Page 139 - Petroleum and Gas Field Processing

4.5.1 Sizing Equations for Horizontal Separators
As with two-phase separators, consideration of the gas capacity constraint
and the liquid retention time constraint results in developing two
equations; each relates the vessel diameter to its length. Analysis of the
two equations determines the equation that governs the design and that
should be used to determine possible combinations of diameters and
lengths. For three-phase horizontal separators, consideration of the
settling of water droplets in oil results in a third equation that determines
the maximum diameter of the separator. Therefore, in determining the
vessel’s diameter–length combinations, the diameters selected must be
equal to or less than the determined maximum diameter.

Water Droplet Settling Constraint

In comparison to two-phase separators, the additional constraint in the
design of three-phase horizontal separators is that the oil retention time
should be sufficient for the water droplets of certain minimum size to
settle out of the oil. To be on the conservative side, we shall assume that
the water droplets to be separated are at the top of the oil pad.
Therefore, such droplets have to travel a distance equal to the thickness
of the oil pad before they reach the water–oil interface. This constraint
can be translated into a useful relationship by equating the time needed
for the water droplets to travel through the oil pad thickness to the oil
retention time.
The time needed for the water droplets to travel through the oil pad,
t wd min, is obtained by dividing the oil pad thickness, H o (in.), by the
water settling velocity given by Eq. (7); therefore,

1 ðH o =12Þ
t wd ¼ min ð8Þ
6 2
60 1:787 10 ð
Þd m = o
Equating Eq. (8) to the oil retention time, t o , and solving for H o , we obtain
the maximum allowable oil pad thickness, H o,max expressed as follows:

3 2
1:28 10 t o ð
Þd m
H o, max ¼ in: ð9Þ
o
The minimum water droplet diameter to be removed, d m ,is
determined, as discussed earlier, from laboratory tests. In case such data
are not available, d m may be assigned the value of 500 mm.

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