ass Transfer 2 M ass
CPB 20104
CPB 20104 MASS TRANSFER 2 TUTORIAL 3 FILTRATION OPERATIONS
1. McMillen and Weber using a filter press with an area of 0.0929 m 2, performed constant pressure filtration at 34.5 kPa of a 13.9 wt% CaCO3 solids in water slurry at 300 K. The mass ratio of wet cake to dry cake was 1.59. The dry cake density was 1017 kg/m 3. The data obtained are as follows; Table 1 Mass of filtrate, W (kg) 0.91 1.81 2.72 3.63 4.54 5.44 6.35 7.26 8.16 Calculate the values of
and
Time, t (sec) 24 71 146 244 372 524 690 888 1188
Rm.
2. The data given in the table below were obtained from the constant constant pressure period of a pilot scale plate and frame filter press. The mass of dry cake per unit volume of filtrate is 125 kg/m3, filter area is 2.72 m 2, viscosity is 10-3 Pa.s and pressure drop is 3 bar. Calculate the cake resistance and the filter medium resistance.
Time t (s) 92 160 232 327 418 472 538
Table 2 Filtrate volume V (m3) 0.024 0.039 0.054 0.071 0.088 0.096 0.106
3. The slurry of calcium carbonate (CaCO3) is to be filtered in a press having a total area of 8 m 2 and operated at a constant pressure drop of 2 atm. The frames are 36 mm thick. Assume that the filter medium resistance in the large press is the same as that in the laboratory filter. Calculate the filtration time required and the volume of filtrate obtained in one cycle.
FG/T5/July2011
M ass Transfer 2
CPB 20104
Additional data:
Viscosity of f iltrate, Density of dry cake,
6.6 104 lb / ft . s
c
73.0lb / ft 3 3
Slurry concentration, c 10.9lb / ft Cake resistance,
10
12.7 10
Filter medium resistance, Rm
ft / lb 10
1.55 10
Newton’s law proportionality factor g c
ft 1 32.174 ft / lb / lb f .s 2
4. The data below were taken in a constant pressure drop filtration of slurry of CaCO3 in H 2O. The pressure drop for this operation is 15 lbf /in2. The filter was a 6 inch filter press with an area of 1.0 ft2. The mass fraction of solids in the feed to the press was 0.169. Calculate the values of cake resistance ( ), filter medium resistance (R m) and cake thickness. Table 3 Filtrate, m (lb) 0 2 4 6 8 10 12 14 16 18
Time,t (s) 0 24 71 146 244 372 524 690 888 1188
Additional data: 4 Kinematic viscosity of the slurry 0.982cP 6.6 10 lb / ft .s Mass ratio of wet cake to dry cake ( m F / mc ) = 1.47 Density of dry cake
c
Density of filtrate, F
63.5lb / ft 3
62.3lb / ft 3
Newton’s law proportionality factor g c
32.174 ft .lb / lb f .s 2
FG/T5/July2011
M ass Transfer 2
CPB 20104
5. Calculate the relationship between the average cake resistance and the filtration pressure from the following data, obtained from a series of constant pressure filtration experiments. Table 5 Cake resistance, (m/kg) Pressure drop, P (kPa) 70 1.4 x 1011 104 1.8 x 1011 140 2.1 x 1011 210 2.7 x 1011 400 4.0 x 1011 800 5.6 x 1011 6. Data for the filtration of CaCO3 slurry in water at 298.2 K (25oC) are reported as follows at a constant pressure of 46.2 kN/m 2 (6.70 psia). The area of the plate and frame press was 0.0439 m2 (0.473 ft2) and the slurry concentration was 23.47 kg solid/m 3 filtrate. a) Calculate the constants and Rm. b) The same slurry is to be filtered in a plate and frame press having 30 frames and 0.873 m2 are per frame. The same pressure, 46.2 kN/m2 will be used in a constant pressure filtration. Assume the same filter cake properties and filter cloth used. Calculate the time to recover 2.26 m3 of filtrate. c) At the end, using through washing and 0.283 m3 of wash water, calculate the time of washing and total filter cycle time if cleaning the press takes 30 minutes.
Table 6 Volume of filtrate, V (m 3) 0.5 x 10-3 1.0 x 10-3 1.5 x 10-3 2.0 x 10-3 2.5 x 10-3 3.0 x 10-3
Time, t (sec) 17.3 41.3 72.0 108.3 152.0 201.7
7. Data for constant pressure filtration at 194.4 kN/m2 are reported for the same slurry and press as in Question 4 as follows; Table 7 (m3)
Volume, V 0.5 x 10-3 1.0 x 10-3 1.5 x 10-3
Time, t (sec) 6.3 14.0 24.2
FG/T5/July2011
M ass Transfer 2
CPB 20104
2.0 2.5 3.0 3.5 4.0 4.5 5.0 Calculate the constant
x x x x x x x
10-3 10-3 10-3 10-3 10-3 10-3 10-3
and
37.0 51.7 69.0 88.8 110.0 134.0 160.0 Rm.
8. An experimental filter press having an area of 0.0414 m 2 is used to filter an aqueous BaCO3 slurry at constant pressure of 267 kPa. The filtration equation obtained was t 6 3 10.25 10 V 3.4 10 V where t is in seconds and V in m 3. a) If the same slurry and conditions are used in a leaf press having an area of 6.97 m2, calculate the time required to obtain 1.00 m 3 of filtrate. b) After filtration, the cake is to be washed with 0.100 m3 of water. Calculate the time of washing. 9. A rotary vacuum drum filter having a 33% submergence of the drum in the slurry is to be used to filter a CaCO 3 slurry using a pressure drop of 67.0 kPa. The solids concentration in the slurry is 0.191 kg solid/kg slurry and the filter cake is such that the kg wet cake/kg dry cake is 2.0. The density and viscosity of the filtrate can be assumed as those of water at 298.2 K. Calculate the filter area needed to filter 0.778 kg slurry/s. The filter cycle time is 250s. The specific cake resistance can be 9 0.3 represented by (4.37 10 )(p) , where p is in Pa and in m/kg.
FG/T5/July2011
