Hydrocarbon Processing - June 2021 - 27

Process Optimization
Weber number is approximately 17 and increases with
increasing viscosity.5
However, the Weber number (Eq.
10) does not include the influence of viscosity. Turner et
al. also indicated that the critical Weber number for freefalling
droplets in a vertical turbulent gas flow was found
to be approximately 20-30.7
Eq. 9 is obtained based on
the critical Weber number of 17.
17 × σ
D =
We =
ρv × uv−reentrainment
2
D × ρg × u2
σ
3. Calculate the Froude number at the onset liquid
re-entrainment vapor velocity conditions, using Eq.
11. The Froude number is a measure of the ratio
of aerodynamic forces from the vapor phase to
gravitational effects on the liquid phase. Therefore,
liquid droplets settle when the Froude number is
reduced as the vapor velocity decreases.
Fr =
uv−reentrainment
2
g × D
×
ρg
ρf −ρg
4. Calculate the axial vapor velocity limit at the target
liquid droplet particle size, using Eq. 12. It is assumed
that the Froude number at the onset liquid reentrainment
velocity is still valid for the target liquid
droplet particle size to become suspended in the vapor
phase. The axial vapor velocity expected is smaller than
the onset liquid re-entrainment vapor velocity, since the
target particle size is smaller.
uv−maxmum = g × Dp × Fr ×
ρf −ρg
ρg
(12)
Rearranging Eq. 12-in terms of fluid physical properties-
becomes Eq. 13, which can be used to estimate the maximum
horizontal KO drum vapor velocity to remove the intended liquid
droplets and prevent them from being entrained in the vapor
phase. Eq. 13 is expressed in international system (SI) units
in Eq. 14. In U.S. customary units:
uv−maximum = 4.5064 × ρf × σ1.5 × ⎜
⎡
⎣
⎢
⎢
⎢
where
uv - maximum
⎛
⎝
Dp
ρg
⎞
⎠
⎟
2.5
×
⎛
⎝
⎜
⎜
Dp = the liquid droplet diameter, ft
g = the acceleration due to gravity, 32.174 ft/sec2
TABLE 2. Optimizing results of the API 521 sample calculations
Trial no.
1
2
3
4
Drum diameter,
ft
8
7.5
7
6.5
Drum length,
ft
19
20.5
22.5
25
Vapor space
area, ft2
20.43
16.52
13.29
10.51
Vertical depth of
vapor spaces, in.
41
36
31.7
27.6
Vapor retention
time, sec
1.45
1.28
1.13
0.98
Axial vapor
velocity, ft/sec
12.76
15.78
19.62
24.82
Minimum drum
length, ft
18.5
20.2
22.1
24.3
Hydrocarbon Processing | JUNE 2021 27
g × ρf −ρg
µf
(
= the axial vapor velocity limit, ft/sec
)
⎞
⎠
⎟
⎟
2
⎤
⎦
⎥
⎥
⎥
0.2
(13)
(11)
In SI units:
(9)
(10)
uv−maximum = 0.4839 × ρf × σ1.5 × ⎜
⎡
⎣
⎢
⎢
⎢
where
uv - maximum
⎛
⎝
Dp
ρg
⎞
⎠
⎟
2.5
×
⎛
⎝
⎜
⎜
Dp = the liquid droplet diameter, m
g = the acceleration due to gravity, 9.807 m/sec2
ρf
ρg
= the density of liquid at operating conditions, kg/m3
= the density of vapor at operating conditions, kg/m3
σ = the liquid surface tension, mN/m (dyn/cm)
μf
= the viscosity of liquid in millipascal-seconds (mPa-sec).
Comparison of various axial vapor velocity guidelines.
The following example for the API 521 sample calculations is
used to compare the various vapor velocity guidelines. The operating
conditions include the following:
* Vapor flowrate of 169,000 lb/hr, with a vapor density
of 0.18 lb/ft3
* Liquid flowrate of 31,000 lb/hr, with a liquid density
of 31 lb/ft3
* Drop size selected, as allowable: 300 µm (0.000984252 ft)
* Viscosity of the vapor: 0.01 cP
* Viscosity of the liquid: 0.5 cP (assumed for this evaluation)
* An assumed liquid surface tension of 20 dynes/cm
(0.0441 lbm/sec2
)
* Flare vapors that are assumed wet and combustible
for this evaluation.
TABLE 2 is a result of the API 521 optimized designs of the horizontal
KO drum. The droplet settling velocity obtained from Eq. 1 is
2.35 ft/sec. The onset liquid re-entrainment velocity, obtained
from Eq. 8, is 18.76 ft/sec. CCPS recommends limiting the axial
vapor velocity below the onset liquid re-entrainment velocity to
prevent re-entrainment from the liquid surface in the horizontal
flare KO drum. However, the axial vapor velocities in trial numbers
3 and 4 exceed the liquid re-entrainment velocity because
API 521 does not have any vapor velocity limit guidelines.
TABLE 3 shows comparisons of the axial vapor velocity
guidelines presently available. The API 521 guidelines predict
velocities that are too high and that could exceed the liquid reentrainment
limit. While the API 12J specification is not applicable
for a horizontal separator without an internal demister,
g × ρf −ρg
µf
(
= the axial vapor velocity limit, m/sec
)
⎞
⎠
⎟
⎟
2
⎤
⎦
⎥
⎥
⎥
0.2
(14)
ρf = the density of liquid at operating conditions, lb/ft3
ρg = the density of vapor at operating conditions, lb/ft3
by 453.6 to convert to lbm/sec2
μf = the viscosity of liquid in cP.
σ = the liquid surface tension, lbm/sec2 (divide dynes/cm
)
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