Page 330 - Chemical process engineering design and economics

Separator Design 309

In many cases, the pressure drop across the filter medium is low, and P is
;
approximately equal to the pressure at the downstream side of the filter medium. If
the pressure, P v, is produced by the vacuum pump, then P ; » P v, and
a = a 0(P 0-P v) n (6.24)

After substituting Equation 6.24 into Equation 6.23, we obtain

(P 0 - P v) ct u v s m s
————— = ————— (6.25)
(1-n) A F

The superficial velocity,

(6.26)
v s = (dV/dt)/A F
The dry solids, m s = Ci )2 V ]; where the first subscript (1) in the solids concen-
tration refers to the incoming stream and the second subscript (2) to the solids. The
filtrate volume, V, is the total volume of filtrate collected up to time t. Now, sub-
stitute Equation 6.26 and the expression for the mass of dry solids into Equation
6.25.

(Po-Pv) «H c u V dV
(6 .27)
(1-n) A F 2 dt

Assume that the filtration is conducted at constant pressure. Then, after sepa-
rating variables and integrating from 0 to tp and 0 and V F, we obtain

(P 0-Pv) auc,, 2 V F 2
(6.28)
2
2A F
2 2
Next, solve for A F .
i c 1<2V' 2
———— (6.29)
2t F (P 0 -P v )

The total drum area, A, is greater than the filtering area because of the need
T
to wash, dewater, and dry the cake. Thus,
A T = A F /f (6.30)

Copyright © 2003 by Taylor & Francis Group LLC