Hydrocarbon Processing - July 2022 - 26

Valves, Pumps and Turbomachinery
For 12 < C ≤ 160:
n = 2.5343E-11 × C4
C2
For C > 160:
n = 3.8459E-13 × C5
-8.3347E-10 × C3
-2.433E-6 × C + 3.3047E-5
- 3.7986E-10 × C4
+ 1.7953E-7 ×
C3-3.3542E-5 × C2 + 4.6767E-3 × C - 2.1238E-1 (17)
A new method for sizing compressible fluids. Sizing
methods for significantly non-ideal vapors and two-phases-
including slightly subcooled liquids-have not yet been standardized.
However, many effective new methods have been
developed over the last few decades. A new method for sizing
compressible fluids using a simple vapor equation is proposed
here to be a standard sizing method. All equations required for
the new method are summarized here based on the standard
steps in a work procedure (Eqs. 1, 6, 9, 10, 15, 16 and 17 ):
W
A =
v
v0
⎡
Pec =
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
C × Kd × P0 × Kb × Kc
β
⎡
⎣
− 1 =α × ⎢
⎛
⎝
P0
P
⎞
⎠
−2 × α × β × P0
Psc−max = p0 +
⎣ ( 1−α) × p−p0
p0
⎛
⎝
⎜
⎜
⎜
)+
(
1
C = 520 ×
×
α × β
For 12 < C ≤ 160:
n = 2.5343E-11 × C4
C2
For C > 160:
n = 3.8459E-13 × C5
( p0 −psc
⎤
⎦
β× α ×
⎡
⎣
⎢
⎢
α × p0
1−β
)
2 × α × β
⎛
⎜⎝
pc
p0
⎞
⎟⎠
β+1
(15)
-8.3347E-10 × C3
-2.433E-6 × C + 3.3047E-5
- 3.7986E-10 × C4
+ 1.7953E-7 ×
C3-3.3542E-5 × C2 + 4.6767E-3 × C - 2.1238E-1 (17)
Detailed standard steps in a work procedure. The following
procedure can be used for sizing compressible fluids (including
slightly subcooled liquids) using a simple vapor equation:
1. Calculate the two parameters, α and β, in Eq. 6 using
three pressure-specific volume data:
* Two flash calculations should be carried out
at constant entropy
* P0 is at the PRV inlet
* P0 is at the saturated pressure for slightly subcooled
liquids; do not include the subcooled region
* P2 is at the backpressure or 50% of P0
26 JULY 2022 | HydrocarbonProcessing.com
+ 7.4632E-6 ×
(16)
β
× p1−β− p0
1−β
(
⎛
⎜⎝
p0
p
⎞
⎟⎠
β
− α+ 1
) +
⎞
⎠
⎟
⎟
⎟
⎤
⎦
⎥
⎥
−2
×
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
(10)
−1⎥
×
T×Z
M
(1)
(6)
1
⎤β+1
+ 7.4632E-6 ×
(16)
(not greater than the critical pressure)
* P1 is the average pressure of P0
* Higher P2
would improve the calculation accuracy
and P2
* Use a goal seek feature or a simple macro program.
2. Calculate the C value in Eq. 15:
* For subcooled liquids, determine if the fluid
is compressible or incompressible using Eq. 10;
do not use this method for incompressible fluids
* Psc = P0 if the fluid is not subcooled
* Specify the Psc
(Psc
≤ Psc-max
)
* Calculate the Pc (Pec-max
until the Pec
Pec instead of Pc (Pec-max
the Pc (Pec-max
if the fluid is slightly subcooled
) iteratively using Eq. 9
is equal to P; alternatively, Eq. 11
can be used to avoid iteration
* For a subcritical flow with conventional valves,
calculate the Pec
without iteration; use the
) and use Kb
) using Eq. 9 until the Pec
* For a subcritical flow with balanced valves, use the
Pc
to P and use Kb = Cat Pec /Cat Pc
(Pec-max
factor (Kb
), and apply the backpressure correction
) supplied by valve manufacturers
* Use a goal seek feature or a simple macro program.
3. Calculate the n using Eqs. 16 and 17:
* n (constant isentropic expansion coefficient)
is specified on the PRV specification sheet.
4. As usual , size PRVs using Eq. 1:
* Eq. 1 can size vapors and two-phases, including
slightly subcooled liquids.
(9)
Validation of new method. This section is included to validate
the proposed method by comparing it with the existing
HDI and Omega methods using readily available example
problems from API 520 Part 1-API 520 Part 1 does not
cite an example for slightly subcooled liquids. Case 1 is from
Simpson's Example 1.2 TABLE 1 shows comparisons with different
sizing method results for the following four cases.
Case 1 : Simpson's Example 1
Fluid: Subcooled water at 66 psia and 298°F (148°C),
saturated at 65 psi
HDI: Used 12-point data at 0.2 psi constant
pressure intervals
Omega: Used two-point data at 65 psia (0.017433 ft3
and 58.5 psia (0.074177 ft3
/lb)
New: Used three-point data at 65 psia (0.017433 ft3
48 psia (0.205211 ft3
/lb),
/lb), and 32 psia (0.612741 ft3
Case 2: API 520 Part 1, Example Problem C.2.1.2
Fluid: Two-phase containing a significant amount of
hydrogen at 2,168.5 psia and 80.3°F (27°C)
HDI: Used 14-point data at 86.7 psi constant
pressure intervals
Omega: Used two-point data at 2,168.5 psia (5.18 lb/ft3
and 1,908.3 psia (4.77 lb/ft3
)
New: Used three-point data at 2,168.5 psia (5.18 lb/ft3
1,648.1 psia (4.28 lb/ft3
),
) and 1,040.9 psia (2.96 lb/ft3
)
Case 3: API 520 Part 1, Example Problem B.1.3
Fluid: Supercritical ethylene at 797.7 psia and 80.33°F (27°C)
)
/lb)
/lb)
= 1, or calculate
is equal
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