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

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Subcriticality level inferring in the ADS
systemsspatial corrective factors for Area
Method
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
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Layout of the presentation

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

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Principle of Reactivity Measurements

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 ? 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
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Principle of Reactivity Measurements

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.
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MUSE-4 experiment layout
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.
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MUSE-4 experiment layout and objectives
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).
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Experimental techniques analyzed
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PNS Area Method
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 of ?), 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.
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PNS Area Method a static approach
Neutron source is represented by
Q(r,?,E,t)Q(r,?,E)d(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
and the initial condition ?p(r,?,E,t)0
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Defining the prompt neutron flux
Fp(r,O,E)?Fp(r,O,E,t)dt and after integrating
over the time
0
Where the initial condition was used and the fact
that lim (t??) Fp0 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 Reactor
Theory, Van Nostrand Reinhold Company, 1970
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PNS Area Method a static approach
The time integrated prompt-neutron flux satisfies
the ordinary time-independent transport equation

The total time-integrated flux F(r,O,E) satisfies
the same equation with ?p(1-ß) replaced by ?
Prompt Neutron Area

Prompt Neutron Area
-?()
Delayed Neutron Area
Delayed Neutron Area


S. Glasstone, G. I. Bell, Nuclear Reactor
Theory, Van Nostrand Reinhold Company, 1970
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ERANOS (European Reactor ANalysis Optimized
System) calculation description

• 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

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MUSE-4 SC0 1108 Fuel Cells Configuration DT
Source
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 PT 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.
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Sc0 results
MUSE-4 SC0 1108 cells configuration, D-T Source,
3 SR up SR1 down PR down Dispersion means the
ratio ?(MSM)/ ?(AREA)exp or calc.
Reactivity ?() Reactivity ?() Dispersion Dispersion Dispersion
Detector Experimental Calculated Experimental Calculated (E-C)/C ()
I -14.3 -13.1 0.8762 0.9561 7.5
L -12.9 -13.0 0.9713 0.9658 -0.6
F -11.9 -11.8 1.0529 1.0603 0.7
M -12.7 -12.8 0.9866 0.9783 -0.8
G -13.0 -12.4 0.9638 1.0121 5.0
N -12.1 -11.8 1.0355 1.0587 2.2
H -12.6 -12.1 0.9944 1.0369 4.3
A -12.7 -12.4 0.9866 1.0140 2.8
B -13.0 -12.8 0.9638 0.9824 1.9
E. Gonzáles-Romero (ADOPT 03)
Mean/St.Dev -12.6 0.4
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MUSE-4 SC2 1106 Fuel Cells Configuration DT
Source
Reference Reactivity (Rod Drop MSM) -8.7
0.5
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SC2 results
MUSE-4 SC2 1106 cells configuration, D-T
Source Dispersion means the ratio ?(Reference)/
?(AREA)exp or calc.
Reactivity ?() Reactivity ?() Dispersion Dispersion Dispersion
Detector Experimental Calculated Experimental Calculated (E-C)/C ()
I -8.6 -8.6 1.012 1.012 0.0
L -8.8 -8.9 0.989 0.978 1.1
F -8.9 -9.0 0.978 0.967 1.1
C -8.7 -8.8 1.000 0.989 1.1
G -9.0 -8.8 0.967 0.989 -2.2
D -8.9 -8.7 0.978 1.000 -2.2
H -8.9 -8.7 0.978 1.000 -2.2
A -8.9 -8.8 0.978 0.989 -1.1
B -9.0 -8.8 0.967 0.989 -2.2
Mean/St.Dev -8.86 0.16
E. Gonzáles-Romero, ADOPT 03
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MUSE-4 SC3 1104 Fuel Cells Configuration DT
Source
Reference Reactivity (Rod Drop MSM) -13.6
0.8
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SC3 results
MUSE-4 SC3 972 cells configuration, D-T
Source Dispersion means the ratio ?(Reference)/
?(AREA)exp or calc.
Reactivity ?() Reactivity ?() Dispersion Dispersion Dispersion
Detector Experimental Calculated Experimental Calculated (E-C)/C ()
I -12.9 -13.0 1.054 1.046 0.8
L -14.4 -13.8 0.944 0.986 -4.2
F -14.0 -14.0 0.971 0.971 0.0
C -13.7 -13.7 0.993 0.993 0.0
A -13.8 -13.6 0.986 1.000 -1.4
B -13.8 -13.6 0.986 1.000 -1.4
J -12.9 -12.9 1.054 1.054 0.0
K -12.9 -12.8 1.054 1.063 -0.8
Mean/St.Dev -13.7 0.5
From Y. Rugama
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Experimental results for a-fitting analysis
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PNS a-fitting analysis in MUSE-4
Concerning the PNS a-fitting method (which
invokes the evaluation of ?), three types of
possible MUSE-4 responses to a short pulse may be
obtained

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

1. The system responses show a 1/t-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.

1. The system responses do not show any 1/t-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.

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Corrective factors approach to the a-fitting
analysis
When PNS a-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
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Corrective factors approach to the a-fitting
analysis flow chart
Prompt version of the inhour equation (apgtgtli)
Directly evaluated by the a-eigenvalue equation
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Corrective factors approach to the a-fitting
analysis flow chart
It is possible to follow the standard way to
calculate ap starting from the k eigenvalue
equation
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Prompt a Calculation procedure performed by means
of ERANOS
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
K1
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Prompt a Calculation procedure MUSE-4 SC0
analysis
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)
keff ? ßeff ?K(ms) ap,k (s-1)
k calculation 0.95970 -0.04200 0.00335 0.4683 -96821
kd ? ßeff,d ?d(ms) ap (s-1)
a calculation 0.95843 -0.04337 0.00368 1.0069 -46730
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Reactivity values calculated by using fK and ?
eigenfunctions are similar (compensation in the
product a ?)
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Spectra in the shielding and in the reflector
? eigenfunctions (a calculation) fk
eigenfunctions (k calculation)
Reflector
Shielding
According to the theory, differences between ?
and fk 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 a/v is equal or greater than the St
term. Such happens at low energies and inside, or
near, reflecting regions at low absorption, where
the profile of the ? shapes functions spectra
will be more marked than those of the fk
functions, because of the lower absorptions.
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Comparison among the calculated results
yexp(apt)
In any case, point kinetics ap slope seems to
agree with exponential 1/t-slope only in the
shield and for a short time period.
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MCNP Vs Experimental results
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.
Experimental results show that for large
subcriticalities, 1/t-slopes are different for
core, reflector and shield detectors positions.
MCNP results well reproduce in the core the
experimental responses.
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Conclusions

• 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.

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THANK YOU FOR YOUR KIND HOSPITALITY
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Prompt a Calculation procedure pre-analysis
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
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Prompt a Calculation procedure pre analysis
results
Red data indicate eigenvalues directly evaluated
by ERANOS (RZ model)
keff ? ßeff ?K(ms) ap,k (s-1)
k calculation 0.97124 -0.02961 0.00335 0.51634 -63834
kd ? ßeff,d ?d(ms) ap (s-1)
a calculation 0.97166 -0.02916 0.00369 0.81633 -40240
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ap / ap,k Ratio at Different Reactivity Levels
ap/ap,k ratio deviates from the unity depending
on the subriticality level
ap / ap,k
Far from criticality, the deviation is mainly due
to the differences between the mean neutron
generation times ?K and ?d evaluated using
respectively fK and ? eigenfunctions.
keff
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Spectra in the core
Core
? eigenfunctions (a calculation) fk
eigenfunctions (k calculation)
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Spectra in the shielding and core selected
positions
? eigenfunctions (a calculation) fk
eigenfunctions (k calculation)
Reflector
Shielding
According to the theory, differences between ?
and fk 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 a/v is equal or greater than the St
term. Such happens at low energies and inside, or
near, reflecting regions at low absorption, where
the profile of the ? shapes functions spectra
will be more marked than those of the fk
functions, because of the lower absorptions.
a5