Size Reduction.pdf 437173

Mechanical Unit Operation Lecture Note

Addis Ababa Science and Technology University

School of Chemical and Material Science and Engineering Department of Chemical Engineering Mechanical Unit Operation (ChEg2048) Lecture Note

Prepared and Organized by: Belachew Zegale

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Chapter One Particle Technology 1.1. Introduction The three most important characteristics of an individual particle are its composition, its size and its shape. Composition determines such properties as density and conductivity, provided that the particle is completely uniform. In many cases, however, the particle is porous or it may consist of a continuous matrix in which small particles of a second material are distributed. Particle size is important in that this affects properties such as the surface per unit volume and the rate at which a particle will settle in a fluid. A particle shape may be regular, such as spherical or cubic, or it may be irregular as, for example, with a piece of broken glass. Regular shapes are capable of precise definition by mathematical equations. Irregular shapes are not and the properties of irregular particles are usually expressed in of some particular characteristics of a regular shaped particle. Large quantities of particles are handled on the industrial scale, and it is frequently necessary to define the system as a whole. Thus, in place of particle size, it is necessary to know the distribution of particle sizes in the mixture and to be able to define a mean size which in some way represents the behavior of the particulate mass as a whole. Important operations relating to systems of particles include storage in hoppers, flow through orifices and pipes, and metering of flows. It is frequently necessary to reduce the size of particles, or alternatively to form them into aggregates or sinters. Sometimes it may be necessary to mix two or more solids, and there may be a requirement to separate a mixture into its components or according to the sizes of the particles. In some cases the interaction between the particles and the surrounding fluid is of little significance, although at other times this can have a dominating effect on the behavior of the system. Thus, in filtration or the flow of fluids through beds of granular particles, the characterization of the porous mass as a whole is the principal feature, and the resistance to flow is dominated by the size and shape of the free space between the particles. In such situations, the particles are in physical with ading particles and there is little relative movement between the particles. In processes such as the sedimentation of particles in a liquid, however, each particle is completely surrounded by fluid and is free to move relative to other particles. Prepared and Organized by: Belachew Zegale

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1.2. Particle Characterization Individual solid particles are characterized by their size, shape, and density. Particles of homogeneous solids have the same density as the bulk material. Size and shape are easily specified for regular particles, such as spheres and cubes, but for irregular particles the size and shape are not so clear and must be arbitrarily defined. 1.2.1. Single Particle shape and size Analysis a) Particle Shape The shape of an individual particle is conveniently expressed in of the sphericity ϕ s, which is independent of particle size. For a spherical diameter Dp, ϕs = 1; for a non spherical particle, the sphericity is defined by the relation

ϕs =

where: Dp = nominal diameter of particle Sp = surface area of one particle vp = volume of one particle An equivalent diameter can be defined as the diameter of a sphere of equal volume. For fine granular materials, however, it is difficult to determine the exact volume and surface area of particle, and Dp is usually taken to be the nominal size based on screen analyses or microscopic examination. b) Particle Size In general, diameters may be specified for any equidimensional particle. Particles that are not equidimensional, that is, that are longer in one direction than in others, are sometimes characterized

1.2.2. Mixed particle sizes and size analysis (see hard copy)

1.2.3. Measurement of Particle Size Measurement of particle size and of particle size distribution is a highly specialized topic, and considerable skill is needed in the making of accurate measurements and in their interpretation. Prepared and Organized by: Belachew Zegale

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The ability to make accurate and reliable measurements of particle size is acquired only after many years of practical experimental experience. Before a size analysis can be carried out, it is necessary to collect a representative sample of the solids, and then to reduce this to the quantity which is required for the chosen method of analysis. A wide range of measuring techniques is available both for single particles and for systems of particles. In practice, each method is applicable to a finite range of sizes and gives a particular equivalent size, dependent on the nature of the method. The principles of some of the chief methods are now considered together with an indication of the size range to which they are applicable.

Sieving (>50 μm): Sieve analysis may be carried out using a nest of sieves, each lower sieve being of smaller aperture size. Generally, sieve series are arranged so that the ratio of aperture sizes on consecutive sieves is 2, 21/2 or 21/4 according to the closeness of sizing that is required. The sieves may either be mounted on a vibrator, which should be designed to give a degree of vertical movement in addition to the horizontal vibration, or may be hand shaken. Whether or not a particle es through an aperture depends not only upon its size, but also on the probability that it will be presented at the required orientation at the surface of the screen. The sizing is based purely on the linear dimensions of the particle and the lower limit of size which can be used is determined by two principal factors. The first is that the proportion of free space on the screen surface becomes very small as the size of the aperture is reduced. The second is that attractive forces between particles become larger at small particle sizes, and consequently particles tend to stick together and block the screen. Sieves are available in a number of standard series. There are several standard series of screen and the sizes of the openings are determined by the thickness of wire used. The efficiency of screening is defined as the ratio of the mass of material which es the screen to that which is capable of ing. This will differ according to the size of the material. It may be assumed that the rate of age of particles of a given size through the screen is proportional to the number or mass of particles of that size on the screen at any instant. Thus, if w is the mass of particles of a particular size on the screen at a time t , then:

where k is a constant for a given size and shape of particle and for a given screen.


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Mechanical Unit Operation Lecture Note Thus, the mass of particles (w1 − w2) ing the screen in time t is given by:

w2=w1e-kt If the screen contains a large proportion of material just a little larger than the maximum size of particle which will , its capacity is considerably reduced. Screening is generally continued either for a predetermined time or until the rate of screening falls off to a certain fixed value. Screening may be carried out with either wet or dry material. In wet screening, material is washed evenly over the screen and clogging is prevented. In addition, small particles are washed off the surface of large ones. This has the obvious disadvantage, however, that it may be necessary to dry the material afterwards. With dry screening, the material is sometimes brushed lightly over the screen so as to form a thin even sheet. It is important that any agitation is not so vigorous that size reduction occurs, because screens are usually quite fragile and easily damaged by rough treatment. In general, the larger and the more abrasive the solids the more robust is the screen required. Microscopic Analysis (1–100 Μm): Microscopic examination permits measurement of the projected area of the particle and also enables an assessment to be made of its two-dimensional shape. In general, the third dimension cannot be determined except when using special stereomicroscopes. The apparent size of particle is compared with that of circles engraved on a graticule in the eyepiece.

Sedimentation and Elutriation Methods (>1 Μm): These methods depend on the fact that the Prepared and Organized by: Belachew Zegale

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terminal falling velocity of a particle in a fluid increases with size. Sedimentation methods are of two main types. In the first, the pipette method, samples are abstracted from the settling suspension at a fixed horizontal level at intervals of time. Each sample contains a representative sample of the suspension, with the exception of particles larger than a critical size, all of which will have settled below the level of the sampling point. In the second method, this involves the use of the sedimentation balance, particles settle on an immersed balance pan which is continuously weighed. The largest particles are deposited preferentially and consequently the rate of increase of weight falls off progressively as particles settle out. Sedimentation analyses must be carried out at concentrations which are sufficiently low for interactive effects between particles to be negligible so that their terminal falling velocities can be taken as equal to those of isolated particles. Careful temperature control (preferably to ±0.1 deg K) is necessary to suppress convection currents. The lower limit of particle size is set by the increasing importance of Brownian motion for progressively smaller particles. It is possible however, to replace gravitational forces by centrifugal forces and this reduces the lower size limit to about 0.05 μm. The elutriation method is really a reverse sedimentation process in which the particles are dispersed in an upward flowing stream of fluid. All particles with terminal falling velocities less than the upward velocity of the fluid will be carried away. A complete size analysis can be obtained by using successively higher fluid velocities. Permeability methods (>1 μm): These methods depend on the fact that at low flowrates the flow through a packed bed is directly proportional to the pressure difference, the proportionality constant being proportional to the square of the specific surface (surface : volume ratio) of the powder. From this method it is possible to obtain the diameter of the sphere with the same specific surface as the powder. The reliability of the method is dependent upon the care with which the sample of powder is packed. Electronic particle counters: A suspension of particles in an electrolyte is drawn through a small orifice on either side of which is positioned an electrode. A constant electrical current supply is connected to the electrodes and the electrolyte within the orifice constitutes the main resistive component of the circuit. As particles enter the orifice they displace an equivalent volume of electrolyte, thereby producing a change in the electrical resistance of the circuit, the magnitude of which is related to the displaced volume. The consequent voltage pulse across the electrodes is fed to a multi-channel Prepared and Organized by: Belachew Zegale

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analyser. The distribution of pulses arising from the age of many thousands of particles is then processed to provide a particle (volume) size distribution. The technique is suitable for the analysis of non-conducting particles and for conducting particles when electrical double layers confer a suitable degree of electrical insulation. The main disadvantage of the method is that the suspension medium must be so highly conducting that its ionic strength may be such that surface active additives may be required in order to maintain colloidal stability of fine particle suspensions. Sub-micron particle sizing: Particles of a size of less than 2 μm are of particular interest in Process Engineering because of their large specific surface and colloidal properties. The diffusive velocities of such particles are significant in comparison with their settling velocities. Provided that the particles scatter light, dynamic light scattering techniques, such as photon correlation spectroscopy (PCS), may be used to provide information about particle diffusion. In the PCS technique, a quiescent particle suspension behaves as an array of mobile scattering centres over which the coherence of an incident laser light beam is preserved. The frequency of the light intensity fluctuations at a point outside the incident light path is related to the time taken for a particle to diffuse a distance equivalent to the wavelength of the incident light. The dynamic light signal at such a point is sampled and correlated with itself at different time intervals using a digital correlator and associated computer software. The relationship of the (so-called) auto-correlation function to the time intervals is processed to provide estimates of an average particle size and variance (polydispersity index). Analysis of the signals at different scattering angles enables more detailed information to be obtained about the size distribution of this fine, and usually problematical, end of the size spectrum. The technique allows fine particles to be examined in a liquid environment so that estimates can be made of their effective hydrodynamic sizes. This is not possible using other techniques. Provided that fluid motion is uniform in the illuminated region of the suspension, then similar information may also be extracted by analysis of laser light scattering from particles undergoing electrophoretic motion that is migratory motion in an electric field, superimposed on that motion. Instrumentation and data processing techniques for systems employing dynamic light scattering for the examination of fine particle motion are currently under development. Prepared and Organized by: Belachew Zegale

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1.3.

Properties of particulate masses

1.3.1. Pressure in masses of particles

Chapter Two 2. Transportation and storage of solids in bulk 2.1.

Introduction

The storage and handling of solids is difficult and costly as compared to fluids due to the following irregularities: particle size, shape, density, stickiness etc. Due to this reason proper choice of storage, handling and transportation equipments for the solids must be done depending on these conditions which are as opposed to fluids where we base our calculations mainly on the fluid density and viscosity during transportation.

2.2.

Storage of solids

Bulk storage – course solids like gravel and coal are stored outside in large piles, unprotected from the weather. The solids are removed from the pile by dragline or tractor shovel and delivered to a conveyor or to the process. Outdoor storage can lead to environmental problems such as dusting or leaching of soluble materials from the pile. Dusting may necessitate a protective cover of some kind for the stored solid; leaching can be controlled by covering the pile or by locating it in a shallow basin with a impervious floor from which the runoff may be safely withdrawn. Bin storage – solids that are too valuable or too soluble to expose in outdoor piles are stored in bins, hoppers, or silos. These are cylindrical or rectangular vessels of concrete or metals. A silo is tall and relatively small in diameter; a bin is not so tall and usually fairly wide. A hopper is a small vessel with a sloping bottom, for temporary storage feeding solids to a process. All these containers are loading from the top by some kind of elevator; discharging is ordinarily from the bottom.

2.3.

Transport of solids by mechanical conveyors

The variety of requirements in connection with the conveying of solids has led to the development of a wide range of equipment. This includes: (a) Gravity chutes—down which the solids fall under the action of gravity.


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(b) Air slides—where the particles, which are maintained partially suspended in a channel by the upward flow of air through a porous distributor, flow at a small angle to the horizontal. (c) Belt conveyors—where the solids are conveyed horizontally, or at small angles to the horizontal, on a continuous moving belt. (d) Screw conveyors—in which the solids are moved along a pipe or channel by a rotating helical impeller, as in a screw lift elevator. (e) Bucket elevators—in which the particles are carried upwards in buckets attached to a continuously moving vertical belt. (f) Vibrating conveyors—in which the particles are subjected to an asymmetric vibration and travel in a series of steps over a table. During the forward stroke of the table the particles are carried forward in with it, but the acceleration in the reverse stroke is so high that the table slips under the particles. With fine powders, vibration of sufficient intensity results in a fluid-like behavior.

2.4.

Hydraulic and pneumatic transport - in which the particles are transported in a stream of air/water.

Chapter Three 3. Size Reduction (comminution) and Agglomeration(size enlargement) of solids Objectives of size reduction 

To produce small particles from large ones which are desired because of their size, shape, number, or large surface area (increasing the surface area to volume ratio so as to: reduce drying time, increase extraction rate, increase reaction rate, decrease heating, cooling and cooking time etc)



Products are to be obtained which meet the requirements concerning the particle size and shape distribution (minimum or maximum size)



Size reduction is used to permit the mechanical separation of unwanted ingredients from valuable substances.



It may help in reducing the bulk of fibrous materials for easier handling and for waste disposal.


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3.1.

Introduction to size reduction

The term size reduction is applied to all the ways in which particles of solids are cut or broken down into smaller pieces. Throughout the process industries solids are reduced by different methods for different purpose, Chunks of crude ore crushed to workable size, synthetic chemicals are ground into powder, sheet of plastics are cut into tiny cubes or diamonds regarding the size and some times the shape of particles they contain. In the chemical industry size reduction is usually carried out in order to increase the surface area, because in most reaction involving solid particles the rate is directly proportional to the area of with the second phase, in food processing industries raw and final processed food material are crushed to facilitate easier handling, leaching, drying e.t.c.. Example: in leaching not only the rate of extraction increased by the virtue of increased area of between the solvent and solute (solid), but the distance solvent has to penetrate into the particle to gain access to the remote pockets of solute is also reduced. This factor is also important in drying porous materials where reduction in particle size cause both an increase in area and reduction in the distance the moisture must travel with in the particle in order to reach the surface, in this case the capillary forces acting on the moisture are also affected.

3.2.

Size reduction operations 3.2.1. Mechanism of size reduction

Theory of size reduction Every true solid material has specific true crystalline structure. That is the atoms in the crystals are arranged in a definite, repeating geometric pattern and there are certain planes in the crystal called cleavage planes, along which breakage occurs when sufficient pressure is applied on the material. When the material is broken into segments during comminution, the shape of the segment depends on its crystalline structure. As a force is applied to a substance, it begins to deform. Unless the stress (force per unit area) exceeds the elastic limit or yield point the substance will return to its original shape when the force is removed, and the stored energy is released as heat. If stress is increased beyond the elastic limit, permanent deformation occurs until the breaking stress is exceeded - at this point the material fractures and breaks along a line of weakness (cleavage plane). As the size of a piece is reduced, there are fewer lines of weakness


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available, and the breaking stress which must be exceedingly increased. There is therefore a substantial increase in energy requirement as the size of particles is reduced.

3.2.2. Factors Influencing Size Reduction operation  Feed and Product Size-the required granulometric state of the product, reduction ratio: RR =Df/Dp, Average size of feed / Average size of product, for coarse crushers: RR = 3 to 20, for fine grinders

: RR  100 Feed Size

Product Size

Coarse Crushers

1500 - 40mm

50 - 5mm

Intermediate Crushers

50 - 5mm

5 - 0.1mm

Fine Crushers/grinders

5 - 2mm

<0.1mm

Fine Milling

<0.2mm

down to 0.01 m

 Nature of Materials -the properties of the rock handled: The state of the raw material (density) granulometric state, hardness, elasticity, toughness, (hard to cut as leather), brittleness (hard but easily breaks glass) grindability of the feed depends: hardness, toughness, crystallinity, cleavage 

Hardness - very hard materials are better in low speed or low machines



Structure - fibrous materials need tearing or cutting action



Moisture content - materials with 5 - 50% moisture does not flow easily and can be difficult to process



Friability



Stickiness - sticky materials need easily cleaned machines



Soapiness - if coefficient of friction is low crushing may be difficult



Explosives - need inert atmosphere



Hazardous to health - need good confinement



Closeness of distribution

 Ways to carry out comminution; the kind and intensity of size reducing action; Free crushing: The product material is continuously discharged,

Choke feeding: It does not freely

discharge the crushed product, Closed circuit operation: With a classifying screen. Prepared and Organized by: Belachew Zegale

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Stressing Mechanisms (Basic Patterns) It is usually associated to subdividing or reducing large lumps to the required particle sizes. It is widely applied in the pretreatment of most process industries. The principal types of forces used in size reduction equipments are shown in fig.. However the mechanics and the geometrical configuration of the equipments could be different even among those using the same type of force. Solids may be broken in many different ways, but only four of them are commonly used in size reduction machine. 1. Compression –put between two rigid surfaces and compressed, used for course reduction of hard solids to give relatively few fines. 2. Impact (collision) - striking against hard body gives coarse, medium or fine product. 3. Attrition (rubbing) - yields very fine products from non abrasive material. 4. Cutting – dicers, knives are used to gives a definite particle size and some times with definite shape with few or no fines.

Compression & Rubbing

Impact

Compression


Cutting

Rubbing (attrition)

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Classification of size reducing operations on their products (according to the minimum particle size of the product)

Max. particle

Operations

equipment

products

size of product > 50 mm

state of material

crushing

Coarse

crusher

lumps

dry

5-50 mm

Fine

grit

0.5-5 mm

Coarse

grinders

gravel

(50 - 500 ) μm grinding

Fine

mills

Powder

dry or

(1-50) μm

ultra-fine

fine powder

wet

CHARACTERIZING THE SIZE REDUCTION EFFECT

The degree of size reduction is the ratio of particle after and before the size reduction.

nr 

X max X max 

nr - the degree of size reduction, Xmax’ - size before crushing and Xmax - size after crushing. Size reduction can be further classified according to the hardness of material to be reduced. Hardness - the resistance a body put up against the penetration of another body. This hardness is generally indicated according to the Moh's hardness scale. This is a ten stage scale, so devised that the body in any one of the stages can scratch the body in previous stage and will itself be scratched by the body in the next stage. The Moh's hardness scale.

Moh's

hardness

product body

degree of size reduction

1

Talcum

Soft

2

gypsum or salt

Soft

scale


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3

Calcite

Soft

4

Fluorite

Medium

5

Apatite

Medium

6

Feldspar

Medium

7

Quartz

hard

8

Topaz

Hard

9

Corundum

Hard

10

Diamond

Hard

3.2.3. Energy and Power requirement for Size reduction The cost of a power is a major expense in crushing and grinding so that the factors control this cost is important during size reduction. An ideal crusher would  be a large capacity  require a small power input per unit of product  Yield a product of the same (single) size or size distribution desired. The usual method of studying the performance of process equipment is set up an ideal operation as a standard, compare the characteristics of the actual equipment with those of the ideal unit and for the difference between the two. When this method is applied to crushing and grinding the difference is too great.

Part of the theory deals with the single particle comminution that means with the microprocesses of reducing the size of a singe particle. The results are hardly applicable for the real processes in a crusher or mill since there are particles collections whose particles are influencing each other, numbers of interactions between machine parts are of statistical character. Therefore these are hard limitations for the theoretical calculations of size reduction.

Unlike an ideal crusher or grinder an actual unit does, not yield uniform product, whether the feed is uniformly sized or not. The product always consist of mixtures of particles ranging from a Prepared and Organized by: Belachew Zegale

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definite maximum size to very small particles some machines (grinder) are designed to control the largest particle, but the fine sizes are not under control. In some fines are minimized but not eliminated.

Compression forces are used to fracture friable or crystalline solids, combined impact and shearing forces are required for fibrous materials, and shearing forces are used for fine grinding of softer materials. Moisture content may significantly affect the energy used and the type of force required eg conditioning of wheat. Too high a moisture content can lead to agglomeration of particles which block the mill. Various equations have been developed to calculate the energy required to reduce the size of particles which will be discussed in this section later on.

Since a unit area of solid has a definite amount of surface energy, the creation of new surface requires work, which is supplied by release of energy of stress when the particle breaks. By conservation of energy all energy of stress in excess of new surface energy must appear as heat.

The Grindability index of a mineral can be determined by the drop weigh method or by the Hard grove method. In the drop weigh method a standard weigh, m (normally 3,5 kg) is allowed to fall freely on a given mass of the feed rock from a given height h (usually 0,787m or 31 inches) The specific surface of the crushed product and that of the feed are determined by screen analysis . Since the energy input is mgh multiplied by the number of falls of the weigh, the increase in surface is plotted against the number of drops or directly against the energy input.

CRUSHING EFFICIENCY The energy efficiency of a crushing equipment can be thus defined in two ways, such as the overall energy efficiency (energy required to create new surface over total energy supplied) and theoretical energy effectiveness (energy required to create new surface over energy supplied minus that required to run empty mill)

The ratio of surface energy created by crushing to the energy absorbed by the solid is the crushing efficiency ηc. If es is surface energy per unit area, in meters times Newton force per Prepared and Organized by: Belachew Zegale

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square meter and Af and Ap are the area per unit mass of the feed and product, respectively, the energy absorbed by unit mass of the material Wn is:

Wn 

es ( Ap  A f )

C

The surface energy created by fracture is small in comparison with the total mechanical energy stored in the material at the time of rupture, and most of latter is converted into heat. Crushing efficiencies are therefore low they have been measured experimentally by estimating es from theory of the solid state, measuring Wn, Ap and Af and substituting in the above equation. The precision of the calculation is poor, primarily because of uncertainty es, but the result do show that efficiency range between 0.06 and 1 percent, in reality 0.1 to 0.2. The energy absorbed by the solid is less than that fed to the machine. Part of the total energy input W is used to overcome friction forces in the bearings and other moving parts and the rest is available for crushing. To for this loss of input energy, the term ηm (mechanical efficiency) is used. Then if W is the energy input.

W

Wn

m



es ( Ap  A f )

 m n

If m is the feed rate, the power required by the machine will be:

P  mW 

mes ( Ap  A f )

 m n

According to the law of conservation of energy, conversion of all losses must appear as heat. The significance of these losses may be illustrated by the fact that about 6% of electric power produced in this world is used for crushing and grinding. Calculation of AP and AF D s 

6 , s Asp  p

6 Asp  Ds  s Zegale p Prepared and Organized by: Belachew

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Ds - Volume surface mean diameter Asp - Specific surface area

 s - Sphericity

P  mW 

m6es

 m n  p

(

1 1  ) s Dp s D f

EMPERICAL RELATIONSHIPS KICK”S LAW

In 1885 Kick proposed another law based on stress analysis of plastic deformation within the elastic limit, which states that, the energy required to produce analogous changes of configuration of geometrically similar bodies varies as the volumes or masses of these bodies. If a particle is only deformed so that only its configuration or surface area is altered, then the above statement remains to be true. However, in comminution where the number of particles increases due to breakage of large particles and new surface are created, the above statement ceases to be applicable. The modified law that can be applied to crushing stated that the work required for crushing a given quantity of material is constant for a given reduction ratio irrespective of original size. Df P  K k ln , where Kk - is Kick's constant. m Dp

Thus, according to this law, commmiution energy depends only on the reduction ratio and is independent of the original size of the feed. This itself speaks for its limitation. It is obviously Prepared and Organized by: Belachew Zegale

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ridiculous to say that the energy required for reducing a 100mm particle to 50mm size will be the same as that required for reducing 1mm to 0.5mm. In fact, higher amount of energy is required for reducing fine particles to still finer size than for breaking down large piece of rock. Kick‘s law can be applied without much error to coarse crushing where the feed size is quit large and the reduction ratio is quite low. A generalized relation for both cases is a differential equation.

RITTINGER'S LAWS

According to the law proposed by Rittinger in 1867 states that the work required in crushing is proportional to the new surface created. This law, which is really no more than hypothesis, it does not for the mechanical losses (due to friction and inertial) and is equivalent to the statement that the crushing efficiency ηc is constant and for a given machine and feed material, is independent of the sizes of the feed and product. If sphericity  p and  f are equal and mechanical efficiency is constant, the various constants in the above equation can be combined into a single constant Kr and Rittinger law will be written as:

P 1 1  Kr (  ) m Dp D f

BOND CRUSHING LAW AND WORK INDEX

Somewhat more realistic method of estimating the power required for crushing and grinding was proposed by Bond in 1952. Bond postulated that the work required to form particle size Dp from very large feed is proportional to the square root of the surface to volume ratio of the product, Sp/Vp where Sp Vp



6V p 6 , s  s Dp Dp S p

Dp - equivalent diameter or normal diameter Sp - surface area of one particle Vp - volume of one particle Prepared and Organized by: Belachew Zegale

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P Kb  m Dp

,

Kb - is a constant that depends on the type of machine and on the material being crushed. This is equivalent to the differential equation with n=1.5 and a feed of infinite size. To use this equation a work index Wi is defined as the gross energy required in kilowatt hours per ton needed to reduce a very large feed to such a size that 80% of the product a 100-mesh screen (0.1mm). This definition leads to a relation between Kb and Wi. If Dp is in millimeters P in kilowatts, and m in ton per hour:

K b  Wi 100  10 3  0.3162Wi

If 80% of the feed es a mesh size of Df millimeters and 80% of the product es a mesh of Dp millimeters it follows from the above two equations that:

P 1  0.3162Wi (  m Dp

1 Df

The work index Wi includes the friction in the crusher, and the power given in this equation is a gross power.

Walker, Lewis, McAdams and Gilliland have combined the above three laws into the form of a differential equation:

dD P d ( )  k ns , where k is constant putting n=1 and integrating from DF to DP we get m Ds D P  k ln F m DP

When n=2 P 1 1  k(  ) m D pb D pa

For all values of n>1 Prepared and Organized by: Belachew Zegale

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P k 1 1  (  ) n 1 n 1 m n  1 D pb D pa

If n=3/2 P 1  k(  m D pb

1 D pa

)

Solution of this equation when n= 1, 3/2 and 2 ... leads to Kick's law, Bonds law and Rittinger's law respectively. Both Kick's law and Rittinger's law have been shown to apply over limited ranges of particle size, provided that Kk and Kr are determined experimentally by tests in a machine of the type to be used and with the material to be crushed. They thus have limited utility and mainly of historical interest.

Table 1 gives a typical work index for some common minerals. These data do not vary greatly for different machines. material

specific gravity

work index Wi

bauxites

2.20

8.78

cement clinker

3.15

13.45

cement raw material

2.67

10.51

Clay

2.51

6.30

Coal

1.4

13.00

Coke

1.31

15.13

granite

2.66

15.13

Gravel

2.66

16.06

gypsum rock

2.69

6.73

iron ore (hematite)

3.53

12.84

lime stone

2.66

12.74

phosphate rock

2.74

9.92

quartz

2.65

13.57

Shale

2.63

15.87

Slate

2.57

14.30


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trap rock

2.87

19.32

For wet grinding multiply the above index by 4/3 Example: What is the power required to crush 200 ton/hour of lime stone if 80% of the feed es a 5cm screen and 80% of the product es a 0.3175 cm screen?

Solution:

From the work index table above work index for limestone is 12.74 m=200ton/hour, Df= 5cm (50mm), Dp = 0.3175cm (3.175mm) the power required is

200  0.3162 12.74(

1 1  )  339.2kw or 454 hp 3.175 50

Since work index has been defined with respect to gross energy, it includes the mechanical losses as well; Bond’s law therefore predicts the gross power consumption in comminution. Its applicability has been found to be best for fine grinders.

3.2.4Equipment for size reduction Modes of operation of size reduction equipment 1. Open circuit reduction-simplest method of operating a mill, product es straight through, no classifying screens, no recycling of oversize, wide size distribution results as some particles through quickly, others stay for some time (also resulting in higher energy consumption) 2.

Free crushing- as with open circuit, but residence time kept to a minimum, often by material falling through action zone under influence of gravity, production of undersize reduced, and lower energy consumption, but large size range

3. Choke feeding- discharge is restricted by inserting a screen in the outlet, so material stays choked in the action zone until reduced to a small enough size, long residence time results in undersize particles and additional energy consumption, useful to prevent oversize, and a large reduction ratio can be achieved


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4. Closed circuit grading- residence time kept short, but classifier system at the outlet separates oversize material and recycles it, more energy efficient, with narrower range of final particle size, additional cost of classifier system 5.

Wet milling- if material can be wet without harm, it may be advantageous to mill it as a slurry with a carrier liquid, often water, eliminates dust problems and allows use of hydraulic separating techniques eg centrifugation, often used where extraction of a soluble component is also required eg maize milling, energy consumption high but tends to produce finer particles.

Types of crushing Equipment 1. Coarse crusher (to produce coarse and fine) The main existing coarse crushers are: Jaw crusher, Gyratory crusher, Roll crusher 2. Grinders (to produce intermediate and fine particles) the main existing equipment are: Hammer mills, impactors, dick mills, -Rolling compression mills such as bowl mills and roller mills, -Attrition mills, -Tumbling mills such as: rod mills, ball mills, pebble mills, tube mills,& compartment mills 3. Ultra-fine grinders: Hammer mills with internal classifications, Fluid energy mills, Agitated mills 4. Cutting machines: Knife cutter, dicers, slicers. Operating principles: In crushers, slow compression will be observed, in grinder’s impact and attrition, some times combined with compression, in ultra-fine grinders in general attrition, in cutting mills cutting action.

Ideal equipment has to full fill the following criteria; -large capacity, -small power required per unit of product and -product of single size or size distribution is desired. The available equipment is only an approach to this ideal particular characteristic of valid (hardness, particle size in product and feed) frequently the combination of different machines and separation processes is applied in order to come to a nearly ideal process.


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Crushers do the heavy work of breaking large pieces of solid materials into small lumps. A primary crusher operates on run-of-mine material, accepting anything that come out of the mine face and breaking it into 150-250 mm lumps. A secondary crusher reduces these lumps to particles perhaps 6mm in size. Grinders reduce crushed feed to powder. The product from an intermediate grinder might a 40-mesh screen; most of the product from a fine grinder would a 200-mesh screen with a 74 μm opening. An ultra-fine grinder accept feed particles no larger than 6mm the product size is typically 1 to 50 μm . Cutters give particles of definite size and some times definite shape 2 to 10 mm in length. Jaw crusher (doge type) - is usually for crushing of hard and intermediate hard substances. The maximum of original lump size for individual performance is at most 1m, the reduction ratio of the size of feed to the size of product is; nr =5....9 Jaw crushers jaws are usually made of brittle materials like chilled iron and lined with manganese steel to protect abrasion. The speed of operation varies from 100 to 400 strokes per minute and maximum convergent faces of the reciprocating crusher at the point of with the feed rock is normally around 300. The maximum distance between the crushing surface gaps is said to be, close-set when the jaws are close to one another and open set when apart from one another. Gyratory crusher has two crushing faces one fixed and the second moving. The fixed have concave shape and mounted on external frame conical crushing head executes gyratory motion. Capacity of gyrator crusher is 2.5 times that of jaw crusher for the same feed and material, same gap and same product size range, the power requirement being essentially the same. Jaw crusher due to its low initial cost preferred for small capacity installation. According to Taggart if T / G 2  0.115 Jaw crusher is to be used T-capacity ton/hr, G-gap in inches, for T / G 2  0.115 gyratory crusher is used. Empirical formula to determine capacity of jaw and

gyratory crusher is: T  93.0( LS )

T= capacity (kg/hr), L-length of feed opening, S-maximum width of discharge opening valid for gaps of (10-60)cm. L is measured normal to the gap in jaw crusher and perimeter of the circle with diameter equal to arithmetic average of diameter of the cones.


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Fig. 2.2. Jaw crusher. 1. feed hopper, 2. wedge block 3. Jaw cam block 4. Movable jaw, 5. Adjustment knob, 6. Grease caps, 7. Stationary jaw, 8. Spring rod assembly

The hammer mill - can be applied for grinding of intermediate hard and soft solids (soft coal, crystalline salts, gypsum). Hammer mill carries heavy block of steel in the form of hammers, (individual hammer could weigh as much as 100-150kg) that are hinged or pinned along the periphery of a rotating disk called the rotor that rotates at high rpm in side a sturdy housing. The fineness of the product can be regulated by changing the number or size of hammers and screen opening the reduction ratio is 10 - 15. Reduction is mainly by impact as the hammers drive the material against the grinder plate (shear may also have a role under choke feeding conditions. Final size is largely determined by the size of the retention screen through which discharge material must . It is regarded as general purpose mill, handling crystalline solids, fibrous materials, vegetables matter, sticky materials etc. Due to excessive wear, hammer mills are not recommended for the fine grinding of very hard materials. The capacity of hammer mill can be computed using one the correlation proposed by Taggart. KD 2 LN 2 Q 3.543( RR  1)


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Q-capacity, kg/hr, D-diameter of rotor, m, L-length of rotor, m, N-rpm or rotor, RR-reduction ratio, K an empirical constant and its value varies from 4.0-6.2.

Fig. 2.3. Hammer mill

Crushing rolls (roller mill)- two or more heavy steel cylinders revolve toward each other. An over load compression spring protects the roller surfaces from damage, but hard foreign bodies should be removed. The distance between the surfaces of the rollers is termed the nip. Force applied to the product is mainly compressive, but the use of fluted rollers and/or differential speeds of rotation can also introduce shear forces. Size reduction ratios are normally below five. Volumetric capacity is affected by speed, nip, diameter and length of the rollers. For the limiting case, when the particle is just pulled into the rolls by friction

A tan( )   2


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A a a a a a

Fig. 2.4. A roll mill

Where A = angle of nip (the angle formed by the tangent s to the roll faces at the points of with particle)  = coefficient of friction between the particle and the rolls. The relation ship of required roll diameter, Dr, to diameter of feed particles, Df, and diameter of product particles, Dp, is given by Dr  D p A cos( )  2 Dr  D f

Example: A roll mill is available with rolls of 400mm diameter, and capable of milling to an average product particle diameter of 0.05mm. If the coefficient of friction for the material on the rolls is 0.12, what is the largest average diameter of feed particle which could be fed to the mill? Ans. Since tan (A/2)=  , A/2= tan 1 0.12 and thus A/2=6.840 that is maximum angle of nip is 13.70. Since cos

A Dr  D p  then for 400mm diameter rolls producing an average product 2 Dr  D f

particle diameter of 0.05mm and cos(6.84) 

0.4  0.00005 0.4  D f

0.993  0.40005 /(0.4  D f )

0.4  D f  .40005 / 0.993 D f  0.4029  0.4  0.0029 and so the maximum diameter of feed

material would be 2.9mm Prepared and Organized by: Belachew Zegale

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Attrition mill- mainly utilize shear between a plate and a stationary surface, or between two plates for fine grinding. In a single disc mill the feed stock es between a high speed rotating proved disc and the stationary casing or the mill. In a double disc mill, two discs are required, rotating in opposite directions. The pin disc mill carries pegs or pins which intermesh on the rotation elements, so that impact forces also play a significant part in the size reduction process. In the Buhr mill, originally used in flour milling, the discs (or stones) are horizontal. The feed es through the centre of the upper (stationary) disc, while the lower disc rotated. The material is subjected to shear between the two stones and exits around the periphery.

Fig. 2.5. Attrition mill

The centrifugal mill- is the especial type of high speed mills acting by impacting. It consist of three sledded rotor interacting with a peripheral corrugated crushing ring which is partially designed as screen according to the high speed of the rotor, extreme grades of fineness are obtainable. So the mill is usable for pulverization of soft to intermediate hard substances, like sugar, color pigments, pharmaceuticals, wood, and kind of fibrous materials. The fineness of a product substantially depends on the opening width of the screen and on the rotor speed.


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Fig. 2.6. Centrifugal mill Ball mills and Rod mills- a rotating (tumbling) or vibrating chamber is filled with steel balls or rods. Feed material is subjected to impact and shear due to the movement of the ball or rods. Shear predominates at low speeds, while impact becomes more important at higher speeds (if speed is too high, balls can be carried around the periphery and grinding ceases). A variation is the use of a vibrating rather than rotating chamber. The speed at which centrifuge just start’s is a critical speed; at critical speed the centrifugal force is equal to the gravitational force.

Fig. 2.7. Ball mills and Rod mills

given as,


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D- diameter of mill, d- diameter of ball, in practice 50-90% of is used.

The cutting mills - where specially designed for processing thermoplastic syrup, but they are also applicable for reduction of cork, cellulose, fabric, leather, etc. the mill consisting of housing in which a cutting rotor with knives, is rotating. The grinded products fall through a screen which, partially encloses, the rotor? The mesh size of this screen essentially influences the particle size of product. To minimize the energy demand to meet particle size requirements combinations of different machines are often useful (so called closed circuit grinding)


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3.3.

Agglomeration

Introduction One of the first difficulties met by anyone attempting to give a survey of agglomeration is to define the term agglomeration comparing with other like granulation, size enlargement, balling, pelletization, tabletting, compaction, flocking, sintering etc. By usage these often include subsequent processing stages such as drying or firing in the overall application on the term. In the broadest sense of the term agglomeration includes all processes in which fine particles, dispersed in either gas or liquid, aggregate to form a coarser product. The collection of particles that results is called an agglomerate or granule. Depending on the process, the size of the agglomerate is between 0.02 Prepared and Organized by: Belachew Zegale

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and 50 mm. In most cases, the preferred particle shape is spherical. In many processes the product is a cylindrical section such as a tablet or some other regular geometrical shape. Agglomeration is used in many industries, such as fertilizer production, iron ore, nuclear fuel, pulverized fuel ash, ceramics, lightweight aggregate production, carbon blacks, catalysts, food powders such as instant coffee and milk powder, pesticides and pharmaceutical products. Agglomeration has been a key technology in traditional engineering fields. At the same time agglomeration is now a key technology also in new developing hitech industries. There are other reasons for the production and use of agglomerates: 1. Plant contamination and nuisance dusts in the workplace are reduced. 2. Hygiene is easier to maintain. 3. Air quality is easier to achieve and in some cases controls can be avoided. 4. The danger of dust explosions is reduced 5. With the increase in air and water pollution control regulations there is a need to install dust and sludge removal equipment. As a result, there is a need to process and dispose of the resulting fines. With agglomeration processes, perhaps with the addition of a binder, dust and sludge can be recycled or disposed of without pollution. 6. There are many problems in the handling of fine particles. The flow properties and consequently dosage control are poor. Agglomeration can eliminate these disadvantages while retaining the desired particulate properties. 7. The chemical industry, with countless intermediate and final products, has a great need for agglomeration technology. Some examples are the agglomeration of simple or complex fertilizers to avoid segregation, agglomeration of fillers used in plastics, to add exact amounts of iron oxide, zinc oxide, stearate or silicate to the molten plastic, production of dust free products, especially these with toxic or corrosive materials. Size enlargement increases the commercial value because of the improved physical properties. A typical example is detergent. Some materials, such as fertilizers, pigments, pesticides and instant foods, are sold in agglomerated form, but instantly decompose when added to liquids. 8. Ore beneficiation produces a large number of finely grained products. Examples are flotation concentrates from selective beneficiation processes, dusty products from roasting, blast furnace


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byproducts, filter cakes and particulates from dust removal equipment. Ores or ore mixtures must be agglomerated for smelting to obtain optimal flow conditions in the roasting process. 9. In addition, agglomeration can cause a delayed action, which is important for pharmaceutical and agricultural applications. This allows good dosage or improves

the

appearance of the product.

Binding Mechanisms and Adhesion Forces A good understanding of the interaction (bonding) between particles in an assembly is fundamental to size enlargement processes. In addition, bonding is important in determining the final properties of the product such as the ability to withstand handling during further processing, its rate of dissolution or reactivity, its density, etc. Attractive forces can be calculated for model systems, such as smooth, fixed, ideal spheres. Even though the values calculated for these models apply only crudely for real systems, they do indicate the effects of important parameters and the agglomeration process. Models are essential for the understanding of the size enlargement process. To calculate the actual attractive forces between real particles is not currently possible because of their irregular shape and usually rough surfaces. The following are among the types of bonding between particles that help agglomeration take place. (1) Mechanical interlocking. This can occur particularly if the particles are long and thin in shape, in which case large masses may become completely interlocked. (2) Surface attraction. Surface forces, including van der Waals’ forces, may give rise to substantial bonds between particles, particularly where particles are very fine (<10 μm), with the result that their surface per unit volume is high. In general, freshly formed surface, such as that resulting from particle fracture, gives rise to high surface forces (3) Plastic

welding. When irregular particles are in , the forces between the particles will be

borne on extremely small surfaces and the very high pressures developed may give rise to plastic welding.


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(4) Electrostatic attraction. Particles may become charged as they are fed into equipment and significant electrostatic charges may be built up, particularly on fine solids.

(5) Effect of moisture. Moisture may have two effects. Firstly, it will tend to collect near the points of between particles and give rise to surface tension effects. Secondly, it may dissolve a little of the solid, which then acts as a bonding agent on subsequent evaporation.

(6) Temperature fluctuations give rise to changes in particle structure and to greater cohesiveness

3.3.1. Agglomeration processes The desired product properties determine which enlargement process is used. Agglomeration processes are classified by the principal mechanism by which the particles are made to come together. The selection of a specific process is only possible if the clearly defines the properties required of the product. Growth Agglomeration (Agitation Methods) Fine particles are brought into with each other in a flowing system or in air when the concentration is higher. This is usually done in the presence of liquid and binders. The particle size enlargement occurs by coalescence or accregation (snowballing) based on capillary forces. In a few exceptional cases, the major cohesive force is the van der Waals force. Usually the agglomerates are spherical with diameters between 0.5 and 20 mm. Typical equipment types are inclined drums, cones, pans, paddle mixers and plowshare mixers. Spray Agglomeration (Spray Methods) This is one of the most commonly used methods in the chemical, pharmaceutical, and food industries. Pumpable suspensions are atomized and the liquid is evaporated from the droplets by means of hot air, as a preliminary drying step. The first cohesive forces are the capillary forces, which are followed by crystal bridges at the points. The agglomerates are 20 - 500 mm. For chemical applications, throughputs of up to 50 t/h are possible. Selective Agglomeration (Spherical Agglomeration) The most recent agglomeration process, a second immiscible phase is added to the Suspension. This Prepared and Organized by: Belachew Zegale

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wets the solid phase and binds the particles together by means of capillary forces. As a results, rounded flocs or agglomerates form with diameters up to 5 mm. Selective agglomeration can be achieved for mixtures of solids. It is currently being studied for many substances. Pressure Agglomeration (Pressure Methods, Compaction) Particles with only slight amounts of moisture are formed in tablets and briquettes in stamp presses, tablet presses and roller presses. The principal binding force is van der Waals attraction. The agglomerates have uniform shapes and range in size from a few millimeters (pharmaceutical tablets) to decimeter size (fuels). In the case of smooth rollers, the resulting flakes are broken up into the desired size. Sintering (Thermal Methods) Fine particles are made into a paste by adding moisture and then processed in a horizontal sintering oven into sinter (burnt agglomerates). This is especially common in the mining and preparative industries. The final sintered product usually has an irregular shape and is usually coarser than other agglomerates. The mechanism of binding is the formation of solid bridges at the points. Sintering plants have throughputs up to 1000 t/h. Example of agglomeration process by steam jet agglomeration mechanism In a jet agglomeration plant, freely moving, wetted particles collide with each other to form agglomerates.


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The device consists of a vertical shaft or pipe with a solids dispenser on top and one or more steam nozzles near the top If the particles are water soluble, wetting them leads to the development of viscous liquid layers that absorb kinetic energy during particle collisions as shown in the figure below.

Provided that the kinetic energy is dissipated completely, the particles agglomerate. The viscous layers also provide binding forces through liquid bridges forming after a collision. The lower part of the pipe serves as drying zone with, for example, warm air flowing upwards countercurrent to the particles. The drying zone may be followed by a device for post treatment, for example a fluidized bed dryer. The substance to be agglomerated is fed to the device as a dry powder, consisting of single particles and aggregates of primary particles bound by van der Waals or electrostatic forces.

Chapter five 5. Mechanical and Hydro-mechanical separations 5.1.

Screening or Sieving

Sieves or screens are used on a large scale for the separation of particles according to their sizes, and on a small scale for the production of closely graded materials in carrying out size analyses. The method is applicable for particles of a size as small as about 50 μm, but not for very fine materials because of the Prepared and Organized by: Belachew Zegale

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difficulty of producing accurately woven fine gauze of sufficient strength, and the fact that the screens become clogged. Woven wire cloth is generally used for fine sizes and perforated plates for the larger meshes. Some large industrial screens are formed either from a series of parallel rods or from H-shaped links bolted together, though square or circular openings are more usual. Screens may be operated on both a wet and a dry basis. With coarse solids the screen surface may be continuously washed by means of a flowing stream of water which tends to keep the particles apart, to remove the finer particles from the surface of larger particles and to keep the screen free of adhering materials. Fine screens are normally operated wet, with the solids fed continuously as a suspension. Concentrated suspensions, particularly when flocculated, have high effective viscosities and frequently exhibit shear-thinning nonNewtonian characteristics. By maintaining a high cross-flow velocity over the surface of the screen, or by rapid vibration, the apparent viscosity of the suspension may be reduced and the screening rate substantially increased.

Mechanically operated screens are vibrated by means of an electromagnetic device as shown in Figure 1.40, or mechanically as shown in Figure 1.41. In the former case the screen itself is vibrated, and in the latter, the whole assembly. Because very rapid accelerations and retardations are produced, the power consumption and the wear on the bearings are high. These screens are sometimes mounted in a multideck fashion with


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Figure 1.40. Hummer electromagnetic screen the coarsest screen on top, either horizontally or inclined at angles up to 45◦. With the horizontal machine, the vibratory motion fulfils the additional function of moving the particles across the screen. The screen area which is required for a given operation cannot be predicted without testing the material under similar conditions on a small plant. In particular, the tendency of the material to clog the screening surface can only be determined experimentally.


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Figure 1.41. Tyrock mechanical screen A very large mechanically operated screen is the trommel, shown in Figure 1.42, which consists of a slowly rotating perforated cylinder with its axis at a slight angle to the horizontal. The material to be screened is fed in at the top and gradually moves down the screen and es over apertures of gradually increasing size, with the result that all the material has to over the finest screen. There is therefore a tendency for blockage of the apertures by the large material and for oversize particles to be forced through. Further, the relatively fragile fine screen is subjected to the abrasive action of the large particles.


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Figure 1.42. Trommel

Screen Analysis (see Smith)

5.2.

Sedimentation

Principle of separation Mechanics of particle motion through fluids Three forces acting on a particle moving through a fluid: 1. The external force, gravitational or centrifugal; 2. The buoyant force, which acts parallel with the external force but in the opposite direction; 3. The drag force, which appears whenever there is relative motion between the particle and the fluid Drag: the force in the direction of flow exerted by the fluid on the solid is called drag.

Equations for one-dimensional motion of particle through fluid Consider a particle of mass m moving through a fluid under the action of an external force Fe. Let the velocity of the particle relative to the fluid be u, let the buoyant force on the particle be Fb and let the drag be FD, then

(5.1) The external force can be expressed as a product of the mass and the acceleration ae of the particle from this force, (5.2) Prepared and Organized by: Belachew Zegale

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Mechanical Unit Operation Lecture Note The buoyant force is, be Archimedes’ law, the product of the mass of the fluid displaced by the particle and the acceleration from the external force. The volume of the particle is m/ p, the mass of fluid displaced is (m/p) , where  is the density of the fluid. The buoyant force is then Fb = m ae/p

(5.3)

The drag force is FD = CDu2 Ap/2

(5.4)

Where CD is the drag coefficient, Ap is the projected area of the particle in the plane perpendicular to the flow direction. By substituting the forces into Eq(1), we have

(5.5) Motion from gravitational force: In this case, ae = g

(5.6) Motion in a centrifugal field: ae = r 2

(5.7) In this equation, u is the velocity of the particle relative to the fluid and is directed outwardly along a radius. Terminal velocity

In gravitational settling, g is constant. Also, the drag always increases with velocity. The acceleration decreases with time and approaches zero. The particle quickly reaches a constant velocity, which is the maximum attainable under the circumstances. This maximum settling velocity is called terminal velocity.

(5.8)

(5.9) Prepared and Organized by: Belachew Zegale

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In motion from a centrifugal force, the velocity depends on the radius and the acceleration is not constant if the particle is in motion with respect to the fluid. In many practical use of centrifugal force, du/dt is small. If du/dt is neglected, then

(5.10)

Motion of spherical particles: If the particles are spheres of diameter Dp, then m =  Dp3 p/6 Ap =  Dp2/4 Substitution of m and Ap into the equation for ut gives the equation for gravity settling of spheres:

(5.11)

Drag coefficient Drag coefficient is a function of Reynolds number. The drag curve applies only under restricted conditions: I. The particle must be a solid sphere; II. The particle must be far from other particles and the vessel wall so that the flow pattern around the particle is not distorted; III. It must be moving at its terminal velocity with respect to the fluid.


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Figure 5.1. CD versus Re for spherical particles

Particle Reynolds number:

(5.12) u: velocity of approaching stream Dp: diameter of the particle  : density of fluid  : viscosity of fluid Stokes’ law applies for particle Reynolds number less than 1.0 CD = 24/NRe,p

(5.13)

From Eq(4)


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Mechanical Unit Operation Lecture Note FD = 3  ut Dp

(5.14)

From Eq(11)

gD p (  p   ) 2

ut 

18

(5.15)

At NRe,p =1, CD =26.5 instead of 24 from the above equation. Centrifugal: r 2  g. For 1000 < NRe,p <200,000, use Newton’s law CD = 0.44 FD= 0.055 Dp2 ut2

(5.16) (5.17)

(5.18) Newton’s law applies to fairly large particles falling in gases or low viscosity fluids Terminal velocity can be found by trial and error after guessing NRe,p to get an initial estimate of CD.

Criterion for settling regime

To identify the range in which the motion of the particle lies, the velocity term is eliminated from the Reynolds number by substituting ut from Stokes’ law

(5.19) If Stokes’ law is to apply, NRe,p <1.0. Let us introduce a convenient criterion K

(5.20) Prepared and Organized by: Belachew Zegale

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Then NRe,p = K3/18. Setting NRe,p = 1 and solving for K gives K=2.6. If K is less than 2.6 then Stokes’ law applies. Substitution for ut using Newton’s law NRe,p = 1.75K1.5 Setting, NRe,p = 1000 and solving for K gives K = 68.9. Setting NRe,p = 200,000 and solving for K gives K =2,360. 

Stokes’ law range: K < 2.6



Newton’s law range: 68.9 < K < 2,360



when K > 2,360 or 2.6 < K < 68.9, ut is found from,

, Using a value of CD found by trial from the curve

Separation of sizes by free settling: Separation of materials by difference in density

If there are particles of two different materials but of the same size, and if the shape of the particles of the two materials is not greatly different, eqn(3.11) may be written for each material u ta 

u tb 

Dividing

4 g (  pa   ) D p 3C Da 

4 g (  pb   ) D p 3C Db 

(  pa   )C Db u ta   pb   C Da u tb

If the drag coefficients are constant (eg. for a turbulent region);


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(  pa   ) u ta   pb    u tb

5.21

Figure 5.2 Separation of two materials by differences in rate of settling

Suppose a mixture of a and b particles of the size range indicated by MN is considered. It is seen that the slowest (and smallest) particles of a is faster than the fastest and (largest) particles of b; hence all materials of a will settle faster than all material b, and separation is possible. On the other hand consider a mixture of a and b particles of size range RS. Here it is apparent that the slowest a particle (of diameter R) is considerably slower than the faster b particle (of diameter S) and every particle of a in the size range RS’ has the same velocity as a larger particle of b in the size range R’S. Thus, there are three fractions possible: a fraction consisting entirely of b, every particle of which is in size range RR’; a fraction consisting of entirely of a, every particle of which is in the size range S’S; and an intermediate mixed fraction of a and b particles, the a particles of which are in the size range RS’, and the particles in the range R’S.

Equal settling velocities;

ut 

4 g  pa   D pa 3C Da 



4 g (  pb   ) D pb 3C Db 

For completely turbulent region; Prepared and Organized by: Belachew Zegale

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Da  pb    Db  pa  

5.22

Eqn(5.22) Can be used ton calculate R’ an S’ from R, S, and densities of the two materials. The ratio of the diameters of the particles of a and b settling at equal rates is a constant, depending only on the densities of the materials and the separating fluid. Thus, the ratio of S and S’ is the same as that of R’ to R or of S” to R”.

Hindered settling In hindered settling, the velocity gradients around each particle are affected by the presence of nearby particles. So the normal drag correlations do not apply. Also, the particles in settling displace liquid, which flows upward and make the particle velocity relative to the fluid greater than the absolute settling velocity. For uniform suspension, the settling velocity us can be estimated from the terminal velocity for an isolated particle using the empirical equation of Maude and Whitmore us = ut( )n

5.23

Exponent n changes from about 4.6 in the Stokes’ law range to about 2.5 in the Newton’s law region. For very small particles, the calculated ratio us/ut is 0.62 for  =0.9 and 0.095 for  =0.6. With large particles, the corresponding ratios are us/ut = 0.77 and 0.28; the hindered settling effect is not as profound because the boundary layer thickness is a smaller fraction of the particle size.

If particles of a given size are falling through a suspension of much finer solids, the terminal velocity of the larger particles should be calculated using the density and viscosity of the fine suspension. The MaudeWhitmore equation may then be used to estimate the settling velocity with  taken as the volume fraction of the fine suspension, not the total void fraction.

Suspensions of very fine sand in water is used in separating coal from heavy minerals and the density of the suspension is adjusted to a value slightly greater than that of coal to make the coal particles rise to the surface, while the mineral particles sink to the bottom. CLASSIFICATIONOF SETTEBLE SOLIDS


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The type of sedimentation encountered in process technology will be greatly affected not only by the obvious factors- particle size, liquid viscosity, and solid and solution densities- but by the characteristics of the particles wit in the slurry. Discrete particles (>20m in diameter)- particles that have a little tendency to cohere Flocculent particles (<20m in diameter) - present in a dispersed state owing to surface charges.  To remove relatively coarse particles, which have reasonable settling velocities, gravity classification under free or hindered settling is satisfactory  To remove fine particles settling velocities are too low, and for practicable operation the particles must be agglomerated or flocculated, in to large particles that do posses a reasonable settling speed. Low concentration Particulate settling Regime

Zone settling Regime High concentration

Compression regime

Degree of particle coherence Totally discrete Particles

Extremely flocculants particles

Figure 5.3 Combined effect of particle coherence and solid concentration of a suspension.

Sedimentation testThe process of settling is best described by batch-settling tests in glass cylinders. Fig 3.4 gives a series of observations of such tests.


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Figure 5.4 Batch sedimentation

 Figure 5.4 (a)- shows a cylinder containing the uniformly mixed suspension.  Figure 5.4 (b)- Layer D-settled solids ,Layer C- transition zone. The boundary between C and D is usually obscure and is marked by vertical channels through which water is escaping from they lower layers which are under compression. Layer B-pulp at original concentration, Layer AClear water. The boundary between layers A&B is usually sharp.  As thickening progress, layers Band C ultimately disappears, but layer D may shrink further because of compression.

-

Laboratory batch-settling tests are the basis for the design of continuous thickener.  In the operation of a continuous thickener the conditions are similar except for one feature. In batch settling, conditions and zone boundaries vary with time. In continuous settling a steady state is setup, in which there are the same zones as in batch settling, but their position and concentration are constant with time.

Application of Batch settling test to design a continuous thickener  The capacity of a continuous thickener is determined by the fact that the solids initially present in the feed must be able to settle through all zones of slurry concentration, from that the initial feed to that of the underflow, at the rate equal to that at which they are introduced in to the thickener. If the area provided is not sufficient the solids will build up through the settling zone and in to the clarification zone until finally some solids are discharged in the overflow.


Page 48


Figure 5.5. Diagram of continuous thickener showing relation to Figure 5.4.

Figure 5.6. Solid concentration in a continuous thickener

Coe and Clevenger assumptions (the earliest method) I. The settling rate was a function only of the solids concentration expressed as volume of solids per unit volume of slurry. II. If batch settling tests were run at different initial pulp concentration, the essential characteristics of the solid (degree of flocculation, for one) were an changed

The kynch theory (recent method) Basic assumptions; Prepared and Organized by: Belachew Zegale

Page 49

Mechanical Unit Operation Lecture Note 

Employs the first assumption from Coe and Clevenger assumptions



Particle concentration is constant across any horizontal layer



Wall effects can be ignored



There is no differential settling of particles as a result of differences in shape, size or cfomposition



The initial concentration is either uniform or increases towards the bottom of the suspension, and



The sedimentation velocity tends to zero as the concentration approaches a limiting value corresponding to that of the sediment layer deposited at the bottom of the vessel

 This method is based on a mathematical analysis of batch settling rate, and the concentration of the zone that limits capacity, can be determined from a single batch settling test (for a given pulp and temperature of operation)  If the solids-handling capacity per unit area is lowest at some intermediate concentration (mostly zone C), a zone of such concentration must start building up, since the rate at which solids inter this zone will be less than the rate at which they will leave this zone. It has been shown that the rate of upward propagation of such zone is constant and is a function of the solids concentration.

vc

dv v dc

5.24

Where:

v =Upward velocity of propagation of concentration zone of minimum settling rate with respect to vessel. v

=settling velocity of solids in concentration zone minimum settling rate with respect to vessel.

c

=concentration of solids, weight of solids/ volume of pulp

From the assumption that the settling rate is a function only of the solids concentration, i.e. that v  f (c) ,  v  cf ' (c)  f (c)

5.25

Plotting of settling rate vs concentration graph from batch sedimentation test Suppose that Co and Zo represent the initial concentration and height, respectively, of a pulp in a batch settling test.


Page 50


1. Consider the test at the instant of time when the layer corresponding to the limiting settling rate has reached the interface between the clear supernatant liquid and the pulp (A-B interface). 2. Plot height (the boundary between zone A and B) vs time graph.(ZL vs tL)

Figure 5.7. Determinations of settling velocities from Bach-settling curve 

Sedimentation test will give a different curve for every precipitate and a somewhat different one for different concentration.

Figure 5.8. Settling curves for different concentration Prepared and Organized by: Belachew Zegale

Page 51


3. Perform the material balance for the interface solid at the instant time and initial condition C L A(v L  v l )t L  C o AZ O , and

,vL 

CO Z O  CL  Z L  vLt L

ZL tL

3.26



4. The value of the settling velocity v L is the slope of the tangent to the curve A at t=tL , this tangent intersects the vertical axis at Z=Zi , since vL 

Zi  Z L 0  tL

 Z i  Z L  t L vL

5.27

Combining equation 3.26 and 3.27, gives

CLZi=CoZo

5.28

vL values

vL1

vL2

vL3

vL4

vL5

 Equation

CL values

CL1

CL2

CL3

CL4

CL5

3.28

states that Zi is the height of uniform slurry of concentration CL which contains the same amount of solids as the initial slurry.

 The settling velocity as a function of concentration developed from a single settling test by using the above relationships. So, the respecting settling rates for the corresponding concentration is determined.

Determination of thickener area  In the case of continuous thickener, the area required determined by that concentration layer for which the solids - handling capacity, expressed as weight of solids per (unit area) unit time), is a minimum Prepared and Organized by: Belachew Zegale

Page 52


 The material valance for the thickener CO-the concentration of feed slurry (mass/volume) C u -Under flow concentration (mass /volume)

F- Feed rate (volume/time) V-over flow rate (volume/time) L-under flow rate (volume/time)  Volume of solid entering thickener per unit time =FCO  Since no solids leaves in the overflow,  FC O  LC u

,

L

FC O CU

5.29

 From a balance for the liquid F (1  C O )  L(1  CU )  V  F (1  C O ) 

FC O 1 1 (1  CU )  FC O (  ) V CU C O CU

5.30

If the cross- sectional area of the thickener be denoted by A, then 

V FC O 1 1  (  ) A A C O CU

*

5.31

V -Is the upward velocity off the clarification zone A  When the thickener is operated at capacity the lowest settling rate encountered must be equal to or greater than this value, otherwise some solids will leave in the overflow. Consequently

V may be A

represented by v.  Further more equation 5.31 may be written in of the concentration of the layer which limits the capacity rather than in of the feed concentration and rate which is set by this capacity; i.e. Prepared and Organized by: Belachew Zegale

Page 53

Mechanical Unit Operation Lecture Note FC O  L L C L

and ,

LC L v  1 1 A  C L CU

5.32

 In other way Equation 5.32 can carefully be rearranged in of the mass ratio of liquid to solid in the feed (Y) and the corresponding value (U) in the Underflow.

Y 

1 CL  S

and U   

1 CU  S

5.33

Then

CL 

1  1     S  Y   

CU 

1  1     S  U   

and

LC L v  A  s (Y  U )

5.34

 By using the settling velocity- concentration curve to obtain corresponding values of v and CL or Y, and using this values in equation 5.32 or 5.34, various values of

LC L , which represents the solids- handling A

capacity per unit area, may be calculated. The lowest value calculated is to be used in determining the area of the thickener.


Page 54


3.3. Gravity Sedimentation Equipments 1. The Thickener

Figure 5.9 Gravity thickener  The thickener is the industrial plant in which the concentration of a suspension is increased by sedimentation, with the formation of clear liquid. Thickeners may operate as batch or continuous units, and consist of tanks from which the clear liquid is taken off at the top and the thickened liquid at the bottom.  Continuous thickeners are used in most applications in which large quantities of solids must be concentrated or removed from large volumes of solid-liquid slurries. Prepared and Organized by: Belachew Zegale

Page 55

Mechanical Unit Operation Lecture Note  Components of a thickener 

A tank to contain a slurry



Feed piping a feed well to allow the feed stream to enter the tank



A rotating rake mechanism to assist in moving the concentrated solids to the withdrawal points



An underflow solid withdrawal system



An overflow launder

 Basic types of continuous thickener 

Conventional thickener



High rate thickener

 Conventional thickeners The conventional thickener can be used with or without flocculants, depending on the application. If employed, flocculants are normally added to the feed launder or in the feed well, and flocculation occurs in resulting turbulence.  High-rate thickeners They are designed to maximize the flocculation efficiency of flocculants. They differ from conventional thickener in feed-well design, size, and control. Unlike conventional units, high-rate thickeners must use flocculants. High- rate thickeners feed wells are designed to it the flocculated slurry into the settling zone of the thickener without destruction of the newly formed floccules.

2. The Clarifiers

 Continuous clarifiers generally employed with dilute suspensions, principally industrial-process streams and domestic industrial wastes, and their primary purpose is to produce a relatively clear overflow.  They are basically identical to thickeners in design and layout except that they employ a mechanism of lighter construction and a drive head with a lower torque capability. These differences are permitted because in clarification applications the thickened pulp produced is smaller in volume and appreciably lower in suspended- solids concentration owing to the large percentage of relatively fine (smaller than


Page 56


10-m) solids. The installed cost of a clarifier therefore is approximately 5 to 10% less than that of a thickener of equal tank size.  Types of clarifiers 

Rectangular clarifiers



Circular clarifiers



Tilted plate clarifiers



Solid- clarifiers

5.3.

Filtration

5.3.1. Definition and Classification Filtration is the removal of solid particles from a fluid by ing the fluid through a filtering medium, or septum, on which the solids are deposited. The fluid may be liquid or gas, the valuable stream from the filter may be fluid, or the solid, or both. Sometimes it is neither, as when waste solid must be separated from waste liquid prior to disposal.

Figure 5.10 Principle of Filtration Filters are divided into three main groups: cake filters, clarifying filters, and cross flow filters. 

Cake filters separate relatively large amount of solids as a cake of crystals or sludge. Often they include provisions for washing the cake and for removing some of the liquid from the solids before discharge. At the start of filtration in a cake filter, some solid particles enter the pores of the medium and are immobilized, Prepared and Organized by: Belachew Zegale

Page 57


but soon others begin to collect on the septum surface. After this brief period the cake of solids does the filtration, not the septum; a visible cake of appreciable thickness builds up on the surface and must be periodically removed. 

Clarifying filters remove small amount of solids to produce a clean gas or a sparkling clear liquid such as beverage. The solid particles are trapped inside the filter medium or on its external surfaces. Clarifying filters differ from screens in that the pores of the filter medium are much larger in diameter than the particles to be removed.



In a cross flows filter, the feed suspension flows under pressure at a fairly high velocity across the filter medium. A thin layer of solids may form on the surface of the medium, but the high liquid velocity keeps the layer from building up. The filter medium is a ceramic, metal, or polymer membrane with pores small enough to exclude most of suspended particles. Some of the liquid es through the medium as clear filtrate, leaving a more concentrated suspension behind.

5.3.2. Filter media and filter aids Filter media The septum in any filter must meet the following requirements: 1. It must retain the solids to be filtered, giving reasonably clear filtrate. 2. It must not plug or blind. 3. It must be resistant chemically and strong enough physically to withstand the process conditions. 4. It must permit the cake formed to discharge cleanly and completely. 5. It must not be prohibitively expensive.

In industrial filtration a common filter medium is canvas cloth, either duck or twill weave. Many different weights and pattern of weave available for different services. Corrosive liquids require the use of other filter media, such as woolen cloth, metal cloth of Monel or stainless steel, glass cloth or paper. Synthetic fabrics like nylon, polypropylene, saran, and Dacron are also highly resistant chemically. Filter -aid and precoating


Page 58


Filter-aid (sometimes also called Body-aid) and precoating are often mentioned in connection with pressure filtration and the difference in their application is: 

Filter-aid is used when the slurry is low in solids content with fine and slimy particles that are difficult to filter. To enhance filtration coarse solids with large surface area are added to the slurry and serve as a body-aid that captures and traps in its interstices the slow filtering particles and produce a porous cake matrix. The amount added depends on the nature of the solids and varies from ½ for non-compressible and up to 5 times for gelatinous solids.

Precoating the plates with a 2-3 mm thick medium of a known permeability and its application requires skills since it takes-up effective cake volume, lengthens the cycle time and an over consumption can be quite costly.

Precoating prior to filtration serves two main purposes: o When the contaminants are gelatinous and sticky it forms a barrier that avoids cloth blinding. Likewise the interface between the precoat and the cloth parts readily so the cake discharges leaving a clean cloth. o When a clear filtrate is required immediately after the filtration cycle commences otherwise recirculation must be employed until a clear filtrate is obtained. The following materials serve as Filter-aid or are used to form a precoat: 

Diatomaceous Earth (also called Diatomite) consisting of silicaceous skeletal remains of tiny aquatic unicellular plants.



Perlite consisting of glassy crushed and heat-expanded rock from volcanic origin.



Cellulose consisting of fibrous lightweight and ashless paper like medium.



Special ground wood is becoming popular in recent years since it is combustible and reduces the high cost of disposal. There are nowadays manufacturers that grind, wash and classify special timber to permeabilities, which can suit a wide range of applications.



All the materials above are produced to specification in a controlled process. However, for applications that do not require high quality any other solid that is readily available and has similar properties may be used as body-aid.


Page 59


5.3.3. The Theory of Filtration Principles of cake filtration From the stand point of fluid mechanics a filter is a flow device. By means of a pressure difference applied between the slurry inlet and the filtrate outlet, filtrate is forced through the equipment. The filtrate es through three kinds of resistance in series: 1. Resistance of the channels conducting the slurry to the upstream face of the cake and the filtrate away from the filter medium. 2. Resistance of the cake. 3. Resistance associated with the filter medium. During the washing of the filter cake the wash water flows through the same resistances that were encountered by the filtrate, although the magnitude of the cake resistance is not the same in both cases. Basis for Filtration calculations Distribution of Overall Pressure Drop

Since the resistance of the channels can be neglected, the overall pressure drop at any time is the sum of the pressure drops over the medium and cake. If pa is the inlet pressure, pb is the outlet pressure and p' the pressure at the boundary between cake and medium,  p  p a  p b   p a  p'   p' p b   p c  p m

5.35

Where: -p = overall pressure drop -pc=pressure drop over cake -pm=pressure drop over medium Consistent with its usual definition,  represents the outlet condition -the inlet condition. Therefore p equals p a  p b and is inherently negative. Pressure drop through filter cake


Page 60


Figure 5.11. Section through filter medium and cake at a definite time t from the start of the flow of the filtrate, showing pressure gradients: p, fluid pressure; ps stress pressure; L, distance from filter medium, Lc thickness of the cake measured from the filter medium. A, the filter area measured perpendicularly to the direction of flow.

Mass Balance

An over all material balances: Mass of slurry= mass of cake + mass of filtrate or

mc mc   V s sc

5.36

Where mc is the total mass of dry cake, V is the filtrate volume, s and sc are, respectively, the mass fraction and average mass fraction of solids in the slurry and cake, and  is the density of the filtrate. Solving for mc yields,


Page 61


mc 

Vs 1 s

 cV

5.37

sc

Where c is the mass of particles deposited in the filter per unit volume of filtrate

In of the concentration of the solids in the slurry cs (mass of solid per unit volume of liquid fed to the filter) and mass of wet cake, including filtrate retained in the voids, mF,

c

cs m c 1   F  1 s  mc 

5.38

The cake thickness L can be related to the cake mass mc by, mc   s (1   ) AL

where s is the true density of the solid and  is the average porosity of the cake. Combining the two mc equations produces L

c V  c LV  c A(1   )

5.39

Where cL is the ratio of cake thickness L to the filtrate volume V. The thickness L is in fact the primary parameter related to filter design. Spacing of leaves, frame thickness, and minimum cake thickness for removal from vacuum drum filters all depend on a knowledge of L.

Rate Equations 

In cake filters, the particles forming the cake are small and the flow through the bed is slow. Streamline conditions are invariably obtained.



As starting point for treating the pressure drop through a cake and for laminar flow



dp  dL

 Sp k1 u (1   ) 2  v  p

   

3


5.40 Page 62


Where :

dp - pressure gradient at thickness L. dL

 - Viscosity of filtrate u-linear velocity of the filtrate Sp-surface area of a single particle Vp-volume of a single particle

 - Porosity of a cake k1-constant For random packed particles of definite size and shape, k1=4.167 The linear velocity u is give by 4.7 Where V is the volume of filtrate, which has ed in time t, and A is the total cross-sectional area of the filter cake. Since the filtrate must through the entire cake,

V is the same for all layers and u is independent of L. A

The mass dm of solids in the layer is dm   p 1   AdL

 Sp k1 u (1   ) v  p   dp  3  p A

   

4.8

dm

For incompressible sludge,  is taken as a constant.

 Sp  k  u ( 1   ) 1 p v  p   dp  3  p A pa

   mc 

 Sp k1 u (1   ) v  p p a  p'  3  p A

   

'

 dm 0

mc  p c


4.9

Page 63


mc=- the total mass of solids in the cake

The variation in resistance of a cake from layer to layer is the result of mechanical effects in the cake. The fluid pressure in the filter cake is a maximum at the up stream face and a minimum at the filter medium. Q. Why the porosity of the cake minimum at the filter medium?

A. The stream of the filtrate flowing past the particle imparts a drag force on the particle tending to move it in the direction of the medium. This drag is resisted by an equal and opposite force from the particles ahead of the particles under consideration. The particle is also acted upon by forces from those immediately upstream from it self. Since each layer of solids, starting from the upstream face of the cake transmits its drag force act cumulatively through the bed and each layer is acted only by a force equal to the sum of the drags of all layers between itself and the upstream face of the cake. Each layer transmits this cumulative drag, augmented by its own drag, to the next layer. These cumulative forces can be converted to pressure by dividing them by A. Such pressures are called stress pressures, ps. With respect to the cake cross section, ps is zero at the cake-slurry interface and reaches its maximum at the cakemedium interface.

The fluid pressure at a given point acts equally in all directions, but the stress pressure acts in a direction parallel with that of flow and tends to squeeze the particles and flatten them.

Figure 4.3. Distortion of particle by stress pressure Prepared and Organized by: Belachew Zegale

Page 64


Specific cake resistance,1 The cumulative drag at the layer a distance L from the filter medium equal pa-p', the fluid pressure drop in the portion of the cake from the upstream face to the plate at L. It fallows that k1, Sp/vp , and  each depends on pap' only and that they vary through out the cake.



 Sp k 1 (1   ) v  p

p

   

4.10

3

 p a  p'  p c 

umc A

4.11

Physically,  is the pressure drop required to give unit velocity of filtrate flow when the viscosity is unity and the cake contains one unit mass of solid per unit area. The dimension of  is LM-1 For incompressible sludge  is independent of the pressure drop. Filter media resistance. Rm2 By analogy with equation p' p b  p m   u Rm Rm

4.12

The dimension of Rm is L-1. Factors controlling the magnitude of Rm 

Pressure drop



Flow rate

mc   s (1   ) LA ALR m Rm R 2   m Filter media resistance also expressed in of equivalent cake thickness, l  mc   s 1    r 1

In Coulson and Richardson’s, CHEMICAL ENGINEERING, VOL 2 it is noted by r,


r

Page 65


Age of the filter medium

From eqn (4.11) and (4.12)

m     p  p c  p m  u c  Rm   A 

4.13

Strictly, the cake resistance  is a function of  p c rather than of p . During the important stage of the filtration, when the cake is of appreciable thickness,  p m is smaller in comparison with  p c , and the effect on the magnitude of  of caring the integration of eqn(4.9) and (4.10) over a range of  p instead of  p c can be safely ignored. In eqn (4.13), then  is taken as a function of p .

Substituting and

4.14

mc=Vc 

  cV dt    Rm   dV A p   A 

4.15

Types of Filtration When the outlet pressure is constant, the pressure drop is controlled by varying the inlet pressure. Constant pressure filtration  The pressure drop is constant; the flow rate is a maximum at the start of the filtration and decreases continuously to the end. Constant rate filtration


Page 66

Mechanical Unit Operation Lecture Note  The pressure drop is varied, usually is kept is small at the start of the filtration and then increased either continuously or in steps, and is a maximum at the end of the filtration, the flow rate constant by continuously increasing the inlet pressure.

Constant Pressure Filtration: p Is constant t



 dt  0

V  c V    VdV  R m  dV   A p   A 0 0 



 c  V  2      Rm  V    t  p   2  A   A  



4.16

Where V is the total volume of filtrate collected to time t, assuming time is counted from the instant the first drop is obtained. Determination of constants,  and Rm 

For a definite pressure drops data of V vs t from an experimental run at that pressure drop are needed.



Linearization of eqn.(4.15) dt  K PV  B dV c KP  2 A (p ) Rm  B A p 



Calculate the quantity

4.17,4.18,4.19

t for any two successive observation, where t is the time between observations V

and V is the increment of filtrate collected over time period t . 

Plot a graph of the arithmetic mean of each of two successive observations of V against

t for the same V

pairs of reading. Prepared and Organized by: Belachew Zegale

Page 67


Obtain the slope of the graph (line), which is the value for Kp, and the ordinate intercept is B.



When Kp and B are known,  and Rm are then calculated.

Empirical equation for cake resistance By conducting constant pressure experiment at various pressure drops, the variation of  and p may be found. If  is independent of p , the sludge is incompressible, ordinarily  increases with  p , as most sludge are at least to some extent compressible. For highly compressible sludge, Kp increases rapidly with  p .

    o  p  

 o and s are empirical constants



s -is compressibility coefficient of the cake.

s

4.20

It is zero for incompressible sludge and positive for compressible ones. It usually falls between 0.2 and 0.8. This equation should not be used in a range of pressure drops much different from that used in the experiments conducted to evaluate  o and s. Continuous Filtration In a continuous filter, say of the rotary drum type, the feed, the filtrate and cake move at steady constant rates. For any particular element of the filter surface, however, conditions are not steady but transient. It is evident that the process consists of several steps in series - cake formation, washing, drying and scraping- and that each step involves progressive and continual change in conditions. The pressure drop across the filter during cake formation is, however, held constant. In continuous filtration the filter medium resistance is often negligible in comparison with the resistance of the cake.


Page 68


dt  K PV dV t

V

0

0

 dt  K p  VdV

4.21

K PV 2 t 2

Where t is the time required for formation of the cake, and it is always less than the total cycle time tc; the relationship is

t  ft c

4.22

Where f is the fraction of the cycle available for cake formation. In a rotating drum filter f equals the fractional submergence of the drum in the slurry. 1

V  2 p  ft c  2   A  c 

4.23

Dividing both sides by tc gives the average rate of filtrate flow per unit area

1

 2 p  f  2 V  Rate    At c  ct c 

4.24

If the specific cake resistance varies with pressure drop

 2 p 1 s V  At c  c o t c

1

f 2  

4.25

When the filter medium resistance is too large to be ignored: becomes


Page 69


1    R m  2  R m   2c  p  f  t c  t c  tc    V    At c  c     

4.26

Eqn (4.25) and (4.26) apply both to continuous vacuum filters and to continuous pressure filters.

Constant rate filtration If filtrate flows at a constant rate, the linear velocity u is constant and



V At

4.27

Eqn (4.11) can be written after substituting mc and u 

 p c





c  V 

2

  t  A

4.28

If  is substituted from eqn (4.20) in eqn (4.28), and if  p  p m  is substituted for  p c , the result is

 p c 

1 s

2

V  1 s   o ct     p  p m   At 

4.29

The simplest method of correcting the overall pressure drop through the filter medium is to assume the filter medium resistance is constant during a constant- rate filtration.

The constants  p m ,  o and s can be evaluated by the fallowing method from measurement of t vs.  p since the only variables in eqn (4.29) are  p and t, the equation can be written as: Prepared and Organized by: Belachew Zegale

Page 70


 p  pm 1s  K r t

4.30

Where Kr is defined by K r  u 2 c o

4.31

Taking logarithm of both sides

log t  1  s  log  p  p m   log K r

4.32

If  p  p m  is plotted on logarithmic paper as the abscissa against t as the ordinate, a straight line should be obtained, the slope of which is 1-s, since the actual data are the overall pressure drop  p and the time t, the pressure drop  p m is not known and must be estimated. A tentative magnitude for  p m can be found by plotting t vs.  p on rectangular coordinates. ing a smooth curve through the points, and extrapolating the curve to the pressure axis, where t=0. A tentative result for  p m is thus found, which can be used for preparing a plot of  p  p m  vs. t on logarithmic coordinates. If the line so obtained is straight, the tentative value of  p m can be taken as a final. If the line is curved, additional approximations for  p m can be made until a straight line is achieved. The factor Kr is calculated by using eqn (4.32), and  o is then evaluated by means of eqn (4.31). Washing Filter Cakes When the wash liquid is miscible with the filtrate and has similar physical properties, the rate of washing at the same pressure difference will be about the same as the final rate of filtration.

Washing can be regarded as taking place in two stages. First, filtrate is displaced from the filter cake by wash liquid during the period of displacement washing; and in this way up to 90% of the filtrate may be removed. During the second stage, differential washing, solvent diffused in to the wash liquid from the less accessible voids and the following relation applies:


Page 71


Volume of wash liquid ed Initial concentration of solute  a cons tan t  log Cake thickness concentration at particular time


Page 72


4.1.3. Filtration Equipments

I. Pressure Filters 

Pressure Filters, with the exception of the Rotary Drum Pressure Filter, are semi-continuous type machines that enter a wash and cake discharge mode at the end of the filtration cycle. The filtration cycle may extend from 5-10 minutes on cake filtration applications and up to 8 or even more hours for the polishing of liquids. Since the operation is in batches, that are usually fed from and discharged to a continuous process, a surge tank is required upstream the filter and batch collection of cake downstream the filter. The collection of filtrate depends on the operating mode of the filter which can be constant flow rate, constant pressure or both with pressure rising and flow rate reducing as for a centrifugal pump.



Most Pressure Filters are batch operated but continuous filters are also available. However, owing to the difficulty in removing the cake they are mechanically complex and expensive so mainly applied in fine chemical processes where the added value to the product is high. There are two constraining factors that determine the duration of the filtration cycle: 

For cake filtration it is the volume available for cake build-up and once the volume is filled the cycle must terminate even if the permissible pressure was not reached.



For polishing, or when the solids are fast blinding, the cycle must terminate once the permissible pressure has been reached regardless of cake thickness.



The filtration rate is influenced, in broad , by the properties of the slurry. The trend is that the rate goes up with increased pressure, coarser particles, particle distribution with high uniformity, non-slimy or nongelatinous solids, non-compressible cakes, lower liquid viscosity and higher temperatures.

The Types of Pressure Filters


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Pressure Filter

Batch Enclosed

Continuous

Open

Vertical leaves

Automatic Filter press

Pressure Drum

Horizontal plates

Recessed plates

Nutche

Plate and frame

Autoclaved

Candle Bag

Figure 4.4 Classifications of Pressure filters The sizes for standard equipment are as follows: 

Filter Press up to 1000 m2 and 20 m3 cake.



Horizontal Plate Filter up to 60 m2 and 4 m3 cake capacity.



Vertical Leaf Filter up to 100 m2 and 7 m3 cake capacity in vertical pressure vessels and up to 300 m2 and 20 m3 cake capacity in horizontal vessels.



Nutsche Filter up to 16 m2 and 8 m3 cake capacity.



Automatic Filter up to 120 m2.



Candle Filter up to 120m2.

The block diagram for a typical filter station and its components may look like this: 

The pressure filter



Slurry feed tank



Slurry feed pump



Mother filtrate collection tank



Wash filtrate collection tank



Cake discharge hopper



Piping and instrumentation


Page 74


The advantages and disadvantages of pressure filtration compared to other separation methods are:

Advantages 

Cakes are obtained with very low moisture content.



Cakes may be disposed and flattened in layers provided they are not thixotropic and sufficiently stable to a tractor.



Intensive soluble recovery or removal of contaminants from the cake may be achieved.



Clean filtrates may be produced by recirculating the filtrate for 1-2 minutes or by precoating if a clear filtrate is required right from the start.



Solutions may be polished to a high degree of clarity.



Except for Filterpresses a gas tight construction may be provided.



Except for Filterpresses it is possible to jacket the tanks with steam if heat preservation is required. This is of particular importance for saturated brines.



The filter bodies and internals may be constructed from a wide variety of alloys including synthetic materials for filterpresses.



Pressure Filters are available in a wide level of automation from labor intensive operator controlled up to fully automatic machines. Disadvantages



Cloth washing is difficult and if the solids are sticky a 3 mm precoat from diatomite or perlite is required. This adds another step prior to filtration and if not done carefully and a too thin precoat is formed it may Prepared and Organized by: Belachew Zegale

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leave areas with exposed cloth which will blind rapidly. Conversely, if a too thick precoat is formed since the operator seeks to be on the safe side, such a precoat consumes effective cake volume. 

The operator can hardly see the forming cake and is unable to carry out an inspection while the filter is in operation.



The internals are difficult to clean and this may be a problem with food grade applications.

1. The Filter press

1.Feed Conn. 2.Filtrate Conn. 3.Head 4.Follower 5.Plate 6.Filter Cloth 7.Cake 8.Filtrate

Figure 4.5 Filter press 

The Filter press consists of a head and follower that contain in between a pack of vertical rectangular plates.



Each plate is dressed with filter cloth on both sides and, once pressed together; they form a series of chambers that depend on the number of plates. The entire pack of plates is ed by side or overhead beams.



The head serves as a fixed end to which the feed and filtrate pipes are connected and the follower moves along the beams and presses the plates together during the filtration cycle by a hydraulic or mechanical mechanism. The plates have generally a centered feed port that es through the entire length of the filter press so that all the chambers of the plate pack are connected together. Likewise, four corner ports connect all the plates and collect the mother and wash filtrates in a "closed discharge" towards outlets that are located on the same side as the feed inlet. Some filter presses have plates that are fitted with cocks at their Prepared and Organized by: Belachew Zegale

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lower side so that the filtrate flows in an "open discharge" to a trough and serve as "tell tales" on the condition of the filter cloth by the clarity of the filtrate that es through each chamber. The disadvantage of this arrangement is that it cannot be used with filtrates that are toxic, flammable or volatile.

Often special measures are taken to ease cake discharge and enhance filtration. The measures are: 

Precoating



Addition of Body Aid

Precoating the plates prior to introducing the feed is done only in the following cases: 

When the contaminants are gelatinous and sticky it forms a barrier that avoids cloth blinding. Likewise the interface between the precoat and the cloth departs readily so the cake discharges leaving a clean clothe.



When a clear filtrate is required immediately after the filtration cycle commences otherwise recirculation must be employed until a clear filtrate is obtained.

Selection criteria Filter presses are best selected in the following instances: 

When very low moisture content is required for thermal cake drying or incineration.



When high filtrate clarity is required for polishing applications.



When good cake release assisted by squeezing is required.



When the cake is disposed as landfill for spreading with a bulldozer provided it is hard enough to carry its weight.



When large filtration areas are required in a limited space.

They should be selected with care: 

When filtering saturated brines since the plates cool-off during cake discharge and require preheating prior to feeding the process slurry. For such brines autoclaved filters such as Horizontal plates, Vertical leaf or Candle filter are better suited as they can be steam jacketed.



When there is a risk of environmental hazard from toxic, flammable or volatile cakes when the plates are opened for discharge at the end of each cycle. Again, the autoclaved filters are better suited. Prepared and Organized by: Belachew Zegale

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When efficient washing is required since with a chamber filled with cake the wash water may not reach its entire surface causing an uneven displacement. This, however, should present no problem when a gap is left between the formed cakes within a chamber so that the wash water is distributed evenly over the cake and reaches its entire surface.

2. The Horizontal Plate Pressure Filter 

Horizontal Plate Pressure Filters were commonly applied to the fine chemical process industries such as antibiotics, pesticides or pigments when the load of impure insoluble is low and polishing is required to obtain high product clarity. However, in recent years they may be seen more and more in heavier industries such as fertilizers or precious metals when the product is the cake and efficient washing and low moistures are required.

1.Slurry Inlet 2.Filtrate Outlet 3.Cake Outlet 4.Air Vent 5.Cake Scrapers 6.Filtering Plates 7.Scavange Plates 8.Sight Glass 9.Drive Shaft 10.Hydraulic Drive

Figure 4.6 Horizontal Plate Pressure Filter 

The slurry is fed under pressure into the vessel and the cake, which is retained by the filter medium, forms on the top of each plate whilst the filtrate es through the hollow shaft further to the process. Prepared and Organized by: Belachew Zegale

Page 78


The Plates 

Each circular plate in the stack is constructed with radial ribs that are welded to the bottom and a horizontal coarse mesh screen which is covered with a finer woven metal screen or filter cloth to retain the cake. The bottom of the plate slopes towards the hollow central shaft, which lets the filtrate flow freely through circumferential holes and further, down the shaft to the filtrate outlet.



The clearance between the plates is maintained by special spacers with "o" rings to positively seal between the slurry that surrounds the plates and the shaft that collects the filtrate. The height of the spacers determines the clearance for cake build-up and may be replaced to meet various process conditions.



One of the obvious differences between polishing and cake filtration is the space between the plates. For polishing applications the clearances are about 20 mm as opposed to cake filtration applications where, depending on the percentage of solids and cake build-up properties, clearances may reach 100 mm. Hence, polishing filters accommodate more plates than cake filters so for the same vessel size more effective area is available with polishers.

Operational sequence  Precoating  Filtration  Heel removal  Cake drying  Cake discharge

Selection Criteria Horizontal Plate Filters are best selected in the following instances: 

When minimum floor space for large filtration areas is required.



When the liquids are volatile and may not be subjected to vacuum. Prepared and Organized by: Belachew Zegale

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When there is a risk of environmental hazard from toxic, flammable or volatile cakes specially secured discharge mechanisms may be incorporated.






When handling saturated brines that require elevated temperatures the tank may be steam jacketed.



When efficient washing is required.



When the cake is heavy and must be ed as opposed to a Vertical leaf filters where the cake forms on a vertical surface and may fall-off once the pressure drops.



When the cake may be discharged either dry or as a thickened slurry.


When the cake does not discharge readily accessing the filter medium between the plates for washing is difficult.



When coarse mesh screens are used the filtration step must be preceded with a precoat to retain cakes with fine particles. Precoating with a thin layer of diatomite or perlite is not a simple operation and should be avoided whenever possible. Advantages



The removal of the plate stack on bottom driven filters is simpler than on top driven machines since on the later the entire drive has to be removed to allow access to the stack.



Plates with the screens mounted on the topside, as opposed to two sided plates, provide good for the forming cake and therefore are always used on applications with thick and heavy cakes.

Disadvantages 

High headroom is required for dismantling the entire plate stack.



The bearing of top and bottom driven filters, that s the rotating plate stack and its sealing, is complex since it has to withstand the internal pressure and the side forces imposed by the mechanical drive. However, side loads on some machines are eliminated by the use of hydraulic motors.



The emptying of the vessel in between cake filtration, washing and drying requires close monitoring of the pressure inside the vessel to ensure that the cake holds on to the candles.

3. The Vertical Pressure Leaf Filter 

Vertical Pressure Leaf Filters are quite similar to the Horizontal plate filters except for the orientation of the filter elements, which are vertical rather than horizontal. They are applied for the polishing slurries with very low solids content of 1-5% or for cake filtration with a solids concentration of 20-25%. Prepared and Organized by: Belachew Zegale

Page 80


Just like the Horizontal plate filters the Vertical Leaf Filters are also very well suited for handling flammable, toxic and corrosive materials since they are autoclaved and designed for hazardous environments when high pressure and safe operation are required. Likewise, they may be readily jacketed for applications whenever hot or cold temperatures are to be preserved. These features are not possible on Filterpress, which require the opening of plates to the atmosphere and shifting them one by one to allow cake discharge at the end of each cycle.

1.Slurry Feed 2.Filtrate 3.Leaf 4.Screen 5.Spacer


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Figure 4.7 Vertical Pressure Leaf Filter

The Leaves 

The slurry is pumped under pressure into a vessel that is fitted with a stack of vertical leaves that serve as filter elements. Each leaf has a centrally located neck at its bottom, which is inserted into a manifold that collects the filtrate. The leaf is constructed with ribs on both sides to allow free flow of filtrate towards the neck and is covered with coarse mesh screens that the finer woven metal screens or filter cloth that retain the cake.



The space between the leaves may vary from 30-100 mm depending on the cake formation properties and the ability of the vacuum to hold a thick and heavy cake to the vertical leaf surface. The space is set by the filtrate necks of the leaves at the bottom end and with spacers at the top end brackets.

The Vessel There are two types of vessel configuration: 

Vertical vessels



Horizontal vessels


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In most of the fine chemicals processes the leaves are fitted into vertical vessels whilst horizontal vessels are used in the heavier process industries such as the preparation of sulfur in phosphoric acid plants. The leaves inside horizontal tanks may be positioned either along the tank axis or perpendicular to the axis. In order to utilize the tank volume for maximum filtration area the width of the leaves is graduated so they fit to the circular contour of the tank. This also reduces the slurry heel volume that surrounds the leaves. The vessels are fitted with highly secured cake discharge openings to ensure safe sealing of the tank under pressure. The cake that accumulates on the leaves may be discharged as a wet thickened sludge or as a dry cake. For wet cakes the vessel will normally have a small outlet that is fitted with a valve whilst for dry cakes the opening is large and the closure locks up electrically or hydraulically with a bayonet wedge. The head cover of vertical vessels is often pivoted so that it is swung away to allow the upward removal of the leaves in the stack. It is good practice to design a special rig that will a leaf that is removed from the vessel. Special quick opening bolts are fitted around the cover so that tightness is secured during operation but enable easy opening when access to the stack is required.

Operational sequence  Precoating  Filtration  Heel removal  Cake drying  Cake discharge

Selection Criteria Vertical Leaf Filters are best selected in the following instances: 




When the liquids are volatile and may not be subjected to vacuum.



When there is a risk of environmental hazard from toxic, flammable or volatile cakes specially secured discharge mechanisms may be incorporated. Prepared and Organized by: Belachew Zegale

Page 83










When the cake is thick and heavy and the pressure is not sufficient to hold it on the leaf.



When coarse mesh screens are used the filtration step must be preceded with a precoat to retain cakes with fine particles. Precoating with a thin layer of diatomite or perlite is not a simple operation and should be avoided whenever possible.

Advantages 

The cloth or woven mesh screens that cover the leaves of horizontal tanks may be accessed easily once the stack is pulled out of the vessel. This allows thorough washing of the medium with high impact jets manually in case that the cake bridges between the leaves. On vertical tanks the head cover must be unbolted and removed in order to access the leaf stack.



Mechanically simple since there are no complex sealing glands or bearings.

Disadvantages 

High headroom is required for dismantling the leaves on vertical vessels.



Large floor space is required for discharging the cake on horizontal vessels.





Page 84


1.Feed Inlet 2.Filtrate Outlet 3.Cake Discharge Outlet

4.The Nutsche Pressure Filter

4.Emergency Overflow 5.Cake Wash Manifold 6.Air Vent 7.Reslurry Paddle/Smoothing Arms 8.Cake Spreader/Auger Arms 9.Stirrer Shaft 10.Hydraulic Cylinder for Spreader Arms 11.Hydraulic Cylinder for Reslurry Arms


Page 85


Figure 4.8 Nutsche Pressure Filter 

Nutsche Filters are constructed to perform a multitude of tasks including reaction, filtration, cake washing and thermal drying on a single unit. As such these are very sophisticated machines with tight process control on parameters such as pressure, temperature and pH.



Nutsche Filters are well suited for handling flammable, toxic, corrosive and odor-noxious materials since they are autoclaved and designed for use in hazardous and ex-proof environments when extremely safe operation is required.



Nutsche Filters are available in almost any size with the larger machines for a slurry filling batch of 25 m3 and a cake volume of 10 m3. Such filters have a filtration area of 15 m2 and are suitable for fast filtering slurries that produce readily 0.5 m thick cakes.

The Nutsche in its full configuration consists of four major components: 

The vessel



The filter floor and cloth, woven mesh screen or sintered metal plate medium



The re-slurry arms for cake washing and smoothing



The cake discharge mechanism

Selection Criteria Advantages


Page 86


Nutsche Filters are best selected in the following instances: 

When minimum floor space is required.



When several unit operations upstream and downstream filtration, such as reaction and thermal drying, are required by the process flow scheme.



When there is a risk of environmental hazard from toxic, flammable or volatile cakes.



When handling saturated brines or process conditions require elevated temperatures the vessel, filter floor and paddles may be heated.



When reslurry washing, being more efficient than in-situ displacement washing, is required.



When sharp separation between the mother and wash solutions is required.



When the cake tends to crack smoothing avoids the wash liquid, air or gas purge from by-ing.

Disadvantages They should be selected with care: 

When cakes are slow to form.



When the cake is sticky and does not part readily from the filter medium.



When the process chain is continuous.



When the product deteriorates during long downtime.

Operational sequence 

Filtration



Cake washing



Cake repulping



Pressure drying



Vacuum drying



Cake discharge


Page 87


5. Candle Filter

Figure 4.9 Candle Filter

The Candle Filters are, as all pressure filters, operating on a batch cycle and may be seen in process lines handling titanium dioxide, flue gas, brine clarification, red mud, china clay, fine chemicals and many other applications that require efficient low moisture cake filtration or high degree of polishing.


Page 88


Candle Filters are also used for thickening to produce concentrated flowable slurry by partial removal of the liquid phase as filtrate. This mode of operation is possible since Candle Filters may operate on very short cycle times taking advantage of the high filtration rates whilst the cakes are still thin. One of the features of Candle Filters when used for thickening is their clear filtrate since gravity Thickeners, in analogy; produce overflows, which always contain a certain amount of fine suspended solids.

Another feature of Candle Filters is the cylindrical shape of the elements that retain the formed cake. This shape, opposed to Plate, Leaf or Filterpress, increases the filtration area as cakes grow thicker and compensate to some extent to the decrease in filtration rates.

Candle Filters are very well suited for handling flammable, toxic and corrosive materials since they are autoclaved and designed for hazardous environments when high pressure and safe operation are required. Likewise, they may be readily jacketed for applications whenever hot or cold temperatures are to be preserved. These features are not possible on Filterpress which require the opening of plates to the atmosphere by one to allow cake discharge at the end of each cycle.

Candle Filters are available in all sizes and the larger types may have an area of 200 m2 and contain 250 or more filtering elements installed in a 2.5 to 3.0 meter diameter vessels. The operating pressure range is quite wide but most of the Candle Filters operate at a pressure of 6 bars

The Candle Filter consists of three major components: 

The vessel



The filtering elements



The cake discharge mechanism

All these components may be constructed from exotic materials of construction and heated to meet the process requirements.

Selection Criteria Candle Filters are best selected in the following instances: Prepared and Organized by: Belachew Zegale

Page 89





When the liquids are volatile and may not be subjected to vacuum.



When there is a risk of environmental hazard from toxic, flammable or volatile cakes specially secured discharge mechanisms may be incorporated.











When the cake is thick and heavy and the pressure is not sufficient to hold it on the candle.



When coarse mesh screens are used the filtration step must be preceded with a precoat to retain cakes with fine particles. Precoating with a thin layer of diatomite or perlite is not a simple operation and should be avoided whenever possible.

Advantages 

Excellent cake discharge.



Adapts readily to slurry thickening.



Minimum floor space.



Mechanically simple since there are no complex sealing glands or bearings.

Disadvantages 

High headroom is required for dismantling the filtering elements.





Page 90


II. Vacuum Filters Vacuum filters are simple and reliable machines and therefore have gained wide acceptance in the chemical, food and pharmaceutical industries. The various types of vacuum filters may be grouped as follows:

Figure 4.10 Classifications of Filters There are two concepts in layout design: 

Barometric leg layouts



Floor mounted layouts


Page 91


Figure 4.11 Drum Filter station Layout

The block diagram for a typical filter station and its components may look like this: 

The vacuum filter



One or two vacuum receivers (if separation of mother filtrate from wash filtrate is required)



One or two filtrate pumps (either receiver mounted or connected to the seal tank of a barometric leg)



Vacuum pump (either liquid ring or rotating vanes type)



Piping and instrumentation


Page 92


The advantages and disadvantages of vacuum filtration compared to other separation methods are: Advantages 

Continuous operation (except for a Nutsche filter)



Intensive soluble recovery or removal of contaminants from the cake by counter-current washing (specially on Horizontal Belt, Tilting Pan and Table Filters)



Producing relatively clean filtrates by using a cloudy port or a sedimentation basin (on Horizontal Belt, Tilting Pan and Table Filters)



Polishing of solutions (on a Precoat Filter)



Convenient access to the cake for sampling or operator's activities



Easy control of operating parameters such as cake thickness or wash ratios



Wide variety of materials of construction

Disadvantages 

Higher residual moisture in the cake



Untight construction so it is difficult to contain gases



Difficult to clean (mainly as required for food grade applications)



High power consumption by the vacuum pump

1. The Rotary Drum Filter The Rotary Vacuum Drum Filter belongs to the bottom feed group and is one of the oldest filters applied to the chemical process industry. The filter consists of the following subassemblies:


Page 93


A drum that is ed by a large diameter trunion on the valve end and a bearing on the drive end. The drum face is divided into circumferential sectors each forming a separate vacuum cell. The internal piping that is connected to each sector es through the trunion and ends up with a wear plate having ports that correspond to the number of sectors.

1.Drum 2.Valve 3.Piping 4.Drive 5.Scraper 6.Agitator 7.Tank

Figure 4.12a Rotary Drum Filter


Page 94


Figure 4.12a Flow sheet of Rotary Drum Filter 

A valve with a bridge setting which controls the sequence of the cycle so that each sector is subjected to vacuum, blow and a dead zone. When a sector enters submergence vacuum commences and continues through washing, if required, to a point that it is cut-off and blow takes place to assist in discharging the cake. The drum deck piping is arranged so that each sector has a trailing pipe to collect the filtrate on the rising side of the drum and a leading pipe to collect the remaining filtrate from the descending side to ensure complete evacuation prior to cake discharge. However, in some instances, only leading or trailing pipes are provided and this depends on process requirements



The valve has on certain filters adjustable blocks and on others a fixed bridge ring. Adjustable bridge blocks enable the optimization of form to dry ratio within the filtration cycle as well as the "effective submergence" of the drum when the slurry level in the tank is at the maximum.



A cake discharge mechanism that can be either a scraper, belt, roll and in very rare cases a string discharge. Blow is applied only to filters with scraper and roll discharge mechanisms but not to filters with a belt or string discharge.


Page 95

Mechanical Unit Operation Lecture Note Selection Criteria In broad drum filters are suitable to the following process requirements: 

Slurries with solids that do not tend to settle rapidly and will remain in a uniform suspension under gentle agitation.



Cakes which do not require long drying times to reach asymptotic moisture values.



Cakes when a single washing stage is sufficient to remove residual contaminants from the cake or yield maximum recovery of filtrate.



Filtrates that generally do not require a sharp separation between the mother and wash filtrates. Some complex valves, however, enable atmospheric purging of the sectors and internal piping to facilitate a sharp separation of filtrates.



Filtrates that are acceptable with a low quantity of fines that trough the filter cloth in the first few seconds of cake formation. Broadly, and depending on particle size and cloth permeability, the filtrate may contain 1000 to 5000 ppm insoluble.

Operational sequence 

Cake Formation



Cake washing and drying



Cake discharge



Dead zone


Page 96


Figure 4.13 Filtration cycle zones

2. The Disc Filter The Disc Filters belong to the side feed group and have been around for many years. They are generally used in heavy-duty applications such as the dewatering of iron ore taconite, hematite, coal, aluminum hydrate, copper concentrate, pyrite flotation concentrates and other beneficiation processes. The high time for Disc Filters was in the 60's when the metallurgical industries were booming and filters with 300 m2 and larger were manufactured. The filter consists of several discs, up to 15 in the larger machines, each made up from sectors, which are clamped together to form the disc. The sectors are ribbed towards the neck and designed for a high capacity drainage rate. One of the main features is that the required floor space taken up by disc filters is minimal and the cost per m2 of filtration area is the lowest when compared to other vacuum filters. During operation each sector enters submergence and a cake is formed on the face of the discs. It then emerges to the drying zone; the liquid drains to a central barrel and from there through a valve to the vacuum receiver. The valve with its bridge setting controls the timing so that once the sector leaves the drying zone it moves over a separating bridge and a snap or low pressure blow is applied to discharge the cake. Scraper blades on the side of each disc guide the cake to discharge chutes, which are positioned between adjacent discs and are wide enough to avoid their clogging by the falling cake. A paddle type agitator located at the bottom of the tank maintains the


Page 97


slurry in suspension, which in most of the metallurgical applications contains solids with high specific gravity, which are fast settling and abrasive.

1.Feed Manifold 2.Overflow Box 3.Disc Sectors 4.Barrel and Valve 5.Swing Blades 6.Cake Snap Blow 7.Discharge Chute 8.Agitator 9.Tank 10.Slurry Drain

Figure 4.14 Disc filter

The filter consists of the following subassemblies: 

Discs and sectors, which may be made in injection, molded polypropylene, metal or special redwood.



A center barrel ed by the main bearings and consisting of piped or trapezoidal filtrate ages. The sectors are attached to the barrel through "o" ring sealed connections in a number equal to the number of disc sectors.



A valve with bridges and internal compartments for form and dry under vacuum and cake discharge under pressure with 2-2.5 bar snap or 0.2-0.25 bar constant blow. Most disc filters are fitted with one valve only however two valves are often mounted on both drive and non-drive ends with long barreled filters or when the hydraulic loadings are high.



An agitator with paddles that are positioned between the discs and far enough not to interfere with the forming cake.


Page 98


A tank which, on its discharge side, has separated slurry compartments for the discs and discharge chutes for the blown-off cake. When the solids are of an abrasive nature it is advisable to line the bottom portion of the tank that cradles the agitator with rubber.



Two cake discharge blades on both sides of each disc are suspended from a frame mounted on the tank and serve to deflect and guide the cake to the discharge chutes. On large diameter filters the blades are of the swing type that float to maintain the cake to disc clearance and so allow for the wobble of the turning discs.



An overflow trough that spans across the entire tank length and ensures full submergence of the sectors in the cake formation zone since an exposed sector in the 6 o'clock position will cause immediate loss of vacuum.

Operational Sequence

The operation sequence of a Disc Filter is, except for washing, similar to a drum filter. Let us follow a sector as it es from zone to zone: 

Vacuum commences when the sector is fully submerged in the slurry and the port of the rotating barrel es the dead zone bridge.



The cake forms until the leading edge of the sector emerges from the slurry and drying commences.



The sector continues to dry the cake under vacuum until the port in the rotating barrel fully covers the bridge in the valve that separates the vacuum from the blow compartments.



The port in the barrel es the bridge and opens to constant low-pressure air blow or snap blow and the cake falls off to the discharge chute.



Once the barrel port es the blow opening of the valve the sector enters a dead zone that continues until the port opens to vacuum with the sector fully submerged.

Selection Criteria The main considerations in selecting a Disc Filter are: When they suit an application that meets the following requirements:  The form to dry time ratio is approximately ½ to 1.  No cake washing is required.  The cake parts easily from the cloth. Prepared and Organized by: Belachew Zegale

Page 99

Mechanical Unit Operation Lecture Note  The cloth does not clog. 

When a cloth on one of the sectors tears the entire sector may be replaced within a very short downtime.



The filtration area may be expanded by adding more discs to a barrel that has unused discs.



The Disc Filter provides for maximum area at minimum cost and floor space.


Page 100


4.2. Expression 4.2.1. Expression Theory Expression is the separation of liquid from a two-phase solid liquid system by compression under conditions that permit the liquid to escape while the solid is retained between the compressing surfaces. Expression is distinguished from filtration in that pressure is applied by movement of the retaining walls instead of by pumping the material in to a fixed space. Application 

Employed to separate systems, that are not readily pumpable.



It is also use instead of filtration or as a post filtration operation where a more through removal of liquid from the cake is desired.



In dewatering of paper, expression is competitive with drying.



Far cheaper than the thermal method in water removal



In vegetable oil production.



In the recovery of juice from sugar cane



The use of belt press for the dewatering of sludges and slurries is increasing.

4.2.2. Expression equipments Batch Presses 1. Box press 

The material to be expressed is wrapped in canvas clothes and placed in a series of steel boxes fitting between the fixed and movable heads of a hydraulic press. Each bag lies on a perforated mat over a grid of drainage channels and is covered and enclosed by the next higher box. The series of loaded boxes is compressed as a unit under hydraulic pressure.

2. Platen press 

The platen press is similar to the box press, but the cloth bags are not enclosed on the sides during pressing. The platen or plates are some times cored for heating and usually have gutters to collect the expressed liquid. The whole press may be tilted backward slightly to provide better drainage. This type of press is also built in horizontal form.


Page 101


3. Pot press 

Material to be pressed is enclosed in cylindrical pot, with filter pads or screens beneath and on top, and is compressed by a ram entering from above. The filter medium is flat and covers only the top and the bottom; hence it is not subjected to stretching or tearing as in box or platen presses. Because the material is entirely enclosed, it may be more fluid than in other types of press. In practice a series of pots is used in each press, the bottom of each pot serving as the ram the pot below.

4. Curb press 

In the curb press, material to be expressed is enclosed in a cylinder of wooden slats or beveled steel bars or even of perforated plate.



Compression by ram causes the liquid to escape through the walls of the cylinder and flow to collecting channels at the base.

5. Cage press 

The cage press is similar to the curb press except that the inside of the cylinder has fine longitudinal grooves leading through the cylinder walls to larger drainage channels.

Continuous Presses 1. Screw press 

It consists of a rotating screw fitting closely inside a slotted or perforated curb.



The curb and the screw may be tapered toward the discharge end to increase the pressure on the material. This may also be achieved by varying the pitch on the screw or the diameter of the screw spindle in a uniform cylinder.



The discharge end of the curb is partly closed by an adjustable cone or other device to change the size of the opening and thus to vary the pressure on the material.



Rotation of the screw moves the material forward; and as the pressure increases, liquid is expelled and escapes through the openings in the curb. The operation is continuous, and the labor and other operating costs are lower than the hydraulic pressing. Screw presses both horizontal and vertical designs are available.



This type of equipment extensively used in the vegetable and animal oil industries and is applied to the dewatering of such materials as paper pulp, plastics, synthetic rubber, and garbage.


Page 102


Figure 4.15. Screw press

2. Roller mills 

Used the cane sugar industry, combine a mechanical breaking and crushing action with the application of pressure to express juice. Three- roll mills are common, with to top roll above and between the other two, and pressed against them by hydraulic rams at each end. Material squeezed between the top and first rolls and is then directed by a turn plate in the nip of the top and second rolls for a second rolling.

3. Belt press 

The belt filter press encloses slurry or sludge between two endless moving belts and expresses the liquid under pressure applied by rollers.



They are currently used in the pulp and paper and the mineral industries as well as for the dewatering of many types of municipal and industrial waste sludges.

A dewatering belt filter may include three regions: 

Gravity drainage or straining zone for the removal of free water.



A low-pressure zone, with gradually increasing pressure, to express surface and interstitial water.



A high-pressure zone to continue their actions and perhaps to induce the separation of cellular or bound water.


Page 103


Figure 4.16. Belt Press


Page 104



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