Hydrocarbon Processing - December 2020 - 75

Maintenance and Reliability
* Sound power level at point B due to pipe section
C-B = 165 dB
* Sound power level at point B due to pipe section
D-B = 167 dB.
Solution: This can be estimated, using following methodologies:
* Consider all sources (Eq. 17):

a. Section (A-B) Mach number
b. Design limit of sound power level for section A-B
c. Sound power level at source A
d. Attenuation along the pipe A-B
e. Sound power level at discontinuity (point B).
Design data:
Mass flowrate, W
= 50,000 kg/hr
Gas molecular weight, MW = 16.8
Ratio of gas specific heats
= 1.3
Compressibility, Z
= 0.98 (downstream
section A-B)
Upstream pressure, P1
= 3,401.3 kPa
Upstream temperature, T1
= 323.15 K
Downstream pressure, P2
= 101.3 kPa
Downstream temperature, T2 = 308.15 K
Section (A-B) OD
= 406.4 mm
Section (A-B) thickness
= 8.38 mm
Section (A-B) length
= 10 m.
Solution:
a. Mach number calculation (Eq. 12):
Pipe ID = 389.64 mm




50,000
5 

Mach = 3.23  10
2 

 389.64 	 
 101.3  

 1,000 
 


PWLalldis = 10log(1016.2 + 1016.5 + 1016.7) = 169.9 dB (17)
* Consider stage calculation: Sound power level for
sections C-B and D-B is calculated, using Eq. 18:
PWLcbdb= 10log(1016.5 + 1016.7) = 169.1 dB

* Combined sound power level, combining the above value
and section A-B is calculated, using Eq. 19:
PWLalldis = 10log(1016.91 + 1016.2) = 169.9 dB
(19)
(as calculated before).
Overall design criteria.4,5,6 Once the sound power level de-

sign limit, source value and value at discontinuity are established, the following design limits are applied to establish the
need for further analysis (Eq. 20):
If PWLS or PWLalldis > PWLD
(12)

0.5
 0.98  308.15 	 = 0.445


16.8

b. Design limit of sound power level (Eq. 13):
PWLD = 173.6  0.125 

389.64
= 167.8 dB
8.38

(13)

c. Sound power level at source (Eq 14):
 3,401.3  101.3 	 3.6

 





3,401.3

 + 126.1 + 0  0
PWLS = 10log 
2
1.2 
  50,000 	   323.15 	 
 16.8  

  3,600 

(14)

The design is considered a failure. In this case, the design
must be modified and analyzed further. Methods to modify the
design include:
* Increase the thickness of the pipe. This will increase
the design limit.
* Reduce the flowrate by increasing the number of PSVs
or blowdown valves. This will reduce the sound power
level at the source.
* If the flow is choked (Mach number ≥ 1), increase the
pipe diameter. This will reduce the sound power level
at the source due to subsonic flow.

C

B

(15)
A

e. Sound power level at discontinuity (point B),
shown in Eq. 16:
PWLdis = 163.9 - 1.54 = 162.4 dB

(20)

PSV-B

= 163.9 dB
The value of K and NLT are zero.
d. Attenuation along the pipe A-B (Eq. 15):
 10,000 
PWL At = 0.06  
= 1.54 dB
 389.64 

(18)

PSV-A

(16)

Example 3. PSV A, B and C are discharging to a single point

(B), as indicated in FIG. 2. Estimate the overall sound power
level at point B using the following information:
* Sound power level at point B due to pipe section
A-B = 162 dB

D
PSV-C
FIG. 2. Multi-PSV discharge.
Hydrocarbon Processing | DECEMBER 2020

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