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Copyright 2001, Society of Petroleum Engineers Inc.

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AbstractThe liquid-liquid Hydrocyclone (LLHC) has been widely used

by the Petroleum Industry for the past several decades. A

large quantity of information on the LLHC available in the

literature includes experimental data, computational fluid

dynamic simulations and field applications. The design of

LLHCs has been based in the past mainly on empirical

experience. However, no simple and overall design

mechanistic 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 new

experimental data. This model will enable the prediction of

the hydrodynamic flow behavior in the LLHC, providing a

design tool for LLHC field applications.

A simple mechanistic model is developed for the LLHC.

The required input for the model is: LLHC geometry, fluid

properties, inlet droplet size distribution and operational

conditions. The model is capable of predicting the LLHC

hydrodynamic flow field, namely, the axial, tangential and

radial velocity distributions of the continuous-phase. The

separation efficiency and migration probability are determined

based on swirl intensity prediction and droplet trajectory

analysis. The flow capacity, namely, the inlet-to-underflow

pressure drop is predicted utilizing an energy balance analysis.

An extensive experimental program has been conducted

during this study, utilizing a 2” MQ Hydroswirl hydrocyclone.

The inlet flow conditions are: total flow rates between 27 to

18 gpm, oil-cut up to 10%, median droplet size distributions

from 50 to 500 µm, and inlet pressures between 60 to 90 psia.

The acquired data include the flow rate, oil-cut and droplet

size distribution in the inlet and in the underflow, the reject

flow rate and oil concentration in the overflow and the

separation efficiency. Additional data for velocity profiles

were taken from the literature, especially from the Colman and

Thew (1980) study. Excellent agreement is observed between

the model prediction and the experimental data with respect to

both separation efficiency (average absolute relative error of

3%) and pressure drop (average absolute relative error of

1.6%).

IntroductionThe petroleum industry has traditionally relied on

conventional gravity based vessels, that are bulky, heavy and

expensive, to separate multiphase flow. The growth of theoffshore oil industry, where platform costs to accommodate

these separation facilities are critical, has provided the

incentive for the development of compact separation

technology. Hydrocyclones have emerged as an economical

and effective alternative for produced water deoiling and other

applications. The hydrocyclone is inexpensive, simple in

design with no moving parts, easy to install and operate, and

has low maintenance cost.

Hydrocyclones have been used in the past to separate

solid-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 latter

case, namely, using the liquid-liquid hydrocyclones (LLHC) to

remove 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 used

to separate most of the multiphase mixture. The small amount

of oil remaining in the water stream, after the primary

separation, has to be reduced to a legally allowable minimum

level for offshore disposal. LLHCs have been used

successfully to achieve this environmental regulation.

There is a large quantity of literature available on the

LLHC, including experimental data sets and computationalfluid dynamic simulations. However, there is still a need for

more comprehensive data sets, including measurements of the

underflow droplet size distribution. Additionally, there is a

need for a simple and overall mechanistic model for the

LLHC.

The objective of the present study is two fold: to develop

a mechanistic model for the LLHC that can predict the flow

behavior in the hydrocyclone and the oil/water separation

efficiency; 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 of Tulsa



2 C. Gomez, J. Caldentey, S. Wang, L. Gomez, R. Mohan, O. Shoham SPE71538

LLHC, including detailed measurements of the droplet size

distributions in the inlet and underflow streams. The

developed mechanistic model can be utilized for the design of

LLHCs, providing the flexibility of designing alternative

LLHC geometries for the same operating conditions for

optimization purposes. It will also allow detailed analysis and

performance prediction for a given LLHC geometry and

operating conditions, including separation efficiency and flowcapacity (pressure drop – flow rate relationship).

LLHC Hydrodynamic Flow Behavior. The LLHC, shown in

Figure 1, utilizes the centrifugal force to separate the dispersed

phase from the continuous fluid. The swirling motion is

produced by the tangential injection of pressurized fluid into

the hydrocyclone body. The flow pattern consists of a spiral

within another spiral moving in the same circular direction

(Seyda and Petty, 1991). There is a forced vortex in the region

close to the LLHC axis and a free-like vortex in the outer

region. The outer vortex moves downward to the underflow

outlet, while the inner vortex flows in a reverse direction tothe overflow outlet. Moreover, there are some re-circulation

zones associated with the high swirl intensity at the inlet

region. These zones, with a long residence time and very low

axial velocity, have been found to be diminished as the flow

enters the low angle taper section (see Figure 1).

An explanation of the characteristic reverse flow in the

LLHC is presented by Hargreaves (1990). With high swirl at

the inlet region, the pressure is high near the wall region and

very low toward the centerline, in the core region. As a result

of the pressure gradient profile across the diameter, which

decreases with downstream position, the pressure at the

downstream end of the core is greater than at the upstream,causing flow reversal.

As the fluid moves to the underflow outlet, the narrowing

cyclone cross-sectional area increases the fluid angular velocity and the centrifugal force. It is due to this force and the

difference in density between the oil and the water, that the oil

moves to the center, where it is caught by the reverse flow and

separated, flowing into the overflow outlet. Instead, if the

dispersed phase is the heavier, like solid particles, it will

migrate to the wall and exit through the underflow.

The amount of fluid going through the different outlets

differs with heavy and light dispersion. It means that for these

two different separation cases, two different geometries are

needed (Seyda and Petty, 1991). In the deoiling case, usually

between 1 to 10 percent of the feed flow rate goes to the

overflow.

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 the

pressure reduction in the core region, migrating fast to the

LLHC axis, and eventually emerging through the overflow

outlet. A significant amount of gas can be tolerated but

excessive amounts will disturb the vortex. An experimental

study on this topic is found in Smyth and Thew (1996).

LLHC Geometry. The deoiling LLHC consists of a set of

cylindrical and conical sections. Colman and Thew’s (1988)

design has four sections, as shown in Figure 2. The inlet

chamber and the reducing section are designed to achieve

higher tangential acceleration of the fluid, reducing the

pressure drop and the shear stress to an acceptable level. The

latter has to be minimized to avoid droplet breakup leading to

reduction in separation efficiency. The tapered section iswhere most of the separation is achieved. The low angle of this segment keeps the swirl intensity with high residence

time. An integrated part of the design is a long tail pipe

cylindrical section in which the smallest droplets migrate to

the reversed flow core at the axis and are being separated

flowing into the overflow exit. This configuration gives a very

stable small diameter reversed flow core, utilizing a very smal

overflow port.

Young et al. (1990) achieved similar results to Colman-

Thew’s LLHC, in terms of separation efficiency, with a

different hydrocyclone configuration. Three sections were

used 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 separation

performance. The principal modification of the enhanced

design was a small change in the tail pipe section. A minute

angle conical section was used rather than the cylindrical pipe.

Another important parameter in the LLHC geometry is the

inlet configuration, as shown in Figure 3. Rectangular and

circular, single and twin inlets have been most frequently used

by different researchers. The main goal is to inject the fluid

with higher tangential velocity, avoiding the rupture of the

droplets. The twin inlets have been considered to maintain better symmetry and for this reason maintain a more stable

reverse core (Colman et al., 1980; Thew et al., 1984). Good

results have also been achieved with the involute single inletdesign.

The last element of the LLHC is the overflow outlet. This

is a very small diameter orifice that plays a major role in the

split ratio, defined as the relationship between the overflow

rate and the inlet flow rate. Most of the commercial LLHCs

permit changing the diameter of this orifice, depending on the

range of operating conditions.

Literature ReviewThere are hundreds of literature references on the LLHC,

including experimental studies, CFD simulations and

modeling. Detailed review of these previous studies can be

found in Caldentey (2000) and Gomez (2001). In this sectiononly pertinent mechastudies are reviewed briefly

Two textbooks that condense pioneering works on

hydrocylones and fundamental theories, including

experimental data, design, and performance aspects, are

Bradley (1965) and Svarovsky (1984). Both refer in most of

the chapters to solid-liquid hydrocyclones, with only a small

section available on liquid-liquid separation and other

application areas.



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

Experimental Studies. Only a representative sample of

previous experimental studies is summarized here. The review

is divided into laboratory studies and design and application

studies, as follows.

Laboratory Studies. Earlier studies were presented by Simkin

and Olney (1956), Sheng (1974), Johnson et al. (1976), Smyth

et al. (1980), Colman et al. (1980) and Colman and Thew

(1980).A general revision of the hydrocyclone developed at

Southampton University was carried out by Thew (1986), who

also 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 a

Colman and Thew (1980) type hydrocyclone, and later

proposed a new modified design. In 1991, Weispfennig and

Petty explored the flow structure in a LLHC using a

visualization technique (laser induced fluorescence). The

performance of a mini hydrocyclones, of 10 mm-diameter,were studied by Ali et al. (1994) and Syed et al. (1994).Design and Appli cations. A summary of the selection, sizing,

installation and operation of hydrocyclones was provided by

Moir (1985). Meldrum (1988) described the basic design and

principle of operation of the de-oiling hydrocyclone.

Choi (1990) tested a system of six hydrocyclones (35 mm

diameter) operating in parallel for produced water treatment

(PWT). The performance of three commercial liquid-liquid

hydrocyclones (two static and one dynamic) in an oil field was

evaluated by Jones (1993).CFD Simulations. Numerical simulations or CFD are used

widely to investigate flow hydrodynamics. As expressed byHubred et al. (2000), the solution of the Navier Stokes

Equations for simple or complex geometry for non-turbulent

flow is feasible nowadays. But current computationalresources are unable to attain the instantaneous velocity and

pressure fields at large Reynolds numbers even for simple

geometries. The reason is that traditional turbulence models,

such as k-?, are not suitable for this complex flow behavior.

On the other hand, more realistic and complicated turbulence

models increase the computational times to inconvenient

limits.

The flow in hydrocyclones has been numerically

simulated by Rhodes et al. (1987), Hsieh and Rajamani (1991)

(see also Rajamani and Hsieh, 1988; Rajamani and

Devulapalli, 1994) and He et al. (1997). In most of these

studies the models were evaluated through comparison with

laser-doppler anemometry (LDA) data. Many researchershave used this technique to measure the velocity field and

turbulence intensities (Dabir, 1983; Fanglu and Wenzhen,

1987; Jirun et al., 1990; and Fraser and Abdullah, 1995).Modeling. Although widely used nowadays, the selection and

design of hydrocyclones are still empirical and experience

based. Even though quite a few hydrocyclone models are

available, the validity of these models for practical

applications 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 e

al. (2000).

The LLHC models can be divided into empirical and

semi-empirical, analytical solutions and numerical simulations

(Chakraborti and Miller, 1992). The empirical approach is

based on development of correlations for the process key

parameters, 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-Stokes

Equation. The former one is a mathematical solution, which is

achieved neglecting some of the terms of the momentum

balance equation. The numerical solution uses the power of

computational fluid dynamics to develop a numerica

simulation of the flow. As Svarovsky (1996) comments, it

seems that the analytical flow models have been abandoned in

favor of numerical simulations due to the complexity of the

multiphase flow phenomena.

From extensive experimental tests, Colman and Thew

(1983) developed some correlations to predict the migration probability curve, which defines the separation efficiency for a

particular droplet size in a similar way that the grade

efficiency does for solid particles. Seyda and Petty (1991)

evaluated the separation potential of the cylindrical tail pipe

section. A semi-empirical model to predict the velocity field in

a cylindrical chamber was developed to calculate the particle

trajectories, and hence, the grade efficiency.

Wolbert et al. (1995) presented a computational model to

determine the separation efficiency based on the analysis of

the trajectories of the oil droplets. An extension of Bloor and

Ingham (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 accurate

experimental data utilizing appropriate sampling procedureand including the measurements of the droplet size

distributions at the inlet and underflow sections, and the need

to develop a simple mechanistic model for the LLHC. These

deficiencies are addressed in the present study.

Experimental ProgramThis section describes the experimental facility, working

fluids, definitions of pertinent separation parameters, and the

experimental results of the LLHC.

Experimental Facility. The experimental three-phase, oil-

water-gas, flow loop is shown Figure 4. The oil-water-gas

indoor flow facility is a fully instrumented state-of-the-artwo-inch flow loop, enabling testing of single separation

equipment or combined separation systems. The test loop

consists of four main components: storage and metering

section, LLHC test section, downstream oil-water separation

facility, and data acquisition system. Following is a brief

description of these sections.Storage and Meteri ng Section . Oil and water are stored in two

tanks of 400 gallons capacity each. Each tank is connected to

two pumps. The first one is a 3656 model pump, 1x2-8 size




cast iron construction with bronze impeller, John Crane Type

21 mechanical seal, 10 HP motor and operates at 3600 rpm. It

delivers 25 gpm @ 108 psig. The second one is a 3656 Model

pump, 1.5x2-10 size, cast iron construction with bronze

impeller, John Crane Type 21 mechanical seal, 25 HP motor

and operates at 3600 rpm. It delivers 110 gpm @ 150 psig.

Both pumps are equipped with return lines. Each fluid is

pumped 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 flow

rate, water-cut, temperature, and mixture density. The signals

from the flow meters and control valves are fed to the data

acquisition system, which will be described later. Check

valves to prevent any back-flow are installed downstream of

the control valves. The metered oil and water are then

combined in a mixing-tee to obtain oil-water dispersion.

Additionally, a static mixer is available in parallel to the

mixing-tee for homogenization of the flow.

Test Section. Figure 5 shows a schematic of the LLHC test

section and Figure 6 presents a photograph of the LLHC

prototype installed in the test section. The LLHC is a 2-inches

NATCO MQ Hydro Swirl Hydrocyclone mounted vertically

with a total height of 62 inches. Water flows into the test

section through a 2” pipe coming from the water tank. This

pipe has a split section where the water split stream mixes

with oil in order to get thorough mixing with the desired oil

concentration. The split section is a ½ inch pipe composed of

a water wheel paddle meter, a mixing tee and a static mixer.

Oil for the mixture is pumped from a 55 gallons barrel with a

gear pump, and metered by means of a gear flow meter. Once

the oil and water are mixed, they pass through a static mixer inorder to get a desired droplet size distribution. After this point

the mixture is directed to the main stream pipe entering it by

means of an inverse pitot tube. Once the mixture enters themain stream line, it can either flow directly to the test section

or be subjected to an additional mixing loop where smaller

droplet size distributions can be achieved. The mixture can be

sent to either the MQ steel hydrocyclone or the MQ acrylic

hydrocyclone. The latter LLHC, which has the same

characteristics as the steel one, is placed for observation

purposes.

In order to measure the droplet size dis tribution, a special

isokinetic sampler is designed and operated in order to get

representative accurate measurements of the distributions, as

shown in Figure 7. Samples from both the inlet and underflow

streams can be obtained. Once the sample is taken, it is placed

in the droplet size distribution analyzer. For this purpose, aLaser scattering device, namely, the Horiba LA -300 analyzer

is used to analyze the samples. . It may be noted that a

surfactant-based additive is utilized, as shown in Figure 7, to

avoid coalescence in the sample when transferred and run in

the droplet size analyzer

The flow in the LLHC is split into two streams: The

overflow stream, with mainly oil, and the down-flow stream,

with mainly water. The overflow is discharged into a 55

gallons barrel and the underflow is sent to the downstream

three-phase separator. Pressure transducers are located on the

upper and the lower outlets of the LLHC. The underflow

stream passes through a metering section, located upstream of

the three-phase separator, where flow rate, density

temperature and water cut are measured using a liquid

Micromotion®

coriolis mass flow meter. Due to the small oi

concentration in some of the experiments, a special oil content

analyzer is utilized to measure the oil concentration of theunderflow. This equipment is a Horiba OCMA 220 modelthat uses infrared spectroscopy technique.

Downstream Oil -Water Separati on Section . The 528 gallon

three-phase flow separator located downstream of the LLHC

test section operates at 10 psig. It consists of three

compartments. In the first compartment the oil-water mixture

is stratified and the oil flows into the second compartment

through flotation. In this compartment, there is a level control

system that activates a control valve discharging the oil into

the oil storage tank. The water flows from the firs

compartment to the third compartment through a channe

located below the second compartment. In this compartment,there is also a level control system, allowing water to flow into

the water storage tank.

Data Acquisition System. IDM variable speed controllers

installed on all the 4 pumps control the oil and water flow

rates into the test section. The flow loop is also equipped with

several temperature sensors and pressure transducers for

measurement of the in-situ temperature and pressure

conditions.

All output signals from the sensors, transducers, and

metering devices are collected at a central panel. A state-of

the-art data acquisition system, built using LabView®

, is used

to both control the flow in the loop and also to acquire datafrom analog signals transmitted from the instrumentation. The

program provides variable sampling rates. The sampling rate

was set at 2 Hz for a 2 minutes sampling period. The finalmeasured quantity results from an arithmetic averaging of 120

readings, after steady-state condition is established.

A regular calibration procedure, employing a high

precision pressure pump, is performed on each pressure

transducer at a regular schedule, to guarantee the precision of

measurements. The temperature transducer consists of a

Resistance Temperature Detector (RTD) sensor and an

electronic transmitter module.

Working Fl uids. Tap water and mineral oil were chosen and a

dye (red) was added to the oil to improve flow visualization

between the phases. The oil has low emulsification, fast

separation, appropriate optical characteristics, non-degrading

properties, and is non-hazardous. The properties of the oil are0API=33.7 and µ O = 13.6 cP at 100

0F. During all the

experimental runs the average temperature in the flow loop

varied between 700

and 800

F.

Definition of Separation Parameters. Following are the

definitions of two important parameters used in this study to

define the total separation efficiency:




Spli t Ratio : The split ratio is the ratio of the overflow rate

to the inlet flow rate, as given below:

%100

inlet q

overflowq

F ⋅= (1)

where F is the split ratio, qoverflow is the total flow rate at the

upper outlet of the LLHC , and q inlet is the total inlet flow rate.

Oil Separation Efficiency : Practical interpretation of separation data is concerned with the purity of individual

discharge streams. Many references quantify the relative phase

composition of the separated streams in the form of a

percentage by volume measurement. In this study a widely

used definition is adapted for the oil separation efficiency,

namely,

%100q

q

inletoil

overflowoil

ff ⋅=−

−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 continuity

relationship, Equation (2) becomes

%100 )

inlet oil c

inlet q

underflowoil c

underflowq

1( ff

⋅−⋅−⋅

−=ε (3)

Note that when coil-underflow tends to zero, the separation

efficiency is maximum.

Experimental Results. A total of 124 runs were conducted in

this study. The data is analyzed and presented, so as to

demonstrate the effect of the flow variables on the separation

efficiency, as given in the following sections.Ef fect of Pressure Drop and Flow Rate. The separation of oil

droplets in the swirl chamber of the hydrocyclone is a result of

the forces imposed on the oil droplets in the spinning fluid and

the residence time in the chamber. Lower flow rates mean

longer residence times but lower acceleration forces.

Conversely higher flow rates result in higher acceleration

forces and smaller residence times. As shown in Figure 8, the

MQ Hydroswirl performance is independent of flow rate in the

range tested. For hydrocyclones of similar geometries, the

literature reports similar results.Ef fect of Underf low Pressure. Back pressure must be applied

at the hydrocyclone underflow, in order to force the corestream containing the oil to the overflow; otherwise, all the

flow will exit through the underflow and no separation would

occur. For a given underflow backpressure, if the overflow

pressure is slowly increased, the core diameter increases,ultimately resulting in part of the oil core discharging out

through the underflow. The MQ Hydroswirl performance is

independent of the underflow pressure, as shown in Figure 9,

provided there is sufficient backpressure to force enough flow

out of the overflow (Young et al. 1990). It is critical that

constant back pressure be applied, since swings in

backpressure result in the oil in the core being rapidly

discharged with the cleaned water.

Effect of Overflow Diameter. Separation efficiency of

LLHCs is independent of overflow diameter (Young et al.

1990). This is confirmed by the results of this study, as shown

in Figure 10. However, the minimum overflow rate to make

an effective separation increases with increasing overflow

diameter. The minimum flow rate for each orifice opening

size is a result of a minimum velocity required for the oil to

move 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 for

each overflow opening size. Increasing overflow size results

in an increased amount of water, which must be removed with

the oil to obtain the same removal efficiency. This of course

means that a greater flow rate of oily wastewater must be

reprocessed. The major advantage of larger overflow

diameters is that it allows more oil to be removed without

affecting the purity of the underflow water stream when large

slugs of oil are encountered in field operations. Furthermore

larger outlets are not as susceptible to blockage as the smaller

ones. Figure 10: Effect of overflow diameter on effic iencyEff ect of I nlet Oil Concentration. Field reports indicate that

with increased oil concentrations, the performance of the MQ

Hydroswirl hydrocyclone improves and can handle the

additional oil. As can be observed in Figure 11, separation is

independent of inlet oil concentration when there is adequate

flow at the overflow to remove the required amount of oil.

The improved separation of field installations with increasing

oil content is probably due to the presence of larger oil droplet

sizes.Ef fect of Oil D roplet Size Di stri bution. The variable having

the greatest impact on oil-water separation is the oil droplet

size distribution. Figure 12 shows the separation performanceof the MQ Hydroswirl hydrocyclone for several droplet size

distributions, with the median droplet size shown. As can be

seen, the oil separation efficiency increases with increase inthe droplet size. This can be intuitively expected as the larger

oil droplets coalesce faster than the smaller ones.

Typical results for the droplet size distributions in the

inlet and underflow streams are given in Figure 13. This

figure demonstrates the removal of the large droplets from the

feed stream. Also, the underflow stream contains smaller

droplets sizes, as compared to the inlet stream, due to breakup

of droplets in the LLHC.

Mechanistic ModelingThe following sections provide details of the mechanistic

model developed for the LLHC in the present study.

Swirl Intensity. The swirl intensity is defined as the ratio of

the local tangential momentum flux to the total momentum

flux. The swirl intensity equation given below is a

modification of the Mantilla (1998) correlation, based on

Erdal (2001) CFD simulations, given by




⋅+

= ) )tan( 2.11( I

M

M Re49.0

15.0

93.0

2

T

t 118.0βΩ

( )( )

+

− 12.0

7 .016 .0

z

35.0

4

T

t tan21 Dc

z

Re

1 I

M

M

2

1 EXP β

(4)

where M t/MT is the ratio of the momentum flux at the inlet slot

to the axial momentum flux at the characteristic diameter

posit ion, calculated as:

is

c

cc

isc

avc

is

T

t

A

A

A / m

A / m

U m

V m

M

M ===

ρ

ρ

&

&

&

&(5)

The variables in the above equations are: O is the swirl

intensity, Re is the Reynolds number, ß is the semi-angle of the conical sections, Dc is the characteristic diameter of the

LLHC (measured where the angle changes from the reducing

section to the tapered section in the Colman and Thew’s

Design, 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 at

Dc, m& is the mass flow rate, Ac is the cross sectional area at

Dc and A is is the inlet cross sectional area.

The Reynolds number is defined in the same way as for

pipe flow with the caution that it refers to a given axial

position, yielding:

c

z avz c z

DU Re

µ

ρ= (6)

where µc is the viscosity of the continuous fluid.

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

−−=

2

n EXP 1 I (7)

where n = 1.5 for twin inlets and n = 1 for involute single

inlet.

Velocity Field. The swirl intensity is related, by definition, to

the local axial and tangential velocities. Therefore, it is

assumed that once the swirl intensity is predicted for a specific

axial 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, is

computed considering the continuity equation and the wall

effect.Tangenti al Velocity. It has been confirmed experimentally

that the tangential velocity is a combination of a forced vortex

near the hydrocyclone axis, and a free-like vortex in the outer wall region, neglecting the effect of the wall boundary layer,

as shown in Figure 14. This type of behavior is known as a

Rankine Vortex. Algifri et al. (1988) proposed the following

equation for the tangential velocity profile:

−−

=

2

c

c

m

avc R

r B EXP 1

R

r

T

U

w (8)

where w is the local tangential velocity, which is normalizedwith the average axial velocity, Uavc, at the characteristic

diameter; R c is the radius at the characteristic location and r is

the radial location. The term Tm represents the maximum

momentum of the tangential velocity at the section and B

determines the radial location at which the maximum

tangential velocity occurs. The following expressions were

obtained by curve-fitting several sets of the experimental data.

Ω=m

T (9)

Involute Single Inlet:

7 .17 .55 B −= Ω (10)

Twin Inlets:

35.28.245 B −= Ω (11)

It can be seen that the above equations are only functions of

the swirl intensity, O. Thus, for a given axial position, the

tangential velocity is only function of the radial location and

the swirl intensity.

Axi al Velocity. In swirling flow the tangential motion gives

rise to centrifugal forces which in turn tend to move the fluid

toward the outer region (Algifri 1988). Such a radial shift of

the fluid results in a reduction of the axial velocity near the

axis, and when the swirl intensity is sufficiently high, reverse

flows can occur near the axis. This phenomenon causes acharacteristic reverse flow around the LLHC axis, which

allows the separation of the different density fluids.

A typical LLHC axial velocity profile is illustrated in

Figure 15. Here, the positive values represent downward flow

near the wall, which is the main flow direction, and the

negatives values represent upward reverse flow near the

LLHC axis. The flow reversal radius, r rev, is the radial position

where the axial velocity is equal to zero.

To predict the axial velocity profile, a third-order

polynomial equation is used with the proper boundary

conditions. The general form is as follows:

43

2

2

3

1 ar ar ar a )r ( u +++= (12)

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

considered are:

1. 0dr

) Rr ( du z =

=The velocity is maximum at the

wall;




2. 0 )r r ( urev

== Zero velocity at the location of

reverse flow, r rev;

3. 0dr

)0r ( du=

=The velocity is symmetric about the

LLHC axis; and

4.2

z c

z R

0 avz c RU rdr )r ( u2 πρπρ ∫ = Mass conservation.

Substituting the boundary conditions in Equation (12)

yields the axial velocity profile, which is a function of the

swirl intensity, O only:

1C

7 .02

R

r

C

33

R

r

C

2

U

u

z z avz

++−=

(13)

7 .0 R

r 23

R

r C

z z

rev

2

rev −

−

= (14)

3.0rev

21.0 R

r

z Ω= (15)

Several assumptions are implicit in these equations. First,

axisymetric geometry is imposed. Then, the effects of the

boundary layer are neglected, and finally the mass

conservation balance does not consider the split ratio. The last

assumption can be considered a good approximation for small

values of split ratios used in the LLHC, usually less than 10%.

Radial Velocity. The radial velocity, v, of the continuous

phase 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 and

wall conditions suggested by Kelsall (1952) and Wolbert

(1995) are used for the radial velocity profile, yielding:

)tan( u R

r v

z

β−= (16)

The radial velocity is a function of the axial velocity and

geometrical parameters. In the particular case of cylindrical

sections, where tan(ß) = 0, the radial velocity, v, is equal to 0.

Droplet Trajectories. The droplet trajectory model is

developed using a Lagrangian approach in which single

droplets are traced in a continuous liquid phase. The droplet

trajectory model utilizes the flow field presented in the

previous section. Figure 16 presents the physical model. A

droplet is shown at two different time instances, t and t + dt.

The droplet moves radially with a velocity Vr and axially with

Vz . It is assumed that in the tangential direction the droplet

velocity is the same as the continuous fluid velocity, as no

force acts on the droplet in this direction. Therefore, the

trajectory of the droplet is presented only in two dimensions,

namely r and z.

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

= dr/dt in the radial direction and Vz = dz/dt in the axial

direction. Combining these two equations and solving for the

axial distance yields the governing equation for the droplet

displacement:

∫ =⇒==dr

V

V z

V

V

dt dr

dt dz

dr

dz

r

z

r

z (17)

Neglecting the axial buoyancy force (no-slip condition), the

droplet axial velocity Vz is equal to the axial velocity of thefluid, u. This simplification is reasonable when the

acceleration due to the centrifugal force in the radial direction

is thousand times larger than the acceleration of gravity. Due

to this aspect, the LLHC is not sensitive to externa

movements and it can be installed either horizontally or

vertically.

The droplet velocity in the radial direction is equal to the

fluid radial velocity, v, plus the slip velocity, Vsr . Rearranging

Equation (17) yields the total trajectory of the droplet, namely

r V v

u z 2r r

1r r

sr

∆∑

+

= == (18)

The only unknown parameter in Equation (18) is the slip

velocity, which can be solved from a force balance on the

droplet in the radial direction, as shown Figure 16.

Assuming a local equilibrium momentum yields:

4

d V C

2

1

6

d

r

w )(

22

sr c D

32

d c

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 slip

velocity, results in:

2

1

D

2

c

d c

sr C

d

r

w

3

4V

−=

ρ

ρρ(20)

where d is the droplet diameter, ?d is the density of the

dispersed phase, ?c is the density of the continuous phase and

CD is the drag coefficient calculated using the following

relationship (Morsi and Alexander, 1972 and Hargreaves

1990):

2

d

3

d

21 D

Reb

RebbC ++= (21)

where the coefficients “b” are dependent on the Reynolds

Number of the droplets, defined as:

c

sr cV d

Red µ

ρ= (22)




The values for the “b” coefficients, as functions of the range

of Red, are shown in Table 1:

Finally, a numerical integration of Equation (18)

determines the axial location of the droplet as a function of the

radial position. The trajectory of a given size droplet is mainly

a function of the LLHC velocity field and the physical

properties of the dispersed and continuous phases.

Separation Efficiency. The separation efficiency of the

LLHC can be determined based on the droplet trajectory

analysis presented above. Starting from the cross sectional

area corresponding to the LLHC characteristic diameter, it is

possible to follow the trajectory of a specific droplet, and

determine if it is either able to reach the reverse flow region

and 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 trajectory

from the wall (r = Rc) does not reach the flow reversal radius,

and thus is not separated but rather carried under. However, if

the starting location is at r < Rc, the chance of this droplet to

be separated increases. When the starting point of the droplettrajectory is the critical radius, r crit, the droplet reaches the

reverse radius, r rev, and is carried up by the reverse flow and is

separated.

Therefore, assuming homogeneous distribution of the

droplets, the efficiency for a droplet of a given diameter, e(d),

can be expressed by the ratio of the area within which the

droplet is separated, defined by r crit, 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 is

given by:

=

<<−−

=

=

ccrit

ccrit rev2

rev

2

c

2rev

2crit

revcrit

Rr if ,1

Rr r if ,r R

r r

r r if ,0

)d ( ππ

ππε (23)

Repeating this procedure for different droplet sizes, the

migration probability curve is obtained as shown in Figure 18.

This function has an “S” shape and represents the separation

efficiency, e(d), vs. the droplet diameter, d. It can be seen that

small droplets have an efficiency very close to zero and as the

droplet size is increased, e(d) increases sharply until it reaches

d100, which is the smallest droplet size with a 100% probability

to be separated.

The migration probability curve is the characteristic curveof a particular LLHC for a given flow rate and fluid

properties. This curve is independent of the feed droplet size

distribution and is used in many cases to evaluate the

separation of a given LLHC configuration.

Using the information derived from the migration probability

curve and the feed droplet size distribution, the underflow

purity, eu, can be determined as follows:

∑

∑=

i i

iii

uV

V )d ( εε (24)

where eu is expressed in %, and Vi is the percentage

volumetric fraction of the oil droplets of diameter di. Theunderflow purity is the parameter that quantifies the LLHC

capacity to separate the dispersed phase from the continuous

one.

Pressure Drop. The pressure drop from the inlet to the

underflow outlet is calculated using a modification of the

Bernoulli’s Equation:

sig)hh(U2

1PV

2

1P

cf cf c2ucu

2iscis

ρ++ρ+ρ+=ρ+

(25)

where ?c is the density of the continuous phase; Pis and Pu are

the inlet and outlet pressures, respectively; Vis is the average

inlet velocity and Uu is the underflow average axial velocity; L

is the hydrocyclone length, ? is the angle of the LLHC axiswith the horizontal; hcf corresponds to the centrifugal force

losses and h f is the frictional losses.

The frictional losses are calculated similar to that of pipe

flow:

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 is

divided into “m” segments and assuming cylindrical geometry

in each segment, the frictional losses can be considered as thesum of the losses in all the “m” segments, as follows.

( )2

V

2

D D

?z z f h

)2

Z )1n2( at (

2r m

1n n1n

)conical ( f

∆−

= −∑ +

= (27)

The resultant velocity, Vr , is calculated as the vector sum of

the average axial and tangential velocities, The annular

downward flow region is only considered, as presented in the

following set of equations:

2

Z

2

Z

2

R W U ) z ( V += (28)

∫ ∫

∫ ∫ =

π

π

φ

φ

2

0 z R

revr

2

0 z R

revr

z rdrd

Wrdrd W (29)

For simplification purposes, the average axial velocity in

Equation (28), Uz, is calculated assuming plug flow, namely

Uz is equal to the total flow rate over the annular area from the

wall to the reverse radius, r rev. The Moody friction factor is

calculated using Hall’s Correlation (Hall, 1957).




+

+=

3 / 16

4

) z Re(

10

) z ( D10 x210055.0 ) z ( f

ε(30)

where e is the pipe roughness and Re is the Reynolds Number,

calculated based on the resultant velocity computed in

Equation (28).

The centrifugal losses are the most important ones in

Equation (25), and account for most of the total pressure drop

in the LLHC. They are calculated using the following

expression:

∫ = u R

revr

2

ucf dr

r

)r ( )nW ( h (31)

where Wu is calculated from Equation (29) at the underflow

outlet and the centrifugal force correction factor, n = 2 for

twin inlets, and n = 3.2 for involute single inlet.

The centrifugal force correction factor compensates for

the use of Bernoulli’s Equation under a high rotational flow

condition. Its meaning is similar to the kinetic energycoefficient used to compensate for the non-uniformity of the

velocity profile in pipe flow (Munson et al., 1994).

Rigorously, the Bernoulli equation is valid for a streamline

and the summation of the pressure, the hydrostatic and the

kinetic terms can only be considered constant in the entire

flow field if the vorticity is equal to zero.

Numerical Solution. The simulation code based on thedeveloped mechanistic model uses mainly two different

numerical methods to obtain the results. The tangential

velocity, given by Equation (29), is solved using the

Trapezoidal Rule, and for the droplet trajectory, a fourth-order

Runge-Kutta method is used to solve Equation (18). Also, acommercial program (Mathematica 4.0) was used to verify the

resulting numerical values given by the computer code.

Resusults and DiscussionThis section presents comparison between the LLHC

mechanistic model predictions and experimental data taken

either at the present study or from the literature. Comparisonsare made for the swirl intensity, velocity profiles, migration

probability, pressure drop, droplet size distribution and global

separation efficiency.

Swirl Intensity. The swirl intensity, which is the ratio of the

local tangential momentum flux to the total momentum flux,can be obtained from Equation (4). Figure 19 provides the

comparison between the model predictions and the Colman

and Thew (1980), Case 2 data. Note that only 1 data point is

plotted, due to availability of axial and tangential velocity

measurements at specific axial location. The results display

the 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. Good

agreement is observed between the data point and the model

predictions. It has been experimentally proven by several

researchers that the swirl intensity decays exponentially with

axial position due to the wall frictional losses (Mantilla, 1998)

The model predictions show the same trend

Velocity Profile. The velocity field predicted by the

mechanistic model is compared with the same experimental

data set used for the swirl intensity comparison, namely, Case2. Figure 20 presents the comparison between theexperimental data and model prediction for the tangentia

velocity. The y-axis corresponds to the axis of the LLHC, and

the x-axis represents the radial position. The units used

originally were conserved, namely, millimeters per second for

the tangential velocity, and millimeters for the radial position

The model predicts with acceptable accuracy the tangential

velocity at the wall, the peak velocity and the radius where i

occurs. The experimental data and the model display a

Rankine Vortex shape, namely, a combination of forced

vortex near the LLHC axis and a free like vortex at the outer

region.The axial velocity profile predicted by the model is next

compared with the experimental data in Figure 21. The

positive values of axial velocities correspond to downward

flow, which is the direction of the main flow, while the

negative values represent the reverse flow. The mechanistic

model performance is excellent with respect to the axial

velocity in the downward flow region, and not so good in the

reverse flow region. Considering the calculations that the

model follows to compute the separation efficiency, the

prediction of the reverse flow velocity profile is not so

important. What is really important is the prediction of the

radius of zero velocity (r rev) since beyond this point the dropletis assumed to be separated, moving upwards to the overflow

exit.

Migration Probability: A comparison between the model

predictions of the migration probability curve as compared

with experimental data of Colman and Thew (1980) is given

in Figure 22. Fair agreement is observed with the data.

Pressure Drop. A comparison between the predicted pressure

drop and experimental data from the present study is shown in

Figure 23, while Figure 24 shows the model predictions of

pressure drop vs. flow rate as compared with the experimenta

data taken by Young et al. (1990). Very good agreement is

observed in both cases, with an average absolute relative erro

of 1.6%.

Droplet Size Distribution. Figure 25 shows a comparison

between the model predictions and experimental data of the

droplet size distribution for runs 101. As shown in the figures

good agreement is observed with experimental results. The

model prediction curves for the underflow droplet size

distribution are shifted to the right, which means that the

model predicts efficiency smaller than the experimental one.

Also there is a discontinuity in the model curve because the

model doesn’t consider either breakup or coalescence. This




means that the smallest droplet that enters the LLHC is also

the smallest one that is found in the underflow stream. On the

other hand, the largest droplet in the underflow stream is the

largest droplet with a calculated efficiency below 100%.

Global Separation Efficiency. Both the underflow purity and

the migration probability curve predicted by the model are

evaluated 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 experimental

data, where cases 9 to 22 are part of the set of experiments

published by Colman et al. (1980). These experimental data

sets are for the LLHC configuration given in Table 4. The

characteristic diameter and operational conditions are reported

in Table 3.

As can be seen from both tables 2 and 3, the model

predictions are in excellent agreement with both data sets,

with an average absolute relative error of 3%. The results are

also plotted in Figures 26 and 27, respectively.

Summary and Conclusions

A new facility for testing LLHCs was designed, constructed

and installed in an existing three-phase flow loop. The test

section is fully instrumented to measure the important flow

and separation variables, including flow rates (inlet, underflow

and overflow) and the respective oil concentrations; droplet

size distributions (inlet and underflow streams); pressures

(inlet and underflow) and temperature. A mixer bypass loop

enables the generation of a wide range of droplet size

distributions.

A set of 124 experimental runs was conducted, with inlettotal flow rates between 18 to 26 GPM, inlet oil cuts between

0 to 10%, inlet droplet size distributions with droplet medians

between 30 to 160 microns, inlet pressures from 60 to 90 psia,underflow pressures between 35 to 63 psia, temperature

between 65ºF – 80ºF, and overflow reject diameter of 3mm

and 4mm. The collected data permitted the calculation of the

LLHC separation efficiency for each of the runs.

The collected data reveals that LLHCs can be used up to

10% inlet oil concentrations, maintaining high separation

efficiency. However, the performance of the LLHC is best for

very low oil concentrations at the inlet, below 1%. For low

concentrations, no emulsification of the mixture occurs in the

LLHC. However, high inlet concentrations, up to 10%,

promote emulsification posing a separation problem in the

overflow stream.

A simple mechanistic model is developed for the LLHC.The model is capable of predicting the LLHC hydrodynamic

flow field, namely, the axial, tangential and radial velocity

distributions of the continuous-phase. The separation

efficiency and migration probability are determined based on

swirl intensity prediction and droplet trajectory analysis. The

flow capacity, namely, the inlet-to-underflow pressure drop is

predicted utilizing an energy balance analysis.

The prediction of the LLHC model was compared against

the data from both the present study and published data for

velocity profiles from the literature, especially from the

Colman and Thew (1980). Good agreement is obtained

between the model predictions and the experimental data with

respect to both separation efficiency (average absolute relative

error of 3%) and pressure drop (average absolute relative error

of 1.6%).

Nomenclature A = cross sectional area B = peak tangential velocity radius factor (Eqs. 10 and 11)

c = Concentration

C D = drag coefficient

d = droplet diameter

D = diameter

Dc = LLHC characteristic diameter

f = friction factor

F = Split ratiog = gravity acceleration

h = losses

I = inlet factor

L = length

m = Nº of segments

m& = mass flow rate

M t = momentum flux at the inlet slot

M T = axial momentum flux at the characteristic diameter

positionn = centrifugal force correction factor, number of inlets

P = pressure

q = volumetric flow rate

r = radial position

R = LLHC radius

Re = Reynolds Number

t = time

T m = maximum tangential velocity momentum (Eq. 9)

u = continuous phase local axial velocityU = bulk axial velocity

v = continuous phase local radial velocity

V = volumetric fraction / velocity

V r = droplet radial velocity

V sr = droplet slip velocity in the radial direction

V z = droplet axial velocity

w = continuous phase local tangential velocity

W = mean tangential velocity

z = Axial position

Greek Letters

O = swirl intensity

ß = taper section semi -anglee = pipe roughness

e ff = efficiency / purity

? = axis inclination angle to horizontal

µ = viscosity

? = density

φ = Horizontal plane angle

Subscripts

av = average




c = characteristic diameter location / continuous phase

cf = centrifugal

crit = critical

d = dispersed phase / droplet

f = frictional

i = inlet

is = inlet section

o = overflowr = resultantrev = reverse flow

sr = Slip radial velocity

u = underflow

z = axial position

AcknowledgmentsThe authors thank Mr. Grant Young from Vortex Fluid

Systems Inc. and Dr. Charles Petty from Michigan State

University for their help and advise during this study.

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Table 2: Efficiency Comparison with Present StudyTest Pinlet ∆P Temp. Q inlet Oilinlet Split Ratio Reject Dia. Experim. Model

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

1 2.3 51 200 92 27 80 25 1 6 3 87 89

3 1.7 33 116 71 18 80 21 1 6 3 64 66

6 1.9 53 200 91 26 79 25 3 6 3 87 90

8 1.7 31 116 70 18 79 21 3 5 3 60 62

11 1.9 56 200 91 27 80 25 5 12 3 89 91

13 1.7 33 133 71 18 80 21 5 6 3 63 66

16 1.9 62 229 90 28 79 25 7 14 3 92 93

18 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 96

23 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 96

102 5.1 133 517 79 23 77 23 1 8 4 98 98

103 7.7 185 592 70 19 78 22 1 13 4 99 98

106 11.6 140 592 90 27 78 26 3 12 4 99 99

111 5.9 133 517 90 27 79 26 5 11 4 98 98

121 8.8 136 517 90 28 72 25 10 11 4 99 99

122 6.7 143 592 79 23 72 23 10 12 4 98 98

123 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 -3.888910 < 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 79

11 30 50 0.84 35 82 84

12 30 60 0.84 35 84 88

13 30 70 0.84 35 88 90

14 58 160 0.84 35 72 66

15 58 190 0.84 35 74 72

16 58 220 0.84 35 78 75

17 58 250 0.84 35 81 79

18 58 220 0.84 17 43 48

19 58 250 0.84 17 47 52

20 58 220 0.84 70 96 92

21 58 250 0.84 70 97 94

22 58 220 0.87 41 80 80

Table 4: Geometrical Parameters for Literature Data (Runs 9 to 22)Case Design Dc(mm) a1 a2 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-PHASE

GR A VITY

S E P A R A T O R

V14

OIL

TANK

TANK

WATER

V23 V2 1

TEST

SECTION

W A T E R L I N E

OIL L IN E

V12

V11

V26

V25

OIL SKIMMER

PG7

PG3

MM

PG5

MM

MIXING UNIT

MV3 CV 3 V8

OIL METERING SECTION

W A TER METER IN G SEC TIO N

V13

PUMP

PUMP

V9 TT3

CV 2 V5V7

V6 TT2

DV 2

DV 3

V20V16 V17

MV2

V10

PG6

PG4

V24

STORAGE SECTION

Figure 4: Schematic of Experimental LLHC Flow Loop

IsokineticSampler

System

MixingLoop

OilTank

GearPump

SpeedController

Water Stream

O i l S t r e a

GearFlowMeter

S t a t i c m i x

PressureTransducer Thermometer

PressureTransducer

A c r y l i c H y d r o c y c l

S t e e l M Q H

y d r o c y c

UnderflowStream

OverflowStream

OverflowDischarge

OilStream

Figure 5: Schematic of LLHC Test Section

Figure 6: Photograph of LLHC Test Section




Flow Direction

InletUnderflow

Flow Direction

Surfactant

S a m p l e H o l d

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

E f f i c i e n c y

DP= 27 psig, Q= 25 GPM

Dp= 22 psig, Q= 23 GPM

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

d50 = 130-150 µm

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


E f f i c i e n c y

Pi= 90 psia, Pu= 63 psia



Coil-inlet = 1 - 10 %

d50 = 130-150 µm

Qinlet = 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


E f f i c i e n c y

Do= 3 mm

Do= 4 mm

Coil-inlet = 1 - 10 %

d50 = 130-150 µm

Qinlet = 25-21 GPM

∆P = 27-18 psig

Figure 10: Effect of overflow diameter on efficiency

0

20

40

60

80

100

1 10 100 1,000 10,0

Inlet Oil Concentration, mg/lt

E f f i c i e n c y

Cinlet = 1%

Cinlet = 3%

Cinlet = 5%

Cinlet = 7%

Cinlet = 10%

Coil-inlet= 1 - 10 %d50 = 130-150 µm

Qinlet = 25-21 GPM

∆P = 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


E f f i c i e n c y

Feed d50 = 30 um, test 3



Coil-inlet = 1 %

Qinlet = 25-21 GPM

∆P = 27-18 psig

Figure 12: Effect of Droplet Size Distribution

on Efficiency

0

2

4

6

8

10

12

1 10 10 0 1000

Microns, um

V o l u m e

F r a c t i o n

Underflow

Inlet

C = 1%

∆P = 27 psig

Q = 25 GPM

d50 = 130µm

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)

S

w i r l I n t e n s

i t y

Experimental Data

Model

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)

T a n g e n t i a

l V e l o c i t y ( m m / s e c )

Experimental Data

Model

Figure 20: Tangential Velocity Comparison (Colman


z / Dc = 10.5

-7000

0

7000

0 4 8 12 16

Radius (mm)

T a n g e n t i a l V e l o c i t y ( m m / s e c )

Experimental Data

Model

Figure 21: Axial Velocity Comparison (Colman


0

10

20

30

40

50

60

70

80

90

100

0 8 16 24 32 40 48 56 64

Droplet Diameter (microns)

S e p a r a

t i o n

E f f i c i e n c y

( % )

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

Pressure Drop, psi

F l o w R a t e ,

G P M

Experimental

Model

∆P 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 20 0

Pressure Drop (psi)

F l o w r a t e ( l p m

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 10 100 100

Microns, um

V o

l u m e

F r a c

t i o n

Underflow

Inlet

LLHC Model

Coil-inlet = 1 %

d50 = 130 µm

Qinlet = 25 GPM

∆P = 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 (%)

M o d e l E f f i c i e n c y ( % )

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 (%)

M o

d e

l E f f i c i e n c y

( %

Model

Experimental

Figure 27: Comparison of Model Efficiency with

Literature Experimental Data

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oil_water_separation_hydrocyclones_2001.pdf