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PERCOBAAN

GRANULAR FILTRATION

1. Objectives

(a) Assessing the filtering capacity of granular filter of a particular grain size, shape, and material:

turbidity reduction vs. flow rate and time.

Hydraulic performance of a particular filter media: pressure drop vs. flow rate, pressure drop distribution within bed.

(b) Back washing performance: backwash water efficiency, backwashing effectiveness (amount of

water necessary for backwashing).

2. Theory

Filtration is the separation of solid particles or liquid ones (droplets) from liquids and gases with the help of a

filter medium also called a septum, which is essentially permeable to only the fluid phase of the mixture being

separated. In earlier times, this process was carried out with felts, and the word “filter” has a common derivation

with “felt”.

The liquid more or less thoroughly separated from the solids is called the filtrate, effluent, permeate or, more

rarely, clean water. As in other separation processes, the separation of phases is never complete: Liquid adheres

to the separated solids (cake with residual moisture) and the filtrate often contains some solids (solids content in

the filtrate or turbidity).

Filtration is effected by application of vacuum, pressure, or of centrifugal force. Vacuum filtration requires a

vacuum pump. The pump evacuates the gas from a filtrate receiver, where the filtrate is separated from the gas.

The filtrate is drained either by a barometric leg of at least 8 to 10 m or by a pump that is able to “run on snore”

(i.e. with a deficiency of feed liquid so that it tends to draw in air). Pressure filtration typically only requires a

pump for delivering of the suspension and the filter is placed within a pressure vessel, hence less easily

accessible. Centrifugal filtration is done in perforated centrifuge rotors.

Various models can describe the physical process of filtration. Four idealized filtration models depicted in

Figure 1. – Cake filtration is the most frequently used model. Here it is assumed that the solids are deposited on a

filter medium as a homogeneous porous layer with a constant permeability. Thus, if the flow rate dV/dt

is constant, the pressure drop will increase linearly, proportional to the quantity of solid deposited. This

model can be applied particularly well for all hard, particulate solids.

– Blocking filtration: The pressure drop is caused by solid particles blocking pores. Soft, gelatinous

particles retained by a sieve exhibit such a behavior. If the flowrate dV/dt is constant, the pressure drop

increases exponentially with the quantity filtered, the number of open pores asymptotically approaching

zero. The pores may belong to a filter medium (screen or filter layer) or it may be pores within a filter

cake of coarse particles, which are blocked by migrating fine particles.

– Deep bed or depth filtration: Solid particles are retained in a deep filter layer. This takes place for

example in sand filters for clarification of drinking water, which retain even colloidal particles. The

typical effect of deep bed filtration is adhesion of solids to the grains of the filter layer, comparable to

charcoal adsorption. Only rather big particles are retained by the screening effect. When the filter bed

has been saturated with solids, the solids concentration in the filtrate leaving the bed progressively

approaches that of the incoming suspension.

– Cross-flow filtration: In cross-flow filtration the suspension flows with high speed tangentially to the

filter surface, preventing the formation of a cake. Only a small flow of liquid passes through the filter

medium. A certain layer of solids accumulates in the boundary layer on the filter surface, and reduces

the flow of filtrate. After an initial period, a dynamic equilibrium is established between convective

transport of solids to the filter surface and removal of solids by turbulence and by diffusion.

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In deep bed filtration (as opposed to cake filtration and cross-flow filtration), the solid particles are separated

mainly by deposition within the pores of the filter medium. The filter medium may consist of – a 0.5–3m layer of coarse grains (e.g., sand 0.3 – 5 mm) or – a layer of a few centimeters of fibers (e.g., wound or resin bonded cartridge filters) or – sheets of a few mm thickness (e.g., made of cellulose). – a layer of granular filter aid (e.g., precoat layer)

All these filter elements have pores that are larger than the particles to be retained. The particles stick in the

pores by adhesion and their accumulation weakens the filtering action and increases the pressure drop, so that

the filter must be cleaned or replaced periodically. This is why deep bed filtration should be used not to recover

solids from a suspension such as cake filtration, but instead to produce a very clean effluent from suspensions

with low solids loading (typically <0.1 g/L) and with very fine particles. Depending on the particle size, the

prevailing effects of retention are summarized in Figure 2:

1) Particles larger than the pores are trapped mechanically. This is typically true for particles ≥10 m. 2) Particles 1 – 10 m in diameter hit the solid surface mainly due to inertia effects and stick there due

to surface forces. 3) Particles <0.1 m reach the solid surface mainly because of diffusion and again they

stick there due to surface forces.

In the range between 0.1 and 1 m the effects of both inertia and diffusion are small and a minimum in transport

and hence in the effectiveness of deep bed filters is observed. The clarification effect must be summarized in an empirical “filter coefficient” λ describing the local decrease in

concentration of the suspension flowing through the bed:

¡@C

@L= ¸C (1)

where c is the concentration of the suspension and L is the distance from the inlet face of the filter. For uniform

conditions, this differential equation can be integrated:

Figure 1: Filtration models

Figure 2.

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d h

c= c0 exp(¡¸0L) (2)

here λ0 is the initial filter coefficient of a clean, homogeneous filter bed. As soon as the bed is loaded with solids,

its efficiency will diminish and that is why the solution of the differential equation becomes rather difficult.

Different models exist to describe the process, but they are rarely used for practical purposes. To find a suitable

filter medium in a deep bed filter which shows good retention efficiency over a long cycle time, laboratory tests

over a realistic cycle time have to be carried out with filter layers of realistic depth. The pressure drop in a deep bed filter can be interpreted as an effect of two different phenomena of blocking

filtration: 1) The filter media exhibit a resistance to flow, which is increased by the solids deposit in the pores.

The quantity of deposit is generally small compared to the pore volume, and the additional

pressure loss per unit depth can be described as proportional to the local specific deposit. For

constant solids concentration at the inlet and constant retention the increase in this pressure drop

with time is therefore approximately constant. 2) In addition there is often a pressure drop due to deposits on the surface of the filter bed. This is a

typical blocking filtration and can be described by Boucher’s law. The total pressure drop of a deep bed filter at constant flow rate can then be approximated by an equation of the

type

p(t) = const1t+ const2eJt (3)

For the case that the driving force is gravity, the pressure profile is shown in Figure 3B. In the static equilibrium,

at flow zero, 1 m of pressure head is gained for every meter of depth. When flow has started, the pressure drop

within the media increases linearly with depth. According to Carman-Kozeny a linear relationship exists between

the head loss of the clean bed and the laminar flow velocity:

¢H = 180º

g

(1¡ ²)2

²3v

d2h

L (4)

in which:

ΔH = head loss (m)

= kinematic viscosity (m /s)

g = gravity acceleration (m/s )

ε = porosity (-)

The porosity is calculated from the bed volume and the mass and density of the filter material.

v = velocity (m/s)

= hydraulic diameter of sand grains ……………………(m)

L = bed height (m) The slope of this linear line can be used to calculate the hydraulic diameter of the sand grains.

d2h =

v

I0

180º

g

(1¡ ²)2

²3 (5)

with I0 = ¢HL . This relationship is valid only for Re · 5. The quotient of and is the permeability

coefficient K (m/s) which is a measure for the ease of flow through a bed of grains.

As solids are deposited in the pores, the local pressure loss will increase in the upper layers and the pressure line

becomes distorted. When the pressure line touches the atmospheric pressure value, the required flow cannot be

maintained and the filter should be cleaned.

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Cleaning of Deep Bed Filters. Sand filters can be cleaned by backflushing (backwashing). The flow is reversed

to wash off deposited solids and flush them, e.g., to a wastewater station. Often air scour is used to increase the

turbulence and reduce the amount of water necessary for fluidization. A typical set of data of a sand filter for

cleaning of water could be [12]:

Medium depth 1 m

Medium size 0.5 – 1 mm (as uniform as possible)

Flow rate during filtration 5 - 10 m3/(m

2 h)

Flow rate air scour 60 m3/(m

2 h) for 10 min

Flow rate water backflow 15 – 30 m3/(m

2 h) for 3 – 8 min after air scour

During backflow the sand grains are classified, the smallest ones are entrained to the top, the coarse ones sink to

the bottom of the filter bed. This effect is undesired, since it leads to premature blocking of the top layer.

Therefore it is important to use sand with grain sizes as uniform as possible.

During backwashing the flow is in the transitional region between laminar and turbulent flow. The Carman-

Kozeny formule is not valid anymore. For this type of flow only empirical formulae can be used. A good

approach is:

¢H = 130º0:8

g

(1¡ ²e)1:8

²3e

v1:2

d1:8h

Le (6)

In which

²e = porosity of the expanded bed = ²+E1+E

E = (Le – L)/L = expansion of the bed

Le = height of the expanded bed.

When the flow rate is increased up to the certain value, the pressure drop (H) will be equal to the bed height

and the bed start to expand. This is the minimum of the backwashing flow rate and can be found from the

following relation:

v1:2 =g

130º0:8

½f ¡ ½w

½w

²3e(1¡ ²e)0:8

d1:8h (7)

.

2.3 Characteristics of the filter material The filter material used in this experiment consists of a sieved fraction of particles of variable size between the

lowest and widest mesh. A sieve analysis gives information about the grain size distribution.

Figure 3.

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Coefficient of uniformity. The spread in grain sizes should not be too big to avoid stratification during

backwashing. The spread is characterized by the coefficient of uniformity, U = d60/d10. Preference is given to a

value of U ≤ 1.2.

Specific diameter and shape factor. The so-called specific diameter of the grains can be found from a sieve

analysis with:

W

ds

=W1

'1

pS1S2

+W2

'2

pS2S3

+W3

'3

pS3S4

+ ¢ ¢ ¢Wn

'n

pSnSn+1

(8)

in which:

W = total weight of the sand sample (g) Wi = weight on sieve i (g) Si = mesh of sieve i (mm)

i = shape factor for fraction between sieve i and sieve i+1 (-)

The ratio between the hydraulic diameter and the specific diameter gives the shape factors for the different

hydraulic conditions:

'e =dh

ds

for expanded beds (9)

'h =dh

ds

for high porosity beds (10)

'l =dh

ds

for low porosity beds (11)

Effective diameter The hydraulic diameter for filter materials with unknown shape factors can be approximated in practice by the

so-called effective diameter de, defined as the d10 from a sieve analysis. The shape factor is determined as

'= de=ds (12)

3. Experimental set-up and procedure

The apparatus for conducting the experiment consists of an acrylic column with a diameter of 67 mm, two

plastic vessels and a set of piping system. Higher turbidity water is collected in the lower vessels and pumped to

the top of the column. The turbid water will drain down by gravity through the granular bed and the rotameter to

the upper vessels. The piping system provides an easy way of changing upward and downward flow direction

(see figure 4). Connections for pressure gauges are spirally mounted on the column. The pressure is measured

with piezometric water manometers.

Head loss through bed test (a) Fully fill the upper vessel with the clean (tap) water.

(b) Fully open valves V1, V2, V4, and V8.

(c) Closed valves V3, V5, V7, and V6.

(d) Redirect the over flow tube to the upper vessel.

(e) Switch on the pump and let the water flow filling the column until overflowing occur.

If pumping fails, call technician for assistance. (f) Observe the water levels at the manometer. If the water levels do not equal, check for the presence

of air bubbles along the tube. Squeeze or tap the tube until it is free of bubble and the levels

become equal.

(g) Start the test by opening the valve V6 to get the required initial flow rate is achieved.

(h) Observe the manometer reading for each observation point. Do not increase the flow rate if the

manometer level reaches the lowest reading board.

Filtration operation (a) Fully fill the lower vessel with the raw water of higher turbidity. Don't forget to measure the

turbidity. Empty the upper vessel to collect the filtered water draining down from the column.

(b) Fully open valves V1, V2, V4, and V7.

(c) Closed valves V3, V5, V8, and V6.

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(d) Switch on the pump and let the water flow filling the column until overflowing occur.

If pumping fails, call technician for assistance. (e) Observe the water levels at the manometer. If the water levels do not equal, check for the presence

of air bubbles along the tube. Squeeze or tap the tube until it is free of bubble and the levels

become equal.

(f) Start the filtration by opening the valve V6 until the required initial filtration flow rate is achieved.

The maximum allowable filtration flow rate is 9 liter per minute in order to get a constant

hydraulic head over the filter.

(g) Monitor the filtration rate, the manometer levels, the turbidity of raw and filtered waters and the

volume of the collected water every minute or shorter.

(h) Run the filtration until there is no filtered water flowing which indicating that blocking occurs.

During filtration, fill up the content of the lower vessel if the level drops to less than 30% of the

top. Discard the content of the upper vessel if it is become full.

Backwashing operation

(a) With the pump still running, close the valves V4 and V6.

(b) Switch off the pump and close the valves V2 and V7.

(c) Redirect the over flow pipe from the lower vessel to the external vessel or sink.

(d) Make sure the upper vessel contains full of clean water suitable for backwashing purpose. Add the

clean water from the tap water if the level drops.

(e) Close the valve V1.

(f) Open the valves V3, V5 and V8.

(g) Measure the granular bed height.

(h) Switch on the pump.

(i) Open the valve V1 slowly, start the timer and observe the flow rate and the bed height. Take note

when the bed becomes fluidized and the entrapped particles (sediment) washed out of the bed.

(j) When the backwash water coming out of the bed is clear, close the valve V3 and switch off the

pump.

(k) Measure the amount of the backwash water used and the settled bed height. Observe any

appearance of segregation of the bed.

V1

V2

V3

V4

V5 V6

V7

V8

Upper Vessel

Lower Vessel

Manometer

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4. Observation and calculation

During the experiment, at least the following data should be collected:

(a) Head loss through the bed test

Manometer reading vs. flow rate

(b) Filtration operation

Water flow rate vs. time

Manometer reading vs. flow rate

Raw water turbidity vs. time

Filtered water (product) turbidity vs. time

(c) Backwash operation

Manometer reading vs. flow rate

Bed height

Volume of water consumed.

By using the collected data, calculate or construct:

Plot of pressure head vs. bed height for various time.

Prove that the equation of Karman-Kozeny is valid.

Plot of the filtered water turbidity vs. initial filtration flow rate.

Filtration capacity vs. initial filtration flow rate.

Figure 4. Experimental apparatus diagram