and the time to 1st power peak is in the range between 0.8 and 1.7s. Most of the codes reproduced the peak power within 30 to 36%, while the released energy to the 1st peak is within up to 4%.

Most of the codes estimated power higher than experiment and the total energy was over estimated up to 16%. One of the reasons may be that a noticeable power dip after the peak could not be simulated well. Due to the over estimation of the total energy, the final solution temperature was also overestimated several degrees by most of the codes.


Table 4.3 Summary of calculation results for R72.

Items B. MARK AGNES CRITEX INCTAC TRACE Max. Inverse Period (s-1) 2.55E+01 2.77E+01 1.76E+01 2.00E+01 3.94E+01

Time to 1st Peak (s) 1.5756 1.5727 1.73 0.848 1.5 Power @ 1st Peak (w) 1.44E+07 1.47E+07 9.10E+06 1.00E+07 9.45E+06 Energy to 1st Peak (J) 1.10E+06 1.14E+06 1.06E+06 1.07E+06 1.02E+06 Fissions to 1st Peak 3.43E+16 3.58E+16 3.31E+16 3.35E+16 3.19E+16 Time to 1st Minimum (s) 14.23 - - - - Power @ 1st Minimum (w) 3.77E+04 - - - - Energy to 1st Minimum (J) 8.75E+06 - - - - Fissions to 1st Minimum 2.74E+17 - - - -




1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1 1.2 1.4 1.6 1.8 2

Time (s)

Pow

er

(W)

Experiment

Analysis


1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

0 50 100

Time (s)

Pow

er

(W)

Experiment

Analysis


1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

1.E+13

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

0 20 40 60 80 100 120 140

Time (s)

Pow

er (f

issi

ons/

s)

Calculations

Experiment

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

0 2 4 6 8 10


102

103

104

105

106

107

108

0 2 4 6 8

0 2 4 6 8

RUN72

10

10

measuredcomputed

reac

tor

powe

r [W]

measured time [sec]

computed time [sec]



102

103

104

105

106

107

108

0 20 40 60 80 100 120 140

0 20 40 60 80 100 120 140


reactor power [W]

measured time [sec]

computed time [sec]



1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

0 20 40 60 80 100 120 140

Time (s)

Pow

er (

W)

Experiment

TRACE


4.4 ID004 -R196(2.0$)

This is the case for which the excess reactivity is so high that core pressure due to radiolytic gas void is observed. As shown in Figures 4.15 to 20, the power increases rapidly to reach the peak at about 0.35s, then decreases about four decades.

Table 4.4 summaries the calculation results. Each code reproduced power profile well. Experimental value was reproduced within up to 8% for maximum inverse period and the estimated time to 1st power peak is in the range between 0.210 and 0.345s. Temperature reactivity feedback was well evaluated and calculated, and most of the codes reproduced the peak power within 0.5 to 8%, and the released energy to the 1st peak is within 0.8 to 7%.

Most of the codes over estimated the power profile and the total energy was over estimated 13 to 19%. Due to the over estimation of the total energy, the final solution temperature was also overestimated several degrees by most of the codes.

Observation of core pressure indicates that a lot of radiolytic gas void was created in the core, which might give rise to four decades of power decrease after the peak due to large negative feedback reactivity. Core pressure due to radiolytic gas void was reproduced well by some codes. Table 4.4 Summary of calculation results for R196.





Pressure Maximum Pressure (MPa) 3.04E-01 3.30E-01 - - 2.08E-02

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

0.2 0.25 0.3 0.35 0.4

Time (s)

Pow

er

(W)

Experiment

Analysis


1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

0 5 10 15 20

Time (s)

Pow

er

(W)

Experiment

Analysis


1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

1.E+13

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

0 2 4 6 8 10 12 14 16 18 2

Time (s)

Pow

er (f

issi

ons/

s)

0

Calculations

Experiment

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

0 1 2 3


101

102

103

104

105

106

107

108

109

0.0 0.2 0.4 0.6 0.8 1.0

0 0.2 0.4 0.6 0.8 1


reactor power [W]

measured time [sec]

computed time [sec]



101

102

103

104

105

106

107

108

109

0 5 10 15 20

0 5 10 15 20


react

or p

ower

[W]

measured time [sec]

computed time [sec]



1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

1.0E+09

0 2 4 6 8 10 12 14 16 18 20

Time (s)

Pow

er

(W)

Experiment

TRACE


4.5 ID005 -R203(2.97$)

This is the case for which the excess reactivity is the largest and core pressure due to radiolytic gas void is observed. As shown in Figures 4.21 to 26, the power increases rapidly to reach the peak at about 0.19s, then decreases about four decades.

Table 4.5 summarizes the calculation results. Each code reproduced power profile well. Experimental value was reproduced within up to 9% for maximum inverse period and the estimated time to 1st power peak is in the range between 0.13 and 0.187s. Temperature reactivity feedback was well evaluated and calculated, and most of the codes reproduced the peak power within 3.8 to 6.3%, and the released energy to the 1st peak is within 1 to 23%.

While the peak power is well estimated, most of the codes reproduced the total energy within -26 to +33% and the estimated final solution temperature was in the range between 58 and 88 °C. These large differences should be due to the estimation of the radiolytic gas void feedback reactivity.

Observation of core pressure indicates that a lot of radiolytic gas void was created in the core, which might give rise to four decades of power decrease after the peak due to large negative feedback reactivity. Core pressure due to radiolytic gas void was reproduced well by some codes. Table 4.5 Summary of calculation results for R203.





Pressure Maximum Pressure (MPa) 8.95E-01 1.01E+00 - 8.4E-01 2.66E-02

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

0.1 0.15 0.2 0.25 0.3

Time (s)

Pow

er

(W)

Experiment

Analysis

Fig.21 AGNES calculation -R203(2.97$).

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

0 2 4 6

Time (s)

Pow

er

(W)

8

Experiment

Analysis


1.E+10

1.E+11

1.E+12

1.E+13

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

0 1 2 3 4 5 6 7 8

Time (s)

Pow

er (f

issi

ons)

Calculations

Experience

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

0.0 0.1 0.2 0.3 0.4 0.5


101

103

105

107

109

0.00 0.10 0.20 0.30 0.40 0.50

0 0.1 0.2 0.3 0.4 0.5


reactor power [W]

measured time [sec]

computed time [sec]



101

103

105

107

109

0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

RUN203

8

8

measuredcomputed

reactor power [W]

measured time [sec]

computed time [sec]



1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

1.0E+09

1.0E+10

0 2 4 6 8 10

Time (s)

Pow

er

(W)

Experiment

TRACE


4.6 SUMMARY Most items such as the maximum inverse period, first peak power, energy to the first power peak and total fissions are reproduced by each code with the difference of less than 20%. Because the codes rather overestimate the power profiles, the difference is up to 50% for the total fission, although such large difference is rare case. The evaluation of the first peak power is much better for the case of more than 2$ insertion, and the difference is less than 9%. However, the difference in the total fission is not so good. It may be due to the large overestimation of the power after the first peak where the effect of radiolytic gas void cannot be ignored. It can be seen that the difference for solution temperature is rather larger for large reactivity insertion cases than those for small reactivity insertion cases. It should be mentioned that the solution temperature is measured at a point in the core tank, so it is not the same as the average values. Therefore there can essentially be some difference between the benchmark value and the average solution temperature evaluated using one-point kinetics code. 5.0 REFERENCES 1) M. Dunenfeld and R. Stitt, “Summary Review of the Kinetic Experiments on Water Boilers,” NAA-SR-

7087 (1963). 2) P.Lécorché, et al., "A Review of the Experiments Performed to determine the Radiological Consequences

of a Criticality Accident," Y-CDC-12 (1973). 3) F.Barbry and J.P.Rozain, "Objectives and Summary of Experiments on The Formation of Radiolysis Gas

Carried Out using The Silene Reactor," SRSC 89.08 (1989). 4) K.Nakajima, et al., "TRACY Transient Experiment Databook 1)Pulse Withdrawal Experiment," JAERI-

Data/Code 2002-005 (2002). 5) K.Nakajima, et al., "TRACY Transient Experiment Databook 2)Ramp Withdrawal Experiment," JAERI-

Data/Code 2002-006 (2002). 6) K.Nakajima, et al., "TRACY Transient Experiment Databook 3)Ramp Feed Experiment," JAERI-

Data/Code 2002-007 (2002). 7) Y. Yamane, et al., “Transient Characteristics Observed in TRACY Supercritical Experiments,” Proc. 7th

International Conference on Nuclear Criticality Safety (ICNC2003), JAERI-Conf 2003-019 (2003). 8) K.Nakajima, et al., "A Kinetics Code for Criticality Accident Analysis of Fissile Solution Systems:

AGNES2," JAERI-Data/Code 2002-004 (2002). 9) D.J.Mather, et al., "CRITEX – A Computer Program to Calculate Criticality Excursions in Fissile Liquid

Systems," SRD R 380 (1984). 10) S. Mitake, et al., “Development of INCTAC code for Analyzing Criticality Accident Phenomena,” Proc.

7th International Conference on Nuclear Criticality Safety (ICNC2003), JAERI-Conf 2003-019 (2003). 11) B.Basoglu, et al., "Development of a New Simulation Code for Evaluation of Criticality Transients

Involving Fissile Solution Boiling," JAERI-Data/Code 98-011 (1998). 12) S.Sakurai and S.Tachimori, “Density Equation of Aqueous Solution Containing Plutonium (IV),

Uranium (VI) and Nitric Acid”, J. Nucl. Sci. Technol., 33, 187(1996). 13) K.Okamura, et al., "SRAC95; General Purpose Neutronics Code System," JAERI-Data/Code 96-015

(1996). 14) R. Alcouffe, et al., "DANTSYS: A Diffusion Accelerated Neutral Particle Transport Code System, " LA-

12969-M (1995). 15) T.Nakagawa, et al., "Japanese Evaluated Nuclear Data Library version 3 revision-2: JENDL-3.2," J. Nucl.

Sci. Technol, 32, 1259 (1995).

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