1. A suspension of aluminum hydroxide in water is to be filtered under constant pressure in a batch Nutsch fdter 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 empirically determined from pilot tests:
r, = r,' (AP)' where r, = specific cake resistance (m">
r,', S' = constants determined to be 0.5 x lo9 and 0.93, respectively The volume ratio of the cake to filtrate (x,,) is 0.01. Assuming that the resistance of the filter plate is negligible, determine the time required for filtering over the same pressure range.
2. A suspension of solid particles in water is to be separated by a Nutsch filter, where A = 1 m2, p = N-sec/m2 and the temperature of the suspension is 23" C. The allowable pressure drop is 20 x lo4 N/m2. The filter plate resistance is R, = 5 x 10" m" 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
218 WATER AND WASlIZWATER TREATMENT TECHNOLOGIES
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 negligble. The following data is available: R'c.in = 0.050 m; Rc,in = 0.100 m; r, = 6.5 x 10'' N-sec/m2; x, = 0.20; AP, = 20 X 10" 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, pw = 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 m3/s of filtrate. The cake is incompressible, with the following characteristics: x,, = 0.10; r, = 2 X 10" m-2 ; R, = 10'' m-'.
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, p (N-sec/m2) = 1.8 x
Washing liquid viscosity, pwe (N-sec/m2) = 1.0 x Specific cake resistance, r, (m"> = 9 x ioi4 Volume ratio of cake to filtrate, = 0.059 Allowable pressure drop, AP (N/m2) = 7 x lo6
Cake porosity, E = 0.49
Weight ratio of dissolved solids extracted to material before washing, G/G, = 0.85
Auxiliary operating time, ,z (min) = 20
The cake is incompressible and the average plate resistance, &, is 2 x lo9 m-'. 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;
WHAT PRESSURE AND CAKE FILTRATION ARE ALL ABOUT 219
(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:
Weight fraction of suspended solids, x' = 0.3 Filtrate density, p = 90 Lbs/ft?
Density of solids in slurry p = 101 Lbs/ft3 Filtrate viscosity, clf = 7 CP
Viscosity of air, pa = 0.018 CP
Surface tension of filtrate, u = 0.006 LbJft Properties of Cake:
Cake porosity, E = 0.55 Particle sphericity, $= 0.80 Mean particle size, dp = 2 10 pm
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, &, 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, p (N-sec/m2) = 0.9 X l W 3 Specific volume cake resistance, r, (m"> = 4 x lo2 Volume ratio of cake to filtrate, = 0.25
Pressure difference, AP (N/m2) = 5 x lo4 Minimum allowable cake thickness, h, (m) = 0.008 Washing time, z, (sec) = 15
Dewatering time, q, (sec) = 25
220 WATER AND WASTEWATER "RF,ATMENT TECHNOLOGIES Belt effective length, !i (m) = 6.0
Belt effective width, b (m) = 0.5
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 criteria for a rotary drum filter - they are very similar.
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 G, = 700 kg/hr. Determine the amount of suspension, the filtrate and the ratio %. The density of the solid phase is 1,600 kg/m3 and that of the liquid phase is 900 kg/m3.
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 is 1 cP.
11. Determine the required surface area of a Nutsch filter operating under the following conditions:
Amount of suspension is Q, = 2500 kg Solid phase concentration = 10 % Cake wetness = 60 %
Filtrate density is p = 1040 kg/m3 Cake density is pc = 1,100 kg/m3
Specific cake resistance is r,, = 1.324 X 1014 m-' Filter plate resistance is R, = 5.69 x 10" me' Amount of washing water = 1.75 m3/m3 of wet cake Filtrate viscosity, k = 1.1 CP
Washing water viscosity, = 1.0 CP Pressure drop, AP = 1.96 x lo5 N/m'
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 weight solids and the cake wetness is 25 % .
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 cake obtained.
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 13.
14.
WHAT PRESSURE AND CAKE FILTRATION ARE ALL ABOUT 221
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.
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?
Determine the required washing time under the following set of conditions:
Washing Intensity = 6 Liters/mz-min., Cake Thickness = 40 mm, Initial Solids Concentration in the Filtrate of the Wash Water = 120 gLiter; Final Concentration = 2 gLiter. Assume a wash rate constant, K = 375 cm3/Liter.
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.
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.
During the filtration test of a water suspension containing 14.5 % calcium carbonate in a filter press (A = 0.1 mz; 50 mm cake thickness;
temperature 23" C), the following data were obtained:
Pressure (atm) Filtrate Obtained (Liter) Time Elapsed (sec.)
0.35 2.92 1.46
7.80 888
1 .os 2.45 50
9.80 660
Determine the filtration constants, K (mz/hr) and C (m3/m2), at the two pressures.
20.
21.
22.
23.
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 am, 32% of wet cake by weight.
Determine the filter cloth resistance for the filtration of calcium carbonate under conditions given in the above questions.
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 m 2 h and C = 1.45 x lo5 m3/m2. Determine the size of the filter.
A rotary drum vacuum filter is fed with 8.5 m 3 h of a suspension containing 17.6% solids by weight. The f d wetness of the cake must be 34%. The
WATER AND WASTEWATER TREATMENT TECHNOLOGlES
Time (sec.) 6.8 19.0 36.4 FiltrateVolume 0.5 1.0 1.5 (Liter)
222
24.
25.
26.
53.4 76.0 102 131.2 163
2 2.5 3 3.5 4
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 Lite?/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,OOO kg/m3.
Determine the filter area and its number of rotations.
How long will it take to wash.a cake of NaCl in a filter press to achieve 5
@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.
For the conditions in the above question, calculate the NaCl concentration in the wash water after 50 min. of washing.
The following data were obtained in a filtration test using a CaCO, suspension on a filter of area A = 500 cm2 at constant pressure:
~~
Determine the filtration constants a and b, where a is the constant characterizing cake resistance related to 1 m2 of filter area in sec/m2, and b characterizes the resistance of the filter medium related to 1 m2 of filter area in sec./m2.
27. Using the filtration constants determined from the above question, determine the filtration time of a 5 m3 CaCO, suspension containing 5 % solids on the filter with 10 m2 area. The cake wetness is 40% and the solids density is 2,200 kg/m3. The density of the liquid is 1,000 kg/m '. Also determine the final filtration rate after 2 hrs. of operation.
A water suspension is filtered in a media of 50 m2 area at 20° C.
Approximately 7 m3 of filtrate was obtained. The filtration constants are a =
1.44 x lo6 sec./m2 and b = 9 X lo3 sec./m. Determine the washing time at 40" C when the water wash rate is 10 Liter/m*.
A suspension of 18 % solids is filtered over an area of 50 m2. The cake's moisture content (by weight) is 40 %. Determine the cake thickness if the filtration and washing time is 10 hrs. The wash water's volume is 1/5th that of the filtrate volume, and the filtration constants are as follows: a = 1.10
X 105 sec./m2 and b = 2.15 X IO3 sec./m. The densities of the solid and liquid phases are 3,100 kg/m3 and 1,000 kg/m3, respectively.
Size a Nutsch filter for processing a suspension containing 15 % solids. The desired cake wetness is 45 % and the filter capacity for the filtrate should be 5 m3/hr. The allowable pressure drop is 500 mm Hg. The cake specific resistance is r, = 9 X 101 1 m-' and the filter plate resistance is R, = 2 x lo9 28.
29.
30.
WHAT PReSSuRE AND CAI(E FILTRATION ARE ALL ABOUT 223
m-'. Solid and liquid phase densities are 2,100 kg/m3 and 1,000 kg/m3, respectively. The cake can be washed with water at 20" C using 1 kg of water per kg of cake.
For the above question, identi@ a suitable vendor and develop a cost estimate for this machine, including controls and installation.
3 1.
Chapter 6