By Roberto L. Machado, P.E.
According to the ASME Code, pressure vessels must be protected against overpressure caused by exposure to external fires. When a vessel containing liquid is exposed to an external fire, the contained liquid will vaporize and, potentially, cause the vessel pressure to exceed its maximum allowable working pressure unless the resulting vapor is relieved at a flow rate equal to the vapor generation rate.
The first step in determining the required safety valve relief area to prevent overpressure due to fire exposure is to calculate the rate of vapor generation associated with the fire. For single component liquids such as water, this is straightforward. The rate of vapor generation is calculated by dividing the rate of heat input into the vessel, Q, by the latent heat of vaporization of the liquid, λ.
API Standard 521 / ISO 23251 provide the following equation to determine the rate of heat input into a vessel exposed to fire:
Q = rate of heat input, Btu/h
C = 21,000 for areas having good drainage (typically paved)
C = 34,500 for areas having poor drainage (typically unpaved)
F = environmental factor = 1.0 for uninsulated vessel
F = environmental factor = 0.075 for insulated vessels
AW = wetted surface of the vessel
Once the rate of heat input has been determined using the above equation, the rate of vapor generation can be obtained by:
λ = latent heat of vaporization at relieving conditions, Btu/lb
The required relief rate for a given vapor generation rate is lower than the rate of vapor generation because part of the vapor generated accumulates in the additional vapor space created in the vessel as the liquid inventory is depleted. To account for this phenomenon, the required relief rate is multiplied by a correction factor that depends on the relative densities of the vapor and liquid in the vessel, as follows:
Wr = mass relief rate, lb/h
rL = liquid density, lb/ft3
rV = vapor density, lb/ft3
In many cases, especially for systems that operate away from the thermodynamic critical temperature, the correction factor is close to unity and is often disregarded.
The latent heat of vaporization for pure component liquids at relieving conditions can be readily obtained from the literature. The relieving conditions are the accumulated relieving pressure and the corresponding saturation temperature (boiling point) of the liquid at the relieving pressure. For overpressure protection of a vessel during a fire, the ASME Code allows an accumulated relieving pressure of up to 121% of the vessel’s maximum allowable working pressure.
When the liquid contained in a vessel is a multicomponent liquid, the calculation of the vapor generation rate is not straightforward. The reason is that, for a multicomponent liquid, the composition, temperature, and heat of vaporization do not remain constant during a fire exposure. At the onset of a fire, the lighter components of the liquid vaporize first and change the composition of the residual liquid. This causes an increase in the boiling temperature of the residual liquid which absorbs part of the heat input into the vessel. Furthermore, as the liquid inventory in the vessel is depleted, the wetted surface also decreases, which results in a reduction in the heat input to the vessel. Thus, when the vessel contains a multicomponent liquid, the rate of vapor generation is not constant and, depending on conditions, may increase or decrease during the fire.
The determination of the limiting relief load caused by fire exposure of a vessel containing a multi-component liquid typically requires a time-dependent analysis that considers all of the above variables. This analysis involves performing a sequential vaporization of the liquid contents to determine the amount of vapor generated during each step and the increment of time over which the vaporization occurs. The analysis must also consider the progressive decrease in wetted surface area as the liquid inventory is depleted. In many cases, the limiting relief load will occur at the onset of vaporization because, at that point, the wetted surface is at a maximum. However, this is not always the case because, at the onset of vaporization, when the vessel is still relatively full of liquid, most of the heat absorbed may go into raising the temperature of the residual liquid (sensible heat) rather than into vaporizing the lighter components (latent heat). One approach for the time dependent analysis is as follows: