Filtration Exercises PDF

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Fundamentals of Industrial Separations, SOLUTIONS TO PROBLEMS

10-1

Chapter 10: Filtration Exercise 10.1 2 A slurry is filtered with a laboratory leaf filter with a filtering surface area of 0.05 m to determine the specific cake and cloth resistance using a vacuum giving a pressure difference of 0.7 bar. The 3 volume of filtrated collected in the first 5 min was 250 cm and, after a further 5 min, an additional 3 -3 150 cm was collected. The filtrate viscosity is 10 Pa.s, the slurry contains 5 vol% of solids with -3 a density of 3000 kg m . Calculate the specific cake resistance α and the cloth resistance RM. Exercise 10.2 The data given in the table below were obtained from the constant pressure period of a pilot scale plate and frame filter press. 3 2 The mass of dry cake per unit volume of filtrate amounts to 125 kg/m , filter area A = 2.72 m , -3 viscosity η = 10 Pa.s, pressure difference ∆P = 3 bar. time: filtrate volume V:

92 0.024

160 0.039

232 0.054

327 0.071

418 0.088

472 0.096

538 0.106

(s) 3 (m )

Calculate the cake resistance α. Exercise 10.3 Calculate the specific cake resistance α and the medium resistance RM when the same slurry data apply from the following constant rate data obtained on the same pilot scale plate and frame filter press: V: ∆P:

0.016 0.9

0.032 1.2

0.040 1.35

0.056 1.7

0.064 1.8

0.072 1.85

0.088 2.3

0.096 2.4

0.114 2.7

3

(m ) (bar)

Exercise 10.4 Laboratory filtrations conducted at constant pressure drop on a slurry of CaCO 3 in water gave the data shown in the following table: Filtrate Volume V (l)

Test I (0.45 bar) t (s)

Test 2 (1.10 bar) t (s)

Test 3 (1.95 bar) t (s)

Test 4 (2.50 bar) t (s)

Test 5 (3.40 bar) t (s)

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

17 41 72 108 152 202

7 19 35 53 76 102 131 163

6 14 24 37 52 69 89 110 134 160

5 12 20 30 43 57 73 91 111 133 157 183

4 9 16 25 35 46 59 74 89 107

10-2

FUNDAMENTALS OF INDUSTRIAL SEPARARTIONS

2

The filter area A = 440 cm , the mass of solid per unit volume of filtrate was 23.5 g/L, viscos-3 ity η = 10 Pa.s and the temperature 25°C. Evaluate the quantities α and RM as a function of pressure drop ∆ P, and fit an empirical equation to the results forα. Exercise 10.5 Calculate the relationship between the average specific resistance and the filtration pressure from the following data, obtained from a series of constant pressure filtration experiments: Filtration pressure ∆P : Specific resistance α :

70 1.4

104 1.8

140 2.1

210 2.7

400 4.0

800 5.6

(kPa) 11 (×10 m/kg)

Exercise 10.6 A slurry, containing 0.1 kg of solid (solid density ρS = 2500 kg m-3) per kilogram of water, is fed to a rotary drum filter with length L = 0.6 m and diameter D = 0.6 m. The drum rotates at a speed of one revolution in 6 min and 20 per cent of the filtering surface is in contact with the slurry at any 10 9 -1 instant. Specific cake resistance α = 2.8*10 m/kg and medium resistance RM = 3.0*10 m . -3 -1 -1 Liquid density ρ L = 1000 kg m , liquid viscosity ηL = 0.001 kg m s . a. Determine the filtrate and dry solids production rate when filtering with a pressure 2 difference of 65 kN/m . b. Calculate the thickness of the cake produced when it has a porosityε = 0.5. Exercise 10.7 A rotary drum filter with 30 percent submergence is to be used to filter an aqueous slurry of CaCO3 containing 230 kg of solids per cubic meter of water. The pressure drop is to be 0.45 bar. Liquid density and viscosity as in previous exercise, solid density ρS as in Exercise 10.4. 11 9 -1 The specific cake resistance α = 1.1*10 m/kg and medium resistance RM = 6.0*10 m . Calculate the filter area required to filter 40 ltr/min of slurry when the filter cycle time is 5 min. Exercise 10.8 2 Calculate the dry solids production from a 10 m rotating vacuum filter operating at 68 kPa vacuum and the following conditions: 10 10 cake resistance α = 1×10 m/kg, medium resistance RM = 1×10 1/m, drum speed = 1 rpm, fraction submerged f = 0.3, solids concentration xS = 0.1 kg solids/kg slurry, cake moisture 3.5 kg wet cake/kg dry cake, liquid density ρ L = 1000 kg/m3, liquid viscosity ηL = 0.001 Pa.s Exercise 10.9 Calculate the filtration time, required area, operational speed and cake thickness required to 3 produce 5 m /h of filtrate with a 1 m wide horizontal belt filter operating at a pressure difference 9 ∆P = 60 kPa. The slurry has the following properties: specific cake resistance α = 5×10 m/kg, 3 3 slurry solids concentration cS = 350 kg/m , solids density ρS = 2000 kg/m , liquid density ρL = 3 1000 kg/m and viscosity η L = 0.001 Pa.s. The cake porosity ε = 0.43. Exercise 10.10 It is proposed to use an existing horizontal belt filter to separate phosphoric acid from a slurry containing gypsum at 30% w/w. Cake formation at a constant pressure difference of ∆P = 50 kPa is to be followed by displacement washing and deliquoring. Of the total 9 m belt length 1.5 m is available for the filtration stage. Calculate the solids production rate (kg/s).

Fundamentals of Industrial Separations, SOLUTIONS TO PROBLEMS

Filter data: Cake properties: Filtrate:

10-3

9

width 2 m, linear velocity 0.1 m/s, medium resistance RM = 2·10 1/m 8 0.46 -0.054 3 , solid density ρ S = 2350 kg/m αav = 7.1·10 ∆P m/kg, ε av = 0.84∆P 3 density ρ L = 1390 kg/m , viscosity η L = 0.001 Pa.s

Exercise 10.11 A tank filter is operated at a constant rate of 25 L/min from the start of the run until the pressure 3 drop ∆P = 3.5 bar, and then at a constant pressure drop of 3.5 bar until a total of 5 m of filtrate is obtained. Given: specific cake resistance α = 1.8·1011 m/kg, medium resistance RM = 1.0·1010 m-1, 3 solids concentration cS = 150 kg/m filtrate, viscosity ηL = 0.001 Pa.s. Calculate the total filtration time required. Exercise 10.12 Calculate the washing rate of a filter cake 0.025 m thick deposited on a centrifuge basket (0.635 m diameter, 0.254 m height) rotating at 20 rps. The cake porosity ε = 0.53, its specific resistance 9 8 -1 α = 6×10 m/kg. A medium with a resistance of RM = 1·10 m is used to line the perforate basket. 3 3 Solid density ρ S = 2000 kg/m , liquid density ρ L = 1000 kg/m and liquid viscosity ηL = 0.001 Pa.s. Assume the cake is incompressible. a. b.

What time is required for the passage of two void volumes of wash if there is almost no supernatant liquid layer over the cake. How does the washing rate change when a 5 cm thick supernatant liquid layer is present?

10-4

SOLUTIONS

FUNDAMENTALS OF INDUSTRIAL SEPARARTIONS

Fundamentals of Industrial Separations, SOLUTIONS TO PROBLEMS

In the graph at the following page a plot at each pressure difference is given. The table summerizes the calculated values of αav and RM.

10-5

10-6

FUNDAMENTALS OF INDUSTRIAL SEPARARTIONS

1 10

10

∆P ⋅ t

V

kg m4 s

8 10

6 10

9

9

Test 1 4 10

9 Test 2 Test 3

2 10

9

Test 4 Test 5

0

Test 1 2 3 4 5

0

0.002

slope 11 7 x 10 kg/m s 6.05 8.37 8.88 9.46 15.5

α 10 x 10 m/kg 4.98 6.89 7.32 7.79 12.8

0.004

intercept 9 x 10 kg/m·s 1.26 1.26 1.88 2.00 3.29

0.006

V /m3

RM 10 x 10 1/m 5.55 5.53 8.29 8.80 14.5

0.008

Fundamentals of Industrial Separations, SOLUTIONS TO PROBLEMS

10-7

A plot of ln(α ) vs ln(∆P) is presented in the following figure:

26

ln α 25

24 10

11

12

13

ln ∆P

Closer inspection of Eqs. 10.14 and 10.15 suggests plotting ∆P ⋅

∆P ⋅ t .

8 10

t vs V ⋅ ∆ P n to get a unified plot V

9

V

kg m4s

6 10

Test 1

9

Test 2 4 10

9 Test 3 Test 4

2 10

9 Test 5

0 0

0.2

0.4

0.6

V ⋅ ∆P n m3Pan

0.8

10-8

FUNDAMENTALS OF INDUSTRIAL SEPARARTIONS

Fundamentals of Industrial Separations, SOLUTIONS TO PROBLEMS

10-9

10-10

FUNDAMENTALS OF INDUSTRIAL SEPARARTIONS

Fundamentals of Industrial Separations, SOLUTIONS TO PROBLEMS

10-11

10-12

FUNDAMENTALS OF INDUSTRIAL SEPARARTIONS

Fundamentals of Industrial Separations, SOLUTIONS TO PROBLEMS

10-13...