A common scenario that is encountered in pressure relief systems design centers around the calculation of vapor generation rates from liquids under external heating, internal heating, or fire exposure.
Pressure relief design is all about a volume balance. As the heating increases the liquid temperature and generates more vapor (volume) in a vessel, the pressure increases to fit the additional vapor generation (volume created) within the confines of the vessel. Relieving the vapor at a specific pressure, removes the additional vapor volume and keeps the pressure in the vessel in check.
This relief design scenario shares some commonalities with batch distillation when the liquid being heated is a chemical mixture. Similar to batch distillation, mixture light ends are preferentially depleted first. The resulting volumetric vapor generation rate depends on the vapor composition. Initially the vapor composition will be rich in light components.
As the light components are preferentially depleted, the vapor composition will become rich in heavier components. Thermodynamic, physical, and transport properties change as the mixture is fractionated for both the liquid and the vapor. The maximum relief requirement may occur anywhere along the fractionation curve.
For reactive mixtures where all vapor venting occurs, special care must be taken to ensure that materials that are preferentially concentrated do not spontaneously decompose or deflagrate.
Simple design equations, such as those provided by API, continue to be widely used. However, these simple equations require a value of the latent heat of vaporization which varies with composition for a liquid mixture as venting is occurring.
Limited guidance provided in API-521 includes the following statements: (a) “The latent heat and relative molecular mass values used in calculating the rate of vaporization should pertain to the conditions that are capable of generating the maximum vapor rate” and (b) “The vapor to be relieved is the vapor that is in equilibrium with the liquid under conditions that exist when the PRD is relieving at its accumulated pressure".
Dynamic software tools such as Process Safety Office® SuperChems™ can automatically identify the mixture conditions leading the the maximum vapor generation rate under equilibrium conditions and can also calculate the vessel wall temperatures and expected time to failure or time to yield as heavies are concentrated. A reclosing pressure relief device can only protect from overpressure and not overtemperature.
Several operating companies have also resorted to rules of thumb on how to calculate a representative latent heat of vaporization value. While it is relatively simple to establish relief requirements for vessels containing a single liquid component, there are many pitfalls associated with vessels containing multicomponent liquid mixtures. The value of the heat of vaporization for mixtures (enthalpy or internal energy) is not straight forward to calculate. The vapor composition is only equal to the bubble point liquid composition at the dew point.
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