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Example 6.5 Sizing a Rotary-Drum Filter____________________

A rotary-drum filter filters 20 m3/h (706 ft3/h) of a calcium carbonate slurry at
20 °C (68 °F). The pressure drop across the cake is 0.658 bar (9.541 psi). If the
slurry contains 0.15 mass fraction of calcium carbonate, and the filter cake con-
tains 0.40 mass fraction of water, estimate the surface area of the rotary-drum fil-
ter.

Data
3
3
water density 998.3 kg/m (62.3 Ib/ft )
water viscosity (20 °C) 0.001 Pa-s (1 cp)
3
3
CaCO 3 density 2709 kg/m (169 Ib/ft )
From Equation 6.18.3, y = 0.85, and from Equation 6.18.7 the average
u
density of the slurry,
3
3
P! = 0.85 (998.3) + 0.15 (2709) = 1255 kg/m (78.35 Ib/ft )
Equation 6.18.4 gives y C2 = 0.60. The formation rate of wet cake, me, can
now be calculated from Equation 6.18.2. Thus,

0.15 1255 kg 20m 3
4
3
me = —— ————— —— = 6.275xl0 kg/h (1.3xl0 Ib/h)
0.60 1 m 3 1 h
The volumetric flow rate of the filtrate, V 2, obtained from Equation 6.18.1, is

yi,i Pi Vj - y c,i me
V, = ———————————

P2.1
0.85 1255 kg 20m 3
4
YuPiV, =—— ———— ——— =2.134x10* kg/h (4.71xl0 lb/h)
1 1 m 3 1 h
3
3
y c,i me = 0.40 (6275 kg/h) = 2.510xl0 kg/h (5.535xl0 Ib/h)
21340-2510
3
V 2 = ——————— =18.86 m /h (666 ftVh)
998.3

Table 6.17 does not contain oc for calcium carbonate. According to Walas
0
[6], the specific cake resistance for filtering CaCO 3, given by Equation 6.18.9, is

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