Analysis of PRV Stability In Relief Systems Part IV

An independent and accurate estimation of the speed of sound can provide an important quality check for a multitude of single and multi-phase flow applications. More recently, proposed screening methods for the calculation of pressure relief valve (PRV) stability require an accurate estimate of the speed of sound for the fluid/piping system. This paper outlines proper methods for the calculation of thermodynamic properties and speed of sound for single and multi-phase systems. Comparisons with actual measurements indicate that credible values can be obtained for single and multi-phase systems.

The speed of sound, c, characterizes the propagation of an infinitesimal pressure wave in a fluid that is unconfined. The speed of sound can be calculated for a single or two-phase unconfined fluid by evaluating the change in mixture density (with or without slip) with respect to pressure. Where the effects of conduction heat transfer are negligible, the equilibrium speed of sound is given by the derivative of pressure with respect to density at isentropic (adiabatic) conditions: where s is the isentropic compressibility,  is the fluid mass density, T is the isothermal compressibility, Cp is the real fluid heat capacity at constant pressure, Cv is the real fluid heat capacity at constant volume, and P is the system pressure. Where the effects of conduction heat transfer are dominant, the frozen speed of sound is given by the derivative of pressure with respect to density at isothermal conditions: The equilibrium (isentropic) speed of sound cs is always larger than the frozen (isothermal) speed of sound cT: For most liquids (see later section on heat capacity ratio) and two phase flow, the heat capacity ratio is typically close to 1 and the change of pressure with respect to density at constant temperature is close to that at constant entropy at low to moderate pressures. As a result, the speed of sound for most liquids can be approximated by: