mech separation 02

1April 21, 2023 MECHANICAL SEPARATIONS

Prepared by:Engineer Waqas QamarLecturer

MECHANICAL SEPARATIONS

Introduction and Fundamentals of Filtration

April 21, 2023 MECHANICAL SEPARATIONS 2

Filtration :

Filtration may be defined as the separation of solid from liquid by passing the suspension through a permeable medium which retains the solids and allows the liquid to pass is termed as filtration.

In order to obtain fluid flow through the filter medium, a pressure drop ∆p has to be applied across the medium.


Particle deposition in filtration :


Nature of Solids in Slurry:

ValuabilityConcentrationSize

Undissolved

Traces to High %

Micro filtrationUltra filtration

Desired

Solubility

Dissolved

Conventional Filtration

Waste


Filtration Mechanisms:

1• Cake Filtration

2• Deep bed Filtration


1. Cake filtration:

By this filtration mechanism, the cake accumulated on the surface of the filter is itself used as a filter.

In some instances the cake formed has a lower permeability than the filter medium and thus becomes the limiting factor in the filtration cycle.


2. Depth/Deep Bed filtration:

This filtration mechanism retains particulate matter not only on the surface of the filter but also at the inside of the filter.

Proportion of solids in suspension is relatively small and the particles are considerably smaller than pore size of filter medium. The particles penetrate into the pores of the filter medium before being captured.

Sieving, Impaction and Interception


Filtration Chart:


Filtration Media:

It can be considered as the heart of the filtration device or machine.

Provides adequate porosity capable of passing liquid through, while retaining solids

Medium is characterized by its filtration properties of permeability and retention.

It can be

• Natural• Synthetic or glass• Woven cloth• Paper• Ceramic


Medium performance criteria:

1. The measured data of how small a particle it can stop;

2. The permeability (the ability of the medium to allow flow);

3. The relationship between build-up of dirt in the medium and

the rate of increase of resistance to flow.


Factors Effecting the Rate of Filtration:

1. The drop in pressure from the feed to the far side of the filter medium.

2. The area of the filtering surface.

3. The viscosity of the filtrate.

4. The resistance of the filter cake.

5. The resistance of the filter medium and initial layers of cake.


Flow rate-Pressure drop relationship:

1. CLEAN MEDIUM:

At the beginning of batch cake filtration, the whole pressure drop available is across the medium itself since as yet no cake is formed.

And the Darcy's basic filtration equation:

where K is a constant referred to as the permeability of the bed. or

where R is called the medium resistance (and is equal to L/K, the medium thickness divided by the permeability of the bed)


2. Medium with a Cake Forming on its Face


Due to the additional resistance caused by cake, Darcy’s relation becomes:

The resistance of the cake may be assumed to be directly proportional to the amount of cake deposited.

where w is the mass of cake deposited per unit area and α is the specific cake resistance . So


Filtration Operations – Incompressible Cake:

The mass of cake deposited per unit area w is a function of time in batch filtration processes. It can be related to the cumulative volume of filtrate V filtered in time t by:

where c is the concentration of solids in the suspension. So

As the total flow volume is an integral function of the flow rate

And



If; and

1. Constant Pressure Filtration:

For;

Then;


2. Constant Rate Filtration:


If the flow rate Q is kept constant and the pressure ∆p varied, then

where V is simply;

So

or

where v is the approach velocity of the filtrate


3. Constant Rate Followed By Constant Pressure Operation:



For such case the equations are:




4. Variable Pressure-Variable Rate Operation:

Flow rate-Pressure drop relationship for centrifugal pump:


Filtration Operations – Compressible Cake:

An obvious way of dealing with compressible cakes is to use the concept of average cake resistance.

∆Pc is the pressure drop across the cake.

For an analytical solution of the filtration of compressible cakes pressure drops across the medium ∆Pm and across the cake ∆Pc have to be treated separately.



1. Constant Pressure Filtration:

This operation is of course unaffected by compressibility and, consequently, the governing relationships remain the same as for incompressible case.

2. Constant Rate Filtration:

A plot of log∆Pc against log t should give a straight line.


4. Variable Pressure-Variable Rate Operation:


And


Classification of Filtration Equipments:

mech separation 02

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