Page 322 - Chemical process engineering design and economics

Separator Design 301

Similarly, for the heavy phase substitute Equation 6.15.15 into Equation
6.15.17. Thus, the superficial velocity for the heavy phase,

V H = 8 V H / 7i D 2

Substituting this equation and Equation 6.15.21 into Equation 6.15.19, the Rey-
nolds number for the heavy phase,

8p H V H
Re H = ——————
(it + 2) U H D H

From Equation 6.15.22 and the Reynolds number for the light phase given
above, the decanter diameter,

3
8 897kg 1 m-s 1.405xlO~ m 3 1
8p L V L
D L = ——————— = —————— -
(7t + 2)u L Re L (3.142 + 2) 1 m 3 0.01 kg 1 s IxlO 4
= 0.01961m (0.06434 ft)

From Equation 6.15.23 and the Reynolds number for the heavy phase given
above, the decanter diameter,

3
8p H V H 8 1000kg 1 m-s 5.04xlO~ m 3 1
= ________ = ______ _____ __ __
D H ——————— —————————— ————
(3.124 + 2) 1 m 3 7.0X10" 4 kg 1 s IxlO 4
(7t + 2)u H Re H
= 1.124m (3.688ft)

Therefore, the decanter diameter is 3.688 ft (1.124 m), which is rounded off
to 4.0 ft (1.219 m). For the same conditions, but with the interface located above
the center of the decanter, Hooper and Jacobs [22] obtained a diameter of 3.0 ft
(0.914 m). Hooper and Jacobs located the interface above the center of the de-
canter, which lowers the heavy-phase velocity and hence the diameter.
The next step is to calculate the length of the decanter. The length is equal to
the sum of the length required for the oil drops to reach the interface and the
length required for the oil drops to coalesce with the oil phase at the interface.
From Equations 6.15.4 to 6.15.6, PC = PH, PD = PL, and LI C = HH- The drop di-
ameter used by Hooper and Jacobs [22] is 150 mm. According to Walas [6], 150
mm is a common drop diameter for the design of decanters. Then, from Equation
6.15.7, the settling velocity of a drop of oil,

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