Hydrocarbon Processing - March 2021 - 80

Maintenance
and Reliability
A. K. DATTA, Process Consultant, Brisbane, Australia

High-frequency acoustic excitation-Part 2
Failure of a piping section at the outlet of pressure safety
valves (PSVs) and control valves-where significant differential pressure exists (particularly in gas processing industries)-
is a common problem in industries. Most failures are caused
by acoustic-induced vibration. High-pressure discontinuity
generates high vibration and sound levels, causing the failure of
the piping system. Generally, the likelihood of failure (LOF) is
established through the calculation of sound power level (represented as PWL) at the source and at different sections of the
downstream piping. Normally, it is the welded joint that fails
due to acoustic excitation. The welded joint can be of any type,
including a branch connection, welded tee, welded support, etc.
Basic understandings of high-frequency acoustic excitation
have been explained in Part 1 of this work (December 2020).
General calculation procedures for design sound power level
(PWLD ) and sound power level at downstream discontinuity
(PWLdis ) have also been explored. Part 2 has been developed
to establish a mathematical calculation approach and to analyze
more complex problems.
The calculation procedure is explained in FIG. 4.
Example 4. Blowdown of a compressor package can be designed to minimize the blowdown time. A choked-flow blowdown is considered (without using any restriction orifice), as
indicated in FIG. 5. The acoustic-induced vibration issue should
be checked for the following conditions.
Assumption and data:
* Settled out pressure (XV-1 and XV-2 closed), 10,000 kPag
* Both blowdown valves (DBV-1 and BDV-2) opened at
the same time (no delay)
* Settled out temperature, 30°C
* Downstream temperature, -10°C
* Equivalent length of Sections A-C, 10 m
* Equivalent length of Sections B-C, 10 m
* Equivalent length of Sections C-D, 5 m
* Pipe diameter (all sections), 100 NB, Sch 120
* Pipe outer diameter (OD), 114.3 mm
* Pipe thickness, 11.31 mm
* Gas molecular weight, 16.8
* Compressibility (discharge), 0.98.
Solution. The main problem of this analysis is the calculation

of maximum blowdown flow. Since the blowdown is from a
source pressure of 10,000 kPag to atmospheric without any re80

MARCH 2021 | HydrocarbonProcessing.com

striction orifice, the flow will be choked. The flowrate at choked
condition must be estimated.
Flowrate calculation.5,6 The volumetric flowrate for compressible fluid is calculated using Eq. 42:
(42)
P  P1
Q = 53.64  Y  d 2
K  T  Sg
where,
Q = volumetric flow, Sm3/sec
Y = expansion factor
d = pipe inside diameter = 0.09168 m
ΔP = differential pressure, kPa
P1 = initial pressure = 10,101.3 kPa
T = temperature = 303.15 K
Sg = 0.58 (MW = 16.8)
K = flow resistance factor
Estimation of flow resistance factor:
Total equivalent pipe length = 25 m
Friction factor (fully turbulent flow) = 0.0175
K (for pipe) = 0.0175*25/0.09168 = 4.8
K (entrance) = 1
K (exit) = 0.5
Total K = 6.3
For a compressible gas with a ratio of specific heats in the
range of 1.3, the pressure ratio is estimated using Eq. 43:

{

0.9054
0.1173
0.0195
P
= 0.9953 +
+

K 0.5
K
K 1.5
P1

}

1

= 0.728 (43)

Therefore,
ΔP = 0.728 × 10,101.3 = 7,353.7 kPa
Pressure at point D = 10,101.3 - 7,353.7 = 2,747.6 kPa
The expansion factor is calculated as (Eq. 44):
Y = 0.0415 ln(K) + 0.6097 = 0.686

(44)

The volumetric flow is calculated as (Eq. 45):

Q  53.64

0.686

0.091682

7,353.7
10,101.3
= 80.09 Sm 3 /s
6.3 303.15
0.58

(45)
= 204,710 kg/h
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