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Difference between revisions of "Separator sizing"

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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.
 
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==
+
== Separator design basics ==
  
1. Estimate diameter and length on basis of liquid requirements.
+
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
Considerations in the design include:
+
 
*drop size removal
+
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:
*retention time
+
 
*coalescers (e.g., plate packs)
+
*Expected perforamance
*surge volume
+
*Overall through put
 +
*Composition of incoming fluids
 +
*Intensity of emulsion
 +
*Retention time of each individal phase
 +
*Types of vessel and internals
 
*levels and alarms
 
*levels and alarms
*motion
 
  
2. Calculate the gas cross-sectional area and vessel length.
+
2. Determination of gas cross-sectional area based on settling theory or empirical correlations, and the other factors include
Considerations in the design include:
+
 
*drop size
+
*Expected liquid carry-over rate
*removal
+
*Avialable mist eliminator
*mist eliminator requirements
+
*Mean velocity of gas flow
*velocity requirements
+
 
 +
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
  
3. Select vessel diameter and length to satisfy Steps 1 and 2.
+
6. Determine vessel length to meet the required retention time for all phases
  
4. Select inlet device and iterate.  
+
7. Select inlet device and iterate.
  
5. Separators are typically sized by the droplet settling theory or retention time for the liquid phase. For the gas phase, the settling theory or requirements of the demister are used.
+
8. Evaluation of separation performance for a specific applocation. .
  
==Settling theory==
+
== Settling theory ==
In gravity settling, the dispersed phase 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.  
+
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.
  
===Horizontal separators===
+
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.
Droplet settling theory, using a ballistic model, results in the relationship shown in '''Eq. 1'''. For liquid drops in gas phase
 
  
[[File:Vol3_page_039_eq_001.PNG]] ................(1)
+
=== Horizontal separators ===
 +
 
 +
Droplet settling theory, using a ballistic model, results in the relationship shown in '''Eq. 1'''. For liquid drops in gas phase
 +
 
 +
[[File:Vol3 page 039 eq 001.PNG|RTENOTITLE]] ................(1)
 +
 
 +
where
  
where
 
 
*d = vessel internal diameter, in.
 
*d = vessel internal diameter, in.
 
*d<sub>m</sub> = drop diameter, μm
 
*d<sub>m</sub> = drop diameter, μm
Line 47: Line 58:
 
*ρ<sub>l</sub> = liquid density, lbm/ft<sup>3</sup>
 
*ρ<sub>l</sub> = liquid density, lbm/ft<sup>3</sup>
 
*ρ<sub>g</sub> = gas density, lbm/ft<sup>3</sup>
 
*ρ<sub>g</sub> = gas density, lbm/ft<sup>3</sup>
*C<sub>D</sub> = drag coefficient. (See below for calculation)  
+
*C<sub>D</sub> = drag coefficient. (See below for calculation)
  
For bubbles or liquid drops in liquid phase:  
+
For bubbles or liquid drops in liquid phase:
  
[[File:Vol3_page_041_eq_001.PNG]] ................(2)  
+
[[File:Vol3 page 041 eq 001.PNG|RTENOTITLE]] ................(2)
  
where  
+
where
  
 
*d<sub>m</sub> = bubble or drop diameter, μm
 
*d<sub>m</sub> = bubble or drop diameter, μm
Line 60: Line 71:
 
*ρ<sub>d</sub> = dispersed liquid-phase density, lbm/ft<sup>3</sup>
 
*ρ<sub>d</sub> = dispersed liquid-phase density, lbm/ft<sup>3</sup>
 
*ρ<sub>c</sub> = continuous liquid-phase density, lbm/ft<sup>3</sup>
 
*ρ<sub>c</sub> = continuous liquid-phase density, lbm/ft<sup>3</sup>
*Q<sub>c</sub> = continuous liquid-phase flow rate, B/D.  
+
*Q<sub>c</sub> = continuous liquid-phase flow rate, B/D.
 +
 
 +
For low Reynolds number flow, '''Eq. 3''' can be further reduced to
  
For low Reynolds number flow, '''Eq. 3''' can be further reduced to
+
[[File:Vol3 page 041 eq 002.PNG|RTENOTITLE]] ................(3)
  
[[File:Vol3_page_041_eq_002.PNG]] ................(3)
+
where
  
where
 
 
*t<sub>rc</sub> = continuous-phase retention time, minutes
 
*t<sub>rc</sub> = continuous-phase retention time, minutes
 
*μ<sub>c</sub> = continuous-phase dynamic viscosity, cp
 
*μ<sub>c</sub> = continuous-phase dynamic viscosity, cp
*Δγ = specific gravity difference (heavy/light) of continuous and dispersed phases.  
+
*Δγ = specific gravity difference (heavy/light) of continuous and dispersed phases.
 +
 
 +
=== Vertical vessels ===
  
===Vertical vessels===
+
Settling theory results in the following relationship. For liquid drops in gas phase,
Settling theory results in the following relationship. For liquid drops in gas phase,  
 
  
[[File:Vol3_page_042_eq_001.PNG]] ................(4)
+
[[File:Vol3 page 042 eq 001.PNG|RTENOTITLE]] ................(4)
  
For bubbles or liquid drops in liquid phase,  
+
For bubbles or liquid drops in liquid phase,
  
[[File:Vol3_page_042_eq_002.PNG]] ................(5)
+
[[File:Vol3 page 042 eq 002.PNG|RTENOTITLE]] ................(5)
  
Assuming low Reynolds number flow, '''Eq. 5''' can be further reduced to  
+
Assuming low Reynolds number flow, '''Eq. 5''' can be further reduced to
  
[[File:Vol3_page_043_eq_001.PNG]] ................(6)
+
[[File:Vol3 page 043 eq 001.PNG|RTENOTITLE]] ................(6)
  
===Drop/bubble sizes===  
+
=== 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.
 
  
<gallery widths=300px heights=200px>
+
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.
 +
 
 +
<gallery widths="300px" heights="200px">
 
File:Vol3 Page 052 Image 0001.png|'''Table 1'''
 
File:Vol3 Page 052 Image 0001.png|'''Table 1'''
 
</gallery>
 
</gallery>
<br>
 
  
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.  
+
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.
  
Compressor scrubbers are typically designed large enough so that a mist extractor, which can remove 10- to 20-μm drops and smaller, can fit inside the shell. Because the gas has already been conditioned by passing through an upstream separator containing a mist extractor, there is no need during normal operations to precondition the gas for the scrubber mist extractor by removing large droplets. The scrubber serves as a safety function to trap slugs of liquid that can occur as a result of failure (liquid carryover) from the upstream separator. Thus, the separator should be able to separate a slug and provide a high liquid level, which will allow the compressor to shut down prior to ingesting liquid. Normally, this is accomplished by sizing the vessel shell for a 300- to 600-μm drop removal.
+
== Retention time ==
 +
 
 +
=== Horizontal vessels ===
  
==Retention time==
 
===Horizontal vessels===
 
 
The relationship of vessel diameter and length is given by '''Eq. 7'''.
 
The relationship of vessel diameter and length is given by '''Eq. 7'''.
  
[[File:Vol3_page_045_eq_001.PNG]] ................(7)
+
[[File:Vol3 page 045 eq 001.PNG|RTENOTITLE]] ................(7)
 +
 
 +
where
  
where
 
 
*t<sub>ro</sub> = oil retention time, minutes
 
*t<sub>ro</sub> = oil retention time, minutes
 
*t<sub>rw</sub> = water-retention time, minutes
 
*t<sub>rw</sub> = water-retention time, minutes
 
*Q<sub>o</sub> = oil flow rate, B/D
 
*Q<sub>o</sub> = oil flow rate, B/D
 
*Q<sub>w</sub> = water flow rate, B/D
 
*Q<sub>w</sub> = water flow rate, B/D
*F<sub>l</sub> = fraction of vessel cross-sectional area filled by liquid.  
+
*F<sub>l</sub> = fraction of vessel cross-sectional area filled by liquid.
 +
 
 +
=== Vertical vessels ===
  
===Vertical vessels===
 
 
Similarly for vertical vessels, the relationship of vessel diameter and liquid pad heights is given by '''Eq. 8'''.
 
Similarly for vertical vessels, the relationship of vessel diameter and liquid pad heights is given by '''Eq. 8'''.
  
[[File:Vol3_page_045_eq_002.PNG]] ................(8)
+
[[File:Vol3 page 045 eq 002.PNG|RTENOTITLE]] ................(8)
 +
 
 +
where
  
where
+
*h<sub>o</sub> = oil pad height, in.
*h<sub>o</sub> = oil pad height, in.  
 
 
*h<sub>w</sub> = water pad height, in.
 
*h<sub>w</sub> = water pad height, in.
  
==Demister sizing==
+
== Demister sizing ==
As discussed previously, many types of demisters are limited by a maximum velocity given by
 
  
[[File:Vol3_page_045_eq_003.PNG]] ................(9)
+
As discussed previously, many types of demisters are limited by a maximum velocity given by
  
where  
+
[[File:Vol3 page 045 eq 003.PNG|RTENOTITLE]] ................(9)
 +
 
 +
where
  
 
*K<sub>d</sub> = demister capacity factor, ft/sec and depends upon the demister type
 
*K<sub>d</sub> = demister capacity factor, ft/sec and depends upon the demister type
 
*V<sub>m</sub> = maximum velocity, ft/sec
 
*V<sub>m</sub> = maximum velocity, ft/sec
 
*ρ<sub>L</sub> = liquid density, lbm/ft<sup>3</sup>
 
*ρ<sub>L</sub> = liquid density, lbm/ft<sup>3</sup>
*ρ<sub>g</sub> = gas density, lbm/ft<sup>3</sup>  
+
*ρ<sub>g</sub> = gas density, lbm/ft<sup>3</sup>
  
For horizontal vessels, the required demister area (A<sub>d</sub>) is given by  
+
For horizontal vessels, the required demister area (A<sub>d</sub>) is given by
  
[[File:Vol3_page_046_eq_001.PNG]] ................(10)  
+
[[File:Vol3 page 046 eq 001.PNG|RTENOTITLE]] ................(10)
  
[[File:Vol3_page_024_eq_001.PNG]] ................(11)
+
[[File:Vol3 page 024 eq 001.PNG|RTENOTITLE]] ................(11)
  
For vertical vessels, '''Eq. 11''' is also valid. The vessel diameter is then obtained as  
+
For vertical vessels, '''Eq. 11''' is also valid. The vessel diameter is then obtained as
  
[[File:Vol3_page_046_eq_002.PNG]] ................(12)
+
[[File:Vol3 page 046 eq 002.PNG|RTENOTITLE]] ................(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.  
+
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'''.
 
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'''.
  
<gallery widths=300px heights=200px>
+
<gallery widths="300px" heights="200px">
 
File:Vol3 Page 052 Image 0002.png|'''Table 2'''
 
File:Vol3 Page 052 Image 0002.png|'''Table 2'''
 
</gallery>
 
</gallery>
<br>
 
  
==Seam to seam length==
+
== Seam to seam length ==
Horizontal Vessels. The seam-to-seam length, Lss, of the 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.  
+
 
 +
=== 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.
 +
 
 +
[[File:Vol3 page 047 eq 001.PNG|RTENOTITLE]] ................(13)
  
[[File:Vol3_page_047_eq_001.PNG]] ................(13)
+
The ratio of length to diameter is typically in the 3 to 5 range.
  
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:
  
===Vertical vessels===
 
The seam-to-seam length of the 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
 
*the inlet nozzle
 
*space above the liquid level
 
*space above the liquid level
Line 164: Line 185:
 
*for any space below the water outlet as shown in '''Fig. 1'''
 
*for any space below the water outlet as shown in '''Fig. 1'''
  
<gallery widths=300px heights=200px>
+
<gallery widths="300px" heights="200px">
 
File:Vol3 Page 051 Image 0001.png|'''Fig. 1—Approximate shell length for vertical vessels (courtesy of CDS Separation Technologies Inc.).'''
 
File:Vol3 Page 051 Image 0001.png|'''Fig. 1—Approximate shell length for vertical vessels (courtesy of CDS Separation Technologies Inc.).'''
 
</gallery>
 
</gallery>
<br>
 
  
For screening purposes, the following approximations can be used, where d is the vessel diameter).  
+
For screening purposes, the following approximations can be used, where d is the vessel diameter).
  
[[File:Vol3_page_048_eq_001.PNG]] ................(14)
+
[[File:Vol3 page 048 eq 001.PNG|RTENOTITLE]] ................(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.  
+
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.
 
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==
+
== Nozzle sizing ==
Nozzles are generally sized by momentum or velocities. '''Table 3''' gives guidelines that can be used for sizing nozzles, where ρ<sub>m</sub> is the bulk density and V<sub>m</sub> the bulk velocity.
 
  
<gallery widths=300px heights=200px>
+
Nozzles are generally sized by momentum or velocities. '''Table 3''' gives guidelines that can be used for sizing nozzles, where ρ<sub>m</sub> is the bulk density and V<sub>m</sub> the bulk velocity.
 +
 
 +
<gallery widths="300px" heights="200px">
 
File:Vol3 Page 052 Image 0003.png|'''Table 3'''
 
File:Vol3 Page 052 Image 0003.png|'''Table 3'''
 
</gallery>
 
</gallery>
<br>
 
  
In addition, the API RP14E<ref name="r1" /> on erosion velocity should be included. This relationship is also given by an inlet momentum criterion as ρ<sub>m</sub>V<sub>m</sub><sup>2</sup> = C<sup>2</sup>, 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'''.
+
In addition, the API RP14E<ref name="r1">API RP14E, Recommended Practice for Design and Installation of Offshore Production Platform Piping Systems, fifth edition. 1991. Washington, DC: API.</ref> on erosion velocity should be included. This relationship is also given by an inlet momentum criterion as ρ<sub>m</sub>V<sub>m</sub><sup>2</sup> = C<sup>2</sup>, 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'''.
  
<gallery widths=300px heights=200px>
+
<gallery widths="300px" heights="200px">
 
File:Vol3 Page 053 Image 0001.png|'''Fig. 2—Typical vortex breaker (courtesy of CDS Separation Technologies Inc.).'''
 
File:Vol3 Page 053 Image 0001.png|'''Fig. 2—Typical vortex breaker (courtesy of CDS Separation Technologies Inc.).'''
 
</gallery>
 
</gallery>
<br>
 
  
==Examples of separator sizing==
+
== 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.  
+
=== Example 1: vertical two-phase separator with a mesh pad demister given values ===
 +
 
 +
The given values for '''Example 1''' are listed next.
  
 
{| class="wikitable"
 
{| class="wikitable"
      |Gas rate
+
|-
      |10 MMscf/D
+
| Gas rate
    |-
+
| 10 MMscf/D
      |Gas specific gravity
+
|-
      |0.6
+
| Gas specific gravity
    |-
+
| 0.6
      |Gas z-factor
+
|-
      |0.84
+
| Gas z-factor
    |-
+
| 0.84
      |Gas density
+
|-
      |3.7 lbm/ft3
+
| Gas density
    |-
+
| 3.7 lbm/ft3
      |Oil rate
+
|-
      |2,000 B/D
+
| Oil rate
    |-
+
| 2,000 B/D
      |Oil density
+
|-
      |50 lbm/ft3
+
| Oil density
    |-
+
| 50 lbm/ft3
      |Operating pressure
+
|-
      |1,000 psia
+
| Operating pressure
    |-
+
| 1,000 psia
      |Operating temperature
+
|-
      |60°F
+
| Operating temperature
    |-
+
| 60°F
      |OperMesh pad K-factor
+
|-
      |0.35 ft/sec  
+
| OperMesh pad K-factor
    |-
+
| 0.35 ft/sec
      |Mesh pad thickness
+
|-
      |6 in.
+
| Mesh pad thickness
    |-
+
| 6 in.
      |Liquid-retention time
+
|-
      |1 minute
+
| Liquid-retention time
    |-
+
| 1 minute
      |Inlet nozzle
+
|-
      |4 in.
+
| 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 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'''. h<sub>o</sub> = 74 in.
  
'''Step 2.''' Calculate the height for liquid retention time with '''Eq. 2.13'''. h<sub>o</sub> = 74 in.  
+
'''Step 3.''' Compute seam-to-seam length with '''Eq. 9'''.
  
'''Step 3.''' Compute seam-to-seam length with '''Eq. 9'''.  
+
The L<sub>eff</sub>/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 L<sub>eff</sub>/D ratio. '''Table 4''' shows L<sub>eff</sub>/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 L<sub>eff</sub>/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 L<sub>eff</sub>/D ratio. '''Table 4''' shows L<sub>eff</sub>/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).
+
<gallery widths="300px" heights="200px">
 
 
<gallery widths=300px heights=200px>
 
 
File:Vol3 Page 053 Image 0002.png|'''Table 4'''
 
File:Vol3 Page 053 Image 0002.png|'''Table 4'''
 
</gallery>
 
</gallery>
<br>
 
  
 
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.
 
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===
+
=== 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:
+
Size a horizontal separator to remove 100 μm drops in the gas phase.
  
    {| class="wikitable"
+
'''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/ft<sup>3</sup>
 
    |-
 
      |Gas viscosity
 
      |0.012 cp
 
    |-
 
      |Oil rate
 
      |2,000 B/D
 
    |-
 
      |Oil density
 
      |50 lbm/ft<sup>3</sup>
 
    |-
 
      |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.)
 
    |}
 
  
 +
{| class="wikitable"
 +
|-
 +
| Gas rate
 +
| 10 MMscf/D
 +
|-
 +
| Gas specific gravity
 +
| 0.6
 +
|-
 +
| Gas z-factor
 +
| 0.84
 +
|-
 +
| Gas density
 +
| 3.7 lbm/ft<sup>3</sup>
 +
|-
 +
| Gas viscosity
 +
| 0.012 cp
 +
|-
 +
| Oil rate
 +
| 2,000 B/D
 +
|-
 +
| Oil density
 +
| 50 lbm/ft<sup>3</sup>
 +
|-
 +
| 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.  
+
'''Step 1.''' Calculate vessel diameter and length with '''Eq. 1''' for gas capacity.
  
[[File:Vol3_page_054_eq_001.PNG]] ................(15)
+
[[File:Vol3 page 054 eq 001.PNG|RTENOTITLE]] ................(15)
  
Assume h<sub>g</sub> = 0.5 d so that F<sub>g</sub> = 0.5.  
+
Assume h<sub>g</sub> = 0.5 d so that F<sub>g</sub> = 0.5.
  
[[File:Vol3 page 054 eq 002.PNG]] ................(16)
+
[[File:Vol3 page 054 eq 002.PNG|RTENOTITLE]] ................(16)
  
From '''Appendix A''', using a gas viscosity of 0.012 cp, CD = 1.42.  
+
From '''Appendix A''', using a gas viscosity of 0.012 cp, CD = 1.42.
  
[[File:Vol3_page_054_eq_003.PNG]] ................(17)
+
[[File:Vol3 page 054 eq 003.PNG|RTENOTITLE]] ................(17)
  
[[File:Vol3_page_054_eq_004.PNG]] ................(18)
+
[[File:Vol3 page 054 eq 004.PNG|RTENOTITLE]] ................(18)
  
'''Step 2.''' Calculate Leff and Lss = Leff + d/12 for different values of d.  
+
'''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 3.''' Calculate the vessel diameter and length for liquid retention time with '''Eq. 7'''.
  
[[File:Vol3_page_054_eq_005.png]]  
+
[[File:Vol3 page 054 eq 005.png|RTENOTITLE]]
  
'''Step 4.''' Calculate Leff and Lss = Leff + d/12 for different values of d.  
+
'''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.  
+
'''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.
 
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.
  
<gallery widths=300px heights=200px>
+
<gallery widths="300px" heights="200px">
 
File:Vol3 Page 054 Image 0001.png|'''Table 5'''
 
File:Vol3 Page 054 Image 0001.png|'''Table 5'''
  
 
File:Vol3 Page 054 Image 0002.png|'''Table 6'''
 
File:Vol3 Page 054 Image 0002.png|'''Table 6'''
 
</gallery>
 
</gallery>
<br>
 
  
===Example 3: Vertical three phase separator===
+
=== Example 3: Vertical three phase separator ===
''Given values''. The given values for '''Example 3''' are listed next:
 
  
    {| class ="wikitable"
+
''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/ft<sup>3</sup>
 
    |-
 
      |Oil rate
 
      |5,000 B/D
 
    |-
 
      |Oil density
 
      |50 lbm/ft<sup>3</sup>
 
    |-
 
      |Oil viscosity
 
      |10 cp
 
    |-
 
      |Water rate
 
      |3,000 B/D
 
    |-
 
      |Water density
 
      |66.8 lbm/ft<sup>3</sup>
 
    |-
 
      |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
 
    |}
 
  
 +
{| class="wikitable"
 +
|-
 +
| Gas rate
 +
| 5 MMscf/D
 +
|-
 +
| Gas specific gravity
 +
| 0.6
 +
|-
 +
| Gas z-factor
 +
| 0.84
 +
|-
 +
| Gas density
 +
| 3.7 lbm/ft<sup>3</sup>
 +
|-
 +
| Oil rate
 +
| 5,000 B/D
 +
|-
 +
| Oil density
 +
| 50 lbm/ft<sup>3</sup>
 +
|-
 +
| Oil viscosity
 +
| 10 cp
 +
|-
 +
| Water rate
 +
| 3,000 B/D
 +
|-
 +
| Water density
 +
| 66.8 lbm/ft<sup>3</sup>
 +
|-
 +
| 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'''.  
+
'''Step 1.''' Calculate vessel diameter based on gas capacity from '''Eq. 4'''.
  
[[File:Vol3_page_055_eq_001.PNG]] ................(19)
+
[[File:Vol3 page 055 eq 001.PNG|RTENOTITLE]] ................(19)
  
From the previous example:  
+
From the previous example:
  
[[File:Vol3_page_055_eq_002.PNG]] ................(20)
+
[[File:Vol3 page 055 eq 002.PNG|RTENOTITLE]] ................(20)
  
[[File:Vol3_page_055_eq_003.PNG]] ................(21)
+
[[File:Vol3 page 055 eq 003.PNG|RTENOTITLE]] ................(21)
  
[[File:Vol3_page_055_eq_004.PNG]] ................(22)
+
[[File:Vol3 page 055 eq 004.PNG|RTENOTITLE]] ................(22)
  
'''Step 2.''' Calculate the vessel diameter based on water drop removal from '''Eq. 6''' for a 500-μm drop.  
+
'''Step 2.''' Calculate the vessel diameter based on water drop removal from '''Eq. 6''' for a 500-μm drop.
  
[[File:Vol3_page_055_eq_005.PNG]] ................(23)
+
[[File:Vol3 page 055 eq 005.PNG|RTENOTITLE]] ................(23)
  
[[File:Vol3_page_055_eq_006.PNG]] ................(24)
+
[[File:Vol3 page 055 eq 006.PNG|RTENOTITLE]] ................(24)
  
At this point, we know that the water-drop removal is the dominant sizing parameter in comparison to the gas capacity.  
+
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'''.  
+
'''Step 3.''' Calculate liquid levels for retention time based on '''Eq. 8'''.
  
[[File:Vol3_page_056_eq_001.PNG]] ................(25)
+
[[File:Vol3 page 056 eq 001.PNG|RTENOTITLE]] ................(25)
  
'''Table 7''' shows liquid levels for different vessel diameters.  
+
'''Table 7''' shows liquid levels for different vessel diameters.
  
<gallery widths=300px heights=200px>
+
<gallery widths="300px" heights="200px">
 
File:Vol3 Page 056 Image 0001.png|'''Table 7'''
 
File:Vol3 Page 056 Image 0001.png|'''Table 7'''
 
</gallery>
 
</gallery>
  
'''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 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.
  
<gallery widths=300px heights=200px>
+
<gallery widths="300px" heights="200px">
 
File:Vol3 Page 036 Image 0001.png|'''Table 8'''
 
File:Vol3 Page 036 Image 0001.png|'''Table 8'''
 
</gallery>
 
</gallery>
Line 421: Line 441:
  
 
== Drag coefficients ==
 
== Drag coefficients ==
 +
 
The balance of drag and buoyancy is given as
 
The balance of drag and buoyancy is given as
  
[[File:Vol3_page_058_eq_001.PNG]] ................(26)
+
[[File:Vol3 page 058 eq 001.PNG|RTENOTITLE]] ................(26)
 +
 
 +
where
  
where
 
 
{|
 
{|
|''V''<sub>''T''</sub>
 
|=
 
|terminal velocity, cm/sec;
 
 
|-
 
|-
|''C''<sub>''D''</sub>  
+
| ''V''<sub>''T''</sub>
|=  
+
| =
|drag coefficient of drop/bubble;  
+
| terminal velocity, cm/sec;
 
|-
 
|-
|''ρ''<sub>''c''</sub>  
+
| ''C''<sub>''D''</sub>
|=  
+
| =
|continuous phase density, g/cm<sup>3</sup>;  
+
| drag coefficient of drop/bubble;
 
|-
 
|-
|''ρ''<sub>''d''</sub>  
+
| ''ρ''<sub>''c''</sub>
|=  
+
| =
|dispersed phase density, g/cm<sup>3</sup>;  
+
| continuous phase density, g/cm<sup>3</sup>;
 
|-
 
|-
|''g''  
+
| ''ρ''<sub>''d''</sub>
|=  
+
| =
|gravitational constant, 981 cm/sec<sup>2</sup>;  
+
| dispersed phase density, g/cm<sup>3</sup>;
 
|-
 
|-
|and
+
| ''g''
 +
| =
 +
| gravitational constant, 981 cm/sec<sup>2</sup>;
 
|-
 
|-
|''d''<sub>''v''</sub>  
+
| and
|=  
+
|-
|dispersed phase drop/bubble size, cm.  
+
| ''d''<sub>''v''</sub>
 +
| =
 +
| dispersed phase drop/bubble size, cm.
 
|}
 
|}
  
 
'''Eq.26''' can be rewritten as
 
'''Eq.26''' can be rewritten as
  
[[File:Vol3_page_058_eq_002.PNG]] ................(27)
+
[[File:Vol3 page 058 eq 002.PNG|RTENOTITLE]] ................(27)
 +
 
 +
where
  
where
 
 
{|
 
{|
|''μ''<sub>''c''</sub>
 
|=
 
|continuous phase viscosity, g/(cm/sec) = poise,
 
 
|-
 
|-
|Re
+
| ''μ''<sub>''c''</sub>
|=
+
| =
|Reynolds number, ''V''<sub>''T''</sub>   ''d''<sub>''v''</sub>   ''ρ''<sub>''c''</sub>/''μ''<sub>''c''</sub>,  
+
| continuous phase viscosity, g/(cm/sec) = poise,
 
|-
 
|-
|and
+
| Re
 +
| =
 +
| Reynolds number, ''V''<sub>''T''</sub>   ''d''<sub>''v''</sub>   ''ρ''<sub>''c''</sub> /''μ''<sub>''c''</sub>,
 
|-
 
|-
|Ar  
+
| and
|=  
+
|-
|Archimedes number.  
+
| 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''. <ref name="r2" />
+
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''. <ref name="r2">Perry, R.H. and Green, D.W. 1984. Perry’s Chemical Engineers’ Handbook, fifth edition, 5-66. New York City: McGraw-Hill Book Co.</ref>
  
[[File:Vol3_page_058_eq_003.PNG]] ................(28)
+
[[File:Vol3 page 058 eq 003.PNG|RTENOTITLE]] ................(28)<br/>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<ref name="r3">Darby, R. 1996. Determining Settling Rates of Particles. Chemical Engineering (December): 109.</ref>.
<br>
 
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<ref name="r3" />.
 
  
[[File:Vol3_page_058_eq_004.PNG]] ................(29)
+
[[File:Vol3 page 058 eq 004.PNG|RTENOTITLE]] ................(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, ''C''<sub>''D''</sub>.  
+
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, ''C''<sub>''D''</sub>.
  
 
== Nomenclature ==
 
== Nomenclature ==
 +
 
{|
 
{|
|''A''<sub>''d''</sub>
 
|=
 
|required demister area
 
 
|-
 
|-
|''C''  
+
| ''A''<sub>''d''</sub>
|=  
+
| =
|API ''RP14E'' erosion constant, (lbm/ft-sec<sup>2</sup>)<sup>1/2</sup>  
+
| required demister area
 +
|-
 +
| ''C''
 +
| =
 +
| API ''RP14E'' erosion constant, (lbm/ft-sec<sup>2</sup>)<sup>1/2</sup>
 
|-
 
|-
|''C''<sub>''D''</sub>  
+
| ''C''<sub>''D''</sub>
|=  
+
| =
|drag coefficient (see Appendix A for calculation)  
+
| drag coefficient (see Appendix A for calculation)
 
|-
 
|-
|''d''  
+
| ''d''
|=  
+
| =
|vessel internal diameter, in.  
+
| vessel internal diameter, in.
 
|-
 
|-
|''d''<sub>''h''</sub>  
+
| ''d''<sub>''h''</sub>
|=  
+
| =
|hydraulic diameter, in. (or consistent units for '''Eq. 11''')  
+
| hydraulic diameter, in. (or consistent units for '''Eq. 11''')
 
|-
 
|-
|''d''<sub>''m''</sub>  
+
| ''d''<sub>''m''</sub>
|=  
+
| =
|bubble or drop diameter, μm  
+
| bubble or drop diameter, μm
 
|-
 
|-
|''d''<sub>''pp''</sub>  
+
| ''d''<sub>''pp''</sub>
|=  
+
| =
|perpendicular spacing of plates, m  
+
| perpendicular spacing of plates, m
 
|-
 
|-
|''D''  
+
| ''D''
|=  
+
| =
|vessel diameter, ft  
+
| vessel diameter, ft
 
|-
 
|-
|''F''<sub>''c''</sub>  
+
| ''F''<sub>''c''</sub>
|=  
+
| =
|fractional continuous-phase cross-sectional area  
+
| fractional continuous-phase cross-sectional area
 
|-
 
|-
|''F''<sub>''g''</sub>  
+
| ''F''<sub>''g''</sub>
|=  
+
| =
|fractional gas cross-sectional area  
+
| fractional gas cross-sectional area
 
|-
 
|-
|''F''<sub>''l''</sub>  
+
| ''F''<sub>''l''</sub>
|=  
+
| =
|fraction of vessel cross-sectional area filled by liquid  
+
| fraction of vessel cross-sectional area filled by liquid
 
|-
 
|-
|''h''  
+
| ''h''
|=  
+
| =
|liquid height, in.  
+
| liquid height, in.
 
|-
 
|-
|''h''<sub>''c''</sub>  
+
| ''h''<sub>''c''</sub>
|=  
+
| =
|continuous liquid-phase space height, in.  
+
| continuous liquid-phase space height, in.
 
|-
 
|-
|''h''<sub>''g''</sub>  
+
| ''h''<sub>''g''</sub>
|=  
+
| =
|gas-phase space height, in.  
+
| gas-phase space height, in.
 
|-
 
|-
|''h''<sub>''o''</sub>  
+
| ''h''<sub>''o''</sub>
|=  
+
| =
|oil pad height, in.  
+
| oil pad height, in.
 
|-
 
|-
|''h''<sub>''w''</sub>  
+
| ''h''<sub>''w''</sub>
|=  
+
| =
|water pad height, in.  
+
| water pad height, in.
 
|-
 
|-
|''K''  
+
| ''K''
|=  
+
| =
|mesh capacity factor, m/s or ft/sec  
+
| mesh capacity factor, m/s or ft/sec
 
|-
 
|-
|''L''<sub>eff</sub>  
+
| ''L''<sub>eff</sub>
|=  
+
| =
|effective length of the vessel where separation occurs, ft  
+
| effective length of the vessel where separation occurs, ft
 
|-
 
|-
|''L''<sub>''ss''</sub>  
+
| ''L''<sub>''ss''</sub>
|=  
+
| =
|seam-to-seam vessel length, ft  
+
| seam-to-seam vessel length, ft
 
|-
 
|-
|''P''  
+
| ''P''
|=  
+
| =
|operating pressure, psia  
+
| operating pressure, psia
 
|-
 
|-
|''Q''<sub>''c''</sub>  
+
| ''Q''<sub>''c''</sub>
|=  
+
| =
|continuous liquid-phase flow rate, B/D  
+
| continuous liquid-phase flow rate, B/D
 
|-
 
|-
|''Q''<sub>''g''</sub>  
+
| ''Q''<sub>''g''</sub>
|=  
+
| =
|gas flow rate, MMscf/D  
+
| gas flow rate, MMscf/D
 
|-
 
|-
|''Q''<sub>''o''</sub>  
+
| ''Q''<sub>''o''</sub>
|=  
+
| =
|oil flow rate, B/D  
+
| oil flow rate, B/D
 
|-
 
|-
|''Q''<sub>''w''</sub>  
+
| ''Q''<sub>''w''</sub>
|=  
+
| =
|water flow rate, B/D  
+
| water flow rate, B/D
 
|-
 
|-
|Re  
+
| Re
|=  
+
| =
|Reynolds number  
+
| Reynolds number
 
|-
 
|-
|''T''  
+
| ''T''
|=  
+
| =
|operating temperature, °R  
+
| operating temperature, °R
 
|-
 
|-
|''t''<sub>''rc''</sub>  
+
| ''t''<sub>''rc''</sub>
|=  
+
| =
|continuous-phase retention time, minutes  
+
| continuous-phase retention time, minutes
 
|-
 
|-
|''t''<sub>''ro''</sub>  
+
| ''t''<sub>''ro''</sub>
|=  
+
| =
|oil-retention time, minutes  
+
| oil-retention time, minutes
 
|-
 
|-
|''t''<sub>''rw''</sub>  
+
| ''t''<sub>''rw''</sub>
|=  
+
| =
|water-retention time, minutes  
+
| water-retention time, minutes
 
|-
 
|-
|''V''  
+
| ''V''
|=  
+
| =
|bulk velocity, m/sec  
+
| bulk velocity, m/sec
 
|-
 
|-
|''V''<sub>''c''</sub>  
+
| ''V''<sub>''c''</sub>
|=  
+
| =
|continuous-phase velocity, m/s (or consistent units for '''Eq. 11''' )
+
| continuous-phase velocity, m/s (or consistent units for '''Eq. 11''' )
 
|-
 
|-
|''Z''  
+
| ''Z''
|=  
+
| =
|gas compressibility  
+
| gas compressibility
 
|-
 
|-
|''α''  
+
| ''α''
|=  
+
| =
|inclination angle, degrees  
+
| inclination angle, degrees
 
|-
 
|-
|Δ''γ''  
+
| Δ''γ''
|=  
+
| =
|specific gravity difference (heavy/light) of continuous and dispersed phases  
+
| specific gravity difference (heavy/light) of continuous and dispersed phases
 
|-
 
|-
|''μ''<sub>''c''</sub>  
+
| ''μ''<sub>''c''</sub>
|=  
+
| =
|continuous phase dynamic viscosity, cp  
+
| continuous phase dynamic viscosity, cp
 
|-
 
|-
|''π''  
+
| ''π''
|=  
+
| =
|constant, 3.14159  
+
| constant, 3.14159
 
|-
 
|-
|''ρ''  
+
| ''ρ''
|=  
+
| =
|density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>  
+
| density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>
 
|-
 
|-
|''ρ''<sub>''m''</sub>  
+
| ''ρ''<sub>''m''</sub>
|=  
+
| =
|bulk density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>  
+
| bulk density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>
 
|-
 
|-
|''ρ''<sub>''c''</sub>  
+
| ''ρ''<sub>''c''</sub>
|=  
+
| =
|continuous liquid-phase density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>
+
| continuous liquid-phase density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>
 
|-
 
|-
|''ρ''<sub>''d''</sub>  
+
| ''ρ''<sub>''d''</sub>
|=  
+
| =
|dispersed liquid-phase density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>  
+
| dispersed liquid-phase density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>
 
|-
 
|-
|''ρ''<sub>''g''</sub>  
+
| ''ρ''<sub>''g''</sub>
|=  
+
| =
|gas density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>  
+
| gas density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>
 
|-
 
|-
|''ρ''<sub>''l''</sub>  
+
| ''ρ''<sub>''l''</sub>
|=  
+
| =
|liquid density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>  
+
| liquid density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>
 
|-
 
|-
|''ρ''<sub>''o''</sub>  
+
| ''ρ''<sub>''o''</sub>
|=  
+
| =
|oil density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>  
+
| oil density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>
 
|-
 
|-
|''ρ''<sub>''w''</sub>  
+
| ''ρ''<sub>''w''</sub>
|=  
+
| =
|water density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>  
+
| water density, kg/m<sup>3</sup> or lbm/ft<sup>3</sup>
 
|-
 
|-
|Ar  
+
| Ar
|=  
+
| =
|Archimedes number  
+
| Archimedes number
 
|-
 
|-
|''C''<sub>''D''</sub>  
+
| ''C''<sub>''D''</sub>
|=  
+
| =
|drag coefficient of drop/bubble  
+
| drag coefficient of drop/bubble
 
|-
 
|-
|''d''<sub>''v''</sub>  
+
| ''d''<sub>''v''</sub>
|=  
+
| =
|dispersed phase drop/bubble size, cm  
+
| dispersed phase drop/bubble size, cm
 
|-
 
|-
|''g''  
+
| ''g''
|=  
+
| =
|gravitational constant, 981 cm/sec<sup>2</sup>  
+
| gravitational constant, 981 cm/sec<sup>2</sup>
 
|-
 
|-
|Re  
+
| Re
|=  
+
| =
|Reynolds number, VTdvρc/μc  
+
| Reynolds number, VTdvρc/μc
 
|-
 
|-
|''V''<sub>''T''</sub>  
+
| ''V''<sub>''T''</sub>
|=  
+
| =
|terminal velocity, cm/sec  
+
| terminal velocity, cm/sec
 
|-
 
|-
|''μ''<sub>''c''</sub>  
+
| ''μ''<sub>''c''</sub>
|=  
+
| =
|continuous phase viscosity, g/(cm/sec) = poise  
+
| continuous phase viscosity, g/(cm/sec) = poise
 
|-
 
|-
|''ρ''<sub>''c''</sub>  
+
| ''ρ''<sub>''c''</sub>
|=  
+
| =
|continuous phase density, g/cm3  
+
| continuous phase density, g/cm3
 
|-
 
|-
|''ρ''<sub>''d''</sub>  
+
| ''ρ''<sub>''d''</sub>
|=  
+
| =
|dispersed phase density, g/cm3  
+
| dispersed phase density, g/cm3
 
|}
 
|}
  
Line 703: Line 728:
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 
{|
 
{|
|''m''  
+
|-
|=  
+
| ''m''
|bulk properties
+
| =
 +
| bulk properties
 
|}
 
|}
  
==References==
+
== References ==
<references>
 
<ref name="r1" >API RP14E, Recommended Practice for Design and Installation of Offshore Production Platform Piping Systems, fifth edition. 1991. Washington, DC: API.</ref>
 
  
<ref name="r2">Perry, R.H. and Green, D.W. 1984. ''Perry’s Chemical Engineers’ Handbook'', fifth edition, 5-66. New York City: McGraw-Hill Book Co.</ref>
+
<references />
  
<ref name="r3">Darby, R. 1996. Determining Settling Rates of Particles. ''Chemical Engineering'' (December): 109.</ref>
+
== Noteworthy papers in OnePetro ==
</references>
 
  
==Noteworthy papers in OnePetro==
+
Olotu, C.O. and Osisanya, S. 2013. Development of a User Friendly Computer Program for Designing Conventional Oilfield Separators. SPE-167578-MS Presented at the SPE Nigeria Annual International Conference and Exhibition, Lagos, Nigeria, 5-7 August. [http://dx.doi.org/10.2118/167578-MS http://dx.doi.org/10.2118/167578-MS].
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read
+
 
 +
Laleh, A.P., Svrcek, W.Y. and Monnery, W. 2013. Computational Fluid Dynamics-Based Study of an Oilfield Separator--Part II: An Optimum Design. ''Oil and Gas Fac.'' '''2''' (1): 52-59. SPE-161036-PA. [http://dx.doi.org/10.2118/161036-PA http://dx.doi.org/10.2118/161036-PA].
 +
 
 +
== External links ==
  
==External links==
 
 
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro
 
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro
  
==See also==
+
== See also ==
[[PEH:Oil and Gas Separators]]
+
 
 +
[[PEH:Oil_and_Gas_Separators]]
  
[[Oil and gas separators]]
+
[[Oil_and_gas_separators|Oil and gas separators]]
  
[[Separator types]]
+
== Category ==
 +
[[Category:4.1.2 Separation and treating]] [[Category:YR]]

Latest revision as of 09:43, 6 July 2015

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

RTENOTITLE ................(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:

RTENOTITLE ................(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

RTENOTITLE ................(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,

RTENOTITLE ................(4)

For bubbles or liquid drops in liquid phase,

RTENOTITLE ................(5)

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

RTENOTITLE ................(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.

RTENOTITLE ................(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.

RTENOTITLE ................(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

RTENOTITLE ................(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

RTENOTITLE ................(10)

RTENOTITLE ................(11)

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

RTENOTITLE ................(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.

RTENOTITLE ................(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).

RTENOTITLE ................(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[1] 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.

RTENOTITLE ................(15)

Assume hg = 0.5 d so that Fg = 0.5.

RTENOTITLE ................(16)

From Appendix A, using a gas viscosity of 0.012 cp, CD = 1.42.

RTENOTITLE ................(17)

RTENOTITLE ................(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.

RTENOTITLE

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.

RTENOTITLE ................(19)

From the previous example:

RTENOTITLE ................(20)

RTENOTITLE ................(21)

RTENOTITLE ................(22)

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

RTENOTITLE ................(23)

RTENOTITLE ................(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.

RTENOTITLE ................(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

RTENOTITLE ................(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

RTENOTITLE ................(27)

where

μc = continuous phase viscosity, g/(cm/sec) = poise,
Re = Reynolds number, VTdvρc /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. [2]

RTENOTITLE ................(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[3].

RTENOTITLE ................(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

References

  1. API RP14E, Recommended Practice for Design and Installation of Offshore Production Platform Piping Systems, fifth edition. 1991. Washington, DC: API.
  2. Perry, R.H. and Green, D.W. 1984. Perry’s Chemical Engineers’ Handbook, fifth edition, 5-66. New York City: McGraw-Hill Book Co.
  3. Darby, R. 1996. Determining Settling Rates of Particles. Chemical Engineering (December): 109.

Noteworthy papers in OnePetro

Olotu, C.O. and Osisanya, S. 2013. Development of a User Friendly Computer Program for Designing Conventional Oilfield Separators. SPE-167578-MS Presented at the SPE Nigeria Annual International Conference and Exhibition, Lagos, Nigeria, 5-7 August. http://dx.doi.org/10.2118/167578-MS.

Laleh, A.P., Svrcek, W.Y. and Monnery, W. 2013. Computational Fluid Dynamics-Based Study of an Oilfield Separator--Part II: An Optimum Design. Oil and Gas Fac. 2 (1): 52-59. SPE-161036-PA. http://dx.doi.org/10.2118/161036-PA.

External links

Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro

See also

PEH:Oil_and_Gas_Separators

Oil and gas separators

Category