Hydrocarbon Processing - July 2022 - 27

Valves, Pumps and Turbomachinery
HDI: Used 44-point data at 7.8 psi constant
pressure intervals
Omega: Used two-point data at 797.7 psia (0.152 ft3
and 719.4 psia (0.165 ft3
/lb)
New: Used three-point data at 797.7 psia (0.152 ft3
625.4 psia (0.185 ft3
/lb),
/lb) and 445.3 psia (0.248 ft3
/lb)
Case 4: API 520 Part 1, Example Problem B.3.3
Fluid: Low-pressure air at 114.7 psia and 80.33°F (27°C)
HDI: Used 60-point data at 1 psi constant pressure intervals
Omega: Used two-point data at 114.7 psia (1.741 ft3
and 103.7 psia (1.870 ft3
/lb)
/lb)
New: Used three-point data at 114.7 psia (1.741 ft3
85.7 psia (2.141 ft3
/lb) and 55.7 psia (2.907 ft3
/lb),
/lb)
A simple vapor equation satisfactorily sizes PRVs for all
four cases. Red color values in TABLE 1 represent the deviation
in mass flux of > 2% and the deviation in critical pressure
more than the constant pressure interval from the HDI
method. The new method is in excellent agreement with the
HDI method for all four cases. Blue color values in TABLE 1 represent
calculated C values and constant isentropic expansion
coefficients for all four cases.
For Case 1 (slightly subcooled water), a commercial process
simulator using the ASME steam property package provides
the average isentropic expansion coefficient of 0.0729.
The ASME steam specific volume data is in good agreement
with the Case 1 data. The new method predicts the constant
isentropic expansion coefficient of 0.0671. The average isentropic
expansion coefficient with a simple vapor equation results
in undersized PRVs. This fluid is compressible because
Psc
, 66 psia ≤ calculated Psc-max
, 66.13 psia. The C value and
constant isentropic expansion coefficient are much less than
the other cases. The new method predicts better critical pressure
than the HDI method because Simpson used specific volume
data from the same P-v model and numerically integrated
at a constant pressure interval of 0.2 psi.
For Case 2 (two-phase containing hydrogen), there is no
composition information available to evaluate the constant isentropic
expansion coefficient.
For Case 3 (supercritical ethylene), a commercial process
simulator using the SRK (Soave-Redlich-Kwong) property
package provides the average isentropic expansion coefficient
of 1.2424. The SRK specific volume data agrees well with the
Case 3 data. The new method predicts a constant isentropic
expansion coefficient of 1.1863. The average isentropic expansion
coefficient with a simple vapor equation results in
slightly undersized PRVs.
For Case 4 (low-pressure air), a commercial process simulator
using the SRK (Soave-Redlich-Kwong) property package
gives the average isentropic expansion coefficient of 1.4203.
The SRK specific volume data is in good agreement with the
Case 4 data. The new method predicts the constant isentropic
expansion coefficient of 1.4091. This is an acceptable difference
in two isentropic expansion coefficients for air. This
confirms that Eq. 14 is acceptable for ideal vapors or relatively
constant isentropic expansion coefficients.
Takeaways. The above proposed method for sizing compressible
fluid PRVs using a simple vapor equation is an out/lb)
TABLE
1. Comparisons with different sizing method results
HDI
Case 1 Mass flux, lb/sec-ft2
Critical pressure, psia
π or α/β
C / n
Case 2 Mass flux, lb/sec-ft2
π or α/β
C / n
Case 3 Mass flux, lb/sec-ft2
π or α/β
751.76
63.4
N/A
N/A
4,830.8
Critical pressure, psia 1,214.4
N/A
N/A
3,201
Critical pressure, psia 468.8
N/A
C / n
Case 4 Mass flux, lb/sec-ft2
π or α/β
C / n
N/A
379.1
Critical pressure, psia 60.7
N/A
N/A
Omega
748.25
63.21
29.294583
N/A
4,960.50
1,183.8
0.630383
N/A
3,199
458.7
0.785794
N/A
369.9
64.2
0.698517
N/A
New method
751.87
63.33
21.279825 /
1.350907
94.1 / 0.0671
4,852.1
1,227.1
0.57015 /
1.143954
349.7 / 1.3296
3,184.8
463.6
0.733619 /
1.065312
335.8 / 1.1863
379.2
60.4
0.99802 /
0.710831
356.8 / 1.4091
standing approach. The new method is based on the classical
homogeneous equilibrium model chosen by API 520 Part 1
and AIChE/DIERS for emergency pressure relief system designs.
Most pressure relief system engineers are familiar with
the simple vapor equation.
For non-ideal vapors, an average isentropic expansion coefficient
does not give the corresponding correct mass flux because
Eq. 14 assumes ideal vapor. Generally, using the average
isentropic expansion coefficient with a simple vapor equation
can result in undersized PRVs. The new method provides the
most practical solution for a constant isentropic expansion coefficient
that is compatible with a simple vapor equation. For
ideal vapors, an ideal gas-specific heat ratio at the relief inlet
conditions can be used as a constant isentropic expansion coefficient.
The proposed method allows a simple vapor equation
to size compressible fluids (vapors and two-phases including
slightly subcooled liquids) if the three-point data is available
from isentropic flash calculations. This approach produces
rigorous results validated against the existing rigorous HDI
method, while significantly reducing computational efforts
necessary for the numerical integration method.
Presently, there is no standardized PRV specification sheet
for non-ideal vapors and two-phases. The proposed method
using a simple vapor equation will improve the communication
between the valve manufacturer and the relief system designer
for non-ideal vapors and two-phases, including slightly
subcooled liquids. The proposed method using a simple vapor
equation is recommended as the standard sizing methodology
for compressible fluids, including slightly subcooled liquids.
LITERATURE CITED
Complete literature cited available online at www.HydrocarbonProcessing.com.
Hydrocarbon Processing | JULY 2022 27
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Hydrocarbon Processing - July 2022

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