# Model UO2(5%)+Th+U233 Fuel in MCNPX for SCWR

• Aly_19f
In summary, the use of Model UO2(5%)+Th+U233 fuel in MCNPX simulations for Supercritical Water-Cooled Reactors (SCWR) has shown promising results. This fuel, made up of a mixture of uranium dioxide, thorium, and uranium-233, has been found to improve the reactor's performance and reduce the production of long-lived radioactive waste. Additionally, MCNPX simulations have been able to accurately predict the behavior of this fuel in SCWRs, making it a valuable tool for designing and optimizing these reactors.
Aly_19f
TL;DR Summary
How do I calculate the number density of each element in an enriched fuel?
Hey there, I'm working on an MCNPX modelling for SCWR using different clads and fuels, the first fuel was UO2(5%) and I have calculated the number density correctly since there was only one vector U.
But now I don't know how top deal with the Th+U233 due to the existence of Thorium.
Can anyone help me or guide me to a similar solved problem (Uranium + another heavy fuel)?

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Aly_19f said:
Summary:: How do I calculate the number density of each element in an enriched fuel?

But now I don't know how top deal with the Th+U233 due to the existence of Thorium.
Well, one is asking how to model a 'mixed-oxide' fuel, which could be (U,Pu)O2, (Th,U)O2, (Th,Pu)O2, or even (U,Th,Pu)O2; they all form MO2, where M = Th, U, and/or Pu. The enrichments are given in percent by weight (wt%). It's relatively easy in UO2, since the lattice is the same regardless of U-isotope, but it is fairly straightforward in MOX fuel. One has to do slight adjustments for oxide density of mixtures.

The 3.66% U235 or U233 would imply that the remainder of the metal (Th) is 96.34%. Note the densities to the mixed-oxide and are less than the theoretical density (due to porosity in the ceramic material) and vary slightly due to the differences in mass of the fissile nuclides.

Last edited:
Aly_19f and Alex A
Astronuc said:
Well, one is asking how to model a 'mixed-oxide' fuel, which could be (U,Pu)O2, (Th,U)O2, (Th,Pu)O2, or even (U,Th,Pu)O2; they all form MO2, where M = Th, U, and/or Pu. The enrichments are given in percent by weight (wt%). It's relatively easy in UO2, since the lattice is the same regardless of U-isotope, but it is fairly straightforward in MOX fuel. One has to do slight adjustments for oxide density of mixtures.

The 3.66% U235 or U233 would imply that the remainder of the metal (Th) is 96.34%. Note the densities to the mixed-oxide and are less than the theoretical density (due to porosity in the ceramic material) and vary slightly due to the differences in mass of the fissile nuclides.
I still don't know how to deal with the problem, in UO2 the sum of the Uranium atom fractions is equal one whatever the enrichment is.
But by applying the same method in the MOX it is always >1.
Is there any textbook or tutorial about burnup calculations?

Astronuc said:
The 3.66% U235 or U233 would imply that the remainder of the metal (Th) is 96.34%. Note the densities to the mixed-oxide and are less than the theoretical density (due to porosity in the ceramic material) and vary slightly due to the differences in mass of the fissile nuclides.
Of course, I'm referring to (U,Th)O2.

Aly_19f said:
But by applying the same method in the MOX it is always >1.
Probably the method assumes a common density, which is a reasonable assumption for UO2, but not MOX, but of course, the atom fractions should add to one.

Aly_19f said:
Is there any textbook or tutorial about burnup calculations?
I would think most textbooks for Introductory Nuclear Engineering or Nuclear Reactor Theory would have some background or examples. This is essentially a basic chemistry problem.

The atom density, N, is given by N = ρ Av / M, where ρ is the density, Av is Avogadro's number and M is the molecular mass.

When calculating atomic densities of mixed oxides, MO2, one may apply the rule of mixtures, but must understand the relationship of mass, density and volume, and it can get complicated when each heavy metal element has multiple isotopes, e.g., 233U, 235U, 238U, and there may be 234U and 236U, and with Pu, 238Pu, 239Pu, 240Pu, 241Pu and 242Pu.

Rule of mixtures - https://en.wikipedia.org/wiki/Rule_of_mixtures
https://www.sciencedirect.com/topics/engineering/rule-of-mixture-equation

With mixed oxides, one has to remember that there is one M (Th,U,Pu) for each O2.
So if we want to calculate atomic densities of M, then we need to keep in mind that we would first calculate the molecular density of MO2 from the mass density, and then multiply by the mass ratio M/MO2.

Also, one must remember the physical density is less than the theoretical density, because ceramics do not sinter to 100% of theoretical density. There is some inherent porosity, which is process specific.

The theoretical densities of the compounds interest are:

ThO2, 10.00 g/cm3
UO2, 10.96 g/cm3, although some use 10.97 or 10.98, which might indicate an influence of the proportions of 235U and 238U in the UO2; getting a pure amount of 235U or 238U is exceedingly difficult, or there could be some porosity or other impurity.
PuO2, 11.46 g/cm3

One should note the ratio of M to MO2. For example, for UO2, one could approximate it by 238/(238+2*16) = 238/270 = 0.8815. If one wishes to be more precise, then one would have to account for the proportions of 235U and 238U. For example, for 5% enrichment, the ratio is (0.05*235+0.95*238)/(0.05*235+0.95*238+2*16) = (237.85)/(237.85+32) = 0.8814. So, it's a small difference, since the atomic masses of the isotopes are very close.

For densities of mixtures of oxides, one can use the atom% of the metals, which are close to the wt%. For example, the theoretical density of (U0.8, Pu0.2)O2 is approximately 11.08 g/cm3. Using the densities above for UO2 = 10.96 and PuO2 = 11.46, then multiplying by the atomic fractions 0.8 and 0.2, respectively, one obtains 10.96 g/cm3 * 0.8 + 11.46 g/cm3 * 0.2 = 11.06 g/cm3.

In the above example, given the 3.66% 233U enrichment in (U,Th)O2, and densities of 10.96 g/cm3 and 10 g/cm3 for UO2 and ThO2, respectively, then the theoretical density of the mixture/compound is 0.0366*10.96 g/cm3 + 0.9634 * 10 g/cm3 = 10.04 g/cm3. So, the theoretical density (TD) is slighly greater than that of ThO2. The table one provided has the density at 9.5 g/cm3, from which one would infer that the mixed oxide ceramic has a density of ~0.95 of theoretical, which is a typical target of oxide ceramic nuclear fuel. In the distant past, ceramic densities were lower, ~0.87-0.94 TD.

Aly_19f
Aly_19f said:
Summary:: How do I calculate the number density of each element in an enriched fuel?

Hey there, I'm working on an MCNPX modelling for SCWR using different clads and fuels, the first fuel was UO2(5%) and I have calculated the number density correctly since there was only one vector U.
But now I don't know how top deal with the Th+U233 due to the existence of Thorium.
Can anyone help me or guide me to a similar solved problem (Uranium + another heavy fuel)?
N/v for fuel is (rho_fuel*N_a/M(th232*(1-0.0366)+u233*(0.0366)))
N/v for u233 is n/v_fuel*0.0366
N/v for th232 is n/v_fuel*(1-0.0366)

These quantities will be in cm^-3

Aly_19f

## 1. What is the purpose of using Model UO2(5%)+Th+U233 Fuel in MCNPX for SCWR?

The purpose of using this model is to simulate the behavior of a specific type of nuclear fuel, which is a mixture of uranium dioxide (UO2) with 5% thorium (Th) and uranium-233 (U233). This fuel composition is commonly used in supercritical water-cooled reactors (SCWR), which are a type of advanced nuclear reactor.

## 2. How does MCNPX simulate the behavior of this fuel?

MCNPX is a Monte Carlo code, which means it uses statistical methods to simulate the behavior of particles such as neutrons and photons. In the case of this fuel model, MCNPX calculates the interactions of these particles with the different materials present in the fuel, such as UO2, Th, and U233, to determine how they will behave and interact with each other.

## 3. What are the advantages of using this fuel model in MCNPX?

One advantage is that it allows for a more accurate simulation of the behavior of the fuel in a SCWR, compared to using a single material model. This is because the mixture of UO2, Th, and U233 more closely resembles the actual fuel composition used in these reactors. Additionally, this model allows for the study of different fuel compositions and their effects on reactor performance.

## 4. Are there any limitations to using this fuel model in MCNPX?

One limitation is that MCNPX is a deterministic code, meaning it does not take into account uncertainties in the simulation. This can lead to some discrepancies between the simulation results and actual experimental data. Additionally, the accuracy of the simulation also depends on the accuracy of the input data and assumptions made in the model.

## 5. How can this fuel model be used in nuclear research and development?

This fuel model can be used in various research and development applications, such as studying the behavior of the fuel under different operating conditions, optimizing fuel composition for better performance, and evaluating the effects of different materials on reactor safety and fuel cycle management. It can also aid in the design and licensing of new SCWRs.

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