numerical simulation of multiphase ﬂow in a vertically...

Numerical simulation of multiphase flow in a

vertically mounted Venturi flow meter

A. Fiebach1, E. Schmeyer1, S. Knotek2, S. Schmelter1

1 Physikalisch-Technische Bundesanstalt (PTB), Abbestr. 2-12, 10587 Berlin, Germany2 Czech Metrology Institute (CMI), Okrun 31, 638 00 Brno, Czech Republic

E-mail (corresponding author): [email protected]

Abstract

The objective of the European research project ”Multiphase flow metrology in Oil and Gas production” (MultiFlowMet)is to explain and reduce the uncertainty in multiphase flow metering. A comparison of measurements using multiphasemetering systems with corresponding results from computational fluid dynamics is used to achieve this goal. In thiscontribution, a two-phase flow through a vertically mounted Venturi flow meter is presented. According to the experimentalset-up within the project, the simulations focus on the flow of oil and gas in large pipes of diameter D = 0.104m. Thesimulations represent the whole configuration including a 154D long inflow section, where the flow pattern is formed. Aftera horizontal bend the flow is turned upwards through a blind-T in the vertically mounted measurement unit. This leads toswirl and turbulence and thus another pattern is observed in the Venturi flow meter. The simulation results are comparedwith experimental data obtained in the project. Furthermore, the main features of the flow have been extracted by means ofdata analysis. This allows an easier recognition of the flow pattern and is the basis for a quantitative comparison betweenexperimental and numerical results.

1. Introduction

Energy from oil and gas still plays an important rolein Europe for the near or mid-term future. Since thenumber of large reserves is decreasing, one is interestedin exploiting new smaller deposits which are more remoteand situated in deeper water. New wells are operated andmeasured under seabed, before a mixture of oil, waterand gas is flowing in shared pipelines to the processingfacility. Nowadays multiphase flow measurement systemshave a high level of uncertainty of up to 20%. Theaim of the European research project ”Multiphase flowmetrology in Oil and Gas production” (MultiFlowMet)is to improve these levels of uncertainty and to formthe basis of a sustainable reference network, reducingfinancial exposure and risk for industry. To achieve thisgoal a comprehensive intercomparison on multiphase flowis conducted on one hand. On the other hand the influenceof different parameters is studied by computational fluiddynamics (CFD). As an initial step, the flow of severalphases through the measurement configuration used forthe experimental intercomparison within the project issimulated with the commercial CFD solver ANSYSFluent [1].

There are several papers concerning the CFD modelingof three-dimensional gas-liquid multiphase flows, see [2,4, 5, 11, 12, 13] and the references therein. In [4, 5]the numerical simulation of slug flow in horizontal pipesis studied systematically using CFX-5. It is observedthat the formation of slug flow regimes strongly dependson the perturbation of the inlet boundary conditions.Moreover, the length of the computational domain as well

as the resolution of the velocity gradient in the vicinityof the interface between the different phases plays animportant role in slug formation. A detailed descriptionof multiphase CFD modeling is given in [13]. In thisreference, the transient formation of different patterns issimulated and the results agree qualitatively well withexperimental video observations. However, the predictedamplitude of pressure showed quantitative differences tothe experimental data. Two-phase pipe flow simulationswith the OpenFoam solver interFoam are carried out in[11]. The liquid holdup and pressure drop calculatedwith the CFD model are in good agreement with resultsobtained from a two-phase mechanistic model developedin [7]. In the work of [12] the pattern formation ofan air-water two-phase flow in horizontal pipelines isstudied using the OpenFoam software. The simulationresults agree qualitatively well with experimental videoobservations.

The paper is organized as follows: In Section 2 thegeometry of the measurement configuration is introducedand the numerical scheme used for the CFD simulationwith Fluent is sketched. Simulation results as well asa comparison with experimental data are presented inSection 3. Finally, conclusions are drawn in Section 4.

2. Modeling with Fluent

2.1. Mesh and Boundary Conditions

The simulated geometry represents a measurement set-upcommonly used in multiphase flows, see Figure 1.

According to the specification of the experiments, thediameter of the pipe network D = 0.104m is chosen. In

FLOMEKO 2016, Sydney, Australia, September 26-29, 2016

front of the measurement unit depicted in Figure 1 thereis a horizontal, 16m long inflow section, where the flowpattern is formed according to the prescribed superficialvelocities and fluid parameters of the different phases. Inthe experimental set-up of the project the pattern can beobserved through a glass pipe at the end of this inflowsection. Behind a 90� bend a blind-T is attached sothat the flow is abruptly turned 90� upstream towards themeasuring unit. Hence the flow gets mixed and any priorgravity segregations of the phases break down, c.f., [6].The mass flow rate is measured by the gamma-sourcebased multiphase flow meter PhaseTester Vx.

The end of the pipe network builds a 45� out of planedouble bend.

Plane 3

Plane 2

Plane 1

Blind T

Outlet

153D horizontalupstream pipe

Figure 1: Geometry of the vertical Venturi measurement set-upused within the MultiFlowMet project. In front of Plane 1 thereis an additional 154D long horizontal pipe. The three samplingplanes labeled Plane 1, Plane 2, and Plane 3 are marked in thepicture.

For the numerical simulation, the whole geometry hasbeen meshed with hexahedral elements using the meshgeneration tool ICEM/CFD-Hexa. The mesh consists ofabout 1.1 million hexahedral elements, see Figure 2.ENG58 Multiphase

Figure 2: Inlet section of the grid used for the numerical flow pattern simulations for two-phase flow. Thedifferent colors mark the inlet sections of liquid (bottom) and gas (top), respectively.

– body force weighted for pressure– second order upwind for momentum– compressive for VOF– first order upwind for turbulence parameters

• time discretization: bounded second order implicit, fixed time step size

• solution strategy: PISO with underrelaxation

• convergence criteria: residuals smaller than 0.001 for all equations

For the interface modeling, both explicit and implicit VOF have been tested. Here, the following settings wereused: The “volume fraction cutoff” was set to 1e-6 and the “open channel flow” option was selected. In thecase of implicit VOF, “sharp / dispersed” was chosen for the interface treatment, whereas for the explicit VOF“sharp” with “interfacial anti-diffusion” was used. This option allows to employ “geo-reconstruct” as spatialdiscretization method for the volume fraction.

A description of all the different settings can be found in the Fluent User’s Guide [1].

3.2 Results of the test cases from literature

With Fluent the following test cases (numbering as in Fig. 1) were simulated: 9, 10, 11, 12, 13. These cases aredescribed in detail in [4, 5]. The four different flow patterns (stratified, wavy, slug, and elongated bubble flow)were all reproduced by the numerical simulations.

3

Figure 2: Inlet section of the grid used for the numericalsimulations of two-phase flow. The different colors mark theinlet sections of liquid (bottom) and gas (top), respectively.

The pipe walls are treated as hydraulically smoothwalls with non-slip boundary conditions applied for the

gaseous and liquid phases. At the end of the pipe apressure outlet boundary condition is set. By using theopen-channel option, the solver extrapolates the requiredinformation from the interior.

In a flow-loop experiment, the phases flow together atan injection point further upstream. The CFD modelingof such a mixing section is challenging due to thedifferent flow morphology. Therefore, for the numericalsimulation, the inlet of the pipe is divided into two partsof equal size representing the inflow of the gaseous andliquid phase, respectively. The inlet section is depictedin Figure 2. The layering of both phases imposes lessturbulence into the system than present in reality. Hence,at the inlet, a sinusoidal perturbation is introduced in orderto stimulate the KelvinHelmholtz instability leading to amore natural behavior. The perturbation is implementedby means of Fluent user defined functions (UDFs).

2.2. Numerical Method

The selection of an appropriate multiphase flow modeltogether with a free surface model is the crucial part inthe simulation of multiphase flows in channels and pipes.With today’s computer power it is impossible to resolvethe spatial structure of the free surface down to the microscale for the whole pipe geometry, which has a length ofseveral meters. Hence, the evolution of Kelvin-Helmholtzinstabilities at the free surface can only be resolved ona coarse scale. An interfacial drag law must be used tomodel the influence of these free surface instabilities onthe macro-scale flow properties. Additional instabilitiescan be triggered by introducing an oscillation of the freesurface at the inlet boundary condition, c.f. [13]. By usingthe Volume of Fluid (VOF) method it is only possible toresolve structures that are several times larger than thegrid spacing.

It is common to use the explicit Geo-Reconstructscheme for the interface reconstruction in the VOFmethod in Fluent together with a implicit first order intime discretization, c.f. [1]. This leads to a sharperinterface and thus to a more accurate solution. The poorconvergence on skewed meshes and the Courant numberlimitation of the time step are disadvantages of the method.In [10] the use of an implicit compressive scheme alongwith a bounded second order time discretization schemeis favored. Since this method does not have the Courantnumber limitation, the simulations can be run with largertime steps than with an explicit solver.

As already said, the focus lies on the modeling ofthe macro-scale and non-fluctuating features of the flow.Hence, for every phase the fluid-dependent k-! basedshear stress transport (SST) turbulence model of [3] wasapplied together with a damping of turbulent diffusionat the interface [5, 10]. At the interface between thephases turbulence damping helps to resolve the interfacialinstability, since high velocity gradients lead to turbulencegeneration.

The schemes of the spatial and time discretizationare summarized in Table 1. The Pressure Implicit with


Splitting of Operator algorithm (PISO) together withan Algebraic Multigrid (AMG) is used for solving thediscretized Reynolds-averaged Navier-Stokes equations.

Table 1: Numerical discretization schemes used in Fluent.Gradient Green-Gauss node basedPressure Body force weightedMomentum Second order upwindTurbulence First order upwindPhases Compressive schemeTime discr. Bounded second order

3. Simulation results and analysis

The measurement device is tested for a variety of differentoperational parameters. In the following, we will presentsimulation results for one selected case of the testenvelope, namely a two-phase oil-gas slug flow.

If the superficial velocities of both phases are highenough, the interface between them becomes unstable andwaves occur. For even higher velocities, the waves cangrowth until they touch the top wall of the pipe so that thewhole diameter is covered by liquid phase. Such a flowpattern we call a slug.

This pattern is characterized by its periods, when thepipe is fully filled with liquid, alternating with periods,when the gaseous and liquid phases are separated. Withinthe project slug flows are of special interest due to periodswithout liquid or gas followed by very high liquid and gasrates. Such a behavior causes undesired consequences ina pipe network like emergency shutdown of the platformdue to the high level of liquid in the separators, floods,corrosion and damages to the equipments, c.f. [9].

Here, “slug flow” means that this pattern is observedat the end of the horizontal upstream section, which islocated in front of Plane 1 in Figure 1. After passing theblind-T, which is typically used as a flow conditioner, thephases get mixed so that usually another flow pattern isobserved in the vertical section. The superficial velocitiesas well as the material properties of kerosene and nitrogen,which have been used in this test case, are summarized inTable 2.

Table 2: Fluid properties and superficial velocities of the twophases used for the CFD simulation, see e.g. [8].

at 25 �C kerosene nitrogendensity in kgm�3 825.609 1.138dyn. viscosity in Pa s 1.003 · 10�3 1.663 · 10�5

superficial vel. in ms�1 1.144 1.399

3.1. Simulation results and comparison withexperimental data

In the following, the simulation results for the selected testcase, see Table 2, are compared with experimental video

observations. The data were collected at the NationalEngineering Laboratory (NEL) Multiphase facility.

Figure 3 shows one of the slugs observed CFD travelingin the horizontal upstream pipe close to Plane 1. Thepictures depict the volume fraction of nitrogen in avertical cut through the pipe at different times. In the

(a) Beginning of slug �t = 0.0 s.

(b) Middle of slug �t = 0.25 s.

(c) End of slug �t = 0.7 s.

(d) Waves behind slug �t = 1.2 s.

Figure 3: Gas volume fraction of nitrogen in a vertical crosssection at the end of the horizontal inflow section at differenttime points obtained by CFD. Flow direction is from left to right.

top picture, one can see the front of the slug entering thedisplayed area. In front of the slug, waves can be observed.The next picture shows the middle of the slug. Here thepipe is fully filled with liquid. Gas is only present insmall bubbles within the slug. In the following picturethe end of the slug is depicted. From the time differencebetween the beginning and the end of the slug (first andthird picture), one can roughly estimate that the slug lastsabout 0.7 s.

In the experiments, a glass section is introduced shortlybefore the measurement unit. In Figure 4 a slug travelingthrough this section is depicted. Note that in this case theflow direction is from right to left.

A comparison between the simulation results (Figure 3)and the pictures extracted from the video observations(Figure 4) show that the structure of the slug is reproducedquite well by the numerical simulation. Also the timedifferences between the beginning, middle, and end of theslug match quite well with the experimental observations.Both in the numerical simulation and in the experiment,one observes smaller waves behind most of the slugs, seebottom pictures in Figures 3 and 4. The time it takes


(a) Beginning of slug, �texp

= 0.

(b) Middle of slug, �texp

= 0.38 s.

(c) End of slug, �texp

= 0.88 s.

(d) Waves behind slug, �texp

= 1.18 s.

Figure 4: View through a glass section located at the end of theinlet section at different times. Flow direction is from right toleft. Data were collected at the National Engineering Laboratory(NEL) Multiphase facility.

until these waves occur are also very similar in the CFDsimulation and in the experiments. However, the strongmixing between the phases, which can be seen in theexperiments, cannot be reproduced by the used numericalmethod. This is due to the fact that the mesh is relativelycoarse so that the interface between the phases is resolvedonly roughly.

3.2. Data analysis

In view of a more quantitative comparison betweenexperimental and numerical results, the huge amountof simulation data need to be condensed so that themain features of the flow can be extracted. This thenallows an automatic flow pattern recognition as well as abetter comparison between different simulations and withexperimental data. In the following, some results will bepresented for the selected test case from above.

Figure 5 depicts contours of the gas volume fraction ina horizontal cross section inside the throat of the Venturiat different times. Using the notation from Figure 1, thepictures show Plane 3. The blue color represents volumefractions of nitrogen up to 0.35, the orange one volumefractions of 0.65 and higher. By these classifications, theblue and orange color represents the liquid and gaseousphase, resp.. The green color marks volume fractions

−1.0 −0.5 0.0 0.5 1.0x/R

−1.0

−0.5

0.0

0.5

1.0

y/R

Contour plot of GAS and OIL

OIL Intermediate GAS0

20

40

60

80

100

%

Phase histogramTime t =26.1309162695 s

(a) t = 26.13 s.

−1.0 −0.5 0.0 0.5 1.0x/R

−1.0

−0.5

0.0

0.5

1.0

y/R

Contour plot of GAS and OIL

OIL Intermediate GAS0

20

40

60

80

100

%

Phase histogramTime t =26.7234986134 s

(b) t = 26.72 s.

Figure 5: Left: contours of the gas volume fraction in theVenturi throat at two different times. Right: correspondinghistograms of both phases.

of nitrogen between 0.35 and 0.65 and can thus beinterpreted as a mixture of the two phases. One observesthat due to the blind-T the horizontal slug flow pattern hasbeen transformed into an annular like flow pattern. Thisflow pattern is characterized by the presence of a liquidfilm on the pipe wall. Comparing the left top and bottompictures of Figure 5, one can recognize that the highvolume fraction of liquid in the top picture corresponds toa slug, previously present in the horizontal section beforethe flow conditioning unit.

Figure 6 plots the evolution of the gas volume fractionon lines through the middle of the labeled planes fromFigure 1. The blue color identifies gas volume fractionsgreater or equal 0.65, whereas the orange color standsfor gas volume fractions less or equal 0.35. By thisassociation the flow pattern can be extracted from thediagram. The top picture shows the gas volume fractionalong a vertical line on Plane 1 versus time. One canrecognize the periodic occurrence of slugs (the high bluepeaks, when the whole pipe is filled with liquid) as wellas the waves in between the slugs (the smaller blue peaks).Moreover the green color is an indicator of the height ofthe fluid interface. The middle and bottom pictures showthe gas volume fraction along horizontal lines on Plane 2and Plane 3, respectively. Here the pattern has changedto annular, since the flow has passed the blind-T flowconditioning unit. The liquid film present on the verticalwalls that are typical for annular flow can be recognizedin both the middle and bottom pictures of Figure 6. Theperiodic behavior (previously representing the slugs) is


15 20 25 30 35 40 45t in s

−1.0

−0.5

0.0

0.5

1.0

y/R

Evolution of the volume fraction at line x=0

OIL

Inte

rmed

iate

GA

S

(a) Plane 1.

15 20 25 30 35 40 45t in s

−1.0

−0.5

0.0

0.5

1.0

y/R


OIL

Inte

rmed

iate

GA

S

(b) Plane 2.

15 20 25 30 35 40 45t in s

−1.0

−0.5

0.0

0.5

1.0

y/R


OIL

Inte

rmed

iate

GA

S

(c) Plane 3.

Figure 6: Evolution in time of the gas volume fraction (a)along a vertical line through the middle of Plane 1, (b) alonga horizontal line through the middle of Plane 2, and (c) along ahorizontal line through the middle of Plane 3.

still present in the vertical section. However, it is not sopronounced any more. The fluid is more mixed due to theblind-T.

In Figure 7 the time evolution of the histogramspresented in the right pictures of Figure 5 are plottedfor all of the three planes in Figure 1. Thus, the graphsgive the percentage of very high gas volume fractions(orange) and very low gas volume fractions (blue) in thecorresponding plane. For pattern recognition it is sensibleto associate the orange curves with gas and the blue oneswith oil. Areas where the gas volume fraction is between0.35 and 0.65 are classified as Intermediate. They mayeither indicate the interface between the two phases orcorrespond to areas, where both phases are mixed.

10 15 20 25 30 35 40 45 50t in s

0

20

40

60

80

100

%

Evolution of the phase histogram

OILIntermediateGAS

(a) Plane 1.

10 15 20 25 30 35 40 45 50t in s

0

20

40

60

80

100

%


OILIntermediateGAS

(b) Plane 2.

10 15 20 25 30 35 40 45 50t in s

0

20

40

60

80

100

%


OILIntermediateGAS

(c) Plane 3.

Figure 7: Evolution in time of the histograms representing thetwo different phases (a) at the end of the inflow section, (b)shortly in front of the Venturi, and (c) inside the Venturi.

Figure 8 shows the histograms of the gas phase forthe three planes in one plot. Note that only a smallertime interval is shown in this picture so that the smallertime scales are resolved better. In the plot, cells with gasvolume fractions greater or equal 0.65 are shown. In thispicture one can recognize again the periodic occurrence ofslugs on Plane 1. Furthermore, the slug frequency can beread off, which allows a more quantitative comparisonwith experimental data. On Plane 2 and Plane 3 thecurves are much more oscillating due to the disturbancesintroduced by the blind-T.

Also other test points of the intercomparison testmatrix of the MultiFlowMet project were simulated.The different superficial velocities lead to other slugfrequencies or even other flow patterns. These changescan be observed by the evolution of the histograms.


16 18 20 22 24t in s

0

20

40

60

80

100

%

Evolution of the gaseous Phase Histogram

Plane 1Plane 2Plane 3

Figure 8: Evolution in time of the histograms of the gas phasein three different planes.

4. Conclusion

For this contribution a two-phase oil-gas flow in ameteorologically relevant geometry was simulated by thecommercial CFD solver Ansys Fluent. For tracking theinterfaces between the phases the Volume of Fluid (VOF)method was used.

The numerical results are in good agreement withexperimental video observations provided by NEL. Sinceoptical comparisons are time consuming and inaccurate,appropriate key data describing relevant flow propertieshave to be identified. For slug flow quantities of interestare the frequency and length of a slug, the interface height,etc.

The data analysis provides an approach to condensethe huge amount of data and to extract the characteristicsof the flow. By identifying high and low gasvolume fractions with gas and oil, respectively andby neglecting the areas, where both phases are mixed,patterns can be classified. This forms the basis for aquantitative comparison with experimental data comingfrom tomography or gamma densitometry.

Acknowledgement

The authors acknowledge the support received fromthe European Metrology Research Programme (EMRP)through the Joint Research Project “Multiphase flowmetrology in Oil and Gas production”. The EMRPis jointly funded by the European Commission andparticipating countries within Euramet and the EuropeanUnion. The authors would like to thank Jiri Polansky forhis assistance and for valuable discussions.

References

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[8] K. W. Ragland and K. M. Bryden. CombustionEngineering, Second Edition. Boca Raton: CRCPress, 2011.

[9] A. Sausen, P. Sausen, and M. de Campos. “TheSlug Flow Problem in Oil Industry and Pi LevelControl”. In: New Technologies in the Oil andGas Industry. Ed. by J. S. Gomes. InTech, 2012,pp. 103–118.

[10] J. Seo. “Multiphase Flow Modeling with FreeSurfaces Flow”. In: Presented at the KoreaConvergence Conference, Korea, 2014.

[11] A. M. Shuard, H. B. Mahmud, and A. J.King. “Comparison of Two-Phase Pipe Flow inOpenFOAM with a Mechanistic Model”. In: IOPConf. Ser. Mater. Sci. Eng. 121.1 (2016), p. 012018.

[12] J. P. Thaker and J. Banerjee. “CFD Simulationof Two-Phase Flow Phenomena in HorizontalPipelines using OpenFOAM”. In: Proceedingsof the Fortieth National Conference on FluidMechanics and Fluid Power. 2013.

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