Onda de presión documento sobre las variaciones de presión y las ondas de choque When the positive part of a wave meets the negative part of another one the two parts nullify each other producing the “node” of the standing wave (i.e. a minimum of amplitude). Associated to the pressure variations there are also the speed variations: to an “anti-node” of pressure corresponds a “node” of speed and vice versa. Dimensions of piping, frequencies of the excitation source, characteristics and status of the fluid in suitable combinations can give rise to stationary waves: the appearance of a standing wave set up an “acoustic resonance”. In absence of damping the amplitude of the standing wave tends to the infinite. The damping is produced by the same devices that produce pressure losses (in motion equation).The reciprocating compressor, with its pulsating flow, introduces a periodical excitation with harmonic components, referred to its rotational speed, predominant according to the number of the effects operating in each stage.“Vibration refers to mechanical oscillation about an equilibrium point” The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road. Oscillations often occur together with the motion of mechanical part of a machine. By the energy standpoint, vibration is the transfer phenomena from elastic potential energy to kinetic energy. When a guitar string is pulled, it stores elastic potential energy and when the string is released this energy is converted into kinetic energy (movement). Sound is strictly related to vibration. Sound, i.e. pressure waves, is generated by vibrating structures (e.g. vocal cords) and pressure waves can generate vibration of structures (e.g. ear drum). Free vibration occurs when a mechanical system is set off with an initial input and then allowed to vibrate freely. The mechanical system will then vibrate at one or more of its natural frequencies and damp down to zero. An examples of this type of vibration is hitting a tuning fork and letting it ring, when the beginning energy is totally wasted (hit), no sound is produced.The natural frequencies of a mechanical system are proper of the system itself and they are connected to the masses, the stiffness and the involved constraints. In some way the natural frequency is an oscillating frequency of the system where the inertial forces and the elastic forces are equivalent: this means that any oscillation amplitude satisfy the system.

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Pressure pulsations

2. 2 /
GE /
April 12, 2024
Pressure pulsations
PULSATIONS DAMPENERS

3. 3 /
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April 12, 2024
Pressure pulsations
A perturbation in a fluid generates a wave that propagates in the fluid itself .
The wave is constituted by a variation of the pressure (and density) as regards the
average pressure and propagates spherically with a characteristic speed: the speed
of sound .

p
k
kRTZ
c 

KV = cp/cv
R = constant of the gas [m2/s2°K]
T = temperature [°K]
p = pressure [Pa]
 = density [kg/m3]
[m/s]
The sound speed depends on the characteristics and the
status of the medium, so it strongly depends on the gas
M.W.:
• it increases with the temperature
• it increases with the pressure
PRESSURE WAVE GENERATION

4. 4 /
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April 12, 2024
Pressure pulsations
ISOTACHYPHONIC LINES

5. 5 /
GE /
April 12, 2024
Pressure pulsations
The behavior of such pressure waves inside a piping can be
mathematically represented by the simplified equations of the transient in a fluid:
p instantaneous
pressure
V instantaneous speed
d pipe diameter
c propagation speed of
the pulsation
f friction factor
0
2



x
V
c
t
p
x
p
V







0
2
1




d
V
fV
t
V
x
V
V
x
p







Eq. of motion
Eq. of continuity
Hypothesis:
• one-dimensional flow (all the directions of propagation of the pressure wave can
be neglected except the main one)
• adiabatic flow (heat exchanges with the outside are neglected)
• propagation speed of the pulsation >> speed associated to the average capacity
(the flow of the fluid has only negligible effects on the propagation of the wave)
MATHEMATIC MODEL
x
pA pA+(pA)x x
V
x
d

6. 6 /
GE /
April 12, 2024
Pressure pulsations
When the perturbation is “oscillating”,
zones with  pressure (+) and (-)
traveling along the piping are
generated.
This is the so called “pulsation” .
The pulsation can be represented by a
sinusoidal curve and the space
distribution of the pressure wave in
motion can be defined by the formula:
f
c 

C = sound speed [m/s]
 = wave length [m]
f = frequency [Hz]
PULSATION
The piston generates over pressure during the discharge stroke (+) and rarefaction
pressure (-) during suction stroke.
The reference pressures are, in absolute values, those measured by pressure gages
at suction and discharge side.
The pressure pulsation travels in the pipes with the sound speed.

7. 7 /
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April 12, 2024
Pressure pulsations
Rms = 0,707 Peak = 1,110
Average
Peak = 1,414 Rms = 1,570
Average
Average = 0,637 Peak = 0,900
Rms
Peak-to-peak = 2,000 Peak
SINE WAVES
V = vibration speed [m/se
f = vibration frequency [Hz]
n = compressor speed [rpm]
r = vibration displacement [m]
fr
r
V 
 2



8. 8 /
GE /
April 12, 2024
Pressure pulsations
When a pressure (or acoustic) wave moving inside a piping finds a discontinuity it
generates a “reflection”.
The reflection assumes different characteristics according to the type of discontinuity
found. The two extreme cases are:
• hard end: a compression wave is reflected as compression wave
• soft end: a compression wave is reflected as depression wave
In all other cases there are partial
reflections; in case of a section
variation:
2
1
2
1
A
A
A
A
p
r
p
i 

 1
)
(
2
2
1 

A
A
p
t
p
i
pr = amplitude of reflected wave
pi = amplitude of incident wave
pt = amplitude of transmitted wave
PRESSURE WAVE REFLECTION

9. 9 /
GE /
April 12, 2024
Pressure pulsations
The reflection phenomena
produces the “standing wave”.
These are generated by
overlapping of incident and
reflected waves.
When the positive parts of two
waves meet each other they
sum their amplitude, producing
the “anti-node” (i.e. a maximum
of amplitude) of the standing
wave.
ACOUSTIC RESONANCE
NB : in correspondence of pressure anti-node there is a pressure oscillating with a
frequency equal to the one induced by the perturbation and with maximum
amplitude; in correspondence of a node the amplitude of the pressure oscillation
is reduced to zero.
When the positive part of a wave meets the negative part of another one the two parts
nullify each other producing the “node” of the standing wave (i.e. a minimum of
amplitude).
Associated to the pressure variations there are also the speed variations: to an “anti-
node” of pressure corresponds a “node” of speed and vice versa.

10. 10 /
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April 12, 2024
Pressure pulsations
Dimensions of piping, frequencies of the excitation source, characteristics and status
of the fluid in suitable combinations can give rise to stationary waves: the appearance
of a standing wave set up an “acoustic resonance”.
In absence of damping the amplitude of the standing wave tends to the infinite. The
damping is produced by the same devices that produce pressure losses (in motion
equation).
ACOUSTIC RESONANCE
,...,
3
,
2
,
1
2


n
L
nc
f
The frequency that produces a standing wave and then an acoustic resonance, for a
pipeline “closed-closed” or “open-open”, is given by:
n (=1, 2, 3, …) indicates the order of the resonance,
c is the sound speed [m/s]
L is the length of the pipeline [m]
Hz
The reciprocating compressor, with its
pulsating flow, introduces a periodical
excitation with harmonic components,
referred to its rotational speed,
predominant according to the number of
the effects operating in each stage.

11. 11 /
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April 12, 2024
Pressure pulsations
The pressure pulsation can be decomposed
in several sinusoidal harmonics by means of
Fast Fourier Transform (FFT).
Periodic fluid motion path...
PRESSURE PULSATIONS WAVE PATTERN
r
n
V
60
2

For the 1st
harmonic:
V = vibration speed [m/s]
n = compressor speed [rpm]
r = vibration displacement [m]

12. 12 /
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April 12, 2024
Pressure pulsations
Standing wave patterns due to acoustic propagation in a closed
pipe
PRESSURE PULSATIONS WAVE PATTERN

13. 13 /
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April 12, 2024
Pressure pulsations
The reflection phenomena produce standing waves by overlapping of incident and
reflected ones.
PRESSURE PULSATIONS WAVE PATTERN

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April 12, 2024
Pressure pulsations
PRESSURE PULSATIONS WAVE PATTERN

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Pressure pulsations
PRESSURE PULSATIONS WAVE PATTERN

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April 12, 2024
Pressure pulsations
PRESSURE PULSATIONS WAVE PATTERN

17. 17 /
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Pressure pulsations
Versus:
• cylinder number
• cylinder load
• compression phase among cylinders
• cylinder valve opening degree
PRESSURE PULSATIONS IN MULTI-CYLINDER
RECO
Double acting cylinder flanges

18. 18 /
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April 12, 2024
Pressure pulsations
PRESSURE PULSATIONS
Double acting cylinder
flanges (with ideal valves)
Generic point of
compressor piping

19. 19 /
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April 12, 2024
Pressure pulsations
The damping effect is determined by the
pressure loss: the more is the pressure loss
the more is the damping.
To operate at best the orifices have to be
placed in the points where the stationary wave
has the maximum of flow oscillation (minimum
pressure oscillation). In this way the orifices
operate on the flow peaks introducing high
damping still maintaining limited the losses on
the average speed.
ORIFICES
About the effects of turbulence notice that the
“preferential” frequencies caused by diaphragms,
obstacles or branches are given by:
d
s
N
s
f

 Hz
Ns = Strouhal number
0.2 for diaphragms or obstructions
0.25÷0.5 for traps

20. 20 /
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April 12, 2024
Pressure pulsations
PIPE RESONANT MODE SHAPE
Half wave resonant
Pipes closed Pipes open
on both ends on both ends
Quarter wave resonant
Pipes closed on one end and
open on the other end
L
nc
fr
2

 
L
c
n
fr
4
1
2 


21. 21 /
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April 12, 2024
Pressure pulsations
The devices used to control the amplitudes of the pulsations are:
•acoustic filters
•dampeners
ACOUSTIC FILTERS
Helmholtz
Resonator
Quarter wave
stub
LV
A
c
fr

2

 
L
c
n
fr
4
1
2 


22. 22 /
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April 12, 2024
Pressure pulsations
ACOUSTIC FILTERS
Surge
Volume
L
nc
fr
2

2
2
d
D
m 
Attenuation increases as m
increases
Attenuation increases as m
increases
Helmholtz
Filter
V
C
r
L
mL
c
f
2
1


2
2
d
D
m 
V
p
L
nc
f
2

C
p
L
nc
f
2
 Passband
frequency

23. 23 /
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April 12, 2024
Pressure pulsations
LOW-PASS HELMHOLTZ FILTER
Inlet/outlet diameter: 4” _ Volume w/internals diameter:16”
Attenuation of compressor harmonics

24. 24 /
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April 12, 2024
Pressure pulsations
Damping effect R (Pout/Pin) on each harmonic:
)
(
1
1
cS
fV
R

 f = harmonic frequency
c= sound speed
S= pipe cross-section
V= dampener volume
SURGE VOLUME
The best practices relevant to the proper sizing of the
surge volumes establish that the length of the
volume has to be kept as short as possible.
South West Research Institute
recommendation:
• For Single volumes it is necessary to have a
ratio: L/D<=3
• For header volumes, the length of the volume
has to be limited to the distance from the
centerlines of two contiguous cylinders,
multiplied by the number of the cylinders
connected to the volume itself, with a ratio
L/D=2 and a ratio between the diameter of the
volume and the one of the outlet (or inlet, if
larger) nozzle D/d>=3

25. 25 /
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April 12, 2024
Pressure pulsations
SURGE VOLUME
Inlet/outlet diameter: 4” _ Volume w/internals diameter:16”
Attenuation of compressor harmonics

26. 26 /
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April 12, 2024
Pressure pulsations
VOLUME BOTTLE
Single cylinder bottle Double cylinder bottle

27. 27 /
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April 12, 2024
Pressure pulsations
According to NP experience a ratio L/D<=4 allows still good results, while ratios L/D>6
(more similar to pipe than to damper) do not allow to cut down the harmonics of pressure
pulsation over the 4th, unless the volume is really bigger than the required one.
This produces the following effects:
 Exceed the API std limits for the residual pressure pulsation (to declare to the Client);
 Production of high shaking-forces in the piping connected to such dampers with
consequent need of a more sophisticated and complex supporting system for the
piping itself, in order to keep the vibrations within acceptable limits.
VOLUME BOTTLE

28. 28 /
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April 12, 2024
Pressure pulsations
Ftot = total shaking force acting
Φ = pipe inner diameter [cm]
α = half bending angle of pipe [°]
Po = fluid average pressure in the pipe [kg/cm2]
ΔP = pressure pulsation 0-peak [kg/cm2]
f = pressure pulsation frequency [Hz]
VIBRATIONS INDUCED ON PIPE ELBOW

cos
2
2
1 T
F
F
Ftot 


P
Ftot 






 
 


sin
cos
2
2
The surfaces characterized by the points 1, 7, 4 and 2, 8, 3
being faced each other, are not generating pulsating thrusts.
Vice versa the surfaces with boundary points 6 and 2 and 3 and
5:


sin
4
2


S 






 
 

sin
4
2
P
T
f
P
P
P 
2
cos
0 


For 1st harmonic
60
2 n

  t
P
P
P 
cos
0 

   






 


 


 sin
cos
2
cos
2
t
P
P
F o
tot

29. 29 /
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April 12, 2024
Pressure pulsations
The “shaking forces” are oscillating forces generated owing to the pressure
pulsations operating in correspondence of changes of direction or changes of the
cross-section of the piping in the dampers, separators etc.
They are the main cause of the vibrations of the piping.
To evaluate their effects it has to take in to account at the same time the positions in
which they are generated, the amplitudes and the phases of their harmonic
components.
SHAKING FORCES
Shaking Forces in the dampers
Example:
p = line pressure = 1000 Pa
p = p0 sin t = 10 Pa sin t
For the first harmonic (fundamental) it is:
Fleft = (1010-990) * Area
Fright = (990-1010) * Area (180° lagging)
Total Shaking Force = 20 * Area (0-P)

30. 30 /
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April 12, 2024
Pressure pulsations
TYPICAL PULSATION DAMPERS SHAPES
1. no shaking forces
2. no shaking forces
3. possible high shaking
forces
4. shaking forces ≈ 0
5. negligible shaking forces
6. no shaking forces
7. no shaking forces
8. possible high shaking
forces
9. shaking forces ≈ 0
10. negligible shaking forces

31. 31 /
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April 12, 2024
Pressure pulsations
FUNDAMENTALS OF VIBRATION
“Vibration refers to mechanical oscillation about an equilibrium point”
The oscillations may be periodic such as the motion of a pendulum or random such
as the movement of a tire on a gravel road.
Oscillations often occur together with the motion of mechanical part of a machine.
By the energy standpoint, vibration is the transfer phenomena from elastic potential
energy to kinetic energy.
When a guitar string is pulled, it stores elastic potential energy and when the string
is released this energy is converted into kinetic energy (movement).
Sound is strictly related to vibration. Sound, i.e. pressure waves, is generated by
vibrating structures (e.g. vocal cords) and pressure waves can generate vibration of
structures (e.g. ear drum).
Free vibration occurs when a mechanical system is set off with an initial input and
then allowed to vibrate freely. The mechanical system will then vibrate at one or more
of its natural frequencies and damp down to zero.
An examples of this type of vibration is hitting a tuning fork and letting it ring, when
the beginning energy is totally wasted (hit), no sound is produced.

32. 32 /
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April 12, 2024
Pressure pulsations
FUNDAMENTALS OF VIBRATION
Forced vibration occurs when an alternating force or motion is applied to a
mechanical system. In forced vibration the frequency of the vibration is the frequency
of the force or motion applied, but the magnitude of the vibration is strongly
dependent on the mechanical system itself.
Examples of this type of vibration include a shaking washing machine due to an
imbalance, transportation vibration (caused by truck engine, springs, road, etc), or
the vibration of a building during an earthquake.

33. 33 /
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April 12, 2024
Pressure pulsations
0

kx
x
m

m
k
n 

n = natural frequency of the system
The natural frequencies of a mechanical
system are proper of the system itself and
they are connected to the masses, the
stiffness and the involved constraints.
In some way the natural frequency is an
oscillating frequency of the system where the
inertial forces and the elastic forces are
equivalent: this means that any oscillation
amplitude satisfy the system.
MECHANICAL NATURAL FREQUENCY
The natural frequencies of a system
with n degrees of freedom are n.
To each natural frequency corresponds
a characteristic “shape”.
For example the system in the figure
beside, where the 3 masses are “m”
and the 3 stiffnesses are “k”, we obtain:
m
k
445
.
0
1 

m
k
25
.
1
2 

m
k
80
.
1
3 


34. 34 /
GE /
April 12, 2024
Pressure pulsations
0


 kx
x
c
x
m 


Considering also the damping a term, depending on the
oscillation speed, is added to the forces balance.
So that also the solution depends on a new entity: the
critical damping
km
cc 2

c
c
c /


 < 1  =1  >1
)
1
(
)
sin (
2
2
/








 
n
d
m
ct
t
Ce
x m
ct
e
Bt
A
x 2
/
)
( 


)
( 1
1
2
/
2
2





 


 n
n t
t
m
ct
B
Ae
e
x
There are no
oscillations
There are no
oscillations: the
system gradually
tends to a balance
position.
By introducing:
We get:
DAMPED RESPONSE

35. 35 /
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April 12, 2024
Pressure pulsations
In case of forced vibrations, with damping, the equation
becomes:
t
sin
F
kx
x
c
x
m 
0


 


An elastic system is said in resonance when the exciting
frequency coincides with one of the natural frequencies
of the system.
Without damping, the amplitudes of the oscillations
could tend to infinite, with damping the oscillations (in
case of  < 1) have limited amplitude.
FORCED (AND DAMPED) RESPONSE
In general, for a system having N degrees of freedom
the response to a sinusoidal excitation is given by:
)
(
)
/
2
(
)
/
1
(
1
2
2
2
2
1
2 n
n
n
N
n n
n
n
kn
k t
sin
m
F
D
x 









 

xk = displacement of the k-th degree of freedom
Dkn= oscillation amplitude of the k-th degree of
freedom in the n-th natural mode
Fn = generalized force on the n-th mode = jFjDjn
mn = generalized mass on the n-th mode = jmjDjn
n = angle of phase

36. 36 /
GE /
April 12, 2024
Pressure pulsations
The developments of the last years leads to a direct link between the acoustic study
with a program based on finite element for the calculation of the mechanical natural
frequencies and the mechanical piping response: this allows the direct use of the
various limits imposed by the normative (i.e pressure pulsation, vibrations and
cyclic stress, etc.).
LAST DESIGN METHODS DEVELOPMENT

37. 37 /
GE /
April 12, 2024
Pressure pulsations
API 618 standard appendix N 3.1 defines necessary data and acceptance limits of
these analysis.
Acoustic analysis must take into account all the piping and the appliances to the
extent to which any additional change produces negligible effects on the results.
This condition is usually satisfied starting the study from the inlet of the largest
separator at suction, going then through the various interstages (if any) and ending
the study at the outlet of the largest separator at discharge. Of course the study
includes all the branch lines having significant diameters like by-pass or safety
valves lines.
ACOUSTIC AND MECHANICAL ANALYSIS – INPUT
DATA
In practice the study can be ended at the following points:
• Large volumes (compared with the dampeners)
• Piping of “infinite” length (some hundreds meters)
• Closed valves
• Valves or other devices with very high concentrated pressure loss
• Point of complete gas condensation
Of course the extension of the mechanical analysis should be even more limited if
the acoustical analysis indicates that the forces operating on some parts of the
plant are negligible.

38. 38 /
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April 12, 2024
Pressure pulsations
Data for ACOUSTIC ANALYSIS:
• P&Id (or equivalent) of all the piping involved in the study
• Isometric drawings of all the piping involved in the study, including the branch
lines (if any), showing the normally closed valves
• Inside diameters of all involved piping
• Indication of all significant concentrated pressure losses present on the plant
(through calibrated orifices, valves, filters, heat exchangers, separators, etc.)
showing the conditions to which the pressure losses are referred
• Data sheets and fabrication drawings of all the appliances involved in the analysis
(separators, heat exchangers, reactors, etc) with the indication of the inside liquid
level (if any)
• Type and location of any flow-meter
• For the piping where gas data are different from the ones of compressor operating
it is necessary to provide flow Capacity, Temperature, Compressibility factor (Z),
Cp/Cv and Molecular weight. If the piping includes some liquid it is necessary to
provide relevant flow Capacity and Specific Gravity
• In case of parallel operating compressors it is necessary to specify the various
operating sequences to consider
ACOUSTIC ANALYSIS – INPUT DATA

39. 39 /
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April 12, 2024
Pressure pulsations
Data for MECHANICAL ANALYSIS
• Isometric drawing of all the piping involved in the study, showing the location of
the supports and the one of all the concentrated masses (valves, flanges, etc.)
• Outside diameter and thickness of all involved piping
• Weights of all concentrated masses (valves, flanges, etc.)
• Fabrication drawings of piping supports.
• As alternative the indication of the directions (displacements and rotations)
restrained by the supports themselves
• Fabrication drawings of the structures sustaining the supports (or their stiffness
values) in case it is not realistic consider them rigid
MECHANICAL ANALYSIS – INPUT DATA

40. 40 /
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April 12, 2024
Pressure pulsations
Topic: Sect. 3.9, GENERAL RULE (3.9.2.2.1):
The compliance with the general rule can be got by the application of three
approaches.
The pulsation and/or mechanically induced vibration shall not cause cyclic
stress level higher than the endurance limit of the materials used for the
components subject to these cyclic loads.
STANDARD API 618 4TH EDITION JUNE 1995
k = Cp/Cv= isentropic exponent
Ts = suction temperature [°K]
M = molecular weight [kg/kmole]
PD = total net displaced volume per revolution [m3]
R = compression stage pressure ratio at cylinder flanges
Pcf(%) = peak-to-peak pulsation at the flange of the cylinders [% of Pl]
P1(%) = peak to peak pulsation allowed for each harmonic [%
of Pl]
P(%) = total % loss
Pl = average absolute line pressure [bar]
ID = Inside pipe diameter [mm]
f = pulsation frequency [Hz]
n = harmonic component (1st, 2nd, etc.)
rpm = compressor rotation speed [RPM]
VS = minimum volume for the suction dampener [m3]
VD = minimum volume for the discharge dampener [m3]
60
n
rpm
f 

41. 41 /
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April 12, 2024
Pressure pulsations
The use of volume dampeners according Approach 1 allows to limit the pulsation on
line side to the value calculated by:
The experience gained over years of analysis has proved that the formulas used to
design the volume bottles according to the Approach 1 may lead to volumes not
adequate to the application (sometimes smaller, sometimes larger), so that it is more
appropriated to design the dampeners by suitable calculating programs.
STANDARD API 618 4TH EDITION JUNE 1995
3
1
.
4
(%)
1
Pl
P 
APPROACH 1 ( par 3.9.2.2.2 - 3.9.2.5)
It can be used for pressures up to 35 bar and for powers not higher than 110 kW.
It does not require any type of analysis.
It only requires :
4
1
,
8
M
kT
PD
V S
S 









k
S
D
R
V
V 1
6
,
1
D
S V
V 
028
,
0

S
V

42. 42 /
GE /
April 12, 2024
Pressure pulsations
APPROACH 2 ( par 3.9.2.2.2 -3.9.2.5 )
It can be used for pressures up to 200 bar.
It requires an Acoustic Analysis to proper size the dampener and to limit the
residual pulsation in the plant determined by:
2
1
.
397
(%)
1
f
ID
Pl
P 
STANDARD API 618 4TH EDITION JUNE 1995




%
7
3
(%)
R
Pcf
To reduce pulsation within the above limits, it is possible to use dampening
elements (calibrated diaphragms, “choke tube” etc.) with a total pressure loss
lower than P(%):
R
R
P
)
1
(
67
.
1
(%)



It requires also a MECHANICAL ANALYSIS that, once fixed the highest (significant)
exciting frequency, calculates, by means of experimental formulas, the maximum
spans between the supports (guide for supports positioning).
The insertion of a suitable number of supports (usually “Clamp” type), so
calculated, guarantees a mechanical natural frequency of the piping higher
(generally by 50%) than the highest exciting frequency, so avoiding the use of more
sophisticated calculation methods.

43. 43 /
GE /
April 12, 2024
Pressure pulsations
STANDARD API 618 4TH EDITION JUNE 1995
• APPROACH 3 (see para 3.9.2.2.2 -3.9.2.5 )
It requires an ACOUSTIC ANALYSIS with procedure and limits as per Approach 2.
It requires also a MECHANICAL ANALYSIS to determine the mechanical natural
frequencies and the “mode shape” by the simulation of the true model of the piping
and relevant supports.
This to guarantee the effective separation between the exciting frequencies (acoustic
calculation) and the mechanical natural frequencies of the piping, in order to avoid
resonant phenomena.
Referring to the GENERAL RULE API 618 (par 3.9.2.2.1) it is possible to limit directly
the cyclic stresses with no obligation to comply with the pulsation level limits.
This requires the fulfillment of more complex and onerous calculation to determine
the amplitudes of the vibration and relevant cyclic stress to keep the last one within
the limits, gradually operating on both pulsation pressure reduction and supports
insertion.
For carbon steel the limit of the cyclic stress is fixed to 179 N/mm2 peak-to-peak
(26.000 Psi-a).
To take into account the stress concentration factor and a safety factor, above value
is reduced to 20.6 N/mm2 .

44. 44 /
GE /
April 12, 2024
Pressure pulsations
ALLOWABLE PIPING VIBRATION LEVEL

45. 45 /
GE /
April 12, 2024
Pressure pulsations
According to NP experience also vibrations has to be limited in order to get the
maximum reliability for plant, machine and relevant accessories (valves,
instrumentation, etc.).
The limits for vibrations amplitude considered by NP are based on SWRI
"Standardized piping vibration criteria" and verified on site by dedicated
measurements fulfilled by NP.
ALLOWABLE PIPING VIBRATION LEVEL

46. 46 /
GE /
April 12, 2024
Pressure pulsations
2.4.1. Problem minimization on Design phase.
The standard limitation, exception made for the case where cyclic stress limitation
is directly used , imposes limits to the residual pressure pulsation:
Base rule: cyclic stress limitation
•Acoustical frequencies calculation
•Pressure pulsation limitation
Combined acoustic and
mechanical study for cyclic
stress evaluation
ACOUSTIC ANALYSIS
The first step for pressure pulsation amplitude limitation is a proper compressor
dampers/volume bottles design.
The dampers/volume bottles are sized during the compressor design with a
simplified model which only considers the system “compressor - dampers/volume
bottles - endless piping line ”, on the various operating conditions.
On the final acoustic analysis:
• the endless piping line is replaced with the real plant layout
• then all modifications necessary, to eliminate the acoustic resonance and to
reduce residual pressure pulsation (and relevant shaking forces) within the
required limits, are studied.

47. 47 /
GE /
April 12, 2024
Pressure pulsations
• K.O drum/Separator must be located as close as possible to compressor.
• Points of shaking forces application such as elbows, tee connection and size variation must be
limited to the minimum required one.
• closed valve on branch lines must be positioned as close as possible to the branch point from
main line.
• Maintain the gas velocity within acceptable limit (e.g. 30 m/s max) to avoid negative effects
such as gas turbulence/vortex, high pressure drop , noise etc.
• In case of compressors operating in parallel, the manifold must be of the greatest size and the
Block valves should be positioned as close as possible to the branch point of main line
(manifold). If not feasible, the insertion of a flange at that branch point is suggested to allow the
insertion of an orifice which may be necessary
• Device sensitive to flow pulsation such as flow measurements must be located as far as
possible from the compressor (orifice type is preferred)
ACOUSTIC ANALYSIS – BEST PRACTICE
Possible modifications required from the study are:
• Insertion of orifices (pressure drops).
Most common way to reduce pressure pulsation amplitudes are the orifices but their pressure
drop must be limited to the one allowed by API or other rule.
• Changes of geometry
Used to detune acoustic resonance out of the operating range, when the insertion of orifices is
not sufficient/effective. They are effective when compressor operating conditions are limited.
This can means change in piping length or in size, but practically the most suggested one is the
increase of piping size for a small amount of meters maintaining the original piping routing,
since generally it is the only feasible.
• Insertion of Additional volume
Used to reduce pressure pulsation below the values allowed by API.

48. 48 /
GE /
April 12, 2024
Pressure pulsations
2.5.1. Problem minimization on
Design phase.
Once the pressure pulsations are
reduced to the required levels,
API 618 standard recommend to
check that the piping mechanical
natural frequencies are not
coincident (i.e. there is sufficient
margin) with the acoustic
excitation frequencies (shaking
forces), to avoid the phenomena
of mechanical resonance.
Practically once the acoustical
study has established the highest
order harmonic of the exciting
frequency a mechanical analysis
is to be performed to assure that
the minimum mechanical natural
frequency (1st mode shape) of
the piping system is sufficiently
higher than the exciting shaking
forces (generally of 20%/50%).
MECHANICAL ANALYSIS
( 1.5 times )
Safety
Margin
FREQUENCY (Hz)
SHAKING
FORCES
(daN)
Harmonic
Negligible
27
6 12 18 24
s
i
g
n
i
f
i
c
a
n
t
n
e
g
l
i
g
i
b
l
e
Non-acceptable
Natural
Mechanical
Frequencies
Acceptable
Natural
Mechanical
Frequencies
Highest order significant
harmonic of pulsation
induced forces

49. 49 /
GE /
April 12, 2024
Pressure pulsations
Basic rule: cyclic stress limitation
•Acoustical frequencies calculation
•Pressure pulsation limitation.
APPROACH. 2
Location of piping supports (Clamp)
on the basis of max allowed piping
span depending upon:
•highest order of significant exciting
frequency
•piping size and layout configuration
APPROACH. 3
Location of piping supports of various
type (i.e. rest, guide, anchor etc.)
based on calculation sufficiently
accurate to determine the mechanical
natural frequencies (normally
performed by finite elements
programs) of piping model.
Combined acoustic and
mechanical study for cyclic
stress evaluation
PRESSURE PULSATION REDUCTION: API 618
APPROACHES

50. 50 /
GE /
April 12, 2024
Pressure pulsations
Based on studies
experience, piping
layout configuration and
compressor RPM, is
established the
minimum mechanical
natural frequency
required for piping
system.
GUIDELINE FOR SUPPORT LOCATIONS
(APPROACH 2)

51. 51 /
GE /
April 12, 2024
Pressure pulsations
A specific table relevant to
the length of the maximum
span is elaborated to
guarantee the compliance
with the mechanical
frequency
GUIDELINE FOR SUPPORT LOCATIONS
(APPROACH 2)

52. 52 /
GE /
April 12, 2024
Pressure pulsations
GUIDELINE FOR SUPPORT LOCATIONS
(APPROACH 2)

53. 53 /
GE /
April 12, 2024
Pressure pulsations
GUIDE FOR DESIGN OF SINGLE BEAMS
SUPPORT

54. 54 /
GE /
April 12, 2024
Pressure pulsations
FRICTION CONSTRAINTS
Most of thermal stress issues due to fulfillment of the modifications to the supports
requested by the mechanical analysis can be fixed by using “friction constraints”.
Those constraint are based on the fact that the magnitude of the dynamic forces
(some kN) is smaller then the one of relevant thermal loads (tenths of kN).
Consequently by using support “Clamp” or “Hold down” type, above difference of
entity can be exploited blocking by friction the dynamic force, through a suitable
tightening of the support itself, and leaving the pipe to thermally extend since the
relevant loads exceed the resistance due to the friction.
In NP mechanical studies, for each request of modification of one support, the
dynamic force to be constrained is shown.
That force (“shaking force”) represents the maximum value recorded in the various
operating conditions and already includes a safety factors.
The knowledge of these values allows the fulfillment of the friction constraint and, in
the same time, get an approximate information about the amount of the dynamic
load that can operate on that constraint.
In fact to forecast, for any support, the actual dynamic force to which it will be
loaded in the various directions, it should be necessary to impose precise
constraints to each support and perform the calculation for a forced response (i.e:
vibration calculation and relevant cyclic stresses).

55. 55 /
GE /
April 12, 2024
Pressure pulsations
FRICTION CONSTRAINTS
The force shown in the reports is the axial “shaking force” operating between two
consecutive curves then in case of more supports placed on long rectilinear bays
the same value of total force is shown.
In this case the friction force requested to have an axial constraint can be get in the
shown position (i.e: at that specific support) or through the sum of the axial friction
produced by the supports placed in the same rectilinear bay.
On the contrary, when a lateral constraint is required, it is necessary to get the
friction in that specific position, otherwise it is necessary to insert a real mechanical
guide.

56. 56 /
GE /
April 12, 2024
Pressure pulsations
SUPPORTS TYPE
CLAMP
TYPE
HOLD DOWN TYPE

57. 57 /
GE /
April 12, 2024
Pressure pulsations
PULSATION DAMP SPECIAL SUPPORT
Good maintainability

58. 58 /
GE /
April 12, 2024
Pressure pulsations
MAXIMUM SHAKING FORCES ON PIPING
SUPPORTS

59. 59 /
GE /
April 12, 2024
Pressure pulsations
• Keep the piping as close as possible to the ground to make the support more stable and
simpler
• Insert the supports in correspondence of concentrated masses (valves, flanges, etc.)
• Insert the supports close to elbows, T-joints and cross-section variations: points where the
shaking forces are discharged
• For separators and filters, skirt type supports have to be preferred to leg type ones
• Make load bearing structures and supports sensibly stiffer than the supported structure
• Place in the straight sections of piping exceeding a given length at least one constraint in
the axial direction (in case it is not possible to perform the axial constraint by friction with a
clamp)
• Avoid, where possible, series of bays of equal length
• Usually small diameter branch lines like vents, drains, level indicators and instruments in
general are not considered in the analysis, but they can be an issue. The behavior guideline
is:
o Use these components only when strictly necessary
o Avoid not supported cantilevered weights
o Place the valves as close as possible to the main line
o Prefer light weight valves and flanges (wafer type)
o Support cantilevered weights directly on the piping or on the appliances to which they
are connected (a constraint on the ground or on other pipe could determine a relative
movement)
PLANT ARRANGEMENT RECOMMENDATIONS
Impact of mechanical recommendations on original Design
• Modifications of the existing supports: in general they are least onerous, but they can
involve the necessity to newly fulfill thermal verifications
• Insertion of new supports: they often require the construction of new structures for the new
supports anchorage and the need of a new thermal verification; their optimal insertion is not
always possible in already designed plants
• Modifications to supports of appliances: the use of legs to support appliances (filters,
separators, etc) often leads to the need to replace them by skirt support or to install wind-
bracings

60. 60 /
GE /
April 12, 2024
Pressure pulsations
The purpose of this analysis is to calculate the low fatigue stresses on volume
bottles due to the alternate cycles of standby condition and operating condition of
the compressors.
The volume bottles are modeled by solid or shell elements and are restrained at the
cylinder flanges and at the saddles.
The piping loads are applied in correspondence of the inlet nozzles for the suction
volume bottles and of the outlet nozzles for the discharge nozzles.
The low cycle fatigue analysis is carried out following the procedure described by
ASME VIII div.2 Appendix 5 Article 5-1:
•Calculate stress components at Standby condition
•Calculate stress components at Operating condition
•Subtract stress components Operating Conditions from Standby Conditions
•Calculate one-half Stress Intensity with the resultant stress components
•Compare the Stress Intensity versus Allowable Alternate Stress
LOW FATIGUE ANALYSIS

61. 61 /
GE /
April 12, 2024
Pressure pulsations
VOLUME BOTTLE STRESS ANALYSIS - SHELL

62. 62 /
GE /
April 12, 2024
Pressure pulsations
Static stresses
Dynamic
stresses
Shell location Max Static Stress
N/mm2
Allowable
Static stress
Alternate stress
N/mm2
Allowable
alternate stress
Top 5.238 118 13.894 20.6
Meddle 2.927 118 8.014 20.6
Bottom 6.060 118 10.326 20.6
Stresses Summary
VOLUME BOTTLE STRESS ANALYSIS - SHELL

63. 63 /
GE /
April 12, 2024
Pressure pulsations
The purpose of this analysis is to calculate dynamic and static stresses on pulsation
volume bottle internals caused by pressure pulsation produced by compressor.
The loads are represented by internal static
pressure and pressure pulsation.
The pressure pulsation (in amplitude and phase)
for each different position inside the equipment
are defined from plant acoustic analysis.
The following procedure is applied:
• The worst case is identified as the one with
higher shaking forces applied on the pulsation
volume bottle
• The pressure pulsation inside the pulsation
volume bottle is analysed and two load cases
with the worst combination of amplitude and
phase are defined
• The pulsating pressure is added to the static
pressure and applied to the model
VOLUME BOTTLE STRESS ANALYSIS -
INTERNALS

64. 64 /
GE /
April 12, 2024
Pressure pulsations
11
8
11
6
11
0
11
2
10
8
10
2
21
2
21
8
10
6
10
5
10
4
Pulsating loads
point location
-0,5
-0,4
-0,3
-0,2
-0,1
0
0,1
0,2
0,3
0,4
0,5
0 20 40 60 80 100 120 140 160 180 200
102
103
104
105
106
107
108
110
112
116
118
212
218
Pressure pulsation
[bar]
Point Static Pressure
N/mm2
Load case 1 “Positive”
N/mm2
Load Case 2 “Negative”
N/mm2
118 0.013 0.0271 0.0002
108 0.013 0.0990 0.0163
218 0.013 0.5000 -0.0260
112 0.013 -0.0001 0.0281
102 0.013 0.0164 0.0101
212 0.013 -0.0251 0.0538
VOLUME BOTTLE STRESS ANALYSIS -
INTERNALS

65. 65 /
GE /
April 12, 2024
Pressure pulsations
The purpose of this analysis is to calculate the mechanical natural frequencies and
mode shape of the cylinder manifold system and to show that there is a sufficient
margin (frequency separation) from the significant mechanical and acoustic
excitation frequencies.
The analysis involves
modelling the properties of :
• cross-head guides,
• distance pieces,
• cylinders,
• flanges,
• compressor nozzles,
• branch connections,
• pulsation suppression
devices
• inlet and outlet piping
CYLINDER MANIFOLD STRESS ANALYSIS

66. 66 /
GE /
April 12, 2024
Pressure pulsations
CYLINDER MANIFOLD STRESS ANALYSIS

67. 67 /
GE /
April 12, 2024
Pressure pulsations
A = tightening force [N]
F = dynamic force to be restrained [N]
X = 2 (assuming l= L/2)
 = friction coefficient (usually 0.2 for steel on steel)
SUPPORTS TIGHTENING FORCE
Sometimes also the force due to the weight of the pipe together with the thermal
stresses can be sufficient to guarantee a friction force higher than the dynamic one,
avoiding the insertion of the support.
X
F
A


Analysis Results are:
• mechanical natural frequencies
• mode shape
Mode Frequency
Number Hz
1 21.499
2 36.805
3 39.881
4 45.099
5 45.685
6 57.727
7 61.961
8 63.461
9 80.633
10 103.20

68. 68 /
GE /
April 12, 2024
Pressure pulsations
THE END

69. 69 /
GE /
April 12, 2024
Pressure pulsations
ISOTACHYPHONIC LINES
Hydrogen Oxygen
Nitrogen

70. 70 /
GE /
April 12, 2024
Pressure pulsations
ISOTACHYPHONIC LINES
CO2 NH3 Ethylene

71. 71 /
GE /
April 12, 2024
Pressure pulsations
ISOTACHYPHONIC LINES
Ethane Propane Butane
Methane

72. 72 /
GE /
April 12, 2024
Pressure pulsations
RE = electrical resistance
R = acoustic resistance consists of restricted passage
causing energy dissipation
L = electrical inductance
M = acoustic inductance consists of a mass of gas,
contained in a relatively small pipe which, when
forced into
motion, causes a change in velocity
CE = electrical capacitance
C = acoustic capacitance consists in a volume acting as
one storage element,
which opposes change in pressure
ANALOGY BETWEEN ELECTRICAL AND ACOUSTICAL
ELEMENTS

73. 73 /
GE /
April 12, 2024
Pressure pulsations
From the electric-acoustic analogy:
REVERSE FLOW IN THE PIPE
ΔV = voltage variation
Z = impedance
ΔI = current variation
ΔP = pressure variation
k = pipe and check valve loss factor
ΔQ = gas flow variation
k
P
Q
I
Z
V







In case loss factor k becomes to small, for
example when gas capacity is strongly
reduced, negligible pressure variation ΔP
can generate very high flow variation ΔQ.
Gas flow variation ΔQ can be so high to
reach negative values for a portion of the
wave during which the gas is temporary
back in the pipe. This condition can
generate fluttering phenomena of moving
items of check valve, with possible serious
damages of these and of valve seat.

74. 74 /
GE /
April 12, 2024
Pressure pulsations
Instantaneous gas capacity Q, with the hypothesis of sine wave and connecting rod
with infinite length, can be estimated as follows:
MATHEMATIC APPROACH
A = piston pumping area [m2]
ω = angular speed [rad/sec]
r = crank radius [m]
θ = crank angle while cylinder valve is open

 cos
r
A
Q 
Maximum gas capacity:
So, the gas capacity pulsation can be studied as a sine wave having amplitude as
follows:
r
A
Q 

Average gas capacity: m
Q
 
m
m Q
r
A
Q 

 

75. 75 /
GE /
April 12, 2024
Pressure pulsations
A = piston pumping area [m2]
ω = angular speed [rad/s]
n = compressor rotation speed [giri/1’]
r = crank radius [m]
Qm = gas capacity handled by the cylinder @ the conditions P, T [m3/s]
MATHEMATIC APPROACH
 
m
m Q
r
A
Q 

 

Vn = gas capacity referred to 0[°C] and 1,013 [bar-a] [Nm3/h]
T = gas temperature [°K]
P = gas pressure [bar-a]
Z = compressibility factor @ the conditions P, T [---]
R = gas constant [m/°K]
φ = crank angle at which the valves open [°]
θ = 180-φ = crank angle during which the valves are opened [°]
L = connecting rod length
3600
15
,
273
013
,
1
P
Tz
V
Q N
m 
Introducing Pressure Pulsation Correction Factor :
β = 1 if θ angle is equal or higher than 90°
β = sin φ + (rL/2) sin (2φ) if θ angle is smaller than 90°

76. 76 /
GE /
April 12, 2024
Pressure pulsations
In order to avoid underestimation due to unfavorably phased harmonics, which can
increase the gas capacity pulsation generated by the only first harmonic, the
following equation is recommended.
PRESSURE PULSATION GENERATION
 
m
m Q
r
A
Q 

 
5
,
1
Pressure pulsation ΔP can be estimated by the following equation:
Sc
Q
Pk
P m
v



P = gas pressure [bar-a]
kv = ratio Cp/Cv or compression exponent
S = gas crossing area of the pipe [m2]
c = sound speed @ the conditions P, T [m/sec]
ΔQm = gas capacity pulsation [m3/sec]
valid for:
• gas pipe with infinite length
• first harmonic highly prevailing on the other ones

77. 77 /
GE /
April 12, 2024
Pressure pulsations
PRESSURE PULSATIONS WITH PULSATION
DAMPENER
 
m
m Q
r
A
Q 

 

Sc
Q
Pk
P m
v


 Sc
Q
r
A
k
P
P m
v


 

Pressure pulsation with damper, Δp/p can be estimated by the following:
2
2
2
2
2
1
1
c
S
V
N
Sc
Q
r
A
k
P
P
e
m
v







Ne = number of cylinder ends pumping
V = damping volume [m3]

78. 78 /
GE /
April 12, 2024
Pressure pulsations
The pressure drop Δpo of the gas crossing the orifice can be calculated by the
following formula:
GAS CAPACITY MEASURE VITIATED BY
PULSATIONS
ξ = loss coefficient
Qo = steady gas capacity [m3/s]
A = pipe cross area [m2]
g = gravity acceleration m/s2]
J = gas specific weight @ P, T conditions
[kg/m3]
g
J
A
Q
P
2
2
0
0 






  [kg/m2
]
Considering sine gas capacity fluctuation “Q1senωt” the instantaneous gas
capacity “Q” can be considered as follows:
t
Q
Q
Q 
sin
1
0 

Therefore the total pressure drop Δp across the orifice, assuming:
g
A
J
K
2
2


 
t
sen
KQ
t
sen
KQoQ
KQo
t
sen
Q
Qo
K
KQ
P



2
2
1
1
2
2
1
2
2 






