VibrationFailureAnalysisandCountermeasuresoftheInlet ...concluded that the inlet pipeline modiﬁcation model C is better than models A and B with regard to vibration sup-pression

Research ArticleVibration Failure Analysis and Countermeasures of the InletPipelines at a Gas Compressor Station

Shuangshuang Li 1 Liwen Zhang2 and Chunyan Kong1

1School of Mechanical Engineering Xihua University Chengdu 610039 China2School of Architectural Engineering Chengdu Textile College Chengdu 611731 China

Correspondence should be addressed to Shuangshuang Li 15882068051163com

Received 14 August 2019 Accepted 18 October 2019 Published 6 November 2019

Academic Editor Stefano Manzoni

Copyright copy 2019 Shuangshuang Li et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

A gas compressor station only had its about 35 design processing capacity as a result of the abnormal piping vibrations on theinlet pipelines Characterization diagnostics analysis and elimination of piping vibration were performed e root causes andsources of the abnormal vibration were investigated by on-site measurements and analysis of vibration and pulsation undervarious load conditions of compressorse results revealed that it was not mechanical resonance but the high pressure pulsationand acoustic resonance occurred on the inlet pipelines which resulted in the severe vibrationree different modificationmodelsagainst vibration were proposed by shortening the length of the pipe to avoid acoustic resonance enlarging the volume of thegathering manifold to buffer pressure pulsation and adding supports to increase the stiffness A better modification model wasapplied by performing modal analysis and fluid-structure interaction (FSI) vibration analysis using the finite element methodeeffect of countermeasures was evaluated by vibration and pulsation measurements during operation after modifications whichresults showed the level of piping vibration and pressure pulsation was within the allowable limits e processing capacity of thegas station has reached its design requirement as a result of the desired reduction in vibrations

1 Introduction

Reciprocating compressors are most commonly used be-cause of their flexibility with regard to operating modes inthe gas industry However due to the intermittent com-pressor suction and discharge pipeline vibration induced bypressure pulsation in the piping system connected to thereciprocating compressor is inherent which may result indamage of pipes supports foundations and instrumentsunstable process operation malfunction of instruments etcExcessive piping vibration is a potential threat to the safetyand reliability of the compressor system Consequently it isimportant to study and then analyze the vibration phe-nomena to avoid such possible problems

e researches concerning piping vibration and vibra-tion control mainly include vibration theoretical studies andapplications in engineering [1ndash3]eoretical studies includebuilding mathematical modeling of pipelines vibration ex-periments and investigation using numerical analysis such as

modal analysis acoustic analysis and fluid-structure in-teraction between pipe and fluid in pipe [4ndash6] e acousticwave theory transfer matrix method and finite elementmethod have been proposed to analyze gas pulsation in thepiping system [7 8] Engineering applications mainly focuson vibration measurement techniques investigation usingsimulation techniques vibration analysis techniques faultdiagnosis technology piping design and vibration controlsolutions [9ndash13] ese researches have laid a good foun-dation for the piping vibration analysis and control ofcompressor piping systems

As the inlet pipelines at a gas compressor station sufferedfrom excessive vibration this paper was devoted to in-vestigate the main causes and the elimination of the vi-bration problem e root causes and sources of pipingvibration were investigated by vibration measurements andpulsation analysis under the various load conditions ofcompressors ree models of the inlet pipeline modifica-tions based on countermeasures against vibration were

HindawiShock and VibrationVolume 2019 Article ID 6032962 8 pageshttpsdoiorg10115520196032962

proposed A modification model was applied after accom-plishing modal analysis and fluid-structure interaction (FSI)vibration analysis for the three models e effect ofcountermeasures applied was evaluated by vibration andpulsation measurements after modifications

2 Vibration Problems and Cause Analysis

21 Vibration Problems A gas compressor station with atotal design processing capacity of 183times104m3d employedthree reciprocating compressors (No 1simNo 3) with a ratedpower of 1250 kW and a capacity of 64times104m3d each andone compressor (No 4) with a rated power of 1030 kW and acapacity of 55times104m3d ree of the four compressorswere needed to be in operation simultaneously to meet thedesign processing capacity e schematic of the inletpipelines for the four compressors is illustrated in Figure 1To control the piping vibration the gathering manifold wasreinforced by pouring cement and pipe clamps were in-stalled on the inlet pipelines during construction as shownin Figure 2 [14]

However the inlet pipelines encountered severe vibra-tion with 3426mms velocity when three compressors (No1simNo 3) were in operation simultaneously during com-missioning and trial operation which was considered to bedangerous and can cause damage to the piping system It wasnecessary to suppress the resulting vibration velocity tovalues less than 178mms to ensure the safety and reliabilityof the compressor station according to the standard ISO10816-6 Worse still only one compressor was allowed torun in order to ensure pipeline safety In other words thecompressor station only operated at its about 35 designcapacity Hence it was necessary to perform in depth vi-bration analysis to identity the root causes and sources ofpiping vibration and take practical and useful vibrationreduction countermeasures to limit the vibration level of theinlet pipelines within the allowable range and improve theprocessing capacity of the compressor station

22 On-Site Measurements and Analysis

221 VibrationMeasurements and Analysis It is a good wayto understand vibration characteristics of the pipe by vi-bration measurements As the vibration of the pipe con-nected to the reciprocating compressor is generally a lowfrequency vibration vibration velocity can be used toevaluate the vibration characteristics well Here the totalvelocity of vibration vTotal is defined to indicate the severityof piping vibration which is calculated by

vTotal v2x + v2y + v2z

1113969 (1)

where vTotal is the total velocity of vibration (mms) and vxvy and vz are the velocity of vibration in x y and z di-rections (mms) respectively

As vibration is sensitive to the speed and load conditionsof the compressor vibration measurements and analysisunder different operating conditions were performed tostudy how the pipeline system responds to the changes in the

conditions No 1 compressor had four different load con-ditions which were at 950 RPM with full load 1000 RPMwith full load 1050RPM with full load and 1050 RPM withidle load respectively e five vibration measuring points(P1ndashP5) are presented in Figure 1 e comparison of vi-bration velocity of P1ndashP5 under the four load conditions isshown in Figure 3e vibration severity is weak under No 1compressor operating at 1050 RPM with idle load conditionbut strong under its other load conditions So it can beconcluded that piping vibration is not induced by me-chanical resonance e total velocity of vibration vTotal foreach measuring point increases with the speed or load of No1 compressor e velocity in the z direction is usuallygreater than that in the x and y directions which is due to thehigh pulsation forces acting on the pipe resulting frompressure and velocity fluctuations without mechanicalresonance

4000

ϕ 273 times 10

No 1

Inlet 1

Inlet 2

1800ϕ 426 times 11

ϕ 219 times 10

ϕ 273 times 10

ϕ 273 times 10

2450

14300

2400

1400

ϕ 323 times 101

P5

P4

P1

P2P3x

y

z

Unit mm

No 2

No 3No 4

Gatheringmanifold

Figure 1 Schematic of the inlet pipelines at a gas compressorstation

(a)

Pouring cement

(b)

(c)

Figure 2 e inlet pipelines after pouring cement and installingsupports during construction

2 Shock and Vibration

Meanwhile the vibration velocity spectrum of P1 wasanalyzed to reveal the vibration level as a function of fre-quency and the obtained results are plotted in Figure 4 No1 compressor operating at 1050 RPM would produce thefundamental frequency at 175Hz As shown in Figure 4(a)the velocity peak occurs at 175Hz (1050RPM) lower ve-locity peaks are observed at 35Hz and 525Hz and thevelocity is small or zero at other frequencies in each di-rection From Figure 4(b) the velocity peak in the z directionstill occurs at the fundamental frequency of compressorspeed and increases with the increase in the compressorspeed e spectrum results of the other points (P2ndashP5) aresimilar to that of P1 ese spectrum characteristics areclosely related to the acoustic resonance problem

222 Pulsation Measurements and Acoustic AnalysisPressure pulsation is inevitable in the reciprocating com-pressor because of the intermittent suctiondischarge flowe resulting pressure pulsation contains many harmoniccomponents of the compressor speed which would be asource of low frequency vibration in the piping system eseverity of pressure pulsation can be evaluated by thepressure unevenness δ which is calculated by equation (2)API 618 has recommended the maximum allowable level ofpressure pulsation P1 which is acquired by equation (3)

δ Pmax minus Pmin

(12) Pmax + Pmin1113858 1113859ΔPP0

(2)

P1

a

350

1113970

times1265

P0 times D1 times fex

1113968 (3)

where δ is the pressure unevenness () Pmax and Pmin arethe maximum and minimum absolute pressure (MPa) re-spectively P0 is the mean absolute pressure (MPa) and ΔP isthe peak-to-peak pressure (MPa) P1 is the maximum al-lowable level of pressure pulsation () a is the sound speedof gas in the pipe (ms) D1 is the inner diameter of the pipe(mm) and fex is the excitation frequency related to com-pressor rotational speed (Hz)

To determine the pressure pulsation level pressurepulsation measurement at measuring point① (see Figure 1)was conducted when No 1 compressor was in operation at1050 RPM with full load From Figure 5(a) the pressureunevenness δ of point① is 259 calculated by equation (2)which far exceeds the maximum allowable level being 091acquired by equation (3) e pulsation is strongest at thefirst compressor harmonics 175Hz (1050 RPM) but spikesat other harmonics exist as well which is most likely inducedby acoustic resonance

Gas in the piping system can be considered an elasticsystem and also has its acoustic natural frequency eacoustic frequency of gas depends on its sound speed in thepipe and pipe length Gas pulsation is generally too weak tocause any problem but may be amplified and induce ex-cessive piping vibration due to acoustic resonance Whenacoustic resonance occurs in the piping system the length ofpipe is called as resonant piping length ldquoLrdquo which can bedetermined by equation (4) [15 16] e words ldquoopenrdquo andldquoclosedrdquo present the boundary condition of the pipe endepipe connected to a large volume can be regarded as an openend or a closed end

L

kvZRgT

1113969

2fex

⎛⎜⎜⎝ ⎞⎟⎟⎠i (open-openorclosed-closed)

L

kvZRgT

1113969

4fex

⎛⎜⎜⎝ ⎞⎟⎟⎠(2i minus 1) (open-closed)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)

where L is the resonant piping length (m) kv is the ratio ofspecific heat Z is the compressibility factor of real gas Rg isthe gas constant (J(kgmiddotK)) T is the absolute temperature (K)and i is the harmonic order of frequency

e resonant piping length ldquoLrdquo of the inlet pipelines islisted in Table 1 To avoid acoustic resonance the length ofpipe should be away from ldquoLrdquo Badly the actual length of theinlet pipelines was 1851m which was within the range ofthe second resonant piping length ldquoLrdquo So the pressurepulsation in piping reached a high level due to the secondorder acoustic resonance which caused the high pipingvibration

In summary the root causes of the excessive pipingvibration were not mechanical resonance but high pressurepulsation and the second order acoustic resonant Mean-while there are several drawbacks in the configuration of theinlet pipelines (see Figure 1) For example the gatheringmanifold was too small to buffer pulsation in the pipingsystem and the locations and directions of the inlet andoutlet of the gathering manifold were unreasonable whichcould aggravate pressure pulsation It can be seen that pipingvibration caused by acoustic resonances and pressure pul-sation still cannot be controlled radically although the inletpipelines were reinforced by cement and clamps duringconstruction because the pulsation forces acting on the pipecannot be reduced

xy

zTotal

P1P2

P3P4

P5

02468

10

Direction

Measuring point

Vel

ocity

(mm

s)

Load (1050RPM)Load (1000RPM)

Load (950RPM)Idle load (1050RPM)

Figure 3 Comparison of velocity of P1ndashP5 when No 1 compressorran alone

Shock and Vibration 3

3 Countermeasures against Vibrationand Analysis

Piping vibration induced by pressure pulsation cannot beeliminated completely but can be minimized by various

methods installation of an orifice to add fluid dampingapplication of a pressure fluctuation absorber to reduce thepulsation itself adjusting piping length to change thestructural and acoustic resonance frequency etc In thisstudy according to the causes and sources of vibrationanalyzed above the key countermeasures against vibrationincluded shortening the length of the inlet pipelines from1851m to 1475m to avoid the resonant piping length ldquoLrdquo(see Table 1) enlarging the nominal diameter of the gath-ering manifold from DN400mm to DN800mm to suppressgas pulsation in the piping system and adding piping

x

y

z0 1020 30

4050 60

0

2

4

6

8

1

2

3

4

5

67

89

Vel

ocity

(mm

s)

DirectionFrequency (Hz)

Freq(Hz)

Velocity(mms)

175 81135 152

525 089175 39335 12

525 041175 14135 0838

525 028

123456789

(a)

950

1000

10500 10 20 3040

50 60

0

2

4

6

8

4

56

7

89

1

2

3

Vel

ocity

(mm

s)

Speed (rmin)Frequency (Hz)

Freq(Hz)

Velocity(mms)

175 81135 152

525 08916875 4623375 039

50625 0315625 31653125 045

46875 01

123456789

(b)

Figure 4 e velocity spectrum of P1 (a) No 1 compressor operating at 1050 RPM (b) in the z direction

P0

42

422

424

426

428

43

Pres

sure

(MPa

)

02 04 06 08 10Time (s)

(a)

00002000400060008001000120014

Am

plitu

de (d

B)

20

1

23

40 60 80 1000Frequency (Hz)

Freq(Hz)

Amplitude(dB)

175 001335 000158

875 000042

123

(b)

Figure 5 e pressure pulsation of ① (a) pressure-time curve (b) frequency spectrum

Table 1 e first three resonant piping length ldquoLrdquo of the inletpipelines

Order First Second irdL (m) 593sim655 1778sim1966 2964sim3277


supports to alter the natural frequency of the inlet pipelinesree models of the inlet pipeline modifications for vibra-tion reduction are proposed based on different processes asshown in Figure 6

31 Modal Analysis Mechanical resonance will be inducedwhen the excitation frequency is within plusmn10 of the me-chanical natural frequency of the piping system Modalanalysis is an effective method to obtain the natural fre-quencies and mode shapes of the piping system which is ofgreat useful to avoid mechanical resonance by adjusting thepiping layout and support during the design phase estructural models for the three models (A B and C) wereestablished from their structural drawing and physical di-mensions obtained on site which were used to predict thenatural frequencies and mode shapese accuracy of modalanalysis is highly dependent on the assumptions of theboundary conditions of the pipe In the paper the pipe endmounted to the equipment with a larger stiffness such ascompressor body and gathering manifold can be defined asthe fixed ende pipe end connected to the structure with asimilar stiffness can be defined as the elastic support Anelastic support or clamp can be simplified as a spring withdifferent axial and radial stiffness e boundary conditionsand locations of supports of the three models are presentedin Figure 7

In this study the axial stiffness of the pipe support in thez direction was kz 2times106Nm and the radial stiffness ofthe pipe support in the x direction was kx 4times106Nm andin the y direction ky 2times107Nm Youngrsquos modulus E andPoissonrsquos ratio μ of the pipe were set to 206GPa and 03respectively Modal analysis of the three models was per-formed by using the finite element method e naturalfrequencies of the inlet pipelines for each model are allgreater than the range of compressor excitation frequencyfrom 1583Hz to 175Hz as shown in Figure 8 So the lowmechanical resonance can be avoided In terms of me-chanical resonance the first mode shape for each model isbending vibration in the x direction and the weak regionwith high deflection is highlighted in red in Figure 9

32 Fluid-Structure Interaction Vibration Analysis Pipingvibration induced by gas pulsation in the piping system is atypical FSI vibration which contains the structure analysis ofthe pipe and CFD analysis of the fluid in the piping system[17] For the pipe connected to the natural gas compressorthe maximum allowable deformation is 710 micron based onISO 10816-6 which is much smaller than its diameter In thiscase one-way FSI vibration analysis is appropriate becausethe pipe deformation is not large enough to have a signif-icant impact on the gas pulsation In this study the boundaryconditions of the three models for structure analysis were thesame as that for modal analysis as mentioned above and theboundary conditions for CFD analysis are listed in Table 2e vibration level of the three models was evaluated by one-way FSI vibration analysis under the three compressors (No1simNo 3) operating at 1050RPM with full load simulta-neously and the obtained results are presented in Figure 10

From Figure 10 the maximum vibration velocity foreachmodificationmodel is less than the maximum allowablelevel being 178mms e vibration level of modificationmodel C is lower than that of models A and B As the highvibrations are observed at the bend of the inlet pipelinesbecause of the insufficient stiffness of pipe supports asupport with higher stiffness should be installed during themodification phase According to Figures 9ndash11 it can beconcluded that the inlet pipeline modification model C isbetter than models A and B with regard to vibration sup-pression because it has a higher natural frequency and alower vibration severity

4 Effect of Countermeasures

e inlet pipelines were modified on the basis of themodification model C to mitigate the abnormal vibration(see Figure 11) Meanwhile the weak regions in Figure 10(c)

No 1

10300

2400

1400

ϕ813 times 24

Inlet 1

Inlet 2

ϕ323 times 10

x

y

z

Unit mm

ϕ813 times 24

Gatheringmanifold

No 2No 3

No 4

(a)

7000

2400

1400

Inlet 1

Inlet 2

3300 T-branchϕ 323 times 10

ϕ 813 times 24

Gatheringmanifold

No 1

No 2No 3

No 4

(b)

10300

2400

1400Inlet 1

Inlet 2

ϕ323 times 10

ϕ813 times 24

Gatheringmanifold

P5P4

P1P2

P32

No 1No 2

No 3No 4

(c)

Figure 6 ree models of the inlet pipeline modifications forvibration reduction (a) Model A one manifold (b) model B twomanifolds connected by T branch (c) model C two manifolds


which were sensitive to vibration were strengthened by pipeclamps To evaluate the effect of countermeasures aftermodifications vibration measurements were completedunder two different load conditions No 1 and No 2compressors operating at 1050 RPM with full load and No 1compressor operating at 1050 RPM with full load e inputparameters and operating conditions of the compressorswere approximate to those before modifications e

vibration measuring points from P1 to P5 and pulsationmeasuring point ② are illustrated in Figure 6

As seen in Figure 12 the total vibration velocity vTotal isreduced after modifications especially for measuring pointP1 e vibration velocity increases with the compressorload Although the piping vibration intensity became largerwhen No 1 and No 2 compressors operated at 1050 RPMwith full load all vibration velocity was still within the limits

16003400

50007200

9500

kxkz

ky

yx

z

Unit mm

10300

Figure 7 Boundary conditions and locations of supports of the inlet pipeline modifications

First Second Third Fourth Fifth SixthOrder

ABC

0

10

20

30

40

50Fr

eque

ncy

(Hz)

Figure 8 Comparison of the first six natural frequencies of the inlet pipeline modification models

26019Hzx

yz

Unit mm

06670778

055604450334022201110

(a)

26179Hzx

yz

Unit mm

06670778

055604450334022201110

(b)

26763Hzx

yz

Unit mm

06670778

055604450334022201110

(c)

Figure 9 e first frequency and mode shape of the inlet pipeline modifications (a) Model A (b) model B (c) model C

Table 2 Boundary conditions of the inlet pipeline modification models for CFD analysis

PositionModel A Model B Model C

Boundary condition Value Boundary condition Value Boundary condition ValueInlet1 Pressure inlet 42MPa Pressure inlet 42MPa Pressure inlet 42MPaInlet2 Wall mdash Wall mdash Pressure inlet 42MPaNo 1 Velocity outlet 089ms Velocity outlet 089ms Velocity outlet 089msNo 2 Velocity outlet 089ms Velocity outlet 089ms Velocity outlet 089msNo 3 Velocity outlet 089ms Velocity outlet 089ms Velocity outlet 089msNo 4 Wall mdash Wall mdash Wall mdashVelocity 089ms is converted by 64times104m3d based on the gas equation of state and the diameter of pipe


being 178mms us any three of the four compressorscan operate well at the same time without any abnormalpiping vibration and the capacity of the gas station wasincreased to the design processing capacity aftermodifications

Pressure pulsation analysis of measuring point② whenNo 1 and No 2 compressors ran simultaneously wasconducted after modifications and the obtained results arepresented in Figure 13 e maximum pressure unevennessof ② is 063 which is limited within the maximum al-lowable level being 091 Comparing Figure 5(b) withFigure 13(b) shows that the pressure pulsation peak at175Hz is 00048 dB after modifications but 0013 dB beforemodifications As the length of the inlet pipelines avoidedthe second order resonant piping length ldquoLrdquo after modifi-cations the pressure pulsation was not amplified withoutacoustic resonance

5 Conclusions

e paper presents the characterization diagnostics anal-ysis and elimination of vibration in the inlet pipelinesconnected to reciprocating compressors at a gas station emost important conclusions are as follows

(1) e results of on-site vibration and pulsation mea-surements under various load conditions of com-pressors showed the abnormal vibration of the inletpipelines was not induced by mechanical resonancebut the second order acoustic resonance occurred inthe inlet pipelines

1102

x

yz

Unit mms11489848206564923281640

(a)

1145

x

yz

Unit mms11489848206564923281640

(b)

819

752

x

yz

Unit mms11489848206564923281640

(c)

Figure 10 Results of vibration velocity of the inlet pipeline modification models evaluated by FSI vibration analysis (a) Model A (b) modelB (c) model C

Figure 11 e inlet pipelines after modifications

xy

zTotal

P1P2

P3P4

P5

02468

10

Direction

Measuring point

Before modifications (No 1 1050RPM)After modifications (No 1 1050RPM)After modifications (No 1 and No 2 1050RPM)

Vel

ocity

(mm

s)

Figure 12 Comparison of velocity before and after modifications

Pres

sure

(MPa

)

P0

4125

413

4135

414

4145

02 04 06 08 10Time (s)

(a)A

mpl

itude

(dB)

1

23

0001

0002

0003

0004

0005

20 40 60 80 1000Frequency (Hz)

Freq(Hz)

Amplitude(dB)

175 0004835 000081

525 000024

123

(b)

Figure 13 e results of pressure pulsation of ② after modifi-cations (a) Pressure-time curve (b) frequency spectrum


(2) ree modification models were proposed to sup-press piping vibration and pressure pulsation whichmainly focused on shortening the length of pipe toavoid acoustic resonance enlarging the volume ofthe gathering manifold to buffer pressure pulsationand adding supports to increase the stiffness Modalanalysis and FSI vibration analysis for each modi-fication model were conducted to understand theirmodal characteristics and vibration level and theresults revealed that the piping vibration level underthe design processing capacity conditions of thecompressor station was within the allowable limitswithout mechanical and acoustic resonance

(3) e inlet pipelines were modified based on modi-fication model C to suppress piping vibration andthe weak regions which were sensitive to vibrationwere strengthened by installing pipe clamps aftermodifications e results showed the piping vi-bration and pressure pulsation level were within theacceptable limits of standard which means thecountermeasures adopted indeed eliminated thepiping vibration after modifications

Piping vibration is an inescapable reality for the pipingsystem connected with a reciprocating compressor Gen-erally vibration induced by pressure pulsation is small on apipe without acoustic or mechanical resonance ereforeeliminating the acoustic or mechanical resonance can be aneffective measure to reduce piping vibration

Data Availability

Data and models used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is work was supported by the Key Scientific ResearchFund of Xihua University (Grant No Z17118) the NaturalScience Foundation of the Education Department of SichuanProvince (Grant No 18ZB0574) and the Open ResearchSubject of Key Laboratory (Research Base) of Fluid andPower Machinery of Xihua University Ministry of Educa-tion (Grant No szjj2017-081)

References

[1] N Lieberman Troubleshooting Natural Gas ProcessingWellhead to Transmission PennWell Publishing CompanyTulsa OK USA 1987

[2] B Xu Q Feng and X Yu ldquoPrediction of pressure pulsationfor the reciprocating compressor system using finite distur-bance theoryrdquo Journal of Vibration and Acoustics vol 131no 3 Article ID 031007 2009

[3] S K Loh W F Faris M Hamdi and W M Chin ldquoVi-brational characteristics of piping system in air conditioning

outdoor unitrdquo Science China Technological Sciences vol 54no 5 pp 1154ndash1168 2011

[4] T Nakamura S Kaneko F Inada et al Flow-Induced Vi-brations Classifications and Lessons from Practical Experi-ences Butterworth-Heinemann Oxford UK 2013

[5] G Liu S Li Y Li and H Chen ldquoVibration analysis ofpipelines with arbitrary branches by absorbing transfer matrixmethodrdquo Journal of Sound and Vibration vol 332 no 24pp 6519ndash6536 2013

[6] S Li B W Karney and G Liu ldquoFSI research in pipelinesystemsmdasha review of the literaturerdquo Journal of Fluids andStructures vol 57 pp 277ndash297 2015

[7] B Liu J Feng Z Wang and X Peng ldquoAttenuation of gaspulsation in a reciprocating compressor piping system byusing a volume-choke-volume filterrdquo Journal of Vibration andAcoustics vol 134 no 5 Article ID 051002 2012

[8] F Trebuna F Simcak R Hunady and M Pastor ldquoIdentifi-cation of pipes damages on gas compressor stations by modalanalysis methodsrdquo Engineering Failure Analysis vol 27pp 213ndash224 2013

[9] S-H Lee S-M Ryu and W-B Jeong ldquoVibration analysis ofcompressor piping system with fluid pulsationrdquo Journal ofMechanical Science and Technology vol 26 no 12pp 3903ndash3909 2012

[10] H Ashrafizadeh M Karimi and F Ashrafizadeh ldquoFailureanalysis of a high pressure natural gas pipe under split tee bycomputer simulations and metallurgical assessmentrdquo Engi-neering Failure Analysis vol 32 pp 188ndash201 2013

[11] H G Varghese M Saad Ahamed and K Srikanth ldquoPipelinevibration reduction in reciprocating compressorsrdquo In-ternational Journal of Innovation and Applied Studies vol 6no 3 p 629 2014

[12] I Hayashi and S Kaneko ldquoPressure pulsations in pipingsystem excited by a centrifugal turbomachinery taking thedamping characteristics into considerationrdquo Journal of Fluidsand Structures vol 45 pp 216ndash234 2014

[13] M Udagawa Y Li A Nishida and I Nakamura ldquoFailurebehavior analyses of piping system under dynamic seismicloadingrdquo International Journal of Pressure Vessels and Pipingvol 167 pp 2ndash10 2018

[14] Z Liang S Li J Tian L Zhang C Feng and L ZhangldquoVibration cause analysis and elimination of reciprocatingcompressor inlet pipelinesrdquo Engineering Failure Analysisvol 48 pp 272ndash282 2015

[15] P Cyklis ldquoExperimental identification of the transmittancematrix for any element of the pulsating gas manifoldrdquo Journalof Sound and Vibration vol 244 no 5 pp 859ndash870 2001

[16] Y Zhao B Zhao Q Zhou X Jia J Feng and X PengAnalysis and Control of Severe Vibration of a Screw Com-pressor Outlet Piping System Purdue University Purduee-Pubs West Lafayette Indiana 2016

[17] M Siba W Wanmahmood M Z Nuawi R Rasani andM Nassir ldquoFlow-Induced vibration in pipes challenges andsolutionsmdasha reviewrdquo Journal of Engineering Science andTechnology vol 11 no 3 pp 362ndash382 2016


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

proposed A modification model was applied after accom-plishing modal analysis and fluid-structure interaction (FSI)vibration analysis for the three models e effect ofcountermeasures applied was evaluated by vibration andpulsation measurements after modifications

2 Vibration Problems and Cause Analysis

21 Vibration Problems A gas compressor station with atotal design processing capacity of 183times104m3d employedthree reciprocating compressors (No 1simNo 3) with a ratedpower of 1250 kW and a capacity of 64times104m3d each andone compressor (No 4) with a rated power of 1030 kW and acapacity of 55times104m3d ree of the four compressorswere needed to be in operation simultaneously to meet thedesign processing capacity e schematic of the inletpipelines for the four compressors is illustrated in Figure 1To control the piping vibration the gathering manifold wasreinforced by pouring cement and pipe clamps were in-stalled on the inlet pipelines during construction as shownin Figure 2 [14]

However the inlet pipelines encountered severe vibra-tion with 3426mms velocity when three compressors (No1simNo 3) were in operation simultaneously during com-missioning and trial operation which was considered to bedangerous and can cause damage to the piping system It wasnecessary to suppress the resulting vibration velocity tovalues less than 178mms to ensure the safety and reliabilityof the compressor station according to the standard ISO10816-6 Worse still only one compressor was allowed torun in order to ensure pipeline safety In other words thecompressor station only operated at its about 35 designcapacity Hence it was necessary to perform in depth vi-bration analysis to identity the root causes and sources ofpiping vibration and take practical and useful vibrationreduction countermeasures to limit the vibration level of theinlet pipelines within the allowable range and improve theprocessing capacity of the compressor station

22 On-Site Measurements and Analysis

221 VibrationMeasurements and Analysis It is a good wayto understand vibration characteristics of the pipe by vi-bration measurements As the vibration of the pipe con-nected to the reciprocating compressor is generally a lowfrequency vibration vibration velocity can be used toevaluate the vibration characteristics well Here the totalvelocity of vibration vTotal is defined to indicate the severityof piping vibration which is calculated by

vTotal v2x + v2y + v2z

1113969 (1)

where vTotal is the total velocity of vibration (mms) and vxvy and vz are the velocity of vibration in x y and z di-rections (mms) respectively

As vibration is sensitive to the speed and load conditionsof the compressor vibration measurements and analysisunder different operating conditions were performed tostudy how the pipeline system responds to the changes in the

conditions No 1 compressor had four different load con-ditions which were at 950 RPM with full load 1000 RPMwith full load 1050RPM with full load and 1050 RPM withidle load respectively e five vibration measuring points(P1ndashP5) are presented in Figure 1 e comparison of vi-bration velocity of P1ndashP5 under the four load conditions isshown in Figure 3e vibration severity is weak under No 1compressor operating at 1050 RPM with idle load conditionbut strong under its other load conditions So it can beconcluded that piping vibration is not induced by me-chanical resonance e total velocity of vibration vTotal foreach measuring point increases with the speed or load of No1 compressor e velocity in the z direction is usuallygreater than that in the x and y directions which is due to thehigh pulsation forces acting on the pipe resulting frompressure and velocity fluctuations without mechanicalresonance

4000

ϕ 273 times 10

No 1

Inlet 1

Inlet 2

1800ϕ 426 times 11

ϕ 219 times 10

ϕ 273 times 10

ϕ 273 times 10

2450

14300

2400

1400

ϕ 323 times 101

P5

P4

P1

P2P3x

y

z

Unit mm

No 2

No 3No 4

Gatheringmanifold

Figure 1 Schematic of the inlet pipelines at a gas compressorstation

(a)

Pouring cement

(b)

(c)

Figure 2 e inlet pipelines after pouring cement and installingsupports during construction




δ Pmax minus Pmin

(12) Pmax + Pmin1113858 1113859ΔPP0

(2)

P1

a

350

1113970

times1265


1113968 (3)




L

kvZRgT

1113969

2fex


L

kvZRgT

1113969

4fex


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)




xy

zTotal

P1P2

P3P4

P5

02468

10

Direction

Measuring point

Vel

ocity

(mm

s)








x

y

z0 1020 30

4050 60

0

2

4

6

8

1

2

3

4

5

67

89

Vel

ocity

(mm

s)


Freq(Hz)

Velocity(mms)

175 81135 152

525 089175 39335 12

525 041175 14135 0838

525 028

123456789

(a)

950

1000

10500 10 20 3040

50 60

0

2

4

6

8

4

56

7

89

1

2

3

Vel

ocity

(mm

s)


Freq(Hz)

Velocity(mms)

175 81135 152

525 08916875 4623375 039

50625 0315625 31653125 045

46875 01

123456789

(b)


P0

42

422

424

426

428

43

Pres

sure

(MPa

)

02 04 06 08 10Time (s)

(a)

00002000400060008001000120014

Am

plitu

de (d

B)

20

1

23


Freq(Hz)

Amplitude(dB)

175 001335 000158

875 000042

123

(b)












No 1

10300

2400

1400

ϕ813 times 24

Inlet 1

Inlet 2

ϕ323 times 10

x

y

z

Unit mm

ϕ813 times 24

Gatheringmanifold

No 2No 3

No 4

(a)

7000

2400

1400

Inlet 1

Inlet 2


ϕ 813 times 24

Gatheringmanifold

No 1

No 2No 3

No 4

(b)

10300

2400

1400Inlet 1

Inlet 2

ϕ323 times 10

ϕ813 times 24

Gatheringmanifold

P5P4

P1P2

P32

No 1No 2

No 3No 4

(c)






16003400

50007200

9500

kxkz

ky

yx

z

Unit mm

10300



ABC

0

10

20

30

40

50Fr

eque

ncy

(Hz)


26019Hzx

yz

Unit mm

06670778

055604450334022201110

(a)

26179Hzx

yz

Unit mm

06670778

055604450334022201110

(b)

26763Hzx

yz

Unit mm

06670778

055604450334022201110

(c)








5 Conclusions



1102

x

yz

Unit mms11489848206564923281640

(a)

1145

x

yz

Unit mms11489848206564923281640

(b)

819

752

x

yz

Unit mms11489848206564923281640

(c)



xy

zTotal

P1P2

P3P4

P5

02468

10

Direction

Measuring point


Vel

ocity

(mm

s)


Pres

sure

(MPa

)

P0

4125

413

4135

414

4145

02 04 06 08 10Time (s)

(a)A

mpl

itude

(dB)

1

23

0001

0002

0003

0004

0005

20 40 60 80 1000Frequency (Hz)

Freq(Hz)

Amplitude(dB)

175 0004835 000081

525 000024

123

(b)






Data Availability




Acknowledgments


References






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




δ Pmax minus Pmin

(12) Pmax + Pmin1113858 1113859ΔPP0

(2)

P1

a

350

1113970

times1265


1113968 (3)




L

kvZRgT

1113969

2fex


L

kvZRgT

1113969

4fex


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)




xy

zTotal

P1P2

P3P4

P5

02468

10

Direction

Measuring point

Vel

ocity

(mm

s)








x

y

z0 1020 30

4050 60

0

2

4

6

8

1

2

3

4

5

67

89

Vel

ocity

(mm

s)


Freq(Hz)

Velocity(mms)

175 81135 152

525 089175 39335 12

525 041175 14135 0838

525 028

123456789

(a)

950

1000

10500 10 20 3040

50 60

0

2

4

6

8

4

56

7

89

1

2

3

Vel

ocity

(mm

s)


Freq(Hz)

Velocity(mms)

175 81135 152

525 08916875 4623375 039

50625 0315625 31653125 045

46875 01

123456789

(b)


P0

42

422

424

426

428

43

Pres

sure

(MPa

)

02 04 06 08 10Time (s)

(a)

00002000400060008001000120014

Am

plitu

de (d

B)

20

1

23


Freq(Hz)

Amplitude(dB)

175 001335 000158

875 000042

123

(b)












No 1

10300

2400

1400

ϕ813 times 24

Inlet 1

Inlet 2

ϕ323 times 10

x

y

z

Unit mm

ϕ813 times 24

Gatheringmanifold

No 2No 3

No 4

(a)

7000

2400

1400

Inlet 1

Inlet 2


ϕ 813 times 24

Gatheringmanifold

No 1

No 2No 3

No 4

(b)

10300

2400

1400Inlet 1

Inlet 2

ϕ323 times 10

ϕ813 times 24

Gatheringmanifold

P5P4

P1P2

P32

No 1No 2

No 3No 4

(c)






16003400

50007200

9500

kxkz

ky

yx

z

Unit mm

10300



ABC

0

10

20

30

40

50Fr

eque

ncy

(Hz)


26019Hzx

yz

Unit mm

06670778

055604450334022201110

(a)

26179Hzx

yz

Unit mm

06670778

055604450334022201110

(b)

26763Hzx

yz

Unit mm

06670778

055604450334022201110

(c)








5 Conclusions



1102

x

yz

Unit mms11489848206564923281640

(a)

1145

x

yz

Unit mms11489848206564923281640

(b)

819

752

x

yz

Unit mms11489848206564923281640

(c)



xy

zTotal

P1P2

P3P4

P5

02468

10

Direction

Measuring point


Vel

ocity

(mm

s)


Pres

sure

(MPa

)

P0

4125

413

4135

414

4145

02 04 06 08 10Time (s)

(a)A

mpl

itude

(dB)

1

23

0001

0002

0003

0004

0005

20 40 60 80 1000Frequency (Hz)

Freq(Hz)

Amplitude(dB)

175 0004835 000081

525 000024

123

(b)






Data Availability




Acknowledgments


References






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





x

y

z0 1020 30

4050 60

0

2

4

6

8

1

2

3

4

5

67

89

Vel

ocity

(mm

s)


Freq(Hz)

Velocity(mms)

175 81135 152

525 089175 39335 12

525 041175 14135 0838

525 028

123456789

(a)

950

1000

10500 10 20 3040

50 60

0

2

4

6

8

4

56

7

89

1

2

3

Vel

ocity

(mm

s)


Freq(Hz)

Velocity(mms)

175 81135 152

525 08916875 4623375 039

50625 0315625 31653125 045

46875 01

123456789

(b)


P0

42

422

424

426

428

43

Pres

sure

(MPa

)

02 04 06 08 10Time (s)

(a)

00002000400060008001000120014

Am

plitu

de (d

B)

20

1

23


Freq(Hz)

Amplitude(dB)

175 001335 000158

875 000042

123

(b)












No 1

10300

2400

1400

ϕ813 times 24

Inlet 1

Inlet 2

ϕ323 times 10

x

y

z

Unit mm

ϕ813 times 24

Gatheringmanifold

No 2No 3

No 4

(a)

7000

2400

1400

Inlet 1

Inlet 2


ϕ 813 times 24

Gatheringmanifold

No 1

No 2No 3

No 4

(b)

10300

2400

1400Inlet 1

Inlet 2

ϕ323 times 10

ϕ813 times 24

Gatheringmanifold

P5P4

P1P2

P32

No 1No 2

No 3No 4

(c)






16003400

50007200

9500

kxkz

ky

yx

z

Unit mm

10300



ABC

0

10

20

30

40

50Fr

eque

ncy

(Hz)


26019Hzx

yz

Unit mm

06670778

055604450334022201110

(a)

26179Hzx

yz

Unit mm

06670778

055604450334022201110

(b)

26763Hzx

yz

Unit mm

06670778

055604450334022201110

(c)








5 Conclusions



1102

x

yz

Unit mms11489848206564923281640

(a)

1145

x

yz

Unit mms11489848206564923281640

(b)

819

752

x

yz

Unit mms11489848206564923281640

(c)



xy

zTotal

P1P2

P3P4

P5

02468

10

Direction

Measuring point


Vel

ocity

(mm

s)


Pres

sure

(MPa

)

P0

4125

413

4135

414

4145

02 04 06 08 10Time (s)

(a)A

mpl

itude

(dB)

1

23

0001

0002

0003

0004

0005

20 40 60 80 1000Frequency (Hz)

Freq(Hz)

Amplitude(dB)

175 0004835 000081

525 000024

123

(b)






Data Availability




Acknowledgments


References






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









No 1

10300

2400

1400

ϕ813 times 24

Inlet 1

Inlet 2

ϕ323 times 10

x

y

z

Unit mm

ϕ813 times 24

Gatheringmanifold

No 2No 3

No 4

(a)

7000

2400

1400

Inlet 1

Inlet 2


ϕ 813 times 24

Gatheringmanifold

No 1

No 2No 3

No 4

(b)

10300

2400

1400Inlet 1

Inlet 2

ϕ323 times 10

ϕ813 times 24

Gatheringmanifold

P5P4

P1P2

P32

No 1No 2

No 3No 4

(c)






16003400

50007200

9500

kxkz

ky

yx

z

Unit mm

10300



ABC

0

10

20

30

40

50Fr

eque

ncy

(Hz)


26019Hzx

yz

Unit mm

06670778

055604450334022201110

(a)

26179Hzx

yz

Unit mm

06670778

055604450334022201110

(b)

26763Hzx

yz

Unit mm

06670778

055604450334022201110

(c)








5 Conclusions



1102

x

yz

Unit mms11489848206564923281640

(a)

1145

x

yz

Unit mms11489848206564923281640

(b)

819

752

x

yz

Unit mms11489848206564923281640

(c)



xy

zTotal

P1P2

P3P4

P5

02468

10

Direction

Measuring point


Vel

ocity

(mm

s)


Pres

sure

(MPa

)

P0

4125

413

4135

414

4145

02 04 06 08 10Time (s)

(a)A

mpl

itude

(dB)

1

23

0001

0002

0003

0004

0005

20 40 60 80 1000Frequency (Hz)

Freq(Hz)

Amplitude(dB)

175 0004835 000081

525 000024

123

(b)






Data Availability




Acknowledgments


References






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





16003400

50007200

9500

kxkz

ky

yx

z

Unit mm

10300



ABC

0

10

20

30

40

50Fr

eque

ncy

(Hz)


26019Hzx

yz

Unit mm

06670778

055604450334022201110

(a)

26179Hzx

yz

Unit mm

06670778

055604450334022201110

(b)

26763Hzx

yz

Unit mm

06670778

055604450334022201110

(c)








5 Conclusions



1102

x

yz

Unit mms11489848206564923281640

(a)

1145

x

yz

Unit mms11489848206564923281640

(b)

819

752

x

yz

Unit mms11489848206564923281640

(c)



xy

zTotal

P1P2

P3P4

P5

02468

10

Direction

Measuring point


Vel

ocity

(mm

s)


Pres

sure

(MPa

)

P0

4125

413

4135

414

4145

02 04 06 08 10Time (s)

(a)A

mpl

itude

(dB)

1

23

0001

0002

0003

0004

0005

20 40 60 80 1000Frequency (Hz)

Freq(Hz)

Amplitude(dB)

175 0004835 000081

525 000024

123

(b)






Data Availability




Acknowledgments


References






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




5 Conclusions



1102

x

yz

Unit mms11489848206564923281640

(a)

1145

x

yz

Unit mms11489848206564923281640

(b)

819

752

x

yz

Unit mms11489848206564923281640

(c)



xy

zTotal

P1P2

P3P4

P5

02468

10

Direction

Measuring point


Vel

ocity

(mm

s)


Pres

sure

(MPa

)

P0

4125

413

4135

414

4145

02 04 06 08 10Time (s)

(a)A

mpl

itude

(dB)

1

23

0001

0002

0003

0004

0005

20 40 60 80 1000Frequency (Hz)

Freq(Hz)

Amplitude(dB)

175 0004835 000081

525 000024

123

(b)






Data Availability




Acknowledgments


References






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Data Availability




Acknowledgments


References






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

VibrationFailureAnalysisandCountermeasuresoftheInlet ...concluded that the inlet pipeline modiﬁcation model C is better than models A and B with regard to vibration sup-pression