Vessels and pipes filled with fluids require pressure relief in order to protect from loss of containment caused by fluid thermal expansion. Thermal expansion of fluids occurs when the fluid is heated as a result of steam tracing, solar radiation, external fire, etc.
In addition to establishing the required thermal relief requirements, it is also useful to establish the maximum pressure that can be reached during limited heating for either non-vented or partially vented fluid filled systems. In order to obtain better estimates of the maximum pressure reached, the elasticity of the piping/vessel should be considered. For partially vented systems, the excess volumetric expansion (fluid expansion - vessel/piping expansion) rate will govern the relief requirements.
This paper examines theoretical and dynamic methods for determining pressure rise rates and relief requirements caused by the thermal expansion of liquids, gases, and supercritical fluids in enclosed equipment. It demonstrates that the standard thermal expansion relief requirement calculated by Equation 29 in API Standard 521 typically yields oversized relief devices because it neglects factors such as vessel thermal inertia and dynamic heat transfer dynamics. Additionally, the paper addresses the severe risks of equipment failure, including superheat limit BLEVEs and BLCBEs, when thermal relief is omitted or when system pressures drop below thermodynamic stability limits.
The volume of a solid, just like a fluid, expands and contracts due to changes in temperature and pressure. Because the change in volume for solids is smaller than the volume change for liquids and gases, it is normally neglected in most fluid flow applications. There are some practical applications where the volume change of a pipe or vessel can be important when considering scenarios dealing with loss of containment. Thermal expansion of liquid full vessels and/or piping is one such application. The depressuring of long high pressure pipelines is another practical application.
For vessels or piping containing liquids or vapors that are subjected to heating, the overall change of vessel volume due to thermal expansion and increase in internal pressure as a function of time is given by:
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