Research Article Modeling and Experiments of Severe ...

Research ArticleModeling and Experiments of Severe Slugging in a Riser System

Lin Wang12 Yuxing Li12 Chang Liu12 Qihui Hu12 Yating Wang3 and Quan Wang12

1College of Pipeline and Civil Engineering China University of Petroleum Qingdao 266580 China2Shandong Provincial Key Laboratory of Oil amp Gas Storage and Transportation Safety Qingdao 266580 China3CCTEG Chongqing Engineering Co Ltd Chongqing 400016 China

Correspondence should be addressed to Yuxing Li liyxupceducn

Received 23 October 2015 Revised 10 January 2016 Accepted 2 February 2016

Academic Editor Eleonora Bottani

Copyright copy 2016 Lin Wang et alThis is an open access article distributed under theCreativeCommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A transient mathematical model based on continuity equations for liquid and gas phases with a momentum equation for themixture was developed and numerical solutions and simulations corresponding to severe slugging in pipeline-riser system werepresented and the results were compared with the experimental data to verify the mathematical model In numerical solutionsbackward Euler schemes were adopted as predictors and trapezoidal methods were used as correctors Variable time steps wereemployed for higher computational efficiency and accuracy in the integration Experiments of severe slugging characteristics wereperformed and the simulation results of the cycle periods and bottompressurewere comparedwith experimental values Finally thecalculation results of detailed characteristics were analyzed thoroughly The results show that the developed mathematical modelcan accurately predict the cycle time and the detailed characteristics of severe slugging Under the experimental conditions theliquid slug length can reach 16 times the height of the riser and the maximum instantaneous gas velocity of outlet is 50 times theinlet gas velocity and the maximum instantaneous liquid velocity of outlet is 28 times the inlet liquid velocity having importantimplications for the hazard assessment of severe slugging

1 Introduction

In the offshore and deep water oil and gas development mul-tiphase transportation is more economic as a transportationway The mixture of oil and gas is transported through thehilly terrain subsea pipeline and the riser to the offshoreproduction platform for oil gas and water processing [1]Severe slug flow occurs at low gas and liquid flow rateswith the downward inclined pipe in stratified flow and ischaracterized by the generation of liquid slugs at the baseof the riser ranging in length from one to several riser pipeheights The process of severe slugging in a riser system wasconsidered as a cycle consisting of four steps [2] (1) slugformation (2) slug movement out of the riser (3) blowoutand (4) liquid fallback The pressure and the instantaneousvelocities of gas and liquid flow in the riser system oscillateviolently which may shock the downstream equipment andinduce damage such as severe vibration of the riser systemand equipment Therefore it is essential to simulate the

detailed characteristics of severe slugging accurately for thehazard assessment of severe slugging

Since the severe slugging induced problems were iden-tified by Yocum [3] a great deal of theoretical explorationand experimental studies on severe slugging were devel-oped In [2] an experiment was carried out to study thecharacteristics of severe slugging and a simplified modelwas presented for simulating the severe slugging [4] Boe[5] and Jansen et al [6] presented respectively flow regimemaps for predicting the severe slug flow regimes where theboundaries were determined analytically Huawei [7] studiedthe characteristics of severe slugging in pipeline-riser systemand catenary riser system by detailed laboratory experimentand developed a mathematical model for severe sluggingZhang et al [8] set up a one-dimensional quasi-equilibriumsimplified calculation model for the unsteady flow in the L-type riser system which ignores the effects of friction andacceleration Balino et al [9 10] presented a mathematicalmodel considering continuity equations for liquid and gas

Hindawi Publishing CorporationChinese Journal of EngineeringVolume 2016 Article ID 4586853 8 pageshttpdxdoiorg10115520164586853

2 Chinese Journal of Engineering

phases with a simplified momentum equation for the mix-ture neglecting inertia and considering inertia respectivelyand simulated the transient characteristics of severe sluggingA computational fluid dynamics (CFD) method is proposedfor numerically simulating the gas-liquid severe slugging ina pipeline-riser system Gao et al [11 12] implemented 2Dnumerical simulations of severe slugging by using a CFDsoftware FLUENT Araujo et al [13] studied the dynamicsof individual and a pair of Taylor bubbles rising in verticalcolumns of stagnant and cocurrent liquids numerically usingthe volume of fluid (VOF) methodology implemented in thecommercial code ANSYS FLUENT Li et al [14] developed atransient model using OLGA to study the dynamic behaviorof severe slugging in a pipeline-riser system and comparedthe simulation results with the experimental data Xing et al[15 16] carried out 2D CFD simulations for severe sluggingand attempted to develop a 3D-1D coupling simulationthat is STAR-OLGA coupling for mitigating hydrodynamicslug flows with a wave pipe where the 1D simulation forthe entire pipeline coupled with the 3D simulation of thepartial flow field was implemented to control the scale ofcalculation Looking through current literatures numericalsimulation methods are mainly divided into two categories(1) numerical simulation of the whole flow field based onCFD (2) simplified one-dimensional transient model Theformer methodrsquos advantage is that the detailed characteristicparameters of flow field and the liquid-gas interfaces can bedescribed precisely However this method is computation-ally expensive and difficultly simulates the full-scale of thephysical phenomena so it is difficult to apply this methodeffectively The simplified one-dimensional transient modelis not only efficient in computation but also more accuratewhen empirical correlations and experiential parameters areintroduced appropriately and then this method can simulatethe engineering scales of multiphase transportation

In this paper a modified mathematical model is devel-oped for the severe slugging flow in risers the continuityequations andmomentum equations are described as a seriesof differential equations for the enhancement of suitabilityThe numerical integration methods for the mathematicalmodel are presented in detail The simulation of the liquidfallback is added to improve the accuracy of simulationsof the flowing characteristics and cycle period of severeslugging

2 The Development of theMathematical Model

The hybrid riser facility which consists of a downwardinclined pipeline and a riser was built up to simulate theriser system (Figure 1) Liquid and gas flow in the downwardinclined pipeline simultaneously and move out at the top ofthe riser

A transient model based on continuity equations forliquid and gas phases with a momentum equation for themixture is developed to calculate the characteristic param-eters including pressure position of slug front and tail voidfraction and flow velocities of gas and liquid

P0

se YshXse

P1 V1

Y

OX

sh

120573

mgmL

Figure 1 Schematic view of the riser system

The model considers one-dimensional flow in the risersystem The liquid phase is assumed to be incompressiblewhile the gas phase is considered as an ideal gas Bothphases flow in isothermal conditions The flow pattern in thedownward inclined pipeline is assumed to be stratified andthe liquid holdup along the pipeline is constant A cycle ofsevere slugging can be described as taking place according tothe following stages

21 Stage 1 Slug Formation Stage 2 Discharge out of the RiserIn the stage of slug formation both gas and liquid flow inthe riser system and the liquid accumulates at the bottom ofthe riser and the gas channel is blocked The liquid continuesto flow in and gas already in the riser continues to flow outand then the slug front (liquid level) rises and pressure atthe bottom of the riser increases compressing the gas inthe downward pipeline and creating a liquid accumulationregion As the slug front reaches the top while the gas channelis kept blocked at the bottom the bottom pressure reaches amaximum value and there is only liquid flowing in and out ofthe riser which is the stage of slug discharge out of the riser

The governing equations are developed based on continu-ity equations for the liquid and gas phases and themomentumequation for themixture For the stages of slug formation andslug discharge out of the riser the continuity equation for theliquid is as follows

VLb = 120572PVse +119898L0120588L119860

(1)

where VLb is the liquid superficial velocity at the bottom of theriser 120572P is the void fraction of the downward pipeline Vse isthe movement velocity of the slug tail 119898L0 is the mass flowrate for the liquid injected in the downward pipeline 120588L is theliquid density and 119860 is the flow passage area

Using the ideal gas relation (11987511198811

= 119872g0119877119879120583g where119872g0 is gasmass and119881

1is gas volume) for the gas in the down-

ward pipeline differentiating it with time and considering 1198751

and 119883se as a function of time the gas continuity equation isobtained

d1198751

d119905=

minus1198751120572PVse + 119898g0119877119879120583g119860

(119871 + 119883se) 120572P + 119871119890

(2)

where 119905 is time 1198751is the pressure of the gas in the downward

pipeline 119898g0 is the mass flow rate for the gas injected in

Chinese Journal of Engineering 3

the downward pipeline 119883se is the displacement of the slugtail relative to the bottom of the riser set as reference point119871 is the downward pipeline length 119871119890 is the equivalent pipelength of the buffer vessel 119877 and 119879 are respectively the gasconstant and temperature and 120583g is the gas molar mass

The gas pressure 1198751in the downward pipeline depends on

the variations of the positions of the slug front and tail in thesestages Therefore the momentum equation for the mixture isas follows

d1198751

d119905=

120597119875

120597119884

d119884shd119905

+

120597119875

120597119883

d119883sed119905

(3)

where 119875 is the local static pressure of the fluid 120597119875120597119884 isthe pressure gradient along the riser 120597119875120597119883 is the pressuregradient along the downward inclined pipeline and 119884shconsidered as a function of time is the displacement of theslug front relative to the bottom of the riser set as referencepoint

In (2) and (3)d119883sed119905

= Vse (4)

For the stage of slug formationd119884shd119905

= VLb = Vsh (5)

where Vsh is the movement velocity of the slug front and VLbis the liquid superficial velocity at the bottom of the riser

For the stage of slug discharge out of the riserd119884shd119905

= VLb = 0 (6)

In the above equations there are 4 unknown independentvariables (119883se 119884sh 1198751 and 120572P) that need to be solved and theother parameters are known parameters or intermediate vari-ables However there are 3 independent equations including(1)ndash(3) Therefore another equation should be introduced tomake the system of equation closed

The void fraction of the downward pipeline is calculatedfrom the liquid holdup correlations for inclined two-phaseflow [17] which can be calculated by

120572P = 1 minus exp[(minus13 + 48 sin120573 + 42 sin2120573 + 563119873

2

L)

sdot

119873

008

gw

119873

0505

Lw]

(7)

where 119873gw is gas velocity number 119873Lw is liquid velocitynumber and 119873L is liquid viscosity number calculated asfollows

119873gw = Vsg (120588L119892120590

)

025

119873Lw = VsL (120588L119892120590

)

025

119873L = 120578L (119892

120588L1205903)

025

(8)

where 120578L is dynamic viscosity of liquid 120590 is surface tensionand 120573 is pipe inclination angle from horizontal

22 Stage 3 Blowout As the gas phase penetrates into theriser the column becomes lighter decreasing the pressureand then the gas expands to rise and push the liquid slug toaccelerate The governing equations for the stage of blowoutare presented as follows

The continuity equation for the liquid is

d (119884se120572r)

d119905+ VsL minus VLt = 0

(9)

The continuity equation for the gas is

d1198751

d119905=

minus1198751Vgb + 119898g0119877119879120583g119860

119871120572P + 119871119890

(10)

The momentum equation for the mixture is

120597119875

120597119884

+ 120588L120597 [(1 minus 120572r) (Vsg + VsL)]

120597119905

+ 120588L119892 (1 minus 120572r) +4120591w119863

= 0

(11)

In (9)d119884sed119905

= Vse (12)

where Vsg = Vgb 120572r = VgbVse VLb = 119898L0120588L119860 119884se and Vse arerespectively the position and the movement speed of the slugtail in the riser VLt is the liquid superficial velocity at the topof the riser and Vse can be calculated by Nicklin et al [18] asfollows

Vse = 1198620(Vsg + VsL) + 119881

0 (13)

where Vsg and VsL are the local gas superficial velocity and thelocal liquid superficial velocity respectively

In the above equations the independent equations are(9)ndash(11) and (13) and the unknown variables are 119875 119884se VLtand Vgb The system of equation is closed

When gas reaches the top of the riser two-phase gas-liquid flow in the riser exhibits a chaotic flow patternconsisting of Taylor bubbles and liquid slug is identified aschurn flow by Tengesdal et al [19] and the gas velocity iscalculated using Tengesdal et al correlations

Vg = 1198620Vm + VD (14)

23 Stage 4 Liquid Fallback The gas and liquid blow out ofthe riser until the gas flow rate becomes too low to drive theliquid rising in the riser and then the liquid falls down to thebottom of the riser The liquid fallback can be described asfollows

dVfdd119905

= 119892 minus 120582d

119881f = int

119867

0

(1 minus 120572r) 119860 d119884

119875f = 120588L119892119881f119860

(15)


Table 1 Parameters of the riser system and severe slugging flow

Parameter Value amp unitPipe OD 63mmWall thickness 58mmRiser height 35mPipeline length 12mInclination angle 4∘

Liquid density 1000 kgsdotmminus3

Liquid viscosity 0001 PasdotsSurface tension 728 times 10minus2Nsdotmminus1

Gas molar mass 29 gsdotmolminus1

Gas constant 831 Jsdotmolminus1sdotKminus1

where Vfd 120582d and 119881f are the falling down velocity frictioncoefficient and volume of the liquid respectively 119875f ispressure at the bottom of the riser caused by the falling liquidand 119892 is gravitational acceleration

After the liquid falls down at the bottom of the riserthe liquid flows back into the downward pipeline because ofthe potential energy of the falling liquid The process can bedescribed as follows

dVfbd119905

= 119892 minus 120582b (16)

where Vfb and 120582b are respectively the flowing back velocityand friction coefficient of the liquid

3 Boundary and Initial Conditions

Theboundary conditions of inlet are the liquidmass flow rateand the gas mass flow rate which are constants (Table 1) andthe temperature is 300KThe boundary condition of outlet isthe pressure at the top of the riser

119875 (119884 = 119867r 119905) = 1198750 (17)

where 1198750is approximately equal to the atmospheric pressure

(101325 kPa)The initial conditions including the positions and the

velocities of slug tail and front are given as follows

119883se (119905 = 0) = minus14

119884sh (119905 = 0) = 0

Vse (119905 = 0) = 0

Vsh (119905 = 0) = 0

(18)

Thepressure and superficial velocities at the bottomof theriser are continuous

119875 (119883 = 0 119905) = 119875 (119884 = 0 119905)

Vsg (119883 = 0 119905) = Vsg (119884 = 0 119905) = Vgb (119905)

VsL (119883 = 0 119905) = VsL (119884 = 0 119905) = VLb (119905)

(19)

4 Discretization of the Model

41 Slug Formation and Discharge out of the Riser Theequations are discretized using explicit schemes for the stagesof the slug formation and discharge out of the riserThe Eulerscheme for (2) is

119875

K+11

=

119875

K1

+ (119898g0119877119879120583g119860) (Δ119905

119870 ((119871 + 119883

Kse) 120572P + 119871119890))

1 + (120572PVKseΔ119905

K ((119871 + 119883

Kse) 120572P + 119871119890))

(20)

Combining (1) into (3) the discretization scheme for (3)is

119875

K+11

= 119875

K1

+ 120588L119892(

119898L0120588L119860

+ 120572PVKse + VKse sin

1003816100381610038161003816

120573

1003816100381610038161003816

) Δ119905

K (21)

The discretization scheme for (4) is

119883

K+1se = 119883

Kse + VKseΔ119905

K (22)

where Δ119905

K(= 119905

K+1minus 119905

K) is the time step and the superscripts

119870 and 119870 + 1 denote variables correspondingly at times Inparticular VKse is defined as the average velocity of the slug tailin Δ119905

K Therefore the difference schemes are unconditionallyconvergent to the time step and larger time step can beadopted to improve the calculation efficiency in the stages ofthe slug formation and movement out of the riser

42 Blowout In the stage of blowing out because of theexistence of the fluid acceleration term the time step shouldbe smaller in the integration process for higher calculationaccuracy and the trapezoidal methods are used to correct thepredicted valuesThe equations are discretized using implicitschemes with a predictor-corrector method for the stages ofblowout For (9)ndash(12)

119875

K+11

=

119875

K1

+ (119898g0119877119879120583g119860) (Δ119905

K (119871120572P + 119871119890))

1 + (VK+1gb Δ119905

K (119871120572P + 119871119890))

119875

119870+1119873+1

= 119875

K+1119873

minus Δ119884N [120588L (1 minus 120572

K+1) +

4120591w119863

]

+ Δ119884N120588LVK+1m (120572

K+1minus 1) minus VKm (120572

Kminus 1)

Δ119905

K

(23)

The position of the slug tail can be predicted by abackward Euler method and the prediction formula is

(i)119884

K+1se = 119884

Kse + VK+1se Δ119905

K (24)

The correction formula with the trapezoidal method is

(119894+1)119884

119870+1se = 119884

119870

se + (V119870se +(119894)V119870+1se )

Δ119905

119870

2

(25)

where Δ119884N is the space interval subscript 119873 indicates thenumber of the space intervals (119894+1)119884119870+1se is the correction valueof 119884119870+1se and 119894 + 1 is the number of correction iterations Forinstance it is the 1st correction when 119894 = 0 and 119894 + 1 = 1 andthe 2nd correction when 119894 = 1 and 119894 + 1 = 2


Pump

Air

CompressorBuffer vessel

Liquidflow meter

GasFT

FT

flow meter

Watertank

Downwardpipeline

Riser

Pressuresensor

Displacementsensor

Figure 2 Schematic diagram of experimental facility of riser system

43 Fallback The analytic solutions of characteristic param-eters of this stage can be distinctly solved for (15)-(16)

5 Simulation Results and Discussion

51 Experimental Verification Figure 2 shows a schematic ofthe riser test facility with the instrumentation The test loopconsists of a 35m long horizontal pipeline and a 12m long514mm diameter pipeline which is inclined to minus4∘ from thehorizontal connected to a 35m high vertical riser

The water is supplied from two 05m3 storage tanksalso acting as receivers for the water returning from the testloop Water is delivered into the test loop using two pumpswhich can be operated either individually or in series Eachof the pumps has 125m3h capacity andmaximum dischargepressure of 05MPa Air is supplied from a reciprocatingcompressor with a maximum capacity of 615 Ls at 125MPaThe compressor supplies air into a 2m3 buffer vessel whichacts as an air receiver and smoothes any pressure fluctuationsfrom the compressor Gas flow rates are controlled using aneedle valve downstream of the air receiver The detailedparameters of the experimental facility and the gas-liquidtwo-phase flow are shown in Table 1

The characteristic parameters of the severe sluggingunder different inlet conditions were measured in the lab-oratory and the characteristics were simulated using themathematical method described above The experimentaland the theoretical results are summarized in Table 2 Theexperimental results for the cycle time under different exper-imental conditions are presented and the theoretical resultsfor these variables and the relative errors are also given inTable 2 It shows that the simulation results agree with theexperimental results essentially However the error will belarger when the gas superficial velocity increases which isbecause the flow regime gradually deviates from the typicalsevere slugging and cannot be described by the mathematicalmodel accurately when the gas flow rate increases Otherwisethe measurement error can cause the bigger simulation error

Original pressure signals measured in experiment weredenoised using wavelet analysis method and the denoisedsignals were compared with the simulation results As shown

Table 2 Comparison between experimental and theoretical results

Inlet conditions Experimental Theoretical ErrorVsg (ms) VsL (ms) cycle time (s) cycle time (s) ()00407 0240 70 81 15700696 0207 60 57 minus5000830 0215 53 48 minus9401446 0324 25 26 4002060 0379 25 22 minus12002060 0423 15 17 1330250 0402 15 18 20002819 0423 16 17 6302956 0339 25 18 minus28003791 0152 23 21 minus8703823 0369 18 16 minus11104311 0121 52 32 minus385

in Figure 3 the original pressure signal under the inlet con-dition (Vsg = 0083ms and VsL = 0215ms) is discomposedto get wavelet of various scales and the a8 component isreconstructed as the denoised signal Figure 3 shows thecomparison of the original pressure signal and the denoisedsignal

Figure 4 shows the different stages in the pressure historyat the bottom of the riser calculated from the transient modelagainst the experimental data under laboratory conditionsThe four stages of the severe slugging aremarked in the figureand the time span of each stage and the cycle period areobtained distinctly Agreement seems to be good althoughthe blowout time (stage 3) calculated by mathematical modelis slightly shorter than the experimental value which isbecause the predicted value of the friction coefficient instage 3 is slightly smaller The simulation results and theexperimental results of the falling back (stage 4) are inagreement but the details are difficult to match because themathematical model cannot describe the gas-liquid exchangeprocess when the liquid flows back into the downwardinclined pipeline

6 Chinese Journal of EngineeringPr

essu

re (P

a)

Original signaltimes105

times105

14

13

12

11

10

Pres

sure

(Pa)

14

13

12

11

10

0 50 100

100

150 200 250

0 50 150 200 250

Reconstructed signal

Time (s)

Time (s)

Figure 3 Denoising with wavelet analysis method

140000

130000

120000

110000

1000000 10 20 30 40 50 60 70

Time (s)

1 2

3 4

Pres

sure

(Pa)

MeasuredPredicted

Figure 4 Comparison of simulation and experiment results ofthe pressure at the bottom of the riser (Vsg = 0083ms and VsL =0215ms)

52 Transient Characteristics of Severe Slugging The fol-lowing figures show the transient simulations correspond-ing to different variables necessary to characterize thesevere slugging the positions of the slug front and theslug tail (Figure 5(a)) void fraction of the two-phase flow(Figure 5(b)) in the riser gas superficial velocity (Figure 5(c))and liquid superficial velocity (Figure 5(d)) at the bottom ofthe riser and gas superficial velocity (Figure 5(e)) and liquidsuperficial velocity (Figure 5(f)) at the top of the riser

Figure 5(a) shows the time history of the positions of theslug front and tail of severe slugging The slug length can becalculated by the difference of the positions of the slug frontand tail and the maximum of slug length can reach 55m

The void fraction of the two-phase flow (Figure 5(b)) inthe riser reaches the maximum (095) and the minimum(023) in the stage of blowing outwhile the riser is full of liquidduring other stages The gas superficial velocity (Figure 5(c))at the bottom of the riser reaches the maximum (4ms)in the stage of blowing out The liquid superficial velocity(Figure 5(d)) at the bottom of the riser keeps a stable levelbetween 019 and 021ms

The gas superficial velocity (Figure 5(e)) of the blowingflow reaches the maximum (40ms) and the liquid super-ficial velocity (Figure 5(f)) of the blowing flow reaches themaximum (60ms) at the top of the riser in the stage ofblowing out

6 Conclusions

A transient mathematical model for severe slugging basedon continuity equations andmomentum equation was devel-oped to simulate the characteristics of severe slugging Thelaboratory experiment was implemented and the experimen-tal results were comparedwith the simulation results to verifythe accuracy of the mathematical model The conclusions ofthe study are the following

(1) The process of severe slugging in the riser system isconsidered to consist of four stages and based on thisa transient mathematical model is developed and thenumerical integration methods for the mathematicalmodel are developed

(2) The transient mathematical model has high comput-ing efficiency Moreover the model is more accuratefor calculating the transient parameters of the severesluggingwhen empirical correlations and experientialparameters are introduced appropriately

(3) The characteristic parameters of the severe sluggingunder different inlet conditions were measured inthe laboratory and the experimental results for thecycle time were compared with the simulation resultsfor these variables and the relative errors are alsogiven It shows that the simulation results agreewith the experimental results essentially howeverthe deviation between the experimental result andthe simulation result will be larger when the gassuperficial velocity increases

(4) The liquid slug length can reach 16 times the height ofthe riser and the maximum of the instantaneous gasvelocity of outlet is 50 times the inlet gas velocity andthe maximum instantaneous liquid velocity of outletis 28 times the inlet liquid velocity under the labora-tory conditions which have important implicationsfor the hazard assessment of severe slugging

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Chinese Journal of Engineering 7Z

(m)

40

35

30

25

20

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus300 20 40 60 80 100

t (s)

Slug frontSlug tail

(a)

0 20 40 60 80 100

t (s)

11

10

09

08

07

06

05

04

03

02

01

00

minus01

120572(mdash

)(b)

gb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(c)

Lb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(d)

gt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(e)

Lt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(f)

Figure 5 Simulation results of transient flow characteristics of severe slugging (Vsg = 0083ms and VsL = 0215ms)


Acknowledgment

For the work described in this paper the authors wouldlike to express their gratitude for the support from theNational Science Fund for Distinguished Young Scholars (no51404290)

References

[1] Y Li and S Feng Oil-Gas-Water Multi-Phase Piping Flow UPCPress Dongying China 2010

[2] Z Schmidt J P Brill and H D Beggs ldquoExperimental studyof severe slugging in a two-phase-flow pipelinemdashriser pipesystemrdquo Society of Petroleum Engineers Journal vol 20 no 5pp 407ndash414 1980

[3] B T Yocum ldquoOffshore riser slug flow avoidance mathematicalmodels for design and optimizationrdquo in SPE European MeetingSPE-4312-MS Society of Petroleum Engineers London UKApril 1973

[4] Z Schmidt D R Doty and K Dutta-Roy ldquoSevere sluggingin offshore pipeline riser-pipe systemsrdquo Society of PetroleumEngineers Journal vol 25 no 1 pp 27ndash38 1985

[5] A Boe Severe Slugging Characteristics Part 1 Flow Regimefor Severe Slugging Part 2 Point Model Simulation Study TwoPhase Flow NTH Trondheim Norway 1981

[6] F E Jansen O A Shoham and Y Taitel2 ldquoThe eliminationof severe sluggingmdashexperiments and modelingrdquo InternationalJournal of Multiphase Flow vol 22 no 6 pp 1055ndash1072 1996

[7] MAHuawei Investigation on Severe Slugging Phenomenon andElimination Methods in Multiphase Riser Pipe System CUPHQingdao China 2008

[8] Q Zhang DDeng YDong et al ldquoSimplified calculationmodelfor unsteady flow in marine L-type riser systemrdquo Oil amp GasStorage and Transportation vol 33 no 1 pp 95ndash107 2014

[9] J L Balino K P Burr and R H Nemoto ldquoModeling and sim-ulation of severe slugging in air-water pipeline-riser systemsrdquoInternational Journal of Multiphase Flow vol 36 no 8 pp 643ndash660 2010

[10] J L Balino ldquoModeling and simulation of severe slugging in air-water systems including inertial effectsrdquo Journal of Computa-tional Science vol 5 no 3 pp 482ndash495 2014

[11] S Gao Y You W Li et al ldquoNumerical simulation of the severeslug flow between water-air phases in a declination pipe-riserrdquoChinese Journal of Theoretical and Applied Mechanics vol 43no 3 pp 468ndash475 2011

[12] S GaoW Li Y-X You and T-Q Hu ldquoNumerical investigationon the gas-liquid severe slugging in a pipeline-riser systemrdquoActa Physica Sinica vol 61 no 10 Article ID 104701 2012

[13] J D P Araujo J M Miranda and J B L M Campos ldquoSimula-tion of slug flow systems under laminar regime hydrodynamicswith individual and a pair of consecutive Taylor bubblesrdquoJournal of Petroleum Science and Engineering vol 111 pp 1ndash142013

[14] S Li L Guo and N Li ldquoTransient simulation of severeslugging and riser topside chokingrdquo Journal of EngineeringThermophysics vol 35 no 1 pp 104ndash108 2014

[15] L Xing H Yeung J Shen and Y Cao ldquoNumerical study onmitigating severe slugging in pipelineriser system with wavypiperdquo International Journal of Multiphase Flow vol 53 pp 1ndash102013

[16] L Xing H Yeung Y Geng Y Cao and J Shen ldquoStudy onhydrodynamic slug flowmitigation with wavy pipe using a 3Dndash1D coupling approachrdquoComputers amp Fluids vol 99 pp 104ndash1152014

[17] H Mukherjee and J P Brill ldquoLiquid holdup correlations forinclined two-phase flowrdquo Journal of Petroleum Technology vol35 no 5 pp 1003ndash1008 1983

[18] D JNicklinMAWilkes and J FDavison ldquoTwo-phase flow invertical tubesrdquo Transactions on Institute of Chemical Engineersvol 40 pp 61ndash68 1962

[19] J Oslash Tengesdal A S Kaya and C Sarica ldquoFlow-patterntransition and hydrodynamic modeling of churn flowrdquo SPEJournal vol 4 no 4 pp 342ndash348 1999

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



phases with a simplified momentum equation for the mix-ture neglecting inertia and considering inertia respectivelyand simulated the transient characteristics of severe sluggingA computational fluid dynamics (CFD) method is proposedfor numerically simulating the gas-liquid severe slugging ina pipeline-riser system Gao et al [11 12] implemented 2Dnumerical simulations of severe slugging by using a CFDsoftware FLUENT Araujo et al [13] studied the dynamicsof individual and a pair of Taylor bubbles rising in verticalcolumns of stagnant and cocurrent liquids numerically usingthe volume of fluid (VOF) methodology implemented in thecommercial code ANSYS FLUENT Li et al [14] developed atransient model using OLGA to study the dynamic behaviorof severe slugging in a pipeline-riser system and comparedthe simulation results with the experimental data Xing et al[15 16] carried out 2D CFD simulations for severe sluggingand attempted to develop a 3D-1D coupling simulationthat is STAR-OLGA coupling for mitigating hydrodynamicslug flows with a wave pipe where the 1D simulation forthe entire pipeline coupled with the 3D simulation of thepartial flow field was implemented to control the scale ofcalculation Looking through current literatures numericalsimulation methods are mainly divided into two categories(1) numerical simulation of the whole flow field based onCFD (2) simplified one-dimensional transient model Theformer methodrsquos advantage is that the detailed characteristicparameters of flow field and the liquid-gas interfaces can bedescribed precisely However this method is computation-ally expensive and difficultly simulates the full-scale of thephysical phenomena so it is difficult to apply this methodeffectively The simplified one-dimensional transient modelis not only efficient in computation but also more accuratewhen empirical correlations and experiential parameters areintroduced appropriately and then this method can simulatethe engineering scales of multiphase transportation

In this paper a modified mathematical model is devel-oped for the severe slugging flow in risers the continuityequations andmomentum equations are described as a seriesof differential equations for the enhancement of suitabilityThe numerical integration methods for the mathematicalmodel are presented in detail The simulation of the liquidfallback is added to improve the accuracy of simulationsof the flowing characteristics and cycle period of severeslugging

2 The Development of theMathematical Model

The hybrid riser facility which consists of a downwardinclined pipeline and a riser was built up to simulate theriser system (Figure 1) Liquid and gas flow in the downwardinclined pipeline simultaneously and move out at the top ofthe riser

A transient model based on continuity equations forliquid and gas phases with a momentum equation for themixture is developed to calculate the characteristic param-eters including pressure position of slug front and tail voidfraction and flow velocities of gas and liquid

P0

se YshXse

P1 V1

Y

OX

sh

120573

mgmL

Figure 1 Schematic view of the riser system

The model considers one-dimensional flow in the risersystem The liquid phase is assumed to be incompressiblewhile the gas phase is considered as an ideal gas Bothphases flow in isothermal conditions The flow pattern in thedownward inclined pipeline is assumed to be stratified andthe liquid holdup along the pipeline is constant A cycle ofsevere slugging can be described as taking place according tothe following stages

21 Stage 1 Slug Formation Stage 2 Discharge out of the RiserIn the stage of slug formation both gas and liquid flow inthe riser system and the liquid accumulates at the bottom ofthe riser and the gas channel is blocked The liquid continuesto flow in and gas already in the riser continues to flow outand then the slug front (liquid level) rises and pressure atthe bottom of the riser increases compressing the gas inthe downward pipeline and creating a liquid accumulationregion As the slug front reaches the top while the gas channelis kept blocked at the bottom the bottom pressure reaches amaximum value and there is only liquid flowing in and out ofthe riser which is the stage of slug discharge out of the riser

The governing equations are developed based on continu-ity equations for the liquid and gas phases and themomentumequation for themixture For the stages of slug formation andslug discharge out of the riser the continuity equation for theliquid is as follows

VLb = 120572PVse +119898L0120588L119860

(1)

where VLb is the liquid superficial velocity at the bottom of theriser 120572P is the void fraction of the downward pipeline Vse isthe movement velocity of the slug tail 119898L0 is the mass flowrate for the liquid injected in the downward pipeline 120588L is theliquid density and 119860 is the flow passage area

Using the ideal gas relation (11987511198811

= 119872g0119877119879120583g where119872g0 is gasmass and119881

1is gas volume) for the gas in the down-

ward pipeline differentiating it with time and considering 1198751

and 119883se as a function of time the gas continuity equation isobtained

d1198751

d119905=

minus1198751120572PVse + 119898g0119877119879120583g119860

(119871 + 119883se) 120572P + 119871119890

(2)

where 119905 is time 1198751is the pressure of the gas in the downward

pipeline 119898g0 is the mass flow rate for the gas injected in





d1198751

d119905=

120597119875

120597119884

d119884shd119905

+

120597119875

120597119883

d119883sed119905

(3)


In (2) and (3)d119883sed119905

= Vse (4)


= VLb = Vsh (5)



= VLb = 0 (6)




2

L)

sdot

119873

008

gw

119873

0505

Lw]

(7)


119873gw = Vsg (120588L119892120590

)

025

119873Lw = VsL (120588L119892120590

)

025

119873L = 120578L (119892

120588L1205903)

025

(8)




d (119884se120572r)


(9)


d1198751

d119905=

minus1198751Vgb + 119898g0119877119879120583g119860

119871120572P + 119871119890

(10)


120597119875

120597119884

+ 120588L120597 [(1 minus 120572r) (Vsg + VsL)]

120597119905

+ 120588L119892 (1 minus 120572r) +4120591w119863

= 0

(11)

In (9)d119884sed119905

= Vse (12)


Vse = 1198620(Vsg + VsL) + 119881

0 (13)




Vg = 1198620Vm + VD (14)


dVfdd119905

= 119892 minus 120582d

119881f = int

119867

0

(1 minus 120572r) 119860 d119884

119875f = 120588L119892119881f119860

(15)










dVfbd119905

= 119892 minus 120582b (16)




119875 (119884 = 119867r 119905) = 1198750 (17)




119883se (119905 = 0) = minus14

119884sh (119905 = 0) = 0

Vse (119905 = 0) = 0

Vsh (119905 = 0) = 0

(18)


119875 (119883 = 0 119905) = 119875 (119884 = 0 119905)

Vsg (119883 = 0 119905) = Vsg (119884 = 0 119905) = Vgb (119905)

VsL (119883 = 0 119905) = VsL (119884 = 0 119905) = VLb (119905)

(19)



119875

K+11

=

119875

K1

+ (119898g0119877119879120583g119860) (Δ119905

119870 ((119871 + 119883

Kse) 120572P + 119871119890))

1 + (120572PVKseΔ119905

K ((119871 + 119883

Kse) 120572P + 119871119890))

(20)


119875

K+11

= 119875

K1

+ 120588L119892(

119898L0120588L119860


1003816100381610038161003816

120573

1003816100381610038161003816

) Δ119905

K (21)


119883

K+1se = 119883

Kse + VKseΔ119905

K (22)

where Δ119905

K(= 119905

K+1minus 119905





119875

K+11

=

119875

K1

+ (119898g0119877119879120583g119860) (Δ119905

K (119871120572P + 119871119890))

1 + (VK+1gb Δ119905

K (119871120572P + 119871119890))

119875

119870+1119873+1

= 119875

K+1119873

minus Δ119884N [120588L (1 minus 120572

K+1) +

4120591w119863

]

+ Δ119884N120588LVK+1m (120572


Kminus 1)

Δ119905

K

(23)


(i)119884

K+1se = 119884


K (24)


(119894+1)119884

119870+1se = 119884

119870

se + (V119870se +(119894)V119870+1se )

Δ119905

119870

2

(25)



Pump

Air


Liquidflow meter

GasFT

FT

flow meter

Watertank

Downwardpipeline

Riser

Pressuresensor

Displacementsensor













essu

re (P

a)


times105

14

13

12

11

10

Pres

sure

(Pa)

14

13

12

11

10

0 50 100

100

150 200 250

0 50 150 200 250


Time (s)

Time (s)


140000

130000

120000

110000

1000000 10 20 30 40 50 60 70

Time (s)

1 2

3 4

Pres

sure

(Pa)

MeasuredPredicted






6 Conclusions









(m)

40

35

30

25

20

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus300 20 40 60 80 100

t (s)

Slug frontSlug tail

(a)

0 20 40 60 80 100

t (s)

11

10

09

08

07

06

05

04

03

02

01

00

minus01

120572(mdash

)(b)

gb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(c)

Lb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(d)

gt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(e)

Lt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(f)



Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













d1198751

d119905=

120597119875

120597119884

d119884shd119905

+

120597119875

120597119883

d119883sed119905

(3)


In (2) and (3)d119883sed119905

= Vse (4)


= VLb = Vsh (5)



= VLb = 0 (6)




2

L)

sdot

119873

008

gw

119873

0505

Lw]

(7)


119873gw = Vsg (120588L119892120590

)

025

119873Lw = VsL (120588L119892120590

)

025

119873L = 120578L (119892

120588L1205903)

025

(8)




d (119884se120572r)


(9)


d1198751

d119905=

minus1198751Vgb + 119898g0119877119879120583g119860

119871120572P + 119871119890

(10)


120597119875

120597119884

+ 120588L120597 [(1 minus 120572r) (Vsg + VsL)]

120597119905

+ 120588L119892 (1 minus 120572r) +4120591w119863

= 0

(11)

In (9)d119884sed119905

= Vse (12)


Vse = 1198620(Vsg + VsL) + 119881

0 (13)




Vg = 1198620Vm + VD (14)


dVfdd119905

= 119892 minus 120582d

119881f = int

119867

0

(1 minus 120572r) 119860 d119884

119875f = 120588L119892119881f119860

(15)










dVfbd119905

= 119892 minus 120582b (16)




119875 (119884 = 119867r 119905) = 1198750 (17)




119883se (119905 = 0) = minus14

119884sh (119905 = 0) = 0

Vse (119905 = 0) = 0

Vsh (119905 = 0) = 0

(18)


119875 (119883 = 0 119905) = 119875 (119884 = 0 119905)

Vsg (119883 = 0 119905) = Vsg (119884 = 0 119905) = Vgb (119905)

VsL (119883 = 0 119905) = VsL (119884 = 0 119905) = VLb (119905)

(19)



119875

K+11

=

119875

K1

+ (119898g0119877119879120583g119860) (Δ119905

119870 ((119871 + 119883

Kse) 120572P + 119871119890))

1 + (120572PVKseΔ119905

K ((119871 + 119883

Kse) 120572P + 119871119890))

(20)


119875

K+11

= 119875

K1

+ 120588L119892(

119898L0120588L119860


1003816100381610038161003816

120573

1003816100381610038161003816

) Δ119905

K (21)


119883

K+1se = 119883

Kse + VKseΔ119905

K (22)

where Δ119905

K(= 119905

K+1minus 119905





119875

K+11

=

119875

K1

+ (119898g0119877119879120583g119860) (Δ119905

K (119871120572P + 119871119890))

1 + (VK+1gb Δ119905

K (119871120572P + 119871119890))

119875

119870+1119873+1

= 119875

K+1119873

minus Δ119884N [120588L (1 minus 120572

K+1) +

4120591w119863

]

+ Δ119884N120588LVK+1m (120572


Kminus 1)

Δ119905

K

(23)


(i)119884

K+1se = 119884


K (24)


(119894+1)119884

119870+1se = 119884

119870

se + (V119870se +(119894)V119870+1se )

Δ119905

119870

2

(25)



Pump

Air


Liquidflow meter

GasFT

FT

flow meter

Watertank

Downwardpipeline

Riser

Pressuresensor

Displacementsensor













essu

re (P

a)


times105

14

13

12

11

10

Pres

sure

(Pa)

14

13

12

11

10

0 50 100

100

150 200 250

0 50 150 200 250


Time (s)

Time (s)


140000

130000

120000

110000

1000000 10 20 30 40 50 60 70

Time (s)

1 2

3 4

Pres

sure

(Pa)

MeasuredPredicted






6 Conclusions









(m)

40

35

30

25

20

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus300 20 40 60 80 100

t (s)

Slug frontSlug tail

(a)

0 20 40 60 80 100

t (s)

11

10

09

08

07

06

05

04

03

02

01

00

minus01

120572(mdash

)(b)

gb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(c)

Lb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(d)

gt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(e)

Lt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(f)



Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















dVfbd119905

= 119892 minus 120582b (16)




119875 (119884 = 119867r 119905) = 1198750 (17)




119883se (119905 = 0) = minus14

119884sh (119905 = 0) = 0

Vse (119905 = 0) = 0

Vsh (119905 = 0) = 0

(18)


119875 (119883 = 0 119905) = 119875 (119884 = 0 119905)

Vsg (119883 = 0 119905) = Vsg (119884 = 0 119905) = Vgb (119905)

VsL (119883 = 0 119905) = VsL (119884 = 0 119905) = VLb (119905)

(19)



119875

K+11

=

119875

K1

+ (119898g0119877119879120583g119860) (Δ119905

119870 ((119871 + 119883

Kse) 120572P + 119871119890))

1 + (120572PVKseΔ119905

K ((119871 + 119883

Kse) 120572P + 119871119890))

(20)


119875

K+11

= 119875

K1

+ 120588L119892(

119898L0120588L119860


1003816100381610038161003816

120573

1003816100381610038161003816

) Δ119905

K (21)


119883

K+1se = 119883

Kse + VKseΔ119905

K (22)

where Δ119905

K(= 119905

K+1minus 119905





119875

K+11

=

119875

K1

+ (119898g0119877119879120583g119860) (Δ119905

K (119871120572P + 119871119890))

1 + (VK+1gb Δ119905

K (119871120572P + 119871119890))

119875

119870+1119873+1

= 119875

K+1119873

minus Δ119884N [120588L (1 minus 120572

K+1) +

4120591w119863

]

+ Δ119884N120588LVK+1m (120572


Kminus 1)

Δ119905

K

(23)


(i)119884

K+1se = 119884


K (24)


(119894+1)119884

119870+1se = 119884

119870

se + (V119870se +(119894)V119870+1se )

Δ119905

119870

2

(25)



Pump

Air


Liquidflow meter

GasFT

FT

flow meter

Watertank

Downwardpipeline

Riser

Pressuresensor

Displacementsensor













essu

re (P

a)


times105

14

13

12

11

10

Pres

sure

(Pa)

14

13

12

11

10

0 50 100

100

150 200 250

0 50 150 200 250


Time (s)

Time (s)


140000

130000

120000

110000

1000000 10 20 30 40 50 60 70

Time (s)

1 2

3 4

Pres

sure

(Pa)

MeasuredPredicted






6 Conclusions









(m)

40

35

30

25

20

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus300 20 40 60 80 100

t (s)

Slug frontSlug tail

(a)

0 20 40 60 80 100

t (s)

11

10

09

08

07

06

05

04

03

02

01

00

minus01

120572(mdash

)(b)

gb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(c)

Lb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(d)

gt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(e)

Lt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(f)



Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Pump

Air


Liquidflow meter

GasFT

FT

flow meter

Watertank

Downwardpipeline

Riser

Pressuresensor

Displacementsensor













essu

re (P

a)


times105

14

13

12

11

10

Pres

sure

(Pa)

14

13

12

11

10

0 50 100

100

150 200 250

0 50 150 200 250


Time (s)

Time (s)


140000

130000

120000

110000

1000000 10 20 30 40 50 60 70

Time (s)

1 2

3 4

Pres

sure

(Pa)

MeasuredPredicted






6 Conclusions









(m)

40

35

30

25

20

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus300 20 40 60 80 100

t (s)

Slug frontSlug tail

(a)

0 20 40 60 80 100

t (s)

11

10

09

08

07

06

05

04

03

02

01

00

minus01

120572(mdash

)(b)

gb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(c)

Lb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(d)

gt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(e)

Lt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(f)



Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










essu

re (P

a)


times105

14

13

12

11

10

Pres

sure

(Pa)

14

13

12

11

10

0 50 100

100

150 200 250

0 50 150 200 250


Time (s)

Time (s)


140000

130000

120000

110000

1000000 10 20 30 40 50 60 70

Time (s)

1 2

3 4

Pres

sure

(Pa)

MeasuredPredicted






6 Conclusions









(m)

40

35

30

25

20

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus300 20 40 60 80 100

t (s)

Slug frontSlug tail

(a)

0 20 40 60 80 100

t (s)

11

10

09

08

07

06

05

04

03

02

01

00

minus01

120572(mdash

)(b)

gb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(c)

Lb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(d)

gt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(e)

Lt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(f)



Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(m)

40

35

30

25

20

15

10

05

00

minus05

minus10

minus15

minus20

minus25

minus300 20 40 60 80 100

t (s)

Slug frontSlug tail

(a)

0 20 40 60 80 100

t (s)

11

10

09

08

07

06

05

04

03

02

01

00

minus01

120572(mdash

)(b)

gb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(c)

Lb

(mmiddotsminus

1)

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(d)

gt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(e)

Lt

(mmiddotsminus

1)

65

60

55

50

45

40

35

30

25

20

15

10

05

00

minus050 20 40 60 80 100

t (s)

(f)



Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Modeling and Experiments of Severe ...

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