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Subcriticality level inferring in the ADS systems: spatial corrective factors for Area Method

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### Subcriticality level inferring in the ADS systems:spatial corrective factors for Area Method

### Layout of the presentation

### Principle of Reactivity Measurements

### Principle of Reactivity Measurements

### MUSE-4 experiment: layout

### MUSE-4 experiment: layout and objectives

### PNS Area Method

### PNS Area Method: a static approach*

### PNS Area Method: a static approach*

### ERANOS (European Reactor ANalysis Optimized System) calculation description

### MUSE-4 SC0 1108 Fuel Cells Configuration – DT Source

### Sc0 results

### MUSE-4 SC2 1106 Fuel Cells Configuration – DT Source

### SC2 results

### MUSE-4 SC3 1104 Fuel Cells Configuration – DT Source

### SC3 results

### PNS α-fitting analysis in MUSE-4

### Corrective factors approach to the α-fitting analysis

### Corrective factors approach to the α-fitting analysis: flow chart

### Corrective factors approach to the α-fitting analysis: flow chart

### Prompt α Calculation procedure performed by means of ERANOS

### Prompt α Calculation procedure: MUSE-4 SC0 analysis

### Spectra in the shielding and in the reflector

### Comparison among the calculated results

### MCNP Vs Experimental results

### Conclusions

### Prompt α Calculation procedure: pre-analysis

### Prompt α Calculation procedure: pre analysis results

### αp / αp,k Ratio at Different Reactivity Levels

### Spectra in the shielding and core selected positions

F. Gabrielli

Forschungszentrum Karlsruhe, Germany

Institut für Kern- und Energietechnik (FZK/IKET)

Second IP-EUROTRANS Internal Training Course

June 7 – 10, 2006

Santiago de Compostela, Spain

1

- Principle of Reactivity Measurements
- MUSE-4 Experiment
- PNS Area Method: a static approach
- Analysis of the Experimental results: Area method analysis
- PNS α-fitting method: L and ap evaluation
- Analysis of the Experimental results: Slope analysis by α-fitting method
- Conclusions

2

Several static/kinetics methods are available to infer the reactivity level of a subcritical system.

All these methods are based on the point kinetics assumption, then assuming that:

- Reactivity does not depend on the detector position, detector type, …
- Some quantities, i.e. the mean neutron generation time Λ which is used in the slope method, do not depend on the subcritical level.

If point kinetics assumptions fail, correction factors are needed.

MUSE-4 experiment supplied a lot of information about this subject

3

Depending on the subcriticality level and on the presence of spatial effects, the subcriticality level of the system may not be inferred by the detectors responses in different positions on the basis of a pure point kinetics approach.

In this case, corrective spatial factors, evaluated by means of calculations, should be applied to the experimental results analyzed by means of one of the point kinetics based methods, in order to infer the actual subcriticality level of the system.

Depending on the used method, corrective factors may have a different amplitude. Thus, from a theoretical point of view, the reliability of a method for inferring the reactivity will be given by the magnitude of the corrective factors to be associated.

4

MUSE(MUltiplication avec Source Externe) program was a series of zero-power experiments carried out at the Cadarache MASURCA facility since 1995 to study the neutronics of ADS.

The main goal was investigating several subcritical configurations (keff is included in the interval 0.95-1) driven by an external source at the reactor center by (d,d) and (d,t) reactions, the incident deuterons being provided by the GENEPI deuteron pulsed accelerator.

5

In particular, the MUSE-4 experimental phase aimed to analyze the system response to neutron pulses provided by GENEPI accelerator (with frequencies from 50 Hz to 4.5 kHz, and less than 1 μs wide), in order to investigate by means of several techniques the possibility to infer the subcritical level of a source driven system, in view of the extrapolation of these methods to an European Transmutation Demonstrator (ETD).

6

is based on the following relationship relative to the areas subtended by the system responses to a neutron pulse:

Concerning the method (which does not invoke the estimate ofΛ), it is not possible "a priori" to evaluate the order of magnitude of correction factors even if the system response appears to be different from a point kinetics behaviour.

This aspect is strictly connected with the integral nature of the PNS area methods

Because of spatial effects, reactivity is function of detector position. These spatial effects can be taken into account by solving inhomogeneous transport time-independent problems.

8

Neutron source is represented by Q(r,,E,t)=Q(r,,E)δ+(t) and

a signal due to prompt neutrons alone is considered

The prompt flux p(r,,E,t) satisfies the transport equation

With the usual free-surface boundary conditions andtheinitial condition p(r,,E,t)=0

∞

~

Defining the prompt neutron flux Φp(r,Ω,E)=∫Φp(r,Ω,E,t)dtand after integrating over the time…

0

Where the initial condition was used and the fact that lim (t)Φp=0 because the reactor is subcritical

Therefore, the time integrated prompt-neutron flux satisfies the ordinary time-indipendent transport equation

Hence, it can be determined by any of standard multigroup methods

[*]

S. Glasstone, G. I. Bell, ‘Nuclear ReactorTheory’, Van Nostrand Reinhold Company, 1970

9

∞

~

∫ D(r,t)dt=∫∫∫σd(r,E)ΦpdVdΩdE

0

~

~

∫∫∫ σd(Φ - Φp)dVdΩdE

The time integrated prompt-neutron flux satisfies

the ordinary time-independent transport equation

~

The total time-integrated flux Φ(r,Ω,E)satisfies the same equation with χp(1-β) replaced by χ

Prompt Neutron Area =

Prompt Neutron Area

-ρ($)=

Delayed Neutron Area

Delayed Neutron Area =

[*]

S. Glasstone, G. I. Bell, ‘Nuclear ReactorTheory’, Van Nostrand Reinhold Company, 1970

10

- A XY model of the configurations was assessed
- The reference reactivity level was tuned via buckling
- JEF2.2 neutron data library was used in ECCO (European Cell Code) cell code
- 33 energy groups transport calculations were performed by means of BISTRO core calculation module

11

The configuration with 3 SR up, SR 1 down and PR down was analyzed

Reference Reactivity:

-12.53 $

(Evaluations based on MSA*/MSM+ measurements in a previous configuration)

*Modified Source Approximation

+Modified Source Multiplication

Experimental data from

E. González-Romero et al., "Pulsed Neutron Source measurements of kinetic parameters in the source-driven fast subcritical core MASURCA", Proc. of the "International Workshop on P&T and ADS Development", SCK-CEN, Mol, Belgium, October 6-8, 2003.

F. Mellier, ‘The MUSE Experiment for the subcritical neutronics validation’, 5th European Framework Program MUSE-4 Deliverable 6, CEA, June 2005.

12

MUSE-4 SC0 1108 cells configuration, D-T Source, 3 SR up SR1 down PR down

Dispersion means the ratio ρ(MSM)/ ρ(AREA)exp or calc.

[*] E. Gonzáles-Romero (ADOPT ’03)

Mean/St.Dev: -12.6 ± 0.4

13

Reference Reactivity

(Rod Drop + MSM):

-8.7 ± 0.5 $

14

MUSE-4 SC2 1106 cells configuration, D-T Source

Dispersion means the ratio ρ(Reference)/ ρ(AREA)exp or calc.

Mean/St.Dev: -8.86 ± 0.16

[*] E. Gonzáles-Romero, ADOPT ‘03

15

Reference Reactivity

(Rod Drop + MSM):

-13.6 ± 0.8 $

16

MUSE-4 SC3 972 cells configuration, D-T Source

Dispersion means the ratio ρ(Reference)/ ρ(AREA)exp or calc.

Mean/St.Dev: -13.7 ± 0.5

[*] From Y. Rugama

17

Concerning the PNS α-fitting method (which invokes the evaluation of Λ), three types of possible MUSE-4 responses to a short pulse may be obtained:

- The system responses show the same 1/τ-slope in all the positions (core, reflector and shield), thus the system behaves as a point.

- The system responses show a 1/τ-slope only in some positions, but not all the slopes are equal; the system does not show an ‘integral’ point kinetics behavior and a reactivity value position-depending will be evaluated. Thus, corrective factors have to be applied in order to take into account the reactivity spatial effects.

- The system responses do not show any 1/τ-slopes; the system does not behave anywhere as a point and only experimental data fitting can try to solve the problem. As in the previous case, corrective factors have to be applied.

19

When PNS α-fitting method is performed, we assumed that, at least in the prompt time domain, the flux behaves like:

if we are coherent with this hypothesis, we have to perform the substitution of our factorised flux into:

Consequently in the prompt time domain, the (time-constant) shape of the flux obeys the eigenvalue relationship:

20

“Prompt version” of the inhour equation (ap>>li)

Directly evaluated by the α-eigenvalue equation

21

It is possible to follow the standard way to calculate αp starting from the k eigenvalue equation:

22

ERANOS core calculation transport spatial modules (BISTRO and TGV/VARIANT)

solve the k eigenvalue equation:

While, for our purpose, the following eigenvalue relationship has to be solved:

…that means performing the following substitution if ERANOS is used

K=1

23

1108 Fuel Cells Configuration (3 SR up, SR 1 down and PR down) – DT Source

Red data indicate eigenvalues directly evaluated by ERANOS (XY model)

-48%

+47%

Reactivity values calculated by using φK and ψ eigenfunctions are similar (compensation in the product α· Λ)

24

ψ eigenfunctions (α calculation)

φk eigenfunctions (k calculation)

Reflector

Shielding

According to the theory, differences between ψ and φk eigenfunctions energy profiles at low energies are mainly observed in the reflector and in the shielding regions: in fact, besides the different fission spectrum, the main differences will be localized in the spatial and energetic regions where α/v is equal or greater than the Σt term. Such happens at low energies and inside, or near, reflecting regions at low absorption, where the profile of the ψ shapes functions spectra will be more marked than those of the φk functions, because of the lower absorptions.

25

Results seem to provide a coherent picture concerning the system location where α-fitting method (with refined Λ evaluation) could be applied, i.e. far from the source.

y=exp(αpt)

In any case, point kinetics αp slope seems to agree with exponential 1/τ-slope only in the shield and for a short time period.

26

Experimental results show that for large subcriticalities, 1/τ-slopes are different for core, reflector and shield detectors positions. MCNP results well reproduce in the core the experimental responses.

Reflector and shield experimental slopes show a double exponential behavior which is not reproduced by MCNP calculations; on the contrary, it looks evident a good agreement for a short time period.

27

- For large subcriticalities, PNS area method seems to be more reliable respect to a-fitting method, for what concerns the order of magnitude of the spatial correction factors (about 5%).
- Concerning the application to the ADS situation, because of the beam time structure required for an ADS, it does not allow an on-line subcritical level monitoring, but can be used as “calibration” technique with regards to some selected positions in the system to be analyzed by alternative methods, like Source Jerk/Prompt Jump (which can work also on-line).
- Codes and data are able to predict the MUSE time-dependent behavior in the core region. The presence of a second exponential behavior in the reflector and shield regions is not evidenced either by the deterministic or by the MCNP simulations.

28

169.6

159

148.4

137.8

121.9

116.6

100.7

95.4

84.8

74.2

63.6

42.4

31.8

21.2

10.6

Positions for neutron spectra analysis

Lead

Shield

66.4 cm, 129.9 cm

Reflector NA/SS

Reflector

57.5 cm, 92.8 cm

MOX1

Radial Shielding

Core

17 cm,92.8 cm

Axial Shielding

Homogenized Beam Pipe

Z (cm)

MOX3

R (cm)

8.28 18.5 33.1 39.7 55.9 97.03

MUSE-4 Sub-Critical ERANOS RZ model: symmetry axis around the Genepi Beam Pipe axis

a1

Red data indicate eigenvalues directly evaluated by ERANOS (RZ model)

-37%

+37%

a2

αp/αp,k ratio deviates from the unity depending on the subriticality level

αp / αp,k

Far from criticality, the deviation is mainly due to the differences between the mean neutron generation times ΛK and Λdevaluated using respectively φK and ψ eigenfunctions.

keff

a3

ψ eigenfunctions (α calculation)

φk eigenfunctions (k calculation)

Reflector

Shielding

According to the theory, differences between ψ and φk eigenfunctions energy profiles at low energies are mainly observed in the reflector and in the shielding regions: in fact, besides the different fission spectrum, the main differences will be localized in the spatial and energetic regions where α/v is equal or greater than the Σt term. Such happens at low energies and inside, or near, reflecting regions at low absorption, where the profile of the ψ shapes functions spectra will be more marked than those of the φk functions, because of the lower absorptions.

a5

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