Single & Headered Relief Vent Piping Analysis

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Single & Headered Relief Vent Piping Analysis

Todd Jekel, Ph.D., P.E.Industrial Refrigeration Consortium

2005 Research & Technology ForumJanuary 21, 2005

Madison, WI

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Purpose

Vent piping requirementsPressure drop calculation & basis Valve back-pressure allowances

Single relief exampleHeadered relief vent systems

MethodologyExample

Vent piping recommendations

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Relief Piping Length Limits(ANSI/ASHRAE Standard 15-2004 Appendix H)

L = equivalent length of pipe system (ft)Cr = rated capacity of relief device(s) (lbair/min)f = Moody friction factor (-)d = inside diameter of pipe (in)Po = allowed backpressure at relief valve outlet (psia)P2 = absolute pressure at outlet of discharge piping (psia)

( )fPPd

CfPPdL

o

r

o

⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

−⋅

−⋅⋅=

6

ln214.0 2

2

22

25

This equation is for subsonic, isothermal, compressible flow of air at a temperature of 60oF.

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Discharge Pressure Limit –Choked Flow

C = rated capacity through pipe segment (lbair/min)d = inside diameter of pipe (in)P2,min = absolute pressure at outlet of discharge piping (psia)

The outlet pressure cannot be less than P2,min. Therefore, use P2,min in place of P2 in the length equation if P2 < P2,min

2,min 20.6226 CPd

= ⋅

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Fully Rough Friction Factor

ε = pipe roughness (ft)d = inside diameter of pipe (in)f = Moody friction factor (-)

1 122.0 log3.7

df

ε⋅⎛ ⎞= − ⋅ ⎜ ⎟⎝ ⎠

Commercial steel piping roughness 0.00015 ft assumed.

Schedule 80Schedule 40

3.8260.01554.0265”5.047

3.0682.4692.0671.61

1.381.0490.8240.622

ID

0.0149

0.01630.01730.01820.0190

0.02020.02100.02250.0240

f

4.8136”

2.94”2.3233”1.9392-½”

0.01931.52”

0.02051.2781-½”0.02140.9571-¼”0.02300.7421”0.02470.546¾”

fIDNPS

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What is compliance?

Is it having sufficient installed PRV capacity?Yes, but must also include vent piping system effects.

Is it having installed vent pipe equivalent length less than limit?

Works alright for relief vent systems with one PRVToo simplistic for headered vent systems?

Is it limiting back-pressure on the PRV to that required for a given valve?

Yes…works as a test of compliance for both single and headered vent piping systems!

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Back Pressure: Po

Use percent set pressure, P, specified by valve manufacturer – or if no specific guidance exists–

for conventional relief valves, 15% of set pressure [Po = (0.15 * P) + atmospheric pressure]for balanced relief valves, 25% of set pressure[Po = (0.25 * P) + atmospheric pressure]for rupture members, fusible plugs, and pilot operated relief valves, 50% of set pressure[Po = (0.5 * P) + atmospheric pressure]

Source: ANSI/ASHRAE 15-2004 Appendix H

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Example

One vessel with relief to atmosphere

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Vessel Specifics and PRV Choice

V-1 HPR72” Diameter, 13’-4” Long (1” relief connection)MAWP = 250 psigCrequired = 40 lb/min

250 psig PRVCr = 47.5 lb/min¾” FPT inlet, 1” FPT outlet

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Situation

This represents the minimum line size allowed by ASHRAE 15-2004

Is this compliant?

1” NPS Schedule 80Leq = 40 ft

14.67 psia

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Initial Results

V-1: Po,max = 52.17 psia (15%)

Calculated126 psia (45%)

14.67 psia

1” NPS Schedule 80Leq = 40 ft

In this case, the predicted pressure at the outlet of the pressure relief valve (126 psia) is greater than the allowable limit of 52 psia. This vent pipe system would NOT comply with ASHRAE 15. Rather than a 15% back pressure, this vent pipe system would impose a 45% back pressure on the relief valve.

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Compliant Results

V-1: Po,max = 52.17 psia

Calculated45 psia √

14.67 psia

1-½” NPS Schedule 80Leq = 40 ft

In this case, the predicted pressure at the outlet of the pressure relief valve (45 psia) is less than the allowable limit of 52 psia. This vent pipe system would comply with ASHRAE 15.

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Headered Relief Vent Systems

Multiple pressure relief valves (PRVs) piped on a single vent main

Common in the ammonia refrigeration industryHeaders may contain PRVs with different set points

Define simultaneous relief scenarioUsually consider all relieving if they are in a single space

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Relief Vent Pipe Sizing

Header main minimum sizeSum of area of connected relief device outlets with “due allowance for pressure drop” (ASHRAE 15-2004 §9.7.8.4)

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Solution Methodology

Apply the “length equation” to each constant area segment of piping

Analysis considers all branch lines relieving simultaneously at their rated capacity

Start at the header outlet (known pressure point) & proceed back to outlet of each PRV

Does the design result in a back pressure less than the maximum allowable back pressure for the PRV?

Based on methodology outlined in API 521 Guide for Pressure-Relieving and Depressuring Systems, 4th Edition, March 1997.

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Example

Two vessels simultaneously relieving to a common relief

vent to atmosphere

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Vessel Specifics and PRV Choice

V-1 HPR72” Diameter, 13’-4” Long (1” relief connection)MAWP = 250 psigCrequired = 40 lb/min

250 psig PRVCr = 46 lb/min ¾” FPT inlet, 1-¼” FPT outlet

V-2 LPR54” Diameter, 151” Long (¾” relief connection)MAWP = 150 psigCrequired = 28.3 lb/min

150 psig PRVCr = 31.3 lb/min ½” FPT inlet, ¾” FPT outlet

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Vent Piping RequirementPRV inlet size

Maximum of relief connection size on the protected vessel

V-1: 1” relief connection > ¾” FPT PRV inlet √V-2: ¾” relief connection > ½” FPT PRV inlet √

Branch relief piping sizeMinimum of outlet connection size on PRV

V-1: 1-¼” outlet

V-2: ¾” outlet

Header main sizeMinimum area of sum of outlet areas of connected PRVs

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Header Minimum Size

PRV outlet area

Header

Simplification

where dPRV,i is outlet of ith relief valve, N is number of PRVs upstream of header section

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2,iPRV

i

dA

⋅=π

∑=

⋅≥

⋅=

N

i

iPRVheaderheader

ddA1

2,

2

44ππ

∑=

≥N

iiPRVheader dd

1

2,

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Header Piping Size

Assuming Sch. 80 piping for all piping less than 2” NPS

For ¾”, internal d = 0.742”For 1-¼”, internal d = 1.278”Minimum header main internal d = 1.478”

Smallest allowable header is 1-½” Sch. 80d = 1.5”

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Initial SchematicThis represents the minimum line sizes allowed by ASHRAE 15-2004

Is this compliant?

1-¼” NPS Schedule 80Leq = 20 ft

¾” NPS Schedule 80Leq = 10 ft


14.67 psia

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Step 1: Header main

Start with minimum size (area equal to sum of attached PRV outlets)

Must iteratively solve the length equation for Po

Is Po > the maximum allowable back pressure for any of the attached PRVs?

If YES, increase the size & recalculate.

If NO, continue.

P2

Po

1-½” Schedule 80d = 1.5”f = 0.0205C = 77.3 lbm/min

( )fPPd

CfPPdL

r ⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

−⋅

−⋅⋅=

6

ln2146.0 2

0

2

22

20

5

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Step 2: V-2 Branch

Use the pressure at the tee from Step 1 for P2

Iteratively solve the length equation for Po

Is Po > the maximum allowable back pressure for the PRV?

If YES, increase the size & recalculate.

If NO, continue.

P2

Po

¾” Schedule 80d = 0.724”f = 0.0247 C = 31.3 lbm/min

( )fPPd

CfPPdL

r ⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

−⋅

−⋅⋅=

6

ln2146.0 2

0

2

22

20

5

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Step 3: V-1 Branch

Use the pressure at the tee from Step 1 for P2.Must iteratively solve the equation for Po

Is Po > the maximum allowable back pressure for the PRV?

If YES, increase the size & recalculate.If NO, DONE.

P2

Po

1-¼” Schedule 80d = 1.278”f = 0.0214 C = 46 lbm/min

( )fPPd

CfPPdL

r ⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

−⋅

−⋅⋅=

6

ln2146.0 2

0

2

22

20

5

25


Initial Results


Calculated

76 psia (25%)


Calculated

103 psia (59%) ¾” NPS Schedule 80Leq = 10 ft


14.67 psia

67.2 psia

With branch piping sized at the PRV outlet and the main sized to be the sum of the outlet areas, this sizing would be insufficient to limit the built-up back pressure at the outlet of both relief valves. It would not comply.

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Compliant ResultsV-1: Po,max = 52.17 psia

Calculated

48.9 psia √


Calculated

32 psia √1-¼” NPS Schedule 80Leq = 13 ft

14.67 psia

2-½” NPS Schedule 40Leq = 52.5 ft

23.8 psia

To make this simple headered relief vent piping system comply, we have to upsize the branch line for V-2 and the header main.

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Diffusion TankV-1: Po,max = 52.17 psia

Calculated43.4 psia √


Calculated37.17 psia √



2-½” NPS Schedule 40Leq = 52.5 ft

30 psia

35.8 psia

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Tips for Relief Piping Design

Size mixing tees to be the largest of the connected piping

Mixing tees should be piped as to right

Leq = 10 ft Leq = 10 ft

Leq = 5.2 ft

Leq = 11.2 ftAll equivalent lengths for 2” NPS Schedule 40 fittings

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Locate lower pressure set point valves near header outlet

If given the choice don’t mix set points

Consider up-sizing headers in machinery rooms for future expansion

Nearly always upsize branch lines

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ASME BPVC Section VIII, Division 1 UG-135 Installation

(a)PRVs intended for vapor service shall be connected above the liquid surfacePRVs intended for liquid service shall be connected below the liquid surface

(f)Discharge lines for PRVs shall be designed to facilitate drainage

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Conclusion

New ASHRAE 15-2004 vent piping requirements are more stringent than previous versions

Complicated equation, simplified demonstration of compliance for headeredvent piping systems

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Questions?

Documents

Single & Headered Relief Vent Piping Analysis