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Parameters

Gas Flow Rate Qg 5 MMscfd

Gas Specific Gravity S 0.6

Gas Viscosity g 0.013 cP

Compressibility Factor Z 0.84

Oil Flow Rate Qoil 5000 BOPD

Oil API Gravity SGoil 30 API

Oil Viscosity oil 1 cP

Water Flowrate Qw 3000 BWPD

Water Viscosity

w 10 cPWater Specific Gravity SGw 1.07

Operating Pressure P 100 psia

Operating Temperature T 90 F

Droplet Size Removal dm 100 micron

Retention time for Oil and Water Tr 10 minute

Droplet Size for Water dw 500 micron

Droplet Size for Oil do 200 micron

Fractional height of liquid in Separator ho+hw 55 %

Fractional height of Water in Separator hw 28 %

1 Calculation of CD(Drag Coefficient) and Terminal Velocity

First Calculate Liquid and Vapor Densities

Liquid Density liquid 54.67 lb/ft3

Vapor Density g 0.351 lb/ft3

Assume CD(First Iteration) 0.34

Calculate Terminal Velocity Vt 2.540 ft/sec

Calculate Reynold's number NRe 33.6

Calculate CD 1.573

Second Iteration for CD 1.573

Calculate Terminal Velocity Vt 1.181 ft/sec

Calculate Reynold's number NRe 15.6

Calculate CD 2.637

Solution

Horizontal 3-Phase Separator Sizing

Example 5-2

Input Data

Input value

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Fourth Iteration for CD 3.195

Calculate Terminal Velocity Vt 0.829 ft/sec

Calculate Reynold's number NRe 11.0

Calculate CD 3.438

Sixth Iteration for CD 3.536

Calculate Terminal Velocity Vt 0.788 ft/sec

Calculate Reynold's number NRe 10.4

Calculate CD 3.575

Final Values

Final CDvalue 3.591

Final Terminal Velocity Vt 0.783 ft/sec

2 Calculate difference in Specific Gravities

S.G. 0.19

3 Calculate Area required for Gas (Same as 2-Phase Separator)

Calculation for Actual Gas Flow using General Gas Equation

Actual Gas Flow Qact 0.78 MMACFD

9.00 ft3/sec

Area required for gas Ag 11.49 ft2

Total area of Separator AT 25.53 ft2

Overall diameter of vessel D 5.70 ft

68.41 inch

L / D ratio 4.5

Length 25.65 ft

4 Calculate area and retention time for Water

Height of water in Separator hw 19.16 inch

As per Cricle formulas, following to be determined to find segmental area for wate

- Angle AOB

- Sector (OADB) area

- Triangle (OAB) Area

Goto No. 4 (Radius AO and Apothem OE) on attached circle formulas

Segment Height ED (hw) 19.16 inch

Apothem OE 15.05 inch

AE (Trianlge Base) can be find using phytoghorous theorem

AE 30.717 inch

Angle AOE 1.12 radians

63.90 degrees

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Central Angle AOB 127.80 degrees

Sector Area 9.062 ft2

Triangle Area 3.210 ft2

Segemental area for water 5.851 ft2

Water flow rate Qw 3000 BWPD

11.700 ft3/min

Retention time 12.83 min

Retention time ok for water

5 Calculate area and retention time for Oil

Segmental area for oil Aoil 8.19 ft2

Oil Flow Qoil 5000 BOPD

19.499 ft3/min

Retention time T 10.772 min

Retention time ok for water

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Third Iteration for CD 2.637

Calculate Terminal Velocity Vt 0.912 ft/sec

Calculate Reynold's number NRe 12.1

Calculate CD 3.195

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Fifth Iteration for CD 3.438

Calculate Terminal Velocity Vt 0.799 ft/sec

Calculate Reynold's number NRe 10.6

Calculate CD 3.536

Seventh Iteration for CD 3.575

Calculate Terminal Velocity Vt 0.783 ft/sec

Calculate Reynold's number NRe 10.4

Calculate CD 3.591

P1V1/T1 = P2V2/T2

Using Q = A Vt

(diameter x fractional height of water)

r

(Radius - Segment height)

(hyp2 - perp2)

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(perp (OE) x base (AE))

time = volume available / flow rate

='Total area - gas area - water area