Question 1. (a) State four factors which affect the rate of filtration of a slurry.

(b) For each factor, explain briefly how it affects the rate of filtration.

Question 2. All parts of this question refer to the same slurry feed.

(a) Calculate the specific surface area 'S' of a bed of spherical particles having a diameter of 0.1 mm.

(b) If the spherical voidage 'e' of the bed is 0.4, calculate the specific resistance 'r'.

(c) 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 x 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 (rμv) remains at the value used previously and filtration to be at constant pressure.

Question 3. A plate-and-frame press is to be assembled to handle a cake that has 0.1 m³ solids per m3 of filtrate and a value for (rμv) of 5 x 10¹⁰.

The data was obtained from a filter test.

The press is to operate at the optimum condition, with constant pressure filtration at 500 kN m^-2 and with cycle times of:
140 seconds to dismantle the press 100 seconds to clean EACH plate 140 seconds to reassemble the press.
The plate size is 0.5 m square. The frames are 25 mm thick.

(a) State the condition for optimum overall rate of filtration for a filter press.
(b) Write an equation that relates the filtration time under optimum conditions to the out of service time, in terms of 'n' plates.
(c) By expressing the cake volume in terms of the number of plates 'n' and expressing the filtrate volume 'V', also in terms of the number of plates 'n', calculate the filtration time.
(d) Calculate the number of plates required.