## Questions For Thinking And Discussing

1. A suspension of aluminum hydroxide in water is to be filtered under constant pressure in a batch Nutsch filter having a filtering area of 1 m2. Each filter cycle is estimated to separate out 0.5 m3 of suspension. The operating temperature is 25° C. The following expression for the cake resistance was r0', S' = constants determined to be 0.5 x 109 and 0.93, respectively

The volume ratio of the cake to filtrate (xj is 0.01. Assuming that the resistance of the filter plate is negligible, determine the time required for filtering over the

2. A suspension of solid particles in water is to be separated by a Nutsch filter, where A = 1 m2, fj. = 103 N-sec/m2 and the temperature of the suspension is

23° C. The allowable pressure drop is 20 x 104 N/m2. The filter plate resistance is Rf = 5 x 1010 m'1 and is independent of the pressure drop. The volume ratio of the cake to filter is \ = 0.025, and the filter capacity is 0.2 x

10"3 m3/sec of filtrate. The relationship between cake resistance and pressure drop is the same as described in question 1. Determine the following: (a) the filtration time; (b) the filtration volume; (c) the cake thickness.

3. A suspension is filtered using a filter cloth media. The resistance of the cloth is negligible. The following data is available: R'c in = 0.050 m; R'c in = 0.100 m; r0 = 6.5 X 1010 N-sec/m2; Xo = 0.20; AP, = 20 X 104 N/m2. Determine the difference in filtration times between a cylindrical and flat surface filter medium.

4. An aqueous solution of sodium bicarbonate (t = 20° C, fi" = 10"3 N-sec/m2) is being filtered under vacuum in a Nutsch filter. The filtration area is 1.5 m2. The operation is performed in two stages: The first filtration stage is at constant rate and the second is at constant pressure drop. The allowable pressure drop is 80,000 N/m2 and the permissible cake thickness is 0.2 m. The filter capacity at constant rate is 0.5 X 10"3 m3/s of filtrate. The cake is incompressible, with the following characteristics: Xo = 0.10; r0 = 2 X 1012 m"2 ; Rf = 1010 m"1. Calculate the total filtration time of both steps and the volumes of filtrate, cake and separated slurry. Assume for these calculations that the operation is performed without any washing and dewatering stages.

5. The system described in question 4 has an auxiliary time of t^ = 1800 sec. Determine the total filtration time at constant pressure drop, cake thickness and filtrate volume.

6. A filter press with a hydraulic drive has 35 frames with internal dimensions of 1900 X 1200 mm. The unit operates under the following set of conditions:

• Filtrate viscosity, ¡i (N-sec/m2) = 1.8 X 10"3

• Washing liquid viscosity, /¿w! (N-sec/m2) = 1.0 X 10"3

• Specific cake resistance, r„ (m"2) = 9 X 1014

• Weight ratio of dissolved solids extracted to material before washing, G/G0 = 0.85

The cake is incompressible and the average plate resistance, Rf, is 2 X 109 m'1. The suspension passes through all the frames and in one direction. The cake is not dewatered. Determine the following:

(a) the rate of filtration and washing under conditions of maximum filter press capacity;

(b) the required times of filtration and washing,

(c) the capacity of the filter press,

(d) the rate of washing liquor; and

(e) the cake thickness.

7. Determine the blower requirements for a rotary vacuum filter used for filtering solids from a liquid suspension under the following set of conditions:

Properties of Slurry:

• Surface tension of filtrate, o = 0.006 Lbf/ft Properties of Cake:

The drum has a diameter of 4.5 ft and is 2.7 ft wide. The washing ratio is 0.12. The unit operates at 2 rpm and under 5 in. Hg vacuum pressure. The cake thickness, hc, is 3 in.

8. The operating cycle of a belt vacuum filter consists of filtration, washing and dewatering stages. The solids suspension in water is separated under the following set of conditions:

• Liquid-phase viscosity, /x (N-sec/m2) = 0.9 X 10"3

• Specific volume cake resistance, r0 (m"2) = 4 x 102

• Minimum allowable cake thickness, hc (m) = 0.008

The resistance of the filter medium is negligible. Determine the filter's capacity in filtrate and the velocity of the belt. To solve this problem take a look at the design

9. A suspension containing 50 % solids is to be filtered in a filter press, achieving a concentrated cake of 40 % water (on a weight basis). The filter capacity for the cake is Gc = 700 kg/hr. Determine the amount of suspension, the filtrate and the ratio x0. The density of the solid phase is 1,600 kg/m3 and that of the

10. For question 9, determine the washing time if 2 kg of water is used per 1 kg of cake. The filtrate viscosity is 0.7 cP and the viscosity of the washing liquor

11. Determine the required surface area of a Nutsch filter operating under the

• Amount of washing water = 1.75 m3/m3 of wet cake

The total time for cake removal and filter preparation is 20 min.

12. Determine the amount of wet cake obtained from filtering 10 m3 of suspension with a relative specific weight of 1.12. The suspension is 20% by

13. Approximately 15 m3 of filtrate was removed from a suspension containing 20% by weight solids. The cake wetness is 30%. Calculate the amount of dry

14. The filtration time of 20 m3 of a suspension in a filter press is 2.5 hours. Determine the approximate washing time of the cake for 2 m3 of water, assuming that the washing rate is 4 times less than that of filtration at the end of the process. The resistance of the filter cloth may be neglected. The viscosity of the filtrate is approximately the same as that of the washing liquor.

15. For question 14, how much will the washing time change if the filtrate viscosity is double and the viscosity of the wash water is 1 cP?

16. Determine the required washing time under the following set of conditions: Washing Intensity = 6 Liters/m2-min., Cake Thickness = 40 mm, Initial Solids Concentration in the Filtrate of the Wash Water = 120 g/Liter; Final Concentration = 2 g/Liter. Assume a wash rate constant, K = 375 cm3/Liter.

17. Calculate the required filtration time for 10 Liters of liquid through 1 m2 of filter area if tests have shown that 1 Liter of filtrate is obtained after 2.25 min. and 3.2 Liters after 14.5 min. from the start of the process.

18. For the conditions described in the above question, determine the washing time if the amount of wash water is 2.4 Liter/m2 and the washing is cocurrent with the filtrate.

19. During the filtration test of a water suspension containing 14.5 % calcium carbonate in a filter press (A = 0.1 m2; 50 mrn cake thickness; temperature 23° C), the following data were obtained:

Pressure (atm) Filtrate Obtained (Liter) Time Elapsed (sec.)

7.80 888

9.80 660

Determine the filtration constants, K (m2/hr) and C (m3/m2), at the two pressures.

20. For the conditions described in the above question, compute the specific cake resistance of calcium carbonate. The wetness of the cake at 0.35 atm is 37 %, and at 1.05 atm, 32% of wet cake by weight.

21. Determine the filter cloth resistance for the filtration of calcium carbonate under conditions given in the above questions.

22. A suspension is to be processed in a filter press to obtain 6 m3 of filtrate in 3 hours. A filtration test in the lab under the same pressure and cake thickness showed that the filtration constants for 1 m2 of filter area are as follows: K = 20.7 x 10-4 m2/hr and C = 1.45 x 10-3 m3/m2. Determine the size of the filter.

23. A rotary drum vacuum filter is fed with 8.5 m3/hr of a suspension containing 17.6% solids by weight. The final wetness of the cake must be 34%. The vacuum is 600 mm Hg. During a filtration test on a model at a vacuum of 510 mm Hg, it was found that the desired wetness is achieved in 32 sec. when operating in the filtering zone. The filtration constants related to 1 m2 of area are K = 11.2 Liter2/m4-sec. and C = 6 Liter/m2. The specific weight of the suspension is 1,120 kg/m3 and that of the filtrate is 1,000 kg/m3. Determine the filter area and its number of rotations.

24. How long will it take to wash a cake of NaCl in a filter press to achieve 5 g/Liter NaCl in washing water? Washing is performed with clean water at an intensity of 0.33 m3/m2-hr. The cake thickness is 35 mm and the washing constant, K, is 520 cm3/Liter. At the beginning of the washing, the NaCl concentration in the wash water is 143 g/Liter.

25. For the conditions in the above question, calculate the NaCl concentration in the wash water after 50 min. of washing.

26. The following data were obtained in a filtration test using a CaCO; suspension on a filter of area A = 500 cm2 at constant pressure:

 Time (sec.) 