Download - PSV Sizing Calculations
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4. Relief Valve Sizing
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Topics to be CoveredGeneral Sizing Sizing Procedure
API KA vs. ASME KA
Gas / Vapor Sizing Sonic Flow
Equations, Variables, Units of Measure
Gas Properties
Back Pressure Rupture Disc
Gas / Vapor Sub-Sonic Flow
Equations, Variables, Units of Measure
Pressure & Vacuum
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Topics to be CoveredSteam Sizing Equations, Variables, Units of Measure
Sec. VIII vs. Sec I
Sonic vs. Subsonic
Liquid Sizing
Equations, Variables, Units of Measure
Back PressureFire Sizing
API 521 Unwetted Vessels
API 521 Wetted Vessels
API 2000
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Must Consider TheOne Worst Case Scenario
Blocked Discharge
External Fire
Thermal Expansion
Runaway Reaction
Tube Rupture In Heat Exchanger
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Basic Sizing Procedure
Establish Set Pressure of PSV
Determine Required Relief Capacity
Select PSV Size That Will Flow At Least
That Capacity At The Relieving Pressure
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In 1962, the ASME Section VIII Code
Was Revised, Requiring That K
Be Used In Sizing Calculations
(10% Safety Factor) Instead of KD
K = KD x 0.90
API & ASME KA Values
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The NB Red Book is a Bi-Annualpublication of the Pressure Relief DeviceCertifications by the National Board of
Boiler and Pressure Vessel Inspectors.
The NB allows advertised deviations
from the Red Book K and A values,however
Advertised KA ASME KA(per NB Red Book)
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Since 1962, most PRV manufacturers
have Overstated their K values,
and Understated their A values.
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API vs ASME Orifice AreasAGC JOS-E Series
API DESIGNATION API EFFECTIVE AREA(SQ IN)
ASME / NB CERT.AREA (SQ IN)
D 0.110 0.124
E 0.196 0.221F 0.307 0.347
G 0.503 0.567H 0.785 0.887
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API vs ASME Orifice AreasAGC JOS-E Series
API DESIGNATION API EFFECTIVE AREA(SQ IN)
ASME / NB CERT.AREA (SQ IN)
J 1.287 1.453
K 1.838 2.076L 2.853 3.221
M 3.600 4.065N 4.340 4.900
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API DESIGNATION API EFFECTIVE AREA(SQ IN)
ASME / NB CERT.AREA (SQ IN)
P 6.380 7.205
Q 11.05 12.47R 16.00 18.06
T 26.00 29.35
API vs ASME Orifice AreasAGC JOS-E Series
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Example of Different Manufacturers KA Values
J Orifice (API = 1.287 in2)
NATIONAL BOARD CATALOG
K KA K KA
0.859 0.9531.287
[8.303]
0.855 0.95
0.877 0.975
A, in2 [cm2]A, in2 [cm2]
1.287
[8.303]
1.287
[8.303]
1.226
[7.910]
1.223
[7.888]
1.255
[8.095]
1.228
[7.925]
1.279
[8.252]
1.312
[8.464]
1.430
[9.226]
1.496
[9.652]
1.496
[9.652]
FARRIS
POPRV
CONSOLID.
DSOPRV
AGC
POPRV
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API & ASME KA ValuesAPI Preliminary Sizing
ASME Models Actual Valve Performance
API Uses API 526 Standard Orifice Areas
ASME Uses NB-18 Actual Certified Orifice Areas
API Coefficients of Discharge Gas / Vapor = 0.975
Liquid = 0.650
ASME Coefficients of Discharge Use De-rated Value (K) for sizing Varies from Manufacturer to Manufacturer and Model Type to
Model Type
Advertised KAASME KA
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Gas / Vapor Sizing
ENGLISH UNITS
OR
METRIC UNITS
OR
SONIC Flow - Generally When Set Pressure 15 psig [1.03 barg]
cbKKCKP
MTZVA
102.17
cbKKCKP
MTZVA
132.6
MKKCKP
TZWA
cb1
MKKCKPTZWAcb1
316.1
VOLUMETRIC FLOW
MASS FLOW
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Formula SymbolsSYMBOL
A
P1V
W
ZC
KDK
KbKcT
M
DESCRIPIPTION
Calculated Orifice Area
Inlet Flowing Pressure [P1 = Pset + Pover Ploss + Patm]
Volumetric Flow Rate
Mass Flow Rate
Compressibility Factor(if unknown, assume Z = 1.0)Gas Constant (if unknown, assume C = 315)
Actual Coefficient of Discharge
ASME Coefficient of Discharge [K=0.90 x Kd]
Back Pressure Correction Factor
Rupture Disc Combination Correction Factor
Relieving Temperature
Molecular Weight
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UnitsSYMBOL
A
P1V
W
ZC
KDK
KbKcT
M
ENGLISH
in2
psia
SCFM
lb/hr
------
---
---
---
---
R = F + 460
---
METRIC
cm2
bara
Nm3/hr
kg/hr
------
---
---
---
---
K = C + 273
---
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Compressibil ity Factor, Natural Gas, 0.60 SG
PRESSURE, psig [barg]
1.2
1.1
1.0
0.5
0.9
0.8
0.7
0.6
0 500
[34]
1000
[69]
1500
[103]
2000
[138]
2500
[172]
3000
[207]
3500
[241]
4000
[276]
4500
[310]
5000
[345]
MW = 17.40
(0.6 sp gr)
T = F [C]
500 [260]400 [204]300 [149]
200 [93]100 [38]0 [-18]
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Gas Constant
RATIO OF SPECIFIC HEATS, k
C
400
380
360
340
320
1.0 1.2 1.4 1.6 1.8 2.0
1
1
1
2520
k
k
kkC
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Typical Properties of Gases
ACETYLENE 26 343 1.26
AIR 29 356 1.40AMMONIA 17 348 1.31
ARGON 40 378 1.67
BENZENE 78 329 1.12
BUTADIENE 54 329 1.12
CARBON DIOXIDE 44 345 1.28CARBON MONOXIDE 28 356 1.40
ETHANE 30 336 1.19
ETHYLENE 28 341 1.24
FREON 22 86 335 1.18
HELIUM 4 377 1.66
HEXANE 86 322 1.06
GasMolecular
Weight
C
Factor k , Ratio Of
Specific Heats
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Typical Properties of Gases (contd)
HYDROGEN 2 357 1.41
HYDROGEN SULFIDE 34 349 1.32METHANE 16 348 1.31
METHYL MERCAPTON 48 337 1.20
N-BUTANE 58 326 1.09
NATURAL GAS (SG=0.60) 18.9 344 1.27
NITROGEN 28 356 1.40
OXYGEN 32 356 1.40
PENTANE 72 323 1.07
PROPANE 44 330 1.13
PROPYLENE 42 332 1.15
STEAM 18 348 1.31
SULPHUR DIOXIDE 64 346 1.29VCM 62 335 1.18
GasMolecular
Weight
C
Factor
k , Ratio Of
Specific Heats
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Back Pressure
Correction Factor
1.001.00
0.900.90
0.800.80
0.700.70
0.600.60
0.000.00
00 1010 2020 3030 4040 5050
% Built-Up Back Pressure (gauge)% Built-Up Back Pressure (gauge)
At 110% of
Set Pressure
At 110% of
Set Pressure
~
Unbalanced Conventional Direct Spring PRVUnbalanced Conventional Direct Spring PRV
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Back Pressure
Correction FactorBalanced Bellows Direct Spring PRVBalanced Bellows Direct Spring PRV
1.001.00
0.900.90
0.800.80
0.700.70
0.600.60
0.500.50
00 1010 2020 3030 4040 5050
% Back Pressure (gauge)% Back Pressure (gauge)
At 110% of
Set Pressure
At 110% of
Set Pressure
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Effect of Back Pressure on Lift
of Pressure Relief Valve Types
100
90
80
70
60
50
0 10 20 30 40 50 90 100
%R
at
edLift
Conventional
Spring Operated
PRV
Pilot Operated PRV
(Standard)
Balanced Bellows
Spring Operated PRV
% Back Pressure (gauge)% Back Pressure (gauge)
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A Perfect Nozzle (KD = 1.0)100
% Back Pressure
%R
atedCapacity
80
60
40
20
0
0 20 40 60 80 100
k=1.3
53%
P1
P
2
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Back Pressure Correction Factor
AGC Piston POPRV (Gases)
Kb
= Absolute Pressure Ratio
0.0
k = 1.0
k = 1.2
k = 1.4
k = 1.6
k = 1.8
k = 2.0
0.0 0. 2 0.4 0.6 1.00.8
1.0
0.8
0.6
0. 4
0.2
P2
P1
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PSV With Rupture DiscAt Inlet
Do PSV Calculation, thenApply Combination Factor for that
Model PSV & Model/Material of RD*
As Established by the NB Testing.
*Listed in back of NB Red Book
OR
De-rate PSV Capacity by 10%.
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PRV With Rupture DiscAt Outlet
No PSV De-Rating Necessary
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Gas / Vapor Sizing
ENGLISH UNITS
OR
METRIC UNITS
OR
SUBSONIC Flow - Generally When Set Pressure < 15 psig [1.03 barg]
112510 PFK
MTZVA
D
14645 PFK
MTZVA
D
MPFK
TZWA
D 1735
MPFKTZWAD 1558
VOLUMETRIC FLOW
MASS FLOW
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Formula Symbols
SYMBOL
AP1V
WZ
KDM
T
F
DESCRIPIPTION
Calculated Orifice AreaInlet Flowing Pressure [P1 = Pset + Pover Ploss + Patm]
Volumetric Flow Rate
Mass Flow RateCompressibility Factor(if unknown, assume Z = 1.0)
Actual Coefficient of Discharge
Molecular Weight
Relieving Temperature
Subsonic Flow Factor
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Units
SYMBOL
AP1V
WZ
KDM
T
F
ENGLISH
in2
psia
SCFM
lb/hr---
---
---
R = F + 460
---
METRIC
cm2
bara
Nm3/hr
kg/hr---
---
---
K = C + 273
---
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Subsonic Flow Factor
k
k
k
P
P
P
P
k
kF
1
1
2
2
1
2
1
For Pressure:
P1 = Inlet Flowing Pressure [P1 = Pset + Pover Ploss + Patm]
P2 = Pressure at Valve Outlet [P2 = Pback + Patm]
For Vacuum:
P1 = Atmospheric Pressure [P1 = Patm]
P2 = Pressure at Valve Outlet [P2 = Pvacuum set + Punder + Patm]
k = ratio of specific heats
WHERE:
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FFactor
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
1.00 0.90 0.80 0.70 0.60 0.50 0.40
k = 1.90
k = 1.40
k = 1.00
F
= Absolute Pressure RatioP2
P1
AGC Series90 & 9000
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Steam Sizing
ENGLISH UNITS
METRIC UNITS
SONIC Flow - Generally When Set Pressure 15 psig [1.03 barg]
15.51 PKKKK
WA
bPS
15.52 PKKKK
WA
bPS
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Formula Symbols
SYMBOL
AP1W
KKSKPKb
DESCRIPIPTION
Calculated Orifice AreaInlet Flowing Pressure [P1 = Pset + Pover Ploss + Patm]
Mass Flow Rate
ASME Coefficient of DischargeSuperheat Correction Factor
High Pressure Correction Factor(over 1600 psig)
Back Pressure Correction Factor
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UnitsSYMBOL
AP1W
K
KSKPKb
ENGLISH
in2psia
lb/hr
------
---
---
METRIC
cm2bara
kg/hr
------
---
---
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KS Superheat Correction Factor
SetPres.
psig15
20
40
6080
100
120
140
160
180200
220
240
260
280
300
350400
450
500
Sat.Steam
oF250
259
287
308324
338
350
361
371
380388
395
403
409
416
422
436448
460
470
Total Steam Temperature, oF280
1.00
1.00
300
1.00
1.00
1.00
320
1.00
1.00
1.00
1.00
340
0.99
0.99
1.00
1.001.00
1.00
360
0.99
0.99
0.99
0.991.00
1.00
380
0.98
0.98
0.99
0.990.99
1.00
1.00
1.00
1.00
400
0.98
0.98
0.98
0.980.99
0.99
0.99
1.00
1.00
1.00
1.00
1.00
420
0.97
0.97
0.97
0.970.98
0.98
0.98
0.99
0.99
0.99
0.99
1.00
1.00
1.00
1.00
440
0.96
0.96
0.96
0.960.97
0.97
0.97
0.98
0.98
0.98
0.99
0.99
0.99
0.99
1.00
1.00
1.00
460
0.95
0.95
0.95
0.950.96
0.96
0.96
0.96
0.97
0.97
0.97
0.98
0.98
0.98
0.99
0.99
1.001.00
480
0.94
0.94
0.94
0.940.94
0.95
0.95
0.95
0.95
0.96
0.96
0.96
0.97
0.97
0.97
0.98
0.990.99
1.00
1.00
520
0.93
0.93
0.93
0.930.93
0.94
0.94
0.94
0.94
0.94
0.94
0.95
0.95
0.96
0.96
0.96
0.970.97
0.98
0.99
[ENGLISH]
500
0.93
0.93
0.93
0.930.93
0.94
0.94
0.94
0.94
0.95
0.95
0.95
0.95
0.96
0.96
0.96
0.970.98
0.99
0.99
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KS Superheat Correction Factor
SETPRES.
barg
1.03
1.38
2.76
4.145.52
6.90
8.27
9.65
11.0
12.4
13.8
15.2
16.6
17.9
19.3
20.7
24.127.6
31.0
34.5
SAT.STEAM
oC
121
126
142
153162
170
177
183
188
193
198
202
206
210
213
217
225231
238
243
TOTAL STEAM TEMPERATURE, oC
138
1.00
1.00
149
1.00
1.00
1.00
160
1.00
1.00
1.00
1.00
171
0.99
0.99
1.00
1.001.00
1.00
182
0.99
0.99
0.99
0.991.00
1.00
193
0.98
0.98
0.99
0.990.99
1.00
1.00
1.00
1.00
205
0.98
0.98
0.98
0.980.99
0.99
0.99
1.00
1.00
1.00
1.00
1.00
216
0.97
0.97
0.97
0.970.98
0.98
0.98
0.99
0.99
0.99
0.99
1.00
1.00
1.00
1.00
227
0.96
0.96
0.96
0.960.97
0.97
0.97
0.98
0.98
0.98
0.99
0.99
0.99
0.99
1.00
1.00
1.00
238
0.95
0.95
0.95
0.950.96
0.96
0.96
0.96
0.97
0.97
0.97
0.98
0.98
0.98
0.99
0.99
1.001.00
249
0.94
0.94
0.94
0.940.94
0.95
0.95
0.95
0.95
0.96
0.96
0.96
0.97
0.97
0.97
0.98
0.990.99
1.00
1.00
260
0.93
0.93
0.93
0.930.93
0.94
0.94
0.94
0.94
0.95
0.95
0.95
0.95
0.96
0.96
0.96
0.970.98
0.99
0.99
271
0.93
0.93
0.93
0.930.93
0.94
0.94
0.94
0.94
0.94
0.94
0.95
0.95
0.96
0.96
0.96
0.970.97
0.98
0.99
[METRIC]
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KP - High Pressure Correction Factor
Pressure, psig [barg]
1.25
1.15
1.05
0.951500
[103.4]
1900
[131.0]
2300
[158.6]
2700
[186.2]
3100
[213.8]
3500
[241.3]
KP
0.1906P - 10000.2292P - 1061
KP =
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Steam Sizing Notes
Sec. VIII Use 10% over pressure
Sec. I Use 3% over pressure
Sonic Flow Use Steam Equations
Sub-Sonic Flow Use Gas/Vapor Equations
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Liquid Sizing
ENGLISH UNITS
METRIC UNITS
BAVW
L
PPKKK
GVA
38
BAVW
L
PPKKK
GVA
094.5
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Formula SymbolsSYMBOL
APAPBV
LG
K
KW
KV
DESCRIPIPTION
Calculated Orifice AreaInlet Flowing Pressure [P1 = Pset + Pover Ploss]
Outlet Flowing Pressure [P2 = Pback]
Required Capacity
Specif ic Gravity
ASME Coefficient of Discharge [K=0.90 x Kd]
Back Pressure Correction Factor
Viscosity Correction Factor
NOTE: Temperature is not required to calculate orifice area.
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UnitsSYMBOL
APAPBV
LG
K
KW
KV
ENGLISH
in2psig
psig
gpm
---
---
---
---
METRIC
cm2barg
barg
m3/hr
---
---
---
---
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Liquid Thermal Expansion Relief
GC
BH
VL 500
VL=
B =H =
G =
C =
Liquid Flow Rate, gpm
Cubicle Expansion Coefficient per FTotal Heat Transfer Rate, BTU/hr
Specif ic Gravity
Specific Heat, BTU/lbF
Per API 521, Section 3.14
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Fire SizingThe Procedure Used In Fire Sizing Depends On The Codes
And Engineering Practices Applied At Each Installation.
Some Procedures That May Be Used For Fire Sizing:
The Procedure Used In Fire Sizing Depends On The Codes
And Engineering Practices Applied At Each Installation.
Some Procedures That May Be Used For Fire Sizing:
Recommended Practices For The Design
And Installation Of Pressure Relieving
Systems In Refineries. (SET 15 psig [1.03 barg])
Venting Atmospheric And Low Pressure
Storage Tanks (SET < 15 psig [1.03 barg])
Design Of Lp Gas Installations
Storage And Handling Liquefied Petroleum
Gasses (National Fire Protection Association)
Stationary Storage Tanks
Recommended Practices For The Design
And Installation Of Pressure Relieving
Systems In Refineries. (SET 15 psig [1.03 barg])
Venting Atmospheric And Low Pressure
Storage Tanks (SET < 15 psig [1.03 barg])
Design Of Lp Gas Installations
Storage And Handling Liquefied Petroleum
Gasses (National Fire Protection Association)
Stationary Storage Tanks
API RP 521
API 2000
API 2510
NFPA 58
CGA S-1.3
API RP 521
API 2000
API 2510
NFPA 58
CGA S-1.3
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API 521 (Fire) Unwetted Vessels
1
'
P
AFA S
A =
F =
AS =
P1
=
Calculated PSV Orifice Area, in2
Relates to Bare Vessel MetalTemperature at Relief(if unknown, F=0.042)
Exposed Surface Area of Vessel, ft2
Relieving pressure, psia
[P1 = Pset + Pover Ploss + Patm]
Per API 521, Section 3.15
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API 521 (Fire) Unwetted Vessels
F Operating Factor
FG
as
FG
as
700
600
500
400
300
200
100
0
0.005 0.015 0.025 0.035 0.045 0.055
k = 1.001
k = 1.4
Operating Factor, F
Conservative
6506.0
1
25.1
11406.0
'
CKT
TTF
wall
Minimum
Twall, R
T1, R
Step 1
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API 521 (Fire) Wetted Vessels
82.0000,21 wetAFQ
Q =
F =
Awet =
Total Heat Input to Wetted Surface, BTU/hr
Environmental Factor
Total Wetted Surface Area, ft2
Per API 521, Section 3.15
82.0500,34 wetAFQ
Prompt Fire-Fighting Efforts &Adequate Drainage
Exists
Prompt Fire-Fighting Efforts &Adequate Drainage
Does Not Exists
p
( )
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Vertical
Vessel
Horizontal
Vessel
Sphere
Max.Dia.
25 ft.
Ground
API 521 (Fire) Wetted VesselsTotal Vessel Wetted Surface Area, ft2, Up to 25 ft. Above
Ground Level or, (in the Case of a Sphere) to the
Elevation of Largest Diameter - Whichever Is Greater.
API 521 (Fi ) W tt d V l
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API 521 (Fire) Wetted Vessels
VESSEL F
Bare (Un-Insulated) 1.0
InsulatedConductance Value: 4 btu/hr/ft2/F 0.3
2 0.15
1 0.075
Earth Covered, Above Grade 0.03
Bare With Water Spray 1.0
Underground 0.0
VESSEL F
Bare (Un-Insulated) 1.0
InsulatedConductance Value: 4 btu/hr/ft2/F 0.3
2 0.15
1 0.075
Earth Covered, Above Grade 0.03
Bare With Water Spray 1.0
Underground 0.0
API 521 (Fi ) W tt d V lStep 2
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API 521 (Fire) Wetted Vessels
vapH
QW
W =Q =
Hvap =
Required Valve Capacity, lb/hrTotal Heat Input to Wetted Surface, BTU/hr
Latent Heat of Vaporization, BTU/lb
EXAMPLES: AMMONIA 589
BENZENE 169
BUTANE 166
CO2 150
ETHANE 210
ETHYLENE 208
METHANE 219
PROPANE 183
WATER 970
EXAMPLES: AMMONIA 589
BENZENE 169
BUTANE 166
CO2 150
ETHANE 210
ETHYLENE 208
METHANE 219
PROPANE 183
WATER 970
API 521 (Fi ) W tt d V lStep 3
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API 521 (Fire) Wetted Vessels
MKKCKP
TZW
Acb1
MKKCKP
TZW
Acb1
316.1
ENGLISH METRIC
Use Vapor Equations to Calculate Required
Orifice Area.Use the Boiling Temperature of the Liquid(Flash to Vapor) for T .
Use Relieving Temperature for orifice sizing.
Use Operating Temperature for soft goodselection.
If unknown, we suggest using 200F [93C]
API 2000 (Fi )
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API 2000 (Fire)
82.0
1107FAV
V =F =
A =
Venting Requirement, ft3/hr, air (60F)Environmental Factor (if unknown, F=1.0)
Exposed Surface Area of Vessel, ft2
Set Pressure < 15 psig [1.03 barg]
API 2000 (Fire) S rface Area 2800 ft2
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API 2000 (Fire) - Surface Area 2800 ft2
A, ft2
20
3040
50
60
70
8090
100
120
140
160
180200
250
300
SCFM
AIR
352
527
702
878
1053
1228
14031580
1780
2100
2450
2800
31673517
2983
4417
A, ft2
350
400
500
600
700
800
9001000
1200
1400
1600
1800
20002400
2800
over 2800
SCFM
AIR
4800
5200
5900
6533
7133
7700
82178733
9283
9783
10,233
10,650
11,03311,733
12,367
use formula
Using the calculated, required,
relief valve capacity and setpressure, use air capacity tables
(10% overpressure) in catalogs
to select ori fice area and
valve size. For set pressures
15 psig and below, be sure
to use the actual KD
Reference: API 2000, Sections 1.5.2 and 2.3
ASME K
0.90KD =