Maximum Condensable Pressure in a Sealed Container With Arbitrary Temperature Distribution

Pressure Vessels and sealed canisters are designed to maintain seal integrity under a maximum internal pressure. When the temperature inside the canister rises, the internal pressure rises accordingly. The presence of condensable liquid-vapor mixtures can create a strong relationship between the pressure and temperature. An isothermal container admits a straightforward thermodynamic pressure calculation; however, large temperature gradients inside the container require complex multiphase conjugate heat transfer calculations to predict accurate pressures. A simplified prediction using the peak internal temperature to find the saturated pressure of the condensable fluid may introduce unrealistic pressures when significant fluid mass is in a cooler location of the container.

This work presents methodology to calculate the pressure of a condensable fluid in a sealed container with large internal temperature differences using a two-temperature approach to predict saturated boiling and superheating of the vapor phase. An arbitrary temperature distribution allows for pressure calculations by considering the expected location of the liquid mass and the peak internal temperature. An enthalpy balance provides the effects of the temperature distribution. Here, a known liquid mass reaches saturation at a specified location and temperature. The resulting saturated vapor phase is no longer constrained to the same location as the liquid, and exchanges heat with the peak temperature location inside of the container, changing to a superheated vapor at the peak temperature. The vapor then comes to phase equilibrium with the remaining liquid phase to find a resulting fluid pressure, based on the total specific volume and enthalpy of the saturated liquid and superheated vapor phases. This work finds a strong dependence of the final pressure on the initial specific volume of the condensable fluid. Low initial fluid volumes show a linear increase of pressure with specific volume, expected of a high-temperature superheated vapor. High fluid volumes show minor pressure increases over the initial saturated fluid state since the relative amount of energy added by the high-temperature superheated vapor contributes little to the final specific enthalpy of the mixture. The highest pressure exists when the initial fluid is a saturated vapor, creating a high-temperature superheated vapor at the minimum specific volume.

An example calculation using water in a sealed canister with temperatures between 250ºF and 500ºF shows a 40% increase in the final pressure compared to the saturated pressure at 250ºF. This represents a significant reduction in pressure compared to the pressure of saturated or superheated water at 500ºF. Because the peak pressure condition is easily predicted and calculated using the proposed method, this work provides a means to calculate the maximum internal pressure of a sealed container with a condensable fluid without the need for complex multiphase computer modeling.