FO-PR-001 r2
GERENCIA DE INGENIERÍA NUCLEAR
TÍTULO:
1.
DEPARTAMENTO FÍSICA DE NEUTRONES
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INFORME TÉCNICO
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Dispersión de neutrones térmicos en iones H+ en soluciones ácidas acuosas
(Thermal neutron scattering in H+ ions in aqueous acid solutions)
OBJETIVO
Desarrollo de una biblioteca de secciones eficaces neutrónicas para representar el scattering
de neutrones en iones H+ libres en soluciones acuosas, y su aplicación a sistemas críticos.
2.
ALCANCE
Cálculo de reactores con ácidos en solución.
Alcance de distribución del documento: Gerencia de Ingeniería
Preparó
Intervino
calidad
Revisó
J.R.
Granada
J.I. Márquez
Damián
Aprobó
J.
Dawidowski
REVISIONES
Rev.
Fecha
Modificaciones
FECHA DE VIGENCIA:
ESTADO DEL DOCUMENTO
DISTRIBUCIÓN
Copia N◦ :
Distribuyó:
Fecha:
Firma:
NOTA: Este documento es propiedad de CNEA y se reserva todos los derechos legales sobre él. No está
permitida la explotación, transferencia o liberación de ninguna información en el contenido, ni hacer
reproducciones y entregarlas a terceros sin un acuerdo previo y escrito de CNEA.
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ÍNDICE
1. OBJETIVO
1
2. ALCANCE
1
3. INTRODUCTION
3
4. THERMAL NEUTRON CROSS SECTION FOR H+ IONS
3
4.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
5. APPLICATION
4
5.1 Pseudo-material method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
5.2 Test 1: UO2 pin cell with HNO3 at pH = 3 . . . . . . . . . . . . . . . . . . . . . . .
5
5.3 Test 2: Plutonium nitrate solution benchmark (PU-SOL-THERM-018, case 1) . .
6
6. CONCLUSIONS
7
7. REFERENCES
8
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Thermal neutron scattering in H+ ions in aqueous
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INTRODUCTION
In many critical and subcritical systems, acids are present in aqueous solution in the moderator,
either as means of reactivity control (boric acid in LWRs) or for fuel dissolution (nitric acid in reprocessing plants). In all of these cases, it is important to model the thermal scattering of neutrons with
the moderator correctly to calculate the multiplication factor and other reactor physics parameters.
When dissolved in aqueous solutions, strong acids dissociate almost completely, generating H+
ions. These ions have a much different dynamics than the H atoms bound in water and, in principle,
should be treated separately from the perspective of thermal neutron scattering.
The thermal neutron scattering in H atoms bound in water is affected by the dynamics and
structure of the molecule. Water molecules can diffuse, vibrate and rotate, and these degrees of
freedom have to be taken into account to develop a model to calculate the scattering law. On the
other hand, H+ have a much simpler dynamics. Not having molecular structure means the ions do
not have internal degrees of freedom or the ability to rotate: they can only diffuse. The diffusion
coefficient of H+ ions in water is 9.311 × 10−5 cm2 /s[1].
4.
THERMAL NEUTRON CROSS SECTION FOR H+ IONS
4.1
Model
Considering that the H+ ions can only diffuse, the thermal scattering cross section can be calculated using the Egelstaff-Schofield diffusion model [2].
In the LEAPR [3] implementation, the Egelstaff-Schofield model has two parameters: a nondimensional diffusion coefficient c and the translational weight wt .
The translational weight can be computed as:
wt =
mH
mdiff
(1)
Since the diffusional unit is the atom itself, mdiff = mH ⇒ wt = 1.0. This value can also be
deduced from the normalization of weights:
X
wi = 1.0
(2)
i
Being diffusion the only available dynamical mode, it has to have weight equal to unity.
The non dimensional diffusion coefficient can be computed as:
c=
mH D
~wt
(3)
where, in the apropriate units, D = 0.009311 nm2 /ps is the molecular diffusion coefficient, mH =
10.4466 meVps2 nm−2 is the atomic mass of hydrogen, and ~ = 0.6582119 meVps is Dirac’s constant. Using these values, the non-dimensional diffusion coefficient is:
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Thermal neutron scattering in H+ ions in aqueous
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c = 0.1478
4.2
(4)
Results
Using LEAPR, an ENDF-6 MF=7 S(α, β) file was computed. This file was processed with
THERMR to calculate the scattering cross section. In Fig. 1 the total scattering cross section for
H+ ions calculated with this model is compared with the free gas total scattering cross section, and
the scattering cross section of H bound in H2 O.
1000
1
H+ ion
H free gas
H(H2O)
Scattering cross section per H atom [b]
1
100
10
0.0001
0.01
Energy [eV]
1
Figure 1: Scattering cross section for different models of thermal neutron scattering in H atoms.
5.
APPLICATION
5.1
Pseudo-material method
To test the cross section library in MCNP, there is one limitation: two different thermal scattering
treatments have to be applied to the same isotope. To overcome this problem, the pseudo-material
method can be used [4]:
• In the definition of the material that contains the acid, two lines are used to define the proportion
of H1 present in the composition: one for the H1 bound in water, and one for the H+ ions.
• Bound H1 is treated as usual, using the existing cross section set for the library (for ENDF/BVII.0, it is 1001.70c).
• The tool makxsf is used to copy the 1001.70c library into a separate file, and the ZAID
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identifier is changed to an unused, fictitious value (1014.00c).
• When processed in ACER, the thermal scattering library is associated to this new ZAID.
The resulting material cards for MCNP will look like this:
m1
1001.70c <H(H2O) number density>
1014.00c <H+ number density>
mt1 lwtr.10t hion.00t
5.2
Test 1: UO2 pin cell with HNO3 at pH = 3
The first test of the libraries was done with a simple problem: a 1.5 cm-pitch infinite 2D lattice
composed by a 0.5 cm-radius, 3.0 at% enriched UO2 fuel region, and pH = 3 nitric acid aqueous
solution. The geometry for this problem is shown in Fig. 2.
Figure 2: Pin cell geometry used for the test.
The MCNP input for the explicit treatment of the scattering by H+ ions is listed below:
UO2
1 1
2 2
999
pin cell with HNO3 at pH=3 - Explicit treatment of H ions
-10.0 -1 imp:n=1 $ UO2
-1
1 2 -3 4 -5 imp:n=1 $ Nitric acid aqueous solution
0 -2:3:-4:5 imp:n=0
1 cz
*2 px
*3 px
*4 py
*5 py
c UO2
m1
c
m2
0.5
-0.75
+0.75
-0.75
+0.75
92235.70c 0.03 &
92238.70c 0.97 &
8016.70c 2.00
1014.00c 6.0220E-07 &
1001.70c 6.6911E-02 &
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8016.70c 3.3457E-02 &
7014.70c 6.0220E-07
mt2 hion.00t lwtr.10t
c
kcode 10000 1.0 10 10010
ksrc 0.0 0.0 0.0
print
To check the effect of the thermal treatment, a second calculation was performed applying
H(H2 O) thermal scattering treatment to all hydrogen. The difference between the two MCNP input
files is listed below:
1c1
< UO2 pin cell with HNO3 at
--> UO2 pin cell with HNO3 at
16,17c16
< m2
1014.00c 6.0220E-07
<
1001.70c 6.6911E-02
--> m2
1001.70c 6.6912E-02
20c19
< mt2 hion.00t lwtr.10t
--> mt2 lwtr.10t
pH=3 - Explicit treatment of H ions
pH=3 - H ions treated as H(H2O)
&
&
&
The results of these calculations are shown in Table 1.
Table 1: Calculated multiplication factor for the pin cell problem.
Case
keff
H+ ion
1.41871(2)
H(H2 O)
1.41875(3)
According to these results, the explicit treatment of thermal scattering in H+ has no significant
effect in the multiplication factor for this type of problems. This is probably caused because the
amount of ions present in the solution is relatively small: pH = 3 is equivalent to an acid molarity of
0.001M. This corresponds to a number density of 6.0220 × 10−7 atoms/(cm · b), which is 5 orders of
magnitude smaller than the number density of hydrogen atoms bound in water.
5.3
Test 2: Plutonium nitrate solution benchmark (PU-SOL-THERM-018, case 1)
Some of the fissile solution benchmarks available in the ICSBEP Handbook [5] have acid concentrations much higher than the problem analysed above, and could in principle be more sensitive
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to the explicit treatment of thermal scattering in ions. A quick search on the Handbook leads to the
case 1 of benchmark PU-SOL-THERM-018: Water-reflected 24-inch diameter cylinder of Plutonium
(42.9% 240Pu) nitrate solution. This system has a reported acid molarity of 5.02M, which is 5020
times higher than the acid molarity in the previously analysed pin cell.
The number density of H+ ions corresponding to this acid molarity is 3.0230×10−3 atoms/(cm·b).
This value has to be subtracted from the hydrogen composition and introduced separately in the
MCNP input file. The following listing shows the differences that have to be made to the MCNP input
file:
64c64,65
<
1001.70c 5.523500e-02
-->
1001.70c 5.2212E-02
>
1014.00c 3.0230E-03
77c78
< mt1
lwtr.10t
--> mt1
lwtr.10t hion.00t
The results for the calculation using the two approximations are shown in Table 2.
Table 2: Benchmark and calculated multiplication factors for the PU-SOL-THERM-018 benchmark,
case 1.
Case
Benchmark ion
keff
1.00000(340)
H+ ion
1.00910(3)
H(H2 O)
1.00938(3)
In this problem there is a small (28 ± 5 pcm) improvement in the calculation when the new library
is introduced.
6.
CONCLUSIONS
In this paper we presented a simple model for the scattering of thermal neutrons on H+ ions,
using the Egelstaff-Schofield diffusion model. The use of this model included the assumption that all
solvent water behaves like bulk water. Hydration layer effects are not considered.
The effect of this model was tested on two criticality calculations: a fuel pin moderated by an acid
aqueous solution, and a fissile solution benchmark with high acid molarity.
The effect of the library was found to be negligible in the pin cell calculation, and a small improvement was found in the fissile solution system. This result is encouraging, and further testing on other
fissile solution thermal benchmarks should be done.
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Thermal neutron scattering in H+ ions in aqueous
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REFERENCES
[1] Lide, D., 2005. CRC Handbook of Chemistry and Physics. Section 5: Thermochemistry, Electrochemistry, and Kinetics; Ionic Conductivity and Diffusion at Infinite Dilution.
[2] Egelstaff, P., and Schofield, P., 1962. “On the evaluation of the thermal neutron scattering law”.
Nuclear Science and Engineering, 12, pp. 260–270.
[3] MacFarlane, R., 1994. New thermal neutron scattering files for ENDF/B-VI release 2. LA–12639MS. Tech. rep., Los Alamos National Laboratory.
[4] Ivanov, A., Sanchez, V., Stieglitz, R., and Ivanov, K., 2013. “High fidelity simulation of conventional
and innovative lwr with the coupled monte-carlo thermal-hydraulic system mcnp-subchanflow”.
Nuclear Engineering and Design, 262, pp. 264–275.
[5] J. Bess (ed.), 2014. International Handbook of Evaluated Criticality Safety Benchmark Experiments. Tech. rep., OECD/NEA.