(55ao) Thermodynamics and Computational Methods for Relief Valves

This paper discusses the thermodynamics and computational methods for relief valves. It is based on a careful review of the technical literature on the thermodynamics of flow through relief valves and also consultations with major simulation vendors. The discussion below is relevant primarily for gas flows.

It is common practice to use isentropic nozzle formulas for calculating conditions at the throat. These are not appropriate for sizing or estimation of relief rates because a relief valve is a stationary device that does no work and has no heat transfer. This process must be treated as an IRREVERISBLE adiabatic expansion (Joule-Thompson expansion). Otherwise, we would violate the First Law of Thermodynamics, as expressed by the steady flow energy equation (SFEE) for flowing systems.

Any temperature change in flow through a valve would generally be minor, depending on how far the gas behavior is from ideal – ideal gas enthalpy is not a function of pressure. Also, since there can be a significant velocity change, an additional term needs to be applied to the enthalpy change (equaling the change in kinetic energy). In addition, we must include the limitation that velocity at the throat cannot exceed the sonic limit. For a fixed valve size, this limits the maximum feasible flow. Several examples of the proper computational methods for these calculations are presented in this paper.

As the enthalpy doesn’t change (much), neither does the temperature. Accordingly, the density at the valve throat could be a lot lower than if the gas were much colder, as it would be had there really been an isentropic expansion. In effect, valve sizing using the isentropic assumption could result in under-sized valves. Also, from a thermodynamic point of view, a relief valve is the same as any other valve. These concepts should apply for sizing of normal valves in gas service and also estimation of relief rates.