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IISPE 36644A Simulation Model for Three-Phase Gravity SeparatorsA. Hallanger, Christian Michelsen Research AS; F. Soenstaboe,-t 19SS. SCICWY of Polrowum EngwWom, IncTfIIs IXPOI wm Prcxmd Ici grcsmlalIwI at lh* 19SS SPE #mnual Tochn!wl Cealorooco tnd*iMkm MM h oNIVW, COkWakI Lt S A S-O OCIobof 1=Thm paper was se lec ted f or p resenta ti on by an SPE Program Comnwtee (OI 1OWIW rev iew ofI nlo rmatum umta ined man ab8 f1aci subm$tkd by the authcx (s) Cont en ts of the paper have no tbeen rewewed by ihe Society of Petroleum Engineers and are subjecf fo mrmckm by fheau thor (s ), The mater ia l, as presen ted &es not necassar !ly ref lect any pes ltlon of the soc iet y o fPetroleum Eng ineers, I ts of llcers, o r members Pa&ws presen tti a t SPE meeli ngs are $ub&ttopublcatikm review by Edi torial Gammmees of the Scmety of Pet roleum Engmeefs Permiss!M10copy ISrestrmled to an abstract o

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2A,HALLANGER,F.SOENSTABOE,T.KNUTSEN

This is a good approximation when the flow-rates through thevessel are high, with typical residence times for the oil in thevessel of 2-3 minutes.We also assume that the phases are close to thermodynamic

equilibrium. Flashing will then not take place inside theseparator, but is restricted to the inlet pipe. The validity of thisassumption will depend on the upstream geometry, i.e. distancebetween choke and separator vessel.Foam and emulsions can in some cases, depending on

composition of the hydrocarbons, strongly influence the internalflow (for a discussion of the basic see Ref. 4). In the followingthese effects will be neglected, and the discussion restricted tothree phases - free gas, oil containing dispersed water and freewater.With the assumptions above the energy equations can be

neglected, and the flow in the separator is given by the continuityand momentum equations together with closure relations andboundary conditions. The governing equations are then given by

~akp~ + V. (a,p,%) - r, k.1,.3 (1)

In order to satisfy the conservation of volume, mass andmomentum the following constraints must be fulfilled

(3)

Closure laws for phase interactions termThe interaction terms between the fluid phases in the momentumequations consist of several forces. The relative strength of theforces can be found from the equation of motion for one particle.This equation (Basset-Boussinesq-Oseen equation) can bewritten as 3

J!.!j! . ;p#.ApcDla,l(iF tip)+I?vp(Pp-PF)

The force terms on the right hand side represent drag,gravityhroyancy, pressure gradient, added mass and history

SPE 36644

force. The added mass and history force have been neglected inthe simulation code. This will tend to overestimate the slipvelocities between oil and water in the inlets and outlets andwhere there are local accelerations. Elsewhere in the separatorthey will be of less importance, For liquid drops in the gas phase,added mass and the history term can safely be neglectedcompared with the drag force since PC

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SPE 36644ASimulationModelforThree-Phase GravitySeparators 3

volume it is assumed that one phase is continuous and the twoother, if present, are dispersed. A phase is considered to bedispersed when the value of the volume fraction in the controlvolume is less than 0.4, Above 0.4 it is continuous in the controlvolume, Control volumes containing a phase interface cancontain two continuous phases, Eq. (5) is then applied twice,switching between the continuous and dispersed phase, and theresults are averaged.The particle diameter is present both in Eq. (5) and through the

Reynolds-number in Eq. (6). Average diameters are used in thecalculations. Coalescence and break-up of fluid particles areneglected. The particle diameters are set al the inlet to the vessel.The size of liquid dispersions will be determined by a balancebetween break-up in the up-stream choke and coalescence in theinlet pipe. The coalescence process is in general a function of thewater cut i. For liquid drops in the gas phase the particle sizesare determined by the break-up of the liquid inlet flow on lhemomentum deflector 9.Turbulence modelIn the inlet the flow is turbulent due to high velocities and strongshear forces. In the bulk of the vessel the velocities are small andrelatively uniform, and the turbulence level will decay. Thepresence of internal equipment such as vanes can however giveaccelerations and a local increase in the turbulence level. Theturbulent stress tensor (Reynolds-stresses), is model led using theeddy-viscosity concept. The turbulent viscosity is taken to beconstant ( we assume that the phases are Newtonian, this may notbe true for heavy oils or at low temperatures). The stresses arethen given by

au,Tti. p, (-. :)ax, , (8)P, - pcul

The turbulent fluctuating velocity is set equal to the averageinternal bulk velocity of the continuous fluid, while 10% of theheight of the stratification layer is used for the turbulent lengthscale. In a three-phase separator there are then three effectiveviscosities, one for each stratification layer. The stress tensor isonly applied for the continuous phase in the control volume, thestresses on the disperse phases are set to zero. This model givesa reasonable correspondence between calculated velocity profi Iesand data from experimental air-water separators 2Y. Theseseparators are however in I/10 scale, data for velocity profilesfrom full-scale separators are missing.Particle distributionsThe separation will depend both on the average value as well as

the shape of the distribution of particles dispersed in thecontinuous phase. In Eq. (5) and (6) only average diameters wereused for the particles. To have a better representation of theseparation of water drops from oil we introduce a model wherealso the shape of the distribution is inchrded.The particle distribution function will be approximated by a

finite number of groups as shown in Figure 2. Each group isrepresented by an average particle diameter and a volumefraction giving the integrated volume of the particles in thegroup.The flow of oil and water drops is calculated using a mixture

model, [t is assumed that [he mixture consists of niiisp parts, onecontinuous fraction (oil) and rrdisp-1groups of water drops, Thefollowing definitions are used:Mixture density

Mixture momentum

(9)

(lo)

The mixture volume fraction is retained in Eq. (9) and (10)since both gas and free water can co-exist in a control VOIumewith the mixture phase of oi1and water drops. We will then haveam

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where tt,~~isdetinedas.U,,k = izmIiti

- rl-r7c~r7rM k. I,ndip (15)

An expression for the relative velocity in Eq. (1 I ) cart befound from the Basset-Boussinesq-Oseen equation. If the particlerelaxation time is shorter than the characteris tic time for changein the flow, the left hand side in Eq. (4) can be neglected.Insert ing the expression for the drag coet%cient Eq. (6) in Eq. (4)we get (for N= < 1000)

ri;g(Pp P.r)r, = 1f4sCf~,J/(Nh) - (1 . o.lgs)

(16)

The factor f(NJ in the denominator is the deviation of the dragcoefficient from the Stokes drag law. ti, is implicitly definedthrough the Reynolds number dependence on the right hand side,and Eq. (16) must be solved by iteration. iSolution algorithmThe discretization of the equations follows Patarrkar 2.A controlvolume approach with staggered grids for the velocities is usedwith upstream differencing of the convective terms and centraldifferencing of the diffusion terms. The solution of themultiphase equations is based on the IPSA algorithm by Spalding3. To obtain a steady state solution for the equation set, asequential time-stepping procedure is applied. The steps are asfollows.

1)Initialize all variables, appIy initial conditions.2)Apply the boundary conditions.3) Solve for the phase velocities from the momentum

equations.4) Solve for the pressure correction. Add the pressure

correction to the pressure and correct for the velocities .

5)Solve for the volume fractions from the phase continuityequations.6)If not converged, advance the time and repeat from 2),We have previously assumed that the phase densities are

constant. For the mixture phase, however, this assumption mustbe modified. Eq. (9) shows that the mixture density will changeas the particle groups separate from the continuous fraction. Withthis in mind the following solution algorithm has been applied forthe mixture model:1)Solve the multifluid equations Eq.( I ) and Eq. (2), using Eq,

(14) with the extra source term for the momentum of the mixturephase.2)Find the relative velocity of the particle groups using Eq.

(16).3)Calculate the velocity of the continuous part, Eq. (12).4)Solve the continuity equations for the ndisp parts of the

mixture, Eq. (13).S)Find the new mixture density from Eq. (9) using the mixture

volume fraction from step 1),

6)Iterate from step 2) until convergence..

Boundary conditionsAt inflow boundaries the values for the volume fractions andphase velocities are prescribed, The mass and momentum fluxesare then calculated. At outflow boundaries , extrapolation of thedependent variables in the flow direction (zero gradient) is used.Summation of the continuity equations for gas, free water, oilfraction and water drops in the mixture phase gives, usingincompressibility and the constraint on phase fractions

2~~V.(a,r7,) .0 (17)Integration of Eq. (17) over the separator shows that the total

volumetric outflow will equal the total volumetric inflow at anytime. This result is enforced on the computed outflow at everyiteration step to promote convergence and stability.For separators, the total volumetric split between the outlets

must be specified in order to get an unique solution. This can bedone either by fixing the outlet pressures or, as it has been done

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SPE 36644ASimulationModel for Three-Phase GravitySeparators 5

here, specify the total volumetric flow through each outletinitialy. The total volumetric flow at the water , oil and gasoutlets are set equal to the total inflow of dispersed water, oil andgas respectively. Since there are some cross-entrainment, thevolumetric split between the outlets must be corrected during theiterations. If this is not done, the heights of the fluid interfaceswill not stay constant, and the separator can ultimately beemptied of one phase during the simulation. Due to thiscorrection, the height of the interfaces are in fact determined bythe initial phase fractions in the separator.At free water/oil-water mixture interfaces, consideration must

be given to the coalescence of water drops with the free waterphase. Thecoalescence or mass transfer from the mixture phaseto the tlee water phase should be proportional to the mass of thedispersions in the control volume It will also depend on theparticle diameter 4.The proportionality factor, or relaxation time,is here set equal to 0.2 for all particle groups. The total masstransfer at fluid interfaces is then given by

r . r; 5UMPMk-2 (18)As long as the mass transfer rate is sufficiently high, integratedresult such as entrainment of water in oil is not sensitive to theexact value of the relaxation time.Sub-grid modelsSome of the separator internals, like weir plates, can be resolvedon the grid through the closing (blocking) of control volumes orthe sides of control volumes to flrud flow. But internals likevanes, wire mesh and plate separators where the smallest internaldimensions are on the cm or mm scale, cannot be resolved in thesimulation of a separator with a length scale in meter. Thesegeometries must be modelled as porous regions where a fractionof the control volume is open to the flow through the use of areaand volume porosities. The resulting pressure drops in theinternals due to the sub-grid obstructions are included in themomentum equations as flow resistances. This is done usingempirical formulas for single phase flow. The vahre of the dragcoefficient CDwill depend on the geometry

Fk - -CDai ptlrlkl aik (19)

Simulation resultsThe multiphase model outlined above has been applied on a firststage separator from Norsk Hydros Oseberg field. The geometryof the separator is shown in the symmetry plane through the

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separator axis in Fig. 3. The vessel is 13.1 m long and with adiameter of 3.15 m. The inlet has a vertical orientation, The flowis deflected by a momentum breaker before it is diverteddownwards through a pallring box and into the main separatorvessel. Downstream of the inlet is a flow straightener for the gasphase. Further down there are two perforated plates to smooththe flow in the liquid phase. KJpstream of the gas outlet there isa demi ster. The weir plate reaches 1,0 m over the separatorbottom.A grid of 49 x 10 x 20 control volumes was used in the

simulations. Due to symmetry only half of the vessel wasincluded in the computational domain. This gave a spatialresolution of 0.27m in the axial direction and 0.1575 m in thetransverse and vertical directions.The process data for the fluid phases are given in Table 1. Six

cases with different positions of the fluid interfaces wereconsidered. The values for NIL and NOL are given in Table 2together with the water cut and measured values for theermainment of water in oil. The inlet distribution of water is log-normal and found from a correlation based on data from someNorth Sea oilfields 6.An average diameter of 0.25 mm was usedin the simulations with a normalized standard deviation of 3. Thedistribution was divided into 7 particle groups. In order toresolve the lower part of the distribution particles larger than 0.4mm are lumped into one group.For gas bubbles in liquid and liquid particles in gas averagediameters of 1 mm were used. These values gave very goodseparation between liquid and gas, with negligible cross-entrainment, Oil -drops in the free water phase should havediameters on the pm level, and with an entrainment on the ppmlevel. In the simulations we used a diameter of 1 mm, which gavean entrainment of the right order. A correct value for the dropsize would demand a physical model for the mixing rate of oildrops into the free water,Simulation results for Case 1 are shown in Figure 4, giving

flow velocities and the positions of the fluid interfaces in thesymmeb-y plane for each of the three phases. The oil velocity ina horizontal cut plane just below the oil/gas interface is given inFig. 5,The volume fractions of the smallest and largest drop classesin the symmetry plane are shown in Fig, 6.The specified distribution of water drops in the inlet and the

calculated distribution of drops in the oil outlet are shown inFigure 7. The simulated results of water entrainment , togetherwith the measurements from Norsk Hydro, are given in Figure 8plotted against the oil residence time. The residence time in thevessel is here an average time calculated from the volumetricflow rates, NIL and NOL using the methods from the API designrules ,

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Discussionhisseen from Fig. 4 that the phases separate very easily. Behindthe first flow straightener the interfaces are well established. Thisis not surprising since the oil viscosity is rather low. After thefirst flow straightener the gas flow is homogeneous. The plots ofoil velocities show that the separator has a reasonably goodhydraulic function. The flow is, besides the inlet region, ratheruniform except for recirculation zones around the pallring boxand behind the first flow straightener. There is a flow of oilbelow the two perforated plates in the middle. This could havebeen suppressed by moving the plates further down into the waterphase. The acceleration of oil through the perforations is alsoclearly seen. In the water phase there are a recirculation zonewhich is driven by the tliction from the moving oil layer above.The plots of the drop classes in Fig. 6 shows that most of the

smallest drops will be entrained with the oil, while nearly all ofthe largest drops will coalece with the free water. There is a smallstagnant zone between the inlet and the end bottom where dropswilI agglomerate,The plot of the inlet and outlet distribution of water drops in

Fig. 7 shows that most of the drops smaller than 0.15 mm areerrtrained with the oil. Nearly aU of the drops larger than 0.5 mmwill separate and coalesce with free water.The correspondence between data and simulations in Fig.8 is

satisfying. The simulations represent the main trend ofdecreasing entrainment with increasing recidence time. For thelargest residence times there are some deviations betweensimulations and measurements. It is not clear if this is due to aspread in data from small variations in oil composition during thetest period at the platform.ConclusionsThere is a strong dependency of drop diameters on entrainment.Test simulations using different average drop diameters gavevery different results, This is not surprising since the separationvelocity is approximate] y proportional with the square of theparticle diameter.The mixture model for the water drops could also be used on

the liquid drops in the gas phase. The entrainment of the liquidin gas would however be most influenced by the efficiency of thedemister.Nomenclature

C = drag coefficientd = diameter of the dispersed particles, L, mf = friction factorg = constant of gravity, g = 9.81 m/s2m = mass, m, kgM = momentum source term, en/L2t2,kg/m2s2N.= Reynolds number

p = pressure, nr/Lt2, kg/ms2t = time, t,su = velocity, L/t, rds

NIL = normal interface level oil/water, L, mmNOL = normal oil level, L, mmQ = volumetric flowrate, L/t, m3/ha = vo]ume fraction.

r = mass transfer rate, tmh, kg/sp = fluid density, m/L3, kglm3p = dynamic viscosity, mfLt, kg/insT = stress tensor, m/Lt2, kg/tn.s2

Subscriptsc = continuousd = dispersedF = fluidk,l = phase number, particle classm = mixturen = number of phasesp = particler = relative, relaxation. .I,J = space directionst = turbulent

AcknowledgementThe field data have been made available through the courtesy ofNorsk Hydro, Oseberg Production.References

1. API Specification 12J (SPEC 12J), Seventh Edition,October 1, 1989.2. Bratseth, A. (1988) Studie av vaske/gass separasjon i enhorizontal separator. Matematisk model] fors@k baser-tpa vann-hsftseparasjon. Dr.ing thesis, NTH Trondhei m3. C1ift, R,, Grace, J. R. and Webcr, M. E, (1 978). Bubbles,Drops and Particles. Academic Press.4. Davies, G.A. (1992). Mixing and coalescence phenomenain fiquid-liquid systems. In J,D. Thornton (cd): Science and Practiceof Liquid-liquid Extraction. Oxford Engineering Science Series, 27.Oxford University Press.5. Fewel Jr., K. J,,Kean, J.A. Computer modelling aidsseparator retrofit , Gas & Oil Journal, Juty 6, 1992,6. Gramme, P. E,, Norsk Hydro Research Cerrtre Porsgrunn,Private communication7. Hafskjold B., Morrow T,, Celius H.K, and Johnson D.R,Drop-drop Coalescence in OWWater Separation, SPE ATCE, NewOrleans, Sept. 19948. Hinze, J.O. (1955) AIChE J. 1 (289-295).9. ISEP (1988) Improved Separator Efficiency andPerformance Study, Vol. 111

10. Ishii, M, and Zuber, N. ( 1979). Drag Coefficient and

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SPE 36644A Simulation Model for Three.Phase Gravity Separatora

Relative Velocity in Bubbly, Droplet or Particulate Flows. AIChEJournal Vol. 25, No. 5,843-855.

1I. lshii, M. (1975) Thermo-Fluid Dynamic Theory of TwoPhase Flow, Chapters IX and X, Eyrolles, Paris, or Scientific andMedical Publication of France, N. Y.

12. Patankar, S. V., (1980) Numerical Heat Transfer and FluidFlow, Hemisphere Publishing Corporation, USA.

13. Spalding, D. B. (1983) Developments in the IPSAprocedure for numerical computation of multiphase flowphenomena with interphase slip, unequal temperatures, etc. Irr Shih,T, M,, cd.; Numerical prop. and methodologies in heat transfer,p.421-437.

Table 1. Process data

Phase Density Viscosity Q(kg/m) (CP) (m/h)Gas 48.0 0.014 2408Oil 762.0 0.689 1398Water 976.0 0.353 30.0 -35,6

Table 2. Interface levels and water cut

Case NIL NOL Water cut inlet WiO(entrained)(mm) (mm) (%) (%)

1 620 1690 2.3 I .22 610 1740 2.5 1.43 620 1610 2.4 1.54 620 I61O 2.5 1.45 460 1630 2.4 0.66 270 1630 2. I 0.6

7

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8A.HALLANQER,F.SOENSTABOE,T.KNUTSEN

Mixttm viscosityOil viscosity ..... 0.5CP ,.. ,.....

SPE 36644

-- i::; I .,,,.........~,...,,.., 0,. ..., ,/. . .,. ...,, /. . . . . . . . // ///

////~//~

1

-L. ..1 --- -.--J- .--_. ..-1-. --- -- _0,2 0,4 0,6 0,8 0,11

Waterfraction

Fig. 1- Mixture viscosity as a function of water fraction. Water viscosity is 1.0 cP. The inversion from an oil-continuous to a water-continuous mixture is assumed to take place at a water-cut of 0.6

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SPE 36644A Simulation Model for Three.Phase Gravity Separators

N\

I 1I 1,:

\--i

Fig. 2 Drop distributionand discreterepresentation.lhe volume fraction of each particle class is equal to the area of the correspondingbox

Fig. 3 Geometry of Oseberg separator

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10A.HALLANGER,F.SOENSTABOE,T.KNUTSEN SPE 36644

,..-....a..a. . . . . .. . . . .

Fig. 4a Gas volumetric flow, average velocities 15 cmh

-----. ..-. . .. . . . . . . . . . . . * . . . . . . .

Fig. 4b Oil volumetric flow, average velocities 10 cmk

-------- .-. ----- -, ..-1---,..:!:: :s ~ b ., 7Fig. 4CWater volumetric flow, average velocities 0.5 cmk704

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SPE 36644A Simulation Model for Three.Phase Gravity Separators 11

---- -..- . . . . - ------- --- -. . . . . . . . . .* -.4 -----------, . . . . ---- .,- --.:: -- _: .- ..-

4... . q$.-< .. - ..- .- --- .- .... ..-.-. * . . .. *,,+.,..- + .- +--- A . ..-+-> \ . ,,-- ---- - ---- * ++.-+

z --z-z- :::2 ~x:xz .?+ .+*~-99~ . .A ----- ~---Fig. 5 Oil flow velocities. Vector plot are shown in a horizontal cut plane below the gas/oil interface.

.......... .....................

Fig 6a Contour plot of 60 pm water drop class

\ bFig. 6b Contour plot of 510 pm water drop class

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A.tiALLANGER,F.SOENSTA130E,T.KNUTSEN12 SPE 36644

~- OtmetI0,5

0,4i?

!- 0,3!g0,2

0,1 -.

-. -A0 /.. 10 l W 200 im 400 JoDnp dmneter (pm)

Fig. 7 Volume fractions of water drops in inlet and oil outlet.

x

SW

x MMumm3ntA .%WMWI I

x

AxA

x

1 1 1 1 11,s 1,7 f,8 1,9 2 2, f 2,2m mshimxw Oim (mi ll )

Fig. 8 Water entrainment in oil, simulated and measured values

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