Hydrocarbon Processing - August 2021 - 36

Valves, Pumps and Turbomachinery
TABLE 3. Input data and results of Example B
Input data
P
ρ
Polynomial
Equations
Exponential
-
-
G2
Results
2
= Gs
G
A
+ Gf1
2
-
-
1,419,799,000
37,680
131.4
For all possible fluid states to be relieved, one example was
provided and compared with other sizing methods to support
the approach. The results show that a second-order polynomial
can represent a density-pressure relationship for all fluids
through an isentropic pressure reduction process. However, the
equations derived for targeting the throat pressure are implicit
and must be solved by an appropriate algorithm. The linear
model provides an explicit equation with less accuracy for calculating
the throat pressure.
In the case of subcooled liquid flashing through the nozzle, an
exponential function may offer a more accurate fitting curve to
the density-pressure relationship, leading to an explicit expression
for the throat pressure calculation as well. In general, the
presented analytical solution is accurate enough to be applied
to all fluid states for PSV sizing. It can be extended to take into
account the homogenous non-equilibrium directed integration
model, as well as the slip model recommended for two-phase
flow relief.2,3,9
The density at each step should be corrected accordingly
before using the analytical solution. Also, for twophase
relief sizing, if the density-pressure relationship shows a
high degree of non-linearity, the two-point Omega method is
not recommended for PSV sizing due to the linear interpolation
assumption behind the model development.
NOTES
a Aspen HYSYS
ACKNOWLEDGEMENT
The authors would like to show their gratitude and appreciation to Tony
Steinicke (WSP Process Manager) and Tao Song (WSP Lead Process Engineer) for
their support and feedback.
NOMENCLATURE
a, b and c Coefficients of fitted equations
A
CP
G
h
Kb
Kc
Kd
Kv
m˙
P
Nozzle cross-section area, mm2
Liquid specific heat capacity, kJ/kg-K
Mass flux, kg/sec-m2
Specific enthalpy, kJ/kg
Backpressure correction factor, dimensionless
Combination correction factor, dimensionless
Discharge coefficient, dimensionless
Viscosity correction factor, dimensionless
Mass flowrate, kg/hr
Absolute pressure, kPaa
36 AUGUST 2021 | HydrocarbonProcessing.com
Complete Literature Cited available online at www.HydrocarbonProcessing.com
HOSSEIN HOJJATI has more than 25 yr of industrial and
academic experience. Working mostly in the oil and gas
segments, Dr. Hojjati has been involved in the design of many
conventional and SAGD upstream facilities, as well as natural
gas plants. He graduated from Western University in Canada.
BEHNAZ HOJJATI has more than 20 yr of research, industrial
(EPC companies) and academic experience. Dr. Hojjati has
received numerous acknowledgements and awards, including
the Ontario Graduate Scholarship in Science and Technology
(OGSST) and Industrial R&D Fellowships from the Natural
Science and Engineering Research Council. She graduated from
Western University in Canada.
6
-
-
Using Eq. 24
Using Eq. 2
R2
T
v
Greek letters
α
ρ
Subscripts
b
C
f
lg
l
max
r
sat
s
S
t
v
1
2
3
4
5
G2
2,073.2
510.24
(Pt)C
(Pt)S
Gs
2
-
Subcooled regime
1,400.2
509.28
ρ = 1.3229 × 10−8
R2
p2
+ 1.3775 × 10−3
= 1.0000
-
722.2
1,370,926,972
-
-
Case: 2
-
-
Using Eq. 14
-
(Pt)C
(Pt
)S
Gf2
2
2
= Gs
G
A
+ Gf2
2
722.2
508.32
P + 507.322
722.2
508.32
(Pt
(Pt
)C
)S
Flashed regime
446.2
77.882
ρ = 2.4181 × 10−3 p2
R2
= 1.0000
608.4
608.4
48,872,027
ρ = 5.1874e6.2831 × 10-3 P
611.9
611.9
38,584,370
1,409,511,342
37,543
131.9
R2
170.2
15.845
− 1.2658P + 161.230
Case: 1
Using Eq. 13
-
Using Eq. 10
= 0.9978
Using Eq. 22
-
Using Eq. 21
Using Eq. 24
Using Eq. 2
A statistical measure of goodness of regression, dimensionless
Temperature, K
Specific volume, m3/kg
Actual gas volume fraction
Density, kg/m3
Properties at total backpressure
Calculated
Flashed
Difference between gas and liquid property
Liquid
Maximum
Properties at relief pressure
Saturation
Subcooled
Selected
Properties at throat pressure
Vapor
LITERATURE CITED
American Petroleum Institute (API), " Sizing, selection and installation of pressure-relieving
devices-Part 1: Sizing and selecting, " 9th Ed., 2014.
Darby, R., " Evaluation of two-phase flow models for flashing flow in nozzles, "
Process Safety Progress, 2000.
Darby, R., " Size safety-relief valves for any conditions, " Chemical Engineering,
2005.
Darby, R. et al., " Select the best model for two-phase relief sizing, " Chemical
Engineering Progress, 2001.
Darby, R. et al., " Properly size pressure-relief valves for two-phase flow, " Chemical
Engineering, 2002.
Kim, J. S. et al., " Sizing calculations for pressure-relief valves, " Chemical Engineering,
2013.

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