The thermal properties of the 3013 storage container plus plutonium bearing materials are fundamental to understanding behavior during storage and transportation. For instance, as the temperature increases, outgassing in the container, fill-gas pressure, and water vapor pressure all increase. Changes also occur in the distribution of water between solid phases such as salt, oxide, and container walls and the kinetics of reactions affecting hydrogen gas generation and corrosion. Because of the direct effect that temperature has on pressure and corrosion in this sealed material-storage system, an accurate analysis is needed to correctly anticipate these effects.
Two extensive thermal analyses have been carried out on 3013 containers holding pure plutonium dioxide (PuO2) powders. Both studies were limited by the lack of information available for plutonium dioxide powder thermal conductivity, which controls the thermal behavior in these containers. One study, reported in 1997 by Thad Knight and Robert Steinke of Los Alamos, used the Deissler-Eian correlation for packed beds to estimate the powder thermal conductivity as a function of the porosity and the gas and solid thermal conductivities. They predicted that the thermal conductivity for a plutonium dioxide powder with a porosity of 74 percent at 100 degrees Celsius in air was equal to 0.10 watt per meter kelvin, or W/(m K). In the second study, reported in 1998, Steve Hensel of Savannah River Site estimated that the oxide powder in air had a constant thermal conductivity of 0.079 W/(m K), but no information was provided on how this estimate was made. These two estimates of the powder thermal conductivity differ by 20 percent.
Thermocouples are placed along the diameter of a British Nuclear Fuels, Ltd. (BNFL) 3013 container about 2.5 inches from the bottom. The container is filled with 5 kilograms of plutonium dioxide powder, which extends to within 1.5 inches of the top of the container. Additional thermocouples were located on the outside of the container for measurement.
In an effort to decrease the uncertainty in the current temperature-profile predictions for the plutonium dioxide powder beds, experimental measurements were made of the thermal behavior of pure plutonium oxide powder over a wide range of pressures-0.05 to 334 kilopascals (kPa)-with two different fill gases: argon and helium. In addition, an analytical thermal conductivity model was developed to aid in the analysis of the experimental data and to provide predictive capabilities. The model uses the porosity, pore size, interstitial gas pressure, and the thermal conductivities of the gas and solid to calculate the thermal conductivity of the powder. With the new model, the previous predictions of the thermal profiles in the container can be compared and assessed.
Experimental thermal measurements
Thermal conductivity measurements were performed on a plutonium-239 dioxide bed in a cylindrical stainless steel container equipped with ten thermocouples located radially across the container for temperature profile measurement. The container was loaded with 5.0 kilograms (kg) of plutonium dioxide with a porosity of 77.4 percent and a constant heat generation rate of 2.06 watts per kilogram (W/kg). Because the powder generates heat, it provides a constant heat source. After about four hours, a steady-state temperature profile is achieved and measured.
Helium and argon were used as fill gases because of the large gas conductivity range (thermal conductivities for helium and argon are 0.16 and 0.018 W/(m K) at 27 degrees Celsius, respectively). Typically, at higher gas pressures (greater than 10 kPa), the powder thermal conductivity is controlled by the gas thermal conductivity, so significant differences in the powder thermal behavior would be expected with these two gases.
When plotting the effects of pressure and fill gas on the centerline temperature in the plutonium dioxide bed, it was noted that the centerline temperature increased with decreasing pressure. This effect arises because the gas transitions from the continuum limit to the free molecular flow limit where the gas thermal conductivity is proportional to the pressure. At the lowest pressures used in this study (less than 0.1 kPa), the powder conductivity becomes independent of both pressure and fill gas because solid-solid conduction and thermal radiation pathways are the dominant contributors to temperature in the bed.
Radial temperature profiles with argon and helium as fill gases at pressures greater than 80 kilopascals. The measured pressure dependence at these conditions was unexpected. Red is argon data and blue is helium data.
At higher pressures, the powder thermal behavior does not scale with the fill-gas thermal conductivity as initially hypothesized. From the temperature profiles the estimated powder thermal conductivities at 82 kPa for argon and helium are 0.077 and 0.22 W/(m K), respectively. The powder thermal conductivity with helium as fill gas is only three times that with argon as fill gas. This was surprising because the helium gas thermal conductivity is nine times that of argon under these conditions. These results indicate that the solid conduction pathways are important in the fine plutonium dioxide powder even at higher pressures.
Also, at higher gas pressures the thermal behavior is interesting because the thermal conductivity of the powder is still changing even at pressures greater than 200 kPa. At these pressure the gas thermal conductivity is usually assumed to be in the continuum limit and, therefore, independent of pressure. Further analysis revealed that the small pore and particle sizes in the plutonium powder appear to be responsible for the pressure dependence at higher pressures.
Plutonium dioxide powder thermal conduction model
A thermal conductivity model was developed to predict the thermal behavior of this fine, highly porous powder because the experimental measurements could not be reasonably interpreted using existing thermal conductivity models. The thermal conductivity expression for keff shown in the box below was derived using the powder schematic shown below it.
In this expression, keff is the effective thermal conductivity of the powder, is the porosity of the powder, kg.o is the thermal conductivity of the fill gas in the outer pore region, kg.in is the thermal conductivity of the fill gas in the interparticle contact fraction (L/D), ksolid is the thermal conductivity of the PuO2 solid, is the contact roughness, and defines the solid-solid contact region in the interparticle contact fraction. The interparticle contract fraction (L/D) defines the region where conduction occurs between the solid particles across a small gap. To calculate the thermal conductivity from this expression, the porosity () is experimentally measured, the gas and solid thermal conductivities are available from the literature, and the sphericity (), contact roughness (), and interparticle contact fraction (L/D) are fit parameters.
Measured centerline temperatures (indicated by points) and calculated centerline temperatures (indicated by lines) for plutonium dioxide powder with argon and helium as fill gases at different pressures. Temperatures would be similar in an ARIES container filled with calcined pure plutonium oxide powder.
With the thermal conductivity expression in the equation to the left, the radial temperature profiles were calculated using a finite difference code that included radial and axial heat conduction, thermal radiation in the powder bed, and convection to the surrounding air as heat transfer pathways. The fit parameters for the powder were =0.0037, =0.00018, L/D=0.10 and the thermal radiation emissivity view factor product=0.015. Because the gas conductivity is a function of the pore size () in the free molecular region, the inner pore size (in) of 0.68 micrometer (µm) in the contact area and the outer pore size (o) of 17 µm in the outer pore region were also estimated. The calculated centerline temperatures were in good agreement with the measured temperatures for both fill gases over the entire range of pressures. The thermal conductivity expression effectively captures that the thermal conductivities with argon and helium as fill gas approach each other at low pressures and that the thermal conductivity with argon is higher than expected at the higher pressures.
The relatively high thermal conductivity with argon as fill gas, which results in lower centerline temperatures, is important because packaging atmospheres no longer need to be strictly helium to hold centerline temperatures down. The model was able to correctly predict these data because it accounts for significant conduction through the interparticle contact area where the gases are not in the continuum limit and the argon and helium gas thermal conductivity values are much closer to each other. The model also correctly predicted the observed pressure dependence on temperature that exists at high pressures attributed to the small interparticle pore size present in these powders.
Measured centerline temperatures (indicated by points) and calculated centerline temperatures (indicated by lines) for plutonium dioxide powder with argon and helium as fill gases at different pressures. Temperatures would be similar in an ARIES container filled with calcined pure plutonium oxide powder.
This schematic for the powder thermal conductivity model shows two parallel pathways through the gas and solid regions of the powder with the fractions determined by the powder porosity (O). Within the solid 1- region, conduction occurs between the two solid particles through a small contact length, L (nondimensionalized as the parameter L/D). The relative areas of the solid-solid contact versus the solid-gas-solid contact in the interparticle contact fraction (L/D) are set by the parameter, , the sphericity. The other parameter in this model, , is the interparticle distance, d, divided by the total cell distance (D).
Comparison with previous plutonium dioxide powder thermal conductivity models
By using the new thermal conductivity model for the plutonium dioxide powder, we can assess the predicted thermal conductivities and centerline temperatures from the previous two studies. The earlier studies both predicted the thermal behavior of the plutonium dioxide powder in air. The new thermal conductivity model predicts that the powder conductivity is 0.15 W/(m K), compared to 0.079 W/(m K) from the Hensel study and 0.10 W/(m K) from the Knight and Steinke study. Assuming typical packaging conditions for the storage containers from
Predicted oxide temperature profiles in a storage container with air as a fill gas at a pressure of 3,930 kilopascals and at a wall temperature of 173 degrees Celsius The thermal conductivities from studies by Hensel (1998) and Knight and Steinke (1997) along with the predicted thermal conductivity from the current study were used to calculate the temperature profiles.
Hensel's study where the wall temperature was set equal to 173 degrees Celsius and the pressure was 3,930 kPa, we calculate the temperature profile for each set of thermal conductivity values. The temperature profiles are compared in the figure below where the predicted maximum temperature, using our new thermal conductivity expression, is 227 degrees Celsius, almost 50 degrees less than that calculated using Hensel's estimated thermal conductivity. The calculated temperature drop across the oxide bed decreases by almost half from Hensel's value of 103 degrees Celsius to our value of 55 degrees Celsius.
The wide range of the predicted temperatures between the three conductivity values demonstrates the importance of an accurate thermal conductivity value in estimating the thermal profile of storage containers with pure plutonium dioxide powder. The higher thermal conductivity predicted in our current study that results in a lower temperature profile will also lead to a lower estimate of the container pressure, since one of the effects of increased temperatures in the container is expansion of the fill gas and subsequent pressure increase. Because our thermal conductivity value is derived from plutonium powder data, these predictions provide a more accurate estimate of the temperatures and pressures in 3013 storage containers.
This article was contributed by Patricia Bielenberg with significant contributions from Kirk Veirs, John Berg, Dennis Padilla, Alex Carrillo, and Laura Worl, all of Nuclear Materials Technology Division; and David Harradine, Chemistry Division. Principal developers of the model are Coyne Prenger, Engineering Sciences and Applications Division, and Jerry Jones, Villanova University.
For further reading:
"Thermal Analysis of the 9975 Package with the 3013 Configuration as a Plutonium Storage Container," S.J. Hensel, Westinghouse Savannah River Report, WSRC-TR-98-00420, 1998.
"Thermal Analyses of Plutonium Materials in Stainless Steel Containers," T. Knight and R. Steinke, Transactions of the American Nuclear Society, 1997.
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