Page 137 - Petroleum and Gas Field Processing

centipoise and d m be the droplet diameter in micrometers, the above
equation becomes
6 2
ð Þð3:281 10 d m Þ
u ¼ 5
18ð2:088 10 Þ
2 ft
u ¼ 2:864 10 8 ð Þd m ð6Þ
s
or
2 ft
u ¼ 1:787 10 6 ð
Þd m ð7Þ
s

where

¼

o
w

o and
w are the specific gravity of oil and water, respectively, u is the
terminal settling velocity of the droplet (ft/s), d m is the diameter of the
droplet (mm), and m is the viscosity of the continuous phase (cP).
Equation 6 [or Eq. (7)] shows that the droplet settling velocity is
inversely proportional to the viscosity of the continuous phase. Oil
viscosity is several magnitudes higher than the water viscosity. Therefore,
the settling velocity of water droplets in oil is much smaller than the
settling velocity of oil droplets in water. The time needed for a droplet to
settle out of one continuous phase and reach the interface between the
two phases depends on the settling velocity and the distance traveled by
the droplet. In operations where the thickness of the oil pad is larger than
the thickness of the water layer, water droplets would travel a longer
distance to reach the water–oil interface than that traveled by the oil
droplets. This, combined with the much slower settling velocity of the
water droplets, makes the time needed for separation of water from oil
longer than the time needed for separation of oil from water. Even in
operations with a very high water–oil ratio, which might result in having
a water layer that is thicker than the oil pad, the ratio of the thickness of
the water layer to that of the oil pad would not offset the effect of
viscosity. Therefore, the separation of water droplets from the continuous
oil phase would always be taken as the design criterion for three-phase
separators.
The minimum size of the water droplet that must be removed from
the oil and the minimum size of the oil droplet that must be removed from
the water to achieve a certain oil and water quality at the separator exit
depend largely on the operating conditions and fluid properties. Results
obtained from laboratory tests conducted under simulated field conditions

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