Page 83 - Handbook Of Multiphase Flow Assurance

78 4. Hydraulic and thermal analysis

PRESSURE DROP IN SLUG BODY
101000
PRESSURE p [Pa] 100600
100800

100400
100200
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
101000
POSITION [m]
PRESSURE p [Pa] 100800
100600
100400
100200
FIG. 4.4 Numerical Simulation of the pressure drop in a slug body. (Reproduced with permission Wenzel, S., Czapp,
M., Sattelmayer, T., 2016. Numerical investigation of slug flow in a horizontal pipe using a multi-scale two phase approach to
incorporate gas entertainment effects. https://www.td.mw.tum.de/en/research/research-areas/projektbeschreibungen/ numerical-
investigation-of-two-phase-flow-in-horizontal-pipes-in-slug-flow-regime-with-special-consideration-of-the-entrainment/
(Accessed 1 June 2018)).

ρ = ρ = ρ ∗volumeFraction + ρ ∗ 1 ( − volumeFraction )
mix liquid liquid gas liiquid
M is the total mass, in pounds, of flowing oil, gas, and water associated with one stock
tank barrel flowing through the system. Change in pressure with distance in psi/ft. due to
3
flow resistance is proportional to density in lb./ft , friction factor, volumetric flow rate, mass,
and pipe inside diameter in inches. The product QM is in pounds of mixture per day. Friction
factor f is determined from a graph plotted as f vs ρ v D and developed based on data from 49
wells on normal depletion and with gas lift.
The graph may be summarized by the following values in Table 4.2 read off the original
chart:
The authors designated W f as energy losses due to irreversibilities of the fluid in flow such
as slippage, liquid hangup or frictional effects, in lbf ft/lbf.
V m is the cubic feet of mixed gas, oil and water at pressure P per barrel of stock tank oil
based on the ratio of fluids flowing into and out of the flow string.
u is integrated velocity of homogeneous mixture in feet per second, average between P 1
and P 2 .
2
g c is a gravitational conversion constant 32.174 lbm ft/(lbf s ).
The summary and comparison with field data for multiphase flow pressure drop correla-
tions for horizontal flow is provided by Al-Ne'aim et al. (1995).

TABLE 4.2 Values read from the friction factor chart by Poettman and Carpenter
.
1 4737 10 −5 MQ 155 28 8.25 2.5 1.65 0.8
ρ
D v =
D
2 gW D 10 10 WD 5
f = c f = 7 413 f 0.001 0.01 0.1 1 10 100
.
(
2
h
2
h
4 uh − ) QV ( h − )
2
2
2
m
1
1