523 The Kynch theory of sedimentation
The behaviour of concentrated suspensions during sedimentation has been analysed by Kynch1-46-1, largely using considerations of continuity. The basic assumptions which are made are as follows a Particle concentration is uniform across any horizontal layer, b Wall effects can be ignored, c There is no differential settling of particles as a result of differences in shape, size, or composition, d The velocity of fall of particles depends only on the local concentration of particles, e The...
47 References
1. Darcy, H. P. G. Les Fontaines publiques de la ville de Dijon. Exposition et application suivre et des formules a employer dans les questions de distribution d'eau Victor Dalamont, 1856 . 2. Eisenklam, P. Chapter 9 Porous Masses in Cremer, H. W. and Davies, T. Chemical Engineering Practice, Vol. 2 Butterworths, 1956 . 3. Brinkman, H. C. Appl. Scient. Res. 1A 1948 81-86. On the permeability of media consisting of closely packed porous particles. 4. Dupuit, A. J. E. J. Etudes theoriques et...
168 Further Reading
Backhurst, J. R. and Harker, J. H. Process Plant Design Heinmann, London, 1973 . Backhurst, J. R., Harker, J. H., and Porter, J. E. Problems in Heat and Mass Transfer Edward Arnold, London, 1974 . Bailey, A. G. Electrostatic Spraying of Liquids John Wiley, New York, 1988 . Barclay, S. F. A Study of Drying Inst. Energy, London, 1957 . Bridgman, M. J. Drying Principles and Practice in the Process Industries Caxton, Christchurch, 1966 . Brown, W. H. An Introduction to the Seasoning of Timber...
1641 Diffusion theory of drying
In the general form of the curve for the rate of drying of a solid shown in Figure 16.2, there are two and sometimes three distinct sections. During the constant-rate period, moisture vaporises into the air stream and the controlling factor is the transfer coefficient for diffusion across the gas film. It is important to understand how the moisture moves to the drying surface during the falling-rate period, and two models have been used to describe the physical nature of this process, the...
97 1
revolutions of the mill. The initial size distribution shows a single mode corresponding to a relatively coarse size, but as the degree of crushing is gradually increased this mode progressively decreases in magnitude and a second mode develops at a particular size. This process continues until the first mode has completely disappeared. Here the second mode is characteristic of the material and is known as the persistent mode, and the first is known as the transitory mode. There appears to be a...
Entrainer sublimation
in entrainer sublimation, an entrainer gas is blown into the vaporisation chamber of a sublimer in order to increase the vapour flowrate to the condensing equipment, thereby increasing the yield. Air is the most commonly used entrainer, though superheated steam can be employed for substances such as anthracene that are relatively insoluble in water. if steam is used, the vapour may be cooled and condensed by direct contact with a spray of cold water. Although the recovery of the sublimate is...
Fractional sublimation
As discussed in Section 15.5.2, the separation of two or more sublimable substances by fractional sublimation is theoretically possible if the substances form true solid solutions. Gillot and Goldberger 100 have reported the development of a laboratory-scale process known as thin-film fractional sublimation which has been applied successfully to the separation of volatile solid mixtures such as hafnium and zirconium tetrachlorides, 1,4-dibromobenzene and 1-bromo-4-chlorobenzene, and anthracene...
5 1
What power would be required to crush 1 kg s of a material of compressive strength 45 MN m2 from a feed of minus 45 mm, plus 40 mm to a product of 0.50 mm average size 2.3. A crusher reducing limestone of crushing strength 70 MN m2 from 6 mm diameter average size to 0.1 mm diameter average size, requires 9 kW. The same machine is used to crush dolomite at the same output from 6 mm diameter average size to a product consisting of 20 per cent with an average diameter of 0.25 mm, 60 per cent with...
I Mno
Whilst the Schildknecht column is essentially a laboratory-scale unit, a melt-crystalliser of the wash-column type was developed by Phillips Petroleum Company in the 1960s for large-scale production of -xylene. The key features of this Phillips pulsed-column crystalliser, as described by McKay etal. 88 , are shown in Figure 15.27. A cold slurry Figure 15.27. Phillips pulsed-column crystalliser1-88-1 Figure 15.27. Phillips pulsed-column crystalliser1-88-1 feed, produced in a scraped-surface...
1473 Natural circulation evaporators
Whilst each of the previous types of evaporator is of considerable importance in a given industry, it is the steam-heated evaporator that is the most widely used unit in the process industries and this is now considered in detail. In Chapter 9 of Volume 1, it is shown that the movement of the liquid over the heating surface has a marked influence on the rate of heat transfer, and it is thus convenient to classify evaporators according to the method of agitation or the nature of the circulation...
1 Wrg
A bed consists of uniform spherical particles of diameter 3 mm and density 4200 kg m3. What will be the minimum fluidising velocity in a liquid of viscosity 3 mNs m2 and density 1100 kg m3 Galileo number, Ga d3p ps p g 2 3 x 10 3 3 x 1100 x 4200 1100 x 9.81 3 x 10 3 2 1.003 x 105 Assuming a value of 0.4 for emf, equation 6.14 gives Remf 25.7 V 1 5.53 x 10 5 1.003 x 105 1 40 and umf 40 x 3 x 10-3 3 x 10-3 x 1100 0.0364 m s or 36.4 mm s Oil, of density 900 kg m3 and viscosity 3 mNs m2, is passed...
Thickening zone
In a continuous thickener, the area required for thickening must be such that the total solids flux volumetric flowrate per unit area at any level does not exceed the rate at which the solids can be transmitted downwards. If this condition is not met, solids will build up and steady-state operation will not be possible. If no solids escape in the overflow, this flux must be constant at all depths below the feed point. In the design of a thickener, it is therefore necessary to establish the...
Solution Idp
Assuming that the salt always travels at its terminal velocity, then for the Stokes law region this is given by equation 3.24. u0 d2 g 18p, p8 p or, in this case, u0 d2 x 9.81 18 x 2 x 10 3 2350 1100 3.406 x 105d2 m s The rate of dissolution dd dt 3 x 10 6 2 x 10 4u m s and substituting dd dt 3 x 10 6 2 x 10 4 x 3.406 x 105d2 3 x 10 6 68.1d2 The velocity at any point h from the top of the reactor is u dh dt and -- 3.406 x 10 d 3 x 10 6 - 68.1 d2 d 3 x 10-6 68.1d2 d dd Cx C 2 C iJo C. C d2
Centrifugal attrition mills
The Babcock mill. This mill shown in Figure 2.19, consists of a series of pushers which cause heavy cast iron balls to rotate against a bull ring like a ball race, with the pressure of the balls on the bull ring being produced by a loading applied from above. Material fed into the mill falls on the bull ring, and the product is continuously removed in an upward stream of air which carries the ground material between the blades of the classifier, which is shown towards the top of the photograph....
55 References
1. Kaye, B. H. and Boardman, R. P. Third Congress of the European Federation of Chemical Engineering 1962 . Symposium on the Interaction between Fluids and Particles 17. Cluster formation in dilute suspensions. 2. Coe, H. S. and Clevenger, G. H. Trans. Am. Inst. Min. Met. Eng. 55 1916 356. Methods for determining the capacities of slime-settling tanks. 3. Robinson, C. S. Ind. Eng. Chem. 18 1926 869. Some factors influencing sedimentation. 4. Einstein, A. Ann. Phys. 19 1906 289-306. Eine neue...
204 References
1. Danckwerts, P. V. Chem. Eng. Sci. 2 1953 1. Continuous flow systems. Distribution of residence times. Chem. Eng. Sci. 7 1958 116. Measurement of molecular homogeneity in a mixture. Chem. Eng. Sci. 8 1958 93. The effect of incomplete mixing on homogeneous reactions. A.I.Ch.E.Jl. 1 1955 456. Gas absorption accompanied by chemical reaction. 2. Danckwerts, P. V. Gas-Liquid Reactions. McGraw-Hill, New York, 1970 . 3. Cussler, E. L. and Moggridge, G. D. Chemical Product Design. Cambridge...
Batch type vacuum filters
Batch vacuum filters were developed from gravity filters and, in essence, Buchner funnels as used in laboratories and Nutsche type filters as used in industry are similar to gravity filters, except that they feature a vacuum pump or some other vacuum generating equipment to reduce the pressure under the filter medium, thereby increasing the driving force across the filter medium. Simple filters operating in this manner are often referred to as pan filters, and they incorporate certain features...
Example 105
Halibut oil is extracted from granulated halibut livers in a countercurrent multi-batch arrangement using ether as the solvent. The solids charge contains 0.35 kg oil kg exhausted livers and it is Figure 10.22. Graphical solution to Example 10.3 Figure 10.22. Graphical solution to Example 10.3 desired to obtain a 90 per cent oil recovery. How many theoretical stages are required if 50 kg ether is used 100 kg untreated solids The entrainment data are kg oil kg solution Entrainment kg solution kg...
Overall transfer coefficients and transfer units
The driving force over the gas film is taken as yi y and over the liquid film as x xi . If ye is the concentration in the gas phase in equilibrium with concentration x in the liquid phase, then ye y is taken as the overall driving force expressed in terms of y. Similarly x xe is taken as the overall driving force in terms of x, where xe is the concentration in the liquid in equilibrium with a concentration y in the vapour. The overall driving forces Ay o and Ax o may then be written as Ay 0 ye...
Horizontal continuous filters
One way of limiting still further cyclic variations is to use vacuum filters of the horizontal continuous type, and many designs have been developed which in the main consist of pans arranged in line or in a circle so that each in turn goes through the same cycle of operations, namely feeding, dewatering, washing, drying, automatic solids discharge and cloth washing. The pans move past the stationary feed and wash areas where the feed and wash liquors are continuously introduced to the filter....
722 Relation between thickness of cake and volume of filtrate
In equation 7.2, the variables l and V are connected, and the relation between them may be obtained by making a material balance between the solids in both the slurry and the cake as follows. Mass of solids in filter cake 1 e Alps, where ps is the density of the solids Mass of liquid retained in the filter cake eAlp, where p is the density of the filtrate. If J is the mass fraction of solids in the original suspension then or 1 J 1 e Alps JVp AeJlp If v is the volume of cake deposited by unit...
99 Further Reading
Ambler, C. M. In Encyclopedia of Chemical Processing and Design, Vol. 7. McKetta, J. J. ed. Marcel Dekker, New York, 1978 . Hsu, H-W. Ind. Eng. Chem. Fundamentals 25 1986 588. Separations by liquid centrifugation. Lavanchy, A. C. and Keith, F. W. In Encyclopedia of Chemical Technology, Kirk, R. E. and Ohmer, D. F. eds. Vol. 4, Wiley-Interscience, 1979 710 Centrifugal separation. Mullin, J. W. In Chemical Engineering Practice, Cremer, H. W. and Davies, T. eds. Vol. 6, Butterworths, 1958 p 528....
169 References
1. SHERWOOD, T. K. Trans. Am. Inst. Chem. Eng. 32 1936 150. The air drying of solids. 2. Pearse, J. F., Oliver, T. R., and Newitt, D. M. Trans. Inst. Chem. Eng. 27 1949 1. The mechanism of the drying of solids. Part i. The forces giving rise to movement of water in granular beds, during drying. 3. Oliver, T. R. and Newitt, D. M. Trans. Inst. Chem. Eng. 27 1949 9. The mechanism of drying of solids. Part ii. The measurement of suction potentials and moisture distribution in drying granular...
2025 Twophase flow in a centrifugal field Introduction
As described by Bisschops et al. 20'21 centrifugal technology, using countercurrent contact of the process liquid with micrometer-range adsorbent particles constitutes a new technique for carrying out adsorption and ion-exchange processes in a centrifugal field. Because the use of very small particles results in large interfacial areas and short distances for diffusion, the mass-transfer rates are extremely fast, and centrifugal adsorption equipment is usually much more compact than that used...
1642 Capillary theory of drying Principles of the theory
The capillary theory of drying has been proposed in order to explain the movement of moisture in the bed during surface drying. The basic importance of the pore space between granular particles was first pointed out by Slichter 16 in connection with the movement of moisture in soils, and this work has been modified and considerably expanded by Haines 17 . The principles are now outlined and applied to the problem of drying. Considering a systematic packing of uniform spherical particles, these...
178 Adsorption Equipment
The scale and complexity of an adsorption unit varies from a laboratory chromatographic column a few millimeters in diameter, as used for analysis, to a fluidised bed several metres in diameter, used for the recovery of solvent vapours, from a simple container in which an adsorbent and a liquid to be clarified are mixed, to a highly-automated moving-bed of solids in plug-flow. All such units have one feature in common in that in all cases the adsorbent becomes saturated as the operation...
1659 Turboshelf dryers
The handling of sticky materials can present difficulties, and one type of dryer which is useful for this type of material is the turbo-dryer. As shown in Figure 16.30, wet solid is fed in a thin layer to the top member of a series of annular shelves each made of a number of segmental plates with slots between them. These shelves rotate and, by means of suitably placed arms, the material is pushed through a slot on to a shelf below. After repeated movements, the solid leaves at the bottom of...
The double cone classifier
This classifier, shown in Figure 1.27, consists of a conical vessel, with a second hollow cone of greater angle arranged apex downwards inside it, so that there is an annular space of approximately constant cross-section between the two cones. The bottom portion of the inner cone is cut away and its position relative to the outer cone can be regulated by a screw adjustment. Water is passed in an upward direction, as in the Spitzkasten, and overflows into a launder arranged round the whole of...
1279 The transfer unit
The group f dy ye y , which is used in Chapter 11, has been defined by Chilton and Colburn 52 as the number of overall gas transfer units N0G. The concept of the transfer unit is also introduced in Volume 1, Chapter 10. The application of this group to the countercurrent conditions in the absorption tower is now considered. Over a small height dZ, the partial pressure of the diffusing component A will change by an amount dPAG. Then the moles of A transferred are given by change in mole fraction...
Scaleup problems
Crystalliser design is usually based on data measured on laboratory or pilot-scale units or, in difficult cases, both. One of the main problems in scaling up is characterisation of the particle-fluid hydrodynamics and the assessment of its effects on the kinetics of nucleation and crystal growth. In fluidised-bed crystallisers, for example, the crystal suspension velocity must be evaluated a parameter which is related to crystal size, size distribution, and shape, as well as bed voidage and...
Design considerations
Many of the design problems associated with rotary dryers have been discussed by Friedman and Marshall 24 , by Prutton et al. 25 and by Miller et al. 26 . Heat from the air stream passes to the solid material during its fall through the air stream, and also from the hot walls of the shell, although the first mechanism is much the more important. The heat transfer equation may be written as where Q is the rate of heat transfer, U is the overall heat transfer coefficient, V is the volume of the...
737 Washing of the filter cake
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. If the viscosity of the wash liquid is less, a somewhat greater rate will be obtained. Channelling sometimes occurs, however, with the result that much of the cake is incompletely washed and the fluid passes preferentially through the channels, which are gradually enlarged by its continued passage....
734 Delayed cake filtration
In the filtration of a slurry, the resistance of the filter cake progressively increases and consequently, in a constant pressure operation, the rate of filtration falls. If the build-up of solids can be reduced, the effective cake thickness will be less and the rate of flow of filtrate will be increased. In practice, it is sometimes possible to incorporate moving blades in the filter equipment so that the thickness of the cake is limited to the clearance between the filter medium and the...
Fluid energy mills
Another form of mill which does not give quite such a fine product is the jet pulveriser, in which the solid is pulverised in jets of high pressure superheated steam or compressed air, supplied at pressures up to 3.5 MN m2 35 bar . The pulverising takes place in a shallow cylindrical chamber with a number of jets arranged tangentially at equal intervals around the circumference. The solid is thrown to the outside walls of the chamber, and the fine particles are formed by the shearing action...
The Szego grinding mill
The Szego Mill is a planetary ring-roller mill shown schematically in Figure 2.26. It consists principally of a stationary, cylindrical grinding surface inside which a number of helically grooved rollers rotate. These radially mobile rollers are suspended from flanges connected to the central drive shaft they are pushed outward by centrifugal force and roll on the grinding surface. The material is fed by gravity, or pumped into a top feed cylinder and is discharged at the bottom of the mill....
1211 References
1. Whitman, W. G. Chem. Met. Eng. 29 1923 147. The two-film theory of absorption. 2. Higbie, R. Trans. Am. Inst. Chem. Eng. 31 1935 365. The rate of absorption of pure gas into a still liquid during short periods of exposure. 3. Danckwerts, P. V. Ind. Eng. Chem. 43 1951 1460. Significance of liquid-film coefficients in gas absorption. 4. Danckwerts, P. V. and Kennedy, A. M. Trans. Inst. Chem. Eng. 32 1954 S49. Kinetics of liquid-film processes in gas absorption. 5. Lynn, S., Straatemeier, J....
85 Crossflow Microfiltration
The solids-liquid separation of slurries containing particles below 10 m is difficult by conventional filtration techniques. A conventional approach would be to use a slurry thickener in which the formation of a filter cake is restricted and the product is discharged continuously as a concentrated slurry. Such filters use filter cloths as the filtration medium Membrane flux is denoted by J, the usual symbol in the literature on membranes. It corresponds with uc, as used in Chapters 4 and 7 for...
1151 The heat balance
In previous sections, the case of constant molar latent heat has been considered with no heat of mixing, and hence a constant molar rate of reflux in the column. These simplifying assumptions are extremely useful in that they enable a simple geometrical method to be used for finding the change in concentration on the plates and, whilst they are rarely entirely true in industrial conditions, they often provide a convenient start for design purposes. For a non-ideal system, where the molar latent...
v Nab
Figure 6.8. Bed inversion a Complete segregation b Complete and partial segregation' The relative rates at which the bed densities change as the fluidising velocity is increased may be obtained by differentiating equations 6.42a and 6.42b with respect to uc, and dividing to give _ dpbH j _ dpbL _ dpbH _ psH - p uql_ V n _ PsH - P eH As eH gt eL and psH gt psL, then from equation 6.44, r, which is independent of fluidising velocity, must be greater than unity. It is thus the bed of heavy...
610 References
1. Wilhelm, R. H. and Kwauk, M. Chem. Eng. Prog. 44 1948 201. Fluidization of solid particles. 2. Jackson, R. Trans. Inst. Chem. Eng. 41 1963 13, 22. The mechanisms of fluidised beds. Part 1. The stability of the state of uniform fluidisation. Part 2. The motion of fully developed bubbles. 3. Murray, J. D. J. Fluid Mech. 21 1965 465 22 1965 57. On the mathematics of fluidization. Part 1. Fundamental equations and wave propagation. Part 2. Steady motion of fully developed bubbles. 4. Leva, M.,...
1510 References
1. Mullin, J. W. 'Crystallization' in Kirk-Othmer Encyclopedia of Chemical Technology, Volume 7, 3rd. edition John Wiley amp Sons, New York, 1979 2. Mullin, J. W. 'Crystallization and Precipitation' in Ullmann's Encyclopedia of Industrial Chemistry, Volume B2 VCH Verlagsgesellschaft mbH, Weinheim, 1988 3. Mullin, J. W. Crystallization 4th. edn. Butterworth-Heinemann, Oxford, 2001 4. Feilchenfeld, H. and Sarig, S. Ind. Eng. Chem. Process. Prod. Res. Dev. 24 1985 130-133. Calcium chloride...
1113 References
1. Robinson, C. S. and Gilliland, E. R. Elements of Fractional Distillation, 4th edn. McGraw-Hill, New York, 1950 . 2. Thornton, J. D. and Garner, F. H. J. Appl. Chem. Suppl. 1 1951 61. Vapour-liquid equilibria in hydrocarbon-non-hydrocarbon systems. 1 The system benzene-cyclohexane-furfuraldehyde. 3. Antoine, C. Comptes Rendus 107 1888 681, 836. Tensions des vapeurs nouvelle relation entre les tensions et les temperatures. 4. Boublik, T., Fried, V. and Hala, E. The Vapour Pressure of Pure...
19 Nomenclature
Cross-sectional area of gas inlet to cyclone separator interfacial area per unit volume between constituents Maximum interfacial area per unit volume Volumetric concentration of solids in feed Volumetric concentration of solids in overflow Volumetric concentration of solids in underflow Particle size, diameter of sphere or characteristic dimension
372 Motion of a sphere in the stokes law region
Under these conditions, from equation 3.5 Substituting in equations 3.79, 3.80, 3.81 and 3.82 gives or x ----x a x 3.85 if allowance is made for the added mass. y - -y s 1-- -ay b 3-86 36M . , 2g ps - p , , , ,, or y - _ _ -ay b 3.87 if allowance is made for the added mass. In this particular case, the equations of motion for the X and Y directions are mutually independent and therefore can be integrated separately. Furthermore, because the frictional term is now a linear function of velocity,...
Solution Bbr
This example involves a heat balance over the system. 273 K will be chosen as the datum temperature, and it will be assumed that the flowrate of dry air g kg s. Heat in g kg s dry air enter with 0.006g kg s water vapour and hence the heat content of this stream 1.00g 0.006g x 2.01 385 273 113.35g kW 0.125 kg s enter containing 0.40 kg water kg wet solid, assuming the moisture is expressed on a wet basis. Thus mass flowrate of water 0.125 x 0.40 0.050 kg s and mass flowrate of dry solid 0.125...
The hydraulic jig
The hydraulic jig operates by allowing material to settle for brief periods so that the particles do not attain their terminal falling velocities, and is therefore suitable for separating materials of wide size range into their constituents. The material to be separated is fed dry, or more usually in suspension, over a screen and is subjected to a pulsating action by liquid which is set in oscillation by means of a reciprocating plunger. The particles on the screen constitute a suspension of...
The Dodge jaw crusher
In the Dodge crusher, shown in Figure 2.5, the moving jaw is pivoted at the bottom. The minimum movement is thus at the bottom and a more uniform product is obtained, although the crusher is less widely used because of its tendency to choke. The large opening at the top enables it to take very large feed and to effect a large size reduction. This crusher is usually made in smaller sizes than the Stag crusher, because of the high fluctuating stresses that are produced in the members of the...
Working Of Stag Jaw Crusher
Fixed Jaw Face Swing Jaw Face Swing Jaw Stock Toggle Seating Front Toggle Plate Toggle Seating Back Toggle Plate Springs and Cups Swing Jaw Shaft Eccentric Shaft 14. Flywheel grooved for V rope drive 19. Cheek Plates top 19A. Cheek Plates bottom 21. Swing Jaw Shaft Bearing Caps 22. Eccentric Shaft Bearing Caps 27. Eccentric Shaft Bearing Bush bottom 28. Eccentric Shaft Bearing Bush top Figure 2.4. Typical cross-section of Stag jaw crusher Stag crushers are made with jaw widths varying from...
The Denver DR flotation machine
The Denver DR flotation machine, which is an example of a typical froth flotation unit used in the mining industry, is illustrated in Figure 1.47. The pulp is introduced through a feed box and is distributed over the entire width of the first cell. Circulation of the pulp through each cell is such that, as the pulp comes into contact with the impeller, it is subjected to intense agitation and aeration. Low pressure air for this purpose is introduced down the standpipe surrounding the shaft and...
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...