Sizing - Pietro Fiorentini

Sizing
Pressure Regulators &
Control Valves

Sizing the Pressure Regulators
Sizing of regulators is usually made on the basis of Cg valve and KG sizing coefficients. Flow rates at fully open
position and various operating conditions are related by the following formulae where:
Q = flow rate in Stm 3/h
Pu = inlet pressure in bar (abs)
Pd = outlet pressure in bar (abs).
A > When the Cg and KG values of the regulator are known, as well as Pu and Pd, the flow rate can be calculated
as follows:
A-1 in sub critical conditions: (Pu Vice versa, when the values of Pu, Pd and Q are known,the Cg or KG values, and hence the regulator size,
may be calculated using:
B-1 in sub-critical conditions: (Pu

The above formulae are applicable to natural gas having a relative density of 0.61 w.r.t. air and a
regulator inlet temperature of 15°C. For gases having a different relative density d and temperature
tu in °C, the value of the flow rate, calculated as above, must be multiplied by a correction factor
Fc, as follows:
Fc =
CAUTION:
175.8
S x ( 273.15 + tu )
Correction factors FC
Type of gas
Air
Propane
Butane
Nitrogen
Oxygen
Carbon dioxide
Relative density
1.0
1.53
2.0
0.97
1.14
1.52
Fc Factor
0.78
0.63
0.55
0.79
0.73
0.63
Lists the correction factors Fc for anumber of gases at 15°C.
in order to get optimal performance, to avoid premature erosion phenomena and to limit noise
emissions, it is recommended to check gas speed at the outlet flange does not exceed the values
of the graph below.
The gas speed at the outlet flange may be calculated by means of the following formula:
V
=
345 . 92
Q
x
2
DN
1 - 0.
002 x Pd
x
1 + Pd
Gas speed at the outlet flange [m/sec]
450
400
350
300
250
200
150
100
50
0
0 5 10 15 20 25 30 35 40 45 50 55
Outlet pressure [bar]
where:
V = gas speed in m/sec
Q = gas flow rate in Stm3/h
DN = nominal size of regulator in mm
Pd = outlet pressure in barg.

Cg and Kg valve coefficient
Aperflux 101
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Aperflux 851
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Reflux 819
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Reflux 819/FO
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
25
1"
480
505
113,9
25
1"
575
605
106,78
25
1"
575
605
106,78
Tables
50
2”
1682
1768
103
50
2"
1550
1627
113,9
50
2"
2220
2335
106,78
50
2"
2220
2335
106,78
80
3"
3790
3979
113,9
80
3"
4937
5194
106,78
80
3"
4937
5194
106,78
100
4"
5554
5837
113,9
100
4"
8000
8416
106,78
100
4"
8000
8416
106,78
80
3”
4200
4414
108
150
6"
11112
11678
113,9
150
6"
16607
17471
106,78
150
6"
16607
17471
106,78
200
8"
17316
18199
113,9
200
8"
25933
27282
106,78
200
8"
25933
27282
106,78
250
10"
24548
25850
113,9
250
10"
36525
38425
106,78
250
10"
36525
38425
106,78

Dixi AP
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Staflux 185
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Aperval 101
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Aperval
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
25
1"
159
167
99,5
25
1"
439
462
106,78
25
1"
584
613
90
50
2"
1681
1768
106,78
50
2”
2091
2199
108
80
3"
3764
3960
106,78
50
2"
1978
2077
101
Dival 160 AP
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Staflux 187
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
80
3”
4796
5045
108
65
2"1/2
3530
3706
101
80
3"
4525
4751
101
25
1"
140
147
93,5
25
1"
130
136
106,78
100
4”
7176
7546
108
100
4"
6719
7055
101

Cg and Kg valve coefficient
Reval 182
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Terval
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Terval/R
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Dixi
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
25
1"
575
605
106,78
Tables
50
2"
2220
2335
106,78
65
2" 1/2
3320
4197
106,78
50
2"
1706
1796
108
50
2"
1667
1755
104
25
1"
540
567
96
80
3"
4937
5194
106,78
65
2" 1/2
2731
2875
104
65
2" 1/2
2793
2940
104
40
1" 1/2
983
1034
96
100
4"
8000
8416
106,78
150
6"
16607
17471
106,78
80
3"
3906
4112
100
80
3"
4099
4315
106
50
2"
1014
1066
96
200
8"
25933
27282
106,78
100
4"
5490
5775
100
100
4"
5660
5954
106
250
10"
36525
38425
106,78

Dival 600
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Dival 700
Norval
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Norval 608
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
25
1"
269
283
94
25
1"
331
348
106,78
Head ø 280 Head ø 280/TR
40
1"1/2
652
685
94
40
1"1/2
848
892
106,78
50
2"
1700
1788
106
50
2"
781
821
86
50
2"
1360
1430
106,78
65
2"1/2
2240
2356
106,78
80
3"
3500
3681
106
25
1"
315
331
97
See the capacity Table
80
3"
3395
3571
106,78
40
1"1/2
692
727
95
100
4"
5100
5365
106,78
50
2"
770
809
97
150
6"
10600
11151
106,78
200
8"
16600
17463
106,78

Cg and Kg valve coefficient
Sizing the Control Valve
Choise of the valve is usually on the basis of Cg valve and Cg flow rate coefficients.Cg coefficient corresponds
numerically to the value of air flow in SCF/H in critical conditions with full open valve operating with an upstream
pressure of 1 psia at a temperature of 15°C.KG. coefficient corresponds numerically to the value of natural gas
flow rate in Stm/h in critical conditions with full open valve operating with an upstream pressure of 2 bar abs at a
temperature of 15°C. Flow rates at full open position and various working conditions, are bound by the following
formule where:
Pu = inlet pressure in bar (abs) Q = flow rate in Stm/H
Pd = outlet pressure in bar (abs) KG, Cv, Cg = valve coefficent
1 > When the Cg and KG values of the control valve are known, as well as Pu and Pd, the flow rate can be
calculated as follows:
1.1 > in non critical conditions:
1.2 > in critical conditions:
Reflux 919 - Syncroflux - VLM
Q = KG (Pu - Pd) Pd Q = 16,8 x Cv x Pu x sin 106,78
KG
Q x
= 2
2 > Vice versa, when the values of Pu, Pd and Q are known, calculate the values of Cv, Cg or KG with:
KG =
Q
Pd ( Pu - Pd )
Cv =
Pu - Pd
Pu Q= 16,8 x Cv x Pu Q= 0,526 x Cg x Pu (valid for Pu ≥ 2 x Pd)
Q
.16,8x
Pux
sinx
106,78
Pu - Pd
((
Pu
(valid for Pu < 2 x Pd)
2.2 > in critical conditions: x Q
KG =
(valid for Pu ≥ 2 x Pd)
Pu
2
Q
Q
Cv =
Cg =
16,8 x Pu
0,526 x Pu
Pu
(valid for Pu < 2 x Pd)
Q
A oversizing of 20% on calculated values is raccomanded. Cg formulae give flow rate values more correct while
KG formulae give values 5% higher than real ones only in noncritical conditions. In the case of noise limitation level
a speed at the outlet flange of 130 m/sec. it is also raccomanded. Above formulae are valid for natural gas with a
relative specific gravity of 0,61 compared to air and temperature of 15° C at inlet. For gases with different relative
specific gravity (S) and temperature t (in °C) ), value of flow rate calculated as above, must be adjusted multiplying
by:
175.8
Fc =
S x ( 273.15 + tu )
Reflux 919 - Syncroflux - VLM
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
Cv flow coefficient
Q = 0,526 x Cg x Pu x sin
25
1"
575
605
18
50
2"
2200
2335
69
106,78
80
3"
4937
5194
154
Pu - Pd
100
4"
8000
8416
250
Pu
Cg =
150
6"
16607
17471
519
200
8"
25933
27282
810
250
10"
36525
38425
1141
( (
( (
0,526 . xPux
sinx
106,78
Pu - Pd
((
Pu

Sizing the Control Valve
A. Subcritical conditions
(when ΔP < 0.5F 2 P1)
Volume flow rate (gas and vapor)
Q = 290 Cv
P Δ (P1+P2)
G T
Weight flow rate (gas and vapor)
Q = 355 Cv
GΔP (P1+P2)
T
Weight flow rate (saturated steam)
W = 13,55 Cv ΔP (P1+P2)
Weight flow rate (overheated steam)
Cv ΔP (P1+P2)
W = 13,55
(1+0,00126Δt)
B. Critical conditions
(when ΔP 0.5F2 P1)
Volume flow rate (gas and vapor)
262 F Cv P1
Q =
G T
Weight flow rate (gas and vapor)
W = 321 F Cv P1
G
T
Weight flow rate (saturated steam)
W = 11,73 F Cv P1
Weight flow rate (overheated steam)
F Cv P1
W = 11,73
(1+0,00126 Δ t)
Deltaflux
GAS, VAPOR AND STEAM BIPHASE FLUIDS
A. Subcritical conditions
(when ΔP < 0.5F 2 P1)
Constant liquid/gas mixture ratio (liquid containing
non condensable gas or liquid containing high title
vapor)
W = 19,1 Cv ΔP (w1+w2)
Variable liquid/vapor mixture ratio (liquid containing
low title vapor, less then 0.5)
W = 27,1 Cv ΔP w1
B. Critical conditions
(when ΔP ≥ 0.5F 2 P1)
Constant liquid/gas mixture ratio (liquid containing
non condensable gas or liquid containing high title
vapor)
W = 13,5 F Cv P1 (w1+w2)
Variable liquid/vapor mixture ratio (liquid containing
low title vapor, less then 0.5)
W = 19,1 F Cv P1 w1
100
w1 =
Xg (Vg1-Vf) + 100 Vf
100
w2 =
Xg (Vg2-Vf) + 100 Vf

Cg and Kg valve coefficient
LIQUIDS
Glossary
A. Subcritical conditions
(when ΔP < F 2 ΔPc)
Volume flow rate
Cv ΔP
Qf =
1.17 Gf
Weight flow rate
W = 855 Cv GfΔP
Note:
For values of ΔP ≥ ΔPk the
valve works under cavitation
conditions.
Deltaflux
Cv = valve flow rate coefficient: US gpm of water with
∆P = 1 psi
ΔP = valve pressure drop P1-P2: bar
ΔPc = maximum dimensioning differential pressure: bar
ΔPk = cavitation differential pressure: bar
Δt = overheating temperature delta t1 - ts: °C
F = valve recovery factor: non dimensional
G = gas relative density (air=1): non dimensional
Gf = liquid relative density at operating temperature
(water at 15°C=1)
Kc = valve incipient cavitation factor: non dimensional
Xg = weight percentage of gas or vapor in the mixture at
upstream pressure: %
P1 = valve upstream pressure: bar abs
P2 = valve downstream pressure: bar abs
Pc
Pk
Pv
T
t1
ts
Q
Qf
W
W1
W2
Vf
Vg1
Vg2
B. Critical conditions
(when ΔP ≥ F 2 ΔPc)
Volume flow rate
F Cv ΔPc
Qf =
1.17 Gf
Weight flow rate
W = 855 F Cv Gf Δ Pc
ΔPc = P1-Pc
Pc = Pv (0,96-0,28
Pv
Pk
ΔPk = Kc (P1-Pv)
= vena contracta critical pressure: bar abs
= thermodynamic critical point pressure: bar abs
= vapor pressure at operating temperature: bar abs
= upstream gas absolute temperature (273+°C): °K
= overheated steam upstream temperature: °C
= saturated steam temperature at upstream pressure: °C
= volume flow rate at 15 °C and 1.013 bar abs: Sm3/h
= volume flow rate: m3/h
= weight flow rate: Kg/h
= upstream mixture density: kg/m3
= downstream mixture density: kg/m3
= specific volume of liquid: m3/kg
= specific volume of gas or vapor at upstream pressure: m3/kg
= specific volume of gas or vapor at downstream pressure: m3/kg
)

Cv coefficient
Deltaflux
Dn
2"
3"
4"
6"
8"
10"
12"
14"
16"
18"
20"
24"
Deltaflux
Dn
2"
3"
4"
6"
8"
10"
12"
14"
16"
18"
20"
24"
Cv coefficient
at 100% opening
82
215
405
1080
1750
2860
3980
5000
6800
8400
10600
16100
Cv coefficient
at 100% opening
60
150
290
650
1225
1975
2825
3475
4675
5950
7500
11100
Liquid control application
Liquid trim
Gas control application
Gas trim
Deltaflux
Note: To verify the dimensioning and, in detail, for the dimensioning of Deltaflux control
valves bigger than 24”, always refer to Pietro Fiorentini S.p.A.

Sizing the Slam Shut Valves
Calculation of the pressure drop
The following formula can be used to calculate pressure losses of the slam shut valve in fully
open position:
Δp = KG x Pu - (KG2 x Pu 2) - 4Q 2
2 x KG
Δp = pressure loss in bar
Pu = absolute inlet pressure in bar
Q = flow rate Stm3/h
KG = flow coefficient
Pressure loss calculated as above is referred to natural gas with specific gravity of 0.61 (air=1)
temperature of 15 °C at valve inlet, for gases with different specific gravity S and temperatures t
°C, pressure loss can still be calculated with the above formula, replacing the value of the flow
coefficent in the table with:
KG1 = KG x
S x
175 . 8
( 273 . 15
+ t)

SBC 782
Nominal diameter (mm)
Size (inches)
KG flow coefficient
SCN
Nominal diameter (mm)
Size (inches)
KG flow coefficient
HBC 975
Nominal diameter (mm)
Size (inches)
KG flow coefficient
Dilock 108
Nominal diameter (mm)
Size (inches)
KG flow coefficient
25
1"
510
25
1"
549
50
2"
1970
40
1" 1/2
1116
100
4"
7120
25
1"
500
65
2" 1/2
3550
50
2"
1788
150
6"
14780
40
1" 1/2
860
80
3"
4390
65
2" 1/2
2603
200
8"
23080
50
2"
976
80
3"
4086
100
4"
7120
100
4"
6122
250
10"
32470
150
6"
14780
150
6"
13680
200
8"
23080
200
8"
21700
250
10"
32506

Sizing the Safety Relief Valves
Calculation of the safety relief valves
The flow rate is calculated by the following formulae:
M
q = (0.9 Kc) • (394.9 x C) • P1 A • Q = 23.661
q = maximum flow rate to be discharged, in Kg/h
Q = maximum flow rate (Stm3/h)
A = minimum area (cm2) (see table)
Kc = outflow coefficient
P1= setting pressure plus a 10% overpressure (bar abs)
T1= temperature in °K of the fluid at the valve inlet during
the discarge, reported by user or by designer.
0,9 = safety coefficient
M = molecular mass of the fluid in Kg/Kmol (see table)
Z1 = compressibiliti factor of the fluid under the P1
conditions to be considered approximately equal to
one if the actual values is not known.
k=
Z1 T1
Cp exponent of equation of the isentropic expansion
Cv under the P1 and T1 conditions.
Cp = specific heat at consistant pressure
Cv = specific heat at consistant volume
C = coefficient of expansion = C =
(see table)
2
k ( )
k+1
k-1
k+1
q
M

PVS 782
Nominal diameter (mm)
Size (inches)
Calculation area (cm2)
Outflow coefficient K
Molecular mass and expansion coeff.
Relative density
Carbon dioxide
Hydrogen
Methane
Natural gas*
Nitrogen
Oxigen
Propane
* Medium value
Molecular mass M
28,97
44,01
2,02
16,04
18,04
28,02
32,00
44,09
Capacity table versus pressure
Pressure
Nominal diameter (mm)
Size
2 barg
10 barg
20 barg
30 barg
40 barg
Flow rate (Kg/h)
25
1"
332
1885
2472
5337
7063
25
1"
4,71
0,56
50
2"
20,03
0,56
Coefficient of expansion C
0,685
0,668
0,686
0,669
0,669
0,685
0,685
0,635
50
2"
2144
8016
15357
22697
30038
80
3"
4604
17214
32976
48738
64500
80
3"
43,01
0,56
100
4"
7991
29881
57242
84603
111964
100
4"
74,66
0,56
150
6"
18043
67462
129235
191008
252781
150
6"
168,56
0,56
200
8"
27788
103894
199028
294161
389295
200
8"
259,59
0,56

The data are not binding. We reserve the
right to make eventual changes without
prior notice.
CT-s 570-E June 12
DA SISTEMARE !!!!!!!!
www.fiorentini.com
Pietro Fiorentini S.p.A.
via E.Fermi 8/10
I-36057 Arcugnano (VI) Italy
Tel. +39 0444 968.511
Fax. +39 0444 960.468