In a filter test, 0.18 m3 of filtrate was collected over a period of 5 minutes a

Question

In a filter test, 0.18 m3 of filtrate was collected over a period of 5 minutes at a constant pressure of 50 kN m–2. Due to irregularities in the size and shape of the particles the specific resistance 'r' will be ten times greater than the calculated value for the spherical particles in part (b). The surface area of the filter is 0.2 m2 and the dynamic viscosity of the filtrate is 1 × 10–3 kg m–1 s–1. Calculate the volume of cake deposited, at constant pressure, per unit volume of filtrate, i.e. 'v', and hence calculate the feed slurry concentration. Take the density of the filtrate as 1000 kg m–3, and that of the solid as 2500 kg m–3. (d) Calculate the filtrate flowrate in cubic metres per second per unit of filter area. (e) Calculate the depth of cake at the end of the 5 minute period. (f) If the same test filter was fed at a pressure of 200 kN m–2, how long would it take to collect the same amount of filtrate. Assume (rv) remains at the value used previously and filtration to be at constant pressure.

Explanation / Answer

FILTRATION THEORY
1/A* dV/dt = P/µ(R m + Rc )
|

Filtration Rate   Broth Viscosity

Broth
Viscosity
Resistance to Flow
V=filtrate volume
A=Filter area
t=Time
P=Pressure Driving Force
µ=Broth viscosity
W=Mass of filter cake
R=Resistance
=Specific cake resistance
S=Compressability factor
Rm =
W
A
Cake Resistance
= ' PS
Specific Cake Resistance
The filter resistance is much
less than the cake resistance
Rc<<Rm

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