For heat input to single phase systems, the heat input, heat capacity, and cubic expansion coefficient are used to obtain a required relief rate. The relief requirements discussed below are for heating or cooling of a constant volume container containing a single phase. In the case of single phase systems, hydrodynamics within the container are not normally considered as it is filled with that fluid.

Relief requirements for single phase systems with heat transfer. For containers having only one phase with an expansion that can be characterized using a constant cubic expansion coefficient, the relief flow rate is typically set equal to the rate of volumetric expansion at the maximum allowable relieving pressure and no additional considerations are needed for the behavior of the fluid in the system. For any fluid not undergoing a phase change:

Where W is the required relief rate, C_p is the specific heat capacity at constant pressure (the relief pressure), β_v is the cubic expansion coefficient, ρ is the density of the expanding fluid and ρ_r is the density of the relieving fluid.

The properties are evaluated at maximum relieving pressure conditions. In most cases, the fluid being relieved is the same as the fluid being expanded; therefore, the densities are equivalent and cancel out.

If the heat input rate is negative (cooling), inflow of air or other suitable fluid may be required for vacuum relief if the potential vacuum can exceed the vacuum rating of the vessel.

For containers having only one phase with an expansion that cannot be characterized using a constant cubic expansion coefficient, a dynamic analysis of the system response to the heat input is useful. Alternatively, a step-wise approach using a temperature increment can be employed to effectively decouple the time dependency. At each temperature increment, a thermodynamic property generator or actual physical property data is used to obtain the specific heat capacity at constant pressure and the fluid density at that temperature and the relief pressure.

The venting requirement over that temperature increment can then be calculated using the equation above. The venting requirement on a volumetric basis can be calculated based on the average density over the temperature increment, and the process is repeated until a maximization of the volumetric venting requirement² or required relief area³ is found. Further refinements on this step-wise approach can be made by considering the effects the venting has on the quantity of material left in the system, the thermal inertia and physical response of the fixed volume to increased temperatures, or the effects the elevated relief temperatures have on the heat transfer rates.

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.