numericalinvestigationongasaccumulationandgas...

Research ArticleNumerical Investigation on Gas Accumulation and GasMigration intheWavyHorizontalSectionsofHorizontalGasWells

Yi Huang 12 Jin Yang1 Lingyu Meng13 Xuyue Chen1 Ming Luo2 and Wentuo Li2

1MOE Key Laboratory of Petroleum Engineering China University of Petroleum Beijing 102249 China2CNOOC China Limited Zhanjiang Branch Zhanjiang 524057 China3China Resources Gas (Zhengzhou) Municipal Design and Research Institute Co Ltd Dalian China

Correspondence should be addressed to Yi Huang huangyi_cnooc163com

Received 14 May 2020 Accepted 24 July 2020 Published 12 August 2020

Academic Editor S S Ravindran

Copyright copy 2020 Yi Huang et al )is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Wavy horizontal sections are typically encountered in horizontal gas wells which will result in gas accumulation on top of the wavyhorizontal sections)is gas accumulation can be a problem andmay trigger gas kick or blowout accident while tripping and pullingthis gas into the vertical section In this paper a numerical model for gas accumulation and gas migration in the wavy horizontalsections of the horizontal gas well is developed meanwhile the gas accumulation and gas migration process is numerically in-vestigated )e results show that the gas exhausting time in the wavy horizontal section increases with the increase of the wellborecurvature and the critical drilling fluid flow velocity for gas exhausting increases with the increase of the wellbore curvature Whenthe drilling fluid flow velocity is higher than the critical drilling fluid flow velocity for gas exhausting no gas accumulation will occurWith all other parameter values set constant the number of the wavy horizontal sections has a great effect on the gas-liquid flowpattern while it has little effect on the efficiency of the gas exhausting )is work provides drilling engineers with a practical tool fordesigning the drilling fluid flow velocity to avoid gas kick or blowout accident in horizontal gas well drilling

1 Introduction

Horizontal wells are widely used in petroleum and naturalgas development and they have many advantages overtraditional vertical wells such as increased drainage area andhigh production [1ndash3] However since the wellbore tra-jectory in horizontal drilling is difficult to control thehorizontal section is always not completely horizontal andsometimes wavy horizontal sections are formed )e gas inthe wavy horizontal sections cannot migrate in the directionof flow owing to buoyancy it results in pockets of gas ac-cumulation (see Figure 1) )e gas accumulation can be aproblem and may trigger gas kick or blowout accident whiletripping and pulling this gas into the vertical section [4ndash6]

In the past decades several key studies have beenconducted on horizontal well control and gas migrationVefring et al established new models for the gas slip and risevelocities in near horizontal wells and various models fordifferent gas removal mechanisms [7] Chexal et al proposeda comprehensive drift flux model [8] but the model is

complicated for field applications because the fluid distri-bution is formed by the correlation of multiple empiricalcurve fitting parameters through the distribution parame-ters Hibiki and Ishii proposed a drift velocity equation it isapplied to slug flow [9] Gao et al simulated the storage andremoval processes of the gas slug by experiments and an-alyzed the migration of the gas slug [10] In recent years thedrift speed equation proposed by Woldesemayat and Ghajarconsiders the influences of surface tension and pipelinediameter on drift speed apart from the influences of pipelinedirection and system pressure [11] Wang et al analyzed thevariation of wellbore pressure along the depth of the wellduring the time of gas kick in a horizontal well [12]However previous studies are primarily for completelyhorizontal sections there are few research studies on the gasaccumulation and gas migration in the wavy horizontalsections of the horizontal gas well and few people usednumerical simulation to study them In this paper a nu-merical model for gas accumulation and gas migration in thewavy horizontal sections of the horizontal gas well is

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 7275209 9 pageshttpsdoiorg10115520207275209

developed meanwhile the gas accumulation and gas mi-gration process is numerically investigated

2 Physical Model and Governing Equations

21 Physical Model )e diameter of the borehole in thewavy horizontal sections of the horizontal gas well is02159m Gas is accumulated on the top of the wavy hor-izontal sections )e schematic diagram of the gas accu-mulation in the wavy horizontal sections of the horizontalgas well is shown in Figure 2

Establishing a reasonable two-dimensional physicalmodel of the wavy horizontal sections of the horizontal gaswell according to the actual situation is the key to thesimulation of gas accumulation and gas migration In orderto reduce the calculation amount and improve the simu-lation efficiency only the fluid domain is established )eborehole diameter is 02159m and the horizontal distanceon both sides of the model is 1m A horizontal wellborephysical model with different wavy horizontal sections isestablished as shown in Figure 2

ICEM CFD is selected as the meshing software andquadrilateral meshing is adopted [13 14] )e ratio of thelength and width of the mesh is not greater than 5According to the characteristics of fluidmotion the wall gridis locally encrypted to ensure accurate simulation of gas-liquid two-phase characteristics as shown in Figures 3 and 4

22 Governing Equations )e gas-liquid flow process in thewavy horizontal sections of a horizontal gas well is unstableEven if the boundary conditions remain the same thephysical quantity of the fluid during the flow still has strongpulsation so the simulation model should be run in aturbulent state [15ndash18] By numerical analysis method andsimulating it the results can be compared with the actualsituation Considering the gravity factor VOF model andRNG k-ε turbulence model are selected to simulate the flowchanges under different working conditions )e governingequation is established as follows

(1) Continuity equation

zρzt

+z

zxi

ρvi( 1113857 0 (1)

(2) Momentum equation

z(ρν)

zt+ nabla middot (ρνν) minusnablap + nabla middot μ nablaν + nablaνT

1113872 11138731113960 1113961 + ρg + F

(2)

(3) Turbulence equation

Turbulent energy equation k is

z(ρk)

zt+

z ρkvi( 1113857

zxi

z

zxi

αkμeffzk

zxj

1113888 1113889 + Gk + ρε (3)

(4) Dissipation rate equation ε is

z(ρε)zt

+z ρεvi( 1113857

zxi

z

zxi

αεμeffzε

zxj

1113888 1113889 +Clowast1εk

Gk minus C2ερε2

k

(4)

In the expression v is the fluid velocity ms g is grav-itational acceleration ms2 xi xj are the spatial coordinates ρis the fluid density kgm3 p is static pressure Pa μ is the fluidviscosity Pamiddots F is volume force N μeff is the effective fluidviscosity Pamiddots t is time s k is turbulent kinetic energy J ε isthe turbulent energy dissipation Gk C2ε Clowast1ε αk and αε areconstants

23 Physical Parameter Gas-liquid density and dynamicviscosity are shown in Table 1

24 Equation Discretization and Solving Method An un-steady implicit separation and solving algorithm is used)e governing equations to be solved are continuity equa-tions that satisfy mass conservation momentum conser-vation energy conservation momentum equations energyequations and turbulence equations that take turbulenceproperties into account [19] )e finite volume method isused to discretize the governing equations and a suitablediscretization format is selected )e pressure interpolation

Wavy horizontal sections

Gas pockets

Figure 1 Gas accumulation in the wavy horizontal sections of the horizontal gas well

2 Mathematical Problems in Engineering

format selects the physical strength weighting format theinterpolation formats of density momentum turbulenceenergy turbulence dissipation rate and energy select thefirst-order upwind style high stability and fast calculationspeed and volume fraction interpolation format selects thegeometric reconstruction format pressure-speed couplingalgorithm selects PISO algorithm [20ndash22]

25 Setting of Definite Conditions Definite solution condi-tions consist of a combination of boundary conditions andinitial conditions

(1) Inlet conditions velocity inlet is used and the inletspeed is set to 12ms 16ms and 2ms )e inletboundary is set to a gas inlet volume fraction of 0)e turbulence definition method selects the hy-draulic diameter and turbulence intensity

(2) Outlet conditions the pressure outlet and turbulencedefinition method are used to select the hydraulicdiameter and turbulence intensity

(3) Initial conditions considering the influence ofgravity set Y minus2212981ms2 under the fluentenvironment panel In the initialization panel selectinlet initialization and then perform partial repair onthe initial volume fraction of the gas in the Patchpanel to achieve the setting of the initial concen-tration of gas in the model It is set to record a gas-liquid composition cloud chart every 100 time stepsAfter the simulation is completed an animation canbe formed to observe the flow pattern

26 Convergence Conditions Fluent software uses residualsto reflect the convergence of the calculations and judgeswhether the iterative process converges through the finaliterative residual output of each equation for each iterationstep [23] )e calculation process ends when the residuals ofeach equation reach the set convergence criteria In thismodel all residuals are set to 10times10minus4 the time step is set to001 s and the maximum iteration step is set to 20 steps[24ndash28] )e total time steps are specifically set according tothe actual flow of gas-liquid two-phase tube flow

3 Simulation Results and Analysis

)ere are various combinations of gas accumulation sim-ulations in the wavy horizontal sections of horizontal gaswells Here simulation studies of gas accumulation in singlewavy horizontal section and complex wavy horizontal sec-tions are performed

Gas

Drilling fluid

Flow direction

Figure 2 Schematic diagram of gas accumulation in the wavy horizontal sections of the horizontal gas well

(a) (b)

(c)

Figure 3 Calculation model of wavy horizontal section of the horizontal gas well (a) 1 time wavy horizontal section borehole model (b) 15times wavy horizontal sections borehole model (c) 2 times wavy horizontal sections borehole model

Figure 4 Meshing model

Table 1 Gas-liquid density and dynamic viscosity

Parameter name Density (kgmiddotmminus3) Dynamic viscosity (Pamiddots)Drilling fluid 9970 9028times10minus4

Gas 1185 186times10minus5

Mathematical Problems in Engineering 3

31 Simulation Analysis of Single Wavy Horizontal Section

311 Influence of Curvature According to the actualworking conditions wavy horizontal sections with differentcurvatures are selected and models of gas accumulation ofwavy horizontal sections with different curvatures areestablished to simulate gas-liquid two-phase flow )e di-ameter of the wavy horizontal section is 02159m the totalhorizontal length is 5m the drilling fluid flow velocity is16ms the initial gas accumulation at the top is 03m3 andthe curvature of the wavy horizontal section is 02 03 04and 05 As displayed red is drilling fluid and blue is gas

It can be seen from Figure 5 that at a speed of 16msand different curvatures of 02 03 04 and 05 the gas in thewavy horizontal section of the horizontal gas well isexhausted and there are no phenomenon of gas accumu-lation and inability of exhaust )e gas pocket formed by theaccumulated gas is carried forward by the drilling fluidWhen the gas pocket enters the downward section the gaspocket cannot be exhausted directly)e front end of the gaspocket is broken into small bubbles by the shear force andwavy horizontal section of the horizontal gas well isexhausted in the form of small bubbles With time the gaspocket is gradually becoming smaller and the drilling fluidpushes the bladder out of the wavy horizontal section of thehorizontal gas well As the curvature increases the time ittakes to exhaust the gas increases )erefore the lower thecurvature of the horizontal wellbore the less likely the gasaccumulation will occur

312 Influence of Flow Rate )e borehole diameter is02159m the total horizontal length is 5m the initial gasaccumulation at the top is 03m3 the curvature is 03 andthe drilling fluid flow velocity is 12ms 16ms and 2msas shown in Figure 5

Observing Figure 6 it can be seen that when the drillingfluid flow velocity is 2ms the drilling fluid directly carriesthe entire bladder to discharge the wavy horizontal sectionwithout shear fracture When the drilling fluid flow velocityis 16ms the gas formed by the accumulated gas is carriedby the drilling fluid Forward when the gas pocket enters thedownward section the gas pocket cannot be exhausteddirectly the front end of the gas pocket is broken into smallbubbles by the shear force the gas is exhausted in the form ofsmall bubbles and the drilling fluid is carried out by theremaining gas pocket When the drilling fluid flow velocity is12ms the drilling fluid pushes the gas pocket to thedownward section the gas pocket is stationary and the frontsection of the gas pocket is broken into small bubbles by theshear force to discharge the gas from the wavy horizontalsection Over time part of the gas cannot be broken intosmall bubbles and stays in the wavy horizontal sectioncausing gas accumulation phenomenon

From the above phenomenon it can be seen that there isa critical flow rate to make the gas just exit the wavy hor-izontal section of the horizontal gas well When the drillingfluid flow velocity is higher than the critical velocity gasaccumulation will not occur when the drilling fluid flow

velocity is lower than the critical velocity gas retention willcause gas accumulation At this time the gas can only beexhausted by dissolving in the drilling fluid and increasingthe speed of the drill pipe In order to prevent the accu-mulation of gas in the wavy horizontal section the criticalflow rate needs to be determined )erefore this paperperformed a series of gas-liquid simulation of the wavyhorizontal section of the horizontal gas well with differentcurvatures )e simulation results are shown in Table 2

As known from Table 2 when the curvature is 02 thecritical drilling fluid flow velocity is 08ms when thecurvature is 03 the critical drilling fluid flow velocity is10ms when the curvature is 04 the critical drilling fluidflow velocity is 12ms when the curvature is 05 the criticaldrilling fluid flow velocity is 13ms)e critical drilling fluidflow velocity increases with the curvature

313 Experimental Comparison and Verification Gao et al[10] analyzed the gas migration process in the undulatingsection of a horizontal well through experiments In order toverify the correctness of the simulation results the simu-lation results were compared with their experimental results)e gas traps in the elbows mainly bear the frictional re-sistance of the pipe wall in the initial state When the bubblesenter the downdip sections it is difficult for gas to dischargebecause of the buoyancy ie the flow resistance )e frontends of the bubbles are crushed and separated under theliquid phase flow disturbance conditions but only fewbubbles are separated and migrate mostly in large bubbleform through mainly surface tension and liquid phasefriction

)e simulation results are exactly the same as the ex-perimental results verifying the accuracy of the simulationresults

32 Simulation Analysis of Complex Wavy HorizontalSections Horizontal gas wells may have multiple wavyhorizontal sections so the total horizontal length is 20m theborehole diameter is 02159m the curvature is 02 the initialtop gas accumulation is 098m3 and the critical drilling fluidflow velocity is 1ms 12ms 16ms 2ms and 15 timeswavy horizontal sections and 2 times wavy horizontal sec-tions are simulated )e simulation results are shown inFigures 6 and 7

Observing Figure 7 it can be seen that when the drillingfluid flow velocity is 2ms the drilling fluid carries gas intothe downward section and the front end of the gas pocket issheared and broken)e remaining part is still carried by thedrilling fluid to the second upward section in the form of alarge gas pocket and then exhausted when the drilling fluidflow velocity is 1ms 12ms and 16ms the drilling fluidcarries gas into the downward section and the front end ofthe gas pocket shears and breaks When the gas pocketreaches the bottom of the wavy horizontal section it will stayand can only be exhausted by breaking into small bubblesand as the speed decreases the longer the crushing time thesmaller the broken bubbles


Observing Figure 8 shows that when the drilling fluidflow velocity is 2ms the gas pocket is carried by the drillingfluid to the bottom of the wavy horizontal section and then

it stays and then it is sheared and broken into large bubblesand migrates to the second wavy horizontal section )ere isno gas accumulation at the top and it is directly exhausted

3s 6s

(a)

3s 6s

(b)

3s 6s

(c)

3s 6s

(d)

Figure 5 Flow states under different curvatures (a) Curvature is 02 (b) Curvature is 03 (c) Curvature is 04 (d) Curvature is 05

3s 6s

(a)

3s 9s

(b)

3s 200s

(c)

Figure 6 Flow states at different inlet velocities (a) Drilling fluid flow velocity is 2ms (b) Drilling fluid flow velocity is 16ms (c) Drillingfluid flow velocity is 12ms


Table 2 Exhaust conditions under different curvatures

CurvatureDrilling fluid flow velocity(mmiddotsminus1)

08 09 10 11 12 13 14 16 202 F F Y Y Y Y Y Y Y03 F F F Y Y Y Y Y Y04 F F F F F Y Y Y Y05 F F F F F F Y Y YY exhaust F not exhausted

65s 11s

(a)

65s 18s

(b)

18s 34s

(c)

40s 68s

(d)

Figure 7 Flow states at different velocities during 15 wavy horizontal sections (a) Drilling fluid flow velocity is 2ms (b) Drilling fluid flowvelocity is 16ms (c) Drilling fluid flow velocity is 12ms (d) Drilling fluid flow velocity is 1ms

35s 7s

(a)

10s 125s

(b)

Figure 8 Continued


when the drilling fluid flow velocity is 1ms 12ms and16ms the gas pocket is carried by the drilling fluid into thedownward section the front end of the gas pocket is shearedand broken and the gas pocket is brought by the drilling

fluid to the wavy horizontal sections At the bottom of thesection it stays and breaks into medium and small bubblesand enters the second wavy section At the top of the secondwavy section it begins to gather into an gas pocket and thenthe front end of the gas pocket is sheared and exhausted

Observing Figures 9 and 10 we can see that when theflow velocity is the same the curvature and the total length ofwavy horizontal sections are the same and the samewaveform the exhaust time of 15 wavy horizontal sections isthe same as that of two wavy horizontal sections and thecurve is almost the same therefore the number of wavyhorizontal sections has little effect on the efficiency of theexhaust

4 Conclusions

(1) In the case of the same length and the same flowvelocity the gas exhaust time increases with theincrease of the curvature )erefore the lower thecurvature of the wavy horizontal sections the lesslikely it is to generate gas

(2) When the drilling fluid flow velocity is extremelylarge the drilling fluid directly carries the entiregas pocket out of the wavy horizontal sectionwithout shear fracture as the inlet flow velocitydecreases the gas pocket formed by the accumu-lated gas is carried forward by the drilling fluidWhen the gas pocket enters the downward sectionthe front end of the gas pocket is broken into smallbubbles by the shear force )e gas is exhausted inthe form of small bubbles When the drilling fluidflow velocity is reduced to a certain speed thedrilling fluid pushes the gas pocket downwardsection )en the gas pocket is stationary and thefront section of the gas pocket is broken into smallbubbles by the shear force Over time some of thegas cannot be broken into small bubbles and staysin the wavy horizontal section causing gasaccumulation

13s 235s

(c)

22s 48s

(d)

Figure 8 Flow conditions at different velocities when there are two wavy horizontal sections (a) Drilling fluid flow velocity is 2ms (b)Drilling fluid flow velocity is 16ms (c) Drilling fluid flow velocity is 12ms (d) Drilling fluid flow velocity is 1ms

Gas

vol

ume f

ract

ion

1090807060504030201

0

Exhaust time (s)0 10 20 30 40 50 60 70 80 90

Flow velocity is 2msFlow velocity is 16ms


Figure 9 Curves of gas volume at different flow velocity whenthere are 15 wavy horizontal sections

Gas

vol

ume f

ract

ion

1090807060504030201

0

Exhaust time (s)0 10 20 30 40 50 60 70 80 90 100



Figure 10 Curves of gas volume at different flow velocity whenthere are two wavy horizontal sections


(3) )ere is a critical flow velocity so that the gas is justcompletely exhausted from the wavy horizontalsection When the drilling fluid flow velocity ishigher than the critical velocity gas accumulationwill not occur when the drilling fluid flow velocity islower than the critical velocity gas retention willcause gas accumulation And the critical drilling fluidflow velocity increases with the curvature

(4) When the total length and curvature of the wavyhorizontal sections are the same the number of wavyhorizontal sections has a great effect on the gas-liquid flow pattern but has little effect on the effi-ciency of the exhaust

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)e authors gratefully acknowledge the financial support byldquo)irteenth Five-Year Planrdquo China National Offshore OilCorporation (CNOOC-KJ135ZDXM24LTDZJ01) and theNational Science and Technology Major Project(2017ZX05009-003)

References

[1] X Zhang J Xie and B Yu ldquoNumerical simulation on the gas-liquid two-phase flow in the direct commissioning process ofa hilly pipelinerdquo Journal of the University of Chinese Academyof Sciences vol 34 no 2 pp 265ndash272 2017

[2] E H Vefring ldquoAn advanced kick simulator for high angle andhorizontal wells-part Irdquo in SPEIADC Drilling ConferenceSociety of Petroleum Engineers Amsterdam Nether-landsSociety of Petroleum Engineers Amsterdam Nether-lands March 1995

[3] NWei and Z Cui ldquo)e rule of carrying cuttings in horizontalwell drilling of marine natural gas hydraterdquo Energies vol 13no 5 p 1129 2020

[4] N Liu W Sun Y Meng et al ldquoMultiphase non equilibriumpipe flow behaviors in the solid fluidization exploitation ofmarine natural gas hydrate reservoirrdquo Energy Science ampEngineering vol 6 no 6 pp 760ndash782 2018

[5] N Wei W-T Sun Y-F Meng et al ldquoChange mechanism oftransient gas-liquid two-phase flow in wellbore during marinenatural gas hydrate reservoir drillingrdquo Germal Sciencevol 23 no 4 pp 2179ndash2187 2019

[6] L Yongwang ldquoDiscussion on the trajectory control tech-nology of horizontal section of horizontal wellrdquo ScienceTechnology and Engineering vol 11 no 35 pp 8872ndash8875+8881 2011

[7] E H Vefring Z Wang and R Rommetveit ldquoAn advancedkick simulator for high angle and horizontal wells-part IIrdquo inMiddle East Oil Show Society of Petroleum EngineersManama BahrainSociety of Petroleum Engineers ManamaBahrain March 1995

[8] B Chexal G Lellouche J Horowitz and J Healzer ldquoA voidfraction correlation for generalized applicationsrdquo Progress inNuclear Energy vol 27 no 4 pp 255ndash295 1992

[9] T Hibiki and M Ishii ldquoOne-dimensional drift-flux modeland constitutive equations for relative motion between phasesin various two-phase flow regimesrdquo International Journal ofHeat and Mass Transfer vol 46 no 25 pp 4935ndash4948 2003

[10] Y Gao X Sun T Zhao Z Wang X Zhao and B Sun ldquoStudyon the migration of gas kicks in undulating sections ofhorizontal wellsrdquo International Journal of Heat and MassTransfer vol 127 pp 1161ndash1167 2018

[11] M A Woldesemayat and A J Ghajar ldquoComparison of voidfraction correlations for different flow patterns in horizontaland upward inclined pipesrdquo International Journal of Multi-phase Flow vol 33 no 4 pp 347ndash370 2007

[12] B Kang H Fan P Jiang et al ldquoSimulation and experiment onphase equilibrium of gas hydrate using the t-type pipe con-fluence modelrdquo Mathematical Problems in Engineeringvol 2020 pp 1ndash11 2020

[13] Y Yu Fluent Introduction and Advanced Course BeijingInstitute of Taechnology Press Beijing China 2008

[14] Q Ma ldquoSimulation of slack line phenomena in the big droppipeline under the different conditionsrdquo Journal of LiaoningUniversity of Petroleum amp Chemical Technology vol 35 no 1pp 37ndash40 2015

[15] S A Morsi and A J Alexander ldquoAn investigation of particletrajectories in two-phase flow systemsrdquo Journal of FluidMechanics vol 55 no 02 pp 193ndash208 1972

[16] Q Li ldquoNumerical simulation of oil and water two-phasedispersed flow in horizontal pipe based on fluentrdquoOil and GasField Surface Engineering vol 09 pp 68-69 2013

[17] C Chen Gree-dimensional Simulation and ExperimentalStudy of Gas-Liquid Two-phase Flow in Vertical Riser DissTianjin University Tianjin China 2009

[18] Z Shen ldquoGas-liquid two-phase flow in pipelinesrdquo Petro-chemical Technology vol 25 no 7 p 175 2018

[19] N Wei C Xu Y Meng G Li X Ma and A Liu ldquoNumericalsimulation of gas-liquid two-phase flow in wellbore based ondrift flux modelrdquo Applied Mathematics and Computationvol 338 pp 175ndash191 2018

[20] S Liu and Z Zhu ldquoApplication of composite deflecting modelin horizontal well drillingrdquo Mathematical Problems in Engi-neering vol 2020 pp 1ndash10 2020

[21] X Li Z Han S Yang and G Chen ldquoUnderwater gas releasemodeling and verification analysisrdquo Process Safety and En-vironmental Protection vol 137 pp 8ndash14 2020

[22] S J Perkins and H A Li ldquoElongated bubble centring inhorizontal gas-liquid slug flowrdquo International Journal ofMultiphase Flow vol 123 Article ID 103158 2020

[23] B Sun X Sun Z Wang and Y Chen ldquoEffects of phasetransition on gas kick migration in deepwater horizontaldrillingrdquo Journal of Natural Gas Science and Engineeringvol 46 pp 710ndash729 2017

[24] J-C Feng X-S Li G Li B Li Z-Y Chen and Y WangldquoNumerical investigation of hydrate dissociation per-formance in the south China sea with different horizontalwell configurationsrdquo Energies vol 7 no 8 pp 4813ndash48342014

[25] P V Godbole C C Tang and A J Ghajar ldquoComparison ofvoid fraction correlations for different flow patterns in up-ward vertical two-phase flowrdquo Heat Transfer Engineeringvol 32 no 10 pp 843ndash860 2011

[26] A J Ghajar and C C Tang ldquoVoid fraction and flow patternsof two-phase flow in upward and downward vertical and


horizontal pipesrdquo Advances in Multiphase Flow and HeatTransfer vol 4 pp 175ndash201 2012

[27] C Y Xu ldquoExperimental simulation and numerical modelingof dynamic variations in wellbore pressure during gas-kicksrdquoActa Petrolei Sinca vol 36 no 1 pp 120ndash126 2015

[28] F Ren B Wang L Zhao and A Zhu ldquoExperimental in-vestigation and analysis of dynamic buckling of drill string inhorizontal wellrdquo Shock and Vibration vol 2017 pp 1ndash152017


developed meanwhile the gas accumulation and gas mi-gration process is numerically investigated

2 Physical Model and Governing Equations

21 Physical Model )e diameter of the borehole in thewavy horizontal sections of the horizontal gas well is02159m Gas is accumulated on the top of the wavy hor-izontal sections )e schematic diagram of the gas accu-mulation in the wavy horizontal sections of the horizontalgas well is shown in Figure 2

Establishing a reasonable two-dimensional physicalmodel of the wavy horizontal sections of the horizontal gaswell according to the actual situation is the key to thesimulation of gas accumulation and gas migration In orderto reduce the calculation amount and improve the simu-lation efficiency only the fluid domain is established )eborehole diameter is 02159m and the horizontal distanceon both sides of the model is 1m A horizontal wellborephysical model with different wavy horizontal sections isestablished as shown in Figure 2

ICEM CFD is selected as the meshing software andquadrilateral meshing is adopted [13 14] )e ratio of thelength and width of the mesh is not greater than 5According to the characteristics of fluidmotion the wall gridis locally encrypted to ensure accurate simulation of gas-liquid two-phase characteristics as shown in Figures 3 and 4

22 Governing Equations )e gas-liquid flow process in thewavy horizontal sections of a horizontal gas well is unstableEven if the boundary conditions remain the same thephysical quantity of the fluid during the flow still has strongpulsation so the simulation model should be run in aturbulent state [15ndash18] By numerical analysis method andsimulating it the results can be compared with the actualsituation Considering the gravity factor VOF model andRNG k-ε turbulence model are selected to simulate the flowchanges under different working conditions )e governingequation is established as follows

(1) Continuity equation

zρzt

+z

zxi

ρvi( 1113857 0 (1)

(2) Momentum equation

z(ρν)

zt+ nabla middot (ρνν) minusnablap + nabla middot μ nablaν + nablaνT

1113872 11138731113960 1113961 + ρg + F

(2)

(3) Turbulence equation

Turbulent energy equation k is

z(ρk)

zt+

z ρkvi( 1113857

zxi

z

zxi

αkμeffzk

zxj

1113888 1113889 + Gk + ρε (3)

(4) Dissipation rate equation ε is

z(ρε)zt

+z ρεvi( 1113857

zxi

z

zxi

αεμeffzε

zxj

1113888 1113889 +Clowast1εk

Gk minus C2ερε2

k

(4)

In the expression v is the fluid velocity ms g is grav-itational acceleration ms2 xi xj are the spatial coordinates ρis the fluid density kgm3 p is static pressure Pa μ is the fluidviscosity Pamiddots F is volume force N μeff is the effective fluidviscosity Pamiddots t is time s k is turbulent kinetic energy J ε isthe turbulent energy dissipation Gk C2ε Clowast1ε αk and αε areconstants

23 Physical Parameter Gas-liquid density and dynamicviscosity are shown in Table 1

24 Equation Discretization and Solving Method An un-steady implicit separation and solving algorithm is used)e governing equations to be solved are continuity equa-tions that satisfy mass conservation momentum conser-vation energy conservation momentum equations energyequations and turbulence equations that take turbulenceproperties into account [19] )e finite volume method isused to discretize the governing equations and a suitablediscretization format is selected )e pressure interpolation

Wavy horizontal sections

Gas pockets

Figure 1 Gas accumulation in the wavy horizontal sections of the horizontal gas well










Gas

Drilling fluid

Flow direction


(a) (b)

(c)






















3s 6s

(a)

3s 6s

(b)

3s 6s

(c)

3s 6s

(d)


3s 6s

(a)

3s 9s

(b)

3s 200s

(c)






65s 11s

(a)

65s 18s

(b)

18s 34s

(c)

40s 68s

(d)


35s 7s

(a)

10s 125s

(b)

Figure 8 Continued





4 Conclusions



13s 235s

(c)

22s 48s

(d)


Gas

vol

ume f

ract

ion

1090807060504030201

0

Exhaust time (s)0 10 20 30 40 50 60 70 80 90




Gas

vol

ume f

ract

ion

1090807060504030201

0

Exhaust time (s)0 10 20 30 40 50 60 70 80 90 100







Data Availability




Acknowledgments


References








































Gas

Drilling fluid

Flow direction


(a) (b)

(c)






















3s 6s

(a)

3s 6s

(b)

3s 6s

(c)

3s 6s

(d)


3s 6s

(a)

3s 9s

(b)

3s 200s

(c)






65s 11s

(a)

65s 18s

(b)

18s 34s

(c)

40s 68s

(d)


35s 7s

(a)

10s 125s

(b)

Figure 8 Continued





4 Conclusions



13s 235s

(c)

22s 48s

(d)


Gas

vol

ume f

ract

ion

1090807060504030201

0

Exhaust time (s)0 10 20 30 40 50 60 70 80 90




Gas

vol

ume f

ract

ion

1090807060504030201

0

Exhaust time (s)0 10 20 30 40 50 60 70 80 90 100







Data Availability




Acknowledgments


References















































3s 6s

(a)

3s 6s

(b)

3s 6s

(c)

3s 6s

(d)


3s 6s

(a)

3s 9s

(b)

3s 200s

(c)






65s 11s

(a)

65s 18s

(b)

18s 34s

(c)

40s 68s

(d)


35s 7s

(a)

10s 125s

(b)

Figure 8 Continued





4 Conclusions



13s 235s

(c)

22s 48s

(d)


Gas

vol

ume f

ract

ion

1090807060504030201

0

Exhaust time (s)0 10 20 30 40 50 60 70 80 90




Gas

vol

ume f

ract

ion

1090807060504030201

0

Exhaust time (s)0 10 20 30 40 50 60 70 80 90 100







Data Availability




Acknowledgments


References



































65s 11s

(a)

65s 18s

(b)

18s 34s

(c)

40s 68s

(d)


35s 7s

(a)

10s 125s

(b)

Figure 8 Continued





4 Conclusions



13s 235s

(c)

22s 48s

(d)


Gas

vol

ume f

ract

ion

1090807060504030201

0

Exhaust time (s)0 10 20 30 40 50 60 70 80 90




Gas

vol

ume f

ract

ion

1090807060504030201

0

Exhaust time (s)0 10 20 30 40 50 60 70 80 90 100







Data Availability




Acknowledgments


References



































4 Conclusions



13s 235s

(c)

22s 48s

(d)


Gas

vol

ume f

ract

ion

1090807060504030201

0

Exhaust time (s)0 10 20 30 40 50 60 70 80 90




Gas

vol

ume f

ract

ion

1090807060504030201

0

Exhaust time (s)0 10 20 30 40 50 60 70 80 90 100







Data Availability




Acknowledgments


References


































Data Availability




Acknowledgments


References
































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