(116j) Modelling Multiphase Flows through Restrictions

The accurate prediction of pressurised release rates is critically important in assessing the hazards associated with pipeline failures as well as in designing pressure relief valves.

The above is a particularly difficult task when simulating two-phase hydrocarbon releases due to non-equilibrium effects. The most commonly used approach is based on API 520 [1,2] recommendations for sizing relief valves. However recent studies [3] involving direct comparison with experimental data have shown significant inaccuracies when the percentage of vapour in the upstream fluid mixture becomes appreciable.

This paper describes the development of a robust transient outflow model for predicting two-phase discharge through an orifice. The model is based on the application of conservation equations across the discharge plane. A phase dependent discharge coefficient [4] is used to account for the void fraction of the fluid in the orifice neck. The extended w-method, originally developed by Leung [5], on the other hand accounts for the thermodynamic non-equilibrium effects specifically at the beginning of nucleation for low vapour mass fractions. In addition, a semi-theoretical correlation is given, expressed in terms of a two-phase multiplier to consider the phase slip.

The discharge model is validated against experimental data [3] for a variety of hydrocarbons containing different liquid mass fractions ranging from 0.1 to 0.7 and up to a maximum pressure of 60 bar producing maximum and average errors of ±6% and ±1.3 % respectively. The effects of thermodynamic non-equilibrium and phase slip on the predicted data are discussed in detail.

References:

1.American Petroleum Institute, 1993, Recommended Practice 520, Sizing, Selection and Installation of Pressure-Relieving Devices in Refineries: Part 1-Sizing and Selection, 6th edition.

2.American Petroleum Institute, 2000, Recommended Practice 520, Sizing, Selection and Installation of Pressure-Relieving Devices in Refineries: Part 1?Sizing and Selection, 7th edition.

3.Richardson, S. M., Saville, G., Fisher, A., Meredith, J., Dix, M. J., Experimental Determination of Two-Phase Flow Rates of Hydrocarbons Through Restrictions, Trans IChemE Process Safety and Environmental Protection, 84(B1): 40?53, 2006.

4.Diener, R., Schmidt, J., Sizing of Throttling Device for Gas/Liquid Two-Phase Flow Part2: Control Valve, Orifices, and Nozzle, Process Safety Progress, 24, 29-37, 2005.

5.Leung, J.C., A generalized correlation for one-component homogeneous equilibrium flashing choked flow, AIChE Journal, 32(10), 1743-1746, 1986.