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Sizing for Gas or Vapor Relief
Upstream Downstream
US Customary Units
A=Require eff
w= Required fl
C= Coefficient
Kd= Effective c
P1= Upstream r
SI Units
Kb= Capacity c
Kc= combinatio
T= Relieving te
Z= Compressib
M= Molecular
V= Required fl
G= Specific gr
Sizing for Critical Flow:The pressuredownstream of the nozzle is less than, or
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Example
d. Relieving valve set at 75 psig [517 kPa], which is the design pressure of the eq
Solution
a. Permitted accumulation of 10%, so
b. Relieving pressure, P1 = 75 + (75*0.1) + 14.7 = 97.2 psia [670 kPa]
c. Calculated compressibility, Z, of 0.84 (If a calculated compressibility is not avail
d. Critical flow pressure(from Table 7 ) of 97.2*0.59 = 57.3 psia (42.6 psig) [395 k
Note: Since the back pressure(0 psig[0 kPag])is less than the critical flo
the relief valve sizing is based on critical flow equation (see Equation 3.
e. Cp/Cv = k = 1.09(Table 7). From Table 8,,,at k=1.09, C=326or C=520[k(k/k+f. Capacity correction due to back pressure, Kb of 1.0
g. Capacity Correction for rupture disk, Kc = 1.0 (not installed the rupture disk)
The size of a single pressure relief valve is derive from Equation 3.2 as follows:
A = [53,500/(326*0.975*97.2*1.0*1.0)]*[(627*0.84)/65]^1/2
A=
Further calculated V, required flow through the device
w=
V= 5201.85 SCFM at 14.7 psia and 60 F C=Kd=
P1=
Kb=
Kc=
T=
Z=
M=
for Eq.3.3 V=
for Eq.3.4 G=
a. Required hydrocarbon vapor flow, W, caused by an operational upse, of 53,500
b. The hydrocarbon vapor is a mixture of butane (C4) and (C5). The molecular wei
c. Relieving temperature,T, of 627 R(167 F)[348 K]
e. Back pressure of 14.7 psia (0 psig) [101.3 kPaa(0 kPag)].Kb
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ctive discharge area of the device, in^2 or [mm^2]
ow through the device, lb/hr [kg/hr]
determined from an expression of the specific heat(k=Cp/Cv)
efficient of discharge. For preliminary sizing, use the following values:
Kd = 0.975 when a pressure relief valve is installed w/ or w/o a rupture disk in coKd = 0.62 when a pressure relief valve is not installed and sizing is for a rupture
elieving pressure, psia[kPaa]
,= Set pressure + allowable overpressure(see3.5) + atmosphere pressure
rrection factor due to back pressure, be obtained from te manufacturer's literature or
Kb= 1.0 for conventional and pilot operated valves(see 3.3 Back pressure)
* The back pressure correction factor applies to balanced bellow valve only
* See 3.6.3 for conventional valve applications with back pressure of a magnitude tha
n correction factor for installations with a rupture disk upstream of the pressurerelief
Kc= 1.0 when a rupture disk is not installed
Kc= 0.9 when a rupture disk is installed in combination with a pressure relief valve an
mperature of the inlet gas or vapor, R(F+460)[K(C+273)]
ility factor for the deviation of the actual gas from a perfect gas, a ratio evaluated at i
eight of the gas or vapor at inlet relieving conditions. Various handbooks carry tables
ow through the device, scfm at 14.7 psia and 60 F [Nm3/min at 0 C and 101.325 kPaa
vity of gas at standard conditions refered to air at standard conditions[normal conditi
qual to, the critical flow pressure, Pcf
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ipment
able, a Z value of 1.0 should be used.)
Paa]
pressure (42.6 psig[294 kPag]),
and paragraphs 3.6.1 and 3.6.2)
1)^(k+1)/(k-1)]^1/2
US unit/ [SI unit]
4.93in2/ [mm2]
53500lb/hr /[kg/hr]
326psia/ [kPaa]0.98
97.2
1
1
627 R(F+460)/ [K(C+273)]
0.84
65
scfm at 14.7 psia and 60 F/ [Nm3/min at 0 C and 101.325 kPaa]
Gfluid/(G=1.0 for air at 14.7 psia and 60 F/ [101.325 kPaa and 0 C])
0 lb/hr [24,260 kg/hr]
ght of vapor, M, is 65
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binationdisk in accordance with 3.11.1.2
preliminary sizing from Fig.30.
t will cause subcritical flow
alve(see 3.11.2)
d the combination does not have a published valve.
nlet relieving condition.
of molecular weights of materials, but the composition of the flowing gas or vapor is seld
]
ons]. In other words, G=1.0 for air at 14.7 psia and 60 F [101.325 kPaa and 0 C]
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m the same as that listed in tables. This value should be recieve from the process data. T
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ble 7 lists values for some common fluids, lbm/lbmole [kg/kmole]
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