Page 318 - Chemical process engineering design and economics

Separator Design 297

Therefore, the flow area,

1 Ji D 2
A F= — —— (6.13)
2 4

and the wetted perimeter,

TlD
(6.14)
2
For both phases, the hydraulic radius,

A F 7i D/4
Rh = — = ——— (6.15)
P 2 + 71
provided the interface is in the center of the decanter.
In a horizontal decanter, dispersed phase drops are being carried along the
decanter by the flow of the continuous phase. If the velocity of the two separated
layers is more than a few centimeters per second, the shape of the dispersion zone
will be distorted by drag, and there will be entrainment of drops [21]. Therefore,
the Reynolds number for both phases must be limited. The effect of Reynolds
number on liquid-liquid separation is shown in Table 6.14. This limitation on the
Reynolds number will also be used for the dispersed phase to determine the de-
canter diameter. The minimum diameter is 10.0 cm (0.328 ft) because of wall
effects [19].
Stokes' Law is usually used to estimate the settling time of liquid drops in
decanters, and hence the length of the settling zone, even though the assumptions
used to derive Stokes' Law are not strictly met. These assumptions are:
1. the continuous phase is a quiescent fluid.
2. the drop is a sphere with no internal circulation.
3. the drop moves in laminar flow.
4. the drop is large enough to ignore Brownian motion.
5. the drop movement is not hindered by other droplets or by the wall of the sepa-
rator.
Stokes' Law, which gives the terminal velocity of a drop in a stationary, continu-
ous-phase liquid is given by

2
g d (p H - PL)
v d = ———————— (6.16)
18 ^

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