Analog vs. Implicit keff

 Posts: 35
 Joined: Thu Sep 22, 2011 5:27 pm
Analog vs. Implicit keff
Dear all,
I m a new user to SERPENT. I have been running some simple examples (bwr 1 from the lattice validation package). Looking at the output, 2 values for keff are available, one implicit and one analog...I haven't been able to figure out the difference between the two, difference which can be sometime bigger than a standard deviation.
Can someone help me out with the meaning of the various definition of keff?
Thank you,
Regards,
Mathieu
I m a new user to SERPENT. I have been running some simple examples (bwr 1 from the lattice validation package). Looking at the output, 2 values for keff are available, one implicit and one analog...I haven't been able to figure out the difference between the two, difference which can be sometime bigger than a standard deviation.
Can someone help me out with the meaning of the various definition of keff?
Thank you,
Regards,
Mathieu
 Jaakko Leppänen
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Re: Analog vs. Implicit keff
Analog keff is the ratio of new source neutrons produced in two consecutive generations. Implicit keff is calculated using reaction rate estimators for source and loss terms (more precisely imp_keff = nsf/(fiss + abs + leak  n2n). The values should be equivalent within statistics. What kind of differences do you see?
 Jaakko

 Posts: 35
 Joined: Thu Sep 22, 2011 5:27 pm
Re: Analog vs. Implicit keff
Jaakko,
for the BWR 1 case, after the 500 cycles here is what I obtain:
keff (analog) = 1.07512 +/ 0.00115 [1.07286 1.07738]
keff (implicit) = 1.07705 +/ 0.00060 [1.07587 1.07823]
I m also puzzled by the fact that the standard deviation for the implicit keff is much smaller that the analog one even though the implicit keff comes from the combination of various reaction rates with standard deviation that should be in the range of the analog keff...
Also talking about the different keff in the output, I m guessing that col_keff is the equivalent of k(collision) in MCNP and abs_keff the equivalent of (k absorption). Is that correct?
Thanks for your help,
Mathieu
for the BWR 1 case, after the 500 cycles here is what I obtain:
keff (analog) = 1.07512 +/ 0.00115 [1.07286 1.07738]
keff (implicit) = 1.07705 +/ 0.00060 [1.07587 1.07823]
I m also puzzled by the fact that the standard deviation for the implicit keff is much smaller that the analog one even though the implicit keff comes from the combination of various reaction rates with standard deviation that should be in the range of the analog keff...
Also talking about the different keff in the output, I m guessing that col_keff is the equivalent of k(collision) in MCNP and abs_keff the equivalent of (k absorption). Is that correct?
Thanks for your help,
Mathieu
 Jaakko Leppänen
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Re: Analog vs. Implicit keff
Well, the value of the implicit estimator lies within the 95% confidence interval of the analog estimator, so statistically the difference isn't that significant.
The larger statistical error for the analog estimator comes from the fact that there is more variation in the number of new source points per generation than there is in the source and loss rates.
The naming convention is not the same as in MCNP, and the terms are used somewhat loosely. Collision estimate of keff is similar to the MCNP tracklength estimate, with the difference that the scores are based on collisions instead of track lengths. The absorption estimator, on the other hand, is similar to the collision estimator in MCNP. Notice also that ABS_KEFF and IMP_KEFF are the same parameter.
The naming of the parameters is something I should have payed more attention to in the early stages of code development. The reason I got the terminology confused is that the code was designed more for group constant generation than criticality calculations.
The larger statistical error for the analog estimator comes from the fact that there is more variation in the number of new source points per generation than there is in the source and loss rates.
The naming convention is not the same as in MCNP, and the terms are used somewhat loosely. Collision estimate of keff is similar to the MCNP tracklength estimate, with the difference that the scores are based on collisions instead of track lengths. The absorption estimator, on the other hand, is similar to the collision estimator in MCNP. Notice also that ABS_KEFF and IMP_KEFF are the same parameter.
The naming of the parameters is something I should have payed more attention to in the early stages of code development. The reason I got the terminology confused is that the code was designed more for group constant generation than criticality calculations.
 Jaakko
Re: Analog vs. Implicit keff
Jaakko,
Should it be:
imp_keff = nsf/(abs + leak  n2n)
instead of:
imp_keff = nsf/(fiss + abs + leak  n2n) ?
Should it be:
imp_keff = nsf/(abs + leak  n2n)
instead of:
imp_keff = nsf/(fiss + abs + leak  n2n) ?
 Jaakko Leppänen
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Re: Analog vs. Implicit keff
You are right. By absorption I meant capture. In your formula abs = fiss + capt. so imp_keff = nsf/(abs + leak  n2n) = nsf/(fiss + capt + leak  n2n)
 Jaakko

 Posts: 35
 Joined: Thu Sep 22, 2011 5:27 pm
Re: Analog vs. Implicit keff
Dear all,
I'm studying Molten Salt Reactor type lattice with Thorium/MOX/F,Li,Be fuel. There is an unrealistic discrepancy between kanalog and kimplicit for this type of fuel (k_analog = 0.9 and k_implicit = 1.1)....when replaced with regular UO2 fuel, there is no discrepancy anymore...
Have you come across such behavior? Is that a user error (I couldn't attached the input, so I copied my input below), if so what am I doing wrong?
Thanks for your help,
Mathieu
==========================================================================
%  PWR MOX/UOX lattice (SCALEstyle input format) 
%  Problem title:
set title "MSR lattice"
%  Cross section library file path:
set acelib "/afs/psi.ch/project/fast_lrs/workspace/COD/SERP/xsdata/endfb7/sss_endfb7u.xsdata"
% 
%  Material definitions ("comp block"):
%  Molten Salt Fuel
mat fuel 8.762e2
90232.03c 3.778e3
94238.03c 6.359e3
94239.03c 3.906e5
94240.03c 1.513e5
94241.03c 5.018e6
94242.03c 3.177e6
3007.03c 2.260e2
4009.03c 5.037e3
9019.03c 4.978e2
%  VVER fuel
mat fuel2 10.45700
92235.03c 0.03173
92238.03c 0.84977
8016.03c 0.11850
%  Water with Grid plates:
mat graphite 9.226e2
6000.03c 9.226e2
% 
%  Parameters ("param block"):
%  ptable for unresolved resonance region
set ures 1
%  Periodic boundary condition:
set bc 3
%  Neutron population and criticality cycles:
set pop 2000 50 1
% 
%  Geometry ("geom block"):
%  Core lattice ("global unit 0"):
surf 1 cyl 0.0 0.0 6.64
surf 2 hexyc 0.0 0.0 11.55
cell 100 0 fuel 1
cell 101 0 graphite 1 2
cell 102 0 outside 2
% 
I'm studying Molten Salt Reactor type lattice with Thorium/MOX/F,Li,Be fuel. There is an unrealistic discrepancy between kanalog and kimplicit for this type of fuel (k_analog = 0.9 and k_implicit = 1.1)....when replaced with regular UO2 fuel, there is no discrepancy anymore...
Have you come across such behavior? Is that a user error (I couldn't attached the input, so I copied my input below), if so what am I doing wrong?
Thanks for your help,
Mathieu
==========================================================================
%  PWR MOX/UOX lattice (SCALEstyle input format) 
%  Problem title:
set title "MSR lattice"
%  Cross section library file path:
set acelib "/afs/psi.ch/project/fast_lrs/workspace/COD/SERP/xsdata/endfb7/sss_endfb7u.xsdata"
% 
%  Material definitions ("comp block"):
%  Molten Salt Fuel
mat fuel 8.762e2
90232.03c 3.778e3
94238.03c 6.359e3
94239.03c 3.906e5
94240.03c 1.513e5
94241.03c 5.018e6
94242.03c 3.177e6
3007.03c 2.260e2
4009.03c 5.037e3
9019.03c 4.978e2
%  VVER fuel
mat fuel2 10.45700
92235.03c 0.03173
92238.03c 0.84977
8016.03c 0.11850
%  Water with Grid plates:
mat graphite 9.226e2
6000.03c 9.226e2
% 
%  Parameters ("param block"):
%  ptable for unresolved resonance region
set ures 1
%  Periodic boundary condition:
set bc 3
%  Neutron population and criticality cycles:
set pop 2000 50 1
% 
%  Geometry ("geom block"):
%  Core lattice ("global unit 0"):
surf 1 cyl 0.0 0.0 6.64
surf 2 hexyc 0.0 0.0 11.55
cell 100 0 fuel 1
cell 101 0 graphite 1 2
cell 102 0 outside 2
% 
Re: Analog vs. Implicit keff
Ciao Mathieu!
I don't have serpent on this computer so I can not really help you... sorry.
I have just few considerations, looking at your input:
 can you post the statistical error of k (both) ?
 in mat "fuel" you have a huge amount of Pu238 (94238.03c),
it is probably U238 (92238.03c)
 you put in "set pop" almost no skip cycles,
I believe that in this reactor the distribution of fission source
(near the center of the fuel channel or closer to the graphite)
is quite important
anyway these considerations can not explain such a discrepancy between kanalog and kimplicit...
Ciao
Manu
I don't have serpent on this computer so I can not really help you... sorry.
I have just few considerations, looking at your input:
 can you post the statistical error of k (both) ?
 in mat "fuel" you have a huge amount of Pu238 (94238.03c),
it is probably U238 (92238.03c)
 you put in "set pop" almost no skip cycles,
I believe that in this reactor the distribution of fission source
(near the center of the fuel channel or closer to the graphite)
is quite important
anyway these considerations can not explain such a discrepancy between kanalog and kimplicit...
Ciao
Manu
Manuele Aufiero
LPSC/IN2P3/CNRS Grenoble
LPSC/IN2P3/CNRS Grenoble

 Posts: 35
 Joined: Thu Sep 22, 2011 5:27 pm
Re: Analog vs. Implicit keff
Hey Manu,
The isotope ID was good (Pu238; I m looking at a Th cycle, so no U238) but the amount was wrong...it should have been 6.359e7.
Changing the material description fixed the issue, ie here is the final keff:
keff (analog) = 0.78810 +/ 0.00133 [0.78549 0.79072]
keff (implicit) = 0.78710 +/ 0.00062 [0.78589 0.78831]
I m still wondering why the keff analog was so different from the implicit one with a big amount of Pu238...it is not obvious to me.
Thanks for your help, though !
M
The isotope ID was good (Pu238; I m looking at a Th cycle, so no U238) but the amount was wrong...it should have been 6.359e7.
Changing the material description fixed the issue, ie here is the final keff:
keff (analog) = 0.78810 +/ 0.00133 [0.78549 0.79072]
keff (implicit) = 0.78710 +/ 0.00062 [0.78589 0.78831]
I m still wondering why the keff analog was so different from the implicit one with a big amount of Pu238...it is not obvious to me.
Thanks for your help, though !
M
 Jaakko Leppänen
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Re: Analog vs. Implicit keff
It's probably just statistics. I rerun your calculation and got keff's that were both below unity. Could you try running the same case a couple of time just to see if the problem repeats itself or not? And increase the number of skip cycles from 1 to something like 20.
 Jaakko