Pressurization Analysis for Heating of a Screw Top Utility Can Loaded With Plutonium Oxide Powder by a 1273 K Fire

The Savannah River National Laboratory (SRNL) safety basis utilizes a graded approach to evaluate the radiological dose consequences of a pressurized release of plutonium dioxide powder during a postulated fire in a glovebox. The consequences depend on the maximum venting pressure and the amount of powder that is released. To provide input for the dose consequence evaluation, pressure transients and venting rates are analyzed for the exposure of a screw top utility can containing a standard cylindrical oxide storage vial called a B vial to a 1000 °C (1273 K) fire. During the fire, the vial pressurizes due to heating and evaporation of moisture adsorbed onto the oxide powder that it contains. Venting occurs through a threaded connection between the vial cap and body. The threaded connection sometimes is sealed by an O-ring, which would fail during the early stages of the fire. If the O-ring is absent, the top surface of the threaded portion of the body abuts against the cap. The rate of venting in this case is limited by the clearance between the cap and body surfaces. Venting from the can occurs through the screw top threads and, at higher pressures, along the can seams. The rate of venting from the can is measured rather than calculated from dimensional analysis.

Heat transfer during the fire exposure is modeled using comsolmultiphysics, a finite element code. It is assumed that the rate of heat transfer is determined by the rate of thermal radiation and natural and forced convection to the screw top utility can surfaces. Rates of heat transfer are computed for upright or recumbent cans and vials, either engulfed by the fire or exposed to the fire over half the vial circumference.

The pressurization analysis is performed separately in a microsoftexcel spreadsheet macro, using tabulated results from the heat transfer calculation. The pressurization analysis includes a correction to account for cooling of the oxide powder due to evaporation of the adsorbed moisture.

The B vial has a diameter of 1.0 in. (0.0254 m) and a total height of 1.687 in. (0.0428 m). The B vial capacity is 8.38 × 10⁻⁶ m³. The B vial is constructed of 304 L stainless steel. The B vial has a threaded cap. The threads are Unified Fine, 14 threads per in. (551 threads per m), with a nominal diameter of 0.875 in. (0.0222 m) along the threads. The threads are sealed with a nitrile rubber O-ring that spans the gap between the cap and body. The O-ring is a Parker size 2-116-70, with an inner diameter of 0.737 in. (0.0187 m), a thickness of 0.103 in. (0.00262 m), and a Shore hardness rating of 70.

The screw top can is a 401 × 406 (4 1/16 in. (0.1032 m) diameter by 4 3/8 in. (0.1111 m) high) screw neck type can made by Consolidated Can of Paramount, CA. The capacity of an empty screw top can is 8.49 × 10⁻⁴ m³. The can has dry, no solder seams at the top and bottom and along one circumferential side. Figure 1 shows a B vial, with the O-ring in place, and the screw top can.

For the fire exposure analysis, it is assumed that the can contains one B vial and 0.006 kg of polyethylene bagging. The B vial is assumed to contain 0.005 kg of PuO₂, with adsorbed moisture totaling 5% of the oxide weight. During the fire exposure, it is assumed that the polyethylene bagging forms a melt pool at the bottom of the can. To avoid the complications of moving boundaries inside the can, the analysis assumes that the melt pool geometry exists at the start of the fire.

The temperature transients for the screw top can, the B vial, and their contents are calculated using Version 4.3 of comsolmultiphysics. The finite element model assumes that the can is heated by a 1000 °C (1273 K) fire on its circumference. An accurate geometric model of the vial consisting of the 304 L stainless steel body, the nitrile rubber O-ring, and the plutonium oxide powder contents was constructed. Also included in the model is an air gap above the oxide layer.

The finite element simulation models heat conduction within the stainless steel body, the oxide, and the O-ring, and between their surfaces. The model accounts for heat transfer across the air gaps inside the can and the vial by conduction and thermal radiation. Heat transfer from the fire to the can is modeled by including thermal radiation and forced convection. The emissivity for the stainless steel surfaces is set conservatively at 0.9, which is a value typical for soot-covered surfaces [1]. The O-ring emissivity is set at 0.94 [2]. The heat transfer coefficient for the outside surfaces is evaluated using the Polhausen correlation for flow past a surface with a leading edge [3]. The thermal radiation boundary condition is applied to all surfaces of the recumbent can and to all surfaces except the bottom surface of the upright can, which is assumed to be insulated. The convective heat transfer model is applied only to the circumferential surfaces of both the upright and recumbent cans. The characteristic length for the heat transfer correlation is the height of the upright can and the diameter of the recumbent can. Exposure of one side of the can to the fire is modeled by assuming that heat transfer over half of the circumference is to air at the initial ambient temperature. The top of the upright can and the end surfaces of the recumbent can are assumed to be exposed to the fire, both for cases where the fire engulfs the entire can surface and where only one side of the can is exposed to the fire.

The thermal conductivity of the plutonium oxide powder is calculated using a Los Alamos National Laboratory (LANL) model that accounts for both conduction within and between the powder particles and thermal radiation between particles [4,5]. The properties of other materials are obtained primarily from tabulations of either default data built into comsolmultiphysics or data from external sources. The density and heat capacity of the nitrile rubber O-ring are specified as 1000 kg/m³ and 250 J/kg/K, and the O-ring thermal conductivity is set at 0.24 W/m/K. The plutonium oxide density is specified as 1800 kg/m³, based on typical measured bulk densities for PuO₂ powders.

The maximum vapor pressure for evaporation of all water adsorbed on the plutonium dioxide is calculated using the ideal gas law. The water vapor pressure is given by an Antoine equation [8].

As in the B vial, the rate of pressurization due to gas expansion in the can is based on the ideal gas law. The rate of pressurization due to plastic pyrolysis is computed using the rate of gas generation determined in the heat transfer analysis.

The dominant species of gas generated by the pyrolysis of the polyethylene bagging material is ethylene (C₂H₄), which is the monomeric unit of polyethylene. The heat of reaction for polyethylene is obtained by subtracting the heat of formation of polyethylene from the heat of formation of ethylene. The heats of formation for polyethylene and ethylene are −5.636 × 10⁴ and 5.247 × 10⁴ J/mol C₂H₄, respectively [9]. The polyethylene is not completely pyrolyzed; to account for incomplete pyrolysis, only half of the heat of formation for polyethylene is included in the calculation of the heat of pyrolysis. Therefore, the calculated heat of pyrolysis is 8.065 × 10⁴ J/mol C₂H₄.

The intrinsic reaction rate for the pyrolysis of polyethylene was determined by isothermal and standard thermogravimetric pyrolysis measurements, respectively [11]. The reaction rate is expressed as an Arrhenius function of temperature. Because the pyrolysis reaction is endothermic, the rate of reaction is limited by the rate of heat transfer to the plastic surface. The limiting heat transfer rate is modeled as the sum of the maximum rates of thermal radiation and gaseous convection heat transfer to the plastic surface and conductive heat transfer from the screw top can container walls. The heat transfer area is approximated by assuming that the polyethylene bag melts and collects at the bottom of the screw top can. To bound rate of heat transfer by convection, the screw top can gas thermal conductivity is set at 150 W/m/K once pyrolysis starts. Computationally, pyrolysis is phased in between 617.5 K and 642.5 K (344 °C and 369 °C).

If the B vial is sealed with an O-ring, it is assumed that the B vial might pressurize due to radiolytic hydrogen generation. Accordingly, an additional set of calculations with an initial positive gauge pressure is included to account for this possibility. Hydrogen backpressure measurements performed by Duffey and Livingston [12] indicate that, for a limited amount of moisture adsorbed onto weapons grade plutonium oxide, the maximum gauge pressure due to hydrogen generation is about 0.565 MPa. This maximum pressure is in approximate agreement with the DOE 3013 Standard [13], which states that the primary source of pressurization is radiolytic hydrogen and that the hydrogen gauge pressure is less than 100 psig (0.689 MPa). The screw top can is not sealed and therefore will not pressurize due to generation of radiolytic hydrogen.

The second term in the denominator of Eq. (11) accounts for the effect of the vent flow. The flow term is multiplied by the heat capacity ratio to account for the pressure–volume work performed by the venting gases. The heat capacity ratio is estimated under the assumption that, because the principal component of the gas mixture in the vial at pressures significantly above atmospheric is water vapor, the venting is equivalent to adiabatic expansion of slightly superheated steam. The heat capacity ratio is assigned a value of 1.2, which is between the value of 1.135 for polytropic expansion of saturated (wet steam) and 1.3 for adiabatic expansion of superheated (dry) steam [14].

The vent flow rate is evaluated using the isothermal compressible flow equation, with a heat capacity ratio of 1.2. The friction factor for the compressible flow equation is computed as the sum of the laminar friction factor based on the vent channel length and hydraulic diameter and the Von Karman correlation for turbulent flow, with the roughness factor arbitrarily set at 0.001 [15]. The entrance loss is modeled using a factor recommended by Zuk et al. [16] The compressible flow equation is solved iteratively, using Newton's method with a damping factor of 0.5.

Venting from the screw top can is modeled using a time constant because the pressure decreased exponentially with time during the can venting tests.

For venting of B vials with O-rings, the limiting vent path is assumed to follow the root of the threads between the body and cap of the vial. The threads are Unified Fine, 14 threads per in. (551 threads per m), with a nominal diameter of 0.875 in. (0.0222 m) along the threads. Standard thread design calls for rounded clearances between the troughs and the peaks of each thread. At the clearances, the peaks are truncated to flat surfaces, equal to 0.125 times the thread pitch at the outer thread peak and 0.250 times the thread pitch at the inner thread peak. The troughs are rounded to provide a clearance opposite the truncated peaks. It is assumed that the rounded clearances take the shape of a circular chord section that spans a 120 deg arc. The analysis credits only the flow through the larger inner thread clearance, which has a hydraulic diameter of 1.68 × 10⁻⁴ m.

The analysis for venting through the gap at the thread tip accounts for possible partial pluggage of the flow path by oxide powder particles. It is envisioned that fine particle entrainment could reduce the cross-sectional area of the vent channel to a proportion equal to the void fraction of the bulk powder. The cross-sectional area for partially plugged flow is obtained by multiplying the cross-sectional area by the void fraction in the bulk oxide powder. The bounding value for the hydraulic diameter for flow in the vent channel is obtained by multiplying the hydraulic diameter for the open channel by the square root of the void fraction. The void fraction is set equal to 0.75, based on a comparison of the pycnometric density, 11,460 kg/m³, and the maximum bulk density of 1800 kg/m³, with some allowance for intraparticle voids.

The nominal Shore hardness for the B vial O-ring is 70, with an approximate upper bound of 77 that accounts for stiffening of the O-ring rubber with increasing temperature [18]. To bound the leak pressure, the hardness is set at 77 up to the point where the nitrile rubber in the O-ring begins to soften. The reduction in the hardness at higher temperatures is estimated based on the hardness versus temperature variation for fluorosilicone rubber.

The leak pressure and the static coefficient of friction are evaluated using a measured compression ratio. The compression ratio was determined by measuring the distance that the cap could be turned from first contact where the O-ring exactly fit the gap between the cap and body to hand tight. This distance was 5/32 in. (0.00397 m) measured along the perimeter of the cap. This turning distance translates to a compression ratio of 0.0345, given the cap diameter of 1.0 in. (0.0254 m) and the thread pitch of 14/in (551/m). For this compression ratio, the leak pressure at ambient temperature is calculated to be 0.629 MPa (91.2 psi) and the friction coefficient is computed to be 0.423. The variation of release pressure with temperature is shown by Fig. 2.

In the absence of an O-ring, the hydraulic diameter for contact between the vial body and cap is calculated for a representative diamond-shaped space between two saw tooth surfaces. The peak-to-trough distance for the diamond-shaped gap is assumed to be four times the average surface roughness, which is 63 μin. (1.6 × 10⁻⁶ m). Particle entrainment is not considered for flow in the gap between the vial body and cap surfaces in the absence of an O-ring, due to the small gap size and the high degree of tortuosity of the vent path.

The rate of pressure decrease due to venting from the screw top cans is calculated directly using the results of leak tests, so no analysis of the can vent gaps is needed. Results of the leak tests are presented in the Screw Top Can Leak and Burst Tests section.

R&D Technology/Packaging Technology and Pressurized Systems conducted leak and burst tests to determine the leak rate and the burst pressure for the screw top cans. Physical tests were conducted in lieu of computational structural analyses due to the lack of design specifications for the cans. Physical tests also were performed to obtain uncertainty bounds for the burst pressure and the leak rate.

Both the burst and the leak tests were performed by placing the test can in a Lexan box that is routinely used for low pressure tests. The tests used compressed nitrogen from a cylinder. The compressed gas tubing was connected to the can by drilling a hole in the bottom of the can and installing a tubing connector through that hole. The tubing was then connected using a ferrule seal. During the burst tests, the pressure was slowly increased until the cans burst. For the leak tests, the gauge pressure was increased to a nominal level of 18.0 psig (0.124 MPa). When this pressure was reached, flow to the can was cut off by turning a ball valve and the rate of pressure decrease was electronically recorded. A blank leak test was conducted in which the can was replaced by a ball valve, which was opened at the initial gauge set pressure of 0.124 MPa. The rate of pressure decrease for the blank test was measured to verify that the rate of pressure drop was controlled solely by the leak rate through the can lid connection.

To obtain valid data, it was necessary to slightly alter the test apparatus and procedure. It was determined that the cans could not be pressurized to the burst pressure due to excessive leakage through the screw lid threads, even with the addition of a gasket between the top of the can body and the underside of the lid. Therefore, for the burst tests, the lid was brazed onto the can. In addition, both the burst and leak tests required replacement of the existing 1/8 in. (0.00318 m) OD high pressure tubing connecting the can and the pressure supply tube to the pressure transducer with ¼ in. (0.00635 m) OD, 0.035 in. (0.000889 m) wall tubing to eliminate pressure differences between the transducer and the can. With these changes, the tests were conducted successfully.

Three cans were tested during both the burst and leak tests. For each leak test, the lid was screwed onto the can while holding both the can body and the lid in standard bayonet-style glovebox gloves. The lid was screwed on as tight as possible without applying excessive force. Three leak test trials were conducted for each can, for a total of nine leak tests.

For the nine can leak tests that were run, a preliminary analysis showed that the differences in the average time constants for each can did not differ significantly. Consequently, all nine tests were analyzed as a single group. The Life Distribution tool within jmp was utilized to determine the best fit probability distribution for the time constants. This tool applies the Akaike information criterion, corrected for small sample sizes [20,21]. By a statistically significant margin, the threshold, or three-parameter, Weibull function [22] gave the best fit. The threshold time constant for this distribution is 0.424 1/s. The time constant used in the venting analysis is the 95% lower likelihood bound to this time constant, which is 0.414 1/s. This lower bound and the maximum initial pressure for the tests are used to construct the asymptote shown in Fig. 3.

Three successful bursts tests were conducted. In all these tests, the cans burst along the soldered seam that runs from the bottom to the top of the can body along the circumferential side, as shown by Fig. 4. Bulging of the cans was visible starting about 10 psi (0.069 Pa) below the burst pressure, particularly on the can bottom and at the top of the lid.

Figure 5 plots the pressure transients for the burst tests. It may be noted that the pressure dropped very rapidly after cans 3 and 4 burst, but much more slowly after can 5 burst. This behavior is confirmed by the photos in Fig. 4, which show that only a small gap developed at the solder joint for can 5.

The gauge burst pressures, taken to be the maximum pressures shown in Fig. 5, were 0.239, 0.264, and 0.248 MPa for tests 3, 4, and 5, respectively. Based on these three tests, the average gauge burst pressure is 0.250 MPa, with a 90% confidence that the gauge burst pressure for any given can is between 0.207 and 0.293 MPa. The confidence interval is based on a Student's t statistic. These measured burst pressures bound the burst pressures during exposure to a fire, because the can strength degrades at elevated temperatures.

Figure 6 illustrates the results of the heat transfer analyses for an upright screw top can after 20 s exposure to an engulfing 1000 °C (1273 K) fire. The temperature profile is taken prior to the peak pyrolysis rate. As this profile indicates, the oxide remains considerably cooler than the either the screw top can or the gas space inside the screw top can, due to its low thermal conductivity and high thermal mass. The polyethylene bagging material also remains relatively cool due to the endothermic nature of the pyrolysis reaction.

Temperature and pressure transients for the same heat transfer case are plotted in Figs. 7 and 8. A comparison of the temperature and pressure transients indicates the average plastic temperature plateaus between 400 °C (673 K) and 500 °C (773 K) at the same time that the screw top can pressure increases significantly. This signifies that the rate of pyrolysis is controlled by the rate of heat transfer to the plastic surface, so that the temperature remains relatively constant. It may be noted that after approximately 15 s the can and can gas temperatures drop, while the B vial temperatures rise sharply. These temperature changes result from the computationally stipulated increase in the can gas thermal conductivity to 150 W/m/K at the onset of the polyethylene pyrolysis. The model triggers the onset of pyrolysis over a 25 K plastic temperature interval centered at 630 K (357 °C).

The plotted pressure transients indicate that increases in the B vial pressure result from evaporation of adsorbed moisture, as the pressure rises occur concurrently with increases in the adjusted oxide temperature. Gas generation due to evaporation of adsorbed moisture inside the B vial has little if any effect on the screw top can pressure because of the relatively small volume of the B vial gas space compared to the screw top can gas space. Consequently, only a single screw top can pressure transient is plotted. The can pressure spikes at the same time as the plastic temperature plateaus due to pyrolysis. The model assumes that the can gauge pressure drops to zero once the maximum gauge burst pressure of 0.293 MPa is reached.

Table 1 lists the maximum calculated internal pressures for the B vial when the outer surface of the can is exposed to a 1000 °C (1273 K) fire. Maximum internal B vial gauge pressures range from 0.320 MPa, for a B vial without an O-ring inside an initially unpressurized upright can engulfed by fire, to 0.985 MPa, for a B vial with an O-ring and a partially blocked vent path inside an upright can fully engulfed by the fire when that B vial is initially pressurized to 82 psig (0.565 MPa). The screw top can is predicted to reach its maximum estimated gauge burst pressure of approximately 0.293 MPa ± the pressure change over one time-step in all cases.

The maximum internal pressure for exposure of a screw top can containing 0.006 kg of polyethylene bagging and a B vial to a 1000 °C (1273 K) fire is equal to the measured can gauge burst pressure of 36.3±6.3 psig (0.250±0.043 MPa). The primary source of pressurization is the generation of gases by pyrolysis of the polyethylene bagging inside the screw top can.

The maximum internal gauge pressure inside the B vial is calculated to be 0.985 MPa, for an upright can engulfed by flames, when the B vial is sealed by an O-ring and the O-ring vent path is partially blocked. This maximum pressure increase is significantly less than the increase in the gauge pressure previously calculated for exposure of a bare B vial to a 1000 °C (1273 K) fire, which was 215 psig (1.48 MPa) [4], so the consequences of the exposure of the screw top can to the fire are bounded by the consequences of the exposure of a B vial to the fire.

The assistance of G. L. Crow, D. J. Trapp, and E. P. Shine is greatly appreciated. G. L. Crow and D. J. Trapp conducted the screw top can burst and leak tests in the SRNL High Pressure Laboratory. E. P. Shine performed the statistical analysis of the vent test data.

The United States Government retains and the publisher, by accepting this article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

• Savannah River Nuclear Solutions, LLC (Contract No. DE-AC09-08SR22470; Funder ID: 10.13039/100008972) with the U.S. Department of Energy.

$A,B,C$ =

Antoine equation parameters

$c$ =

speed of sound for gas, m/s

$cp,PuO2$ =

specific heat for solid plutonium oxide, J/kg/K

$cp,PuO2,adj$ =

total effective specific heat for plutonium oxide powder at adjusted oxide temperature, J/kg/K

$cp,PuO2,ev$ =

contribution of moisture evaporation to the effective specific heat for plutonium oxide powder, J/kg/K

$cp,PuO2,tot$ =

total effective specific heat for plutonium oxide powder with adsorbed moisture, including evaporation effects, J/kg/K

$dvial$ =

B vial outer diameter, m

$(dPdt)e$ =

rate of pressure increase due to volumetric expansion of gas inside the vial at the start of the fire, Pa/s (psi/s)

$(dPv,H2OdT)ox,adj$ =

rate of change of water vapor pressure in the B vial at the adjusted oxide temperature, Pa/K (psi/K)

$(dTdt)ox$ =

rate of temperature increase for oxide, from heat transfer analysis, K/s

$(dTdt)ox,adj$ =

rate of temperature increase for oxide, adjusted for additional evaporation due to venting, K/s

$E(H)$ =

modulus of elasticity for the O-ring material, Pa

$fH2O$ =

mass fraction of the plutonium oxide that is adsorbed moisture

$fp$ =

correction factor for choked flow venting at high pressures

$fs$ =

coefficient of static friction for contact between rubber and steel

$H$ =

shore hardness for nitrile rubber

$k$ =

gas heat capacity ratio

$mH2O$ =

mass of adsorbed water, kg

$mPuO2$ =

mass of plutonium oxide, kg

$M0$ =

Mach number for gas flow reference to stagnation pressure

$nH2O$ =

number of moles of water adsorbed onto plutonium oxide

$nH2O,ev$ =

number of moles of water evaporated from plutonium oxide

$P$ =

pressure, Pa (psi)

$Pe$ =

pressure inside the vial due to volumetric expansion, Pa (psia)

$PH2O$ =

pressure increase due to evaporation during the fire transient, Pa (psi)

$Pmax,H2O$ =

maximum water vapor pressure if all adsorbed water evaporates, Pa (psi)

$Pv,H2O$ =

water vapor pressure, Pa (psia)

$Pv,H2O,ox,adj$ =

water vapor pressure in the B vial at the adjusted oxide temperature, Pa (psi)

$Pv,H2O,0$ =

saturation water vapor pressure at temperature prior to fire exposure, Pa (psi)

$Pt$ =

total increase in gauge pressure due to volumetric expansion and evaporation, Pa (psig)

$Pt,adj,j$ =

B vial gauge pressure at previous time-step, adjusted for venting, Pa (psig)

$Pt,adj,j+1$ =

B vial gauge pressure at current time-step, adjusted for venting, Pa (psig)

$Pt,adj,2,j+1$ =

screw top can gauge pressure at current time-step, prior to adjustment for venting, Pa (psig)

$Pt,adj,2a,j+1$ =

screw top can gauge pressure at current time-step, adjusted for venting, Pa (psig)

$P0$ =

pressure inside the vial prior to the fire, Pa (psia), assumed to be ambient pressure

$Q$ =

volumetric vent flow rate, m³/s

$roring$ =

radius of the B vial O-ring groove, m

$Rg$ =

ideal gas law constant, m³ Pa (psia)/mol/K

$T$ =

temperature, K

$Tox,adj$ =

oxide temperature, adjusted for cooling by evaporation, K

$Tr$ =

reference temperature, 273.15 K

$Tsg$ =

pyrolysis gas temperature, K (° C)

$t$ =

duration of exposure to fumes from the fire, s

$V$ =

interior gas space in the B vial or can, m³

$Vg,1$ =

gas space volume inside the screw top can during the fire, m³

$Vg,2,test$ =

volume of gas space inside the screw top can and associated tubing during the venting tests, m³

$Vvent$ =

number of volumes of gas that have vented from the B vial

$woring$ =

width of the O-ring prior to compression at ambient temperature, m

$yM$ =

ratio of pyrolysis gas molecular weight to ethylene molecular weight (0.028 kg/mol)

$ΔPleak$ =

minimum differential pressure for leaking across the O-ring, Pa (psi)

$ΔPrel$ =

differential pressure for release of the O-ring from its seat, Pa (psi)

$λH2O$ =

heat of vaporization for water, J/kg

$μC2H4$ =

viscosity of ethylene gas at the vent, kg/m/s

$μN2,test$ =

viscosity of nitrogen for the venting test, kg/m/s

$ρH2O,v$ =

water vapor density kg/m³

$ρmax,H2O$ =

water vapor density from evaporation if all adsorbed moisture evaporates, kg/m³