A Model To Calculate the Theoretical Critical Flow Rate Through Venturi Gas Lift Valves

A model to calculate the theoretical critical flow rate of nitrogen (N-2) or natural gas through a Venturi gas lift valve is described herein. This new model considers real-gas effects not only in density calculations but also in other thermodynamic properties that are relevant during gas isentropic evolution. For the properties of N-2,, the Bennedict, Webb, and Rubin (BWR) equation of state and an accurate correlation for the ideal-gas isobaric heat capacity were used. For natural gas, the Dranchuk and Abou-Kassem equation, which reproduces the well-known Standing and Katz chart, was used, and, for the ideal-gas isobaric heat capacity, it was assumed that the natural gas was a mixture of methane and ethane only, their individual ideal-gas heat capacity being calculated by updated correlations. To validate the use of the proposed equations of state, a comparison of calculated with experimental or reference data on properties of N-2, and natural gas (including pure methane and some relevant mixtures) was performed with very good results for N-2, and for natural-gas compositions usual in gas lift operations (dry gas with very small amounts of contaminants). For natural gas with moderate amounts of N, and carbon dioxide (CO2), accurate results were obtained after correction of critical conditions and of ideal heat capacity. The model was also compared with other theoretical models found in the literature, which use compositional approaches for natural gas, with excellent results. Some experimental results obtained with commercial Venturi valves manufactured in Brazil are also presented.