Three Phase Separator Design

CHAPTER 4

Three-Phase Oil and WaterSeparators

4.1 Introduction

This chapter discusses the concepts, theory, and sizing equationsfor the separation of two immiscible liquid phases (in thiscase, those liquids are normally crude oil and produced water). Theseparator design concepts presented in Chapter 3 relate to the two-phase separation of liquid and gas and are applicable to the separationof gas that takes place in three-phase separators, gas scrubbers,and any other device in which gas is separated from a liquid phase.

When oil and water are mixed with some intensity and thenallowed to settle, a layer of relatively clean free water will appear atthe bottom. The growth of this water layer, with time, will follow acurve as shown in Figure 4.1.

After a period of time, ranging anywhere from 3 to 30 min, thechange in the water height will be negligible. The water fraction,obtained from gravity settling, is called free water. It is normally ben-eficial to separate the free water before attempting to treat the remain-ing oil and emulsion layers.

Three-phase separator and free-water knockout are terms used todescribe pressure vessels that are designed to separate and remove thefree water from a mixture of crude oil and water. Because flow nor-mally enters these vessels directly from either a producing well or aseparator operating at a higher pressure, the vessel must be designedto separate the gas that flashes from the liquid, as well as separatethe oil and water.

The term three-phase separator is normally used when there is alarge amount of gas to be separated from the liquid, and the dimen-sions of the vessel are determined by the gas capacity equations dis-cussed in Chapter 3.

Free-water knockout is generally used when the amount of gas issmall relative to the amount of oil and water, and the dimensions ofthe vessel are determined by the oil–water separation equations dis-cussed in this chapter. No matter what name is given to the vessel,any vessel that is designed to separate two immiscible liquid phaseswill employ the concepts described in this chapter. For purposes ofthis chapter, we will call such a vessel a three-phase separator.

hw

h

Oil

Emulsion

Water

ho

Time

he

hw

h

FIGURE 4.1. Growth of water layer with time.

132 Gas-Liquid and Liquid-Liquid Separators

The basic design aspects of three-phase separation are identicalto those discussed for two-phase separation in Chapter 3. The onlyadditions are that more concern is placed on liquid–liquid settlingrates and that some means of removing the free water must be added.Liquid–liquid settling rates will be discussed later in this chapter.Water removal is a function of the control methods used to maintainseparation and removal from the oil. Several control methods areapplicable to three-phase separators. The shape and diameter of thevessel will, to a degree, determine the types of control used.

4.2 Equipment Description

4.2.1 Horizontal Separators

Three-phase separators are designed as either horizontal or verticalpressure vessels. Figure 4.2 is a schematic of a typical horizontalthree-phase separator. The fluid enters the separator and hits an inletdiverter. This sudden change in momentum does the initial gross sep-aration of liquid and vapor as discussed in Chapter 3. In most designsthe inlet diverter contains a down-comer that directs the liquid flowbelow the oil–water interface.

This forces the inlet mixture of oil and water to mix with thewater continuous phase in the bottom of the vessel and rise throughthe oil–water interface. This process is called water washing, and itpromotes the coalescence of water droplets, which are entrained inthe oil continuous phase.

Gas Outlet

Oil & Emulsion

Inlet Diverter

Water

Inlet

Mist Extractor

Pressure ControlValve

PC

LC

Oil Out

Gravity Settling Section

LC

Water Out

Level ControlValve

Oil

FIGURE 4.2. Schematic of a horizontal three-phase separator with interfacelevel control and weir.

Three-Phase Oil and Water Separators 133

Figure 4.3 illustrates the principles of water washing. The inletdiverter ensures that little gas is carried with the liquid, and the waterwash ensures that the liquid does not fall on top of the gas–oil or oil–water interface, mixing the liquid retained in the vessel and makingcontrol of the oil–water interface difficult.

The liquid collecting section of the vessel provides sufficienttime so that the oil and emulsion form a layer, or oil pad, on top ofthe free water. The free water settles to the bottom.

Figure 4.4 is a cutaway view of a typical horizontal three-phase sep-aratorwith an interface level controller andweir. Theweirmaintains theoil level, and the level controller maintains the water level. The oil isskimmed over the weir. The level of the oil downstream of the weir iscontrolled by a level controller that operates the oil dump valve.

The produced water flows from a nozzle in the vessel locatedupstream of the oil weir. An interface level controller senses theheight of the oil–water interface. The controller sends a signal to thewater dump valve, thus allowing the correct amount of water to leavethe vessel so that the oil–water interface is maintained at the designheight.

The gas flows horizontally and out through a mist extractor to apressure control valve that maintains constant vessel pressure. The

Oil

Water

Inlet Diverter

Oil–WaterEmulsion

FIGURE 4.3. Inlet diverter illustrating the principles of water washing.


level of the gas–oil interface can vary from 50% to 75% of the diame-ter depending on the relative importance of liquid–gas separation. Themost common configuration is half-full, and this is used for the designequations in this section. Similar equations can be developed for otherinterface levels.

Figure 4.5 shows an alternate configuration known as a “bucketand weir” design. Figure 4.6 is a cutaway view of a horizontal three-phase separator with a bucket and weir. This design eliminates theneed for a liquid interface controller. Both the oil and water flow over

Inlet

Gas

WaterOutlet

OilOutlet

LiquidCollectionSection

Gravity Settling SectionInlet

Diverter

Oil & Emulsion

MistExtractor

LiquidLevelController

Weir

FIGURE 4.4. Cutaway view of a horizontal three-phase separator with inter-face level control and weir.

Gas OutletMist Extractor

Inlet Diverter

Inlet

Level ControlValve

Oil & Emulsion

Oil Out

LC

LC


PC

Water Out

Water Weir

Oil

Oil Bucket


Gas

Water Water

FIGURE 4.5. Schematic of a horizontal three-phase separator with a bucketand weir.


weirs where level control is accomplished by a simple displacer float.The oil overflows the oil weir into an oil bucket where its level is con-trolled by a level controller that operates the oil dump valve. Thewater flows under the oil bucket and then over a water weir. The leveldownstream of this weir is controlled by a level controller that oper-ates the water dump valve.

As shown in Figures 4.5 and 4.6, the back of the oil bucket ishigher than the front of the bucket. This differential height configura-tion assures oil will not flow over the back of the bucket and out withthe water should the bucket become flooded (Figure 4.7). The heightof the oil weir controls the liquid level in the vessel. The differencein height of the oil and water weirs controls the thickness of the oilpad due to specific gravity differences. It is critical to the operation

VorterBreaker

Inlet

PressureRelief Valve

Oil LevelController

Water LevelController

Water SightGauge

Oil Bucket

Inlet Diverter

LCLC

Oil & Emulsion

Gas

Water

Oil Water

Gas

FIGURE 4.6. Cutaway view of a horizontal three-phase separator with abucket and weir.

Oil Weir

DHOil

A

Water

Water Weir

ho

hw

hw'

FIGURE 4.7. Determination of oil pad height.


of the vessel that the water weir height is sufficiently below the oilweir height so that the oil pad thickness provides sufficient oil reten-tion time. If the water weir is too low and the difference in specificgravity is not as great as anticipated, then the oil pad could grow inthickness to a point where oil will be swept under the oil box andout the water outlet. Normally, either the oil or the water weir ismade adjustable so that changes in oil- or water-specific gravities orflow rates can be accommodated.

To obtain a desired oil pad height, the water weir should be set adistance below the oil weir. This distance is calculated by using Equa-tion (4.1), which is developed by equating the static heads at point A.

Dh ¼ ho 1� rorw

� �� (4.1)

where Dh ¼ distance below the oil weir, in (mm), ho ¼ desired oil padheight, in (mm), ro ¼ oil density, lb/ft3 (kg/m3), rw ¼ water density,lb/ft3 (kg/m3).

This equation neglects the height of the oil and water flowingover the weir and presents a view of the levels when there is noinflow. A large inflow of oil will cause the top of the oil pad to rise;the oil pad will thus get thicker, and the oil bucket must be deepenough so that oil does not flow under it. Similarly, a large inflow ofwater will cause the level of water flowing over the water weir to rise,and there will be a large flow of oil from the oil pad over the oilweir until a new hw is established. These dynamic effects can be mini-mized by making the weirs as long as possible.

Three-phase separators with a bucket and weir design are mosteffective with high water-to-oil flow rates and/or small density differ-ences. Interface control design has the advantage of being easily adjus-table to handle unexpected changes in oil or water specific gravity orflow rates. Interface control should be considered for applications withhigh oil flow rates and/or large density differences. However, in heavyoil applications or where large amounts of emulsion or paraffin areanticipated, it may be difficult to sense interface level. In such a casebucket and weir control is recommended.

Free-Water Knockout

The term free-water knockout (FWKO) is reserved for a vessel thatprocesses an inlet liquid stream with little entrained gas and makesno attempt to separate the gas from the oil. Figure 4.8 illustrates ahorizontal FWKO.

Figure 4.9 illustrates a vertical FWKO. The major differencebetween a conventional three-phase separator and an FWKO is that inthe latter there are only two fluid outlets; one for oil and very smallamounts of gas and the second for thewater. FWKOs are usually operatedas packed vessels. Water outflow is usually controlled with an interface


Oil & GasOutlet

Water Outlet

Gas

Inlet Diverter

Inlet

Water

Oil

FIGURE 4.8. Schematic of a horizontal FWKO.

LC

Liquid Inlet

Oil and Gas Outlet

Water Outlet

Inlet Diverter

PC

PressureControl Valve

Water

Oil

Gas

Oil–WaterInlerface

FIGURE 4.9. Schematic of a vertical FWKO.


level control. It should be clear that the principles of operation of such avessel are the same as those described above. The design of an FWKO isthe same as that of a three-phase separator. Since there is very little gas,the liquid capacity constraint always dictates the size.

Flow Splitter

Figure 4.10 illustrates a typical flow splitter. A flow splitter is a spe-cial version of a free-water knockout. Basically, it is an FWKO wherethe oil outlet is split among two or more outlet lines that aredirected to several downstream process components. This vesselcontains several compartments, which are sealed from each other.Each compartment has its own level control and outlet oil valve.Unlike the FWKO, which may be operated as a packed vessel,the flow splitter must be operated with a gas blanket. Adjustableweirs separate the compartments from water and oil outside thecompartments.

Oil flows over the weirs into the individual compartments.The water level control is used to maintain the top of the oil layerabove the highest weir. Individual level controls in each compartmentensure that the oil leaves the compartments at the same rate at whichit enters. The flow of liquid across the notched weir is directly propor-tional to the difference in height between the liquid upstream of theweir and the bottom of the notch. When the weirs of different com-partments are set at different heights, the flow into each compartmentis different. The water level control holds the water level constant,which ensures all oil that enters the separator leaves through thecompartments in proportions related to the weir heights.

Water Outlet

Adjustable Weirs

OilWater

PC

LCGas

Gas out

Gas

Oil Outlet(Typical)

A

A

LC

Gas Outlet

Oil Outlet

SECTION A-A

Oil

Water

FIGURE 4.10. Schematic of a flow splitter with four compartments.


Horizontal Three-Phase Separator with a Liquid Boot

Figure 4.11 shows a horizontal three-phase separator with a water“boot” on the bottom of the vessel barrel. The boot collects smallamounts of water that settle out in the liquid collection section andtravel to the outlet end of the vessel. These vessels are a specialcase of three-phase separators.

Figure 4.12 shows a horizontal two-phase separator with a liquidboot. Because the water flow rate is so low relative to the oil flow rate,

Liquid Level

Interface Level

Inlet Diverter InletMist Extractor

Gas Outlet

Water Outlet

Overflow Baffle

A

SECTION A-A

LC

Oil Outlet

Inlet Diverter

LC

Gas

Oil

A

Water Boot

Water

FIGURE 4.11. Schematic of a horizontal three-phase separatorwith awater boot.

Gas Outlet

Inlet Diverter

Inlet

Mist Extractor


PC

LC

Liquid Out


Level ControlValve

FIGURE 4.12. Schematic of a horizontal two-phase separator with a liquid boot.


the small amount of water retention time provided by the boot issufficient. Thus the diameter of the main body of the vessel can besmaller. The liquid boot collects small amounts of liquid in the liquidcollection section. These vessels are a special case of two-barrel two--phase separators, which are typically used in dry gas applications andshould only be used where separation of the two liquid phases isrelatively easy.

4.3 Vertical Separators

Figure 4.13 shows a typical configuration for a vertical three-phaseseparator. Flow enters the vessel through the side as in the horizontalseparator. The inlet diverter separates the bulk of the gas. A down-comer is required to route the liquid through the oil–gas interface soas not to disturb the oil skimming action taking place. A chimney is

LC

Inlet

Liquid Outlet

Gas Outlet

Oil Outlet

LC

Mist Extractor

Chimney

Spreader

Down-comer

Inlet Diverter

PC

PressureControl Valve

Water

Oil Oil

Level Control Valve

Level Control Valve

Gas

FIGURE 4.13. Schematic of a vertical three-phase separator with interfacelevel control.


needed to equalize gas pressure between the lower section and the gassection.

The spreader, or down-comer, outlet is located just below theoil–water interface, thus water washing the incoming stream. Fromthis point, as the oil rises, any free water trapped within the oil phaseseparates out. The water droplets flow countercurrent to the oil.Similarly, the water flows downward, and oil droplets trapped in thewater phase tend to rise countercurrent to the water flow. Figures 4.14and 4.15 are views of vertical three-phase separators without waterwashing and with interface control.

Figure 4.16 shows the three different methods of control that areoften used on vertical separators.

l The first is strictly level control. A regular displacer float isused to control the gas–oil interface and regulate a controlvalve dumping oil from the oil section. An interface float isused to control the oil–water interface and regulate a wateroutlet control valve. Because no internal baffling or weirs are

Oil Outlet

Down-comer

Inlet

GasOutlet

Inlet Diverter

DistributionBaffle

Oil

LC

LC

Water Outlet

SerpentineVane Mist Extractor

Oil–Water InterfaceWater

FIGURE 4.14. Cutaway view of a vertical three-phase separator with interfacelevel control.


PressureRelief Valve

Gas out

MistExtractor

Isolation Baffle

Down-comer

Oil–Water Interface

Skirt (support)

Water Outlet

Liquid Outlet

Inlet

InletDiverter

FIGURE 4.15. Cutaway view of a vertical three-phase separator without waterwashing.

Water Out

LCOil

Oil Out

LC

Oil LC

LC

Water Out

Oil OutOil

Oil Weir Oil Weir

LC

Oil Out

Water

LC

Water Out

Gas Equalizing Line

Oil

Adjustable Height

Interface Level Control Interface Level Controlwith Oil Chamber

Water Leg with orwithout Oil Chamber

Oil

Water Water Water

FIGURE 4.16. Liquid level control schemes.


used, this system is the easiest to fabricate and handles sandand solids production best.

l The secondmethod shownuses aweir to control the gas–oil inter-face level at a constant position. This results in a better separationof water from the oil as all the oil must rise to the height of the oilweir before exiting the vessel. Its disadvantages are that the oil boxtakes up vessel volume and costs money to fabricate. In addition,sediment and solids could collect in the oil box and be difficultto drain, and a separate low-level shut-down may be required toguard against the oil dump valve’s failing to close.

l The third method uses two weirs, which eliminates the needfor an interface float. Interface level is controlled by the heightof the external water weir relative to the oil weir or outletheight. This is similar to the bucket and weir design of hori-zontal separators. The advantage of this system is that it elim-inates the interface level control. The disadvantage is that itrequires additional external piping and space. In cold climatesthe water leg is sometimes installed internal to the vessel sothat the vessel insulation will prevent it from freezing.

4.4 Selection Considerations

The geometry and physical and operating characteristics give eachseparator type advantages and disadvantages. Gravity separation ismore efficient in horizontal vessels than in vertical vessels. In thegravity settling section of a horizontal vessel, the settling velocityand flow velocity are perpendicular rather than countercurrent in avertical vessel.

Horizontal separators have greater interface areas, whichenhances phase equilibrium. This is especially true if foam or emul-sion collect at the gas–oil interface. Thus, from a process perspective,horizontal vessels are preferred. However, they do have several draw-backs, which could lead to a preference for a vertical vessel in certainsituations:

1. Horizontal separators are not as good as vertical separators inhandling solids. The liquid dump valve of a vertical separatorcan be placed at the center of the bottomhead so that solidswillnot build up in the separator, but continue to the next vessel inthe process. As an alternative, a drain could be placed at thislocation so that solids could be disposed of periodically whileliquid leaves the vessel at a slightly higher elevation. In a hori-zontal vessel, it is necessary to place several drains along thelength of the vessel. Since the solidswill have an angle of repose


of 45� to 60�, the drains must be spaced at very close intervals[usually no farther than 5 ft (1.5 m) apart]. Attempts to lengthenthe distance between drains, by providing sand jets in the vicin-ity of each drain to fluidize the solids while the drains are in theoperation, are expensive and have been only marginally suc-cessful in field operations.

2. Horizontal vessels require more plan area to perform the sameseparation as vertical vessels. While this may not be of impor-tance at a land location, it could be very important offshore. Ifseveral separators are used, however, this disadvantage maybe overcome by stacking horizontal separators on top of eachother.

3. Small-diameter horizontal vessels [3-ft (1.5-m) diameter andsmaller] have less liquid surge capacity than vertical vesselssized for the same steady-state flow rate. For a given changein liquid surface elevation, there is typically a larger increasein liquid volume for a horizontal separator than for a verticalseparator sized for the same flow rate. However, the geometryof a small horizontal vessel causes any high-level shutdowndevice to be located close to the normal operating level. Invery large diameter [greater than 6 ft (1.8 m)] horizontal ves-sels and in vertical vessels, the shutdown could be placedmuch higher, allowing the level controller and dump valvemore time to react to the surge. In addition, surges in horizon-tal vessels could create internal waves, which could activate ahigh-level sensor prematurely.

4. Care should be exercised when selecting small-diameter [5 ft(1.5 m)] horizontal separators. The level controller and levelswitch elevations must be considered. The vessel must havea sufficiently large diameter so that the level switches maybe spaced far enough apart, vertically, so as to avoid operatingproblems. This is important if surges in the flow of slugs ofliquids are expected to enter the separator.

It should be pointed out that vertical vessels have some draw-backs that are not process related and that must be considered whenmaking a selection. For example, the relief valve and some of the con-trols may be difficult to service without special ladders and platforms.The vessel may have to be removed from the skid for trucking due toheight restrictions.

In summary, horizontal vessels are most economical for normaloil–water separation, particularly where there may be problems withemulsions, foam, or high gas–liquid ratios. Vertical vessels work mosteffectively in low gas–oil ratio (GOR) applications and where solidsproduction is anticipated.


4.5 Vessel Internals

Vessel internals common to both two-phase and three-phase separa-tors, such as inlet diverters, wave breakers, defoaming plates, vortexbreakers, stilling wells, sand jets and drains, and mist extractors, arecovered in Chapter 3: Two-Phase Oil and Gas Separation and willnot be repeated here. Additional internals that aid in the separationof oil and water are presented in this section.

4.5.1 Coalescing Plates

It is possible to use various plate or pipe coalescer designs to aid in thecoalescing of oil droplets in the water and water droplets in the oil.The installation of coalescing plates in the liquid section will causethe size of the water droplets entrained in the oil phase to increase,making gravity settling of these drops to the oil–water interface easier.Thus, the use of coalescing plates (Figure 4.17), will often lead to theability to handle a given flow rate in a smaller vessel. However,because of the potential for plugging with sand, paraffin, or corrosionproducts, the use of coalescing plates should be discouraged, exceptfor instances where the savings in vessel size and weight are largeenough to justify the potential increase in operating costs anddecrease in availability.

4.5.2 Turbulent Flow Coalescers

Turbulent flow coalescers, which were marketed under the name SPPacks, utilized the turbulence created by flow in a serpentine pipepath to promote coalescence.

Pressure Control Valve

Inlet

Oil & Emulsion


Water Outlet

Mist Extractor

Water

Inlet Diverter

PC

Oil Outlet

LC

Gas Outlet

LC

Oil

FIGURE 4.17. Schematic of a horizontal three-phase separator fitted with coa-lescing plates.


As shown in Figure 4.18, SP Packs took up more space in thevessel than plate coalescers, but since they did not have small clear-ances, they were not susceptible to plugging. Despite the designadvantages, the units were not well received and, as such, are no longerbeing manufactured.

4.6 Potential Operating Problems

Emulsions. Three-phase separators may experience the same operatingproblems as two-phase separators. In addition, three-phase separatorsmay develop problemswith emulsionswhich can be particularly trouble-some in the operation of three-phase separators. Over a period of time anaccumulation of emulsified materials and/or other impurities may format the interface of the water and oil phases. In addition to adverse effectson the liquid level control, this accumulationwill also decrease the effec-tive oil or water retention time in the separator,with a resultant decreasein water–oil separation efficiency. Addition of chemicals and/or heatoften minimizes this difficulty.

Frequently, it is possible to appreciably lower the settling timenecessary for water–oil separation by either the application of heatin the liquid section of the separator or the addition of de-emulsifyingchemicals.

4.7 Design Theory

Gas separation. The concepts and equations pertaining to two-phaseseparation described in Chapter 3 are equally valid for three-phaseseparation.

Oil OutWater Outlet


Inlet Diverter

Inlet

SP PACK

Pressure Control Valve

Mist Extractor

PC

Gas Outlet

LC

LC

OilWater

Oil & Emulsion

FIGURE 4.18. Schematic of a horizontal three-phase separator fitted with afree-flow turbulent coalescers (SP Packs).


4.7.1 Oil–Water Settling

It can be shown that flow around settling oil drops in water or waterdrops in oil is laminar and thus Stokes’ law governs. The terminaldrop velocity is

Field units

Vt ¼ 1:78� 10�6ðDSGÞd2m

m(4.2a)

SI units

Vt ¼ 5:56� 10�7ðDSGÞd2m

m(4.2b)

where Vt ¼ terminal settling velocity, ft/s (m/s), DSG ¼ difference inspecific gravity relative to water between the oil and the water phases,dm ¼ drop size, mm, m ¼ viscosity of continuous phase, cp.

4.7.2 Water Droplet Size in Oil

It is difficult to predict the water droplet size that must be settled out ofthe oil phase to coincide with the rather loose definition of “free oil.”Unless laboratory or nearby field data are available, good results havebeen obtained by sizing the oil pad such that water droplets 500 mmand larger settle out.

As shown in Figure 4.19, if this criterion is met, the emulsion tobe treated by downstream equipment should contain less than 5–10%water. In heavy crude oil systems, it is sometimes necessary to designfor 1000-mm water droplets to settle. In such cases the emulsion maycontain as much as 20–30% water.

4.7.3 Oil Droplet Size in Water

From Equations (4.2a) and (4.2b) it can be seen that the separation ofoil droplets from the water is easier than the separation of waterdroplets from the oil. The oil’s viscosity is on the order of 5–20 timesthat of water.

Thus, the terminal settling velocity of an oil droplet in water ismuch larger than that of a water droplet in oil. The primary purposeof three-phase separation is to prepare the oil for further treating.Field experience indicates that oil content in the produced waterfrom a three-phase separator, sized for water removal from oil, canbe expected to be between a few hundred and 2000 mg/l. This waterwill require further treating prior to disposal. Sizing for oil droplet


removal from the water phase does not appear to be a meaningfulcriterion.

Occasionally, the viscosity of the water phase may be ashigh as, or higher than, the liquid hydrocarbon phase viscosity. Forexample, large glycol dehydration systems usually have a three-phase

00 100 200 300 400 500 600 700 800

5

10

20

15

Cum

ulat

ive

volu

me

of w

ater

in o

ilab

ove

inte

rfac

e %

Water drop size, microns

FIGURE 4.19. Typical water droplet size distribution.


LIVE GRAPHClick here to view

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flash separator. The viscosity of the glycol/water phase may be ratherhigh. In cases like this, the settling equation should be appliedto removing oil droplets of approximately 200 mm from the waterphase.

If the retention time of the water phase is significantly less thanthe oil phase, then the vessel size should be checked for oil removalfrom the water. For these reasons, the equations are provided so thewater phase may be checked. However, the separation of oil fromthe water phase rarely governs the vessel size and may be ignoredfor most cases.

4.7.4 Retention Time

A certain amount of oil storage is required to ensure that the oilreaches equilibrium and that flashed gas is liberated. An additionalamount of storage is required to ensure that the free water has timeto coalesce into droplet sizes sufficient to fall in accordance withEquations (4.2a) and (4.2b). It is common to use retention times rang-ing from 3 to 30 min depending on laboratory or field data. If thisinformation is not available, the guidelines presented in Table 4.1can be used.

Generally, the retention time must be increased as the oil gravityor viscosity increases. Similarly, a certain amount of water storage isrequired to ensure that most of the large droplets of oil entrained inthe water have sufficient time to coalesce and rise to the oil–waterinterface. It is common to use retention times for the water phaseranging from 3 to 30 min depending on laboratory or field data.If this information is not available, a water retention time of 10 minis recommended for design.

The retention time for both the maximum oil rate and the maxi-mum water rate should be calculated, unless laboratory data indicatethat it is unnecessary to take this conservative design approach.

TABLE 4.1Oil retention time

oAPI Gravity Time (Min)

Condensate 2–5Light crude oil (30�–40�) 5–7.5Intermediate crude oil (20�–30�) 7.5–10Heavy crude oil (less than 20�) 10þNote: If an emulsion exists in inlet stream, increase aboveretention times by a factor of 2–4.


4.8 Separator Design

The guidelines presented here can be used for initial sizing of a hori-zontal three-phase separator 50% full of liquid. They are meant tocomplement, and not replace, operating experiences. Determinationof the type and size of the separator must be made on an individualbasis. All the functions and requirements should be consideredincluding the likely uncertainties in design flow rates and proper-ties. For this reason, there is no substitute for good engineering eva-luations of each separator by the design engineer. The trade-offbetween design size and details and uncertainties in design para-meters should not be left to manufacturer recommendations or rulesof thumb.

4.8.1 Horizontal Separator Sizing—Half-Full

For sizing a horizontal three-phase separator it is necessary to specify avessel diameter and a seam-to-seam vessel length. The gas capacity andretention time considerations establish certain acceptable combinationsof diameter and length. The need to settle 500-mm water droplets fromthe oil and 200-mm oil droplets from the water establishes a maximumdiameter corresponding to the given liquid retention time.

Gas Capacity Constraint

The principles of liquid droplets settling through a gas were given inChapter 3. By setting the gas retention time equal to the time requiredfor a drop to settle to the liquid interface, the following equations maybe derived:Field units

dLeff ¼ 420TZQg

P

� �rg

rl � rg

!CD

dm

" #1=2(4.3a)

SI units

dLeff ¼ 34:5TZQg

P

� �rg

r1 � rg

!CD

dm

" #1=2(4.3b)

where d ¼ vessel inside diameter, in. (mm), Leff ¼ vessel effectivelength, ft (m), T ¼ operating temperature, �R (�K), Z ¼ gas compress-ibility, Qg ¼ gas flow rate, MMscfd (scm/h), P ¼ operating pres-sure, psia (kPa), pg ¼ density of gas, lb/ft3 (kg/m3), pl ¼ density ofliquid, lb/ft3 (kg/m3), CD ¼ drag coefficient, dm ¼ liquid drop to beseparated, mm.


Retention Time Constraint

Liquid retention time constraints can be used to develop the followingequation, which may be used to determine acceptable combinationsof d and Leff

Field units

d2Leff ¼ 1:42½ðQwÞðtrÞw þ ðQ0ÞðtrÞ0� (4.4a)

SI units

d2Leff ¼ 4:2� 104½ðQwÞðtrÞw þ ðQ0ÞðtrÞ0� (4.4b)

where Qw ¼ water flow rate, BPD (m3/h), (tr)w ¼ water retention time,min, Qo ¼ oil flow rate, BPD (m3/h), (tr)o ¼ oil retention time, min.

Settling Water Droplets from Oil Phase

The velocity of water droplets settling through oil can be calculatedusing Stokes’ law. From this velocity and the specified oil phase retentiontime, the distance that awater droplet can settlemaybedetermined.Thissettling distance establishes a maximum oil pad thickness given by thefollowing formula:

Field units

ho ¼ 0:00128ðtrÞoðDSGÞd2m

m(4.5a)

SI units

ho ¼ 0:0033ðtrÞoðDSGÞd2m

m(4.5b)

This is the maximum thickness the oil pad can be and still allow thewater droplets to settle out in time (tr)o. For dm ¼ 500 mm, the follow-ing equation may be used.

Field units

ðhoÞmax ¼ 320ðtrÞoðDSGÞ

m(4.6a)

SI units


m(4.6b)

For a given oil retention time [(tr)o] and a given water retention time[(tr)w], the maximum oil pad thickness constraint establishes amaximum diameter in accordance with the following procedure:


1. Compute (ho)max- Use 500-mm droplet if no other informationis available.

2. Calculate the fraction of the vessel cross-sectional area occu-pied by the water phase. This is given by

Aw

A¼ 0:5

QwðtrÞwðtrÞoQo þ ðtrÞwQw

(4.7)

3. From Figure 4.20, determine the coefficient b.4. Calculate dmax from

dmax ¼ ðhoÞmaxb

(4.8)

Any combination of d and Leff that satisfies all three of Equations(4.3), (4.4), and (4.8) will meet the necessary criteria.

d2

dAo

Aw

ho

hw

0.5

0.4

0.3

0.2

0.1

0.0

0.0 0.1 0.2 0.3 0.4 0.5

Aw

A

h o dβ

=

FIGURE 4.20. Coefficient “b” for a cylinder half filled with liquid.




4.9 Separating Oil Droplets from Water Phase

Oil droplets in the water phase rise at a terminal velocity defined byStokes’ law. As with water droplets in oil, the velocity and retentiontime may be used to determine a maximum vessel diameter. It is rarethat the maximum diameter determined from a 200-mm oil dropletrising through the water phase is larger than a 500-mm water dropletfalling through the oil phase. Therefore, the maximum diameterdetermined from a 500-mm water droplet settling through the oilphase normally governs the vessel design. For dm ¼ 200 mm, the fol-lowing equations may be used:

Field units

ðhwÞmax ¼ ð51:2ðtrÞwðDSGÞÞmw

(4.9a)

SI units

ðhwÞmax ¼ ð1; 520ðtrÞwðDSGÞÞmw

(4.9b)

The maximum diameter may be found from the following equation:

dmax ¼ ðhwÞmax

b(4.10)

4.9.1 Seam-to-Seam Length

The effective length may be calculated from Equations (4.4a) and (4.4b).From this, a vessel seam-to-seam length may be estimated. The actualrequired seam-to-seam length is dependent on the physical design ofthe vessel.

For vessels sized based on gas capacity, some portion of thevessel length is required to distribute the flow evenly near the inletdiverter. Another portion of the vessel length is required for the mistextractor. The length of the vessel between the inlet and themist extractor with evenly distributed flow is the Leff calculated fromEquations (4.3a) and (4.3b).

As a vessel’s diameter increases, more length is required toevenly distribute the gas flow. However, no matter how small thediameter may be, a portion of the length is still required for the mistextractor and flow distribution. Based on these concepts coupled withfield experience, the seam-to-seam length of a vessel may be esti-mated as the larger of the following:

Lss ¼ 4

3Leff (4.11)


Field units

Lss ¼ Leff þ d=12 (4.12a)

SI units

Lss ¼ Leff þ d=1000 (4.12b)

For vessels sized on a liquid capacity basis, some portion of the vessellength is required for inlet diverter flow distribution and liquid outlet.The seam-to-seam length should not exceed the following:

Lss ¼ 4=3Leff (4.13)

4.9.2 Slenderness Ratio

For each vessel design, a combination of Leff and d exists that willminimize the cost of the vessel. In general, the smaller the diameterof a vessel, the less it will cost. However, decreasing the dia-meter increases the fluid velocities and turbulence. As a vessel diam-eter decreases, the likelihood of the gas re-entraining liquids ordestruction of the oil/water interface increases. Experience indicatesthat the ratio of the seam-to-seam length divided by the outside diam-eter should be between 3 and 5. This ratio is referred to as the ‘slender-ness ratio’ (SR) of the vessel. Slenderness ratios outside the 3–5 rangemay be used but are not as common. Slenderness ratios outside the3–5 range may be used, but the design should be checked to assurethat re-entrainment will not occur.

4.9.3 Procedure for Sizing Three-Phase HorizontalSeparators—Half-Full

1. The first step in sizing a horizontal separator is to establish thedesign basis. This includes specifying the maximum and min-imum flow rates, operating pressure and temperature, dropletsize to be removed, and so on.

2. Select a (tr)o and a (tr)w.3. Calculate (ho)max. Use a 500-mm droplet if no other informa-

tion is available.

Field units

ðhoÞmax ¼ 1:28� 10�3 ðtrÞoðDSGÞd2m

m

For 500 mm,


m


SI units

ðhoÞmax ¼ 0:033ðtrÞoðDSGÞd2

m

m

For 500 mm,


m

4. Calculate Aw/A:

Aw

A¼ 0:5

QwðtrÞwðtrÞoQo þ ðtrÞwQw

5. Determine b from curve.6. Calculate dmax:

dmax ¼ ðhoÞmax

b

Note: dmax depends on Qo, Qw, (tr)o, and (tr)w.

7. Calculate combinations of d, Leff for d less than dmax that sat-isfy the gas capacity constraint. Use 100-mm droplet if noother information is available.

Field units

dLeff ¼ 420TZQg

P

� �rg

r1 � rg

!CD

dm

" #1=2

SI units

dLeff ¼ 34:5TZQg

P

� �rg

rl � rg

!CD

dm

" #1=2

8. Calculate combinations of d, Leff for d less than dmax that sat-isfy the oil and water retention time constraints.

Field units

d2Leff ¼ 1:42½ðtrÞoQo þ ðtrÞwQw�SI units

d2Leff ¼ 4:2� 104½ðtrÞoQo þ ðtrÞwQw�


9. Estimate seam-to-seam length.

Field Units

Lss ¼ Leff þd

12ðgas capacityÞ

Lss ¼ 4

3Leff ðliquid capacityÞ

SI units

Lss ¼ Leff þd

1000ðgas capacityÞ

Lss ¼ 4

3Leff ðliquid capacityÞ

10. Select a reasonable diameter and length. Slenderness ratios(12 Lss/d) on the order of 3–5 are common.

11. When making a final selection, it is always more economicalto select a standard vessel size. API sizes for small separatorscan be found in API Spec. 12J. In larger sizes in most loca-tions, heads come in outside diameters, which are multiplesof 6 in. (150 mm). The width of steel sheets for the shells isusually 10 ft (3000 mm), thus it’s common practice to spec-ify Lss in multiples of five.

4.9.4 Horizontal Separators Sizing Other than Half-Full

For three-phase separators other than 50% full of liquid, equations canbe derived similarly, using the actual oil and water areas. The equa-tions are derived using the same principles as discussed in Chapter 3and this chapter.

dLeff ¼ 4201� b1� a

� �TZQg

P

� �rg

r1 � rg

!CD

dm

" #1=2(4.14a)

where1� �

1� �¼ design constant found from Figure 4.21.

SI units

dLeff ¼ 34:51� b1� a

� �TZQg

P

� �rg

rl � rg

!CD

dm

" #1=2(4.14b)

where1� b1� a

¼ design constant found from Figure 4:21


4.9.5 Gas Capacity Constraint (Figures 4.21 and 4.22)

Retention Time Constraint

Field units

d2Leff ¼ðtrÞoQo þ ðtrÞwQw

1:4a(4.15a)

where a ¼ design constant found in Figure 4.22.

400

300

500

600

700

800

900

1000

1100

0.00 0.20 0.40 0.60 0.80 1.00

Fractional liquid height in separator (field units)

Des

ign

equa

tion

cons

tant

, 1

– α

1 –

β (fie

ld u

nits

)

FIGURE 4.21. Gas capacity constraint design constant versus liquid height ofa cylinder for a horizontal separator other than 50% full of liquid.




0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Rat

io o

f liq

uid

heig

ht to

tota

l hei

ght,

β (F

ield

uni

ts)

Relationship Between Ratioof Heights and Ratio of

Areas for HorizontalSeparator

0.0 0.2 0.4 0.6 0.8 1.0

Ratio of liquid area to total area, α (Field units)

FIGURE 4.22. Retention time constraint design constant — ratio of areas (a)versus ratio of heights (b) for a horizontal separator other than 50% full ofliquid.




SI units

d2Leff ¼ 21:000ðtrÞoQo þ ðtrÞwQw

a(4.15b)

where a ¼ design constant found in Figure 4.22.

4.9.6 Settling Equation Constraint

From the maximum oil pad thickness, liquid flow rates, and retentiontimes, a maximum vessel diameter may be calculated. The fractionalcross-sectional area of the vessel required for water retention may bedetermined as follows:

aw ¼ a1QwðtrÞwQoðtrÞo þQwðtrÞw

(4.16)

where al ¼ fractional area of liquids, aw ¼ fractional area of water.The fractional height of the vessel required for the water can be

determined by solving the following equation by trial and error:

aw ¼ 1

80cos�1½1� 2bw� �

1

p

� �½1� 2bw� (4.17)

where bw represents the fractional height of water.A maximum vessel diameter may be determined from the

fractional heights of the total liquids and water as follows:

dmax ¼ ððhoÞmaxÞ=ðb1 � bwÞ (4.18)

where dmax is the maximum vessel internal diameter in inches (mm).Any vessel diameter less than this maximum may be used to sep-

arate specified water droplet size in the specified oil retention time.

4.10 Vertical Separators’ Sizing

As with vertical two-phase separators, a minimum diameter must bemaintained to allow liquid droplets to separate from the verticallymoving gas. The vessel must also have a large enough diameterto allow water droplets to settle in the upward-flowing oil phase andto allow oil droplets to rise in the downward-moving water phase. Theliquid retention time requirement specifies a combination of diameterand liquid volume height. Any diameter greater than the minimumrequired for gas capacity and for liquid separation can be chosen.


4.10.1 Gas Capacity Constraint

By setting the gas velocity equal to the terminal settling velocity of adroplet, the following may be derived:

Field units

d2 ¼ 5040TZQg

P

� �rg

rl � rg

!CD

dm

" #1=2(4.19a)

SI units

d2 ¼ 34; 500TZQg

P

� �rg

rl � rg

!CD

dm

" #1=2(4.19b)

For 100-mm droplet removal, Equations (5.19a) and (5.19b) are reducedto the following:

Field units

d2 ¼ 504TZQg

P

� �rg

r1 � rg

!CD

" #1=2(4.20a)

SI units

d2 ¼ 3450TZQg

P

� �rg

r1 � rg

!CD

" #1=2(4.20b)

4.10.2 Settling Water Droplets from Oil Phase

The requirement for settling water droplets from the oil requires thatthe following equation must be satisfied:

Field units

d2 ¼ 6; 690Qom

ðDSGÞd2m

(4.21a)

SI units

d2 ¼ 6:37� 108Qom

ðDSGÞd2m

(4.21b)


For 500-mm droplets, Equations (4.21a) and (4.21b) become

Field Units

d2 ¼ 0:0267QomDSG

� �(4.22a)

SI units

d2 ¼ 2550QomDSG

� �(4.22b)

4.10.3 Settling Oil from Water Phase

The requirement for separating oil from water requires that thefollowing equation must be satisfied:

Field units

d2 ¼ 6; 690Qom

ðDSGÞd2m

� �(4.21a)

SI units

d2 ¼ 6:37� 108Qom

ðDSGÞd2m

� �(4.21b)

For 200-mm droplets, Equations (4.21a) and (4.21b) become

Field units

d2 ¼ 0:167QomðDSGÞ� �

(4.23a)

SI units

d2 ¼ 1:59� 104QomðDSGÞ� �

(4.23b)

4.10.4 Retention Time Constraint

Field units

ho þ hw ¼ ½ðtrÞoQo þ ðtrÞwQw�0:12d2

(4.24a)

SI units

ho þ hw ¼ ½ðtrÞoQo þ ðtrÞwQw�4:713� 10�8d2

(4.24b)


where ho ¼ height of oil pad, in. (mm), hw ¼ height from water outletto interface, in. (mm). (Note: this height must be adjusted for conebottom vessels.)

4.10.5 Seam-to-Seam Length

As with horizontal three-phase separators, the specific design of thevessel internals will affect the seam-to-seam length. The seam-to-seam length (Lss) of vertical vessels may be estimated based on thediameter and liquid height. As shown in Figure 4.23, allowance mustbe made for the gravity settling (gas separation) section, inlet diverter,mist extractor, and any space below the water outlet. For screeningpurposes, the larger Lss values from Equations (4.25a and 4.25b) and(4.26a and 4.26b) should be used.

Field units

Lss ¼ ho þ hw þ 76

12ðfor diameters � 36 in:Þ: (4.25a)

Lss ¼ ho þ hw þ dþ 40

12ðfor diameters > 36 in:Þ: (4.26a)

SI units


1000ðfor diameters � 914 mmÞ; (4.25b)


1000ðfor diameters > 914 mmÞ (4.26b)

Where ho ¼ height of oil pad, in. (mm), hw ¼ height from water outletto interface, in. (mm), d ¼ vessel’s internal diameter, in. (mm).

The larger of the Lss values from Equations (4.25a) and (4.25b) aswell as (4.26a) and (4.26b) should be used.

4.10.6 Slenderness Ratio

As with horizontal three-phase separators, the larger the slendernessratio, the less expensive the vessel. In vertical separators whosesizing is liquid dominated, it is common to choose slendernessratios no greater than 4 to keep the height of the liquid collectionsection to a reasonable level. Choices between 1.5 and 3 are com-mon, although height restrictions may force the choice of a lowerslenderness ratio.


4.10.7 Procedure for Sizing Three-Phase Vertical Separators

1. The first step in sizing a vertical separator is to establish thedesign basis. This includes specifying the maximum and min-imum flow rates, operating pressure and temperature, dropletsize to be removed, etc.

2. Equations (4.19a) and (4.19b) may be used to calculate the min-imumdiameter for a liquid droplet to fall through the gas phase.

h oh w

Mist Extractor

Drain

Gas Outlet

d = minimum diameter for gas separation

GravitySettlingSection

InletDiverterSection

Inlet

Water OutletOil Outlet Oil

Water

4"d

+6"

or 4

2" m

in.

She

ll Le

ngth

24"

min

.6"

FIGURE 4.23. Approximate seam–seam shell length for a vertical three-phaseseparator.


Use Equations (4.20a) and (4.20b) for 100-mmdroplets if no otherinformation is available.

Field units

d2 ¼ 5040TZQg

P

� �rg

rl � rg

!CD

dm

" #1=2(4.19a)

SI units

d2 ¼ 34; 500TZQg

P

� �rg

rl � rg

!CD

dm

" #1=2(4.19b)

For 100 mm:

Field units

d2 ¼ 504TZQg

P

� �rg

rl � rg

!CD

" #1=2(4.20a)

SI units

d2 ¼ 3500TZQg

P

� �rg

rl � rg

!CD

" #1=2(4.20b)

3. Equations (4.21a) and (4.21b) may be used to calculate theminimum diameter for water droplets to fall through the oilphase. Use Equations (4.22a) and (4.22b) for 500-mm dropletsif no other information is available.

Field units

d2 ¼ 6690Qom

ðDSGÞd2m

(4.21a)

SI units

d2 ¼ 6:37� 108Qom

ðDSGÞd2m

(4.21b)

For 500-mm droplets:

Field units

d2 ¼ ð0:0267Þ QomDSG

� �(4.22a)


SI units

d2 ¼ 2550QomDSG

� �(4.22b)

4. Equations (4.21a) and (4.21b) may be used to calculate theminimum diameter for oil droplets to rise through the waterphase. Use Equations (4.23a) and (4.23b) for 200-mm dropletsif no other information is available.

For 200-mm droplets:

Field units

d2 ¼ 0:167QomðDSGÞ� �

(4.23a)

SI units

d2 ¼ 1:59� 104QomðDSGÞ� �

(4.23b)

5. Select the largest of the three diameters calculated in steps 2–4as the minimum diameter. Any value larger than this mini-mum may be used for the vessel diameter.

6. For the selected diameter, and assumed values of (tr)o and (tr)w,Equations (4.24a) and (4.24b) may be used to determine hoþhw

Field units

ho þ hw ¼ ½ðtrÞoQo þ ðtrÞwQw�0:12d2

(4.24a)

SI units

ho þ hw ¼ ½ðtrÞoQo þ ðtrÞwQw�4:713� 10�8d2

(4.24b)

7. From d and hoþhw the seam-to-seam length may be estimatedusing Equations (4.25a and 4.25b) and (4.26a and 4.26b). Thelarger value of Lss should be used.

Field units


12ðfor diameters � 36 in:Þ (4.25a)


SI units


1000ðfor diameters � 914 mmÞ (4.25b)

Field units


12ðfor diameters > 36 in:Þ (4.26a)

SI units


1000ðfor diameters > 914 mmÞ (4.26b)

8. Check the slenderness ratios. Slenderness ratios between 1.5and 3 are common. The following equations may be used:

Field units

SR ¼ 12Lss

d(4.27a)

SI units

SR ¼ Lss

ð1000Þd� �

(4.27b)

9. If possible, select a standard-size diameter and seam-to-seamlength.

Examples

Example 4.1: sizing a vertical three-phase separator (field units)Given

Qo ¼ 5000 BOPD,Qw ¼ 3000 BWPD,Qg ¼ 5 MMscfd,Po ¼ 100 psia,To ¼ 90 �F,Oil ¼ 30 �API,(SG)w ¼ 1.07,Sg ¼ 0.6,(tr)o ¼ (tr)w ¼ 10 min,


mo ¼ 10 cp,mw ¼ 1 cp,CD ¼ 2.01

Droplet removal ¼ 100 mm liquids, 500 mm water, 200 mm oil.

Solution

1. Calculate difference in specific gravities.

�API ¼ 141:5

ðSGÞo� 131:5

¼ 0:876;DSG ¼ 1:07� 0:876 ¼ 0:194

2. Calculate the minimum diameter required to settle a liquiddroplet through the gas phase [Equation (4.19a)].

d2 ¼ 5040ð550Þð0:99Þð5Þ

ð100Þ

24

35 0:3

ð54:7Þ � ð0:3Þ

0@

1A 2:01

100

24

351=2

;

d ¼ 34:9 in:

3. Calculate the minimum diameter required for water dropletsto settle through the oil phase [Equation (4.21a)].

d2 ¼ 6; 690Qom

ðDSGÞd2m

24

35

¼ 6; 690ð5; 000Þð10Þð0:194Þð500Þ2

24

35;

d¼ 83:0 in:

4. Calculate the minimum diameter required for oil droplets torise through the water phase [Equation (4.23a)].

d2 ¼ 6690Qom

ðDSGÞd2m

24

35

¼ 6690ð3000Þð1Þ

ð0:194Þð200Þ2

24

35;

d ¼ 50:8 in:


5. Select the largest diameter from steps 2–4 as the minimuminside diameter required.

dmin ¼ 83.0 in.

6. Calculate ho þ hw:

ho þ hw ¼ ðtrÞoðQoÞ þ ðtrÞwQw

0:12d2;

ho þ hw ¼ ð10Þð5000þ 3; 000Þ0:12d2

¼ 667; 000

d2

Refer to Table 4.2 for results.

7. Compute seam-to-seam length (Lss). Select the larger valuefrom Equation (4.25a) or (4.26a).


12ðfor diameters � 36 in:Þ;


12ðfor diameters > 36 in:Þ


8. Compute the slenderness ratio.

Slenderness ratio ¼ 12Lss

d

Choices in the range of 1.5–3 are common. Refer to Table 4.2for results.

TABLE 4.2Vertical three-phase separator capacity diameter vs. length for retention timeconstraint (tr)o ¼ (tr)w ¼ 10 min

do (in.) hoþhw (in.) Lss (ft)SR

12Lss

do

� �

84 94.5 18.2 2.690 82.3 17.7 2.496 72.3 17.4 2.2102 64.1 17.2 2.0


9. Make final selection: compute combinations of d and hoþhw

for diameters greater than the minimum diameter. SeeTable 4.2 for results. Select 90 in outside diameter (OD) �20 ft seam-to-seam length (s/s).

Example 4.2: sizing a horizontal three-phase separator (field units)Given

Qo ¼ 5000BOPD,Qw ¼ 3000BWPD,Qg ¼ 5MMscfd,P ¼ 100psia,T ¼ 90�F,Oil ¼ 30� API,(SG)w ¼ 1.07,Sg ¼ 0.6,(tr)o ¼ (tr)w ¼ 10 min,mo ¼ 10 cp,mw ¼ 1 cp,

Droplet removal ¼ 100 mm liquid, 500 mm water, 200 mm oil. Vessel ishalf-full of liquids.

Solution

1. Calculate difference in specific gravities.

�API ¼ 141:5

ðSGÞo� 131:5

ðSGÞo ¼141:5

30þ 131:5¼ 0:876;

DSG ¼ 1:07� 0:876 ¼ 0:194

2. Calculate maximum oil pad thickness (ho)max. Use 500-microndroplet size if no other information is available.

ðhoÞmax ¼ ð1:28� 10�3Þ ðtrÞoðDSGÞd2m

m

¼ 0:00128ð10Þð0:194Þð500Þ2

10

¼ 62:1


3. CalculateAw

A:

Aw

A¼ 0:5

QwðtrÞwðtrÞQo þ ðtrÞwQw

¼ 0:5ð19:8Þð10Þ

ð33Þð10Þ þ ð19:8Þð10Þ¼ 0:1875

4. Determine b from Figure 4.20. with Aw/A ¼ 0.1875, readb ¼ 0.257.

5. Calculate dmax.

dmax ¼ ðhoÞmax

b

¼ 62:1

0:257;

dmax ¼ 241:6 in:

6. Calculate combinations of d, Leff for d less than dmax thatsatisfy the gas capacity constraint. Use 100-mm droplet sizeif no other information is available.

dLeff ¼ 420TZQg

P

0@

1A rg

rl � rg

0@

1ACD

dm

24

351=2

¼ 420ð550Þð0:99Þð5Þ

ð100Þ

0@

1A 0:3

ð54:7Þ � ð0:3Þ

0@

1A 2:01

100

0@

1A

1=2

¼ 120


TABLE 4.3Horizontal three-phase separator diameter vs. length forgas capacity constraint

d (in.) Leff (ft)

60 1.772 1.484 1.296 1.1

Since the values of Leff are low, the gas capacity does not govern.


7. Calculate combinations of d, Leff for d less than dmax thatsatisfy the oil and water retention time constraints.

d2Leff ¼ 1:42½QwðtrÞw þQoðtrÞo�¼ ð1:42Þð10Þð8; 000Þ¼ 113; 600


8. Estimate seam-to-seam length.

Lss ¼ Leff þd

12ðfor gas capacityÞ;

Lss ¼ 4

3Leff ðfor liquid capacityÞ:

9. Select slenderness ratio (12 Lss/d). Choices in the range of 3–5are common.

10. Choose a reasonable size that does not violate gas capacityrestraint or oil pad thickness restraint. Possible choices are72 in. diameter by 30 ft seam-by-seam and 84 in. diameterby 25 ft seam-by-seam.

Nomenclature

Al cross-sectional area of vessel available for liquid retention,ft2 (m2)

AT total cross-sectional area of vessel, ft2 (m2)

TABLE 4.4Horizontal three-phase separator capacity diameter vs. length for liquidretention time constraint (tr)o¼(tr)w 10 mm

d (In.) Leff (ft) Lss (ft)SR

12Lss

d

� �

60 31.6 42.1 8.472 21.9 29.2 4.984 16.1 21.5 3.196 12.3 16.4 2.1108 9.7 13.0 1.4


Aw cross-sectional area of vessel available for water retention,ft2 (m2)

API API gravity of oil, �APICD drag coefficient, dimensionlessDm drop diameter, ft(m)D vessel internal diameter, ft (m)d vessel internal diameter, in. (mm)dl water leg standpipe internal diameter, in. (mm)dm drop diameter, mmdmax maximum vessel internal diameter, in. (mm)dmin minimum allowable vessel internal diameter, in. (mm)do vessel external diameter, in. (mm)FB buoyant force, lb (N)FD drag force, lb (N)g gravitational constant, 32.2lbmft/lbfs

2 (9.81 m/s2)H height of liquid volume, ft (m)h height of liquid volume, in. (mm)Hl height of liquid in horizontal vessel, ft (m)hl height of liquid in horizontal vessel, in. (mm)Ho height of oil pad, ft (m)ho height of oil pad, in (mm)(ho)max maximum oil pad thickness, in. (mm)Hw height from water outlet to interface, ft (m)hw height from water outlet to interface, in. (mm)(hw)max maximum water height, in. (mm)h

0w height of water weir, in. (mm)

Leff effective length of the vessel, ft (m)Lss vessel length seam-to-seam, ft (m)P operating pressure, psia (kPa)Q flow rate, ft3/s (m3/s)Qg gas flow rate, MMscfd (std m3/h)Ql liquid flow rate, BPD (m3/h)Qo oil flow rate, BPD (m3/h)Qw water flow rate, BPD (m3/h)SR Slenderness ratio, dimensionlessSG oil specific gravityT operating temperature, �R (K)T temperature, �F (�C)td droplet settling time, stg gas retention time, sto oil retention time or settling time, str liquid retention time, min(tr)o oil retention time, min(tr)w water retention time, mintw water retention time or settling time, s


V volume, ft3 (m3)Vg gas velocity, ft/s (m/s)(Vg)max maximum gas velocity, no re-entrainment, ft/s (m/s)Vl average liquid velocity, ft/s (m/s)Vo oil volume, ft3 (m3)Vt terminal settling velocity of the droplet, ft/s (m/s)Vw water volume, ft3 (m3)Z gas compressibility factor, dimensionlessa fractional cross-sectional area of liquidal fractional area of liquidsao fractional area of oilaw fractional area of waterb fractional height of liquid within the vessel ¼ hl/dl

bl fractional height of liquidbw fractional height of waterDh height difference between oil weir and water weir, in. (mm)DSG difference in specific gravity relative to water of the drop

and the gasy angle used in determining a, radians or degreesm viscosity of continuous phase, cp (Pa s)ml dynamic viscosity of the liquid, lbm/ft-s (kg/m-s)mo viscosity of oil phase, cp (Pa s)mw viscosity of water phase, cp (Pa s)r density of the continuous phase, lb/ft3 (kg/m3)rg density of the gas at the temperature and pressure in the

separator, lb/ft3 (kg/m3)rl density of liquid, lb/ft3 (kg/m3)ro oil density, lb/ft3 (kg/m3)rw water density, lb/ft3 (kg/m3)


Three Phase Separator Design

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