multivariate production systems optimization - Stanford University
multivariate production systems optimization - Stanford University
multivariate production systems optimization - Stanford University
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V M < 10 δ ≥ -0.065 VM<br />
V M > 10 δ ≥<br />
-VB<br />
VM + VB<br />
37<br />
1 - ρS<br />
ρL<br />
Having obtained the two-phase density, the density component of the total pressure<br />
gradient is<br />
The friction component is given by<br />
dP =<br />
dZ HH<br />
g<br />
gC ρs = g<br />
gC ρL HL + ρG HG<br />
dP =<br />
dZ F<br />
fM ρL VM 2<br />
2 gC D<br />
VSL + VB<br />
VM + VB<br />
where the Moody friction factor is based on the Reynold’s number<br />
Re = ρL VM D<br />
μL<br />
(3.95)<br />
(3.96)<br />
(3.97)<br />
+ δ (3.98)<br />
The acceleration component was considered negligible for the slug flow regime.<br />
Therefore, the total pressure gradient for the slug flow regime is given by<br />
dP =<br />
dZ SLUG<br />
dP +<br />
dZ HH<br />
dP<br />
dZ F<br />
3.6 Implementing the Correlations<br />
(3.99)<br />
(3.100)<br />
Implementing the empirical multiphase flow correlations can be difficult due to the<br />
codependency of the pressure and the fluid properties. Because the fluid properties and the<br />
pressure are mutually dependent--it takes fluid properties to determine the pressure and<br />
conversely it takes pressure to determine the fluid properties--the procedure is iterative and<br />
must be performed for small increments over which the pressure and fluid properties may<br />
be assumed constant. Thus the length of the conduit is traversed in small increments,<br />
determining a new pressure at each step, in what is known as a pressure traverse.
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