SPE 28545

TACITE: A Transient Tool for Multiphase Pipeline andWell SimulationC.L. Pauchon, Inst. Franqais du P&role; Hasmuekh Dhulesia, TOTAL; Georges Binh Cirlot,Elf Aquitaine Production; and Jean Fabre, Inst. de Mecanique des Fluides

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Abstract

The paper presents the principal characteristics of theTACITE code which has been developed to simulatetransient and, steady state multiphase flows, for thedesign and control of oil and gas production networks.

The hydraulic model is presented briefly and theresulting flow regime prediction is compared with

experimental data. The performance of the code isillustrated with respect to steady state and transientexperimental and field data.

1 Introduction

In the design of multiphase pipeline networks it is-- Am+; ?,l tfi knnwV*S-IILI-I ..- ,., ,-.. the anticipated pressure,

temperature and gas and liquid flow rates at differentpoints in the network, and in particular at chokes,valves, pumps, compressors and other equipments.

During transient flow it is important to anticipate thevolume of slugs that can arrive at separators, so that

the latter can be scaled accordingly.

n

The ~Pera!ien and contro! of multiDhase networks also

require tools allowing flow characteristics to bepredicted so that the network can be made to operateunder optimal conditions.

In order to attain these objectives the TACITE code wasdesigned with the following characteristics:

a hydraulic model representative of the phenomenathat control the flow regime, pressure drop and liquidholdup,

a reliable thermal model to allow for the calculationof the heat transfer at the wall,

a precise thermodynamic model to describe thethermodynamic state of the system and to calculate thefluid physical properties,

a set of transport equations to describe continuityand the propagation density anti pressure ‘wsies in !hesystem,- a precise and robust scheme with good front trackingcapabilities.

The development of TACITE results from the

cooperation between the INSTITUT FRANCAIS DU

PETROLE (IFP), TOTAL and ELF AQUITAINE within the

311

2 TACITJ2 SPE 28545A TR4NSIENT TOOL FOR PIPELINE AND WELL SIMULATION

EvE association. It is developed with the assistance of

the “Institut de Mdcanique des Fluides de Touiouse”

(!MFT) b:~~= Rh., #simal

r’ IJUIW-Imn..k.llinn, ,,””-,8 . m~ gfl~ !~~ “Fenlab“”. -

Normale Sup6rieure de Lyon” (ENSL) for the numerical

scheme. IFP is in charge of the integration of these

aspects into an industrial code which is validated by

ELF AQUITAINE and TOTAL

The TACITE code is based on the numerical resolution ofa drift-flux type model applying to any situationencountered in multiphase production with respect toslope, fluid properties and flow pattern. The modelsolves a set of four conservation equations (seereference 1), one for the mass of each phase, one forthe mixture momentum and one for the mixture energy.The missing information about the slip between phasesis restored by a steady state closure relationshipdepending on the flow regime. In order to identify theregimes, the assumption is made that each regime is aspace/time combination of two basic patterns:separated flow (stratified and annular) and dispersedflow (reference 2). The intermittent flow regime isconsidered as a combination of these two basic

patterns, characterised by the fraction of separatedflow p which ensures the continuity of the closure

laws.

The transient resolution is achieved by an explicitsecond order finite volume method. The advantages ofthis method are: its ability to follow wave frontpropagation ; an easy implementation for the resolutionof complex networks and an easy maintenance of thecode in view of future evolutions of the physical modeland the numerical resolution algorithms. Theperformance of the numerical scheme and in particular,it’s ability to follow holdup waves, are illustrated inthis paper.

One of the main objectives of TACITE is to predictaccurately the propagation of large liquid slugs. Thus,an accurate numerical scheme with good shockpreserving capabilities was proposed (reference 3) andimproved (reference 4). The time advancing scheme is---1.-:. .....I.UXPIiWL WILII ~ee~tid ~i(hi au~wu~y Ill wrJw a w S~C~--- . .. . . .. :- *:-A ,. -,4

to limit numerical diffusion. The choice of an explicitscheme presents several advantages which areidentified in this paper.

The determination of physical properties has also beengiven special attention. A thermodynamic package isking deveiop~, .Which ~~e5 ifiie ~eeeuni the ~resen~

of water, glycol, methanol and dissolved salts.

In the present paper,hydrodynamic model in

we give an overview on theTACITE including the transport

equations, closure laws and solution algorithm withemphasis on the flow regime prediction. The flowregime prediction of TACITE is compared with

experimental data for various slopes and pressures.

The time advancing scheme is described. The numericalscheme for regular points and boundary points isctescribed. -------The iRVA6ifii r-~pu[l~u ~f ih~ cede is

demonstrated on the basis of several examples.

2 Hydrodynamic model

In this section, we present the set of transport andclosure equations and we discuss the concept of flowregime transition which is used. The originality of thehydraulic model lies on:

● the set of transport equations which ensuresthe continuity of the model actoss flowregime transitions,

● the choice of a limited set of closure laws,continuous with respect to slope and fluidproperties, which have been qualified againstexperimental results,

● the concept of flow pattern transitions basedon the continuity of the calculated variables.

2.1 Transport equations

The TACITE modei is a drift fiux type modei with onemass consewation equation for each phase (Eqs. 1&2),one mixture momentum equation (Eq. 3) and onemixture energy equation (Eq.4), as given beiow:

gaa maaa conservation

:[PG&]+-&Jw]=m......................(l)

iiquid maas conservation

~[PL~L]+~[PL%UL] =-m . . . .. . . . . .. . . . . . . ...(2)--

= T“ - (pGRG+ /YLRL)&sin@

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SPE 28545 C. PAUCHON, H. DHULESIA, G. BINH ClR.LOT, J. FABRE 3

mixture energy conservation

I“a I

= -Qw - (pGRGUG+pLRLUL)g.sin 8

The subscript k stands for the phase (G for the gasphase and L for the liquid phase), the $ufwscripts S, Dfor the two ba$ic regimes (Separated flow andDispersed flow). p, P, R, U and H are the density, the

pressure the volume fraction, the velocity and theenthalpy respectively. e is the inclination angle with

reepec! !C horiz~nta!, Tw and QW are the contributions

of the wall friction and heat transfer across the wall.

As thermal equilibrium is assumed between the phases,this problem involves five main unknown variables:

● RG the gas voiume fraction,

. P the pressure,

. T the temperature,● UG the gas velocity,

● UL the liquid velocity.

Thus, an additional equation is required to close thissystem of 4 partial differential equations:

fi@@’~,~’’,%,P~ ~]=00 . . . . . . . . .. . . . . . ...(5)

This equation reduces to a slip equation in the case ofdispersed flow. It is a macroscopic momentum balance

in stratified flow and it is a set of algebraic equations

in the case of intermittent flow. Thus, it is flow regimedependent.

In addition, two complementary terms Mc and Ec

appear in the mortrentum and energy equations. Theseterms vanish for dispersed flow (8=0), and forseparated flow (0=1 ); in intermittent flow, theyaccount for the non-homogeneous distribution of voidand velocities in the separated and dispersed parts.They are expressed using the secondary variables

U:, U;, RDk and 0. Moreover, the wail friction and

heat fluxes may be written:

Tw =fl~+(~+)~ti ... . . . . . . . . .. . . . .....(6)

Qw =~~ +(2-~)QwD .. ... . . . . .. . . . . . ....(7)

in which the contributions of separated and dispersed

parts appear. A unified formulation is used for the gasand liquid wall friction and the interfaciai friction. Thatis, the form of these closure laws is independent of theflow regime and has the same structure as a singlephase flow relationship. Furthermore, we must ensurea continuous solution of the hydrodynamic model acrossflow regime transitions, even though the analyticalform of the hydrodynamic model for the two basicregimes is very different.

2,2 Closure laws

In this section the solution algorithm used for the

general case (O<B<l ) corresponding to intermittence,and for the Iwo aegerierated easas i3=0 (dispersedflow) and 8=1 (separated flow) are presented.

2.2.1 Dispersed flow (i3sO)

The closure equation (5) reduces to a drift flux relationexpressing the gas velocity versus the mixture

velocity UD and the bubble drift velocity VB.

(U: =COUD+VB dB,R&@ .. . . . . . .. . . . . . .. ...(8))

The problem is solved implicitly provided the bubblediameter is known. The bubble diameter results from abalance between the work of surface tension and theturbulent dissipation (reference 5):

d, .!,++il-i . . (9)

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4 TACIT12 SPE 28545”A TRANSIENT TOOL FOR PIPELINE AND WELL SIMULATION

where the turbulent dissipation e results from the workof both wall and interracial friction (reference 6):

1- II ) sineR:(u: -Uq4 T“DU: + (PG‘PL g“D

The bubble velocity VB in still liquid is a

continuous function of the bubble diameter. In theviscctus stokes regime, the bubbles are consideredspherical and the bubble velocity results from a balancebetween buoyancy and viscosity. In the distorted bubbleregime, the bubble diameter is larger, and surfacetension effects become important. Of these tworegimes, the one corresponding to the minimum bubblevelocity is considered to prevail. Figure 1 illustratesthe relation between the bubble diameter and velocity.

A

TVb I Distorted bubbles[Stokes Iqime

1/ Ellipsoidal db

Figure 1: Bubble velocity as a function of diameter

2.2.2 Separated flow (0=1)

For separated flow, Eq. (5) is a combination of the gasand liquid momentum equations from which thepressure gradient has been eliminated:

[kTg_ll-——R; R: + RS ‘-*= (PL-PJ?W..(lO)

G G

The iterative solution of this equation is obtained fromthe expressions of the wall and interracial friction,

T~, TN, T’. The key point in the solution of Eq. (1O)

lies in the expression of the interracial friction. It wasfound after comparisons with existing data that thebest choice is the law proposed in reference 7. Thisrelation has been modified to take into account thewave velocity with respect to the liquid C$:

r’=-~~f’PG(u -a-C’JJHJ:-+..(11)

where Pi and S are the interracial perimeter and thecross section area respectively.

2.2.3 Intormlttent flow (O<t3<l)

In intermittent flow, we have a periodic structure ofdispersed and separated flows.The solution of the model depends on an accurate

prediction of the slug velocity. An expression of thelaw derived from the critical review of reference 8 isused, it takes the following form:

V = CO(Re,Bo,Fr, $)UD

JAP ~+ C. (Re, Bo,Fr, 9) Kg ... ... . ... .... ....(12)

where the coefficients CO and CL are function of the

inclination angle, the Bond number, Reynolds numberand Froude number defined as:

Ap@2 ,Re . !_, .Bo=—

0 ‘:! ‘r “&

In order to close the model, the knowledge of thedistribution of gas between the long bubbles and theliquid slugs is needed. Usually, this problem isovercome by using a closure law for the void fractionin the liquid slugs. The accuracy of the model appearsto be very sensitive to this closure law. Aa none of the

existing laws gives satisfactory results for slopesranging between O to 90°, the correlation proposed inreference 9 has been improved to take into account thegas density in the bubble generation at the slug frontWe consider the net gas flux at the slug front @G (see

figure 2)

where 01 is the gas flux from bubbles entrained intothe slug, and 02 is the gas flux from bubbles coalescing

with the leading bubble. @ 1 is assumed to be

proportional to the net flux of liquid ar the slug front,02 is assumed proportional to the gas fraction in the

liquid slug.

The resulting form of the holdup correlation is givenas:

Cl(vp- u~- Uf)E = (v’+uD)(l+cl)-uo~‘“”’”””””’”””’””’”’’””

314

SPE 28545 C. PAUCHON, H. DHULESIA, G. BINH CIRLOT, J. FABRE 5

where UD is the mixture velocity and Uf and U. are

characteristic velocities related to the fluid properties.The effect of inertia is contained in the coefficient Clwhich is a function of the density ratio of the twofluids.

Figure 2: Schematics of bubble flux at theliq;id slug front.

2.3 Flow regime transitions

A standard approach to determine flow regimes is toapply a set of transition criteria. if these criteria arenot iinked to the individual modeis for the differentflow regimes, they wili generaily lead to

discontinuities in the soiution. These discontinuities arenot acceptable for severai reasons which are discussedin reference 1.The averaged equations of motion are based on theassumption that the iength scaie of the flow is smailwith respect to the iength of the control voiume overwhich the equations are averaged. Simiiarly, the fiowregime must be understood as an averaged property ofthe flow structure in the controi volume. Thus, even ifiocally, the void fraction and siip veiocity may presenta discontinuous behaviour, these variables cannot bediscontinuous in an averaged sense.

-l-I _- -- _-.-_,-. *L-. .L _ -- 1-..1-.-4 ..-.: _l- l-- L-I ne c0rr5watn I wri-i[ mu Galculdluu Vdrldulus Uu

continuous across the transitions, impiies that thehydrodynamic models representing the different flowregimes, though very different in form, shouid iead tocontinuous soiutions across transition boundaries.

Consequently, the individual hydrodynamicmodels shouid have identicai solutions at theirtransition.

in practice the basic fiow regime is theintermittent fiow regime. The parameter f3 defined

previously ranges from O to 1, and is a resuit of thecalculation.

When 13= O, the hydrodynamic modei reduces

to the dispersed fiow model, that is a siipequation in the iiquid siug. The transitionbetween dispersed and intermittent fiowoccurs when the void fraction in the liquidslug is equal to the void fraction of puredispersed fiow.

When 13= 1 the hydrodynamic modei reduces

to the stratified flow model, that is , amomentum baiance in the separated region. Toforce the continuity of the hydrodynamicmodei between separated and intermittentfiows, we assume that the prevailing flowregime is the one with the highest RG (or

smaliest reiative velocity between thephases) .This condition ensures the continuitybetween the two flow regimes.

Figure 3 shows typicai flow regime maps as calculated

by TACITE, for siopes ranging from horizontal to

vertical fiow. Good agreement is observed between the

experimental and calculated fiow regimes.

2.3 Thermodynamic treatmentThe giobal composition of the fiuid is assumed

constant along the pipe, so that the fluid properties aregiven in tabuiar form as a function of pressure andtemperature. The thermodynamic state of the mixtureis taken into account through a non equilibrium termwhich enters as a source term in the massconservation equations:

m=K[

pGRGUG

)– Equ.MassFrac ...(14)

PGRGUG + PLRLUL

This mass transfer term takes into account thedifference between the gas “mass fraction computedfrom the hydrodynamic calculation, and the gas massfraction in thermodynamic equilibrium conditions. Thisterm acts as a restoring force. Note that in steadystate conditions, this term vanishes, thus it is

compatible with the steady state calculation.

The coefficient K is flow regime dependent, itcharacterizes the speed at which the system wiii reachthermodynamical equilibrium.

3. Numerical approach

The numerical scheme used in TACiTE was proposedoriginally by Lerat (reference 10), it was firstimplemented in TACiTE by Benzoni-Gavage (reference11). it is a threevoiume scheme. The

point predictor corrector finitetime advancing scheme in TACITE

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6 TACIT13A TRANSIENT TOOL FOR PIPELINE AND WELL SIMULATION

SPE 28545

is explicit, with a second order accuracy. This choiceis dictated by the following requirements:

● Good accuracy and front tracking capability.● Explicit schemes are easy to implement.. Explicit schemes give more flexibility for the

treatment of complex transient networks.

3.1 Time advanaing scheme, spatiaidiscretization

The set of conservation equations given in (1) can bewritten in the following way:

~w+ $~=Q ..... .. . .. . . .. . . . . . .. . . . . . ...- . . . .. . . ...(l5)i%

The time advancing scheme is explicit, so that the stateof the system at iime n+f k caicuiahsd on the basis ofthe flux term F and source terms Q evaluated at time n.

Explicit schemes are stable provided” that the CourantFriedriech Levy criterion is satisfied. in practice thiscondition imposes a limitation on the time step Atdepending on the speed of the fastest wave propagatingin the system Cmax:

AxAts —. . .. . . . . .. . . . . .. .. . . .. . . . . . . . .. . .. . .. . .. . . .. .. . .. . ...(l6)

km

With the evolution towards ever faster computerprocessors, this limitation is bound to become less of aconstraint.

On the other hand, the choice of an explicit timeadvancing scheme presents substantial advantagescompared to implicit or semi-implicit methods:

● For transient simulation of complex networksit allows for the solution of individual networkcomponents sequentially instead of requiringtheir simultaneous soiution.

● It has also the advantage of a clear separationbetween the hydrodynamic calculation moduleand the treatment of the numericai scheme.This aliows an independent evoiution of thephysical modei and tie numericai scheme.

The set of partial differential equationsdiscretized using a finite volume method as follows:

m+lWi -W: + 4:112- 4:1/%= ~;

Al &i

is

where

where the indices a and fi are defined in figure 4,

For p = 1/2, this scheme is independent of the flow

direction, and numerical dissipation is minimized when

a=l+@J2.

This flux preserving method has good conservativeproperties, and it is second order accurate.iiowever, as most second order schemes, it tends to bedispersive. In particular when steep fronts are

encountered, the numerical scheme generates ripples inthe neighborhood of the propagating shock.

n+l

n+a

n

I t-l t-1+ p t t+ p t+ 1

Figure 4 dhition of the discretization

To avoid these oscillations, a hybrid scheme isformulated, combining the Lax Friedriechs first orderscheme with the second orderthen evaluated as follows:

hi+l,z= 8h::~,2+ (1- Oh:://z

O= Ooutside the shock

Lerat scheme. The flux is

with OS@Sl

8 = 1 for strong discontinuities

h(1) is the flux estimation with the first order scheme,

h(2) is the flux estimation with the second order

scheme. The performance of the hybrid scheme isdemonstrated in figure 5. This figure shows how thefirst order scheme smears the shock, the second order

scheme captures the shock with some oscillation, while

316

~pE ~m5 c. PAUGKX’4,H. M’L!!?!A, G. Em. m—m,J: Flmm

the hybrid scheme captures the shock without anynumerical dispersion.This front tracking capability is very irmpotian! when~$!~~ati~g thn siza SMId velocity of large liquid Shqs...- ----

reaching the pipeline outfet.

3.2 Treetment of boundery conditions

The hyperboli$ nature of the problem makes it veryimportant to treat precisely the transport ofinformation through the pipe, and in particular theinformation going in and out of the system. Four typesof waves are identified in the analytical model:

● Void waves traveling downstream.● Pressure waves traveling downstream.● Pressure waves traveling upstream.● Enthalpy waves traveling with the mean flow.

The treatment of boundary conditions takes intoaccount the information going out of the system througha set of compatibility relations, which must be solvedtogether with the imposed boundary conditions. Thus,this system of equation depends on the direction of

-f *ha r!iffnrnnt way~ sp?a~s, in normalpropagation “r .!!- “,.,-. -...subsonic cocurrent flowing conditions, the informationgoing out of the system is as shown in Figure 6. Inthese conditions, the solution of the following set of

eqQa!~OnS @WE@a r@MOUS treatment Of the boundaryconditions:

At the,●

.

.

At th;.●

●

●

●

Inlet :Mass flowrate of gasMass flowrate of ~quidTemperatureCompatibility condition for pressure wavestraveling upstreamHydrodynamic functionoutlet :PressureCompatibility condition for enthalpypropagationCompatibility condition for pressure wavestraveling downstreamCompatibility condition for void fractionwavesHydrodynamic function

lilm4 enthalpy

Ibackwmd 4 void fraction

pesswe wsve

[1 Ftow dice!don ) x

F@rs 6 Ctraractfxistic waves of the system

3.3Treatment of chsnges in slope or diameter

In the case of a diameter change or a change inslope, the response of the physical model isdiscontinuous. Jump conditions must then be resoivecitogether with the hydrodynamic model and thecompatibility relations associated to outgoingcharacteristics on either side of the discontinuity. Inthis case as in the treatment of boundary conditions,!h~ r~s~l~tian of the singular point must take into

account the number of characteristics pointing towardsthe singular point on either side of the discontinuity. Inparticular, in severe slugging, the backflow in the riserafter the liquid carry-over period leads to a

characteristic changing sign at the singular point. In

this case, we must assume that the phase velocities ~i

the singular point are zero.

Figure 7 illustrates the behavior of the model in theneighborhood of the singular points. On this particularcase, the pipe is divided in 5 segments of constantslops. Figure 7 shows a strong discontinuity at eachjunction in the initial state, moreover a void fractionwave is generated at each junction when it is reachedby the first pressure perturbation. This void fractionwave travels along the individual segments until itreaches the next junction and perturbs the f~llowingsegment.

3.4 Numeriesl implementation

3.4.1 First estimation of initial conditionA first estimate of the initial state of the system

is obtained by assuming a constant total flowrate alongthe pipe. The pressure is known at the outlet of the

pipe, thus the gas and liquid superficial velocities areknown, and the holdup and pressure drop along the linecan be determined starting from the outlet computingmesh by mesh towards the inlet of the pipe. This first

estimate of the inlet pressure is used together with theknown inlet temperature and flowrate to compute the

317

pressure profile from the inlet to the outlet. Sucessiveestimates of the pipe pressure profile can then be madeuntil an outlet pressure is reached, which is closeenough to the prescribed outlet pressure value.

3.3.2 True estimation ot the Initial conditionOnce a first estimate of the initial condition has

been obtained, the numerical scheme is used tocalculate the, actual initial condition with constant

boundary conditions. This additional step helps take intoaccount the momentum flux terms which wereneglected in the first estimation. At this step theapproach is not essentially different from a calculationwith transient boundary conditions.

3.3.3 Tranalent calculationThe solution of a hyperbolic set of partial differentialequations of the form given in (1) is required:

~ w(u)+:F(U)=Q(U) .....................(I4)

together with the algebraic constraint:

Hydro(u) = o.. . .. . . .. . . . . . . .. .. . .. . . .. . .. . .. . . .. . .. . ...(15)

U = ‘(RG, UG, UL,P, T) is the set of dependent

variables. At each time step, W is computed by thetime advancing scheme, and the dependent variablesare calculated with the help of the hydrodynamic model(Eq. 16).A first iteration gives the holdup and pressure from theconsewation of mass of each phase, and then themomentum conservation together with thehydrodynamical rnodei gives ine source terms in themomentum equation. With the energy equation, theiteration can no longer be divided in two steps, sincethe fluid properties are functions of both the pressure

and temperature. One option is to solve simultaneouslyfor the 5 dependent variables. A more convenientapproach can be to decouple the energy equation fromthe other consecration equations.

For a given time step, once the interior points arecomputed, the mesh points next to the boundary pointsneed to be evaluated using a substitute of the threepoint discretization. Finally the boundary conditions arecomputed, ensuring that the following conditionsatisfied at all times:

P:::\=-l::::f/+[ ‘::$

is

1

}

(variables J [conditions J (charactensticsj

Thus the treatment of boundary conditions is dependenton the evaluation of the local characteristics of themodel. In particular, in cases of counter current flowor pure backflow, the void wave characteristic changessign and the treatment of the boundary conditions hasto be adapted, based on physical considerations.

4. Validation4.1 Stead y stete

Cooperation between IFP, TOTAL and ELF in the field oftwo-phase flow began in 1974 with the construction ofthe semi-industrial Bouseens test loop. Data from thisloop were used for the development of the steady statesimulation models PEPITE (for horizontal and slightlyinclined pipes) and WELLSITE (for vertical wells).

The hydrodynamic module of TACITE has been testedextensively on the Boussens data, which cover a widerange of inclinations (-30, -.5”, 0°, 10, 40, 150, 45”,75° and 90°) with 3“ and 6“ piping. Diesel oil andcondensate have been used alternatively together withnatural gas as working fluids. The fluid properties weremeasured in the laboratory. Pressures up to 50 barswere investigated over a wide range of flowrates. Thehorizontal and slightly inclined data bank contains about1750 points of which 900 are in stratified flow, 600 in

slug flow, and 250 in dispersed fioii. The data bank onvertical and highly inclined flow consists of about 700measurement points (260 for bubbly flow, 400 for slugflow and 40 for annular flow). More details on this loopare given in reference 12.

4.2 Transient

Transient data from the Tulsa University Fluid FlowProjects (TUFFP) were used to make preliminary testsof TACITE. The flow loop is horizontal, 420 m long witha diameter of 77.9 mm. A schematics of the flow loopis given in figure 8. Air and Kerosene of knownflowrates are sent to a mixing tee. The loop comprisesfour measuring section which enable visualization ofthe flow.Each measuring section is instrumented withan absolute and a deferential pressure transducer, andtwo capacitance sensors to measure the void fraction.The data are sent to a 12 bit ND converter and anexpansion board with a total number of 64 channels. 23signals are fed into this “system with a samplingfrequency of 10 to 50 Hz per channel. 23 experimentalruns were conducted on this rig. 4 Experiments

presenting sharp discontinuities in the measuredvariables were selected in order to assess the

capability of the code to follow wave frontspropagating in the pipe.

318

SPE 28545 C. PAUCHON, H. DHULESIA. G. BINHCIRLGT,J. F-w 9

Case 1:

Start with single phase gas flow; QG =.088 Sm3/sec.

At t = 76 S6C;

+h- Ii-, iid {Inw rata is W! ~? Q~ = ,00066 m3/sec.LIIU tlq”l” ,.” . ,--- ,-

At t = 460 see;the liquid flow rate is stopped. The prediction of themodel is compared with the experimental data on figure9.

Case 2:

Start with a single phase gas flowQG = .065 Sm3/sec.

At t = 280 see;

the liquid flow rate is set at QL = .0018 m3/eec .

The prediction of the model is compared with theexperimental data in figure 10.

Case 3:Start with liquid filled pipe.Between t = 80 to t = 110 see;the gas flow rate is increased to QG = .0366 kg/see ,

the liquid flow rate is increased to $2L.= 0.207 kg/see.

The prediction of the model is compared with theexperimental data in figure 11.

Case 4:Start with liquid filled pipe.Between t = 80 to t = 110 see;the gas flow rate is increased to QG = .0267 kg/see ,

the liquid flow rate is increased to QL = 3.022 kg/see.

The prediction of the model is compared with the

experimental data in figure 12.

These four cases show that TACITE is able to predictwith a reasonable accuracy, the void wave frontpropagation velocity, together with the final steady

state value of the pressure and void fraction.

5 Conclusions

This paper has given an overview of the TACITE codestressing its originalities which can be summarized asfollows:

● The physical model integrates a number ofexisting closure laws into a unified modelworking for all slopes and flow regimes. Someof these closure laws have been improved andevaluated using a large number ofexperimental data. The approach to flowregime characterization is based on a singleconfiguration parameter fl which leads to a

continuous solution across the transitions.

● The numerical scheme, explicit in time, givessecond order accuracy in time and space. Its

ability to follow front propagations without~~m~rica! diffdsion is demonstrated on

several test cases.

-L- ..-1:4-,:-● ..6 *h_ .na~nl -- tr9nei nt AatsI m VUIIUGWA w LIIU II IWU=I “1, .I-. l-oe, i. -q.q

shows that TACITE recovers the dynamicfeatures of the transient and gives goodpredictions of wave front propagationvelocity Moreover the final values of localholdup and pressure are reproduced with goodaccuracy.

6. Nomenclature

ADDhk

*PT

Hk,Hkc

Rint

Rk, Rkc

Uk,Ukc

%mTw

QW

9hVp

w

P&0

*01

q

Pk#kc

0k

v

Subscripts:

cross-section area of the pipediameterhydraulic diameter of phase k

bubble diameter

mixture pressuremixture temperature

enthalpy of phase k in

configuration cthermal resistance

proportion of phase k, and of

ph$ise k in configuration c

supetilcial velocity of. phase k,

and of phase k in configuration cm’ixture velocity

mass transfer between phases

friction at wall

heat flux at wallgravitational accelerationnumerical fluxgas slug velocity

conservative variable

configuration density

rate of energy dissipationinclination of flowline to thehorizontalnet gas flux in the slug region

gas flux from bubbles entering

the slug regiongas flux from bubbles coalescing

with the leading’ bubbledensity of phase k, and of phase

k in configuration csurface tension

conductivity coefficient

viscosity

319

10 TACITIl SPE 28545A TRANSIENT TOOL FOR PIPELINE AND WELL SIMULATION

G Gas phaseL Liquida phase

Superscripts:

D Dispersed region of the slug units Separated region of the slug unit

7. Acknowledgements

The authors are grateful to the Tulsa University FluidFlow Projects (TUFFP) for allowing publication ofcomparisons of TACITE with their experimental data.

n Rnfnranen*“. . ,”.”.”..”””

1.Pauchon, C., Dhulesia, H., Lopez, D., Fabre, J., ,TACITE: A comprehensive mechanistic model for two-phase flow, BHRG Conference on multiphase production,Cannes, june 16.19, 1993

2. Fabre, J., Lin6, A., P6resson L., Two fluid/two flowpattern model for transient gas liquid flow in pipes, Int.Conference on Multi-Phase Flow, Nice, France, pp 269,284, Cranfield, BHRA, 1969

3. Caussade, B., Fabre, J., Jean, C., Ozon, P., Th6ron,B., Unsteady phenomena in horizontal gas-iiquid slug●-.., I..* 6.. - A.---A A- L ,,1*JDhaas C[a.., .f 4Iluw, l!!!. vurl UIUII*U urI I ulu-rllae I iv”, F!KX,

France, Cranfield, BHRA,, 1989

4. Bouvier,V., Ferachneider, G, Fabre, J., Gilquin, H.,A oractical hyprbol!~ pr~!em: the uns!eady gas-!iq~id~. -------flow in pipe, 4th Int. Conf. on Hyperbolic Problems}Taormina , Italy, April 3-8, 1992.

5. Hinze, J.O., Fundamentals of the hydrodynamicmechanism of splitting in dispersion processes. Al~hEJ., Vol 1, Pp 289-295, 1955.

6. Colin, C., Ecoulements diphasiques A bulles et Apoches en micropeaanteur, hvstitut NationalPcdytechnique, Toulouse, 1990.

7. Andristos, N., Hanratty, T. J., Influence ofinterracial waves in stratified gas-liquid flows, AIChEJ., vol. 33, pp 444-454, 1987.

8. Fabre,J., Lin6, A., Modelling of two-phase slug flow,Annu. Rev. Fiuicf M@3h., Voi 24, pp 21-46, 19%?.

9. Andreussi, P., Bendiksen, K., An Investigation of

void fraction in liquid slugs for horizontal and inclined

gas-liquid flow, Int. J. Multiphase Flow, Vol. 15, 2 pp937-948, 1989.

10. Lerat, A., Sur la calcul des solutions faibles dessyst~mes hyperboliques de Iois de conservation ~ I’aidede schdmas aux differences , Thbse. 0NE13A, France,1981.

11. Benzoni-Gavage, S., Analyse des mod61eshydrodynamiques d%coulements diphasiquesinstationnaires clans Ies r6seaux de production

p6troli&re, Th&e. Lyon 1, France, 1991;

12. Corteville, J., Grouvel, J. M., Roux, A., & Lagi6re,M., Exp&imentation des dcoulements diphasiques enconduites pdtrolidres: boucle d’essais de Boussens,Rev. Inst. Fran$ais du P6trole, Vol 36, pp 143-151,1983.

320

Onr mOc.4cm-n LOJWc’ PA1ICHCN H. DHULESIA, G. BJNH CIRLOT, J. FABI@-. . -------- ., --- —————

fin,“.” ,

10.0

Io.of I 1 I

~ 0.1-/ /’7 //l///*/(’=.

-V.bcd. )C—.l$llc, .lobm

s -0.005

O.on1 I + I.

—. W.13*S

low 0.01 0. I I .0

‘:Y0.5

0. I

0.05

I

0.005

1ooo-~

k“’”.

A- /..-/ mu ‘ “y. ””..fzz..*,.---..

(Iml. .si. lotw,

11

0.0

I.0

I.0

M

}. I

0.05

().01

0.005

!-)Ihll

0.05

,,,,,,,,,,,,,,im !

REGIMEs:

0.01v :Slug

0.C05

; :: :

0.001

0.0! 01 I .0 1(10 Illil

1 . . .(), I . 10.1

. .

0.05 0.05

0.01

O.(X)5I. . .

A

.0.01

.O.(X-)5

0.001 II I

+0.001I

ill)! i) I I lb 100 Illno

Figure 3: Flow regime prediction in terme of the gas slug faction p for different

slopes and pressures. The symbols refer to the experimental data. 13= 1 for

stratified flow, p = O for dispersed flow, O < p < 1 for intermittent flow.0.7S 1 1 1 r , I

0.7 -

0.65 -Lax F. scheme (1st order) _ _Hybride scheme ......

0.6 - Lerat scheme (2nd order) _

(jr).;

‘LJ~n IO.-i- \

0.35 -

0.3 I , ,

0 1000 2000 3000 4000 5000 6000 7000 S000 t

Figure 5:FIow rate increase at the inlet of a 10 km line. Comparison between the Hybrid scheme, the

Lerat scheme (second order) and the Lax Freidriech scheme (first order). The hybrid schemepreserves the steepness of the shock without the oscillations of the second order scheme.Ax = 20 m.The comparison is made at x = 10 km

321

12 TACITE: SPE28545A TRANSIENT TOOL FOR PIPELINE AND WELL SIMULATION

ole~ I ! I

L&.-

O.ffi:1 1 I I I # 1 1 1

LTlo” 1“10’ Tlo” 2-10’ 4’10’ Slo’ Clo’ 7’10’ 8-10’ 970’

Length (m)

Figure 7: The flow rate increase at the inlet generates a pressurepulse which propagates along the pipe. As this pressure pulse meets achange of slope, it generates a void fraction wave which propagatesalong each segment of the pipe.

id* ,,,

41Ei!3Yl..”* .— -Ui-s!.!m .

Figure 8 : Schematics of the TUFFP two-phase facility (TUFFP reportby K. Minami , 1991)

322

0.3 --—- -– -- ----

II :’- ‘-”””’

0.2s -——--—.

0,

a ~- ;,, ,’~ ,,

30.15 --l ~

II ? h .:

$ ,’ ‘“\ ~ / * 1,1

0.1I 1 -w‘-- “

t i0.0s — ,-- -- - --\

_. ..-1“, -

I1 I 7*

0,

0 4CQ ~

Time (s)

260 4ca 603

.\

‘-

) 1000 12U0

I 1,

.—.-.

~

0

0

rn i4cu

*104 (Pa)

26-

25-

24-

21.

20

19

(Kg/s)

_-——.~-. __, ___ .. . . ... ..

11-1

m 400 m I

Time (s)

1 I

-m-x. O.m-x= Mm—x. 020E+03mY x - 023E+03 m

— x - 0.40E+LU m

T x - 0.42E*U3 m

72———.

o.12-

0,1- -

0

+

Z’h o.oe- measurement - - -

J simulation __

: 0.06-

: —~ 0.04--

0.02--

m+-i-$-~.0 400

Tlma (s)Time (s)

l-lw

TACI’111A TRANSIENT TOOL FOR PIPELINE AND WELL SIMULATION

Tulsa Minami simulation RUN 18

Horizontal pipe: 420.3m. 0.0762 m

Pressure: 1.95 bar

Gas: 0.754 kg/s/ Liquid: 0, I@ to 1.43 Icg/sat t.280s

sJnsseJd

, l!:0

Figure 10: Step increase in liquid flow rate from a pipe with singlephase gas flow.

SPE 28545 C. PAUCHON, H. DHULESIA, G. BINH CIRLOT, J. FABRE

SUPERflCIAL VELOCITIES

10

,-pA.&A-,-.-+*+A’+*+A %m+fiwd-e

omaoemml~ 1200 1400 Isa woo

TIME (sac)

PRESSURE

3.s

F3 IN [:piiq2 (,+w%, 1---1

G‘----mea-p-asp

: 2“5“ ~~2.s g

m — tao-p.stlm %# 2. j ~, 2=n

— tac-p-ssp! &~’t

1.5 i 1.5

Ozomemm low 130) 14C0 lSCO lm

TIME (aec)

LIQUID HOLDUP

1+ -1

~ 0.0

-~ E

o.8& . . .3

- - mea-hl-stln =

0.8 ~ - - - - - m~h~stqs

G 0.4.

3 ‘~ ,;

0.4 e — tsc-hl-stl

~~ 0.2. ,. .-~ .’, ‘ w’.- 0.2 ~ — tsc-hl-st4‘%,.-=,

07 002c04c060)soJlm la 1400 1s00 1s00

TIME (SSO)

measurement - - -simulation _

15

Figure 11: Increase in gas and liquid flow rate from a still liquidfilled pipe. stl = 61 m, st4 = 400 m.

TACIT’J2A TRANSIENT TOOL FOR PLPELIN’EAND WELL SIMULATION

SUPERFICIAL VELOCITIES

3- -3

2.5<

~

: L

2.5 ‘-- - - mss-vsi-in

— tsc-vsl-inG2

2~

1: ~; 2- 1.5 1.5 - — tsc-vsl-outd. g

9 1. 1 > ----- mss-vsg-in

0.5. 0.5 — tswsg-in

0+ o

0 lcom3coa=~ 7oo~=

TIME (ssc)

PRESSURE

4.5

1 [

4.5

I I

IF4

~>, ,, } L

‘E --mss-p-stl

g 3.5 3s g-----

w msa-p-ssp

53 Sg,, — tec-pstl

% 2,5 ,,UJ

2.5 ;/,

KLX2 *& — tac-pesp

1.5 1.5

0 la)2003004m5m~ 7oo~9’33

TIME (sac)

LIQUID HOLDUP

1.

& 0.8.=n

],

g 0.6.

G! 0.4.30i 0.2.

0+o lco2003m4w200sco 7o0300~

TiME ($SC)

SPE 28545

Figure 12: Increase in gas and liquid fiow rate from a still liquidfilled pipe. stl = 60 m, st4 = 400 m.