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SizingPressure 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 Stm3/hPu = 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.
KsinPuCgQ xxxx= 1526.0)( PdPuPdKG -xx
PuKG
Q x=
Q =
2PuCgQ xx= 526.0
)( PdPuPd
QKG
-x
=
sinPu
QCg
xx
=
526.0
Pu
QKG
x=
2
0,526 x Pu
QCg =
Pu
PdPu - ((
K1xPu
PdPu - ((
REGULATOR INTEGRAL SLAM SHUT
INTEGRAL MONITOR
INTEGRALSILENCER
APERFLUX 851 -5% -5% -5%
REFLUX 819 -7% -7% -5%
REFLUX 819/FO -7% -7% -5%
APERVAL SA-10%
SB-5% -5% -5%
REVAL 182 SA-10%
SB-7% -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 Factor0.780.630.550.790.730.63
Relative density1.01.532.00.971.141.52
Type of gasAirPropaneButaneNitrogenOxygenCarbon dioxide
Correction factors FC
Lists the correction factors Fc for anumber of gases at 15°C.
CAUTION:
where:V = gas speed in m/secQ = gas flow rate in Stm3/hDN = nominal size of regulator in mmPd = outlet pressure in barg.
140
150
160
170
180
190
200
210
220
230
240
250260
0 1 2 3 4 5 6 7 8 9 10 11
Outlet pressure [bar]
Gas
pre
ssur
e at
the
outle
t fla
nge
[m/s
ec]
The gas speed at the outlet flange may be calculated by means of the following formula:
Pd
Pd
DN
QV
+
x-xx=
1
002.0192.345
2
TablesCg and Kg valve coefficient
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Reflux 819/FO
251"
575605
106,78
2008"
2593327282106,78
1506"
1660717471106,78
803"
49375194
106,78
502"
22202335
106,78
1004"
80008416
106,78
25010"
3652538425106,78
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Reflux 819
251"
575605
106,78
2008"
2593327282106,78
1506"
1660717471106,78
803"
49375194
106,78
502"
22202335
106,78
1004"
80008416
106,78
25010"
3652538425106,78
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Aperflux 851
1506"
1111211678113,9
251"
480505
113,9
2008"
1731618199113,9
803"
37903979113,9
502"
15501627113,9
1004"
55545837113,9
25010"
2454825850113,9
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
50 2”
16821768103
80 3”
42004414108
Aperflux 101
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Staflux 185
251"
439462
106,78
803"
37643960
106,78
502"
16811768
106,78
Staflux 187
251"
130136
106,78
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
251"
15916799,5
Dixi AP
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
251"
17017993,5
Dival 160 AP
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Aperval 101
50 2”
20912199108
80 3”
47965045108
1004”
71767546108
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Aperval
251"
58461390
1004"
67197055101
652"1/2 35303706101
502"
19782077101
803"
45254751101
TablesCg and Kg valve coefficient
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Terval
1004"
54905775100
652"1/2
27312875104
502"
17061796108
803"
39064112100
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
251"
575605
106,78
1506"
1660717471106,78
1004"
80008416
106,78
652"1/2
33204197
106,78
502"
22202335
106,78
803"
49375194
106,78
2008"
2593327282106,78
25010"
3652538425106,78
Reval 182
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Terval/R
1004"
56605954106
652"1/2
27932940104
502"
16671755104
803"
40994315106
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Dixi
502"
10141066
96
251"
54056796
401"1/2
9831034
96
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Norval 608
502"
17001788106
803"
35003681106
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Norval
251"
331348
106,78
803"
33953571
106,78
652"1/2 22402356
106,78
401"1/2 848892
106,78
1004"
51005365
106,78
502"
13601430
106,78
1506"
1060011151106,78
2008"
1660017463106,78
Nominal diameter (mm)Size (inches) Cg flow coefficientKG flow coefficientK1 body shape factor
Dival 600
251"
26928394
401"1/2 65268594
502"
78182186
401"1/2 69272795
502"
77080997
Head ø 280 Head ø 280/TR251"
31533197
Dival 700 See the capacity Table
TablesCg and Kg valve coefficient
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/HPd = 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 - VLMSizing the Control Valve
(Pu - Pd) Pd KGQ = 106,78 sinPuCvQ xxx= 16,8Pu
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)
( Pd )PuPd
QKG
-
=
sinPu
QCv
x 106,78xx
=
.16,8Pu
PdPu - ((
Pu
QKG
x=
2
16,8 x Pu
QCv =
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 coefficientKG flow coefficientCv flow coefficient
Reflux 919 - Syncroflux - VLM
251"
57560518
2008"
2593327282
810
1506"
1660717471
519
803"
49375194154
502"
22002335
69
1004"
80008416250
25010"
36525384251141
106,78 sinPuCgQ xxx= 0,526 Pu
Pu - Pd( (
sinPu
QCg
x 106,78xx
=
.0,526Pu
PdPu - ((
0,526 x Pu
QCg =
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/HPd = 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)
DeltafluxSizing 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 CvGΔP (P1+P2)
T
W = 13,55 Cv ΔP (P1+P2)
W = 13,55Cv ΔP (P1+P2)
(1+0,00126Δ t)
Q =262 F Cv P1
G T
W = 321 F Cv P1GT
W = 11,73 F Cv P1
W = 11,73F 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 = 100Xg (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)
GAS, VAPOR AND STEAM BIPHASE FLUIDS
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
DeltafluxCg and Kg valve coefficient
Dn
2"3"4"6"8"10"12"14"16"18"20"24"
Cv coefficient at 100% opening
8221540510801750286039805000680084001060016100
Liquid trim
Deltaflux
Dn
2"3"4"6"8"10"12"14"16"18"20"24"
Cv coefficient at 100% opening
60150290650122519752825347546755950750011100
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.
Liquid control application
Gas control application
DeltafluxCv coefficient
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 = pressure loss in barPu = absolute inlet pressure in barQ = flow rate Stm3/hKG = flow coefficient
)15.273(
8.175
tSKG1 = 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
251"
510
1506"
14780
1004"
7120
652"1/2
3550
502"
1970
803"
4390
2008"
23080
25010"
32506
SBC 782
Nominal diameter (mm)Size (inches) KG flow coefficient
251"
549
803"
4086
1001"1/2
2603
401"1/2
1116
321"1/4
717
502"
1788
1004"
6122
1506"
13680
SCN
2008"
21700
Nominal diameter (mm)Size (inches) KG flow coefficient
1506"
14780
1004"
7120
2008"
23080
25010"
32506
HBC 975
Nominal diameter (mm)Size (inches) KG flow coefficient
401"1/2
860
251"
500
502"
976
Dilock 108
Sizing the Safety Relief Valves
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/hQ = maximum flow rate (Stm3/h)A = minimum area (cm2) (see table)Kc = outflow coefficientP1= 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
2k ( ) k-1
k+1
MZ1 T1
qM
Nominal diameter (mm)Size (inches) Calculation area (cm2)Outflow coefficient K
PVS 782
251"
4,710,56
2008"
259,590,56
1506"
168,560,56
803"
43,010,56
502"
20,030,56
1004"
74,660,56
Relative densityCarbon dioxideHydrogenMethaneNatural gas*NitrogenOxigenPropane* Medium value
Coefficient of expansion C0,6850,6680,6860,6690,6690,6850,6850,635
Molecular mass M28,9744,012,0216,0418,0428,0232,0044,09
Molecular mass and expansion coeff.
Nominal diameter (mm) Size 2 barg 10 barg20 barg30 barg40 bargFlow rate (Kg/h)
251"
3321885247253377063
502"
21448016153572269730038
803"
460417214329764873864500
1004"
7991298815724284603111964
1506"
1804367462129235191008252781
2008"
27788103894199028294161389295
Pres
sure
Capacity table versus pressure
Pietro Fiorentini S.p.A.via E.Fermi 8/10I-36057 Arcugnano (VI) Italy
Tel. +39 0444 968.511Fax. +39 0444 960.468
The data are not binding. We reserve theright to make eventual changes withoutprior notice.
www.fiorentini.com
CT-s 570-E June 10