Hydrocarbon Processing - August 2021 - 34

Valves, Pumps and Turbomachinery
60,969.1 kg/hr liquid) at 427.5 K, which must be relieved to a
storage tank (no credit was taken for the gas outlet). The entire
process was simulated using a proprietary process simulatora
and fluid properties; the hydraulics of vessels and pipes were
also estimated. At relief conditions-427.5 K and 1,201.1 kPaa
(10% overpressure and atmospheric pressure 101.1 kPaa)-
the properties were calculated (TABLE 1) and the two-phase flow
discharge coefficient was estimated to be Kd
method presented by Leung.10
= 0.873 using the
Additionally, the total backpressure
was calculated to be 231 kPag (332.1 kPaa) at the rated
flowrate, resulting in Kb
= 0.990.
= 1 for the balanced PSV (Crosby backpressure
curves were used). The viscosity correction factor was
estimated to be Kv
Through an isentropic process, the fluid relief pressure was
reduced two times (with a 345-kPa interval) and the density
was calculated (TABLE 2). The data was fitted to a linear as well
as a second-order polynomial using a proper regression method
(FIG. 1). The throat pressure and the maximum mass flux were
then calculated. The calculation details and results are summarized
in TABLE 2.
The valve is sized by HDIM as well as a two-point Omega
For HDIM, the density of the fluid was calculated with
method.8
a 7-kPa interval pressure reduction; the mass flux and the required
area were then calculated from the numerical solution of
Eq. 1. For the Omega method, however, the required properties
at 90% of the relief (saturation) pressure (1,081 kPaa) were estimated
through an isentropic process (TABLE 1) and the valve was
then sized. The maximum mass fluxes and required nozzle areas
calculated by both methods are found in TABLE 2 for comparison.
450
350
250
150
50
450
Data
Linear fit
The second-order polynomial fit
For two-phase flow PSV sizing, Simpson9
presented a method
based on a two-point interpolation scheme for properties
estimation and numerical integration of Eq.1. The first point
was at the relief pressure and the second one was at a pressure
between 50% to 95% of the relief pressure (in this example,
700 kPaa). Along an isentropic path, the fluid was flashed from
1,201.1 kPaa to 700 kPaa; the input data are summarized in
TABLE 1. Using provided two-point data, the density was estimated
and then the mass flux and the required area were calculated
from the numerical solution of Eq. 1 with a pressure interval of
10 kPa. The results are summarized in TABLE 2 for comparison.
Although all methods led to a calculated API PSV size of
" L " , the two-point Omega method resulted in a less conservative
nozzle size, which can be related to the linear interpolation
data behind the model. Based on the authors' PSV sizing experiences,
once the density-pressure trend deviates from a linear
behavior, the two-point Omega method is not recommended
for two-phase relief PSV sizing, as it may result in an undersized
PSV. However, a linear trend will result in the same PSV size
using all methods, including the Omega method, which is consistent
with the linear-interpolation assumption applied to the
two points of the Omega method (see the two-phase example
in supporting examples).
For two-phase flow relief, the proposed analytical method is
generally accurate enough to size PSVs; however, if slip effect or
HNE model3
is a concern, the proposed approach is still valid
for PSV sizing. In such cases, the density as a function of pressure
is estimated, corrected using the slip or the HNE model,
and then applied for the illustrated procedure to size PSV for
two-phase relief.
650
850
Pressure, kPaa
FIG. 1. A regression method with linear and second-order
polynomial data.
600
500
400
300
200
100
1,050
1,250
Example B: Subcooled or saturated liquid flashing at
the throat. The most challenging part of the proposed method
is when the PSV sizing process is dealing with saturated or highly
subcooled liquid flashing (the liquid reaches the saturation
pressure flowing through the nozzle). In this condition, two different
regimes have different density trends. In the subcooled
regime, the density is almost constant, whereas high-density
variations can be observed after the liquid starts flashing. These
variations cannot be fitted by an individual equation (FIG. 2).
Fortunately, a solution exists for such a condition. The integral
has an interval addition property allowing us to divide it into
two intervals-in our case, one interval for subcooled liquid
and another one for flashed liquid-that hold the same conditions.
Therefore, Eq. 1 can be rearranged into (Eq. 24):
G2 =Gs
2 +Gf
2 = −2,000×ρsat
2
× ∫
Subcooled regime data
Flashed regime data
Subcooled regime fit
Flashed regime fit
500
1,000
Pressure, kPaa
1,500
2,000
2,500
FIG. 2. Different regimes have different density trends, and variations
cannot be fitted by an individual equation.
34 AUGUST 2021 | HydrocarbonProcessing.com
dP
P ρr
Psat
−2,000×ρt
2 × ∫
dP
P ρsat
Pt
The maximum mass flux of the subcooled regime, Gs
(24)
2, can
be estimated using Eq. 23 as well, if the density does not vary
significantly over the pressure range. The flashing regime can be
fitted into a second-order polynomial or an exponential function.
To show the capability of the proposed solution under
such a condition, consider the example C.2.3.2 of API-520-11
,
in which 378.5 L/min (11,588 kg/hr) of subcooled propane
should be relieved at 2,073.2 kPaa and 288.7 K. The downstream
total backpressure was 170.2 kPaa, leading to a backpressure
correction factor unit. The discharge coefficient was 0.65
and the viscosity correction factor was assumed to be 1. The
Density, kg/m3
Density, kg/m3
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