Filtration EN FS2016 - ETH Zürich · PDF filePraktikum “Mechanical Engineering” Spring semester 2016 Filtration ... Figure 7 shows the piping and instrumentation diagram of the

Process Engineering Practica for Bachelor Students

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Institut für Verfahrenstechnik

Prof. S.E. Pratsinis [email protected] www.ptl.ethz.ch

Praktikum “Mechanical Engineering”

Spring semester 2016

Filtration

Supervisor: Anastasia Spyrogianni ML F24 [email protected] Tel.: 044 632 39 52


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1 Table of Contents

1 TABLE OF CONTENTS...................................................................................... 2

2 INTRODUCTION ................................................................................................. 3

3 EXPERIMENTAL ................................................................................................ 8

3.1 Suspension preparation ......................................................................................................... 8

3.2 Filter placing ............................................................................................................................ 8

3.3 Measure suspension flow rate under constant pressure ................................................... 9

3.4 Measure the pressure-drop under constant flow-rate ........................................................ 9

3.5 Shutting down and cleaning .................................................................................................. 9

4 REPORT ........................................................................................................... 10

4.1 Specific tasks (in results and discussion) ......................................................................... 10 4.1.1 Constant pressure-drop measurements ............................................................................. 10 4.1.2 Constant flow-rate measurements ...................................................................................... 11

4.2 Final discussions .................................................................................................................. 13

5 LIST OF SYMBOLS .......................................................................................... 14

6 CONSTANTS AND GEOMETRICAL DATA ..................................................... 17

7 BIBLIOGRAPHY ............................................................................................... 17

Please note:

This is a very brief summary of the filtration description in German. For

theoretical background in English please refer to Ullmann’s Encyclopedia of

Industrial Chemistry, available online on www.ethbib.ethz.ch. Alternatively, you may

ask your assistant for a hardcopy.


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2 Introduction

In many industrial processes dispersions of particles in a fluid (liquid or gas)

need to be separated from their fluid, either for the removal of valuable product or for

cleaning of a product liquid (e.g. water purification). One of the basic procedures for

this is filtration.

In this filtration practicum we will investigate the separation of CaCO3 particles

from an aqueous suspension (solid-liquid system) by filter pressing. Two different

operation modes will be used: a) constant pressure drop and b) constant suspension

volume flow rate.

The suspension flow rate will be measured during constant pressure filtration

whereas pressure drop across the filter is measured during constant suspension

flow experiment. Information related to the structure of the resulting filter-cake can

be extracted from this data.

In the following you will find the equations based on the classic differential

equations for cake-filtration:

Darcy’s law describes the flow of a liquid through a porous medium:

Vf

∗

AF

=k ⋅ ∆p

hk

=∆p

η ⋅h

k

k ⋅ η

(1)

Here the term η * {hk / k * η } describes the total resistance against flow through

the filter. This law can be used to describe the build-up of a filter cake.

The resistance term η * {hk / k * η } is now separated into a filter medium

resistance βM and a filter cake resistance αc * hk. Here, αc is the height specific cake

resistance and hk is the (time-dependent!) cake height.

{hk / k * η} = (βM + αc * hk) (2)

Combining equation (1) and (2) results in


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Vf

∗

AF

=1

AF

⋅dV

f

dt=

∆p

η⋅(βM

+ αC

⋅ hk)

(3)

For the integration of the differential equation (3) the following assumptions are

made:

a) The filtrate flow is laminar b) The built filtercake is incompressible, therefore its porosity is independent

of the pressure (αc =const). c) The resistance of the filter medium βM is constant for the whole filtration

process.

d) The filter efficiency is 100%

Based on these assumptions equation (3) can be integrated. The cake height hk

is eliminated by a mass balance over the solid material:

A

F⋅ h

k⋅ (1 − ε) ⋅ρ

solid= V

f⋅ c

(4)

Substituting hk from equation (4) into equation (3):

1

AF

⋅dV

f

dt=

∆p

η ⋅ βM

+α

C

ρsol

⋅ (1 − ε)⋅

c ⋅ Vf

AF

=∆p

η ⋅ βM

+ α⋅c ⋅ V

f

AF

(5)

In equation (5) the term αc / ρsol (1-ε) is replaced by the area specific cake

resistance α, which (for convenience) will be called cake resistance from now on.

In this practicum two approaches will be used to solve equation (5):

a) ∆p = ¢

i.e. the filtrate volume flow rate decreases over time


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b) Vf* = dVf / dt = ¢

i.e. the filtration pressure increases over time

Following a), the solution for ∆p = ¢:

For integration of (5) with the boundary conditions Vf = 0 at t = 0 :

ηA

F⋅ ∆p

⋅α ⋅cA

F

⋅Vf

+βM

⋅ dV

f= dt ∫

(6)

ηA

F⋅ ∆p

⋅α ⋅ c

2 ⋅ AF

⋅Vf

2 + βM

⋅ Vf

0

Vf

= t

(7)

t =η ⋅ α ⋅c ⋅V

f

2 + 2 ⋅ AF

⋅βM

⋅Vf( )

2 ⋅AF

2 ⋅ ∆p

(8)

For a graphical analysis of (8) use the following:

t

Vf

=η ⋅c ⋅α

2 ⋅AF

2 ⋅ ∆p⋅ V

f+

η ⋅βM

AF

⋅ ∆p

(9)

A graphic representation of t / Vf as function of Vf gives a straight line (Figure 4).

From the slope the cake resistance α can be calculated, while from the intercept the

filter medium resistance βM can be found.


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t

Vf

Vf

α

βM

Figure 4: t / Vf vs Vf for ∆p = ¢

Following b), the solution for Vf* = dVf / dt = ¢:

With Vf = t . Vf* from (5) you get:

∆p(t) =η ⋅α ⋅c ⋅V

f

∗2

AF

2 ⋅t +β

M⋅ η⋅ V

f

∗

AF

(10)

This means the pressure increases linearly with time. By plotting ∆p as function

of t you can determine α as well as βM (Figure 5).


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α

βM

∆p

t

Figure 5: ∆p versus t, for Vf* = ¢

Plotting the specific cake resistance α from different experiments at different

constant ∆p in double logarithmic scale as function of ∆p, you will find a near to

linear dependency according to the following formula:

α = α

o⋅(∆p / ∆p

o)

n

(11)

From this you can calculate the compressibility n:

n =log α / α

o

log ∆p / ∆po

(12)

For incompressible filter cakes n becomes 0, for compressible cakes n increases

from 0 to approximately 1.2. At n = 1 the filtrate volume is after a certain time quasi-

independent of the filtration pressure.


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Figure 7: Piping and Instrumentation diagram (P&ID) of the plate filter setup.

3 Experimental

Figure 7 shows the piping and instrumentation diagram of the filter press used

for the experiments. Make yourself familiar with the setup before operation. Find the

relevant valves and its proper position on the P&ID for the two modes of operation.

3.1 Suspension preparation

Weigh 250 g of CaCO3, add some water and stir to make a rather thick pre-

suspension. Before water is filled in through valve B, make sure the outlet valve A is

closed and the pressure release valve of the stirrer tank is opened properly. Then fill

approximately 60 L of water through valve B and add the pre-suspension through

valve B as well and fill in water until 70 L are in the tank. Start the stirrer C and the

recirculation pump D to achieve a homogeneous suspension.

3.2 Filter placing

Check that the filter (degas) valves E are closed. Place the filter between the

plates (smooth surface towards the incoming flow). Press the plates together with


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the clamp. After the filter is wetted it might be needed to reinforce the clamp

pressure as the filter settles a bit when wet.

3.3 Measure suspension flow rate under constant pressure

First close the pressure release valve E and the filling valve B on the tank.

Switch the pressurized air supply on (main valve on the wall). Next, the tank needs

to be pressurized to the required pressure level for the corresponding experiment.

This can be done by adjusting the pressure control valve (PIC). Turning clockwise

will increase the pressure and vice versa (please lift the red plastic ring while

adjusting). Air flows into the tank and fills up the volume above the liquid (give it

some time to reach equilibrium). Once the tank is pressurized, check that the flow

through the flow controller (FIC) is bypassed. Let some suspension pass through the

filter press by opening the final valve to the plate filter (valve J) and simultaneously

open the degas valves E until suspension runs out. Close degas valves and start the

measurement.

Measure the flow under constant pressure for 8-12 minutes, recording the flow-

rate every 15 s.

Change the filter (release overpressure through valve E before opening the

press) and redo the measurement at ∆p = 2 bar (set valve F to 2 bar). After the

second experiment you have to drain the remaining suspension in the tank through

valve A and prepare a new 70 L batch of suspension. Change the filter and redo the

measurement at ∆p = 3 bar (set valve F to 3 bar).

3.4 Measure the pressure-drop under constant flow-rate

Set the pressure to 3 bar (valve F) and replace the filter. Set the flow rate on the

FIC to 80 l/h. Open the path leading through the flow meter (G) and close the path

through the bypass line.

Measure the pressure drop during approximately 10 minutes every 15 s. After all

experiments have been carried out you can compare the appearance of the filter

cakes like cake thickness and porosity.

3.5 Shutting down and cleaning

Close the valve to the pressurized air (F). Drain the rest of the suspension by

opening the valve A. Shut down the stirring (C) and suspension circulation (D).

Disconnect all electrics (stirring, pump, flow and pressure-meters). Clean the

working place.


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4 Report

Each group has to write one report. The report should be approximately 8

pages long and include the following chapters:

1. Abstract (describe shortly what was done and what were the major

findings)

2. Theory (equations which will be used in the result part must be

introduced)

3. Experimental (describe the experimental procedure)

4. Results (plot the result curves and perform the needed calculations)

5. Discussions (discuss the results and refer to literature if needed)

6. Conclusions (what are the discoveries of the experiment, what does it

mean in practice)

4.1 Specific tasks (in results and discussion)

4.1.1 Constant pressure-drop measurements

a) Neglecting the filter resistance βM in equation (8), the filtration for constant

pressure is then described by

t =η ⋅c ⋅α ⋅Vf

2

2 ⋅ AF

2 ⋅ ∆p (13)

Vf

AF

=2 ⋅ t ⋅ ∆p

c⋅η ⋅α (14)

Plot the filtrate volume Vf [m3] per filter area Af [m

2] as a function of time t [s] in

double logarithmic scale. Following equation (13) you should get a linear

dependency with a slope of 0.5. Discuss the results and draw some qualitative

conclusions from the plotted results.


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b) Plot t/Vf [s/m3] as a function of Vf [m3] and find the specific cake resistance α

from the regression. Additionally, determine the resistance of the filter medium βM

(m-1), for each pressure drop 1, 2 and 3 bar by using equation (9). Discuss the

results.

4.1.2 Constant flow-rate measurements

c) Plot the pressure drop ∆p [Pa] as a function the time t [s]. Find the cake

specific filter resistance αC [m-2], and resistance of the filter medium βM (m-1), using

the graph and equation (10) where Vf* [m3/s] is the filtrate volume flow.

d) Solve the compressibility n [-] using equation (11) or (12).

e) Find the porosity ε (ratio of void volume to total cake volume) of the filter cake

using the Carman-Kozeny theory. Carman (1939) calculated the pressure loss in the

bulk and modeled the porous filter cake as numerous continuous parallel channels.

The pressure loss in such channels is:

h

kKanal

liq

Kanald

hvp ⋅⋅=∆ 2

2(Re)

ρξ (15)

The pressure drop coefficient is here 64/Re (laminar flow)

The Reynolds number for such channel is:

η

ρ liqhKanal dv ⋅⋅=Re (16)

The mean velocity in the channel is determined by the continuity equation:


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{ F

gkeitGeschwindiLehrrohr

tsflächeQuerschnitfreie

FKanalf AvAvV ⋅=⋅⋅= 0

*

321ε (17)

In reality there are no single and continuous channels. In fact, in porous filter the

channels are curved with changing dimensions depending on the particle properties.

Thus, the main inaccuracy comes from the use of the hydraulic diameter dh which

can be defined as:

dh

=4A

U⋅h

k

hk

(18)

here A is the channel cross section area [m2] and U is the wetted channel

circumference [m].

Another definition of the hydraulic diameter is:

d

h=

4 ⋅ (ε ⋅AF

⋅ hk)

F (19)

where F is the total wetted surface:

{(1 ) F k

solid volume total cakefraction volume

F S A hε

−

= ⋅ − ⋅ ⋅123

(20)

S= Specific particle volume surface

ε = porosity

With (4) and inserting the above in (15) you get:

The pressure drop is:


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∆p = η ⋅ αC− K

⋅c ⋅ V

f

AF

⋅ v

0

(21)

With given equations derive the specific cake resistance, αC-K [m/kg]. Using the

solved cake resistances from the pressure constant experiments α [m/kg] one can

solve for the porosities for each ∆p=const experiment. Which porosities do you get

and what conclusion can be drawn?

4.2 Final discussions

Discuss your results and compare your experimental data to the theory:

• Are the assumptions made for the integration of the filter differential equation reasonable comparing the observed results here?

• How would the porosity change if instead of ideal monodisperse (“single” sized) particles, polydisperse (“several” sizes) particles with broader size distribution would be used?

• How would the plot of t/Vf as a function of Vf change if the filter media resistance (β) would change over time?

• Compare the results of four different filter cake (α) and media (β) resistances, their order of magnitude and ratio to each other. How does the magnitude of the cake (α) and filter media (β) resistances affect the values of the compressibility (n) and porosity (ε)?


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5 List of symbols

A channel cross section [m2]

AF area of the filter [m2]

c solids concentration, mass of solid per total volume [kg/m3]

dh hydraulic diameter [m]

F wetted surface [m2]

hk cake height (channel lenght) [m]

k Durchlässigkeitskoeffizient after Darcy [m3*s/kg]

n compressibility [-]

∆p pressure drop over filter and cake [N/m2]

S specific surface area (surface per volume of the particles) [m-1]

t filtration time [s]

U wetted curcumferance [m]

mean velocity in the channel (pore) [m/s]


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v0 void tube velocity [m/s]

Vf suspension volume [m3]

Vf* suspension volume flow [m3/s]

aC cake height specific cake resistance [m-2]


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α area based cake resistance [m/kg]

αC-K flächenmassenspezifischer Kuchenwiderstand nach

Carman-Kozeny [m/kg]

βM resistance of the filter media [m-1]

ε porosity [-]

η dynam. viscosity [kg/(ms)]

ρliq

fluid density [kg/m3]

ρsol

solid density [kg/m3]

x pressure drop constant [-]


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6 Constants and Geometrical Data

ρsol

= rCaCO3 = 2710 kg/m3

ρliq

(Wasser bei 14 °C) = 1000 kg/m3

S = 9.18 * 105 m2/m3

η = 1197.8 . 10-6 kg/(ms)

AF = 0.0324 m2

7 Bibliography

[1] Darcy, H.: "Les Fontaines Publique de la Ville de Dijon", Herausgeber Victor

Dalmont, Paris, 1856

[2] Carman, P. C.: "Fundamental Principles of Industrial Filtration",

Transactions-Institution of Chemical Engineers, 1939, 168-188

[3] Müller, E.: "Mechanische Trennverfahren", Band 2, Sauerländer, 1983,

(IVUK-Bibliothek CIT 219/II)

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Filtration EN FS2016 - ETH Zürich · PDF filePraktikum “Mechanical Engineering” Spring semester 2016 Filtration ... Figure 7 shows the piping and instrumentation diagram of the