Single & Headered Relief Vent Piping Analysis Todd Jekel, Ph.D., P.E. Industrial Refrigeration Consortium 2005 Research & Technology Forum January 21, 2005 Madison, WI 1
Purpose Vent piping requirements Pressure drop calculation & basis Valve back-pressure allowances Single relief example Headered relief vent systems Methodology Example Vent piping recommendations 2
Relief Piping Length Limits (ANSI/ASHRAE Standard 15-2004 Appendix H) L = L = equivalent length of pipe system (ft) C r = rated capacity of relief device(s) (lb air /min) f = Moody friction factor (-) d = inside diameter of pipe (in) P o = allowed backpressure at relief valve outlet (psia) = absolute pressure at outlet of discharge piping (psia) P 2 d f C 2 2 ( P P ) P o d ln P 6 f 5 0.214 o 2 2 2 r This equation is for subsonic, isothermal, compressible flow of air at a temperature of 60 o F. 3
Discharge Pressure Limit Choked Flow P = 0.6226 C d 2,min 2 C d P 2,min = rated capacity through pipe segment (lb air /min) = inside diameter of pipe (in) = absolute pressure at outlet of discharge piping (psia) The outlet pressure cannot be less than P 2,min. Therefore, use P 2,min in place of P 2 in the length equation if P 2 < P 2,min 4
Fully Rough Friction Factor 1 12 ε d = 2.0 log f 3.7 ε d = pipe roughness (ft) = inside diameter of pipe (in) f = Moody friction factor (-) Commercial steel piping roughness 0.00015 ft assumed. NPS ¾ 1 1-¼ 1-½ 2 2-½ 3 4 5 6 Schedule 40 ID 0.622 0.824 1.049 1.38 1.61 2.067 2.469 3.068 0.0240 0.0225 0.0210 0.0202 0.0190 0.0182 0.0173 0.0163 4.026 0.0155 5.047 0.0149 f Schedule 80 ID 0.546 0.0247 0.742 0.0230 0.957 0.0214 1.278 0.0205 1.5 0.0193 1.939 2.323 2.9 3.826 4.813 f 5
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 PRV Too 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! 6
Back Pressure: P o Use percent set pressure, P, specified by valve manufacturer or if no specific guidance exists for conventional relief valves, 15% of set pressure [P o = (0.15 * P) + atmospheric pressure] for balanced relief valves, 25% of set pressure [P o = (0.25 * P) + atmospheric pressure] for rupture members, fusible plugs, and pilot operated relief valves, 50% of set pressure [P o = (0.5 * P) + atmospheric pressure] Source: ANSI/ASHRAE 15-2004 Appendix H 7
Example One vessel with relief to atmosphere 8
Vessel Specifics and PRV Choice V-1 HPR 72 Diameter, 13-4 Long (1 relief connection) MAWP = 250 psig C required = 40 lb/min 250 psig PRV C r = 47.5 lb/min ¾ FPT inlet, 1 FPT outlet 9
14.67 psia Situation This represents the minimum line size allowed by ASHRAE 15-2004 1 NPS Schedule 80 L eq = 40 ft Is this compliant? 10
14.67 psia Initial Results V-1: P o,max = 52.17 psia (15%) 1 NPS Schedule 80 L eq = 40 ft Calculated 126 psia (45%) 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. 11
14.67 psia Compliant Results V-1: P o,max = 52.17 psia 1-½ NPS Schedule 80 L eq = 40 ft Calculated 45 psia 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. 12
Headered Relief Vent Systems Multiple pressure relief valves (PRVs) piped on a single vent main Common in the ammonia refrigeration industry Headers may contain PRVs with different set points Define simultaneous relief scenario Usually consider all relieving if they are in a single space 13
Relief Vent Pipe Sizing Header main minimum size Sum of area of connected relief device outlets with due allowance for pressure drop (ASHRAE 15-2004 9.7.8.4) 14
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, 4 th Edition, March 1997. 15
Example Two vessels simultaneously relieving to a common relief vent to atmosphere 16
Vessel Specifics and PRV Choice V-1 HPR 72 Diameter, 13-4 Long (1 relief connection) MAWP = 250 psig C required = 40 lb/min 250 psig PRV C r = 46 lb/min ¾ FPT inlet, 1-¼ FPT outlet V-2 LPR 54 Diameter, 151 Long (¾ relief connection) MAWP = 150 psig C required = 28.3 lb/min 150 psig PRV C r = 31.3 lb/min ½ FPT inlet, ¾ FPT outlet 17
Vent Piping Requirement PRV 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 size Minimum of outlet connection size on PRV V-1: 1-¼ outlet V-2: ¾ outlet Header main size Minimum area of sum of outlet areas of connected PRVs 18
Header Minimum Size PRV outlet area Header 2 d PRV,i Ai = π 4 2 π d Aheader = 4 header N i= 1 π d 2 PRV, i 4 Simplification where d PRV,i is outlet of i th relief valve, N is number of PRVs upstream of header section N 2 d header d PRV i= 1, i 19
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. 80 d = 1.5 20
14.67 psia Initial Schematic This represents the minimum line sizes allowed by ASHRAE 15-2004 1-½ NPS Schedule 80 L eq = 40 ft 1-¼ NPS Schedule 80 L eq = 20 ft Is this compliant? ¾ NPS Schedule 80 L eq = 10 ft 21
Step 1: Header main 1-½ Schedule 80 d = 1.5 f = 0.0205 C = 77.3 lb m /min P 2 Start with minimum size (area equal to sum of attached PRV outlets) Must iteratively solve the length equation for P o Is P o > the maximum allowable back pressure for any of the attached PRVs? If YES, increase the size & recalculate. If NO, continue. P o L =.2146 d 2 2 ( P P ) P 0 d ln P 6 f 0 5 0 2 2 2 f Cr 22
Step 2: V-2 Branch ¾ Schedule 80 d = 0.724 f = 0.0247 C = 31.3 lb m /min Use the pressure at the tee from Step 1 for P 2 Iteratively solve the length equation for P o Is P o > the maximum allowable back pressure for the PRV? If YES, increase the size & recalculate. If NO, continue. P 2 P o L =.2146 d 2 2 ( P P ) P 0 d ln P 6 f 0 5 0 2 2 2 f Cr 23
Step 3: V-1 Branch Use the pressure at the tee from Step 1 for P 2. Must iteratively solve the equation for P o Is P o > the maximum allowable back pressure for the PRV? If YES, increase the size & recalculate. If NO, DONE. 1-¼ Schedule 80 d = 1.278 f = 0.0214 C = 46 lb m /min P o P 2 L =.2146 d 2 2 ( P P ) P 0 d ln P 6 f 0 5 0 2 2 2 f Cr 24
Initial Results 1-½ NPS Schedule 80 L eq = 40 ft 14.67 psia V-1: P o,max = 52.17 psia Calculated 76 psia (25%) 1-¼ NPS Schedule 80 L eq = 20 ft 67.2 psia V-2: P o,max = 37.17 psia Calculated 103 psia (59%) ¾ NPS Schedule 80 L eq = 10 ft 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. 25
14.67 psia Compliant Results 2-½ NPS Schedule 40 L eq = 52.5 ft V-1: P o,max = 52.17 psia Calculated 48.9 psia 1-¼ NPS Schedule 80 L eq = 22 ft 23.8 psia V-2: P o,max = 37.17 psia Calculated 32 psia 1-¼ NPS Schedule 80 L eq = 13 ft To make this simple headered relief vent piping system comply, we have to upsize the branch line for V-2 and the header main. 26
30 psia Diffusion Tank V-1: P o,max = 52.17 psia Calculated 43.4 psia 2-½ NPS Schedule 40 L eq = 52.5 ft 1-½ NPS Schedule 40 L eq = 23 ft 35.8 psia V-2: P o,max = 37.17 psia Calculated 37.17 psia 1-½ NPS Schedule 40 L eq = 13 ft 27
Tips for Relief Piping Design Size mixing tees to be the largest of the connected piping L eq = 10 ft L eq = 10 ft Mixing tees should be piped as to right L eq = 5.2 ft L eq = 11.2 ft All equivalent lengths for 2 NPS Schedule 40 fittings 28
Tips for Relief Piping Design 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 29
Tips for Relief Piping Design ASME BPVC Section VIII, Division 1 UG-135 Installation (a) PRVs intended for vapor service shall be connected above the liquid surface PRVs intended for liquid service shall be connected below the liquid surface (f) Discharge lines for PRVs shall be designed to facilitate drainage 30
Conclusion New ASHRAE 15-2004 vent piping requirements are more stringent than previous versions Complicated equation, simplified demonstration of compliance for headered vent piping systems 31
Questions? 32