Oil-Water Separation in Liquid-Liquid Hydrocyclones …tustp.org/publications/SPE00071538.pdf ·...

Copyright 2001, Society of Petroleum Engineers Inc.

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AbstractThe liquid-liquid Hydrocyclone (LLHC) has been widely usedby the Petroleum Industry for the past several decades. Alarge quantity of information on the LLHC available in theliterature includes experimental data, computational fluiddynamic simulations and field applications. The design ofLLHCs has been based in the past mainly on empiricalexperience. However, no simple and overall designmechanistic model has been developed to date for the LLHC.The objective of this study is to develop a mechanistic modelfor the de-oiling LLHCs, and test it against available and newexperimental data. This model will enable the prediction ofthe hydrodynamic flow behavior in the LLHC, providing adesign tool for LLHC field applications.

A simple mechanistic model is developed for the LLHC.The required input for the model is: LLHC geometry, fluidproperties, inlet droplet size distribution and operationalconditions. The model is capable of predicting the LLHChydrodynamic flow field, namely, the axial, tangential andradial velocity distributions of the continuous-phase. Theseparation efficiency and migration probability are determinedbased on swirl intensity prediction and droplet trajectoryanalysis. The flow capacity, namely, the inlet-to-underflowpressure drop is predicted utilizing an energy balance analysis.

An extensive experimental program has been conductedduring this study, utilizing a 2” MQ Hydroswirl hydrocyclone.The inlet flow conditions are: total flow rates between 27 to18 gpm, oil-cut up to 10%, median droplet size distributionsfrom 50 to 500 ìm, and inlet pressures between 60 to 90 psia.The acquired data include the flow rate, oil-cut and dropletsize distribution in the inlet and in the underflow, the rejectflow rate and oil concentration in the overflow and the

separation efficiency. Additional data for velocity profileswere taken from the literature, especially from the Colman andThew (1980) study. Excellent agreement is observed betweenthe model prediction and the experimental data with respect toboth separation efficiency (average absolute relative error of3%) and pressure drop (average absolute relative error of1.6%).

IntroductionThe petroleum industry has traditionally relied onconventional gravity based vessels, that are bulky, heavy andexpensive, to separate multiphase flow. The growth of theoffshore oil industry, where platform costs to accommodatethese separation facilities are critical, has provided theincentive for the development of compact separationtechnology. Hydrocyclones have emerged as an economicaland effective alternative for produced water deoiling and otherapplications. The hydrocyclone is inexpensive, simple indesign with no moving parts, easy to install and operate, andhas low maintenance cost.

Hydrocyclones have been used in the past to separatesolid-liquid, gas-liquid and liquid-liquid mixtures. For theliquid-liquid case, both dewatering and deoiling have beenused in the oil industry. This study focuses only on the lattercase, namely, using the liquid-liquid hydrocyclones (LLHC) toremove dispersed oil from a water continuous stream.

Oil is produced with significant amount of water and gas.Typically, a set of conventional gravity based vessels are usedto separate most of the multiphase mixture. The small amountof oil remaining in the water stream, after the primaryseparation, has to be reduced to a legally allowable minimumlevel for offshore disposal. LLHCs have been usedsuccessfully to achieve this environmental regulation.

There is a large quantity of literature available on theLLHC, including experimental data sets and computationalfluid dynamic simulations. However, there is still a need formore comprehensive data sets, including measurements of theunderflow droplet size distribution. Additionally, there is aneed for a simple and overall mechanistic model for theLLHC.

The objective of the present study is two fold: to developa mechanistic model for the LLHC that can predict the flowbehavior in the hydrocyclone and the oil/water separationefficiency; and to acquire new experimental data for the

SPE 71538

Oil-Water Separation in Liquid-Liquid Hydrocyclones (LLHC) –Experiment and ModelingCarlos Gomez, Juan Caldentey, Shoubo Wang, Luis Gomez, Ram Mohan and Ovadia Shoham, SPE, The University ofTulsa

2 C. GOMEZ, J. CALDENTEY, S. WANG, L. GOMEZ, R. MOHAN, O. SHOHAM SPE71538

LLHC, including detailed measurements of the droplet sizedistributions in the inlet and underflow streams. Thedeveloped mechanistic model can be utilized for the design ofLLHCs, providing the flexibility of designing alternativeLLHC geometries for the same operating conditions foroptimization purposes. It will also allow detailed analysis andperformance prediction for a given LLHC geometry andoperating conditions, including separation efficiency and flowcapacity (pressure drop – flow rate relationship).

LLHC Hydrodynamic Flow Behavior. The LLHC, shown inFigure 1, utilizes the centrifugal force to separate the dispersedphase from the continuous fluid. The swirling motion isproduced by the tangential injection of pressurized fluid intothe hydrocyclone body. The flow pattern consists of a spiralwithin another spiral moving in the same circular direction(Seyda and Petty, 1991). There is a forced vortex in the regionclose to the LLHC axis and a free-like vortex in the outerregion. The outer vortex moves downward to the underflowoutlet, while the inner vortex flows in a reverse direction tothe overflow outlet. Moreover, there are some re-circulationzones associated with the high swirl intensity at the inletregion. These zones, with a long residence time and very lowaxial velocity, have been found to be diminished as the flowenters the low angle taper section (see Figure 1).

An explanation of the characteristic reverse flow in theLLHC is presented by Hargreaves (1990). With high swirl atthe inlet region, the pressure is high near the wall region andvery low toward the centerline, in the core region. As a resultof the pressure gradient profile across the diameter, whichdecreases with downstream position, the pressure at thedownstream end of the core is greater than at the upstream,causing flow reversal.

As the fluid moves to the underflow outlet, the narrowingcyclone cross-sectional area increases the fluid angularvelocity and the centrifugal force. It is due to this force and thedifference in density between the oil and the water, that the oilmoves to the center, where it is caught by the reverse flow andseparated, flowing into the overflow outlet. Instead, if thedispersed phase is the heavier, like solid particles, it willmigrate to the wall and exit through the underflow.

The amount of fluid going through the different outletsdiffers with heavy and light dispersion. It means that for thesetwo different separation cases, two different geometries areneeded (Seyda and Petty, 1991). In the deoiling case, usuallybetween 1 to 10 percent of the feed flow rate goes to theoverflow.

Another phenomenon that may occur in a hydrocyclone isthe formation of a gas core. As Thew (1986) explained,dissolved gas may come out of solution because of thepressure reduction in the core region, migrating fast to theLLHC axis, and eventually emerging through the overflowoutlet. A significant amount of gas can be tolerated butexcessive amounts will disturb the vortex. An experimentalstudy on this topic is found in Smyth and Thew (1996).

LLHC Geometry. The deoiling LLHC consists of a set ofcylindrical and conical sections. Colman and Thew’s (1988)design has four sections, as shown in Figure 2. The inletchamber and the reducing section are designed to achievehigher tangential acceleration of the fluid, reducing thepressure drop and the shear stress to an acceptable level. Thelatter has to be minimized to avoid droplet breakup leading toreduction in separation efficiency. The tapered section iswhere most of the separation is achieved. The low angle ofthis segment keeps the swirl intensity with high residencetime. An integrated part of the design is a long tail pipecylindrical section in which the smallest droplets migrate tothe reversed flow core at the axis and are being separatedflowing into the overflow exit. This configuration gives a verystable small diameter reversed flow core, utilizing a very smalloverflow port.

Young et al. (1990) achieved similar results to Colman-Thew’s LLHC, in terms of separation efficiency, with adifferent hydrocyclone configuration. Three sections wereused instead of four. The reducing section was eliminated andthe angle of the tapered section was changed from 1.5º to 6º.Later, Young et al. (1993) developed a new LLHC design,which resulted in an improvement in the separationperformance. The principal modification of the enhanceddesign was a small change in the tail pipe section. A minuteangle conical section was used rather than the cylindrical pipe.Another important parameter in the LLHC geometry is theinlet configuration, as shown in Figure 3. Rectangular andcircular, single and twin inlets have been most frequently usedby different researchers. The main goal is to inject the fluidwith higher tangential velocity, avoiding the rupture of thedroplets. The twin inlets have been considered to maintainbetter symmetry and for this reason maintain a more stablereverse core (Colman et al., 1980; Thew et al., 1984). Goodresults have also been achieved with the involute single inletdesign.

The last element of the LLHC is the overflow outlet. Thisis a very small diameter orifice that plays a major role in thesplit ratio, defined as the relationship between the overflowrate and the inlet flow rate. Most of the commercial LLHCspermit changing the diameter of this orifice, depending on therange of operating conditions.

Literature ReviewThere are hundreds of literature references on the LLHC,including experimental studies, CFD simulations andmodeling. Detailed review of these previous studies can befound in Caldentey (2000) and Gomez (2001). In this sectiononly pertinent mechastudies are reviewed briefly

Two textbooks that condense pioneering works onhydrocylones and fundamental theories, includingexperimental data, design, and performance aspects, areBradley (1965) and Svarovsky (1984). Both refer in most ofthe chapters to solid-liquid hydrocyclones, with only a smallsection available on liquid-liquid separation and otherapplication areas.

SPE71538 OIL-WATER SEPARATION IN LIQUID-LIQUID HYDROCYCLONES (LLHC)-EXPERIMENT AND MODENLING 3

Experimental Studies. Only a representative sample ofprevious experimental studies is summarized here. The reviewis divided into laboratory studies and design and applicationstudies, as follows.Laboratory Studies. Earlier studies were presented by Simkinand Olney (1956), Sheng (1974), Johnson et al. (1976), Smythet al. (1980), Colman et al. (1980) and Colman and Thew(1980).

A general revision of the hydrocyclone developed atSouthampton University was carried out by Thew (1986), whoalso discussed some issues presented previously by Moir(1985). Other studies were published by Gay (1987),Bednarski and Listewnik (1988), Woillez and Schummer(1989) and Beeby and Nicol (1993).

Young et al. (1990) measured the flow behavior in aColman and Thew (1980) type hydrocyclone, and laterproposed a new modified design. In 1991, Weispfennig andPetty explored the flow structure in a LLHC using avisualization technique (laser induced fluorescence). Theperformance of a mini hydrocyclones, of 10 mm-diameter,were studied by Ali et al. (1994) and Syed et al. (1994).Design and Applications. A summary of the selection, sizing,installation and operation of hydrocyclones was provided byMoir (1985). Meldrum (1988) described the basic design andprinciple of operation of the de-oiling hydrocyclone.

Choi (1990) tested a system of six hydrocyclones (35 mmdiameter) operating in parallel for produced water treatment(PWT). The performance of three commercial liquid-liquidhydrocyclones (two static and one dynamic) in an oil field wasevaluated by Jones (1993).CFD Simulations. Numerical simulations or CFD are usedwidely to investigate flow hydrodynamics. As expressed byHubred et al. (2000), the solution of the Navier StokesEquations for simple or complex geometry for non-turbulentflow is feasible nowadays. But current computationalresources are unable to attain the instantaneous velocity andpressure fields at large Reynolds numbers even for simplegeometries. The reason is that traditional turbulence models,such as k-º, are not suitable for this complex flow behavior.On the other hand, more realistic and complicated turbulencemodels increase the computational times to inconvenientlimits.

The flow in hydrocyclones has been numericallysimulated by Rhodes et al. (1987), Hsieh and Rajamani (1991)(see also Rajamani and Hsieh, 1988; Rajamani andDevulapalli, 1994) and He et al. (1997). In most of thesestudies the models were evaluated through comparison withlaser-doppler anemometry (LDA) data. Many researchershave used this technique to measure the velocity field andturbulence intensities (Dabir, 1983; Fanglu and Wenzhen,1987; Jirun et al., 1990; and Fraser and Abdullah, 1995).Modeling. Although widely used nowadays, the selection anddesign of hydrocyclones are still empirical and experiencebased. Even though quite a few hydrocyclone models areavailable, the validity of these models for practicalapplications has still not been established (Kraipech et al.,2000). A thorough review of the different available models

can be found in Chakraborti and Miller (1992) and Kraipech etal. (2000).

The LLHC models can be divided into empirical andsemi-empirical, analytical solutions and numerical simulations(Chakraborti and Miller, 1992). The empirical approach isbased on development of correlations for the process keyparameters, considering the LLHC as a black box. The semi-empirical approach is focused on the prediction of the velocityfield, based on experimental data. The analytical andnumerical solutions solve the non-linear Navier-StokesEquation. The former one is a mathematical solution, which isachieved neglecting some of the terms of the momentumbalance equation. The numerical solution uses the power ofcomputational fluid dynamics to develop a numericalsimulation of the flow. As Svarovsky (1996) comments, itseems that the analytical flow models have been abandoned infavor of numerical simulations due to the complexity of themultiphase flow phenomena.

From extensive experimental tests, Colman and Thew(1983) developed some correlations to predict the migrationprobability curve, which defines the separation efficiency for aparticular droplet size in a similar way that the gradeefficiency does for solid particles. Seyda and Petty (1991)evaluated the separation potential of the cylindrical tail pipesection. A semi-empirical model to predict the velocity field ina cylindrical chamber was developed to calculate the particletrajectories, and hence, the grade efficiency.

Wolbert et al. (1995) presented a computational model todetermine the separation efficiency based on the analysis ofthe trajectories of the oil droplets. An extension of Bloor andIngham (1973) LLHC model was presented by Moraes et al.(1996). The modification takes into account the difference inthe split ratio for liquid-liquid and solid-liquid hydrocyclones.

The literature review confirms the need for accurateexperimental data utilizing appropriate sampling procedureand including the measurements of the droplet sizedistributions at the inlet and underflow sections, and the needto develop a simple mechanistic model for the LLHC. Thesedeficiencies are addressed in the present study.

Experimental ProgramThis section describes the experimental facility, workingfluids, definitions of pertinent separation parameters, and theexperimental results of the LLHC.

Experimental Facility. The experimental three-phase, oil-water-gas, flow loop is shown Figure 4. The oil-water-gasindoor flow facility is a fully instrumented state-of-the-arttwo-inch flow loop, enabling testing of single separationequipment or combined separation systems. The test loopconsists of four main components: storage and meteringsection, LLHC test section, downstream oil-water separationfacility, and data acquisition system. Following is a briefdescription of these sections.Storage and Metering Section. Oil and water are stored in twotanks of 400 gallons capacity each. Each tank is connected totwo pumps. The first one is a 3656 model pump, 1x2-8 size,


cast iron construction with bronze impeller, John Crane Type21 mechanical seal, 10 HP motor and operates at 3600 rpm. Itdelivers 25 gpm @ 108 psig. The second one is a 3656 Modelpump, 1.5x2-10 size, cast iron construction with bronzeimpeller, John Crane Type 21 mechanical seal, 25 HP motorand operates at 3600 rpm. It delivers 110 gpm @ 150 psig.Both pumps are equipped with return lines. Each fluid ispumped from the storage tank to the metering section. Themetering section comprises of pressure gages, control valves,variable speed controllers and state-of-the-art Micromotion®

net oil computers (NOC), which provide the total mass flowrate, water-cut, temperature, and mixture density. The signalsfrom the flow meters and control valves are fed to the dataacquisition system, which will be described later. Checkvalves to prevent any back-flow are installed downstream ofthe control valves. The metered oil and water are thencombined in a mixing-tee to obtain oil-water dispersion.Additionally, a static mixer is available in parallel to themixing-tee for homogenization of the flow.Test Section. Figure 5 shows a schematic of the LLHC testsection and Figure 6 presents a photograph of the LLHCprototype installed in the test section. The LLHC is a 2-inchesNATCO MQ Hydro Swirl Hydrocyclone mounted verticallywith a total height of 62 inches. Water flows into the testsection through a 2” pipe coming from the water tank. Thispipe has a split section where the water split stream mixeswith oil in order to get thorough mixing with the desired oilconcentration. The split section is a ½ inch pipe composed ofa water wheel paddle meter, a mixing tee and a static mixer.Oil for the mixture is pumped from a 55 gallons barrel with agear pump, and metered by means of a gear flow meter. Oncethe oil and water are mixed, they pass through a static mixer inorder to get a desired droplet size distribution. After this pointthe mixture is directed to the main stream pipe entering it bymeans of an inverse pitot tube. Once the mixture enters themain stream line, it can either flow directly to the test sectionor be subjected to an additional mixing loop where smallerdroplet size distributions can be achieved. The mixture can besent to either the MQ steel hydrocyclone or the MQ acrylichydrocyclone. The latter LLHC, which has the samecharacteristics as the steel one, is placed for observationpurposes.

In order to measure the droplet size distribution, a specialisokinetic sampler is designed and operated in order to getrepresentative accurate measurements of the distributions, asshown in Figure 7. Samples from both the inlet and underflowstreams can be obtained. Once the sample is taken, it is placedin the droplet size distribution analyzer. For this purpose, aLaser scattering device, namely, the Horiba LA-300 analyzeris used to analyze the samples. . It may be noted that asurfactant-based additive is utilized, as shown in Figure 7, toavoid coalescence in the sample when transferred and run inthe droplet size analyzer

The flow in the LLHC is split into two streams: Theoverflow stream, with mainly oil, and the down-flow stream,with mainly water. The overflow is discharged into a 55gallons barrel and the underflow is sent to the downstream

three-phase separator. Pressure transducers are located on theupper and the lower outlets of the LLHC. The underflowstream passes through a metering section, located upstream ofthe three-phase separator, where flow rate, density,temperature and water cut are measured using a liquidMicromotion® coriolis mass flow meter. Due to the small oilconcentration in some of the experiments, a special oil contentanalyzer is utilized to measure the oil concentration of theunderflow. This equipment is a Horiba OCMA 220 modelthat uses infrared spectroscopy technique.Downstream Oil-Water Separation Section. The 528 gallonthree-phase flow separator located downstream of the LLHCtest section operates at 10 psig. It consists of threecompartments. In the first compartment the oil-water mixtureis stratified and the oil flows into the second compartmentthrough flotation. In this compartment, there is a level controlsystem that activates a control valve discharging the oil intothe oil storage tank. The water flows from the firstcompartment to the third compartment through a channellocated below the second compartment. In this compartment,there is also a level control system, allowing water to flow intothe water storage tank.Data Acquisition System. IDM variable speed controllersinstalled on all the 4 pumps control the oil and water flowrates into the test section. The flow loop is also equipped withseveral temperature sensors and pressure transducers formeasurement of the in-situ temperature and pressureconditions.

All output signals from the sensors, transducers, andmetering devices are collected at a central panel. A state-of-the-art data acquisition system, built using LabView®, is usedto both control the flow in the loop and also to acquire datafrom analog signals transmitted from the instrumentation. Theprogram provides variable sampling rates. The sampling ratewas set at 2 Hz for a 2 minutes sampling period. The finalmeasured quantity results from an arithmetic averaging of 120readings, after steady-state condition is established.

A regular calibration procedure, employing a high-precision pressure pump, is performed on each pressuretransducer at a regular schedule, to guarantee the precision ofmeasurements. The temperature transducer consists of aResistance Temperature Detector (RTD) sensor and anelectronic transmitter module.Working Fluids. Tap water and mineral oil were chosen and adye (red) was added to the oil to improve flow visualizationbetween the phases. The oil has low emulsification, fastseparation, appropriate optical characteristics, non-degradingproperties, and is non-hazardous. The properties of the oil are0API=33.7 and µ O = 13.6 cP at 1000F. During all theexperimental runs the average temperature in the flow loopvaried between 700 and 800 F.

Definition of Separation Parameters. Following are thedefinitions of two important parameters used in this study todefine the total separation efficiency:


Split Ratio: The split ratio is the ratio of the overflow rateto the inlet flow rate, as given below:

%100inletq

overflowqF ⋅= (1)

where F is the split ratio, qoverflow is the total flow rate at theupper outlet of the LLHC , and qinlet is the total inlet flow rate.

Oil Separation Efficiency: Practical interpretation ofseparation data is concerned with the purity of individualdischarge streams. Many references quantify the relative phasecomposition of the separated streams in the form of apercentage by volume measurement. In this study a widelyused definition is adapted for the oil separation efficiency,namely,

%100q

q

inletoil

overflowoilff ⋅=

−

−ε (2)

where qoil-overflow is the flow rate of oil at the overflow, qoil-inlet

is the flow rate of oil at the inlet. Utilizing continuityrelationship, Equation (2) becomes

%100)inletoilcinletq

underflowoilcunderflowq1(ff ⋅

−⋅−⋅

−=ε (3)

Note that when coil-underflow tends to zero, the separationefficiency is maximum.

Experimental Results. A total of 124 runs were conducted inthis study. The data is analyzed and presented, so as todemonstrate the effect of the flow variables on the separationefficiency, as given in the following sections.Effect of Pressure Drop and Flow Rate. The separation of oildroplets in the swirl chamber of the hydrocyclone is a result ofthe forces imposed on the oil droplets in the spinning fluid andthe residence time in the chamber. Lower flow rates meanlonger residence times but lower acceleration forces.Conversely higher flow rates result in higher accelerationforces and smaller residence times. As shown in Figure 8, theMQ Hydroswirl performance is independent of flow rate in therange tested. For hydrocyclones of similar geometries, theliterature reports similar results.Effect of Underflow Pressure. Back pressure must be appliedat the hydrocyclone underflow, in order to force the corestream containing the oil to the overflow; otherwise, all theflow will exit through the underflow and no separation wouldoccur. For a given underflow backpressure, if the overflowpressure is slowly increased, the core diameter increases,ultimately resulting in part of the oil core discharging outthrough the underflow. The MQ Hydroswirl performance isindependent of the underflow pressure, as shown in Figure 9,provided there is sufficient backpressure to force enough flowout of the overflow (Young et al. 1990). It is critical thatconstant back pressure be applied, since swings inbackpressure result in the oil in the core being rapidlydischarged with the cleaned water.

Effect of Overflow Diameter. Separation efficiency ofLLHCs is independent of overflow diameter (Young et al.1990). This is confirmed by the results of this study, as shownin Figure 10. However, the minimum overflow rate to makean effective separation increases with increasing overflowdiameter. The minimum flow rate for each orifice openingsize is a result of a minimum velocity required for the oil tomove to the overflow (Young et al. 1990). This minimumvelocity multiplied by the cross sectional area of the overflowresults in a minimum flow rate for effective separation foreach overflow opening size. Increasing overflow size resultsin an increased amount of water, which must be removed withthe oil to obtain the same removal efficiency. This of coursemeans that a greater flow rate of oily wastewater must bereprocessed. The major advantage of larger overflowdiameters is that it allows more oil to be removed withoutaffecting the purity of the underflow water stream when largeslugs of oil are encountered in field operations. Furthermore,larger outlets are not as susceptible to blockage as the smallerones. Figure 10: Effect of overflow diameter on efficiencyEffect of Inlet Oil Concentration. Field reports indicate thatwith increased oil concentrations, the performance of the MQHydroswirl hydrocyclone improves and can handle theadditional oil. As can be observed in Figure 11, separation isindependent of inlet oil concentration when there is adequateflow at the overflow to remove the required amount of oil.The improved separation of field installations with increasingoil content is probably due to the presence of larger oil dropletsizes.Effect of Oil Droplet Size Distribution. The variable havingthe greatest impact on oil-water separation is the oil dropletsize distribution. Figure 12 shows the separation performanceof the MQ Hydroswirl hydrocyclone for several droplet sizedistributions, with the median droplet size shown. As can beseen, the oil separation efficiency increases with increase inthe droplet size. This can be intuitively expected as the largeroil droplets coalesce faster than the smaller ones.

Typical results for the droplet size distributions in theinlet and underflow streams are given in Figure 13. Thisfigure demonstrates the removal of the large droplets from thefeed stream. Also, the underflow stream contains smallerdroplets sizes, as compared to the inlet stream, due to breakupof droplets in the LLHC.

Mechanistic ModelingThe following sections provide details of the mechanisticmodel developed for the LLHC in the present study.

Swirl Intensity. The swirl intensity is defined as the ratio ofthe local tangential momentum flux to the total momentumflux. The swirl intensity equation given below is amodification of the Mantilla (1998) correlation, based onErdal (2001) CFD simulations, given by


⋅+

= ))tan(2.11(I

M

MRe49.0 15.0

93.0

2

T

t118.0 βΩ

( )( )

+

− 12.0

7.016.0

z

35.0

4

T

t tan21Dc

z

Re

1I

M

M

2

1EXP β

(4)

where Mt/MT is the ratio of the momentum flux at the inlet slotto the axial momentum flux at the characteristic diameterposition, calculated as:

is

c

cc

isc

avc

is

T

t

A

A

A/m

A/m

Um

Vm

M

M===

ρρ

&

&

&

& (5)

The variables in the above equations are: Ù is the swirlintensity, Re is the Reynolds number, â is the semi-angle ofthe conical sections, Dc is the characteristic diameter of theLLHC (measured where the angle changes from the reducingsection to the tapered section in the Colman and Thew’sDesign, and at the top diameter of the 3º tapered section of theYoung’s Design), z is the axial position starting from Dc, Vis

is the velocity at the inlet, Uavc is the average axial velocity atDc, m& is the mass flow rate, Ac is the cross sectional area atDc and Ais is the inlet cross sectional area.

The Reynolds number is defined in the same way as forpipe flow with the caution that it refers to a given axialposition, yielding:

c

zavzcz

DURe

µρ

= (6)

where ìc is the viscosity of the continuous fluid.

The inlet factor, I, as suggested by Erdal (2001), isdefined as:

−−=

2n

EXP1I (7)

where n = 1.5 for twin inlets and n = 1 for involute singleinlet.

Velocity Field. The swirl intensity is related, by definition, tothe local axial and tangential velocities. Therefore, it isassumed that once the swirl intensity is predicted for a specificaxial location, it can be used to predict the velocity profiles.Both the tangential and axial velocities are calculatedfollowing a similar procedure as proposed by Mantilla (1998).The radial velocity, which is the smallest in magnitude, iscomputed considering the continuity equation and the walleffect.Tangential Velocity. It has been confirmed experimentallythat the tangential velocity is a combination of a forced vortexnear the hydrocyclone axis, and a free-like vortex in the outerwall region, neglecting the effect of the wall boundary layer,

as shown in Figure 14. This type of behavior is known as aRankine Vortex. Algifri et al. (1988) proposed the followingequation for the tangential velocity profile:

−−

=

2

c

c

m

avc R

rBEXP1

R

r

T

U

w (8)

where w is the local tangential velocity, which is normalizedwith the average axial velocity, Uavc, at the characteristicdiameter; Rc is the radius at the characteristic location and r isthe radial location. The term Tm represents the maximummomentum of the tangential velocity at the section and Bdetermines the radial location at which the maximumtangential velocity occurs. The following expressions wereobtained by curve-fitting several sets of the experimental data.

Ω=mT (9)

Involute Single Inlet:

7.17.55B −= Ω (10)

Twin Inlets:

35.28.245B −= Ω (11)

It can be seen that the above equations are only functions ofthe swirl intensity, Ù. Thus, for a given axial position, thetangential velocity is only function of the radial location andthe swirl intensity.

Axial Velocity. In swirling flow the tangential motion givesrise to centrifugal forces which in turn tend to move the fluidtoward the outer region (Algifri 1988). Such a radial shift ofthe fluid results in a reduction of the axial velocity near theaxis, and when the swirl intensity is sufficiently high, reverseflows can occur near the axis. This phenomenon causes acharacteristic reverse flow around the LLHC axis, whichallows the separation of the different density fluids.

A typical LLHC axial velocity profile is illustrated inFigure 15. Here, the positive values represent downward flownear the wall, which is the main flow direction, and thenegatives values represent upward reverse flow near theLLHC axis. The flow reversal radius, rrev, is the radial positionwhere the axial velocity is equal to zero.

To predict the axial velocity profile, a third-orderpolynomial equation is used with the proper boundaryconditions. The general form is as follows:

432

23

1 ararara)r(u +++= (12)

where a1, a2, a3 and a4 are constants. The boundary conditionsconsidered are:

1. 0dr

)Rr(du z ==

The velocity is maximum at the

wall;


2. 0)rr(u rev == Zero velocity at the location ofreverse flow, rrev;

3. 0dr

)0r(du=

=The velocity is symmetric about the

LLHC axis; and

4. 2zc

zR0 avzc RUrdr)r(u2 πρπρ ∫ = Mass conservation.

Substituting the boundary conditions in Equation (12)yields the axial velocity profile, which is a function of theswirl intensity, Ù only:

1C7.0

2

Rr

C3

3

Rr

C2

Uu

zzavz++−=

(13)

7.0R

r23

R

rC

zz

rev

2

rev −

−

= (14)

3.0rev 21.0R

r

zΩ= (15)

Several assumptions are implicit in these equations. First,axisymetric geometry is imposed. Then, the effects of theboundary layer are neglected, and finally the massconservation balance does not consider the split ratio. The lastassumption can be considered a good approximation for smallvalues of split ratios used in the LLHC, usually less than 10%.

Radial Velocity. The radial velocity, v, of the continuousphase is very small, and has been neglected in many studies.In our case, in order to track the position of the droplets incylindrical and conical sections, the continuity equation andwall conditions suggested by Kelsall (1952) and Wolbert(1995) are used for the radial velocity profile, yielding:

)tan(uRr

vz

β−= (16)

The radial velocity is a function of the axial velocity andgeometrical parameters. In the particular case of cylindricalsections, where tan(â) = 0, the radial velocity, v, is equal to 0.

Droplet Trajectories. The droplet trajectory model isdeveloped using a Lagrangian approach in which singledroplets are traced in a continuous liquid phase. The droplettrajectory model utilizes the flow field presented in theprevious section. Figure 16 presents the physical model. Adroplet is shown at two different time instances, t and t + dt.The droplet moves radially with a velocity Vr and axially withVz. It is assumed that in the tangential direction the dropletvelocity is the same as the continuous fluid velocity, as noforce acts on the droplet in this direction. Therefore, thetrajectory of the droplet is presented only in two dimensions,namely r and z.

During a differential time dt, the droplet moves at velocity Vr

= dr/dt in the radial direction and Vz = dz/dt in the axialdirection. Combining these two equations and solving for theaxial distance yields the governing equation for the dropletdisplacement:

∫=⇒== drVV

zVV

dtdr

dtdz

drdz

r

z

r

z (17)

Neglecting the axial buoyancy force (no-slip condition), thedroplet axial velocity Vz is equal to the axial velocity of thefluid, u. This simplification is reasonable when theacceleration due to the centrifugal force in the radial directionis thousand times larger than the acceleration of gravity. Dueto this aspect, the LLHC is not sensitive to externalmovements and it can be installed either horizontally orvertically.

The droplet velocity in the radial direction is equal to thefluid radial velocity, v, plus the slip velocity, Vsr. RearrangingEquation (17) yields the total trajectory of the droplet, namely:

rVv

uz 2rr

1rrsr

∆∑

+

= == (18)

The only unknown parameter in Equation (18) is the slipvelocity, which can be solved from a force balance on thedroplet in the radial direction, as shown Figure 16.

Assuming a local equilibrium momentum yields:

4d

VC21

6d

rw

)(2

2srcD

32

dc

πρ

πρρ =− (19)

where the left side of the equation is the centripetal force, andthe right side is the drag force. Solving for the radial slipvelocity, results in:

2

1

D

2

c

dcsr C

d

r

w

3

4V

−=

ρρρ

(20)

where d is the droplet diameter, ñd is the density of thedispersed phase, ñc is the density of the continuous phase andCD is the drag coefficient calculated using the followingrelationship (Morsi and Alexander, 1972 and Hargreaves,1990):

2d

3

d

21D Re

b

Re

bbC ++= (21)

where the coefficients “b” are dependent on the ReynoldsNumber of the droplets, defined as:

c

src VdRed µ

ρ= (22)


The values for the “b” coefficients, as functions of the rangeof Red, are shown in Table 1:

Finally, a numerical integration of Equation (18)determines the axial location of the droplet as a function of theradial position. The trajectory of a given size droplet is mainlya function of the LLHC velocity field and the physicalproperties of the dispersed and continuous phases.

Separation Efficiency. The separation efficiency of theLLHC can be determined based on the droplet trajectoryanalysis presented above. Starting from the cross sectionalarea corresponding to the LLHC characteristic diameter, it ispossible to follow the trajectory of a specific droplet, anddetermine if it is either able to reach the reverse flow regionand be separated, or if it reaches the LLHC underflow outlet,dragged by the continuous fluid and carried under.As illustrated in Figure 17, the droplet that starts its trajectoryfrom the wall (r = Rc) does not reach the flow reversal radius,and thus is not separated but rather carried under. However, ifthe starting location is at r < Rc, the chance of this droplet tobe separated increases. When the starting point of the droplettrajectory is the critical radius, rcrit, the droplet reaches thereverse radius, rrev, and is carried up by the reverse flow and isseparated.

Therefore, assuming homogeneous distribution of thedroplets, the efficiency for a droplet of a given diameter, å(d),can be expressed by the ratio of the area within which thedroplet is separated, defined by rcrit, over the total area of flow.This assumption has also been applied by other researchers(Seyda and Petty, 1991; Wolbert et al., 1995 and Moraes et al.,1996). As proposed by Moraes et al. (1996), the efficiency isgiven by:

=

<<−−

=

=

ccrit

ccritrev2rev

2c

2rev

2crit

revcrit

Rrif,1

Rrrif,rR

rr

rrif,0

)d(ππππε (23)

Repeating this procedure for different droplet sizes, themigration probability curve is obtained as shown in Figure 18.This function has an “S” shape and represents the separationefficiency, å(d), vs. the droplet diameter, d. It can be seen thatsmall droplets have an efficiency very close to zero and as thedroplet size is increased, å(d) increases sharply until it reachesd100, which is the smallest droplet size with a 100% probabilityto be separated.

The migration probability curve is the characteristic curveof a particular LLHC for a given flow rate and fluidproperties. This curve is independent of the feed droplet sizedistribution and is used in many cases to evaluate theseparation of a given LLHC configuration.

Using the information derived from the migration probabilitycurve and the feed droplet size distribution, the underflowpurity, åu, can be determined as follows:

∑

∑=

i i

iii

u V

V)d(εε (24)

where åu is expressed in %, and Vi is the percentagevolumetric fraction of the oil droplets of diameter di. Theunderflow purity is the parameter that quantifies the LLHCcapacity to separate the dispersed phase from the continuousone.

Pressure Drop. The pressure drop from the inlet to theunderflow outlet is calculated using a modification of theBernoulli’s Equation:

Lsing)hh(U21

PV21

P cfcfc2ucu

2iscis θρ++ρ+ρ+=ρ+

(25)

where ñc is the density of the continuous phase; Pis and Pu arethe inlet and outlet pressures, respectively; Vis is the averageinlet velocity and Uu is the underflow average axial velocity; Lis the hydrocyclone length, è is the angle of the LLHC axiswith the horizontal; hcf corresponds to the centrifugal forcelosses and hf is the frictional losses.

The frictional losses are calculated similar to that of pipeflow:

2

)z(V

)z(D

z)z(f)z(h

2r

f

∆= (26)

where f is the friction factor and Vr is the resultant velocity.

In the case of conical sections, all parameters in Equation(26) change with the axial position, z. The conical section isdivided into “m” segments and assuming cylindrical geometryin each segment, the frictional losses can be considered as thesum of the losses in all the “m” segments, as follows.

( )2

V

2

DDÄz

zfh)

2

Z)1n2(at(

2rm

1n n1n)conical(f

∆−

= −∑

+= (27)

The resultant velocity, Vr, is calculated as the vector sum ofthe average axial and tangential velocities, The annulardownward flow region is only considered, as presented in thefollowing set of equations:

2Z

2Z

2R WU)z(V += (28)

∫ ∫

∫ ∫= π

π

φ

φ20

zR

revr

20

zR

revrz

rdrd

WrdrdW (29)

For simplification purposes, the average axial velocity inEquation (28), Uz, is calculated assuming plug flow, namely,Uz is equal to the total flow rate over the annular area from thewall to the reverse radius, rrev. The Moody friction factor iscalculated using Hall’s Correlation (Hall, 1957).


+

+=

3/16

4

)zRe(10

)z(D10x210055.0)z(f

ε (30)

where å is the pipe roughness and Re is the Reynolds Number,calculated based on the resultant velocity computed inEquation (28).

The centrifugal losses are the most important ones inEquation (25), and account for most of the total pressure dropin the LLHC. They are calculated using the followingexpression:

∫= uR

revr

2u

cf drr

)r()nW(h (31)

where Wu is calculated from Equation (29) at the underflowoutlet and the centrifugal force correction factor, n = 2 fortwin inlets, and n = 3.2 for involute single inlet.

The centrifugal force correction factor compensates forthe use of Bernoulli’s Equation under a high rotational flowcondition. Its meaning is similar to the kinetic energycoefficient used to compensate for the non-uniformity of thevelocity profile in pipe flow (Munson et al., 1994).Rigorously, the Bernoulli equation is valid for a streamlineand the summation of the pressure, the hydrostatic and thekinetic terms can only be considered constant in the entireflow field if the vorticity is equal to zero.

Numerical Solution. The simulation code based on thedeveloped mechanistic model uses mainly two differentnumerical methods to obtain the results. The tangentialvelocity, given by Equation (29), is solved using theTrapezoidal Rule, and for the droplet trajectory, a fourth-orderRunge-Kutta method is used to solve Equation (18). Also, acommercial program (Mathematica 4.0) was used to verify theresulting numerical values given by the computer code.

Resusults and DiscussionThis section presents comparison between the LLHCmechanistic model predictions and experimental data takeneither at the present study or from the literature. Comparisonsare made for the swirl intensity, velocity profiles, migrationprobability, pressure drop, droplet size distribution and globalseparation efficiency.

Swirl Intensity. The swirl intensity, which is the ratio of thelocal tangential momentum flux to the total momentum flux,can be obtained from Equation (4). Figure 19 provides thecomparison between the model predictions and the Colmanand Thew (1980), Case 2 data. Note that only 1 data point isplotted, due to availability of axial and tangential velocitymeasurements at specific axial location. The results displaythe swirl intensity versus the dimensionless axial position,where z is the axial distance from the characteristic diameter,that is the location where the tapered section begins. Goodagreement is observed between the data point and the model

predictions. It has been experimentally proven by severalresearchers that the swirl intensity decays exponentially withaxial position due to the wall frictional losses (Mantilla, 1998).The model predictions show the same trend

Velocity Profile. The velocity field predicted by themechanistic model is compared with the same experimentaldata set used for the swirl intensity comparison, namely, Case2. Figure 20 presents the comparison between theexperimental data and model prediction for the tangentialvelocity. The y-axis corresponds to the axis of the LLHC, andthe x-axis represents the radial position. The units usedoriginally were conserved, namely, millimeters per second forthe tangential velocity, and millimeters for the radial position.The model predicts with acceptable accuracy the tangentialvelocity at the wall, the peak velocity and the radius where itoccurs. The experimental data and the model display aRankine Vortex shape, namely, a combination of forcedvortex near the LLHC axis and a free like vortex at the outerregion.

The axial velocity profile predicted by the model is nextcompared with the experimental data in Figure 21. Thepositive values of axial velocities correspond to downwardflow, which is the direction of the main flow, while thenegative values represent the reverse flow. The mechanisticmodel performance is excellent with respect to the axialvelocity in the downward flow region, and not so good in thereverse flow region. Considering the calculations that themodel follows to compute the separation efficiency, theprediction of the reverse flow velocity profile is not soimportant. What is really important is the prediction of theradius of zero velocity (rrev) since beyond this point the dropletis assumed to be separated, moving upwards to the overflowexit.

Migration Probability: A comparison between the modelpredictions of the migration probability curve as comparedwith experimental data of Colman and Thew (1980) is givenin Figure 22. Fair agreement is observed with the data.

Pressure Drop. A comparison between the predicted pressuredrop and experimental data from the present study is shown inFigure 23, while Figure 24 shows the model predictions ofpressure drop vs. flow rate as compared with the experimentaldata taken by Young et al. (1990). Very good agreement isobserved in both cases, with an average absolute relative errorof 1.6%.

Droplet Size Distribution. Figure 25 shows a comparisonbetween the model predictions and experimental data of thedroplet size distribution for runs 101. As shown in the figures,good agreement is observed with experimental results. Themodel prediction curves for the underflow droplet sizedistribution are shifted to the right, which means that themodel predicts efficiency smaller than the experimental one.Also there is a discontinuity in the model curve because themodel doesn’t consider either breakup or coalescence. This


means that the smallest droplet that enters the LLHC is alsothe smallest one that is found in the underflow stream. On theother hand, the largest droplet in the underflow stream is thelargest droplet with a calculated efficiency below 100%.

Global Separation Efficiency. Both the underflow purity andthe migration probability curve predicted by the model areevaluated through comparisons with experimental data. Table2 presents a comparison with the experimental data taken atthe present study for a representative sample of the 124 runs,and Table 3 shows a comparison with literature experimentaldata, where cases 9 to 22 are part of the set of experimentspublished by Colman et al. (1980). These experimental datasets are for the LLHC configuration given in Table 4. Thecharacteristic diameter and operational conditions are reportedin Table 3.

As can be seen from both tables 2 and 3, the modelpredictions are in excellent agreement with both data sets,with an average absolute relative error of 3%. The results arealso plotted in Figures 26 and 27, respectively.

Summary and ConclusionsA new facility for testing LLHCs was designed, constructedand installed in an existing three-phase flow loop. The testsection is fully instrumented to measure the important flowand separation variables, including flow rates (inlet, underflowand overflow) and the respective oil concentrations; dropletsize distributions (inlet and underflow streams); pressures(inlet and underflow) and temperature. A mixer bypass loopenables the generation of a wide range of droplet sizedistributions.

A set of 124 experimental runs was conducted, with inlettotal flow rates between 18 to 26 GPM, inlet oil cuts between0 to 10%, inlet droplet size distributions with droplet mediansbetween 30 to 160 microns, inlet pressures from 60 to 90 psia,underflow pressures between 35 to 63 psia, temperaturebetween 65ºF – 80ºF, and overflow reject diameter of 3mmand 4mm. The collected data permitted the calculation of theLLHC separation efficiency for each of the runs.

The collected data reveals that LLHCs can be used up to10% inlet oil concentrations, maintaining high separationefficiency. However, the performance of the LLHC is best forvery low oil concentrations at the inlet, below 1%. For lowconcentrations, no emulsification of the mixture occurs in theLLHC. However, high inlet concentrations, up to 10%,promote emulsification posing a separation problem in theoverflow stream.

A simple mechanistic model is developed for the LLHC.The model is capable of predicting the LLHC hydrodynamicflow field, namely, the axial, tangential and radial velocitydistributions of the continuous-phase. The separationefficiency and migration probability are determined based onswirl intensity prediction and droplet trajectory analysis. Theflow capacity, namely, the inlet-to-underflow pressure drop ispredicted utilizing an energy balance analysis.

The prediction of the LLHC model was compared againstthe data from both the present study and published data for

velocity profiles from the literature, especially from theColman and Thew (1980). Good agreement is obtainedbetween the model predictions and the experimental data withrespect to both separation efficiency (average absolute relativeerror of 3%) and pressure drop (average absolute relative errorof 1.6%).

NomenclatureA = cross sectional areaB = peak tangential velocity radius factor (Eqs. 10 and 11)c = ConcentrationCD = drag coefficientd = droplet diameterD = diameterDc = LLHC characteristic diameterf = friction factorF = Split ratiog = gravity accelerationh = lossesI = inlet factorL = lengthm = Nº of segmentsm& = mass flow rateMt = momentum flux at the inlet slotMT = axial momentum flux at the characteristic diameterpositionn = centrifugal force correction factor, number of inletsP = pressureq = volumetric flow rater = radial positionR = LLHC radiusRe = Reynolds Numbert = timeTm = maximum tangential velocity momentum (Eq. 9)u = continuous phase local axial velocityU = bulk axial velocityv = continuous phase local radial velocityV = volumetric fraction / velocityVr = droplet radial velocityVsr = droplet slip velocity in the radial directionVz = droplet axial velocityw = continuous phase local tangential velocityW = mean tangential velocityz = Axial position

Greek LettersÙ = swirl intensityâ = taper section semi-angleå = pipe roughnessåff = efficiency / purityè = axis inclination angle to horizontalì = viscosityñ = densityφ = Horizontal plane angle

Subscriptsav = average


c = characteristic diameter location / continuous phasecf = centrifugalcrit = criticald = dispersed phase / dropletf = frictionali = inletis = inlet sectiono = overflowr = resultantrev = reverse flowsr = Slip radial velocityu = underflowz = axial position

AcknowledgmentsThe authors thank Mr. Grant Young from Vortex FluidSystems Inc. and Dr. Charles Petty from Michigan StateUniversity for their help and advise during this study.

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Table 2: Efficiency Comparison with Present Study Test Pinlet DP Temp. Q inlet Oilinlet Split Ratio Reject Dia. Experim. Model

(#) dmin (µm) d50(µm) dmax(µm) (psia) (psi) (ºF) (GPM) (%) (%) (mm) Efficien. Efficien.

1 2.3 51 200 92 27 80 25 1 6 3 87 893 1.7 33 116 71 18 80 21 1 6 3 64 666 1.9 53 200 91 26 79 25 3 6 3 87 908 1.7 31 116 70 18 79 21 3 5 3 60 6211 1.9 56 200 91 27 80 25 5 12 3 89 9113 1.7 33 133 71 18 80 21 5 6 3 63 6616 1.9 62 229 90 28 79 25 7 14 3 92 9318 1.7 30 116 70 19 80 22 7 9 3 64 6821 2.3 68 262 90 28 72 25 10 11 3 96 9623 1.7 37 133 70 19 72 22 10 12 3 73 73

101 5.1 133 592 90 27 77 25 1 6 4 96 96102 5.1 133 517 79 23 77 23 1 8 4 98 98103 7.7 185 592 70 19 78 22 1 13 4 99 98106 11.6 140 592 90 27 78 26 3 12 4 99 99111 5.9 133 517 90 27 79 26 5 11 4 98 98121 8.8 136 517 90 28 72 25 10 11 4 99 99122 6.7 143 592 79 23 72 23 10 12 4 98 98123 8.8 181 592 70 19 72 22 10 12 4 97 96

Droplet Size Distribution

Table 1: Drag Coefficient Constants

Range b1 b2 b3

Red < 0.1 0 24 0

0.1 < Red < 1 3.69 22.73 0.0903

1 < Red < 10 1.222 29.1667 -3.8889

10 < Red < 100 0.6167 46.5 -116.67

Table 3: Efficiency Comparison with Literature Data

Case Dc (mm)Flowrate

(lpm)

Oil Density (g/cc)

Mean Drop Size

(mc)

Experimental Underflow Purity (%)

Model Underflow Purity (%)

9 30 60 0.87 41 88 8910 30 40 0.84 35 78 7911 30 50 0.84 35 82 8412 30 60 0.84 35 84 8813 30 70 0.84 35 88 9014 58 160 0.84 35 72 6615 58 190 0.84 35 74 7216 58 220 0.84 35 78 7517 58 250 0.84 35 81 7918 58 220 0.84 17 43 4819 58 250 0.84 17 47 5220 58 220 0.84 70 96 9221 58 250 0.84 70 97 9422 58 220 0.87 41 80 80

Table 4: Geometrical Parameters for Literature Data (Runs 9 to 22) Case Design Dc(mm) á1 á2 D2 L2 Ds Ls Di

8 IV 20 10º 0.75º 0.5Dc 30Dc 2Dc 2Dc 0.35Dc


Figure 1: LLHC Hydrodynamic Flow Behavior

Figure 2: Colman and Thew’s Hydrocyclone Geometry

Figure 3: LLHC Inlet Design

AIR

V15

3-PHASEGRAVITY

SEPARATOR

V14

OILTANK

TANK

WATER

V23 V21

TEST

SECTION

WATER LINE

OIL LINE

V12

V11

V26

V25

OIL SKIMMER

PG7

PG3

MM

PG5

MM

MIXING UNIT

MV3 CV3 V8

OIL METERING SECTION

WATER METERING SECTION

BY P

ASS

LINE

V13

PUMP

PUMP

V9 TT3

CV2 V5V7

V6 TT2

DV2

DV3

V18

V19

V20V16 V17

MV2

V10

PG6

PG4

V24

STORAGE SECTION

Figure 4: Schematic of Experimental LLHC Flow Loop

Isokinetic Sampler System

Mixing Loop

Oil Tank

Gear Pump

Speed Controller

Water Stream

Oil

Str

eam

Gear Flow Meter

Sta

tic m

ixer

Pressure TransducerThermometer

Pressure Transducer

Acr

ylic

Hyd

rocy

clon

e

Ste

el M

Q H

ydro

cycl

one

Underflow Stream

Overflow Stream

Overflow Discharge

Oil Stream

Figure 5: Schematic of LLHC Test Section

Figure 6: Photograph of LLHC Test Section


Flow Direction

InletUnderflow

Flow Direction

Surfactant

Sam

ple

Hol

der

12

3

4

5

6

7

9

8

Figure 7: Schematic of Isokinetic Sampling Probe

0

20

40

60

80

100

0 2 4 6 8 10 12 14 16 18

Overflow Volume Percent

Eff

icie

ncy

DP= 27 psig, Q= 25 GPM

Dp= 22 psig, Q= 23 GPM

Dp= 18 psig, Q= 21 GPMCoil-inlet = 1 - 10 %

d50 = 130-150 mm

Figure 8: Effect of pressure drop or flow rate on Efficiency

0

20

40

60

80

100

0 2 4 6 8 10 12 14 16 18


Eff

icie

ncy

Pi= 90 psia, Pu= 63 psiaPi= 80 psia, Pu= 57 psiaPi= 70 psia, Pu= 52 psia

Coil-inlet = 1 - 10 %

d50 = 130-150 mmQinlet = 25-21 GPM

Figure 9: Effect of underflow pressure on efficiency

0

20

40

60

80

100

0 2 4 6 8 10 12 14 16


Eff

icie

ncy

Do= 3 mmDo= 4 mm

Coil-inlet = 1 - 10 %d50 = 130-150 mmQinlet = 25-21 GPMDP = 27-18 psig

Figure 10: Effect of overflow diameter on efficiency

0

20

40

60

80

100

1 10 100 1,000 10,000

Inlet Oil Concentration, mg/lt

Eff

icie

ncy

Cinlet = 1%

Cinlet = 3%

Cinlet = 5%

Cinlet = 7%

Cinlet = 10%

Coil-inlet = 1 - 10 %d50 = 130-150 mmQinlet = 25-21 GPMDP = 27-18 psig

Figure 11: Effect of oil concentration on efficiency

0

20

40

60

80

100

0 2 4 6 8 10 12 14


Eff

icie

ncy

Feed d50 = 30 um, test 3Feed d50 = 130 um, test 101Feed d50 = 60 um, test 1

Coil-inlet = 1 %Qinlet = 25-21 GPMDP = 27-18 psig

Figure 12: Effect of Droplet Size Distribution on Efficiency

0

2

4

6

8

10

12

1 10 100 1000

Microns, um

Vo

lum

e F

ract

ion

UnderflowInlet

C = 1%DP = 27 psigQ = 25 GPMd50 = 130 mm

Figure 13: Typical Measured Droplet Size Distributions


Figure 14: Rankine Vortex Tangential Velocity Profile

Figure 15: Axial Velocity Diagram

Figure 16: Schematic of Droplet Trajectory Model

Figure 17: Schematic of Droplet Trajectory and Separation Efficiency

Figure 18: Migration Probability Curve

0

0.5

1

1.5

2

2.5

3

3.5

0 200 400 600 800 1000 1200 1400

Z (mm)

Sw

irl I

nte

nsi

ty

Experimental DataModel

Figure 19: Swirl Intensity Comparison (Colman and Thew, 1980, Case 2 Data)


z / Dc = 10.5

0

4000

8000

12000

16000

0 4 8 12 16

Radius (mm)

Tan

gent

ial V

eloc

ity (

mm

/sec

)

Experimental Data

Model

Figure 20: Tangential Velocity Comparison (Colman and Thew, 1980, Case 2 Data)

z / Dc = 10.5

-7000

0

7000

0 4 8 12 16

Radius (mm)

Tan

gent

ial V

eloc

ity (

mm

/sec

)

Experimental Data

Model

Figure 21: Axial Velocity Comparison (Colman and Thew, 1980, Case 2 Data)

0

10

20

30

40

50

60

70

80

90

100

0 8 16 24 32 40 48 56 64

Droplet Diameter (microns)

Sep

arat

ion

Eff

icie

ncy

(%

)

Experimental Data

Model

Figure 22: Migration Probability Comparison, Colman and Thew (1980) Data

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80 90 100

Pressure Drop, psi

Flo

w R

ate,

GP

M

ExperimentalModel

DP range = 45 -4 psig

Figure 23: Comparison of Pressure Drop vs. Flow Rate (Present Study Data)

0

50

100

150

200

250

300

0 50 100 150 200 250

Pressure Drop (psi)

Flo

wra

te (

lpm

)

Young et al (1990)LLHC Model

Figure 24: Comparison of Pressure Drop vs. Flow Rate (Young et al., 1990, Data)

0

2

4

6

8

10

12

0.1 1 10 100 1000

Microns, um

Vo

lum

e F

ract

ion

UnderflowInletLLHC Model

Coil-inlet = 1 %d50 = 130 mmQinlet = 25 GPMDP = 27 psig

Figure 25: Comparison of Droplet Size Distribution Results for Test 101


90

91

92

93

94

95

96

97

98

99

100

90 91 92 93 94 95 96 97 98 99 100

Experimental Efficiency (%)

Mo

del

Eff

icie

ncy

(%

)

Experimental

Model

Figure 26: Comparison of Model Efficiency with Present Study Experimental Data

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Experimental Efficiency (%)

Mo

del

Eff

icie

ncy

(%

)

Model

Experimental

Figure 27: Comparison of Model Efficiency with Literature Experimental Data

Oil-Water Separation in Liquid-Liquid Hydrocyclones …tustp.org/publications/SPE00071538.pdf ·...

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