multivariate production systems optimization - Stanford University

Table 4.1: Empirical Coefficients for Two-Phase Critical Flow Correlations.
Correlation A B C
Gilbert (1954) 10.00 0.546 1.89
Baxendall (1957) 9.56 0.546 1.93
Ros (1959) 17.40 0.500 2.00
Achong (1961) 3.82 0.650 1.88
Omana et al. (1969), Fortunati (1972), Ashford & Pierce (1975), and Sachdeva et al.
(1986). It should be pointed out that only Fortunati (1972), Ashford & Pierce (1975), and
Sachdeva et al. (1986) have attempted to model both critical and subcritical flow.
Ros (1960) extended the work of Tangeren (1949) to account for mist flow where
gas is the continuous phase. Ros (1960) demonstrated that accelerational effects dominate
choke behavior and that slippage effects are negligible. Poetmann & Beck (1963)
converted the Ros (1960) equation to field units and presented it as a series of nomographs.
Omana et al. (1969) conducted experiments with water and natural gas flowing
through restrictions. They performed a dimensional analysis that yielded eight
dimensionless groups to characterize the flow. A regression analysis produced an
empirical correlation based on five of these dimensionless groups. The Omana (1969)
correlation was never widely accepted because it was based on small diameters (4 to 14 /
64ths of an inch), low flow rates (800 bpd maximum), low pressure (400 to 1000 psig),
and the correlation was developed for a water-gas mixture as opposed to an oil-gas
mixture.
Fortunati (1972) demonstrated how to apply the findings of Guzhov and
Medviediev (1962) to model the performance of a surface choke. Guzhov and Medviediev
(1962) developed a curve relating the velocity of the mixture, VM , to the pressure ratio of
downstream pressure to upstream pressure, P2 / P1 , where P1 was constant at 19.8 psia.
Fortunati (1972) showed how to correct the the mixture velocity for the actual downstream
pressure. Having the corrected velocity of the mixture, the determination of the liquid
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