CHN-203 Mechanical Operations Prof. P,P Kundu Department of Chemical Engineering, IT Roorkee 1 Contact Hours: Lod Tr P: 2/2 2. Exarnination Duration (Hrs.): Theory:3 Practical:2 3. Relative Weight: CWS:20 PRS:20 MTE:20 ETE:40 PRE:O 4 Credits:4 5. Objective: To impart Knowledge on particle size analysis, size reduction, separation of solid particles from fluids and flow through porous media.Syllabus of the course: Mechanical Operations, CHN 203 Total Contact Hours : 42 1 6 Particles Size Analysis: Sieve analysis, size distribution, size averaging and equivalence, size estimation in sub-sieve range, Screening, effectiveness of screen. 8 Size Reduction: Theory of crushing and grinding, laws of crushing and grinding, crushing and grinding equipment and their selection. 5 Flow Through Packed Beds and fluidization: Characteristics of packings, flow of a single fluid through a packed bed, problem of channeling and wetting, development of Ergun Equation. 8 Filtration: Flow through filter cake and medium, washing and drying of cake filter aids, selection of filtration equipment, constant rate and constant pressure filtration. 7 Particle Mechanics: Motion of particle in fluid, effect of particle shape, Stoke s law, hindered settling, 6 Sedimentation: Gravity and centrifugal sedimentation, design of sedimentatior tank and continuous thickeners. 8Particle Technology A liquid does not have any definite shape, it takes the shape of the container. But solid particles have specific shape. ‘Thus, handling any solid particle in any chemical process industry, we have to specify both of shape and size of the particle. If the particle conforms itself to any of the standard conligurations such as spherical. cubical, cylindrical, then it 1s easy to define the size of the particle. For example, the size of spherical particle is defined through its diameter, that for a cubical particle is the length of the side. However, many of the particles commonly encountered in industrial practices donot conform to any of these standard configurations. These are irregular shaped particles.Reguk Regular Shaped Particles su Cuboid usand — Three sid height lengths erg rucles of different shapes synthesized by various routesIrregular Shaped Particles = Early method: Obtain projected particle shape by microscopy Equivalont gio diamotor Martins pe Line | diameter bisecting projected area Circle with area equal to projected area of particle Shear = ciameter | {$$ Feret’s diameter | «Parallel tangents | There are limitations in measuring the particle shape through ordinary microscopy. For instance, if the distance between the farthest edges on the particle surface remains the same but the rest of configuration changes, its Ferret’s diameter shall remain unaltered. Thus, such a definition cannot describe the actual size or shape of an irregular particle. The latest system of defining particle size is obtained by its comparison to a standard configuration ‘Thus, the concept of equivalent size or equivalent diameter of irregular shaped particles was developed. _———————————Equivalent Diameter Equivalent diameter is defined as the size of a spherical particle having the same controlling characteristics as the particle under consideration. The controlling characteristics depends on the system and the process in which the particle is involved. For example, for catalyst particles, the surface area is the most controlling parameter. Thus, for defining the size of catalyst particles, the surface area is the most important parameter. So, for catalyst particles, surface diameter is used. This is defined as the diameter of a spherical particle having the same surface area as the particle. If S, 1s the surface area of the particle, then, The gravitational free velocity of a particle in a liquid is very much controlled by the mass of a particle or for a given density, by the volume of a particle. So, for this system, volumetric diameter is important for the measurement of the size of the particle. Volumetric diameter is defined as the diameter of a spherical particle having the same volume as the particle under consideration. Thus, if V, is the volume of the particle, then Or,Equivalent Diameter The dynamics of gas bubbles in a liquid or that of liquid drops in a liquid depend not only on the bubble or drop volume but also on the interfacial tension at gas-liquid or liquid-liquid interface. Thus, both the volume as well as the surface area of the bubble or drop are the controlling parameter. In this case, the bubble size or drop size is defined using the volume -surface diameter or more commonly called Sauter diameter (d.,). This is defined as the diameter of a spherical particle having the same specific surface area (surface area per unit volume) as the particle (bubble or drop) under consideration. = Thus, ml = Ge Where s, 1s the specific surface area (surface area per unit volume) of the particle (bubble or drop) Thus, once the controlling characteristics is specified, we can define the size of any irregular particle * Another particularly popular definition of particle size is the screen size or the screen average dMethods to find particle size for various particle sizing technique: Tat Sam 10am Wn WO nm Sone Tyas Sa TO pe SOs 100 wa Tm Electron Microscopy EM Optical Microscopy om Typical size rang Cuvete centrifuge Host a Capillary Hydrodynamic Fractionation CHOF a Field Flow Fractionation FFF ae | Single Particle Optical Sizing sPos | Electrosensing zone ES EE) Electro acount eA x—=__] GGG Aaueous ana non-aqueous HE svcou http://www.agfa.com/en/agfa-labs/news/FZ_Juelich_chooses_Agfa_Labs_for_PSD.jspshape factor and specific surface ratio + The reciprocal of sphericity is commonly called the shape factor or more precisely, the surface shape factor (shape factor of short fibers used in polymer composites is dependent on the length to diameter, L/D ratio). + Another shape factor, designated as the volume shape factor is sometimes used for calculating the volume of an irregular particle. + The volume of a spherical particle is proportional to the cube of its diameter. By assuming that the same is true for irregular particle, then + The constant of proportionality of the above equation is the volume shape factor. + Another popularly used parameter is the specific surface ratio (n), defined as the ratio of specific surface (surface area per unit mass) of the particle to the specific surface of a spherical particle of the same diameter. + Let the average size of the particle be d,,,, then: wershape factor and specific surface ratio The reciprocal of sphericity is commonly called the shape factor or more precisely, the surface shape factor (shape factor of short fibers used in polymer composites is dependent on the length to diameter, L/D ratio). Another shape factor, designated as the volume shape factor is sometimes used for calculating the volume of an irregular particle. The volume of a spherical particle is proportional to the cube of its diameter. By assuming that the same is true for irregular particle, then 3 Up davg The constant of proportionality of the above equation is the volume shape factor. Another popularly used parameter is the specific surface ratio (n), defined as the ratio of specific surface (surface area per unit mass) of the particle to the specific surface of a spherical particle of the same diameter. + Let the average size of the particle be d,,., then: s n='P (/osdovy) ~~ 1)Screening CHN-203 Mechanical Operation Prof. P. P. Kundu Department of Chemical Engineering, IIT RoorkeeScreening A screen ts called an open container usually cylindrical with uniformly spaced openings at the base It is normally made of wire mesh cloth, the wire diameter and the interspacing between wires being accurately specified The length of clear space between individual wires is called aperture size of the screen Screens are usually designated by their mesh number The mesh number indicates the number of apertures per linear length in inch For example, a screen having 10 square openings per inch may be called a 10 mesh screen and in that case the aperture size of the screen will be 0.1 inch minus the wire diameter. Clearly, higher the mess number, smaller will be the aperture size of the screen As per ASTM, screen is expressed in Number (No), e.g. No 5 screen Whereas, Tyler standard screens are expressed in mess number, e.g mess 5 screen For example, a 200 mesh screen will have very small aperture wic whereas a 20 mesh screen will have a large aperture sizeScreening Indian standard screens follow a different type of designation. For an IS screen, the mesh number is equal to its aperture size expressed to nearest deca-micron (deca-micron = 10 micron = 10° m = 0.01 mm). Thus, an IS screen of mesh number 50 will have an aperture width of 500 microns. The IS method is simple in comparison to the other methods. Standard test screens are usually made of phosphor bronze wires. Brass and mild steel wires are also used. A standard screen interval is always maintained between two successive test screens used in industrial screening like that in a standard sieve shaker. The screen interval is the factor by which the aperture size of a test screen is to be divided to get the aperture size of the next successive test screen. An internationally accepted standard screen interval is (2)'/4, that is 1.189.Methods of Screening = Method of separating particles based on size alone. = The undersized particle — called FINES — pass through the screen opening and the over-sized particles — called TAILS — do not. Materials through single screen: A single screen can make single separation — two fractions. Such a separation is called the unsized fractions, because although either the upper or lower limit of the particle sizes are known as per the single screen used, but the maximum possible limit is not known. Materials through series of screens: In a standard sieve shaker, test screens are stacked one above the other in the ascending order of their aperture size. That is, the top-most screen will have the largest aperture size and the bottom-most screen the smallest. Materials passed through a series of screens of different sizes is separated into sized fractions, that is, fractions in which both the maximum and minimum particle size is known.Screen Errors Although screening one of easiest and most rapid methods of particle separation, it is not at all an accurate method. The probability of a partcile passing through the screen depends very much on the direction or configuration in which the particle approaches the screen This is because for an irregular particle, its surface area exposed to the screen opening is different in different directions. Thus, it is possible that when fed in a particular direction or configuration, the particle may pass through the screen but when fed in another direction, the same particle may be retained by the screen. This induces uncertainties in size analysis as in screening the particle size is measured based on its passage through the screen or its retaining on the screen. To avoid the error in measurement, the test should be conducted three four times until constant results are obtained. The screens should be subjected to type of vibratory, oscillatory, gyratory or rotary motion so that each particle gets chances of approaching the screen in almost all directions or configurations possible.Screen Blinding * The presence of so called “near mesh particles” always causes hindrances in screening operation. Near mesh particles to a screen are those particles having size very close to the aperture size of the screen. * There is the possibility of these particles passing partly through the screen, leading to the clogging or blinding of the screen. * Screen errors are also generated when moist particles are screened. Most particles can stick to the screen surface, causing difficulties in screening. Dry, hard, rounded or cubical grains generally pass through the screen without trouble, but elongated, sticky, flaky or soft particles do not. During screening actions such particles may become wedged into the opening and prevent other particles from passing through. A screen plugged with solid particles is said to be BLINDED.Screening Standard screens range In mesh size from 4 to 400 mesh. But woven motal scroens with openings as small of 1 micrometer are available. Scroens finer than 150 mosh are not used (not economical). Screening material ® Woven wire = Silk ® Plastic cloth = Metal bars = Perforated or slogged metal plates etc Metals used: Steol, Stainless steel, phosphor bronzeScreening Equipment Typical Screen Motions I & Ss McCabe, Smith and Harriot — p986 6' edition + ai = (a) tt) =ah\ & Vibrator, fectanie vibrator (e) FIGURE 30.1 Motions of screens: (a) gyrations in horizontal plane; (6) gyrations in vertical plane; (c) gyrations at ‘one end, shaking at other; (d) shaking; (e) mechanically vibrated; (/) electrically vibrated.Ideal and actual screens Objective of a screen — accept feed containing a mixture of particles of various sizes and separate into two fractions. 4. Under flow - material that passes through the screen 2. Over flow - material that is rejected by the screen to pass. Ideal Screens - sharply separate the feed mixture in such a way that the smallest particle in the overflow would be just greater than the largest particle in the underflow. For such an ideal separation, a cut diameter Dp. is defined — this marks the point of separation between two fractions. Usually D,< is chosen to be equal to the mesh opening of the screen. Actual Screens — do not give a perfect separation, however there is a cut diameter associated with such screens as well.Ideal and actual screens Closest separations are obtained with spherical particles on standard testing screens, but even then there is overlapping between the smallest particles in overflow and largest particles in the underflow. The overlap is pronounced for needlelike or fibrous particles or when particles that tend to aggregate into clusters. Commercial screens usually give poorer separations than standard testing screens of the same mesh opening operating on the same mixture.screen effectiveness The efficiency of an industrial screen depends on two aspects. Firstly, it must separate almost all particles of the desired size from the feed (recovery of desired material). Secondly, the classified product must contain very little number of particles having sizes other than desired size (rejection of undersized material). Therefore, one of the most general method defining or classifying screen effectiveness (Ec) is: E,= (Recovery ) (Rejection) (4.3) If excess fines are not permissible in the product, the oversize is collected as product. If it is desired that the product must contain particles of below a particular size only, then undersize stream shall constitute the final product. meee Desired material in th dl Definition: Recovery = Destredimnacertauln the PrOeUce Desired material in the feed Undersized material in the reject Definition: Rejection = ; Undersized material in the feedMaterial balance over the screen P — Mass flow rate of overflow (or product rate) Yp— Mass fraction of oversized material in overflow (product) 1-yp- Mass fraction of undersized material in overflow F- Mass flow rate of feed (kg/s) Ye—- Mass fraction of oversized material in feed 1-y,;— Mass fraction of undersized material in feed Desired material in the product Desired material in the feed = ee FY Undersized material in the reject Undersized material in the feed _ RG-yr) F(1-yr) Recovery = Rejection = R—- Mass flow rate of underflow Yr— Mass fraction of oversized material in underflow 1-Yp— Mass fraction of undersized material in underflowMaterial balance over screens Material balance on undersized material in the reject, RCL ya) = FO — yr) — PA yp) (4.4) Thus, combining with (4.4), ; : Undersized material in the reject R tf ee JeCO" = “Tndersized material in the feed R(-yr) P(1-yp) = =1- --(4, F(1-yr) F(1-yr) a) = pee eres YP) |Full SP) || Thus, E. = Recovery x Rejection = na [1 () | (4.6) Total material fed on to the screen must leave either as underflow or as over flow F=P+R ----(4.7) Any material (product) in the feed must leave in the two streams — underflow or overflow. Thus, Fy-=Pyp+ Ry -------- (4.8) By replacing the value of R from 4.7 in (4.8), we get: P/e = Or — Yr)/ Op — Yr) ---(4-9) Substituting Eq (4.9) in Eq (4.6), one will get E. in terms of only mass fraction.y) 2) 3) Screen Capacity Capacity of a Screen — Is measured by the mass of material that can be fed per unit time to a unit area of the screen. Capacity and efficiency are opposing factors. For example - for maximum efficiency — capacity must be small. Capacity — controlled by varying feed rate to the screening unit. Efficiency - for a given capacity, depends on nature of screening operation Overall chance of passage of a given under sized particle is a function many parameters — Number of times the particle strikes the screen surface — which depends on the loading. If the screen is overloaded — number of contacts is less. Fraction of the total surface represented by the opening. Ratio of particle diameter to the width of an opening in the screen. Maximum efficiency of a given screen is roughly proportional to the screen opening, D,..pr. P. P. Kundu, Professor, Department of Chemical Engineering IIT RoorkeeParticle Size reduction or Comminution ® Size reduction or communution 1s a unit operation used to create particles of a certain size and shape, to increase the surface area available for chemical reaction or to liberate valuable minerals held within the particles. ® Solids may be broken in many different ways. Commonly used methods are: 1. Compression -- common example- Nutcracker 2. Impact -- common example - Hammer 3. Shear -- Banbury mixer or two roll mill 4. Attrition or rubbing -- File 5. Cutting ortearing ---A pair of scissors = Compressive and impact loads are used for breaking brittle materials like coal and munerals. = Soft rubbery materials are cut into small size by the shear action. = Whereas, fibrous materials like wood and asbestos are disintegrated by exerting tearing loads. » Ina comminution process, the feed rock is crushed into pieces by colliding against the grinding media (such as steel balls, rods etc) or by mutual colliding between particles or by direct collision against the moving parts of the machine.Stressing Mechanism a | 1. Stress applied between two surfaces — at SN wee low velocities — 0.01 to 10 m/s (Crushing + \ \ Attrition). \ Ve = 2. Stress applied at a single solid surface at high velocities — 10 to 200 m/s (Impact facture Figure 124 Stresses applied between two surfaces + Attrition). SO a SS 3. Stress applied by carrier medium — in wet ww grinding to bring about dis-agglomeration or Figure 125. Stresses appliod at a single solid surface breakage. = As the size reduction proceeds, the number of particles increases, thus requiring more number of collisions per unit mass.5 Crushing Operation The capacity of a comminution (crushing) equipment (kg of material handled per unit time) of fixed dimensions will be much less for smaller sizes of particles. The reason is that they have to remain in the crusher for longer time to receive the required number of collisions and thus to achieve the desired degree of size reduction. There is hardly any equipment that is capable of automatically adjusting itself to the varying requirements of contact or collision. In commercial operation, it is desirable to conduct the size reduction process at least in three different stages such as: 4. Coarse size reduction if the feed rock is of size 50 to 250 mm or more (primary crusher). 2. Intermediate size reduction for feed of 25 to 75 mm in size (secondary crusher). 3. Fine size reduction when the feed size is 5 to 15 mm (secondary crusher or more appropriately grinder).[eS Factors Affecting Comminution ss, toughness, crystallinity and The grindability of the feed depends on the hardne! cleavage Hardness of a mineral 1s measured by Moh scale. It denotes the resistance of a material to scr: abrasive character of the muneral and its resis Italso tells about the extent of wear that will Based on Moh scale, materials may be classi atching and is thus a good indicator of the tance to crushing. e caused on the grinding media. fied into three broad categories: 1 Soft materials (Moh hardness= 1-3); example talc, gypsum. 2. Matenals of intermediate har limestone, magnesite, felspar. 3. Hard materials (Moh hardness = quartz. Toughness indicates the impact resistance o brittleness. ness (Moh hardness= 4-6); example: 7 or above); example: diamond, sapphire, the material. It is generally inverse to the But generalization cannot be done as gypsum, horn and i g u 7 some plastics are tough. Whereas, coal is both soft and friable (brittle). , sofas wellas How breaking occurs? The atoms in the crystal are arranged in a de! certain planes in the crystal called cleavage sufficient pressure is applied on the rock, finite, repeating geometric pattern and their planes along which breakage occurs whenFactors Affecting Comminution When the material is broken into segments during comminution, the shape of the segments formed depends on the crystalline structure. For example, galena breaks into cubes, mica into flat scales and magnetite into rounded grains. Fibrous materials like wood and asbestos possess cleavage planes and are thus not crushed and they are to be torn or shredded. The grindability index of a mineral can be obtained by drop weight method. The moisture content in the feed is another important factor in comminution. If the moisture content in the feed is more than 3-4 % (by weight), it forms sticky or pasty mass and tends to clog the screen. Moisture content below 3-4 % is desirable since it acts as a binding agent and helps in preventing loss of fines. Comminution in the presence of large excess of water (50 %) is called wet grinding, which is done to get a slurry or suspension such as paint.Factors Affecting Comminution The reduction ratio (RR) is defined as the ratio of the average size of feed to the average size of product. RR = PF/y, The value of RR for coarse crushers is 3 to 7, whereas for fine grinders, it may be 100. If the comminution process is carried out in such a way that the product is discharged continuously just after its production, then it is called free crushing. The product may be removed either by flow under gravity or by injecting compressed air (pneumatic discharge) or water (hydraulic discharge) or by centrifugal means. Such units have large capacity and prevent formation of excess fines. Conversely, the crusher may be equipped with a feed hopper and kept filled (or choked), so that it does not freely discharge the crushed product. This is called choked feeding. This lowers the capacity of the machine, but employed when a large quantity of fines is desired in the final product.Type of milling circuits Mal ‘s Product Control: residence ima Closed circuit milling: = The material leaving the mill is subjected to some form of classification with oversize being returned to the mill with the feed material. Such system is more flexible Product mean size and size distribution may be controlled, Open circuit milling : Material passes through the mill only once, and the only controllable variable is the residence time of the material, Feed rate governs product size The system is inflexible _ \ fl KS 2 _ ‘Control: residence timo feed to ml % classifier cut so Product,Energy and Power requirements — most important parameter of comminution = Cost of power is a major expense in crushing and grinding and power consumption decides the energy efficiency of the comminution equipment. On reduction of the size of a particle, specific surface area (surface area per unit mass) increases. But, out of the total energy supplied to the equipment, only a small portion is consumed for the creation of new surfaces. The rest is spent or lost to overcome friction (in bearings or other moving parts of the machine) and inertia and for inefficient blows. STAGES DURING SIZE REDUCTION: The feed material is distorted and strained. The work necessary to strain the material is stored temporarily in the solids as mechanical stresses. When additional force is applied to the stressed particles, they are distorted beyond their ultimate strength and suddenly ruptures into fragments and new surface is generated. Ultimate strength is the maximum stress that a material can withstand (without necking -when stretched or pulled) or rapture. = Unit area of a solid has a definite amount of surface energy and creation of new surface requires work, which is supplied by the released stresses when the particle break.The energy absorbed by the solid, W, is less than that fed to the machine. Part of the total energy W is used to overcome friction in bearings and other moving parts, and rest is available for crushing. The ratio of energy absorbed to the energy input is the mechanical efficiency: own Ww wy, = Sluts) 7 n. wy ae lA Aud Ten NnNe If m is the feed rate, the power required by the machine is ne,(A,, —A Pa Win a tess — Ave) By definition . 6 MnTle =z @D v, &,D, Then, _ _Gnite, 1s MaNePp\ PpDy PaDia Volume surface mean diameterEmpirical Relationships: Kick’s law and Rittinger’s law = Kick (1885) proposed a "law," based on stress analysis of plastic deformation within the elastic limit, which states that the work required for crushing a given mass of material is constant for the same reduction ratio, that is, the ratio of the initial particle size to the final particle size. — neo B) sa This leads to the relation —=K,1n ab Kick’s law is applicable to the plastic deformation of solids. According to this law, comminution energy depends only on the reduction ratio and is independent on the original size of the feed. Itindicates that the energy requirement for size reduction for 100 mm to 50 mm and for 1mm to 0.5 mm will be the same. This statement is just ridiculous. Rittinger’s law (1867): Work required in crushing is proportional to the new surface created. This hypothesis is equivalent to the statement that the crushing efficiency is constant for a given machine and feed material. 6e, K,=—s— P 1 1 @ Pig({hb TalPp m Dy, D,, Sphericities of feed and product is same _ _Grite, 1 1 MNP p\ P,Dy, PyDigThe reciprocal of Rittinger’s constant (K,) is called Rittinger’s number. Thus, Rittinger’s number is indicative of the new surface created per unit mechanical energy absorbed by the material being crushed. Its value is usually determined by the drop weight test. In this test, a standard weight, m (normally 3.5 kg) is allowed to fall freely on a given mass of feed rock from a given height h (usually 0.787 m or 31 inch). The specific surface of the crushed product and that of the feed are determined by the screen analysis. Since the energy input is mgh multiplied by the number falls of the weight, the value of Rittinger’s number can be calculated from the Rittinger’s equation. In practice, the increase in surface area of 100 gm of material after 5, 10, 15 and 20 drops are determined and the increase in surface is plotted against the number of drops or directly against the energy input calculated.= Rittinger’s law does not account for the losses due to friction and inertia in the comminution equipment. = Thus, overall energy efficiency =(energy required to create new surface)/(total energy supplied). = Whereas, theoretical effectiveness =(energy required to create new surface)/(total energy supplied minus that required for running the empty mill). = Rittinger’s law is best applicable to coarse and intermediate size reduction. = Generalized relation for Rittinger’s law and Kick’s law =-K— (1) m D’ P —_— a - dD, Putting n= 1, 2 and 3/2 and integrating leads to the Kick’s law, Rittnger's law and Bond’s third law, respectively. = Both Kick's law and Rittinger's law have been shown to apply over limited ranges of particle size, provided K, and K, 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.Factors Affecting Comminution The reduction ratio (RR) is defined as the ratio of the average size of feed to the average size of product. — Of RR = /Dp The value of RR for coarse crushers is 3 to 7, whereas for fine grinders, it may be 100. If the comminution process is carried out in such a way that the product is discharged continuously just after its production, then it is called free crushing. The product may be removed either by flow under gravity or by injecting compressed air (pneumatic discharge) or water (hydraulic discharge) or by centrifugal means. Such units have large capacity and prevent formation of excess fines. Conversely, the crusher may be equipped with a feed hopper and kept filled (or choked), so that it does not freely discharge the crushed product. This is called choked feeding.The energy absorbed by the solid, W, is less than that fed to the machine. Part of the total energy W is used to overcome friction in bearings and other moving parts, and rest is available for crushing. The ratio of energy absorbed to the energy input is the mechanical efficiency: W, Ie = wy, = fA Aas) w ae 8 A= Ave) ui Tw Nnle If mis the feed rate, the power required by the machine is P=Wi= me, (A, — A) By definition . 6 Ue v, bd 9 Then, a Ome, 1 _ 1 AnMePy\, Dy D,D,, / Volume surface mean diameterBond’s law and work index d that the work required to form particles of Definition of Bond’s Law: Bond postulate 1 to the square root of the surface to volume size D, from very large feed is proportional ratio of the product, s,/v,. AS sJVp =6/(®,D,), thus, p x P_ Ky 0) o(2)--« 2 m Vi Dy the type of machine and on the material being 1.5 and a feed of infinite size. (3) Where K, is a constant that depends on crushed. This is equivalent to Eq (1) with n= Bond’s law may be expressed as: P 1 1 —=k,|—-— mo? Lis inl K, is related to work index, w;. W,is defined as the gross energy requirement in kilowatt-hours per ton (1000 kg) of feed i] needed to reduce a very large feed to such a size that 80% of the product passes through a 100 micron (0.1 mm) screen. For D, =0.1 mm, De= infinite , p/m’ = W, kWh/ton, then from Bond’s equation: Ky Or, Ky= 0.316 W W;=— = K,/v0.1Bond’s law and work index Work indexes for dry crushing} or wet grindingt ———— Material Specific gravity Work index, 1; Bauxite 220 8.78 Cement clinker 315 13,45 Cement raw material §=—-2.67 10.51 Clay 251 630 Coal 14 13.00 Coke 131 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 Limestone 266 1274 Phosphate rock 214 9.92 Quartz 265 13,57 Shale 263 15.87 Slate 257 1430 Trap rock 287 1932 For dry grinding, multiply by $. {From Allis-Chalmers, Solids Processing Equipment Div. Appleton, Wisconsin, by permission.Problem 10 A rock of nearly § em ts fed to a gyratory crusher, which requires 12 kW power on no load, The differential screen analysis of the product is given below under column 4 The power requirement for crushing is 4a KW/ton. By reducing the clearance between the crushing head and the cone, the differential screen analysis of the product becomes as shown in column B, Calculate the power requirement for the second operation using Kick’s Law. Mosh no. Size of opening mm Weight A Percent retained dd ~ 4.70 ; ; = 6 My MM | - 4 246 10,8 as w 1.65 | 20.0 82 rt) wy 1.6 2 w 0.83 18.2 13 w 0.59 120 Io Ms 042 98 98 48 0.05 6s 13.8 “ | 021 48 100 O18 0s 6.2 150 0.10 - 40 | =180 - - 03A rock of nearly § cm Ls fed 0 a gyratory crusher, which requ The differential screen analysis of the product ls given below under at for crushing i432 kKWiton, By reducing the clearance between the differential screen analysts of the product becomes ay shown ower requirement for the second operation using Kick's Law.Problem £4 Calculate the specific curface In em?/em of pyrite having screen analysts glyen below, Speeifle gravity of pyrite Is §. Liseh *. Retained Size (em) uM 0 “_ 0467) 16 in 93327 os 132 | 0.2362 wo Ino | 0.1681 | wid 2M O.16s | 120 WA 0.0433 2025 no 0.0889 Problem S11 2700 ke/ir of calcite passes through as crusher and grinder in succession (on the same power drive), Screen analysis from the crusher shows a surface area of product of 3 : . 35 103 m°/ky. Screen analysis of grinder product Indicates a surface area of 865 m*/kg. Estimate the power requirement from the drive to mun the ahove machines if the efficiencies of the crusher . and grinder are 25% and 20%, respectively. Ritlinger's number for calcite = 76 em*/kg.Problem £4 Calculate the specific surface in cm*, a = below, Specific gravity of pyrite Ls 5. cm?/gm of pyrite baving screen analysis given uM ° (04699 Problem 5.11 2700 kg/hr of calclte passes through os crusher and grinder in succession (on the same power drive). Screen analysis from the crusher shows a surface area of product of 103 m*/kg. Screen analysis of grinder product indicates a surface area of 865 m7/kg. Estimate the power requirement from the drive to run the above machines if the efficiencies of the crusher and grinder are 25% and 30 ., respectively. Rittinger’s number for calcite =76 cm*/kg.Problem 5.400 A rock of nearly cm Is fed to a gyratory crusher, which requires 12 kW f power on no load, The differential screen analysts of the product Is given below under column 4 The power requirement for crushing Is 482 KWon, Hy reductny the clearance between the crushing head and the cone, the differential screen analysts of the product becamtes as shown In columa 1. Calculate the power requirement for the second operation using Klek’s Law, Mesh no, Sire of opening mm Welght A Percent retained D 4 4,70 - ” 6 AM Mt - 4 2M 108 As 10 1.65 200 ha it) V7 Iho Wa w On 182 2 y oso 20 wo Ms 042 08 19.4 AN 0,05 68 13.8 6s O21 Ay Hs 100 O18 05 62 160 O10 . 40 ~1f0 - - On i000, 100.0ees 3: Quartz goes through two successive grinders on the same shaft which faws a total of 14.914 kW. The feed average 5.08 cm in dia. The grinder running empty requires 1.4914 kW. Their capacity is 3 ton.hr. The analysis of the product is the following table. Calculate: (a) The HP used in each grinder (b) The efficiency of the grinder if Rittinger’s number is 1753 cm2/kg.m PERE BCID, Cincy | Gillet mm — (96) product (%)} 3.53 8-14 1.765 30 14-28 0.8785 30 28-48 0.442 15 10 48-100 0.221 5 20 100-7 200 0.1105© Motion) in) (a) tumbling) mill Comminution ting: produces) attrition fa Uhl lleads}ito) ‘i AEN Taar yep i: Rotation CEseMiEp (eS TPE : ibreakage|which) (© GEES a Coarser Load eygrinding}inithe|cascade) “ED LERS Cataracting Finer Load L800 iparticles|become)smaller eu oe NEELET ID Le i ai ue Eo sonoae By attrition) Qeeeck aaittel) gf (he chine line) Gee h itheysneiljbyicentritugal|force Cascading © Center of Gravity of Finer Load © Center of Gravity of Coarser LoadComminution : oe we a x 5 A W ) ee achute:) ae ¢ ee ee ., FeedChute] 7 igs ete elie (\ \ ili mele 2 Tati aie ne Baa oe Supportithe a) J iscreen:mupreven rackestan tramp ine), (= ann ae) uutettha {to leaving = [ Grinding Media Trommel ScreenGomminution Or ) the)bull ay portathe) |oi Pie — cascadingjyand)|impacts P) fei (hiears c ; — Sos 4 mM, —? , ee. 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(R =P) g Nellne Gils Sse), l=) (nem Cosel =) “Giles ofelaeh ie ieawhichiis) et Aen) AWD al mn ito Wetiarindingjadvantageoust-jrequires (ss pou {oO Gi 5 te! el Spat CEMChy E TEA pe morejenerayabecau: ip. a ets ism an ee ae ie filly Sie lees fy te WonFiltration Filtration is a process of removal of solid particles from a fluid by passing the fluid through a porous medium, or septum, on which the solids are deposited. The porous medium is permeable only to the fluid. Since, the filter medium is permeable only to the fluid, retaining the solid particles and the fluid passed through it is collected as filtrate. The volume of filtrate collected per unit time is termed as the rate of filtration. As the filtration proceeds, solid particles accumulate on the filter medium, forming a packed bed of solids, called filter cake. The thickness of the cake thus increases as filtration continues and it offers more and more resistance to flow of filtrate and consequently the rate of filtration gradually decreases. If the rate of filtration is to be maintained constant, then the pressure of filtration, more precisely the pressure difference driving force will have to be increased gradually to overcome the increased resistance offered by the cake as it accumulates.A batch filter can thus be operated either at constant pressure (where the rate of filtration decreases with time) or at constant rate where the pressure differential will have to be gradually increased as filtration proceeds. It is preferable to operate the batch filter first at constant rate and then at constant pressure so that the overall output of filtrate will be large. The constant rate filtration is continued until pressure differential becomes sufficiently high, beyond which the process will be uneconomical. Then the filtration is operated at constant pressure until the rate of filtration has fallen to unacceptably low value or until the required amount of filtrate has been delivered. The cake is then washed with wash water and drained The filter is then opened, cake disposed off, cleaned and reassembled. Fresh slurry is now fed and filtration restarted. The batch filtration cycle involves following steps: (1) Filtration, (2) draining the liquor, (3) filling with wash water, (4) washing, (5) draining the wash water, (6) opening, dumping and reassembling, and (7) filling with fresh slurryClassification of filters >In any filter, fluids flow through a filter medium by virtue of a pressure differential across the medium. | ves —Pressure > atm Upstream - di Per Wetton ‘ |pownsteom — Pressure = atm Filteg Medium Down-stream | Upstream — Pressure = atm try Pressure above atmosphere is Altre (Maclin developed by several means-by a pump or blower, centrifugal force or by gravity force acting on a column of liquid | Down-stream — VacuumMechanisms of filtration Cake filters Cross flow filters Concentrated Suspension ‘suspension sane sali Eitiente ° °Mechanisms of filtration Cake filters: separate relatively large amounts of solids as cake of crystals or sludge. Often they have provisions for washing cake or removing some of the liquid from the solids before discharge. Clarifying filters: these filters remove small amounts of solids to produce a clean gas or sparkling clear liquids. Most solids are trapped inside filter medium. Such filters differ from screens in that the pores of the filter medium are much larger than size of the particles to be removed. Cross flow filters — feed suspension flows under pressure at a fairly high velocity across the filter medium. High liquid velocity keeps the layer of solids from building up. Filter medium used S Lrg generally is -ceramic, polymer or metal with pores small enough to exclude most of the suspended particles. Some of the liquid passes through the filter medium, leaving more concentrated suspension behind.Filter Media The filter medium or membrane in any filter must meet the following requirements = Jt must retain the solids to be filtered, giving a reasonably clear filtrate. = Tt must not plug or blind. = It must be resistant chemically and strong enough physically to withstand process conditions. = Jt must permut the cake formed to discharge cleanly and completely. = It must not be prohibitively expensive. Filter Aids = Very fine solids that form a dense impermeable cake and quickly plug any filter medium that is fine enough to retain them. = In practice, to filter such materials, porosity of the cake is increased to permit the passage of the liquid at a reasonable rate. = This is done by adding filter aids such as purified wood cellulose, inert porous solids, diatomaceous silica to the slurry before filtration. = Another way of using a filter aid is by precoating, that is, depositing a layer of it on the filter medium before filtration.Principles of cake filtration Filtration is a special case of flow through packed beds of granular solids as the cake forms over a porous bed of the filter medium. In conventional packed beds, resistance to flow are constant. Since the particles forming the filter cake are normally small and the rate of flow of filtrate is low, we can safely assume that the flow of filtrate through the cake is laminar. Other assumptions are (1) all the particles in the cake are uniformly wet by the filtrate, (2) there is no channelling of the liquid through the cake. In filtration, the flow resistances increase with time as the filter medium becomes clogged or a filter cake builds up. Therefore equations relating flow rates and pressure drops in packed beds have to be modified to allow for this change. Ergun Equation AP _ 150¥,u (1 ey” 1 1.75pV, (l-) L op & oD, & Kozeny-Carman Burke-Plummer Due to Laminar flow due to Turbulent flowFlow through packed beds — laminar flow conditions = Kozeny-Carman for packed beds is _ 2 based on “Capillary Bundle Theory”. AP 150V. ] -€ = Here it is assumed that the total void = 150V,u (1—€)" space of the packed bed (interstitial L op? @ space between particles) is equal to sop the bundle of capillary tubes. = Thus, Hagen-Poiseuille equation for AP _ 32Yu Pressure driven flow though pipes in 2 the laminar region can applied. L D Solids/Particles Va [. Channels for liquid flowFlow through packed beds — laminar flow conditions a Solids/Particles ; _————> Channels for liquid flow Total surface area of n parallel channels nD,,L |_| _ Total volume of solids (or particles) §,L(1—€) Number of particles SpL(1- €) Volume of one particle —————>V,Flow through packed beds — laminar flow conditions eq = Total surface area of n parallel channels nmD,,L L Total volume of solids (or particles) Sp L(-€) Number of particles SyL(1—€) Volume of one particle ———V, S,L(L-8) ’ Total surface area available for n channels Where, S, is the total surface area of the bed, € is the void fraction or porosity of the bed, s, is the specific surface area.Flow through packed beds — laminar flow conditions Deg — Total surface area of n parallel channels naD,,L L S,L0-€) Total surface area available for n | —————— 5, channels vy Sp__ 6 v, OD, nnD,,L = SoL(- € eq 0 ( BD S20, | Where ©, is the sphericity, defined as the surface- volume ratio for a sphere of diameter D, divided by the surface-volume ratio for the particle whose nominal size is Dp.Flow through packed beds — laminar flow conditions D 6 2 nD,,L = SL(- ant (1) sp L Void Volume in the bed = Total volume of n channels nD. SLE =n 7 L (2) Using (1) and (2) D, -29p 73° P(e)Flow through packed beds — laminar flow conditions 2 e =79, . 73 °° ?d-8) AP 32Vu LD Hagen-Poiseuille for Pressure driven flow though pipes The pressure drop depends on average velocity V =~ & ¥, is the empty tower or superficial velocity. This is defined as the volumetric flow rate of the liquid divided by the total or empty cross-sectional area.Flow through packed beds — laminar flow conditions AP _ 32Vyu (1-8) Pipes are not straight — but tortuous 3 “op? : 32VyH (1-e) “|4 0 B ‘ 5Flow through packed beds — laminar flow conditions AP _| 32¥ju d-e) L 4 ep a et AP _ 72AVyu (l-e) 2 2 3 L OD ¢ AP 150%, (1—-€)° L OD é A, 4 =2.1AP = ao oe Kozeny-Carman Equation | eae |||\II|er = Darcy Formula for friction head loss: hy = Ap/p = fpLV2/2Dgq = 2fLV2/Deq ------ (1) = Where fp is Darcy and Weisbach constant (sometimes called Darcy friction factor) and f is Fanning friction factor and fp = 4f. 2 € D,, ==®,D,>--~< paeeeS ’d-e) * Deq and V in terms of Vo in Eq 1, We get: z —) vV=-2 AP 1.75p¥, (1-8) é i Burke — Plummer Equation L OD, € » The constant 1.75 is experimentally found, leading to the value of f =1.75/3= 0.583. = Oncombination of Kozeny-Carman and Burke-Plummer equation, we get Ergun equation ii i AP _ 150Vu (1—€) : 1.75pVy (l-) Rita Oia oructiiesg 3 L @D, € OD, €hr = Ap / p = 2fLV2 / Deg ------ * For non-circular ducts, the plot of friction factor with Reynolds number could be used if we replace the diameter in both the friction factor and the Reynolds number with 4 times the hydraulic radius (ry). * The hydraulic radius (r4) is the cross sectional area perpendicular to flow divided by the wetted perimeter. « For a uniform duct this is a constant. « For a packed bed it varies from point to point. But if we multiply both the cross sectional area and the perimeter by the length of the bed, it becomes, Ty for porous medium = volume open to flow / total wetted surface volume of bed x ¢ ee ea ee 4 ‘No of spherical particlesx surface area of one particle = But, Volume of bed x (1 -€) No. of particles = 4 Volume of one particlea volume of bed x ¢ in = 7 F No of spherical particlesx surface area of one particle «1 _Volume of bed x (1 -£) No. of particles = —————_——_—* e Volume of one particle = On putting the Eq for no of particles in eq for ry: ae volume of bedx ¢ ee volume of bed x (1- €)x euieeeree volume ie., & eT ta (1-2)(#Dp* / = Dp") ie., D, = ma = (=<) ——(2) Replacing Deg in Eq 1 with 41, asin Eq 2, we get: -Ap_D, _Ap4D,(_¢)_1 p 2Lv, p 6 |1-eJ2zv,’ Home work- Deduct Ergun Equation by the use of hydraulic radius concept.Filtration — Lecture 2 CHN-203-— Mechanical operationPrinciples of cake filtration What offers resistance to flow of liquids through cake filters? 1. Filter cake 2. Filter medium = These two resistances are in series The cake resistance is zero at the start and increases with time as the filtration ‘oceeds a : Pr Filter Medium Filter Cake = Total pressure drop AP=(P,-P’) + (P” - P,) AP=AP.+ AP,, = Pressure drop over cake + Pressure drop over medium au Direction of flow of slurryL, — thickness of the cake measured from the filter medium. = A — filter area measured perpendicular to the direction of flow. = Pressure drops through the filter cake cross- aa section and medium at time t from the start of of foe of filtration or from the start of flow of filtrate. e coke = Consider a thin layer of cake of thickness dL in the cake at a distance L from the medium. = p-—pressure at this point. Upstream foce of = This layer consists of a thin bed of solids through which the filtrate is flowing. = Ina filter bed the flow velocity is sufficiently low feus| ject to ensure laminar flow. dp 150uu (l1—e)” epee eet erg crea a Cozeny-Carman Equation a oo = Where, u is the superficial velocity of the filtrate.dp _150uu (1-e)° dL @D? & Definition of sphericity Ss =e Po Direction «of flow of slurry coke = In Cozeny-Carman equation, If we replace sphericity and particle diameter with s,/v,, then: dp _4.17yu(-e)'(s, /v,° fle & Upstream face gf : : dV / dt = Superficial velocity of the filtrate, 1 = ————— aie A = Where, V is the volume of the filtrate collected from the start of the filtration to the present time, when the pressure is p. = Since the filtrate must pass through the entire cake, V/A is same for all layers and therefore u is independent of L.2 2 dp p 4.17pu—€)"(s, /v,) eu dL = ® : ‘ : dV /dt a = Superficial velocity of the filtrate, 1 = Direction A <—of flow of f *wY «The volume of solids in the layeris: AdL(1-€ ) coke = Mass of solids in the layer whose particle density is Ppis given by: Upstream face of dm=AdL(1-€)p, — (Eq 2) = Eliminating dL from Eq 1 and Eq 2: 4 kpu(l—e(s, /v,)° fu >| kat dp= Su 65 Ip) p,Aé = In filtration under low pressure drops of slurries containing rigid uniform particles: dm kK, wc — els, lv) 5 dm -— (Eq 3) p,Ae = Where the marked part in above equation is a constant for a particular slurry and membrane.pul — lv, = On integration of Eq 3, we get: dp = abel NS, Ye) dm p,Ae * p= kyu - Hsp lv.) ik i Pp p Ae 9 = Where m, is the total mass of the cake at the end of filtration. = On further calculation, we get: 7 E k,puu(l— ENG, vm, a en p,A€ a Filter cakes of this type are called incompressible. ® On replacing some terms in Eq 4 by a, called specific cake resistance, we get: apume _ = Ap.A A Ape Hum, Sp_ 6 k ei v ®D Where @ = Ks, vp) d= €) vy) £) f _. p,€ : k,(1—e) Specific cake resistance in terms of particle a= a size is obtained by replacing s,/v,: P,é (®,D,yAp.A Mum, Specific cake resistance a is the resistance of the cake that gives a unit pressure drop when uy, u and mJA are all unity. ais influenced solely by the physical properties of the cake — such as —size, porosity. kuud—- eX(s, /v,ym, = tin Pp AE , a c This expression may not be precise — if the feed does not contain rigid particles. If the Porosity, constant - k;, and s,/v, vary from layer to layer. Such filter cakes are called compressible. Po Direction 2<—of flow of slurry Upstream lace of cai a varies with distance from the septum or filter medium — because the cake nearer to the septum is subjected to greatest compressive force and hence lowest void fraction. Therefore pressure gradient is non-linear.Filter medium resistance Analogy with definition of cake resistance —P— Py _ Pn oa BPA Rn = ue pn (E45) pum, (Eq 6) = Factors that affect filter medium resistance: The filter medium resistance may vary with pressure drop — larger pressure drops cause higher liquid velocity and may force additional solids into the filter medium. = Cleanliness of the filter medium. But these factors are important only during initial stages of filtration and it is satisfactory to assume that the filter medium resistance is constant during any given filtration process. One can get Ap,, from Eq 5 and Ap, from Eq 6 and combining them, we get: a Ap = Ap, + Ap,, = pu mot Ry (Eq 7) Ifc is the mass of the solid (particles) deposited in the filter per unit volume of the filtrate and V is the total volume of the filtrate collected in time t, then m,, the total mass of the solids in the cake is m, = Vc. ld; = By putting the value of m, and u in Eq 7, we get: n= a at dt acV ee 2 +n, ——- (Eq 8) dV AAp\ A ®Eq 8 is known as ultimate or general filtration equation.