multivariate production systems optimization - Stanford University
multivariate production systems optimization - Stanford University
multivariate production systems optimization - Stanford University
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A paper by Hazim and Nimat (1989) proposed that the performance of the Aziz et<br />
al. (1972) correlation could be improved by using other flow-pattern maps instead of the<br />
map proposed by Aziz et al. (1972). For their specific data set, best performance was<br />
attained when the Aziz et al. (1972) correlation was used in conjunction with the Duns and<br />
Ros (1963) flow-pattern map.<br />
Ny<br />
10.<br />
1.0<br />
0.1<br />
.01<br />
Bubble<br />
B12<br />
Slug<br />
29<br />
B23<br />
Transition<br />
B34<br />
Annular-Mist<br />
0.1 1.0 10. 100. 1000.<br />
Figure 3.2: Flow-Pattern Map Proposed by Aziz, Govier, and Fogarasi (1972).<br />
3.4.1 Bubble Flow Regime<br />
To obtain the pressure gradient due to fluid density in the bubble flow regime, Aziz et al.<br />
(1972) proposed to define the liquid holdup as<br />
where the absolute bubble rise velocity is<br />
and the bubble rise velocity is<br />
Nx<br />
HL = 1 - VSG<br />
VBF<br />
VBF = 1.2 VM + VBS<br />
VBS = 1.41 σL g ρL - ρG<br />
ρ L 2<br />
1 4<br />
(3.51)<br />
(3.52)<br />
(3.53)