By Hans K. Fauske, DSc, Regent Advisor, Fauske & Associates, LLC
Introduction - Thermal initiation of monomers due to fire exposure presents an interesting problem in vent sizing in order not to exceed the allowable overpressure. For large atmospheric vessels the potential occurrence of sufficient liquid swell resulting in two-phase flow is of special importance. Since little or no overpressures (< 0.1 psi) can be accommodated in many cases of interest the vent area augmentation due to two-phase flow is to the first order proportional to (
) where 
are the liquid and vapor densities, respectively. It is also of interest to note that for many monomers significant thermal initiation coincides closely with the normal boiling point of the monomer, resulting in a chemical induced self-heat rate of the same order as the equivalent volumetric heating rate due to the fire exposure. Examples of such behavior include monomers like styrene, butyl acrylate, ethyl acrylate, etc.
Fire Exposure Only - For fire exposure heating only and a freeboard of about 10%, Fauske (1986) has demonstrated that for non-foamy systems the vent requirement can be based upon all vapor venting independent of available overpressure. The basis for this argument is the absence of vapor generation throughout the bulk of the liquid and the liquid swell is due entirely to the wall boiling two-phase boundary layer associated with the fire heating. While the recirculation velocity (
) resulting from the wall boiling two-phase boundary layer can exceed the terminal bubble rise velocity which is typically of the order of 
, significant vapor carry-under and hence significant liquid swell, is prevented by static head effects. The increasing subcooling of the liquid as the vapor bubble are dragged under by the recirculating flow results in rapid condensation and collapse of the vapor bubbles (Fauske et al., 1986). This behavior is confirmed by relevant fire simulation experiments and practical industry experience (Fauske et al., 1986).
Fire Exposure and Chemical Heating - The above observation can be extended to include chemical heating as follows. Again, the absence of significant vapor generation throughout the bulk of the liquid is assured by the static head effect if the following inequality is satisfied
(1)
where 
is the chemical self-heat rate, Φ 
is the subcooled temperature gradient due to the liquid static head, and 
is the average liquid recirculation velocity as a result of the wall boiling two-phase boundary layer density effect. Considering typical values for Φ and of about 
and 10 , respectively, chemical self-heat rates well below about 
should assure the absence of volumetric boiling as the bulk of the liquid will remain subcooled. As a result of the liquid recirculation, the sensible heating produced in the bulk liquid from the chemical reaction is largely transferred to the wall two-phase boundary layer in the form of latent heat.
Design Example - Consider an API-650 uninsulated vessel (12’ diameter x 18’ 55 ss vertical on grade) with a 15,000 gallon capacity containing styrene exposed to fire. The volumetric heating rate due to fire exposure is 
, the adiabatic chemical heating rate at a relief set pressure of 0.13 psig is 
(note that this value is much smaller than that required by Ineq. 1), resulting in a combined heating rate of about 
. The maximum allowable venting pressure is 0.19 psig.
For this example, considering bulk volumetric boiling resulting in flashing two-phase venting (the DIERS methodology) requires a vent area of about 2,390
, allowing for an overpressure of 0.06 psi. However, since Ineq. 1 is clearly satisfied in this case the vent area can be estimated from
(2)
where A (
) is the ideal vent area, V (
) is the volume of reactant, P (psig) is the relief set pressure and 
is the combined heating rate from fire exposure and chemical heating at the relief set temperature. Setting V = 56.8, P = 0.13 psig and 
= 
, results in A = 0.2 or 312. Equation 2 is based upon all vapor venting and provides a practical approach to pressure relief evaluation for monomer storage tanks exposed to fire and undergoing chemical heating as well.
Reference
Fauske, Hans K. et al., 1986, “Emergency Relief Vent Sizing for Fire Emergencies Involving Liquid-Filled Atmospheric Storage Vessels,” Plant/Operations Progress, Vol. 5, No. 4, October 1986.
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