A New Correlation For Two-phase Flow Through Chokes
Authors: Al-Towailib A.I. , Al-Marhoun M.A. 
Published: March 2010

Abstract
Chokes are one of if not the most important flow controllers in oil producing wells. Selecting the optimum choke size is the first step in choke design. An empirical correlation that relates the choke size to other parameters was developed. The correlation covers a wide range of flow rates and choke sizes. It was based on 3554 production test data from ten fields in the Middle East. The correlation applies for critical flow conditions which makes it useful for choke design purposes. Statistical error analysis shows that for the data used in this study, the new correlation outperforms all published correlations in the literature.

Introduction
Tangren et al.(1) offered the first significant study on multiphase flow through chokes. His approach is only applicable when liquid is the continuous phase (volumetric gas-liquid ratio is less than 1). Gilbert(2) in 1954 developed the first empirical correlation where he used 268 production tests for choke sizes between 2.38 and 7.14 mm (6 and 18 sixty fourths of an inch). Ros(3,4,5) in 1960 expanded the Tangren approach and studied multiphase flow through chokes when gas is the continuous phase. To make the Ros equation and analysis available to oil field personnel. Poetmann and Beck(6) in 1963 converted the Ros equation to oil field units and reduced it to a graphical form. They tested their charts with 108 field production tests with choke size range of 1.59 ? 11.11 mm (4 ? 28 sixty fourths of an inch) and flow rates of 1.6 ? 206.7 std. m3/day (10 ? 1300 STDB). Omana(7) in 1969 conducted experiments with water and natural gas to derive his correlation. He used dimensionless analysis to come up with the final form of his equation. His range of tests data was 1.56 ? 5.56 mm (4 ? 14 64th of an inch) choke size and 127.2 std. m3/day (800 STDB) maximum flow rate. Fortunati(8) in 1972 developed two correlations for critical and subcritical floe regimes. For subcritical flow regime, he used curves that were previously published by Russian researchers. Guzov and Medviediev, Ashford and Pierce(9) in 1975, followed by Sachdeva(10) in 1986, focused attention on the subcritical flow regime. In both of their correlations, the specific heat ratio has to be known, while in practicality, it is not measured in the field and no reliable correlation exists to approximate it. Osman and Dokla(11) in 1988 also developed a correlation for gas condensate wells. Their data ranges from 11.11 ? 28.58 mm (28 ? 72 64th of an inch) with maximum flow rate of 206.7 std. m3/day (1300 STDB). Surbey(12) in 1989 used the Gilbert form to come up with a correlation for critical flow. He developed an iterative procedure that will give a better definition of the critical flow boundary.

Discussion
Many researchers have studied multi-phase flow through chokes. However, published literature shows that the correlations previously developed were based on a small number of field data: on the other hand, most of them were based on laboratory experiments where limitations prevail in stimulating high flow rates, especially in the magnitudes of Middle East well production rates.