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# Separator sizing

Considerations in separator sizes is important during design. The liquid capacity of most separators is sized to provide enough retention time to allow gas bubbles to form and separate out.

## Separator design basics

Separators are typically sized by the droplet settling theory or retention time for the liquid phase. For illustration purpose, a general procedure based on retention time appraoch is as follows

1. Estimate overall volume based on the retention time and expected separation performance for each phase, and the major factors needed to be considered include:

• Expected perforamance
• Overall through put
• Composition of incoming fluids
• Intensity of emulsion
• Retention time of each individal phase
• Types of vessel and internals
• levels and alarms

2. Determination of gas cross-sectional area based on settling theory or empirical correlations, and the other factors include

• Expected liquid carry-over rate
• Avialable mist eliminator
• Mean velocity of gas flow

3. Determine oil cross-sectional area based on settling theory or empirical correlations by following similar procedure in Steps 1 and 2.

4. Determine water cross-sectional area based on settling theory or empirical correlations by following similar procedure in Steps 1 and 2.

5. Determine vessel diameter based on cross-sectional area for each phase

6. Determine vessel length to meet the required retention time for all phases

7. Select inlet device and iterate.

8. Evaluation of separation performance for a specific applocation. .

## Settling theory

In gravity settling, the dispersed drops/bubbles will settle at a velocity determined by equating the gravity force on the drop/bubble with the drag force caused by its motion relative to the continuous phase.

In horizontal vessels, a simple ballistic model can be used to determine a relationship between vessel length and diameter. In vertical vessels, settling theory results in a relation for the vessel diameter.

### Horizontal separators

Droplet settling theory, using a ballistic model, results in the relationship shown in Eq. 1. For liquid drops in gas phase ................(1)

where

• d = vessel internal diameter, in.
• dm = drop diameter, μm
• hg = gas-phase space height, in.
• Fg = fractional gas cross-sectional area
• Leff = effective length of the vessel where separation occurs, ft
• T = operating temperature, °R
• Qg = gas flow rate, MMscf/D
• P = operating pressure, psia
• Z = gas compressibility
• ρl = liquid density, lbm/ft3
• ρg = gas density, lbm/ft3
• CD = drag coefficient. (See below for calculation)

For bubbles or liquid drops in liquid phase: ................(2)

where

• dm = bubble or drop diameter, μm
• hc = continuous liquid-phase space height, in.
• Fc = fractional continuous-phase cross-sectional area
• ρd = dispersed liquid-phase density, lbm/ft3
• ρc = continuous liquid-phase density, lbm/ft3
• Qc = continuous liquid-phase flow rate, B/D.

For low Reynolds number flow, Eq. 3 can be further reduced to ................(3)

where

• trc = continuous-phase retention time, minutes
• μc = continuous-phase dynamic viscosity, cp
• Δγ = specific gravity difference (heavy/light) of continuous and dispersed phases.

### Vertical vessels

Settling theory results in the following relationship. For liquid drops in gas phase, ................(4)

For bubbles or liquid drops in liquid phase, ................(5)

Assuming low Reynolds number flow, Eq. 5 can be further reduced to ................(6)

### Drop/bubble sizes

If drop or bubble removal is being used for sizing, consult Table 1 for guidelines. Sizing the water phase by oil-drop removal is usually not effective. The water effluent quality is more likely dictated by the added chemicals. Hence, the water-phase volume is typically determined by a retention time, based on experience.

The oil drops to be removed from the gas stream also depend upon the downstream equipment. Flare scrubbers are typically designed for removal of drops that are a few hundred microns in size.

## Retention time

### Horizontal vessels

The relationship of vessel diameter and length is given by Eq. 7. ................(7)

where

• tro = oil retention time, minutes
• trw = water-retention time, minutes
• Qo = oil flow rate, B/D
• Qw = water flow rate, B/D
• Fl = fraction of vessel cross-sectional area filled by liquid.

### Vertical vessels

Similarly for vertical vessels, the relationship of vessel diameter and liquid pad heights is given by Eq. 8. ................(8)

where

• ho = oil pad height, in.
• hw = water pad height, in.

## Demister sizing

As discussed previously, many types of demisters are limited by a maximum velocity given by ................(9)

where

• Kd = demister capacity factor, ft/sec and depends upon the demister type
• Vm = maximum velocity, ft/sec
• ρL = liquid density, lbm/ft3
• ρg = gas density, lbm/ft3

For horizontal vessels, the required demister area (Ad) is given by ................(10) ................(11)

For vertical vessels, Eq. 11 is also valid. The vessel diameter is then obtained as ................(12)

For demisters (horizontal or vertical vessels) sealed in a gas box, in addition to the demister area, some height must be maintained between the bottom of the demister and the highest liquid level for the demister to drain. A pressure drop exists across the demister. If the liquid level is too high, the demister will not drain, and liquid siphoning can occur. A small hole is sometimes drilled into the drainpipe as a siphon breaker.

When using settling theory or demister sizing in horizontal vessels, one should also consider the gas velocity for re-entrainment. Too high of a gas velocity will result in liquid re-entrainment from the liquid surface, which may flood the demister and cause carryover. Typical gas velocities for re-entrainment are shown in Table 2.

## Seam to seam length

### Horizontal Vessels

The seam-to-seam length, Lss, for the horizontal vessel should be determined from the geometry once a diameter and effective length have been determined. Length must be allotted for inlet devices, gas demisters, and coalescers. For screening purposes, the following approximations can be used. ................(13)

The ratio of length to diameter is typically in the 3 to 5 range.

### Vertical vessels

The seam-to-seam length of the vertical vessel should be determined from the geometry, once a diameter and height of liquid volume are known. Allowance must be made for:

• the inlet nozzle
• space above the liquid level
• gas separation section
• mist extractor
• for any space below the water outlet as shown in Fig. 1

For screening purposes, the following approximations can be used, where d is the vessel diameter). ................(14)

The ratio of height to diameter is typically in the 3 to 5 range for two-phase separators. For three-phase separators, the ratio is in the 1.5 to 3 range.

Additional consideration should be given for installation of the internals as well as man-way access. In glycol dehydration towers, a man-way is typically installed above the packing/trays and the demister. Access space must be allotted for installation of the equipment.

## Nozzle sizing

Nozzles are generally sized by momentum or velocities. Table 3 gives guidelines that can be used for sizing nozzles, where ρm is the bulk density and Vm the bulk velocity.

In addition, the API RP14E on erosion velocity should be included. This relationship is also given by an inlet momentum criterion as ρmVm2 = C2, where C is given as 100 for continuous service and 125 for intermittent service. The value of C can also vary with pipe material, solids loading, and service. See the chapter on Piping and Pipelines in this section of the Handbook. Vortex breakers are generally required on the liquid outlets. These are typically perpendicular plates, as shown in Fig. 2.

## Examples of separator sizing

### Example 1: vertical two-phase separator with a mesh pad demister given values

The given values for Example 1 are listed next.

 Gas rate 10 MMscf/D Gas specific gravity 0.6 Gas z-factor 0.84 Gas density 3.7 lbm/ft3 Oil rate 2,000 B/D Oil density 50 lbm/ft3 Operating pressure 1,000 psia Operating temperature 60°F OperMesh pad K-factor 0.35 ft/sec Mesh pad thickness 6 in. Liquid-retention time 1 minute Inlet nozzle 4 in.

Step 1. Calculate the required mesh-pad area with Eq. 10. This mesh area will result in a vessel internal diameter of 15 in.

Step 2. Calculate the height for liquid retention time with Eq. 2.13. ho = 74 in.

Step 3. Compute seam-to-seam length with Eq. 9.

The Leff/D (D = d/12) is 9.2 and is larger than the typical 3 to 5 range. Therefore, the internal diameter must be increased to reduce the Leff/D ratio. Table 4 shows Leff/D for three different vessel IDs. A 24-in. ID vessel has the appropriate Leff/D ratio. The selected vessel would then be 24 in. × 8 ft SS tall (after rounding up the height).

The mesh pad can be installed in two ways, if the 1.15 ft 2 is to be maintained. One, a full-diameter mesh pad can be installed with a blanking annular plate on top. Two, a cylindrical box with a 15-in. diameter can be installed around the gas outlet.

### Example 2: Horizontal two phase separator

Size a horizontal separator to remove 100 μm drops in the gas phase.

Given Values. The given values for Example 2 are listed next:

 Gas rate 10 MMscf/D Gas specific gravity 0.6 Gas z-factor 0.84 Gas density 3.7 lbm/ft3 Gas viscosity 0.012 cp Oil rate 2,000 B/D Oil density 50 lbm/ft3 Operating pressure 1,000 psia Operating temperature 60°F Mesh pad K-factor 0.35 ft/sec Mesh pad thickness 6 in. Liquid retention time 1 minute Inlet nozzle 4 in. Vessel fill 50% (Therefore, Fg = 0.5 and hg = 0.5d.)

Step 1. Calculate vessel diameter and length with Eq. 1 for gas capacity. ................(15)

Assume hg = 0.5 d so that Fg = 0.5. ................(16)

From Appendix A, using a gas viscosity of 0.012 cp, CD = 1.42. ................(17) ................(18)

Step 2. Calculate Leff and Lss = Leff + d/12 for different values of d.

Step 3. Calculate the vessel diameter and length for liquid retention time with Eq. 7.

Step 4. Calculate Leff and Lss = Leff + d/12 for different values of d.

Step 5. Select vessel that satisfies both gas and liquid capacity.

A comparison of Tables 5 and 6 shows that the liquid capacity is the dominant parameter. Hence, a 24-in. × 6.6-ft vessel is sufficient, as it has a slenderness ratio within the typical 3 to 5 range. This size should be rounded up to 24 in. × 7 ft.

### Example 3: Vertical three phase separator

Given values. The given values for Example 3 are listed next:

 Gas rate 5 MMscf/D Gas specific gravity 0.6 Gas z-factor 0.84 Gas density 3.7 lbm/ft3 Oil rate 5,000 B/D Oil density 50 lbm/ft3 Oil viscosity 10 cp Water rate 3,000 B/D Water density 66.8 lbm/ft3 Operating pressure 1,000 psia Operating temperature 60°F Liquid-retention time 10 minutes each phase Inlet nozzle 12 in. Drop removal from gas 100 μm

Step 1. Calculate vessel diameter based on gas capacity from Eq. 4. ................(19)

From the previous example: ................(20) ................(21) ................(22)

Step 2. Calculate the vessel diameter based on water drop removal from Eq. 6 for a 500-μm drop. ................(23) ................(24)

At this point, we know that the water-drop removal is the dominant sizing parameter in comparison to the gas capacity.

Step 3. Calculate liquid levels for retention time based on Eq. 8. ................(25)

Table 7 shows liquid levels for different vessel diameters.

Step 4. Calculate vessel height from Eq. 13. Vales for Lss are given in Table 8. Values for 12 Lss /d should be in the 1.5 to 3 range.

Step 5. Select a vessel size that satisfies gas capacity, water-drop removal, and liquid-retention time requirements. An 84-in. × 13.4-ft separator satisfies the requirements, so you would round up to an 84-in. × 13.5-ft vessel. Similarly, a 90-in. × 12.5-ft separator would also be satisfactory.

## Drag coefficients

The balance of drag and buoyancy is given as ................(26)

where

 VT = terminal velocity, cm/sec; CD = drag coefficient of drop/bubble; ρc = continuous phase density, g/cm3; ρd = dispersed phase density, g/cm3; g = gravitational constant, 981 cm/sec2; and dv = dispersed phase drop/bubble size, cm.

Eq.26 can be rewritten as ................(27)

where

 μc = continuous phase viscosity, g/(cm/sec) = poise, Re = Reynolds number, VT   dv   ρc /μc, and Ar = Archimedes number.

The drag coefficient is a function of the Reynolds number, Re, and is given by a curve-fit of data (up to a Reynolds number of 5,000) from Perry’s Chemical Engineers’ Handbook. ................(28)
The form of Eq. 28 was chosen to allow for an easy solution of Eq. 28 for the Reynolds number as outlined by Darby in Darby. ................(29)

The procedure then to calculate the drag coefficient is to calculate the Archimedes number, Ar, as defined in Eq. 27; solve Eq. 29 for the Reynolds number, Re; and solve Eq. 28 for the drag coefficient, CD.

## Nomenclature

 Ad = required demister area C = API RP14E erosion constant, (lbm/ft-sec2)1/2 CD = drag coefficient (see Appendix A for calculation) d = vessel internal diameter, in. dh = hydraulic diameter, in. (or consistent units for Eq. 11) dm = bubble or drop diameter, μm dpp = perpendicular spacing of plates, m D = vessel diameter, ft Fc = fractional continuous-phase cross-sectional area Fg = fractional gas cross-sectional area Fl = fraction of vessel cross-sectional area filled by liquid h = liquid height, in. hc = continuous liquid-phase space height, in. hg = gas-phase space height, in. ho = oil pad height, in. hw = water pad height, in. K = mesh capacity factor, m/s or ft/sec Leff = effective length of the vessel where separation occurs, ft Lss = seam-to-seam vessel length, ft P = operating pressure, psia Qc = continuous liquid-phase flow rate, B/D Qg = gas flow rate, MMscf/D Qo = oil flow rate, B/D Qw = water flow rate, B/D Re = Reynolds number T = operating temperature, °R trc = continuous-phase retention time, minutes tro = oil-retention time, minutes trw = water-retention time, minutes V = bulk velocity, m/sec Vc = continuous-phase velocity, m/s (or consistent units for Eq. 11 ) Z = gas compressibility α = inclination angle, degrees Δγ = specific gravity difference (heavy/light) of continuous and dispersed phases μc = continuous phase dynamic viscosity, cp π = constant, 3.14159 ρ = density, kg/m3 or lbm/ft3 ρm = bulk density, kg/m3 or lbm/ft3 ρc = continuous liquid-phase density, kg/m3 or lbm/ft3 ρd = dispersed liquid-phase density, kg/m3 or lbm/ft3 ρg = gas density, kg/m3 or lbm/ft3 ρl = liquid density, kg/m3 or lbm/ft3 ρo = oil density, kg/m3 or lbm/ft3 ρw = water density, kg/m3 or lbm/ft3 Ar = Archimedes number CD = drag coefficient of drop/bubble dv = dispersed phase drop/bubble size, cm g = gravitational constant, 981 cm/sec2 Re = Reynolds number, VTdvρc/μc VT = terminal velocity, cm/sec μc = continuous phase viscosity, g/(cm/sec) = poise ρc = continuous phase density, g/cm3 ρd = dispersed phase density, g/cm3

## Subscripts

 m = bulk properties