Transient Reservoir Conditions and Leak Flow Rate for a Choked Orifice: Basic Principles, Estimation and Applications

In the course of risk assessment, consequence modeling or root-cause analysis it is often necessary to quantify the amount of gas leaked from a pressure vessel as a function of time, or to estimate the time-dependent gas concentration if the leak occurs in an enclosed space. In most cases only the initial or design conditions are known for the ruptured vessel, but simple steady state calculations based on these gas conditions often lead to unacceptable errors in estimates for the mass flow rate and time necessary to empty the pressure vessel. Accurate transient calculations are possible using CFD, but ready to use analytical expressions can be derived based on the isentropic flow of gas through an orifice while the flow remains choked. The basic principles of chocked gas flow and the derivation of mathematical expressions for the gas state inside the reservoir (pressure, temperature, and density) are presented along with expressions for the instantaneous mass flow rate and total gas mass leaked. This time-dependant mass flow rate can then be used to calculate the instantaneous concentration in an enclosure using a simple well-stirred reactor model. Although the mathematical expressions can be used directly, several generalized plots are also presented for rapid assessment. The use of the analytical expressions and plots are illustrated with examples related to flammability/explosive limits, odor threshold and toxicity.