psv sizing calculations

7/28/2019 PSV Sizing Calculations

1/53

4. Relief Valve Sizing


2/53

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


Pressure & Vacuum


3/53

Topics to be CoveredSteam Sizing Equations, Variables, Units of Measure

Sec. VIII vs. Sec I

Sonic vs. Subsonic

Liquid Sizing


Back PressureFire Sizing

API 521 Unwetted Vessels

API 521 Wetted Vessels

API 2000


4/53

Must Consider TheOne Worst Case Scenario

Blocked Discharge

External Fire

Thermal Expansion

Runaway Reaction

Tube Rupture In Heat Exchanger


5/53

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


6/53

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


7/53

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)


8/53

Since 1962, most PRV manufacturers

have Overstated their K values,

and Understated their A values.


9/53

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


10/53




J 1.287 1.453

K 1.838 2.076L 2.853 3.221

M 3.600 4.065N 4.340 4.900


11/53



P 6.380 7.205

Q 11.05 12.47R 16.00 18.06

T 26.00 29.35



12/53

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


13/53

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


14/53

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


15/53

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


16/53

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

---


17/53

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]


18/53

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


19/53

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


20/53

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


21/53

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


22/53

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


23/53

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)


24/53

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


25/53


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


26/53

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%.


27/53

PRV With Rupture DiscAt Outlet

No PSV De-Rating Necessary


28/53

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


29/53

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


30/53

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

---


31/53

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:


32/53

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


33/53

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


34/53

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)



35/53

UnitsSYMBOL

AP1W

K

KSKPKb

ENGLISH

in2psia

lb/hr

------

---

---

METRIC

cm2bara

kg/hr

------

---

---


36/53

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


37/53

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]


38/53

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 =


39/53

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


40/53

Liquid Sizing

ENGLISH UNITS

METRIC UNITS

BAVW

L

PPKKK

GVA

38

BAVW

L

PPKKK

GVA

094.5


41/53

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]


Viscosity Correction Factor

NOTE: Temperature is not required to calculate orifice area.


42/53

UnitsSYMBOL

APAPBV

LG

K

KW

KV

ENGLISH

in2psig

psig

gpm

---

---

---

---

METRIC

cm2barg

barg

m3/hr

---

---

---

---


43/53

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


44/53

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


45/53

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]



46/53

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


47/53

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


82.0500,34 wetAFQ

Prompt Fire-Fighting Efforts &Adequate Drainage

Exists

Prompt Fire-Fighting Efforts &Adequate Drainage

Does Not Exists

p

( )


48/53

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


49/53


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


50/53


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


51/53


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 )


52/53

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


53/53

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 =

psv sizing calculations

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