TUBRNP (Transuranus/FRAPCON) model

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The discussion focuses on understanding the TUBRNP model for calculating isotope compositions and radial power profiles in light water reactors using UO2. The user is developing an algorithm to replicate the model's calculations, including matrix creation for isotopic composition and power profile determination. Issues arise with the shape function's volumetric normalization and the conversion factor alpha, particularly regarding discrepancies in units and values between their calculations and published literature. Clarifications are sought on the correct units and references, emphasizing the importance of consistent unit usage in nuclear material calculations. The conversation highlights the complexities involved in accurately modeling nuclear fuel behavior and the need for precise parameter definitions.
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Hello,

I am currently trying to understand the TUBRNP model which is used to calculate the isotope compositions and the radial power profile evolution with the burnup. I am talking about the basic model (the one from 1994 with only 6 isotopes taken into account) in the case of a LWR with UO2.

In order to understand it, I try to create a simple algorithm doing the same thing. i will be the burnup step and n the inner iteration index for convergence.
1) From an initial composition vector N_0 (determined with the enrichment), calculate the parameter A.

2) Determine the matrix M so that I can calculate the next composition N(n)_i+1 with N(n)_i+1*M=b with b depending on the old concentration N_old (see below the code for a given position):
Code:
function [M,b]=create_matrices(delta_BU,A,sigma_abs,sigma_capt,radial_pos,shape_function,N_average,N_old)
f_r=shape_function(radial_pos);

M=zeros(6);
%U235
M(1,1)=1+sigma_abs(1)*A*delta_BU;
%U238
M(2,2)=1;
%Pu239
M(3,3)=1+sigma_abs(3)*A*delta_BU;
%Pu240
M(4,3)=-sigma_capt(3)*A*delta_BU;
M(4,4)=1+sigma_abs(4)*A*delta_BU;
%Pu241
M(5,4)=-sigma_capt(4)*A*delta_BU;
M(5,5)=1+sigma_abs(5)*A*delta_BU;
%Pu242
M(6,5)=-sigma_capt(5)*A*delta_BU;
M(6,6)=1+sigma_abs(6)*A*delta_BU;

b=N_old;
b(2)=b(2)-N_average(2)*sigma_abs(2)*f_r*A*delta_BU;
b(3)=b(3)+N_average(2)*sigma_abs(2)*f_r*A*delta_BU;

3) Calculate the inverse diffusion length (kappa) from this new composition, then the flux with the Bessel function.
4) Calculate the power profile from the average power that I want and the flux.
5) Determine the burnup increment from the power, the initial uranium mass and the simulated time increment
6) Compare the compositions N(n)_i+1 and N(n-1)_i+1. If the difference is small enough, go to next burnup step, otherwise take N(n-1)_i+1 to calculate a new A and a new matrix M, ...

First, does this reproduce properly TUBRNP? I took the cross sections and the p_i parameters for the shape function from the FRAPCON user manual.

Then I have several issues with the shape function f(r). As there is a volumetric normalization step, the outer radius value matters. Thus, the unit of this parameter influences the results and unfortunately in the publication, no unit is given. If I try to reproduce the Plutonium radial profiles given in this paper with cm as units, the shape is not peak enough, but if I try with mm, it is not working either.

Finally, I face some problems calculating the conversion factor alpha. From what I understand, it is a factor created to convert time to burnup units. As I am working with MWd/kg_HM as burnup unit and cm as spatial unit, we have : [BU]=[alpha]*(fission/cm^3)/(kg/cm^3) =MWd/kg_HM
So for me : [alpha]=MWd/fission
alpha=200MeV/reac*1.602e-19/(24*3600)=3.7088e-22
If my calculation is correct, then why in the Lassman's paper the value of alpha is 3.35e-16 in the case of MWd/t_HM ? This 1e6 factor does not make sense to me.

I would really appreciate your help on this ! And if you have questions or if I have not been clear enough on a point, please ask me.
 
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Which version of Frapcon? Besides the Frapcon manual, what are one's references?
I presume one references: K. Lassmann et al, Journal of Nuclear Materials 208, Issue 3, February 1994, pp. 223-231

Also, 1 MeV = 1.60218e-13 J.
 
Hello and thank you for you answer,

I based this on the FRAPCON 3.4 Manual that can be found here : https://www.nrc.gov/docs/ML1110/ML11101A005.pdf from page 2.15 to 2.18

Moreover, the reference you put is the one I was talking about.

Regarding the conversion, I am using 1 Mev = 1.602e-19 MJ because the burnup unit is MWd/kg_HM, and in the case of the paper it is MWd/t_HM. Therefore, to my mind, this cannot be the reason of this 1e6 factor.
 
yrob said:
1 Mev = 1.602e-19 MJ
This is correct, but since one did not put the units, it looked like one off by a factor of 1e6.

In the paper, Lassmann states burnup in units of MWd/tHM, and 1 tHM = 1000 kgHM. Also, I expect he used SI or MKS for other numbers, e.g., density in kg/m3. In one's equation, one uses density in (kg/cm^3). I would recommend caution in mixing units.

Frapcon uses a conversion factor of 3.8e-16 with burnup given in terms of MWd/t, and density of the fuel is in terms of kgHMO2/m3, which is converted to kgHM/m3 by a factor of 0.8815. The FALCON code also uses this approach.
 
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