When evaluating the effect of heat input or removal from a closed system, the rate of heat transfer needs to be identified. Common heat transfer techniques, usually assuming a constant value, are employed while recognizing the imprecision of parameters like heat transfer coefficients create the need for some judgment in selecting values. For the special case of heat input due to an external fire, multiple guidelines exist for the designer to use. The characterization of heat transfer discussed below is one of three elements in the evaluation of relief requirements for overpressure scenarios based on heating or cooling of a constant volume container:¹

1. the characterization of the heat transfer to the container
2. the fluid behavior in response to that heat transfer
3. the hydrodynamics within the container

Heat transfer characterization. The common sources of heat transfer include solar radiation, free ambient convection, radiant and convective heat input due to external fire exposure, and process heat transfer. The amount of solar radiation that may be absorbed by a surface is a function of geographical location, the time of year and day, the absorptive properties of the surface, re-radiation, and convective losses; nonetheless, a common basis is simply to use a heat flux of 1 kW/m². For free convection, many empirical equations have been developed for use and may be found in other references [for example, Perry’s 7th Edition, §5 “Heat and Mass Transfer” or ASTM C680-08]. There is a specific case of ambient heat transfer resulting in a sudden cooling that may occur during a rainstorm that is discussed in more detail in tank breathing. The heat input from fire exposure is the subject of many different codes and standards, and is discussed in more detail in CCPS Guidelines 2nd edition¹ §3.3.1.3.

Process heat transfer includes any system that behaves as a heat exchanger, with the fluid of interest in contact with a surface that facilitates heat transfer with another fluid or heat transfer device, and has a heat input that can be calculated using common heat transfer calculations (as stated in the CCPS Guidelines 1st edition “the familiar q = U_e A ΔT_ln where U_e is the overall heat transfer coefficient, typically taken at its ‘clean’ value without fouling effects to ensure a conservative estimate is used”).

For most situations, the heat transfer is commonly estimated to be constant with respect to time, especially where the heat transfer is limited by the heating or cooling medium itself; however, there are some instances where the duty may change based on the changes in the overall heat transfer coefficient, in the temperature differentials experienced as the system temperature changes in response to the relieving pressure, or in the effective heat transfer area (such as when liquid is being boiled off and the liquid level drops).

While some systems have a specifically calculated heat transfer coefficient obtained during design (such as for heat exchangers), other systems may require estimation of that heat transfer coefficient (such as for steam tracing). The calculation of the heat transfer coefficients for use in these equations is usually not very precise; therefore, care should be taken to use conservative values for the purposes of the design of overpressure protection.

When evaluating the potential changes in heating duty caused by changes to the temperature differentials, the changes the overpressure event has on the fluid is an important consideration. As an example, consider a distillation tower with a reboiler. During an overpressure event, the pressure in the tower increases, and the bubblepoint temperature of the bottoms fluid usually increases as well (thus lowering the temperature differential); however, some causes of overpressure for distillation towers may cause the bottoms composition to resemble the feed more than the normal bottoms, which tends to lower the bubblepoint temperature. As an example, consider a series of distillation towers in which the bottoms of the first tower is fed to the second tower. During an overpressure scenario in which the heat is lost to the first tower, a lighter fluid is fed to the second tower. The distillation that occurs in the second tower during this same overpressure pressure scenario could cause the bottoms fluid of the second tower to be much lighter than normal, with a coincident lowering of bubblepoint temperature.

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.