Selecting the Proper Gas Compressibility Z for Relief Valve Sizing

摘要

Gas sizing of relief valves is commonly performed using the analytical gas formula for choked flow. A major consideration is the selection of the compressibility factor (Z), which establishes the density and ultimately the flow rate. The proper selection of the value of Z will avoid possible over-sizing or under-sizing a relief valve. The basis for sizing is the Bernoulli equation, where the term in the Bernoulli equation that describes flow due to a pressure gradient is configured as an integral since the density changes significantly with pressure. There are two primary methods for solving the integral. One is direct numerical integration of the Bernoulli equation and the other is analytical integration, which results in the gas formula for choked flow. Numerical integration is robust since it step-wise integrates the Bernoulli equation using actual densities. On the other hand, the analytical solution requires two major simplifying assumptions to accomplish the integration. The first is that the gas is ideal, which means the compressibility Z is equal to 1.0. The second is that the density (as a function of pressure) is determined using a specific correlation called the “isentropic expansion expression”. An important consideration is the density at the relief valve inlet (initial pressure), which is established by the compressibility factor using either Z=1.0 (ideal gas value) or Z = actual value. The values of the densities at other pressures are determined by the “isentropic expansion expression”. Therefore, accuracy of the analytical choked gas flow rate calculation depends on both the initial value of the compressibility factor, and how well the densities, represented by the “isentropic expansion expression”, track the actual densities. This paper will explore the two choices of compressibility and provide guidance on the oversizing or under-sizing of a relief valve.