Sizing
Pressure Regulators &
Control Valves
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 Stm3/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<2xPd)
A-2 in critical conditions: (Pu≥2xPd)
B > 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<2xPd)
B-2 in critical conditions (Pu≥2xPd)
NOTE: The sin val is understood to be DEG.
K sin Pu Cg Q = 0.526 x x x 1x ) (Pu Pd Pd KG x x -Pu KG Q = x Q = 2 Q =0.526xCg xPu ) (Pu Pd Pd Q KG -x = sin Pu Q Cg x x = 526 . 0 Pu Q KG= 2x 0,526 x Pu Q Cg = Pu Pd Pu -
(
(
K1x Pu Pd Pu -(
(
REGULATOR INTEGRALSLAM SHUT INTEGRAL MONITOR INTEGRALSILENCER
APERFLUX 851 -5% -5% -5% REFLUX 819 -7% -7% -5% REFLUX 819/FO -7% -7% -5% APERVAL SA -10% -5%SB -5% -5% REVAL 182 SA -10% -7%SB -7% -5%
DIXI -3% Not applicable Not applicable
DIVAL 600 0% Not applicable 0%
NORVAL -7% Not applicable Not applicable
NORVAL 608 -7% Not applicable -10% CAPACITY REDUCTION TABLE:
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:
175.8 S x ( 273.15 + tu ) Fc =
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.
Fc Factor 0.78 0.63 0.55 0.79 0.73 0.63 Relative density 1.0 1.53 2.0 0.97 1.14 1.52 Type of gas Air Propane Butane Nitrogen Oxygen Carbon dioxide Correction factors FC
Lists the correction factors Fc for anumber of gases at 15°C.
CAUTION:
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.
140 150 160 170 180 190 200 210 220 230 240 250 260 0 1 2 3 4 5 6 7 8 9 10 11
Outlet pressure [bar]
Gas pressure at the outlet flange [m/sec]
The gas speed at the outlet flange may be calculated by means of the following formula:
Pd Pd DN Q V + x -x x = 1 002 . 0 1 92 . 345 2
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Reflux 819/FO
25
1"
575
605
106,78
200
8"
25933
27282
106,78
150
6"
16607
17471
106,78
80
3"
4937
5194
106,78
50
2"
2220
2335
106,78
100
4"
8000
8416
106,78
250
10"
36525
38425
106,78
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Reflux 819
25
1"
575
605
106,78
200
8"
25933
27282
106,78
150
6"
16607
17471
106,78
80
3"
4937
5194
106,78
50
2"
2220
2335
106,78
100
4"
8000
8416
106,78
250
10"
36525
38425
106,78
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Aperflux 851
150
6"
11112
11678
113,9
25
1"
480
505
113,9
200
8"
17316
18199
113,9
80
3"
3790
3979
113,9
50
2"
1550
1627
113,9
100
4"
5554
5837
113,9
250
10"
24548
25850
113,9
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
50
2”
1682
1768
103
80
3”
4200
4414
108
Aperflux 101
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Staflux 185
25
1"
439
462
106,78
80
3"
3764
3960
106,78
50
2"
1681
1768
106,78
Staflux 187
25
1"
130
136
106,78
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
25
1"
159
167
99,5
Dixi AP
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
25
1"
140
147
93,5
Dival 160 AP
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Aperval 101
50
2”
2091
2199
108
80
3”
4796
5045
108
100
4”
7176
7546
108
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Aperval
25
1"
584
613
90
100
4"
6719
7055
101
65
2"1/2
3530
3706
101
50
2"
1978
2077
101
80
3"
4525
4751
101
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Terval
100
4"
5490
5775
100
65
2"
1/22731
2875
104
50
2"
1706
1796
108
80
3"
3906
4112
100
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
25
1"
575
605
106,78
150
6"
16607
17471
106,78
100
4"
8000
8416
106,78
65
2"
1/23320
4197
106,78
50
2"
2220
2335
106,78
80
3"
4937
5194
106,78
200
8"
25933
27282
106,78
250
10"
36525
38425
106,78
Reval 182
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Terval/R
100
4"
5660
5954
106
65
2"
1/22793
2940
104
50
2"
1667
1755
104
80
3"
4099
4315
106
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Dixi
50
2"
1014
1066
96
25
1"
540
567
96
40
1"
1/2983
1034
96
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Norval 608
50
2"
1700
1788
106
80
3"
3500
3681
106
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Norval
25
1"
331
348
106,78
80
3"
3395
3571
106,78
65
2"1/2
2240
2356
106,78
40
1"1/2
848
892
106,78
100
4"
5100
5365
106,78
50
2"
1360
1430
106,78
150
6"
10600
11151
106,78
200
8"
16600
17463
106,78
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
K1 body shape factor
Dival 600
25
1"
269
283
94
40
1"1/2
652
685
94
50
2"
781
821
86
40
1"1/2
692
727
95
50
2"
770
809
97
Head ø 280
Head ø 280/TR
25
1"
315
331
97
Dival 700
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:
2 > Vice versa, when the values of Pu, Pd and Q are known, calculate the values of Cv, Cg or KG with:
2.2 > in critical conditions: (valid for Pu ≥ 2 x Pd)
Reflux 919 - Syncroflux - VLM
Sizing the Control Valve
(Pu - Pd) Pd KG Q = Q = 16,8 xCv x Pu xsin 106,78 Pu Pu - Pd ( ( Pu Q= 16,8 x Cv x Pu Q= 0,526 x Cg x Pu (valid for Pu ≥ 2 x Pd) KG Q = x 2 (valid for Pu < 2 x Pd) (Pu Pd ) Pd Q KG -= sin Pu Q Cv x 106,78 x x = .16,8 Pu Pd Pu -
(
(
Pu Q KG= 2x 16,8 x Pu Q Cv =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 S x ( 273.15 + tu ) Fc = (valid for Pu < 2 x Pd)
Nominal diameter (mm)
Size (inches)
Cg flow coefficient
KG flow coefficient
Cv flow coefficient
Reflux 919 - Syncroflux - VLM
25
1"
575
605
18
200
8"
25933
27282
810
150
6"
16607
17471
519
80
3"
4937
5194
154
50
2"
2200
2335
69
100
4"
8000
8416
250
250
10"
36525
38425
1141
106,78 sin Pu Cg Q = 0,526 x x x Pu Pu - Pd ( ( sin Pu Q Cg x 106,78 x x = . 0,526 Pu Pd Pu -(
(
0,526 x Pu Q Cg =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:
2 > Vice versa, when the values of Pu, Pd and Q are known, calculate the values of Cv, Cg or KG with:
2.2 > in critical conditions: (valid for Pu ≥ 2 x Pd)
Deltaflux
Sizing the Control Valve
Volume flow rate (gas and vapor)
Weight flow rate (gas and vapor)
Weight flow rate (saturated steam)
Weight flow rate (overheated steam)
Volume flow rate (gas and vapor)
Weight flow rate (gas and vapor)
Weight flow rate (saturated steam)
Weight flow rate (overheated steam) ΔP (P1+P2) G T Q = 290 Cv Q = 355 Cv GΔP (P1+P2) T W = 13,55 Cv ΔP (P1+P2) W = 13,55Cv ΔP (P1+P2) (1+0,00126Δt) Q =262 F Cv P1 G T W = 321 F Cv P1 G T W = 11,73 F Cv P1 W = 11,73 F Cv P1 (1+0,00126 Δ t) B. Critical conditions (when ΔP 0.5F2 P1) A. Subcritical conditions (when ΔP < 0.5F2 P1) W = 19,1 Cv ΔP (w1+w2) W = 27,1 Cv ΔP w1 W = 13,5 F Cv P1 (w1+w2) W = 19,1 F Cv P1 w1 w1 = 100 Xg (Vg1-Vf) + 100 Vf w2 = 100 Xg (Vg2-Vf) + 100 Vf B. Critical conditions (when ΔP ≥ 0.5F2 P1)
Constant liquid/gas mixture ratio (liquid containing non condensable gas or liquid containing high title vapor)
Variable liquid/vapor mixture ratio (liquid containing low title vapor, less then 0.5)
Variable liquid/vapor mixture ratio (liquid containing low title vapor, less then 0.5)
Constant liquid/gas mixture ratio (liquid containing non condensable gas or liquid containing high title vapor)
A. Subcritical conditions (when ΔP < 0.5F2 P1)
A. Subcritical conditions (when ΔP < F2 ΔPc)
Volume flow rate
Weight flow rate W = 855 Cv GfΔP
Qf = Cv ΔP 1.17 Gf
Note:
For values of ΔP ≥ ΔPk the valve works under cavitation conditions.
LIQUIDS
= valve flow rate coefficient: US gpm of water with ∆P = 1 psi
= valve pressure drop P1-P2: bar
= maximum dimensioning differential pressure: bar = cavitation differential pressure: bar
= overheating temperature delta t1 - ts: °C = valve recovery factor: non dimensional = gas relative density (air=1): non dimensional = liquid relative density at operating temperature (water at 15°C=1)
= valve incipient cavitation factor: non dimensional = weight percentage of gas or vapor in the mixture at upstream pressure: %
= valve upstream pressure: bar abs = valve downstream pressure: bar abs
= 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 ΔP ΔPc ΔPk Δt F G Gf Kc Xg P1 P2 Pc Pk Pv T t1 ts Q Qf W W1 W2 Vf Vg1 Vg2
Glossary
B. Critical conditions (when ΔP ≥ F2 ΔPc)Volume flow rate
Weight flow rate Qf = F Cv 1.17 Gf W = 855 F Cv Gf Δ Pc ΔPc = P1-Pc ΔPk = Kc (P1-Pv) Pc = Pv (0,96-0,28 )Pv Pk ΔPc
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
Liquid trim
Deltaflux
Dn 2" 3" 4" 6" 8" 10" 12" 14" 16" 18" 20" 24" Cv coefficient at 100% opening 60 150 290 650 1225 1975 2825 3475 4675 5950 7500 11100Gas 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.
Liquid control application
Gas control application
Deltaflux
Cv coefficient
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 = pressure loss in bar
Pu = absolute inlet pressure in bar Q = flow rate Stm3/h KG = flow coefficient ) 15 . 273 ( 8 . 175 t S KG1 = KG x + x
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:
Δp = KG x Pu - (KG2 x Pu2) - 4Q2 2 x KG
Nominal diameter (mm)
Size (inches)
KG flow coefficient
25
1"
510
150
6"
14780
100
4"
7120
65
2"
1/23550
50
2"
1970
80
3"
4390
200
8"
23080
250
10"
32506
SBC 782
Nominal diameter (mm)
Size (inches)
KG flow coefficient
25
1"
549
80
3"
4086
65
2"
1/22603
40
1"
1/21116
50
2"
1788
100
4"
6122
150
6"
13680
SCN
200
8"
21700
Nominal diameter (mm)
Size (inches)
KG flow coefficient
150
6"
14780
100
4"
7120
200
8"
23080
250
10"
32470
HBC 975
Nominal diameter (mm)
Size (inches)
KG flow coefficient
40
1"
1/2860
25
1"
500
50
2"
976
Dilock 108
Calculation of the pressure regulator
q = (0.9 Kc) • (394.9 x C) • P1 A • Q = 23.661
The flow rate is calculated by the following formulae:
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= 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) k+1 2 k ( ) k-1 k+1 M Z1 T1 q M
Nominal diameter (mm)
Size (inches)
Calculation area (cm
2)
Outflow coefficient K
PVS 782
25
1"
4,71
0,56
200
8"
259,59
0,56
150
6"
168,56
0,56
80
3"
43,01
0,56
50
2"
20,03
0,56
100
4"
74,66
0,56
Relative density Carbon dioxide Hydrogen Methane Natural gas* Nitrogen Oxigen Propane * Medium value Coefficient of expansion C 0,685 0,668 0,686 0,669 0,669 0,685 0,685 0,635 Molecular mass M 28,97 44,01 2,02 16,04 18,04 28,02 32,00 44,09Molecular mass and expansion coeff.
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 50 2" 2144 8016 15357 22697 30038 80 3" 4604 17214 32976 48738 64500 100 4" 7991 29881 57242 84603 111964 150 6" 18043 67462 129235 191008 252781 200 8" 27788 103894 199028 294161 389295 Pressure
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
The data are not binding. We reserve the right to make eventual changes without prior notice.
