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The Dynamic Two-Fluid Model OLGA:Theory and ApplicationKjen H. Bendlk.en Dag Maine. Randl Moe and Sven Nuland Inst. for Energy Technology

SP 9 4 5Summary. Dynamic two-fluid models have found a wide range of application in the simulation of two-phase-flow systems, particularly for the analysis of steam/water flow in the core of a nuclear reactor. Until quite recently, however, very few attempts have beenmade to use such models in the simulation of two-phase oil and gas flow in pipelines. This paper presents a dynamic two-fluid model,OLGA, in detail, stressing the basic equations and the two-fluid models applied. Predictions of steady-state pressure drop, liquid holdup, and flow-regime transitions are compared with data from the SINTEF Two-Phase Flow Laboratory and from the literature. Comparisons with evaluated field data are also presented.

Introduction

The development of the dynamic two-phase-flow model OLGAstarted as a project for Statoil to simulate slow transients associated with mass transport, rather than the fast pressure transients wellknown from the nuclear industry. Problems of interest included terrain slugging, pipeline startup and shut-in, variable production rates,and pigging. This implied simulations with time spans ranging fromhours to weeks in extreme cases. Thus, the numerical method applied would have to be stable for long timesteps and not restrictedby the velocity of sound.

A first version of OLGA based on this approach was workingin 1983, but the main development was carried out in a joint research program between the Inst. for Energy Technology ( FE) andSINTEF, supported by Conoco Norway, Esso Norge, Mobil Exploration Norway, Norsk Hydro A/S, Petro Canada, Saga Petroleum, Statoil, and Texaco Exploration Norway. In this project, theempirical basis of the model was extended and new applicationswere introduced. To a large extent, the present model is a productof this project.

Two-phase flow traditionally has been modeled by separate empirical correlations for volumetric gas fraction, pressure drop, andflow regimes, although these are physically interrelated. In recentyears, however, advanced dynamic nuclear reactor codes likeTRAC,l1 RELAP-5,2 and CATHARE3 have been developed andare based on a more unified approach to gas fraction and pressuredrop. Flow regimes, however, are still treated by separate flow

regime maps as functions of void fraction and mass flow only. Inthe OLGA approach, flow regimes are treated as an integral partof the two-fluid system.

The physical model of OLGA was originally based on smalldiameter data for low-pressure air/water flow. The 1983 data fromthe SINTEF Two-Phase Flow Laboratory showed that, while thebubble/slug flow regime was described adequately, the stratified/annular regime was not. In vertical annular flow, the predictedpressure drops were up to 50% too high (see Fig. 1). In horizontalflow, the predicted holdups were too high by a factor of two inextreme cases.

These discrepancies were explained by the neglect of a dropletfield, moving at approximately the gas velocity, in the early model.This regime, denoted stratified- or annular-mist flow, has been incorporated in OLGA 84 and later versions, where the liquid flowmay be in the form of a wall layer and a possible droplet flow inthe gas core.

This paper describes the basic features of this extended two-fluidmodel, emphasizing its differences with other known two-fluidmodels.

OLGA-The Extended Two·Fluld ModelPbysical Models. Separate continuity equations are applied for gas,liquid bulk, and liquid droplets, which may be coupled through interphasial mass transfer. Only two momentum equations are used,however: a combined equation for the gas and possible liquiddroplets and a separate one for the liquid film. A mixture energyconservation equation currently is applied.

Copyright 99 Society of Petroleum Engineers

SPE Production Engineering, May 99

Conservation of Mass. For the gas phase,

a 1 a-{VgPg)=- - - (AVgPgvg)+¥tg+Gg . . . . . . . . . . . . . . 1)at A oz

For the liquid phase at the wall,

a 1 a VL- ( V L P L ) = - - - ( AV L P LV L ) - ¥ t g ¥te+¥td+GLat A oz VL+V D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2)For liquid droplets,

a 1 a VD- ( V D P L ) = - - - ( AV D P LV D ) - ¥ t g +¥te-¥td+GDat A oz VL+VD

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3)

In Eqs. 1 through 3, Vg,VVVD=gas, liquid-film, and liquiddroplet volume fractions, p=density, v=velocity,p=pressure, andA = pipe cross-sectional area. ¥ g = mass-transfer rate between thephases, ¥te, ¥td=the entrainment and deposition rates, and Gf =possible mass source ofPhasef Subscripts g L i andD indicategas, liquid, interface, and droplets, respectively.

Conservation of Momentum. Conservation of momentum is expressed for three different fields, yielding the following separate

ID momentum equations for the gas, possible liquid droplets, andliquid bulk or film.For the gas phase,

a op) 1 a 1-(VgPgV g)= - Vg - - - - ( AV g P g Vi ) - A g - P g l v g I V gat oz A oz 2

g 1 Sjx A j P g l v r l v r +VgPgg cos a+¥tgva-F D 4)

4A 2 4A

For liquid droplets,

a op) 1 a 2-(VDPLVD)=-V D - - - - (AVDPLVD)+VDPLg cos aat oz A oz

VD-¥tg Va +¥teVj-¥tdVD+F D · (5)VL+V D

Eqs. 4 and 5 were combined to yield a combined momentum equa-tion, where the gas/droplet drag terms, FD cancel out:

a op) 1 a- V P v +VDPLvD)=-(V + V D) - - - - AV P v2at g g g g oz A oz g g g

2 1 g 1 Sj+ A VDPLvD - Ag - Pg Ivg Ivg - - A j Pg Ivrl v

2 4A 2 4AVL+ VgPg +VDPL)g cos a+¥tg v a + ¥ t ~ V i - ¥ t d v D(6)

VL+V D

7

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'E

:a .oL-

0

IIL-: JVIVI

IIL-a .

0II

+ -u0II

L-a..

1 0 4 ~ r ~

/

5 fo'-./

//

/

//

/

//

/

//

/

10 4

Measured pre ssure drop (N ~ )

FIg. 1 Predlcted pressure drops compared with SINTEF Two-Phase Flow Laboratory data. Annular·mlst diesel/nitrogenflow at 9 MPa vertical. • • original OLGA; X) OLGA Includ·Ing a droplet field.

For the liquid at the wall,

a a p ) 1 a- VLPLvL)=-V L - - - - AVLPLVl)at az Aaz

~ ~-1/Ig va-1/IeVj+1/IdvD-VLd(PL-Pg)g--s in a.

~ ~ •. . . . . . .• . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7)

In Eqs. 4 through 7, a = pipe inclination with the vertical andS , SL and Sj=wetted perimeters of the gas, liquid, and interface.t he internal source, Gf is assumed to enter at a 90° angle to thepipe wall, carrying no net momentum.

va=vL for 1/Ig>O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8a)

and evaporation from the liquid fllm),

va=vD for 1/Ig>O . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . 8b)

and evaporation from the liquid droplets),

and va=Vg for 1/Ig

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where E=internal energy per unit mass, h=elevation, H senthalpy from mass sources, and U=heat transfer from pipe walls.

Thermal Calculations . OLGA can simulate a pipeline with a totally insulated wall or with a wall composed of layers of differentthicknesses, heat capacities, and conductivities. The wall description may change along the pipeline to simulate, for instance, a wellsurrounded by rock of a certain vertical temperature profile, connected to a flowline with insulating materials and concrete coating, and an uninsulated riser.

OLGA computes the heat-transfer coefficient from the flowing

fluid to the internal pipe wall; the user specifies the heat-transfercoefficient on the outside. Circumferential symmetry is assumed;if this is broken, for example, with a partly buried pipe on the seabottom, average heat-transfer coefficients must be specified.

Special phenomena, such as the Joule-Thompson effect, are included, provided that the PVT package applied to generate the fluidproperty tables can describe such effects.

Ruid PropertUs and Phase Transfer. All fluid properties densities, compressibilities, viscosities, surface tension, enthalpies, heatcapacities, and thermal conductivities) are given as tables in pressure and temperature, and the actual values at a given point in timeand space are found by interpolating in these tables.

The tables are generated before OLGA is run by use of any fluidproperties package, based on a Peng-Robinson, Soave-RedlichKwong, or another equation of state, complying with the specifiedtable format.

The total mixture composition is assumed to be constant in timealong the pipeline, while the gas and liquid compositions changewith pressure and temperature as a result of interfacial mass transfer. In real systems, the velocity difference between the oil and gasphases may cause changes in the total composition of the mixture.This can be fully accounted for only in a compositional model.

Interfacial Mass Transfer. The applied interface mass-transfermodel can treat both normal condensation or evaporation and retrograde condensation, in which a heavy phase condenses from thegas phase as the pressure drops. Defining a gas mass fraction atequilibrium conditions as

Rs=mgl(mg+mL +mD), 17)

we may compute the mass-transfer rate as

t/lg=[(iJRs) iJp + iJRs) iJp iJziJp r iJt iJp r iJz iJt

+ iJRs) iJT + iJRs) iJT iJz ](m g+mL +mD) 18)iJT p iJt iJT p iJz iJt

The term iJRsliJp)T iJpliJt) represents the phase transfer froma mass present in a section owing to pressure change in that section. The term iJR/iJP)r iJpliJz) iJzliJt) represents the mass transfer caused by mass flowing from one section to the next. Becauseonly derivatives of Rs appear in Eq. 18, errors resulting from theassumption of constant composition are minimized.

Numer ical Solution Scheme. The physical problem, as formulated previously, yields a set of coupled first-order, nonlinear, ID

partial differential equations with rather complex coefficients. Thisnonlinearity means that no single numerical method is optimal fromall points of view. In fact, the codes TRAC,l RELAP, 2CATHARE,3 and OLGA all use different solution schemes. Details are presented elsewhere. 4

Most two-fluid models, including those listed above, apply fmitedifference staggered mesh, donor cell methods. In explicit integration methods, the timestep, ilt, is limited by the Courant FriedrichLevy criterion based on the speed of sound:

ilt:sminVj{Jlzj/Ivfj ±cf j }. . . . . . . . . . . . . . . . . . . . . . . . . 19)Implicit methods are not limited by Eq. 19, but for dynamic prob

lems a mass-transport criterion applies:

Jlt:Sminvj{Jlzj/lvfj }. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20)


Strutified nnular.• "0· :. ... . .. .2..

Slugl Bubble

v

Fig. 2 Schematlc of stratified annular mist and slug flow.

Because the speed of sound typically is about 10 2 to 10 3 timeslarger than the average phase velocities, explicit integration methodsrequire timesteps up to 10 3 times smaller than implicit methods.

Traditionally, most nuclear reactor safety analysis codes e.g.,NORA5) applied explicit methods because they are simpler to formulate and code, and the time scales of interest for typical problems pressure transients) were given by the speed of sound. Becauseof stability problems, however, and the need to simulate slow, smallbreaks, implicit methods are now favored.

Flow Regime escriptionThe friction factors and wetted perimeters depend on flow regime.Two basic flow-regime classes are applied: distributed, which contains bubble and slug flow, and separated, which contains stratifiedand annular-mist flow. Because OLGA is a unified model, it doesnot require separate user-specified correlations for liquid holdup,etc. Thus, for each pipeline section, a dynamic flow-regime prediction is required, yielding the correct flow regime as a functionof average flow parameters.

Separated Flow. Stratified- and annular-mist flows are characterized by the two phases moving separately Fig. 2). The phase distributions across the respective phase areas are assumed constant.The distribution slip ratio, RD in Eq. 9 then becomes 1.0. Thetransition between stratified and annular flow is based on the wetted perimeter of the liquid film; annular flow results when thisperimeter becomes equal to the film inner circumference.

Stratified flow may be either smooth or wavy. An expression forthe average wave height, hw, may be obtained by assuming thatthe mass flow forces in the gas balance the gravitational and surface tension forces, or

(lI2)P g Vg -VL)2=h w PL -Pg)g sin ex+(u/hw) . . . . . . . . . 21)

1 [ piVg-VL)2orh =

w 2 2(PL -Pg)g sin ex

4u } 22)PL -Pg)g sin ex

When the expression in the square root is negative, hw is zero andstratified smooth flow is obtained.

The onset of waves starts with capillary waves with wavelengthsof about 2 to 3 mm. As the mass-flow forces increase, surface tension becomes negligible and gravity dominates, resulting in longerwavelengths. For air/water pipe flow at 1 bar, the onset of2D wavescorresponds very well with the data of Andreussi and Persen 6Fig. 3).

Friction Factors. The applied wall friction factors for gas andliquid are those of either turbulent or laminar flow in practice, themaximum one is chosen), given as

[2 X 1 4 ~106 v,]

A1 =0.0055 1 . . . . . . . . . . . . . . . . 23)d h N Re

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400

200

zi 'e100~ ~

40

20

Val =0.028 m/sec ®o Andreussi Persen'®OLGA

1 0 ~ ~ ~ ~ ~ ~ ~ ~100

Vog (m/sec)

Fig. 3 Presaure gradient at the transition to 20 wavesIlLL = .001 kg/( sec' m), a =- 0.65°].

and At= 64/N Re , • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • (24)

where e=absolute pipe roughness and dh=hydraulic diameter.For stratified-mist flow, the wall liquid fraction, wetted

perimeters, and other flow parameters are defined by the wettedangle, 3, as indicated in Fig. 2.

Wallis 7 proposed the following equation for interfacial frictionin annular flow:

Ai =0.02[1 +75(1- Vg ] • • • • • • • • • • • • • • • • • • • • • • (25)

which has been applied for vertical flow. For inclined pipes, Eq.26 is used for annular-mist flow:

Ai=O.02 1+KV L , (26)

where is an empirically determined coefficient of the form

K=K[ [g(PL p g ] J. . . . . . . . . . . . . . . . . . . . . . . . . . (27)

For stratified smooth flow, the standard friction factors with zeropipe roughness are used; for wavy flow, the minimum value of Eq.26 and

Aj=hw/d hj (28)

are used because Eq. 26 is assumed to yield an upper limit for wavyflow. Eq. 28 then provides an improved description in the regionfrom smooth flow to higher velocities, where Eq. 26 applies.

Entrainment/Deposition. A droplet field was not incorporatedinto the original version of OLGA. Compared with the SINTEF

Two-Phase Flow Laboratory data, the predicted pressure drops invertical annular flow were up to 50 too high (Fig. 1). In horizontalflow, the pressure drop was well predicted, but the liquid holdupwas too high by a factor of two in extreme cases.

For droplet deposition, the following equation for vertical flowmay be obtained from Andreussi's8 data:

1 / t d = ~VDPL2.3XlO_4 PL)0.8 1+ 1 ) (29)d Vg Pg O.I+vsL

For inclined pipes another, extended correlation is applied.A modified expression is proposed for liquid entrainment based

on that of Dallman et al. 9 for vertical flow and Laurinat et al. 10for horizontal flow.

174

0 . 8 . ~ ~ r r ~ ~ r ~ ~

a.:>IC

'0.c

C

':;. : '

0.6

0.4

0.2

~ _ _ L __ L __ L _ _ _ _ _ _ _ _ L __

o 0.2 0.4 0.6 0.8Measured liqu id hold - up

Fig. 4 Comparlson between measured and predicted liquidholdup [diesel and nitrogen horizontal stratified flow at3 x 10 8 Pa and 30°C; X) OLGA].

Distributed Flow. As Malnes 11 showed, in the general bubbleor slug-flow case, the average phase velocities satisfy the following slip relation:

vg=RD VL+v r , • • • • • • • • • • • • • • • • • • • • • • • • • • • • • (30)

where vr and RD are determined from continuity requirements. ForVgs=O, Eq. 30 reduces to the general expression for pure slugflow:

Vg [ V b ]vg= (lIC

o) - Vg vL+ C

o l - V

g) (31)

For fully developed turbulent slug flow with sufficiently largeslug lengths ~ lOD), Bendiksen 12 showed that the velocity of slug(or Taylor) bubbles, Vb, may be approximated for all inclinationsby

VB=CO VsL+Vsg)+VOb, . . . . . . . . . . . . . . . . . . . . . . . . . . . . (32)

_ [ 1.05+0.15 cos 2 a for N Fr 3.5

_ [ vov cos a+vOH sin a for N Fr < 3.5and vOb- , . . . . . . . . (34)

vov cos a for N Fr > 3.5

where vov and vOH are the bubble velocities in stagnant liquid (neglecting surface tension) in vertical and horizontal pipes, respectively:

vov=0.35.Jgd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (35)and vOH=0.54.Jgd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (36)

For pure bubble flow, Eq. 30 reduces to

Vg=R VL+VOS) , • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • (37)where R= (1 - Vg)/(K - Vgs) . . . . . . . . . . . . . . . . . . . . . . . . . . 38)

and = Co is a distribution parameter.Malnes 13 gives the average bubble-rise velocity as

[gC1 PL-P ) ] 4

vos=1.18 p i g [(1-Vg)lcos a l ~ 39)

with positive values upward.


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4.0

]

- - l i n e s of constant ap/az 9 o Stratified flowx Slug flowV Annular flowI:. Dispersed flow

Superficial gas velocity Imlsl

FIg. S-Pr essure gradient - - -) and slug-flow boundaries compared with OLGA predictions -ClpIClz: - - slug-flow boundaries) for horizontal flow. (Diesel and nitrogen at 3 MPa and30°C.)

Using Gregory and Scott s14 data, Malnes ll proposed the following equation for the void fraction in liquid slugs:

Vsg VsLVgs= , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (40)C Vsg VsL

where C is a constant detennined empirically and the void fractionis limited upward.

This correlation (Eq. 40) is applied for small-scale systems only.For high-pressure, large-diameter pipes, another set of empiricalcorrelations based on the data from the SINTEF Two-Phase FlowLaboratory was used.

The total pressure drop in slug flow consists of three terms:

iJzliJp)= lIL) i1ps +i1pb +i1pac), . . . . . . . . . . . . . . . . . . . (41)

where i1ps=frictional pressure drop in the liquid slug, i1pb=frictional pressure drop across the slug bubble, and i1pac=acceler-

400

- E- c 1N-0 . 0

Val =0.0083 m/sa =0·

II

I

/ 0

I,

10

Ii>,

r f

20Vog (mi.)

I

0.10

0.05

30

Fig. 7-Comparlsons of pressure and liquid holdup-OLGApredictions ( - ) and Crouzler's measurements (10 = .045 m:• stretlfled pressure drop: • slug pressure drop; 0 stratified holdup; t. slug holdup).


>- ::uo. . JW>o:::Jo:::;

. . J<Uu:Q:

wa:::JCf)

2 0 r - - - - - r - - - - - -- - - - - - - - - - - - -. - - - - - - - - -

1 0 r - - - ~ - - - - - - - - - - - - - - ~ ~ - - - r

0 11 - ~ - - - _ _ n_ _ +_, .... w-+, . tT- - - -____1___t

00

o 0 0 2 0 ' - : . 0 ~ 2 - - - - : 0 : L . l : - - - - - - - - ~ - - - - . l L . . . - - ; 1 0 : - - - lSUPERFICIAL GAS VELOCITY m s)

Fig. 6-Flow-reglme transitions from Ref. 17 compared withOLGA [2° upward InClination, 2.5-cm 10: -) OLGA flowregime transition].

ation pressure drop required to accelerate the liquid under the slugbubble, with velocity vLb up to the liquid velocity in the slug, vLSi1pac=O at present). L is the total length of the slug and bubble.

These terms are dependent on the slug fraction, the slug bubblevoid fraction, and the fIlm velocity under the slug bubble. The voidfraction in the slug bubble, Vgb, is obtained by treating the flowin the fIlm under the slug bubble as stratified or annular flow. Thisis further described by Malnes, 11 who gives additional equations.For slug flow, the wall friction terms will be more complicatedthan shown in Eqs. 6 and 7 because liquid friction will be dependent on g and the gas friction on vL

Flow-Regime Transitions. As stated, the friction factors and wetted perimeters are dependent on flow regime. The transition be-

Val = 0.0083 m/s

a = 1 15° I,,400 • , 0.20

II

II- , 0 15300E I- IZ I 0, I,c IN

I 100 - 0 200 II

II

0I/ 0.05/

0

~ ~ ~_____

~_____

~ ~o 10 20 30

Vog mi.)

Fig. a-Comparisons of pressure and liquid holdup-OLGApredictions ( - ) and Crouzler's measurements (10 = .045 m;• stretlfled pressure drop: • slug pressure drop: 0 stretlfled holdup; t . slug holdup).

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E

- 0 1N-0 -0

400

200

100

oo

•

V. L =0.0083 m s

a =2.86-

I1

I

0 /0,.

o

10 20V , (m/s)

II

I

00.20

II

I1

I0.15

I

0, . ;I II - 0.10

0.05

•30

Fig. 9-Comparlsons of pre88ure and liquid holdup-OLGApredictions - ) and Crouzler's measurements 10 = .045 m;• stra tified pre88ure drop; A slug pre88ure drop; 0 stratified holdup; I:: slug holdup).

tween the distributed and separated flow-regime classes is basedon the assumption of continuous average void fraction and is determined according to a minimum-slip concept. That is, the flow regime yielding the minimum gas velocity is chosen. Wallis 15

empirically found a similar criterion to describe the transition fromannular to slu g flow very well. This criterion covers the transitionsfrom stratified to bubble flow, stratified to slug flow, annular toslug flow, and annular to bubble flow.

In distributed flow, bubble flow is obtained continuously whenall the gas is carried by the liquid slugs (when the slug fraction,F

s approaches unity). This occurs when the void fraction in the

liquid slug, VgS becomes larger than the average void fraction, Vg •The stratified-to-annular flow transition is obtained when the wave

height, hw (Eq. 22) reaches the top of the tube (or SL =71-D).

Comparison With Steady Stat Experiments

OLGA has been compared with data from different experimentalfacilities, covering a wide range of geometrical sizes, fluid types,pressure levels, and pipe inclinations. The bulk of the data was obtained from experiments at the SINTEF Two-Phase Flow Laboratory. These unique data have increased our confidence in the appliedtwo-phase models. A detailed description of the experimental facilities is presented in Bendiksen et al 16

Fig. 4 (from Ref. 16) compares predicted and measured holdupfor stratified flow for diesel and nitrogen at 3 x 10 6 Pa and 30°C.The predictions are generally within ± 10 %

Fig. 5 compares OLGA-predicted pressure gradients and slugflow boundaries with data from the SINTEF Two -Phase Flow Laboratory. The predictions are quite good, although the pressure dropin the aerated slugs is somewhat low.

Barnea et al 17 measured flow patterns for air/water flow inhorizontal and inclined tubes at near-atmospheric conditions for1.95- and 2.55-cm diameters. Fig. 6 shows a typical example ofpredicted flow regime transitions compared with the experimental

flow map for + r inclinationCrouzier 18 measured pressure drop and holdup in horizontal andupwardly inclined pipes for air/water at near-atmospheric pressuresin a 4.5-cm tube.

In Figs. 7 through 9, OLGA predictions are compared to Crouzier s data. The calculated and measured pressure drop and holdup generally agree quite well, considering the spread in data. Theflow-regime transitions are observed when the holdup calculationsfor slug flow cross the predictions from stratified/annular mist. Theregime with minimum holdup is that predicted by OLGA, and theagreement is quite good.

The pressure drop from sluglbubble to stratified-/annular-mistflow experiences a discontinuity at upsloping angles, which is justified partly by the experiments.

omparison With Dynamic ExperimentsThe OLGA model has been compared with data from two different types of experimental setups. Schmidt et al 19 performed experiments at laboratory conditions with a pipeline ID of 5.08 cmat atmospheric pressure. The SINTEF Two-Phase Flow Laboratory has be en producing data for gas and oil in 19-cm-1D pipes withtotal lengths of 450 m at pressures up to 10 MPa (Fig. 10).

Terrain-Slugging Data. Terrain slugging is a transient flow typeassociated with low flow rates. It may, for instance, be observedin pipelines where a downsloping pipe terminates in a riser. Theslugging is initiated by liquid accumulating at the low point. Refs.19 and 20 give more detailed descriptions of the phenomenon.

SINT F Two-Phase Row Laboratory Data. The test section ofthe SINTEF laboratory is sketched in Fig. 10; further details aregiven in Refs. 16 and 21. In the reported experiments, the fluids

applied were diesel oil and nitrogen.One terrain-slugging flow map obtained with OLGA is shown

in Fig. 11 for a system pressure of 3 MPa. The agreement withthe experimental map is quite good, although the OLGA predictions are somewhat conservative for low liquid superficial velocities. Note that OLGA can properly distinguish between the two typesof terrain slugging (1, II) with or without aerated slugs.

Data o f Schmidt et aI This nitrogen/kerosene low-pressure loopincluded a nearly horizontal pipe and a vertical riser test sectionof 30- and 15-m lengths, respectively, and 5-cm diameters. Schmidtet al. 's19 test matrix was reproduced for downsloping pipes, particularly for - 5 ° inclination. The results are shown in Fig. 12,where the solid lines are the results of the OLGA simulations. Fig.

Mixingpoint Pressure reference (ine

176

1 •334m

Fig. 10-Plpe geometry of the SINTEF Two-Phase Flow Laboratory (1983) . single-beamdensitometer; • differentia l pressure transmitter).

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3.0

AI xo Terrain slugging I

E 2.5 t: TerrQin slugging I I>-

-- x No terrQin slugging-g -2.0 0 8,xii> t: '4x0 x:; 1.5 ,

.20 A i

1:1 \·u 1.0 i J X00- I..8. X I::I 0.5 '/)

)So ........

x

00 3.0

SuperficiQI gQS velocity m/s)

FIg. 11-Terraln-slugglng flow map from the SINTEF TwoPhase Flow Laboratory. TerraIn sluggIng I -) and II (- --)boundarIes predIcted by OLGA.

~z.....to

. 0E::Ic:::

>-:t:u0

>I I::I.Il

1 ~ ~ ~

10

• SEVERE SlUGGING 1o SEVERE SLUGGING11A TRANS TO SLUGGING

CJ 0CJ CJ

0. +

+ +++ . . . . .

Il. + + M

+ M M M M

Ga. velocity number, N .

FIg. 12-Rlser flow-pattern map wIth - 5° pIpeline InclinatIon 18 ( - OLGA predIctIons).

13 compares experimental and predicted pressure oscillations in

the horizontal line and at the bottom of the riser for one particularexperiment.

Transient Inlet-Flow Data. The dynamic experiments in the SINTEF laboratory with time-dependent inlet flow rates were performedwith a completely horizontal flowline terminating into the riser22(see Fig. 14). The fluids were naphtha and nitrogen. The inlet liquid superficial velocity was kept constant at 1.08 mis while thesuperficial gas velocity was increased from 1.0 to about 4.2 mlsin a period of 20 seconds (Fig. 15).

The increase in the gas flow rate results in a decrease in the liquid holdUp. This discontinuity in liquid holdup tends to be smearedout and broken up into slugs as it travels along the pipeline. TheOLGA model applies a mean-slug-flow description but clearly is


N 240E

' 0 210 , .,I

X /Ia.. 180

I,I

llJ Ia:: I

=>I

I/) 150 I( / ) IllJ

I,a:: Ia.. 120

380 400

225NE

'0)

a

llJa::=>(J)(J )wa::a..

75300

FIg. 13-Pressure oscillatIons of severe sluggIng 19 for flowrates-N I = 1.5 and N o = 3.6, the upper In the horIzontalline and the lower In the rIser (- - • experImental values; -OLGA; _. OLGA predIctIon wIth refined mesh).

able to simulate the time evolution of holdup and the pressureresponse to the inlet conditions (Figs. 16 through 20). The predicted time response is good, but slightly too slow.

Excerpts of Comparisons gainst Field ataTo test the extrapolation capabilities of OLGA, a separate studywas performed, comparing this model with evaluated field data. 4The results of one of these studies, the Vic Bilh-Lacq oil/associatedgas line, are presented here. This is an onshore field of relativelyheavy crude in southwestern France.

The pipeline is 43.8 km long and has a 25 .1-cm ID, and an absolute roughness of 0.03 mm. Flow conditions are characterizedby low superficial liquid velocities of about 0.17 mls and superficial gas velocities ranging from 0.02 to 0.4 mls. See Refs. 23 and24 for further details. The inclines are very steep, resulting in upsloping sections almost filled with oil and downsloping ones nearly filled with gas. Because of the very low velocities, the pressuredrop is dominated by gravity in the upsloping parts, with a slightrecovery in the downsloping parts.

Pressure-drop data are reported along the pipeline at four locations for a pressure at Lacq of 1.7 MPa and a flow rate of 700m 3 /d, which has been assumed to represent a total mass flow of7.28 kg/so In Table 1, the results from OLGA (Version 87.0) and

177

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( I --457Distance frommixing point

Aprml 4 --4290 10 49 13 178 299 328I I I I I I II I I I I : '-:J ~ 0 7- -

l

Ap

Fig. 1 4 - Test section of the SINTEF Two·Phase Flow Laboratory for the dynamic Inlet ex·perlments ( . liquid holdup measurements; A absolute pressure recordings .

:2:::: :::00 620 6'1> 660 68 700

TIME IS

Fig. 15-Superflclal-gas-veloclty recordings for the dynamicInlet·f low experiments at the SINTEF Two-Phase Flow Laboratory -appl ied In OLGA .

i 1 ; ~ ~ S ; ; ~0.1 L - - - L _ L - - - - _ - - - - - - - - - - - - - - - _ - - - - - _ - - L - - - l

580 600 620 640 660 680 700TIME IS)

; : f : ~ : S q ; , ; d580 600 620 640 660 680 700

TIME 151

1.2

1:>

0:I:

Q::>0::; 02

058 600 620 640 660 680 700

TIME lSI

Fig. 16-l .lquld· holdup recordings In the horizontal comparedwith OLGA( - ) at locations 49, 178, and 299 m from the mix·Ing point.

the steady-state model PEPITE23 are compared with the measuredvalues using the terrain profJIe reported by Lagiere et al 3

The pressure drop calculated by OLGA is 15 % too low, whereasthe reported PEPITE calculations are extremely good. To checkthe input data, an available PEPITE version was run with the sameinput data used in OLGA. As can be seen from Table I, the pres-

178

l i ~ E ~ "80 600 620 64 660 680 700

TIME IS I

i { l ~ ~ ~ ~80 600 620 640 660 680 7

TIME 151

Fig. 17 L1quld·holdup racordlngs In the riser compared withOLGA ( - ) at locations 7 and 29 m from the riser bottom.

i t l ~ l j ~~ , , . , . ~6 3 . 0 - - - - - - - - - - - - - - --..1 --..1 -..1500 550 600 650 700 750 800

TIME lSI

Fig. 18-Absolute pressure recorded 10 m from the mixingpoint compared with OLGA ( - ) .

sure drop from PEPITE is even lower than the OLGA values, or28 too low.

The discrepancies were found to result from the terrain profIlereported by Lagiere et al being too coarse. Table 2 shows new,substantially improved results from OLGA based on a more detailed pipeline profIle obtained from TOTAL.

onclusions

The OLGA model was presented, with emphasis on the particulartwo-fluid model applied and the flow-regime description. The importance of including a separate droplet field was discussed. Neglecting the droplet field in vertical annular flow was shown tooverpredict pressure by 50% in typical cases.

Closure laws are still, at best, semimechanistic and require experimental verification.

The OLGA model has been tested against experimental data overa substantial range in geometrical scale (diameters from 2.5 to 20cm, some at 76 em; pipeline length/diameter ratios up to 5,000;


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500 550 600 650 700 750 800TIME 51

Fig. 19-Pressure difference over a part of the horizontal linecompared with OLGA - ) .

and pipe inclinations of -15 to +90° , pressures from 1 kPato 1 MPa, and a variety of different fluids.

The model gives reasonable results compared with transient datain most cases. The predicted flow maps and the frequencies ofterrain slugging compare very favorably with experiments.

The model was also tested on a number of different oil and gasfield lines. The OLGA predictions are generally in good agreementwith the measurements. The Vic Bilh-Lacq oil/associated-gas linewas a good test case because of the extremely hilly terrain and lowflow rates, which imply that, to obtain a correct pressure drop, theliquid holdup prediction must be very accurate. The pressure droppredicted by OLGA was 6.85 MPa compared with a measured drop

of 6.8 MPa.The actual number of available field lines where the fluid composition and line profIle are sufficiently well documented for ameaningful comparison is, however, stilllirnited. Further verification of this type of two-phase flow models is clearly needed.

omenclature

A = pipe cross-sectional area, m 2c = speed of sound, mlsC = constant

Co = distribution slip parameterd = diameter, mE = internal energy per unit mass, J kg

FD = drag force, N/ m 3Fs = slug fraction, Ls/ LB+Ls)

g = gravitational constant, mls 2G = mass source, kg/s·m 3h = height, m

hf = average fIlm thickness, mH = enthalpy, J/kg

Hs = enthalpy from mass sources, J/kgK = coefficient, distribution slip parameterL = length, m

mD = VDPL kg/m3mg = VgP g , kg/m3mL = VLPL kg/m3

N = numberN Fr = Froude numberN Re = Reynolds number

p = pressure, N/ m2

IIp = pressure drop, N/m 2

45.0.35.

oS 30. 0.8 25.

20.15.10.

500 550 600 750 800TIME 51

Fig. 2 0 - The pressure difference over the riser compared with

OGLA -) the pressure difference Is recalculated as equivalent liquid height .

R = slip ratioRD = distribution slip ratioRs = gas/oil mass ratio

S = perimeter, mSf = wetted perimeter, Phase J, m

t = time, secondsJ.t = timestep, secondsT = temperature, °CU = heat transfer per unit volume, J/m 3v = velocity, m s

Vb = velocity of large slug bubble, m sVF = volumetric fractions F=g, L, D)

z = length coordinate, mJ.z = mesh size, ma = angle with gravity vector, rad3 = angle, rade = absolute roughness, mA = friction coefficientp. = viscosity, kg/m sP = density, kg/m3q = surface tension, N/mif; = mass-transfer term, kg/m 3 . s

Subscriptsac = acceleration

b = bubbled = droplet deposition

D = droplete = droplet entrainmentf = Phase f G,L,D)F = frictiong = gash = hydraulicH = horizontalhi = hydraulic, interfacial

i = interfacial£ = laminar

L = liquidr = relatives = superficialS = slugt = turbulent

V = verticalw = wave

TABLE 1-COMPARISON OF MEASURED AND PREDICTED PRESSURE DROPSON THE VIC BILH-LACQ PIPELINE·

Length Measurement PEPITE OLGASection km) bar) Reported bar) Actual bar) bar)

ic Bilh-Claracq 8.7 18 16.9 15.5 17.7Claracq-Morlanne 21.1 31 30.9 22.0 24.4Morlanne-Lacq 14.0 19 18.4 12.7 15.9Vic Bilh-Lacq 43.8 68 66.2 50.2 58.0

·Terrain profile from Laglere et 81 23

SPE Production Engineering, May 1991 179

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Authors

K.H. Bencllksen Ishead of the Dept.for Fluid Flow andGas Technology atIFE at Kjeller, Nor·way. He holds anMS degree In physIcs and a PhDdegree In fluid

mechanics fromthe U. of Oslo,Maines Bendlksen where he Is also a

professor of applied fluid mechanIcs. His technicalInterests Includeresearch, development, and promotion of multlphaset r anspor t a t iontechnology In theoffshore 11 and gasIndustry. He hasbeen In charge of

Moe Nuland the OLGA devel-opment project

since Its start In 1980. D••

Maine., a senior research scientist at IFE has been working with two-phase flow, heat transfer, and dynamic simulation for 30 years. He holds MS andDr. Ing. degrees In mechanical engineering from the Norwegian Inst. of Technology. Randl Moe Is a senior physicistat IFE, working on physical and numerical modeling of multlphase flow. She holds an MS degree In fluid flow from theU. of Oslo. Sven Nuland Is chief engineer at IFE where heIs working on multlphase flow problems, both experimentsand modeling. He has been working on the OLGA projectsince 1980. He holds an MS degree from the U. of Oslo.

W = wallo = relative zero liquid flow at infInity

Reference1. TRAC-PFI An Advanced Best Estimate Computer Program for Pres

surized Water Reactor Analysis NUREG/CR-3567, LA-994-MS (Feb.1984).

2 RELAP51MODI Code Manual Volume 1: System Models and Numerical Methods NUREG/CR-1826, EGG-2070 (March 1982).

3. Micaelli, J.C.: 1987 CATHARE an Advanced Best-Estimate CodeforPWR Safety Analysis SEThiLEML-EM/87-58.

4. Bendiksen, K., Espedai, M., and Maines, D.: Physical and Numerical Simulation of Dynamic Two-Phase Flow in Pipelines with Application to Existing Oil-Gas Field Lines, paper presented at the 1988Conference on Multiphase Flow in Industrial Plants, Bologna, Sept .27-29.

5. Maines, D., Rasmussen, J. , and Rasmussen, L. : A SOOrt Descriptiono the Blowdown Program NORA SD-129, IFE, Kjeller (1972).

6. Andreussi, P. and Persen, L.N.: Stratified Gas-Liquid Flow in Down-wardly Inclined Pipes, Inti. 1 Multiphase Flow (1987) 13, 565-75.

7. Wallis, G.B.: Annular Two-Phase Flow, Part I: A Simple Theory,1 Basic Eng. (1970) 59.8 . Andreussi, P.: Droplet Transfer in Two-Phase Annular FloW, Inti.

1. Multiphase Flow (1983) 9, No.6, 697-713.9. Dalhnan, J.C., Barclay, G.J., and Hanratty, T.J.: Interpretation of

Entrainments in Annular Gas-Liquid Flows, Two-Phase MomentumHeat and Mass Transfer F. Durst, G.V. Tsildauri, and N .H. Afgan(eds.) .

180

TABLE 2-COMPARISON OF MEASURED AND PREDICTEDPRESSURE DROPS ON THE VIC BILH-LACQ PIPELINE

WITH NEW PROFILE

Length Measurement OLGASection km) bar) bar)

Vic Bilh-Claracq 8.7 18 18.6Claracq-Morlanne 21.1 31 32.4Morlanne-Lacq 14.0 19 17.5Vic Bilh-Lacq 43.8 68 68.5

10 . Laurinat, J.E., Hanratty, T.J., and Dallman, J.C.: Pressure Dropsand Film Height Measurements for Annular Gas-Liquid Flow, Inti .1 Multiphase Flow (1984) 10, No.3, 341-56.

11. Maines, D.: Slug Flow in Vertical Horizontal and Inclined PipesIFEIKRIE-83/002 (1983).

12. Bendiksen, K.H.: An Experimental Investigation of he Motion of LongBubbles in Inclined Tubes, Inti. 1 Multiphase Flow (1984) 10, No.4,467-83.

13. Maines, D.: Slip Relations and Momentum Equations in Two-PhaseFlow, IFE Report EST-I, Kjeller (1979).

14 . Gregory, G.A. and Scott, D.S.: Correlation of Liquid Slug Velocityand Frequency in Horizontal Co-Current Gas-Liquid Slug Flow, AlChE.1. (1969) 15, No.6, 933.

15 . Wallis, G.B.: One-Dimensional Two-Phase Flow McGraw Hill BookCo. Inc., New York City (1969).

16. Bendiksen, K. et aI. : Two-Phase Flow Research at SINTEF and IFE.

Some Experimental Results and a Demonstration of the Dynamic TwoPhase Flow Simulator OLGA, paper presented at the 1986 OffshoreNorthern Seas Conference , Stavanger .

17. Bamea, D. et al.: Flow Pattern Transition for Gas-Liquid Flow inHorizontal and Inclined Pipes, IntI. 1 Multiphase Flow (1980) 6,217-26.

18. Crouzier, 0.: Ecoulements diphasiques gaz-liquides dans les conduitesfaiblement inclinees par rapport a I'horizo ntale , MS thesis, I'Universit6 Pierre et Marie Curie, Paris (1978).

19. Schmidt, Z., Brill, J.P., and Beggs, H.D.: Experimental Study ofSevere Slugging in Two-Phase-Flow Pipeline-Riser System, SPEI (Oct.1980) 407-14.

20. Bendiksen, K., Maines, D., and Nuland, S.: Severe Slugging in TwoPhase Flow Systems, paper presented at the third Lecture Series onTwo-Phase Flow , Trondheim , IFE Report KRIE-6, Kjeller (1982).

21. Norris, L. etal : Developments in the Simulation and Design of Multiphase Pipeline Syst ems, paper SPE 14283 presented at the 1985 SPE

Annual Technical Conference and Exhibition, Las Vegas, Sept. 22-25.22. Linga, H. and 0stvang, D . : Tabulated Data From Transient Experi

ments With Naphtha, SINTEFIIFE project, Report No. 41 (Feb. 1985).23. Lagiere, M., Miniscloux, C., and Roux, A.: Computer Two-Phase

Row Model Predicts Pipeline Pressure and Temperature Profiles, Oiland Gas 1 (April 1984) 82-92.

24. Corteville, J. , Lagiere, M., and Roux, A. : Designing and OperatingTwo-Phase Oil and Gas PipeIines, Proc. 11th World Pet. Cong., London (1983) SP 10.

81 Metric Conversion Factorsbar x 1.0* E+05bbl x 1.589 873 E-Ol

ft x 3.048* E-Olft2 x 9.290 304 E-02ft3 x 2.831 685 E-02OF OF-32)/1.8in. x 2.54*lbf x 4.448222

Ibm x 4.535 924

·Converslon factor is exact.

E+OOE+OOE-Ol

Pam3mm2m3

°CemNkg

SPEPEOriginal SPE manuscript received fo r review Jan . 4, 1989 . Paper (SPE 19451) acceptedfor publication Dec . 11,1990 . Revised manuscript received April 30, 1990.


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Bendik Sen 1991