multivariate production systems optimization - Stanford University

Mass
Flow
Rate
Critical Flow
Downstream to Upsteam Pressure Ratio
43
Subcritical Flow
Y
0.4 0.5 0.6 0.7 0.8 0.9
Figure 4.2: Mass Flow Rate versus Pressure Ratio.
4.1 Literature Review
Tangeren et al. (1949) were among the first to publish significant findings on multiphase
flow through chokes. The importance of their research was that it demonstrated that for a
compressible mixture, there exists a critical flow velocity above which pressure fluctuations
cannot be transmitted upstream.
Gilbert (1954) published a simple formula based on daily production data of a
California oil field that related the liquid flow rate, the gas-liquid ratio, the choke diameter,
and the upstream pressure. His equation is
where
PWH = 435 R P 0.5 QL
S 1.89
P WH = flowing wellhead pressure, psia
(4.1)