COMPUTATIONAL STUDY OF STRATIFIED TWO PHASE OIL/WATER FLOW IN HORIZONTAL PIPES

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1 HEFAT h Inernaional Conference on Hea Transfer, Fluid Mechanics and Thermodynamics 30 June o 2 July 2008 Preoria, Souh Africa Paper number: KW1 COMPUTATIONAL STUDY OF STRATIFIED TWO PHASE OIL/WATER FLOW IN HORIZONTAL PIPES W.A.S. Kumara, G. Elseh, B.M. Halvorsen and M.C. Melaaen* *Auhor for correspondence Telemar Universiy College and Tel-Te, PO.Box 203, N-3901 Porsgrunn, Norway, Moren.C.Melaaen@hi.no ABSTRACT Sraified oil/waer wo-phase flow in a horizonal ube is numerically simulaed using commercial CFD pacage FLUENT 6.3. The simulaions are based on Volume of Fluid (VOF) model. I solves a single momenum euaion shared by he fluids, and he volume fracion of each of he fluid in each compuaional cell is raced hroughou he domain. The RNG - model ogeher wih sandard wall reamen as he nearwall modelling mehod is used for urbulence modelling. The effecs of surface ension along he inerface beween wo fluids are calculaed using Coninuum Surface Force (CSF) model. The simulaion is performed in a ime-dependen way so ha he numerical sabilizaion could be achieved. The final soluion which corresponds o seady-sae flow is analyzed. Resuls of pressure drop, slip raio, inerface heigh and he axial velociy profiles are verified by experimenal daa. The predicions of pressure drop, slip raio and inerface heigh are observed o compare favourably wih experimenal measuremens, and esimaed flow uaniies such as axial velociy profiles are also saisfacory. INTRODUCTION The simulaneous flow of oil and waer in pipelines is a common occurrence in he peroleum indusry. Increased offshore oil and gas exploraion and producion have resuled in ransporaion of well fluids in pipelines over relaively long disance. Ofen, he fluid delivered by he well conains waer, which is already presen wihin he sraum. Waer fracions ofen increase during he producing life of a well. The well migh be economical o operae even for waer cus as high as 90% [1]. The presence of waer mus be properly accouned in designing and predicing he flow behavior in boh wells and pipelines. Numerous experimenal sudies have been published in recen years in oil/waer flow hrough pipes [1-7]. Bu very few references are found in lieraure relaed o numerical sudies of oil/waer flow sysems [3]. In he presen paper, Compuaional Fluid Dynamics (CFD) is applied o predic flow behaviour of sraified oil/waer flows in horizonal pipes. NOMENCLATURE A [m 2 ] Flow cross-secional area C 1,C 2, [-] Coefficien in euaion (11) C µ [-] Coefficien in euaion (12) F [N/m 3 ] Surface ension erm g [m/s 2 ] Graviaional acceleraion G [m/s 3 ] Generaion of urbulence ineic energy [m 2 /s 2 ] Turbulence ineic energy n [-] Uni normal vecor o a surface p [N/m 2 ] Pressure s [-] Slip raio S [g/m 3 s] Source erm in euaion (1) [s] Time v [m/s] Velociy vecor U [m/s] Superficial velociy x,y,z [m] Caresian axis direcions Special characers α [-] Volume fracion of phases [m 2 /s 3 ] Turbulence dissipaion µ [g/ms] Dynamic viscosiy κ [1/m] Curvaure ρ [g/m 3 ] Densiy σ [N/m] Surface ension coefficien σ, σ [-] Turbulen Prandl numbers for and Subscrips O M SO SW W Oil phase Mixure Phase Superficial for oil phase Superficial for waer phase Turbulence Waer phase In early effor o undersand and model oil/waer flow and predic he influence on pressure gradien when waer is inroduced ino an oil pipeline, Russel and Charles (1959) carried ou an analysis for he case when boh oil and waer flow are laminar [7]. They developed a numerical procedure, in

2 order o model he laminar sraified oil/waer flow in a circular pipe. Exending his analysis, Charles and Lillelehe (1969) used he similariy mehod developed by Lochar and Marinelli (1949) for gas/liuid flow, o presen pressure gradien daa in he sraified flow of wo liuids when one was in laminar and he oher in urbulen flow [7]. Arirachaaran e al. (1983) developed a model for sraified oil/waer flow based on no-slip beween phases [9-10]. This no-slip model is expeced o give accepable pressure drop predicions when close o no-slip condiions apply such as for low viscosiy oils and inermediae waer cu ( ). For higher oil viscosiies he slip beween he oil and waer is generally higher and he deviaion increases as observed by Herm Sapelberg and Mewes [11]. The mahemaical model developed by Taiel and Duler [12] for gas/liuid flows was used o calculae he pressure drop of oil/waer flows by Kurban e al. [13]. Oil and waer were represened as wo separae regions and empirical correlaions were used for he wall and he inerfacial shear sresses. The wo fluid model developed for gas/liuid flow has been exended o predic oil/waer flows [14]. The validiy of he model and is pracical significance for analyzing sraified flows were evaluaed in view of experimenal daa of he in siu flow configuraion and he associaed pressure drop in an oil/waer sysem repored by Valle and Kvandal [8]. Finally, he accuracy of he wo-fluid model for oil/waer flows was evaluaed by comparing is predicions for laminar flows wih he resuls of he exac soluion of he Navier Soes euaions for laminar-sraified flows wih curved inerfaces [14]. The exising mechanisic models for sraified oil/waer flow have been developed based on he inerpreaion of he dominan physical mechanisms of he flow process. For he lac of nowledge abou he disribuion of wall and inerface shear in sraified pipe flows, uned or empirical or semiempirical relaionships are ofen used, wih a resuling loss in compuaional accuracy. Therefore Compuaional Fluid Dynamics (CFD) echniues have been applied o model sraified oil/waer flow. Rhyne proposed a mechanisic mulilayer model based commercial CFD code, CFX by AEA Technology, and daa from oil/waer flow projec a he NSF I/UCRC, Corrosion in Muli-phase Sysems Cener [15]. However, he muli-layer model needs deailed experimenal daa for he implemenaion. In he presen paper, sraified oil/waer wo-phase flow in a horizonal pipe is numerically simulaed using he Volume of Fluid (VOF) model. The RNG - model ogeher wih sandard wall reamen as he near-wall modelling mehod is used for urbulence modelling. The Coninuum Surface Force (CSF) model proposed by Bracbill e al. [16] is used o include he effec of surface ension. The simulaion is performed in a imedependen way and he final soluion which corresponds o seady-sae flow is analyzed. The predicions of pressure drop, slip raio, inerface heigh and he axial velociy profiles are verified by experimenal daa. MODELING METHOD The commercial CFD sofware pacage, FLUENT 6.3, which is based on he finie volume approach [17], was used for solving he se of governing euaions. The discreized euaions, along wih he iniial and boundary condiions, were solved using he segregaed soluion mehod o obain a numerical soluion. Using he segregaed solver, he conservaion of mass and momenum were solved ieraively and a pressure-correcion euaion was used o ensure he conservaion of momenum and conservaion of mass. The RNG model ogeher wih sandard wall reamen as he near-wall modelling mehod was used o rea urbulence phenomena in boh phases. A sech of he geomery of he compuaional domain for oil/waer sraified flow is given in Figure 1. Oil Flow Waer Flow Figure 1 Schemaic represenaion of sraified oil/waer flow The VOF model is a surface-racing echniue applied o a fixed Eulerian mesh. In his model, fields for all variables and properies are shared by he phases and represen volume average values. A single se of momenum euaion is solved and he volume fracion of all he fluids in each compuaional cell is raced hroughou he domain [17]. This is accomplished by he soluion of a coninuiy euaion for he volume fracion of one of he phases. For he h phase, he euaion has he following form [17]: α S α + v α = ρ The source erm on he righ-hand side of he above euaion is assumed o be negligible for he case of sraified oil/waer flow wihou inerfacial mass ransfer. The volume fracion euaion will no be solved for he primary phase and i is compued based on he following consrain: n = 1 (1) α = 1 (2) The single momenum euaion shown below is solved hroughou he domain. The momenum euaion is dependen on he volume fracions of wo phases hrough he properies ρ and µ as: T ρ v + ρ v v = p+ µ v + v + ρ g + F (3) The volume fracion averaged densiy and viscosiy ae on he following form: ρ = α ρ (4)

3 µ = α µ (5) The las erm in euaion (3), F, is he exernal force per uni volume and can be modeled using he Coninuum Surface Force (CSF) model developed by Bracbill e al. [16]. An inerface is inerpolaed as a ransien region wih a finie hicness. Thus he surface ension localized in he region is convered ino a volume force wih he help of a Dirac dela funcion concenraed in he inerface as: F = 2 σκα α (6) The curvaure κ is compued from local gradiens in he surface normal a he inerface. Le n be he surface normal vecor, defined as he gradien ofα, he volume fracion of he h phase: n = α (7) The curvaureκ is defined in erms of he divergence of he uni normal, n [17]: κ = n (8) Where, n n = n In order o calculae convecion and diffusion fluxes hrough he conrol volume faces, geomeric reconsrucion scheme is applied for he inerface beween fluids using a piecewise linear approach. I assumes ha he inerface beween wo fluids is a linear slope wihin each cell, for calculaing he advecion of fluid hrough he cell faces. Firsly, he posiion of he linear inerface relaive o he cener of each parially filled cell is calculaed, based on informaion abou he volume fracion and is derivaives in he cell. Then, he advecing amoun of fluid hrough each face is obained using he compued linear inerface represenaion and informaion abou he normal and angenial velociy disribuion on he face. Finally, he volume fracion in each cell is given using he balance of fluxes calculaed during he previous sep. As shown (a) (b) Figure 2 Sech of he inerface calculaion: (a) Acual inerface shape and (b) Inerface shape represened by VOF he geomeric reconsrucion (piecewise-linear) scheme (9) in Figure 2, he reconsrucion of he inerface is accomplished via he use of he geomeric reconsrucion scheme. The RNG - model ogeher wih sandard wall reamen as he near-wall modelling mehod is used for urbulence modelling. The RNG-based urbulence model is derived from he insananeous Navier-Soes euaions, using a mahemaical echniue called renormalizaion group (RNG) mehods. I is similar in form o he sandard model, bu addiional erms and funcions are included in he ranspor euaions for and. A more comprehensive descripion of RNG heory and is applicaion o urbulence can be found in [17]. For he presen sysem, he governing euaions are: Turbulen ineic energy: µ ρ + ρu = µ + + σ i G xi xi x j ( ) ( ) ρ (10) Dissipaion rae of urbulen ineic energy: 2 µ ( ρ ) + ( ρui ) = µ + C1 G C2 ρ xi x + i σ x j (11) In hese euaions, G represens he generaion of urbulence ineic energy due o he mean velociy gradiens. The uaniies σ and σ are he urbulen Prandl numbers for and respecively. The urbulen ineic energy and is dissipaion rae are coupled o he governing euaions via he relaion: 2 = ρ C (12) µ µ The empirical consans for he urbulence model are assigned he following: C µ =0.0845, C 1 = 1.42, C 2 = 1.68, σ =1.0, σ = 1.3 The sandard wall funcion proposed by Launder and Spalding is used for modelling near wall flow in boh phases [17]. A he inle, uniform profiles for all he dependen variables are employed. The specified inle condiions are assumed consan over he cross-secional area. The axial velociy is calculaed using specified mixure velociy and waer cu. The velociies in he oher coordinae direcions are assumed o be zero. The urbulen ineic energy and is dissipaion rae are calculaed from a urbulence inensiy of 5 % and corresponding hydraulic diameer of each phase. The non-slip boundary condiion is imposed on he wall of he pipe. The oule boundary condiion was se up as a pressure oule wih a consan oule pressure. The gradiens for he enire variables in exi direcion were se o be zero. NUMERICAL METHOD The governing euaions were solved wih he finie volume mehod and he commercial CFD code FLUENT 6.3 is used as he numerical solver. The PISO algorihm is used o resolve he

4 coupling beween velociy and pressure. The more accurae second-order upsream advecion scheme is applied o momenum, urbulen ineic energy and urbulen dissipaion rae euaions. The PRESTO scheme is used for pressure discreizaion. These schemes improve he accuracy and he convergence of he soluion. The convergence crierion is based on he residual value of he calculaed variables, i.e., mass, velociy componens, urbulen uaniies. In he presen calculaions, he hreshold residual value for all he variables were se o The sraified oil/waer wo-phase urbulen flow in a mm diameer, 5 m long horizonal ube is numerically simulaed. An unsrucured non-uniform grid sysem was used o discreize he governing euaions. Figure 3 illusraes he grid opology used on one cross-secion. A boundary layer mesh is used close o he wall. The hree dimensional mesh, used for he compuaion consiss of 214,956 conrol volumes. A fine grid is used close o he inle of he pipe, where he flow field is developing. The lengh of he conrol volumes in axial direcion is gradually increased owards he end of he pipe, where he flow field is fully developed giving negligible changes of flow properies along he pipe. Waer Cu [-] U M U SO U SW Table1 Experimenal flow cases simulaed he experimenal measuremens and simulaions. The prediced resuls agree well wih he experimenal daa when he waer cu is in he range The experimenal resul shows a maximum pressure drop a waer cu This is probably due o he dispersion effec in he oil phase [2]. Bu he model gives a significan under-predicion of 18.4 % when waer cu is I may be due o inheren limiaion of he presen model in predicing dispersed flow condiions. The VOF model ha solves a single momenum euaion gives beer resuls when he flow is sraified. When he waer cu is 0.85, a significan difference beween he prediced and experimenal axial velociy profiles was observed and i can be he reason for he deviaion of he pressure drop predicion. [100*Pa/m] Figure 3 Grid opology on pipe cross-secion EXPERIMENTAL DETAILS The experimenal aciviies have been performed in he muliphase flow loop a Telemar Universiy College, Porsgrunn, Norway [1]. The muliphase flow loop consiss of a 14m long pipe wih an inner diameer of mm. Waer (densiy 998 g/m 3, viscosiy 1 mpa s) and Exxsol D60 oil (densiy 790 g/m 3, viscosiy 1.6 mpa s) were used as es fluids. The experimens have been performed a differen mixure velociies and waer cus. The insananeous local velociies were measured using Laser Doppler Anemomery (LDA), and ime average cross-secional disribuions of oil and waer were measured wih a raversable gamma densiomeer. The pressure drop along he es secion of he pipe was also measured. Some of he experimenal flow cases are simulaed as lised in Table 1. RESULTS AND ANALYSIS Predicions of axial pressure gradien from he presen model are compared wih he experimenal daa in Figure 4. In general, he agreemen is accepable, given he uncerainies in Waer Cu [-] Figure 4 Comparison beween prediced and experimenal resuls of axial pressure gradien The prediced inerface heigh is compared wih he experimenal daa presened by Elseh e al. [2] in Figure 5. The verical disance from he boom of he pipe o he poin where he waer cu is 0.5 is considered as he inerface heigh. The agreemen is uie favourable. However, he model underpredics he experimenal daa wih an absolue average error of 3.3 %. The deviaion is higher a lower and higher waer cus. The error is 8.0 % and 3.4 % when he waer cu is 0.15 and 0.85, respecively. This can be aribued o he inheren limiaion of he presen model in predicing dispersed flow. A low waer cus a significan par of he waer layer is dispersed in oil layer and he flow regime can be caegorized as oil coninuous dispersed flow [1]. This flow siuaion can no be handled accuraely wih he presen model based on VOF

5 approach, which is designed for sraified flow. Therefore a deviaion of he inerface heigh predicions can be observed a low waer cus. A inermediae waer cus, he flow was sraified wih wea mixing a he inerface. Few droples were observed close o he inerface [1]. In his case he flow regime can be considered as sraified flow. Therefore he model gives beer predicions a inermediae waer cus. Inerface Heigh [m] Figure 5 Comparison beween prediced and experimenal resuls of inerface heigh Finally a higher waer cus, mos of oil is dispersed in waer layer and waer coninuous dispersed flow is creaed. A large number of oil droples are presen a he inerface and a hic inerface region has been observed experimenally [1]. Again he presen model fails o give beer predicions for boh inerface heigh and pressure drop as shown in Figure 5 and Figure 4, respecively. The model gives more accurae resuls for boh pressure drop and inerface heigh a inermediae waer cus Slip Raio [-] Waer Cu [-] Waer Cu [-] Figure 6 Comparison beween prediced and experimenal resuls of slip raio Figure 6 shows a comparison beween he prediced slip raio and experimenal daa of Elseh e al. [2]. The slip raio s, is calculaed by: A W SO s = (13) A O U U SW Where AW and AO is he flow area of waer and oil, respecively. U SO is he superficial velociy of oil and U SW is he superficial velociy of waer. The prediced flow area was calculaed assuming a fla inerface. As shown in Figure 6 he prediced slip raio is observed o compare favourably wih experimenal measuremens. However he model slighly under-prediced he slip raio wih an average absolue error of 5.5 %. The deviaion is higher a lower and higher waer cus compared o inermediae waer cus. The slip raio is mainly influenced by flow area occupied by oil and waer when he same superficial velociies are used for boh experimens and simulaions. Therefore sligh deviaion in inerface predicion, gives an error in prediced slip raio due o inaccuracy of calculaing he flow area occupied by oil and waer. This can be he reason for he under-prediced slip raio a lower and higher waer cus. The prediced axial velociy profiles are compared wih Laser Doppler Anemomery (LDA) measuremens presened by Elseh [1] in Figure 7, where agreemen is seen o be uie reasonable. In Figure 7(a) and (b) sill picures of he flow are used as he bacground in order o visualise he flow. Figure 7(a) shows he axial velociy profiles when he mixure velociy and waer cu are 1.06 and 0.40, respecively. As shown in he image of Figure 7(a) he flow is sraified wih very wea mixing a he inerface. Few droples were formed by brea-up of he inerfacial waves [1]. Therefore he presen model based on VOF approach is used o predic he flow phenomena. Boh experimenal and he simulaed resuls shows he maximum velociy in oil phase as expeced. However he maximum velociy in oil phase is slighly under-prediced and also he posiion of he pea velociy is locaed slighly above compared o he experimenal daa. The velociy in waer phase is slighly over-prediced bu closely follows he experimenal resuls. The complex effecs of inerfacial waves and droples on inerfacial fricion and hereby pressure and velociy fields can no be prediced accuraely wih he presen model. This can be he reason for he deviaions in velociy profile. A waer cu 0.50 he oil/waer flow is sraified wih only small waves a he inerface. Mixing a he inerface is very wea and few droples were observed close o he inerface [1]. Therefore he prediced axial velociy profile agrees very well wih he experimenal daa as shown in Figure 7(b). I is noable ha he model can predic he posiion and he magniude of he pea velociies in boh phases. However he expecaions based upon classic laminar flow heory sugges higher velociy in he less viscous phase a eual volumeric flows as in his case wih waer cu Bu boh experimenal and prediced resuls show an opposie effec giving maximum velociy in oil phase. The reason for his effec is no obvious. A low flow velociies (laminar flow) he inerfacial fricion is governed by he viscosiies of differen phases and herefore a higher mean velociy can be expeced in less viscous fluid in order o mainain he coninuiy of he inerfacial shear. However, for

6 urbulen flows boh viscosiy and densiy influence he inerfacial fricion and herefore he posiion of he maximum velociy can no be prediced using classic laminar flow heory. A waer cu 0.50 he Reynolds numbers for oil and waer phases are 17,893 and 35,234, respecively. Therefore he flow is fully urbulen and he maximum velociy is locaed in oil phase. Posiion [-] Posiion [-] Axial Velociy [m/s] (a) Mixure velociy 1.06 m/s and waer cu Axial Velociy [m/s] (b) Mixure velociy 1.06 m/s and waer cu 0.50 Figure 7 Comparison of prediced and experimenal axial velociy CONCLUSION Sraified oil/waer wo-phase flow in a horizonal ube is numerically simulaed using commercial CFD pacage FLUENT 6.3. The simulaions are based on Volume of Fluid (VOF) model. The RNG - model ogeher wih sandard wall reamen as he near-wall modelling mehod is used for urbulence modelling. The predicions of pressure drop, slip raio and inerface heigh are observed o compare favourably wih experimenal measuremens. The predicions of he velociy profiles are uie saisfacory. The inerfacial fricion and he posiion of he inerface have found o have a profound effec on flow predicions. The presen model based on VOF approach has inheren deficiencies in predicing dispersed flow condiions a low and high waer cus. The model gives beer predicions a inermediae waer cus Alhough he presen formulaion is raher complex and demands much compuaion ime, due o he naure of he muliphase urbulen flow and he fine grid reuired for is implemenaion, i does appear o demonsrae ha he CFD echniue can be successfully applied o predic oil/waer sraified flow in pipes. REFERENCES [1] Elseh G., An Experimenal Sudy of Oil/Waer Flow in Horizonal Pipes, PhD Thesis, The Norwegian Universiy of Science and Technology (NTNU), [2] Elseh G., Kvandal H.K., and Melaaen M.C., Measuremen of velociy and phase fracion in sraified oil/waer flow, Inernaional Symposium on Muliphase Flow and Transpor Phenomena, Analya, Turey, 2000, pp [3] Lovic J. and Angeli P., Experimenal sudies on he dual coninuous flow paern in oil waer flows, Inernaional Journal of Muliphase Flow, 30, 2004, pp [4] Lovic J. and Angeli P., Drople size and velociy profiles in liuid liuid horizonal flows, Chemical Engineering Science, 59, 2004, pp [5] Angeli P. and Hewi G.F., Pressure gradien in horizonal liuid-liuid flows, Inernaional Journal of Muliphase Flow, 24, 1998, pp [6] Rodriguez O.M.H. and Oliemans R.V.A, Experimenal sudy on oil waer flow in horizonal and slighly inclined pipes, Inernaional Journal of Muliphase Flow, 32, 2006, pp [7] Valle A., Muliphase pipeline flows in hydrocarbon recovery, Muliphase Science and Technology, vol. 10 No.1, 1998, pp [8] Valle A. and Kvandal H., Pressure drop and dispersions characerisics of separaed oil/waer flow, Proceedings of he 1 s In. Symp. On Two-Phase Flow Modeling and Experimenaion, Rome, Ialy, [9] Arirachaaran, S., An experimenal sudy of wo-phase oil waer flow in horizonal pipes, MS Thesis, U. of Tulsa, [10] Arirachaarn, S., Oglesby, K.D. and Brill, J.P., An Analysis of Oil/ Waer Flow Phenomena in Horizonal Pipes, SPE, pp [11] Herm Sapelberg H. and Mewes D., Three phase flow (oil, waer and gas) in horizonal ubes, Proceeding of The Inernaional Conference on Muliphase Flows, 91-Tsuuba, 1994, pp [12] Taiel, Y. and Duler, A.E., A model for predicing flow regime ransiions in horizonal and near horizonal gas liuid flow. AIChE J. 22, 1976, pp [13] Kurban, A.P.A. and Angeli, P., Sraified and dispersed oil waer flows in horizonal pipes. BHRA95, 1995, pp [14] Brauner N., Moalem Maron D. and Rovinsy J., A wo-fluid model for sraified flows wih curved inerfaces. In. J. Muliph. Flow 24 (6), 1998, pp [15] Rhyne L., Oil waer mechanisic model. Advisory Board Meeing, NSF I/UCRC Corrosion in Muliphase Sysems Cener, April, [16] Bracbill J.U., Kohe D.B. and Zemach C., A coninuum mehod for modelling surface ension, J. Comp. Phys., 100, 1992, pp [17] Fluen, Fluen 6.2 Users Guide, Fluen Inc., Lebanon, NH, USA, 2005.