Relief requirements for two phase systems with heat transfer without a phase change
For heat input to two phase systems without a phase change, the expansion of the individual phases causes a displacement of the phase in contact with the relief device, and that displacement is the basis of the required relief rate. The relief requirements discussed below are for heating or cooling of a constant volume container containing a dense phase and a sparse phase in which no phase change occurs. In the case of these systems, hydrodynamics within the container are not normally considered as it is assumed that the phases remain separated during the event (that is, completely disengaged).
Relief requirements for two-phase systems with heat transfer but without a phase change. For containers having two phases without a phase change occurring in response to the heat input, the phases are expected to remain completely disengaged. The expanding fluid nearest the relief device is that which is relieved, and the relieving requirements should account for the volumetric displacement caused by the expansion of the phase not in contact with the relief device. For example, consider a pressure relief device installed on top of a vessel containing a liquid and vapor phase experiencing process heat input that expands both the liquid and vapor phases without vaporizing the liquid. This situation is uncommon, but could occur in a steam-traced vessel containing a heavy gas oil with a pad gas of methane, as an example – the steam would be able to heat the HGO and methane, but would not be able to vaporize the HGO. In this instance, the net effect of the volumetric expansion of the liquid is to displace the vapor above the liquid. The relieving requirement should thus be based on the expansion of the vapor phase as well as the displacement caused by the expansion of the liquid phase. It is important to note that it is uncommon for this situation to result in overpressure; therefore, it is useful to evaluate whether the compression of the vapor phase can actually result in overpressure before determining relieving requirements.
When adding heat to a non-boiling system, temperature gradients are expected within the container depending on the means of heat input. External heat input, such as that from fire exposure, will usually result in stratification of both the liquid and gas phase phases with higher temperature zones at the top of each phase and with the gas being hotter than the liquid; nonetheless, the assumption of a uniform temperature for non-reactive, non-boiling systems is commonly employed and provides a reasonable estimate of the relieving requirements. If the phases are assumed to be at the same temperature, then the heat input to each phase is given by:
Where the subscripts f and g represent the liquid and gas phases, respectively, q is the individual phase heat input, Q is the total heat input, x is the mass fraction of gas, and Cp is the specific heat capacity at constant pressure.
Alternatively, heat transfer correlations can be used to determine the heat input to each phase.
The expansion of each phase in response to the respective heat input can then be used to determine the relieving requirements, as described in Relief requirements for single phase systems with heat transfer. For relief devices located in the vapor space of the container, the relief requirements are based on the sum of the expansion rate of the vapor space and the rate of displacement of the vapor caused by the expansion of the liquid. For relief devices located in the liquid space of the container, the relief requirements are based on the sum of the expansion rate of the liquid and the rate of displacement of the liquid caused by the expansion of the vapor.
Blog series information. This blog is part of a series on the proposed updates to the CCPS Guidelines 2nd edition §3.3 Venting Requirements for Nonreacting Cases that were removed during final editing. See the general CCPS Guidelines for Pressure Relief and Effluent Handling 2nd Edition review for more information.
 AIChE Center for Chemical Process Safety. “CCPS Guidelines for Pressure Relief and Effluent Handling Systems”. 2nd Edition, 2017; New Jersey: John Wiley & Sons, Inc.