Heating or cooling of a constant volume container
The transfer of heat into or out of a constant volume container results in an attempt of the entrapped fluid to change in overall density, leading to pressure increases or decreases. The change in fluid density can be caused by the expansion or contraction of the individual fluid phases within the system, which usually results in a modest density change, or by a change in phase (for example, vaporization of liquid), which usually results in a significant density change. For a constant volume container, the relieving requirements are based on the rate of density change in response to the heat transfer, essentially removing mass from the vessel at a rate sufficient to remove the change in volume caused by that heat transfer.
It is useful to note that while the common estimation techniques assume the container volume does not change in response to the heat transfer, some expansion or contraction of container is expected, and the evaluation of this volume change may assist in the determination of whether or not small fluid density changes will in fact result in overpressure. Interestingly, the calculation for the rate of pressure rise due to thermal expansion of a confined single-phase fluid was present in the 1st edition of the CCPS Guidelines, but removed in the 2nd edition. Luckily, the information can still be found in API Standard 521 (at least in an integrated form along with a factor to account for leakage)2, and is discussed in more detail in our Fireside Chat Hydraulic expansion pressure rise.
As indicated in the CCPS Guidelines 2nd edition:1
The common calculation models for evaluation of the relieving requirements are comprised of three elements:
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 amount of heat applied to the contents of the container needs to be quantified, and may include solar radiation, ambient convection, fire exposure, or process heat input. These are discuss in more detail in Heat transfer characterization.
Fluid behavior. The response of the fluid during an overpressure scenario is dependent on whether a phase change occurs. For fluid responses without a phase change, the CCPS Guidelines 2nd edition removed much of what was in the 1st edition, as well as the proposed changes. These are discussed in more detail in Fluid response to heat transfer without a phase change. For fluid responses with a phase change, methodologies for determining an effective heat of vaporization were removed in favor of retaining the 1st edition ‘latent heat of each component’ or ‘dynamic simulation with SuperChems™ for DIERS’ methods. We provide the proposed alternative methods in Fluid response to heat transfer with a phase change and discuss the Multi-component effective heat of vaporization method in more detail.
Vessel hydrodynamics. The impact of the fluid’s transition from vessel contents to relief system piping is described in detail in the CCPS Guidelines 2nd edition. Three categories of hydrodynamics are discussed: complete disengagement of vapor (which is common for non-reactive boiling systems), partial disengagement, and homogeneous venting.
Relief requirements. With these three elements in hand, relief requirements can then be evaluated:
- Relief requirements for single phase systems
- Relief requirements for two-phase systems without a phase change
- Relief requirements for boiling systems
The common overpressure scenarios that these calculations methodologies apply to, namely hydraulic expansion, fire exposure, and loss of heating/cooling are discussed in further detail in the CCPS Guidelines 2nd edition (p. 178-187)1.
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.
 American Petroleum Institute. “API Standard 521-Pressure-relieving and Depressuring Systems”. 6th Edition, April 2014.