Page 140 - Petroleum and Gas Field Processing

The oil and water flow rates and retention times and the vessel
diameter control the height of the oil pad. Considering a separator that is
half full of liquid, the following geometrical relation is easily derived:
2 3
! 0:5
2

A 1 1 2H o 2H o 4H o

¼ 4 cos 1 2 5 ð10Þ
A w D D D
where A w and A are the cross-sectional area of the separator occupied by
water and the total cross-sectional area of the separator, respectively, and
D is the diameter of the vessel. For a given oil and water flow rates and
retention times, the ratio A w /A can be determined as follows. For a
separator that is half full of liquid, the total cross-sectional area of the
separator, A, is equal to twice the area occupied by the liquid, which is
equal to the area occupied by water, A w , and the area occupied by oil, A o ;
therefore,
A ¼ 2ðA o þ A w Þ
It follows that

A w A w
¼ 0:5
A A o þ A w
Because the volume occupied by each phase is the product of the
cross-sectional area and the effective length, the cross-sectional area is
directly proportional to the volume. Further, the volume occupied by any
phase is also determined as the product of the flow rate and retention
time. Therefore,

A w Q w t w
¼ 0:5 ð11Þ
A Q o t o þ Q w t w
Therefore, once the ratio A w /A is determined from Eq. (11), Eq. (10) can
be solved to determine the ratio H o /D. This is then used with the value of
H o,max determined from Eq. (9) to determine the maximum vessel diameter
associated with the maximum oil pad height according to Eq. (12):
H o, max
D max ¼ ð12Þ
H o =D
This, therefore, sets the upper limit for the separator diameter. To obtain
the value of H o /D from Eq. (9) it is convenient to use the graphical
solution of Eq. (10) (given in Fig. 6).
Equations similar to Eqs. (10) and (11) could be derived for other
cases where the liquid may occupy more or less than half the volume of
the separator.

Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved.