Modeling and Control of Three-Phase Gravity Separators in OilProduction Facilities

Atalla F. Sayda and James H. Taylor

Abstract Oil production facilities exhibit complex andchallenging dynamic behavior. A dynamic mathematical mod-eling study was done to address the tasks of design, controland optimization of such facilities. The focus of this paper ison the three-phase separator, where each phases dynamicsare modeled. The hydrodynamics of liquid-liquid separationare modeled based on the American Petroleum Institutedesign criteria. Given some simplifying assumptions, the oiland gas phases dynamic behaviors are modeled assumingvapor-liquid phase equilibrium at the oil surface. In order tovalidate the developed mathematical model, an oil productionfacility simulation was designed and implemented based onsuch models. The simulation model consists of a two-phaseseparator followed by a three-phase separator. An upset in theoil component of the incoming oil-well stream is introducedto analyze its effect of the different process variables andproduced oil quality. The simulation results demonstrate thesophistication of the model in spite of its simplicity.

I. INTRODUCTIONThe function of an oil production facility is to separate the

oil well stream into three components or phases (oil, gas,and water), and process these phases into some marketableproducts or dispose of them in an environmentally accept-able manner. In mechanical devices called separators, gasis flashed from the liquids and free water is separatedfrom the oil. These steps remove enough light hydrocarbonsto produce a stable crude oil with the volatility (i.e., vaporpressure) to meet sales criteria. Separators are classified astwo-phase if they separate gas from the total liquid streamand three-phase if they also separate the liquid stream intoits crude oil and water components. The gas that is separatedis compressed and treated for sales [1]. Modeling suchfacilities has become very crucial for controller design, faultdetection and isolation, process optimization, and dynamicsimulation. In this paper, we focus on three-phase gravityseparators as they form the main processes in the upstreampetroleum industry, and have a significant economic impacton produced oil quality.

Three-phase separators have rich and complex dynam-ics, which span from hydrodynamics to thermodynamicsand conservation laws. Many modeling techniques andapproaches have been used to model three-phase separators.As far as the thermodynamics aspects of the separator areconcerned (i.e., the oil and gas phases), many modelingapproaches have been suggested in the literature. The phaseequilibrium modeling approach have been used for 50 years

James H. Taylor is a professor with the Department of Electrical &Computer Engineering, University of New Brunswick, PO Box 4400,Fredericton, NB CANADA E3B 5A3 jtaylor@unb.ca

Atalla F. Sayda is a PhD candidate with the Department of Electrical& Computer Engineering, University of New Brunswick, PO Box 4400,Fredericton, NB CANADA E3B 5A3 atalla.sayda@unb.ca

and has provided satisfactory results for such equipment asflash tanks and distillation columns [2]. The basic equationsin this approach are used to describe the material balances,equilibrium relations, the composition summation equa-tions, and the enthalpy equations. Nonequilibrium modelshave been developed to describe real physical separationprocesses; other modeling approaches were also consideredsuch as the computational model, the collocation model,and the bubble residence contact time model [3].

Historically, the hydrodynamics of the separators aque-ous part have been modeled using complex mathematical-numerical models, which describe the coalescence andsettling of oil droplets in oil-water dispersions. Such modelstake into account separator dimensions, flow rates, fluidphysical properties, fluid quality and drop size distribution.The output of these models is the quality of the outputoil [4]. Other models, which describe the kinetics of lowReynolds number coalescence of oil droplets in water-oil dispersions, have been developed to give the volumesof separated continuous-phase and coalesced drops [5]. Acomputational fluid dynamic (CFD) model was developedto model the hydrodynamics of a three-phase separator,based on the time averaging of Navier-stokes equations forthree phases; it takes into consideration the non-ideal flowdue to inlet /outlets and internal equipment for separationenhancement [6]. The alternative path model approach,which exploits the residence time distribution (RTD) of bothoil and aqueous phases in three-phase separators, was de-veloped to give a quantitative description of hydrodynamicsand mixing in the aqueous phase [7]. Powers [8] extendedthe American Petroleum Institute (API) gravity separatordesign criteria to design free-water knockout vessels forbetter capacity and performance. Powers showed that theAPI design criteria can handle nonideal flow by performingpractical RTD experiments.

This paper extends the API static design criteria tomodel the hydrodynamics of three phase separators, whichresults in a simpler modeling approach. Furthermore, asimple phase equilibrium model is developed to model thethermodynamic aspects of the separator. We describe theoperation of gravity three-phase separators in section 2. Adynamic model of the separator is developed for each phasein section 3, where it can be used to estimate the steadystate flows and to study the separator behavior during otheroperating conditions. An oil production facility simulationmodel is designed, implemented and tested to validate anddemonstrate the separator behavior during normal operationand upsets in section 4. Finally, simulation results arediscussed and summarized in section 5.

II. THREE-PHASE GRAVITY SEPARATION PROCESSDESCRIPTION

Three-phase separators are designed to separate and re-move the free water from the mixture of crude oil and water.Figure 1 is a schematic of a three phase horizontal separator.The fluid enters the separator and hits an inlet diverter.This sudden change in momentum does the initial grossseparation of liquid and vapor. In most designs, the inletdiverter contains a downcomer that directs the liquid flowbelow the oil /water interface. This forces the inlet mixtureof oil and water to mix with the water continuous phase (i.e.,aqueous phase) in the bottom of the vessel and rise to theoil /water interface. This process is called water-washing;it promotes the coalescence of water droplets which areentrained in the oil continuous phase. The inlet diverterassures that little gas is carried with the liquid and assuresthat the liquid is not injected above the gas /oil or oil /waterinterface, which would mix the liquid retained in the vesseland make control of the oil /water interface difficult.

Some of the gas flows over the inlet diverter and thenhorizontally through the gravity settling section above theliquid. As the gas flows through this section, small drops ofliquid that were entrained in the gas and not separated bythe inlet diverter are separated out by gravity and fall to thegas-liquid interface. Some of the drops are of such a smalldiameter that they are not easily separated in the gravitysettling section. Before the gas leaves the vessel it passesthrough a coalescing section or mist extractor to coalesceand remove them before the gas leaves the vessel.

Fig. 1: Three phase horizontal separator schematic.

III. THREE PHASE GRAVITY SEPARATORMATHEMATICAL MODELING

When the hydrocarbon fluid stream enters a three-phaseseparator, two distinctive phenomena take place. The firstphenomenon is fluid dynamic, which is characterized bythe gravity separation of oil and water droplets entrainedin the aqueous and the oil phases respectively, the gravityseparation of gas bubbles entrained in the stream, and thegravity separation of liquid droplets which are dispersed inthe gas phase. The second phenomenon is thermodynamic,in the sense that some light hydrocarbons and gas solutionflash out the oil phase and reach a state of equilibrium dueto the pressure drop in the separator. Due to the complexity

of such phenomena, we are going to focus on the hydro-dynamic separation of oil droplets entrained in the aqueousphase and the thermodynamic separation of gas and lighthydrocarbons from the oil phase. This decision is justifiedby the fact that the water washing process minimizes thewater entrained in the oil phase. Furthermore, precedinggravity separation processes minimize the amounts of gasentrained in the main stream.

Figure 2 illustrates the simplified separation process,where an oil-well fluid with molar flow Fin and gas, oil,and water molar fractions Zg, Zo, Zw respectively entersthe separator. The hydrocarbon component of the fluidseparates into two parts; the first stream Fh1 separates bygravity and enters the oil phase, and the second stream Fh2stays in the aqueous phase due to incomplete separation.The liquid discharge from the aqueous phase FWout isa combination of the dumped water stream FW plus theunseparated hydrocarbon stream Fh2. The gas componentin the separated hydrocarbon stream, which enters the oilphase, separates into two parts; the first gas stream Fg1flashes out of the oil phase due to the pressure drop in theseparator, and the second gas stream Fg2 stays dissolved inthe oil phase. The oil discharge Foout from the separatorcontains the oil component of the separated hydrocarbonFo and the dissolved gas component Fg2. The flashed gasFgout flows out of the separator for further processing.

Fig. 2: Main separated component streams in three-phasegravity separator

We model the dynamics of each phase of the separa-tor in the subsequent sections, to simplify the modelingprocess. Additionally, some simplifying assumptions haveto be made. The separation processes are assumed to beisothermal in all phases of the separator at 100 oF . We alsoassume that the flow pattern in the liquid phases is plugflow, especially in the aqueous phase. Furthermore, the oildroplets in the aqueous phase have a uniform droplet sizedistribution with a diameter of dm = 500 micron. The oildroplets rising velocities are assumed to obey Stokes law.We model the equilibrium thermodynamics phenomenonunder the assumption that Raoults law is valid. We assumethat only one light hydrocarbon gas flashes out the oil phaseinto the gas phase, namely methane. Methane in the vaporphase is also assumed to be an ideal gas (i.e., the ideal gaslaw applies). Finally, there is liquid-vapor equilibrium atthe oil surface and liquid-liquid equilibrium at the water-oilinterface.

A. The aqueous phaseIn order to model the aqueous phase of the separator, we

will follow the API static design criteria under the usual

simplifying assumptions. The API specification permitshydrocarbon droplets (i.e., oil and dissolved light gas) ofdesign diameter to rise from the bottom of the separator tothe surface during the water retention period, as illustratedin figure 3. A hydrocarbon droplet located on the cylinderbottom has the greatest distance to traverse to the oil-waterinterface. Therefore, modeling the oil separation hydrody-namics based on removal of this droplet would ensure re-moval of all others of the same or larger diameter. Given thesimplifying assumptions, the traversing hydrocarbon dropleton its path to the oil-water interface is subjected to a verticalrising velocity component vv governed by Stokes law, anda horizontal velocity component vh governed by the plugflow pattern of the aqueous phase. The vertical velocitycomponent is estimated from Stokes law by equation (1):

vv = 1.7886 106 (SGh SGw)d2m

w(1)

where SGh, SGw are the specific gravities of the hydro-carbon droplets and water, respectively, dm is the dropletdiameter in microns, and w is the water viscosity in CPat 100 oF . The horizontal velocity component is estimatedfrom the aqueous phase retention as vh = L/ , where Lis the length of the separator and = Vwat /Fwat is theretention time of the aqueous phase; Vwat is the volume ofthe aqueous phase, and Fwat is the water outflow. The levelof the oil-water interface h is determined from equations(2):

Ac = Vwat/L= R2 0.5R2 sin(2)

h = R(1 cos()) (2)where Ac is the cross-sectional area of the aqueous phase,R is the separator radius and is the angle which definesthe circle sector of the cross sectional area Ac. The angle of the longest droplet path to the oil-water interface canbe estimated from equation (3):

= tan1vvvh

(3)

Fig. 3: Oil separation hydrodynamics under normaloperation conditions

The design parameters {Ac, h, , } of the aqueousphase will take their nominal values under normal operatingconditions of the three-phase separator, i.e., for the nominalvalue of Fwat which leads to complete separation, as shown

in figure 3. However, our model must also be valid for off-nominal values. This is complicated at higher flow values,since we can no longer achieve complete separation. Letus assume that the water outflow Fwat has increased by avalue of Fwat due to a corresponding increase in inflow.This will result in an increase in vh to vh + vh and anangle change of the longest path of a traversing hydrocarbondroplet from to 1 < . Figure 4 illustrates the conceptof virtually extending the tank so that complete separationwould be achieved at L1 = L + L, although this isfictional. Assuming that the design parameters {Ac, h, }remain the same, as shown in figure 4, we have:

1 = tan1(vv + vv)

vh(4)

L1 = h cot(1)

We have to make a simplifying assumption in order toestimate the volume fraction of unseparated hydrocarbon, .As shown in figure 5 (top), we assume that the unseparatedoil droplets in the aqueous phase form a tail extendinginto the virtual separator extension, as also shown bydashed lines in figure 5 (bottom, labelled S3) that undergoesturbulent flow and exits with the water. The accuracy of thisassumption is, of course, dependent upon the geometry ofthe tank and structure of the water and oil outlets.

Fig. 4: Oil separation hydrodynamics under high wateroutflow condition

Under this assumption, region S3 in the bottom fig-ure represents the volume of the unseparated hydrocarbonfluid VS3. It can be seen from figure 5 that region S3is the difference between the hydrocarbon fluid volumein the virtual separator (represented by region S1), VS1and the hydrocarbon fluid volume in the actual separator,VS2 (represented by region S2). The volume VS1 can becalculated as the difference between the volume of thecylindrical segment defined by the parameters {h, L1, }and the cylindrical wedge parameterized by {h, L1, 1},as in equation (5):

VS1 = R2L1{ 0.5 sin(2) 3 sin 3 cos sin3

3(1 cos ) }(5)

Furthermore, again referring to figure 5, the volume VS2can be estimated as the difference between the volume ofthe cylindrical segment parameterized by {h, L, } and thecylindrical wedge parameterized by {h1, 1, L, 1}, as inequation (6):

VS2 = R2L{0.5 sin(2)3 sin 1 31 cos 1 sin3 1

3(1 cos 1) }(6)where the virtual oil-water interface h1 and angle 1 aredefined by equations (7):

h1 = L tan(1)

1 = cos1(1 h1R) (7)

Consequently, we can estimate the unseparated hydrocar-bon fluid volume fraction from equation (8):

={

1 VS2VS1 , L1 > L0 else

(8)

Fig. 5: Unseparated hydrocarbon fluid volume under highwater outflow condition

Having estimated the unseparated hydrocarbon fluid vol-ume fraction , we can calculate the separated and unsepa-rated volumetric flow components of the hydrocarbon fluidFh1v , Fh2v respectively. Finally we can write the dynamicmaterial balance of the aqueous phase by using equations(9), after we convert the molar flows to volumetric flows:

Fh1v =(Zg + Zo)FinMwh

62.43SGh

Fh2v =(1 )(Zg + Zo)FinMwh

62.43SGh

FWout =ZwFinMww62.43SGw

+ Fh2v

dVwatdt

=FinMwin62.43SGin

FWout Fh1v (9)

where {Mwh, Mww, Mwin} are the hydrocarbon,water, and incoming mixture molecular weights;{SGh, SGw, SGin} are the hydrocarbon, water, andincoming mixture specific gravities; Vwat is the aqueous

phase volume; and FWout is the water discharge volumetricoutflow.

B. The oil phaseIn order to model the thermodynamic phenomenon in the

oil phase, we first do the flash calculations to estimate theamounts of gas which will flash out of solution. Since weassumed that ideal phase equilibrium state is valid, then byapplying Raoults law we can tell how much methane willstay entrained in the oil phase. Raoults law relates the vaporpressure of components to the composition of the solution.This can be formulated mathematically as yiP = xiPviwhere yi is the mole fraction of the component i in the vaporphase, xi is the mole fraction of component i in the liquidphase, P is the total pressure of the vapor phase (i.e., theseparator working pressure), and Pvi is the vapor pressureof component i [9], [10].

Since we have only one flashing light hydrocarbon (i.e.,methane), this implies that the mole fraction of methanein the vapor phase is y = 1, and that the mole fractionof methane entrained in the liquid phase is x = P/Pv .Given the composition {Zg1, Zo1} of the separated hy-drocarbon stream Fh1, we can estimate the amounts offlashing methane Fg1 and dissolved methane in the oil phaseFg2. The oil discharge flow Foout can also be estimatedalong with its average molecular weight Mwo1 and itsspecific gravity SGo1. The complete dynamic model of theoil phase, which is given by equations (10), can be thenformulated by taking the material balance:

Fg1 = (1 x)Zg1Fh1Fg2 = xZg1Fh1

Foout = Fo + Fg2dNoildt

= Fh1 Fg1 FooutMwo1 = xMwg + (1 x)MwoSGo1 =

xMwgNoil + (1 x)MwoNoilxMwgNoil

SGg+ (1x)MwoNoilSGo

(10)

where Noil is the number of liquid moles in the oil phase;Fo is the molar oil component in the oil discharge flowFoout ; {Mwg, Mwo} are the gas and oil molecular weights;and {SGg, SGo} are the gas and oil specific gravities.

C. The gas phaseGiven the ideal gas law assumption, the gas phase of the

separator is modeled by taking the material balance. We canestimate the gas pressure P by applying the ideal gas law,as described by equations (11):

dNgasdt

= Fg1 FgoutVoil =

Mwo1Noil62.43SGo1

Vgas = Vsep Vwat VoilP =

NgasRT

Vgas(11)

where Ngas is the number of gas moles in the gasphase; Fgout is the gas molar outflow from the separator;{Voil, Vgas, Vsep} are the volumes of the oil phase, gasphase, and separator respectively; R is the universal gasconstant; and T is the absolute separator temperature.

IV. SEPARATOR MODEL VALIDATIONHaving obtained the dynamic model of the three-phase

gravity separator, we design a simulation model whichemulates an oil production facility to validate the modelbehavior under several scenarios. The simulation modelbasically consists of three processes, as depicted in figure6. The first is a two-phase separator in which hydrocarbonfluids from oil wells are separated into two phases (gas,oil + water) to remove as much light hydrocarbon gases aspossible. The separator is 15 ft long and has a diameter of 5ft. The two-phase separator model was developed based onthe models of the oil and gas phases of the three-phase sep-arator. That is, we have modeled only the thermodynamicphenomenon of gas flashing out the liquid phase. The liquidproduced is then pumped to the three-phase separator (i.e.,the second process), where water and solids are separatedfrom oil. The oil produced is then pumped out and sold torefineries and petrochemical plants if it meets the requiredspecifications. The three-phase separator has length of 8.6ft and a diameter of 4.8 ft. Flashed light and medium gasesfrom the separation processes are sent to a gas scrubberwhere medium hydrocarbon and other liquid remnants areseparated from gas and sent back for further treatment.Produced gas is then compressed by a compressor (i.e., thethird process) and pumped out for sales. The third processmodel was not included in the simulation model for thesake of simplicity.

The two separation processes in the simulation model arecontrolled to maintain the operating point at its nominalvalue, and to minimize the effect of disturbances on theproduced oil quality. As shown in figure 6, the first separa-tion process is controlled by two PI controller loops. In thefirst loop, the liquid level is maintained by manipulating theliquid outflow valve. The second loop controls the pressureinside the two-phase separator by manipulating the amountof gas discharge. The second separation process has three PIcontroller loops. An interface level PI controller maintainsthe height of the oil /water interface by manipulating thewater dump valve, while the oil level is controlled by thesecond PI controller through the oil discharge valve. Thevessel pressure is maintained constant by the third PI loop.

V. SIMULATION RESULTSThe two-phase separator process operates at a liquid

phase volume of 146 ft3 and working pressure of 625PSI. In contrast, the three-phase separator operates at waterphase volume of 77.5 ft3, oil phase volume of 46.5 ft3, andworking pressure of 200 PSI. The working temperaturesof the two separation processes are 100oF . The facilityprocesses hydrocarbon streams of 25.23 moles /sec from oilwells under pressure of 1900 PSI. The incoming streamhas mole fractions of 22.61% gas, 7.79% oil, and 69.6%

water. In order to demonstrate the dynamic behavior of theseparators, the oil content of the incoming stream has beenincreased linearly by 2 moles /sec between the time instantst1 = 150 sec and t2 = 250 sec of the simulation time.Figure 7 portrays this change in the incoming stream flowand in its molar composition; the oil mole fraction increasedwhile the water and gas mole fractions decreased.

Fig. 7: Incoming hydrocarbon fluid and its molarcomposition

The ramp increase in the oil component of the incomingstream caused the liquid volume and gas pressure in thetwo-phase separator to peak to 167 ft3 and 630 PSI respec-tively, as shown in figure 8. The two PI control loops ofthe two-phase separator intervened to correct such operatingpoint errors by manipulating the liquid and gas outflows.This operating point disturbance took approximately 300sec to be totally rejected by the separator control system.Figure 8 also reveals the difference between the dynamics ofthe two phases of the separator. The liquid phase has slowerdynamics than the gas phase dynamics, i.e., the pressurechanges faster than the liquid volume. It is interesting to no-tice that the liquid molar outflow increased by 2 moles /sec,which is the same applied change in the incoming stream.This reflects on the quality of the liquid produced in termsof its specific gravity, which increased from 31.7o API to35.3o API. The quality change can be verified by plottingthe molar composition of the liquids produced, as shownin figure 9. The oil mole fraction of the produced liquidincreased, while the mole fractions of dissolved gas andwater decreased.

Although the incoming stream upset was rejected andcorrected in the two-phase separator, the resulting change inthe quantity and quality of the produced liquid transmittedthe upset to the three-phase separator and other downstreamprocesses. As portrayed in figure 10, the upsets in theseparator process variables did not have much impact, asthe three PI control loops corrected such an upset. Given thedifference between the three phases dynamics (i.e., the fast

Group

Separator

Oil Treator

Gas

Scrubber Gas

compressor

Oil well

Water treatment

Water

CV1 CV5

CV3

CV2

CV4

Water

Oil & water mix

Water

Oil

CV7

P

PT1

P

PT2

P

PT3

I-8

I-10

I-11

I-13

I-14

I-15

I-16

I-17

I-18

CV6

I-19

To water

treatment

Oil sales

Gas sales

Disposal

CV8

P

PT4

I-22

Gas

Gas

Gas

Pipe line

Signal line

LCL : Level control loop

LCL 1

LCL 2

LCL 3

LCL 4

PCL : Pressure control loop

PCL 1

PCL 2

PCL 3

PCL 4

FT1

FT2

FT6

FT3

FT4

FT5

FT7 FT8

MotorLT1

LT3

LT2

LT4

FT : Flow transmitter

PT : Pressure transmitter

LT : Level transmitter

CV : Control valve

N1

Fig. 6: The oil production facility schematic diagram

!

"

"! #

Fig. 8: Two-phase separator process variables changeduring the incoming stream upset

gas phase dynamics compared to the two liquid phases), theupsets are rejected in approximately 300 seconds. However,two main events should be noticed; the first event is theslight increase in the water discharge molar flow. Thiscan be attributed to inefficiency in the gravity separationhydrodynamics, which implies that some oil could not beseparated and was discharged with water. We can verify thisevent by plotting the volumetric composition of the dumpedwater (1st phase), as shown by the top plots in figure11. The dumped water volumetric composition reveals thatsome amounts of unseparated oil has been lost.

Fig. 9: Two-phase separator liquid discharge molarcomposition

Although the volume loss of oil is slight (around 1.6%),it represents a major economic loss of approximately $ 50million per year at current prices. On the other hand, theseparator did compensate for the incoming fluid upset byincreasing the produced oil outflow, as illustrated in figure10. The second interesting event is the decrease in theflashed gas amounts (i.e., gas outflow) due to the qualitychange in the incoming fluid stream. This can be verifiedby plotting the molar composition of the produced oil,as shown in the bottom plots of figure 11. While the oilmole fraction in the produced oil increased, the dissolved

gas mole fraction decreased. This simulation study demon-strated the sophistication of the three-phase separator model,in spite of its simplicity. Not only did the model addressthe quantity dynamics of separator process variables, butthe quality of the produced oil and water also.

Fig. 10: Three-phase separator process variables changeduring the incoming stream upset

Fig. 11: Three-phase separator produced water and oilcompositions

VI. CONCLUSIONSA dynamic mathematical model was developed for an

oil production facility. The focus of this study was on thethree-phase separator, where each phases dynamics weremodeled. The hydrodynamics of liquid-liquid separationwere modeled based on the API design criteria, whichwas extended to address the process dynamics in addition

to its statics. The oil and gas phases dynamic behaviorswere modeled assuming vapor-liquid phase thermodynamicequilibrium at the oil surface.

An oil production facility simulation was designed basedon such model, in order to test and validate the developedmathematical model. The simulation model consisted ofa two-phase separator followed by a three-phase model.The separation processes were controlled by PI controlloops to maintain the operating point at its nominal value.An upset in the oil component of the incoming oil-wellstream was introduced to analyze its effect of the differentprocess variables and produced oil quality. The simulationresults proved the sophistication of the model in spite ofits simplicity. Furthermore, this study demonstrated thechallenging task of modeling and controlling oil and gasproduction facilities, and that more work has to be done todevelop higher fidelity models.

VII. ACKNOWLEDGEMENTThis project is supported by the Atlantic Canada Op-

portunities Agency (ACOA) under the Atlantic InnovationFund (AIF) program. The authors gratefully acknowledgethat support and the collaboration of Cape Breton University(CBU), the National Research Council (NRC) of Canada,and the College of the North Atlantic (CNA). The first-named author also acknowledges the support of the NaturalSciences and Engineering Research Council of Canada(NSERC) for funding this research.

REFERENCES[1] K. Arnold and M. Stewart, Surface Production Operation: Design

of Oil-Handling Systems and Facilities, 2nd ed. Woburn, MA:Butterworth-Heinemann, 1999, vol. 1.

[2] R. Taylor and A. Lucia, Modeling and analysis of multicomponentseparation processes, Separation Systems and Design, pp. 1928,1995.

[3] M. M. Dionne, The dynamic simulation of a three phase separator,Masters thesis, University of Calgary, 1998.

[4] B. Hafskjold, H. K. Celius, and O. M. Aamo, A new mathematicalmodel for oil/water separation in pipes and tanks, SPE Production& Facilities, vol. 14, no. 1, pp. 3036, February 1999.

[5] S. A. K. Jeelani, R. Hosig, and E. J. Windhab, Kinetics of lowreynolds number creaming and coalescence in droplet dispersions,AIChE Journal, vol. 51, no. 1, pp. 149161, January 2005.

[6] A. Hallanger, F. Soenstaboe, and T. Knutsen, A simulation modelfor three-phase gravity separators, in Proceedings of SPE AnnualTechnical Conference and Exhibition. Denver, Colorado: SPE,October 1996, pp. 695706.

[7] M. J. H. Simmons, E. Komonibo, B. J. Azzopardi, and D. R. Dick,Residence time distribution and flow behavior within primary crudeoil-water separators treating well-head fluids, Chemical EngineeringResearch & Design, vol. 82, no. A10, pp. 13831390, October 2004.

[8] M. L. Powers, Analysis of gravity separation in freewater knock-outs, SPE Production Engineering, vol. 5, no. 1, pp. 5258, February1990.

[9] R. G. E. Franks, Modeling and Simulation in Chemical Engineering.Wiley, 1972.

[10] C. D. Holland, Fundamentals and Modeling of Separation Processes:Absorption, Distillation, Evaporation, and Extraction. EnglewoodCliffs, N.J.: Prentice-Hall, 1974.