1654 Rotary Dryers

For the continuous drying of materials on a large scale, 0.3 kg s (1 tonne h) or greater, a rotary dryer, which consists of a relatively long cylindrical shell mounted on rollers and driven at a low speed, up to 0.4 Hz is suitable. The shell is supported at a small angle to the horizontal so that material fed in at the higher end will travel through the dryer under gravity, and hot gases or air used as the drying medium are fed in either at the upper end of the dryer to give co-current flow or...

Effect of feed system on economy

In the case of forward feed systems, all the liquor has to be heated from Tf to T1 by steam although, in the case of backward feed, the heating of the feed in the last effect is done with steam that has already evaporated (N 1) times its own mass of water, assuming ideal conditions. The feed temperature must therefore be regarded as a major feature in this class of problem. Webre(15) has examined the effect of feed temperature on the economy and the evaporation in each effect, for the case of a...

1443 Comparison of forward and backward feeds

In the unit considered in Example 14.2A, the weak liquor is fed to effect (0 and flows on to 0 and then to (0. The steam is also fed to (0, and the process is known as forward-feed since the feed is to the same unit as the steam and travels down the unit in the same direction as the steam or vapour. It is possible, however, to introduce the weak liquor to effect (3 and cause it to travel from (3 to (2 to (1 , whilst the steam and vapour still travel in the direction of (0 to (0 to (0. This...

1172 Feed and product compositions

With a binary system, if the feed composition Xf and the top product composition xd are known for one component, then the composition of the bottoms xw may have any desired value, and a material balance will determine the amounts of the top and bottom products D and W. This freedom of selecting the compositions does not apply for mixtures with three or more components. Gilliland and Reed1 37 have determined the number of degrees of freedom for the continuous distillation of a multicomponent...

1154 Multiple feeds and sidestreams

The enthalpy-composition approach may also be used for multiple feeds and sidestreams for binary systems. For the condition of constant molar overflow, each additional sidestream or feed adds a further operating line and pole point to the system. Taking the same system as used in Figure 11.22, with one sidestream only, the procedure is as shown in Figure 11.30. Figure 11.30. Enthalpy-composition diagram for a system with one sidestream Figure 11.30. Enthalpy-composition diagram for a system...

05

For values of (Nd2p f) greater than 67,000. In equation 10.6 h is the heat transfer coefficient, k is the thermal conductivity of the liquid, and Cp is the specific heat of the liquid. It may be seen from equations 10.5 and 10.6 that at high degrees of agitation the ratio of the heat and mass transfer coefficients is almost independent of the speed of the agitator and Piret et al.(3) attempted to reproduce the conditions in a porous solid using banks of capillary tubes, beds of glass beads and...

747 The tube press

One of the major problems in coal preparation is the dewatering of fine coal to a moisture content sufficiently low enough both to meet market requirements and to ease the problems of handlability encountered at some collieries and there is an interest in different types of dewatering equipment in addition to the conventional rotary vacuum filter. As a result, a tube press built by the former English China Clays Limited, now Imerys, was installed at a colliery where it was used to treat raw...

00065

In the spray tower, the gas enters at the bottom and the liquid is introduced through a series of sprays at the top. The performance of these units is generally rather poor, because the droplets tend to coalesce after they have fallen through a few metres, and the interfacial surface is thereby seriously reduced. Although there is considerable turbulence in the gas phase, there is little circulation of the liquid within the drops, and the resistance of the equivalent liquid film tends to be...

Rates of absorption in terms of mole fractions

The mass transfer equations can be written as N'a k'G(yA - yAi) KG(yA - yAe) ( 12.20) and NA (xM - xa) K' (xAe - *a) ( 12.21) where xA, yA are the mole fractions of the soluble component A in the liquid and gas phases, respectively. k'G, k'L, K'G, K'L are transfer coefficients defined in terms of mole fractions by equations 12.20 and 12.21. If m is the slope of the equilibrium curve approximately (yAi - yAe) (xAi - xA) , it can then be shown that Ka ka kL which is similar to equation 11.151...

Population balance

Growth and nucleation interact in a crystalliser in which both contribute to the final crystal size distribution (CSD) of the product. The importance of the population balance(37) is widely acknowledged. This is most easily appreciated by reference to the simple, idealised case of a mixed-suspension, mixed-product removal (MSMPR) crystalliser operated continuously in the steady state, where no crystals are present in the feed stream, all crystals are of the same shape, no crystals break down by...

77

By interpolation, yr yro 0.5 when f 4.4 h. Because of the difficulty of ensuring that the solid moves steadily and at a controlled rate with respect to the containing vessel, other equipment has been developed in which solid and vessel move together, relative to a fixed inlet for the feed and a fixed outlet for the product. Figure 17.29 shows the principle of operation of a rotary-bed adsorber used, for example, for solvent recovery from air on to activated-carbon. The activated-carbon is...

1

The solutions given by Thomas are expressed as complex functions of x, x, and Ki. For design purposes, these are more conveniently presented in graphical form. Vermeulen1-12-and Hester and Vermeulen1-17-1 have extended their use to include diffusion control. When film-diffusion controls, the kinetics step, given by equation 18.36, is essentially at equilibrium. Hence

1852 Film diffusion

Diffusion through liquid films is usually better understood than that through porous bodies. In ion exchange, however, there is an additional flux through the film of mobile co-ions which are not present in the resin. The co-ions will be affected by the relative mobilities of the counter-ions. If a cationic resin contains the more mobile counter-ion A, a negative potential tends to build up at the outer surface of the resin and co-ions are repelled. Conversely, a slow resin counter-ion will...

C Inertia or momentum separators

Momentum separators rely on the fact that the momentum of the particles is far greater than that of the gas, so that the particles do not follow the same path as the gas if the direction of motion is suddenly changed. Equipment developed for the separation of particles from mine gases is shown in Figure 1.57, from which it may be seen that the direction of the gas is changed suddenly at the end of each baffle. Again, the separator shown in Figure 1.58 consists of a number of vessels up to about...

106 Number Of Stages For Countercurrent Washing By Graphical Methods

It is sometimes convenient to use graphical constructions for the solution of countercurrent leaching or washing problems. This may be done by a method similar to the McCabe-Thiele method for distillation which is discussed in Chapter 11, with the overflow and underflow streams corresponding to the vapour and liquid respectively. The basis of this method is now given, although a generally more convenient method involves the use of triangular diagrams which will be discussed in some detail. For...

11101 Types of trays

The main requirement of a tray is that it should provide intimate mixing between the liquid and vapour streams, that it should be suitable for handling the desired rates of vapour and liquid without excessive entrainment or flooding, that it should be stable in operation, and that it should be reasonably easy to erect and maintain. In many cases, particularly with vacuum distillation, it is essential that the drop in pressure over the tray should be a minimum. The arrangements for the liquid...

373 Vertical motion general case

For the Stokes' law regime equations 3.88, 3.89 and 3.90 are applicable. For the Newton's law regime, R' pu2 is a constant and equal to 0.22 for a spherical particle. Therefore, substituting in equation 3.81 and putting x 0 for vertical motion, and using the negative sign for downward motion (and neglecting the effect of added mass) When t 0, y v, say, and therefore the constant In i 1 s 1 ft 2 In--b constant

Draughttube agitated vacuum crystallisers

A Swenson draught-tube-baffled (DTB) vacuum unit is shown in Figure 15.17. A relatively slow-speed propellor agitator is located in a draught tube that extends to a small distance below the liquor level. Hot, concentrated feed-stock, enters at the base of the draught tube, and the steady movement of magma and feed-stock to the surface of the liquor produces a gentle, uniform boiling action over the whole cross-sectional area of the crystalliser. The degree of supercooling thus produced is less...

1532 Evaporating crystallisers

If the solubility of a solute in a solvent is not appreciably decreased by lowering the temperature, the appropriate degree of solution supersaturation can be achieved by evaporating some of the solvent and the oldest and simplest technique, the use of solar energy, is still employed commercially throughout the world(66). Common salt is produced widely from brine in steam-heated evaporators, multiple-effect evaporator-crystallisers are used in sugar refining and many types of forced-circulation...

Example 133

In the extraction of acetic acid from an aqueous solution with benzene in a packed column of height 1.4 m and of cross-sectional area 0.0045 m2, the concentrations measured at the inlet and outlet of the column are as shown in Figure 13.22. Figure 13.21. Height of the transfer unit HOE as a function of mLE LR for the transfer of diethylamine from water to dispersed toluene using various packings'-4-1 Figure 13.21. Height of the transfer unit HOE as a function of mLE LR for the transfer of...

771

In applying this equation to evaporators, there may be some difficulty in deciding the correct value for the temperature difference because of what is known as the boiling point rise (BPR). If water is boiled in an evaporator under a given pressure, then the temperature of the liquor may be determined from steam tables and the temperature difference is readily calculated. At the same pressure, a solution has a boiling point greater than that of water, and the difference between its boiling...

10000

Carman's graph of R pu2 against Re1 The form of equation 4.16 is similar to that of equation 4.17 proposed by Forchheimer(8) who suggested that the resistance to flow should be considered in two parts that due to the viscous drag at the surface of the particles, and that due to loss in turbulent eddies and at the sudden changes in the cross-section of the channels. Thus The first term in this equation will predominate at low rates of flow where the losses are mainly attributable to...

1242 Coefficients in packed towers

The majority of published data on transfer coefficients in packed towers are for rather small laboratory units, and there is still some uncertainty in extending the data for use in industrial units. one of the great difficulties in correlating the performance of packed towers is the problem of assessing the effective wetted area for interphase transfer. It is convenient to consider separately conditions where the gas-film is controlling, and then where the liquid film is controlling. The...

The number of plates at total reflux Fenskes method

For conditions in which the relative volatility is constant, Fenske 29 derived an equation for calculating the required number of plates for a desired separation. Since no product is withdrawn from the still, the equations of the two operating lines become If for two components A and B, the concentrations in the still are xsA and xsB, then the composition on the first plate is given by where the subscript outside the bracket indicates the plate, and s the still. ) ai I I aias yBj 1 VW 1 xB s If...

N d e fi2 i Ga e

Since n is found experimentally to be independent of e (see Figure 5.15) f13 Ga, J (5.78) Equations 5.72 and 5.74 similarly become, respectively Re0< 0.2 , iRe0> 500 0 and 1 0 Experimental results generally confirm the validity of equation 5.80 over these ranges, with n & 4.8 at low Reynolds numbers and & 2.4 at high values. Equation 5.78 is to be preferred to equation 5.79 as the Galileo number can be calculated directly from the properties of the particles and of the fluid, whereas...

Calculation of number of plates using the Lewis Sorel method

If a unit is operating as shown in Figure 11.13, so that a binary feed F is distilled to give a top product D and a bottom product W, with xf, xd, and xw as the corresponding mole fractions of the more volatile component, and the vapour Vt rising from the top plate is condensed, and part is run back as liquid at its boiling point to the column as reflux, the remainder being withdrawn as product, then a material balance above plate n, indicated by the loop I in Figure 11.13 gives Figure 11.13....

02

Ge Pl Pw The equation of the curve is then found to be when a column is operating under reduced pressure and the pressure drop is of the same order of magnitude as the absolute pressure, it is not immediately obvious whether the onset of flooding will be determined by conditions at the top or the bottom of the column. If Gf is the gas flowrate under flooding conditions in the column, then Substituting in equation 4.51 gives 1 GiS, 1 u, 021 L' 4 --N8 For a column operating at a given reflux...

Falling rate period diffusion control

In the falling-rate period, the surface is no longer completely wetted and the rate of drying steadily falls. In the previous analysis, it has been assumed that the rate of drying per unit effective wetted area is a linear function of the water content, so that the rate of drying is given by ( In many cases, however, the rate of drying is governed by the rate of internal movement of the moisture to the surface. It was initially assumed that this movement was a process of diffusion and would...

Pun

The contactor finds extensive use where high performance phase separation and countercurrent extraction or washing in the one unit are required. Particularly important applications are the removal of acid sludges from hydrocarbons, shown in Figure 13.40, hydrogen peroxide extraction, sulphonate soap and antibiotics extraction, the extraction of rare earths such as uranium and vanadium from leach liquors, and the washing of refined edible oils. Figure 13.40. Application of the Podbielniak...

Note to Fourth Edition Revised Impression 1993

In this reprint corrections and minor revisions have been incorporated. The principal changes are as follows (1) Addition of an account of the construction and operation of the Szego Grinding Mill (Chapter 2). (2) Inclusion of the Yoshioka method for the design of thickeners (Chapter 5). (3) Incorporation of Geldart's classification of powders in relation to fluidisation characteristics (Chapter 6). (4) The substitution of a more logical approach to filtration of slurries yielding compressible...

Rosens solutions

Rate equations, such as equation 17.85, make no attempt to distinguish mechanisms of transfer within a pellet. All such mechanisms are taken into account within the rate constant k. A more fundamental approach is to select the important factors and combine them to form a rate equation, with no regard to the mathematical complexity of the equation. In most cases this approach will lead to the necessity for numerical solutions although for some limiting conditions, useful analytical solutions are...

1441 General principles

If an evaporator, fed with steam at 399 K with a total heat of 2714 kJ kg, is evaporating water at 373 K, then each kilogram of water vapour produced will have a total heat content of 2675 kJ. If this heat is allowed to go to waste, by condensing it in a tubular condenser or by direct contact in a jet condenser for example, such a system makes very poor use of steam. The vapour produced is, however, suitable for passing to the calandria of a similar unit, provided the boiling temperature in the...

08

Cumulative oversize distribution Fu(d) as a function of F(d) for various particle sizes (d) Figure 1.11. Cumulative oversize distribution Fu(d) as a function of F(d) for various particle sizes (d) Grade efficiency in a centrifugal separator The behaviour of suspended particles in a centrifugal field is considered in detail in Chapter 3. It is, however, convenient to consider here the extension of the preceding treatment of grade efficiency to centrifugal separators. In the case of...

1533Vacuum adiabatic cooling crystallisers

A vacuum crystalliser operates on a slightly different principle from the reduced-pressure unit since supersaturation is achieved by simultaneous evaporation and adiabatic cooling of the feedstock. A hot, saturated solution is fed into an insulated vessel maintained under reduced pressure. If the feed liquor temperature is higher than the boiling point of the solution under the low pressure existing in the vessel, the liquor cools adiabatically to this temperature and the sensible heat and any...

Directcontact cooling

The occurrence of crystal encrustation in conventional heat exchangers can be avoided by using direct-contact cooling (DCC) in which supersaturation is achieved by allowing the process liquor to come into contact with a cold heat-transfer medium. Other potential advantages of DCC include better heat transfer and lower cooling loads, although disadvantages include product contamination from the coolant and the cost of extra processing required to recover the coolant for further use. Since a...

1272Mass transfer coefficients and specific area in packed towers

Traditional methods of assessing the capacity of tower packings, which involve the use of the specific surface area S and the voidage e, developed from the fact that these properties could be readily defined and measured for a packed bed of granular material such as granite, limestone, and coke which were some of the earliest forms of tower packings. The values of S and e enabled a reasonable prediction of hydraulic performance to be made. With the introduction of Raschig rings and other...

125 Efficiency of separation and grade efficiency

It is useful to represent the efficiency with which various sizes or grades of particles are distributed between the outputs of separation devices. Although separation may be effected by exploiting various particle properties, process efficiency is commonly represented as a function of particle size, termed grade efficiency. This function is most useful when it is based on data obtained from representative samples of process feed material, although it does provide a guide to separation, which...

732Blocking filtration

In the previous discussion it is assumed that there is a well-defined boundary between the filter cake and the filter cloth. The initial stages in the build-up of the filter cake are important, however, because these may have a large effect on the flow resistance and may seriously affect the useful life of the cloth. The blocking of the pores of the filter medium by particles is a complex phenomenon, partly because of the complicated nature of the surface structure of the usual types of filter...

400

Heat transfer coefficient from a surface to 78 xm glass spheres fluidised by air. AB fixed bed B minimum fluidising velocity C maximum coefficient CD falling coefficient D minimum coefficient DE final region of increasing coefficient of the gas bubbles which are responsible for the continual replacement of the solids in the vicinity of the heat transfer surface. The nature of the curves depicted in Figures 6.24 and 6.25 shows just how difficult it is to compare heat transfer...

2

Formation of styrene-based cationic and anionic resins When the resin is incompletely ionised, its effective capacity will be less than the maximum. If equilibrium between resin and liquid is not achieved, a dynamic capacity may be quoted which will depend on the contact time. When equipment is designed to contain the resin, it is convenient to use unit volume of water-swollen resin as the basis for expressing the capacity. For fixed-bed equipment, the capacity at breakpoint is...

3

From equations 5.76 and 5.84 and neglecting the tube wall effect e48(for Rex < 0.2) (5.102) The functions e3 6.7(1 e) and e48 are both plotted as a function of e in Figure 5.20, from which it is seen that they correspond closely for voidages less than 0.75. 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 e4-8 and e3 6.7(1-e) Figure 5.20. Comparison of two functions of voidage used as correction factors for sedimentation velocities 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 e4-8 and e3 6.7(1-e) Figure...

Info

0.01 0.02 0.04 0.08 0.2 0.3 0.5 0.8 1 0.03 0.06 0.1 0.4 0.6 0.01 0.02 0.04 0.08 0.2 0.3 0.5 0.8 1 0.03 0.06 0.1 0.4 0.6 Figure 6.7. Bed expansion for the fluidisation of 0.5-0.6 mm lead shot in water in a 100 mm tube It is, however, surprising that a reduction in particle size should also cause increased deviations from the ideal system. It may be noted from Figure 6.7 that, over a wide range of liquid velocities, the mean voidage of the bed is less than that predicted by equation 6.31. This...

High gradient magnetic separation

The removal of small quantities of finely dispersed ferromagnetic materials from fine minerals, such as china clay, may be effectively carried out in a high gradient magnetic field. The suspension of mineral is passed through a matrix of ferromagnetic wires which is magnetised by the application of an external magnetic field. The removal of the weakly magnetic particles containing iron may considerably improve the brightness of the mineral, and thereby enhance its value as a coating or filler...

031

The inclusion of the characteristic dimension d is necessary dimensionally, though its value does not affect the result obtained for hb. This equation predicts the heat transfer coefficient for a single isolated tube and is not applicable to tube bundles, for which Palen and Taborek(2) showed that the use of this equation would have resulted in 50-250 per cent underdesign in a number of specific cases. The reason for this discrepancy may be explained as follows. In the case of a tube bundle,...

1112 Further Reading

Process Plant Design (Heinemann Educational Books, London, 1973). Billet, R. Distillation Engineering (Heyden and Sons Ltd., 1979). Buckley, P. S., Luyben, W. L. and Shunta, J. P. Design of Distillation Column Control Systems (Edward Arnold, New York, 1985). Hoffman, E. J. Azeotropic and Extractive Distillation (Interscience Publishers, Inc., New York, 1964). Holland, C. D. Fundamentals of Multicomponent Distillation (McGraw-Hill Book Co., New York, 1981)....

B10h14

Naphthalene Quinoline, 6-decyl-1, 2, 3, 4-tetrahydro-naphthalene, 2-butyl-l-hexylindan Size limit for Linde sieve 10X about here ( 0.8 nm) Size limit for Linde sieve 13X about here ( 1.0 nm) oxidised at temperatures in excess of 1000 K in atmospheres of materials such as steam or carbon dioxide. Activated carbon has a typical surface area of 106 m2 kg, mostly associated with a set of pores of about 2 nm in diameter. There is likely to be another set of pores of about 1000 nm in diameter, which...

5000

Volume as function of time for delayed cake and constant pressure filtration as a function of The concentration of solids in the slurry in the feed vessel to the filter at any time can be calculated by noting that the volumetric rate of feed of slurry must be equal to the rate at which filtrate leaves the vessel. For a rate of flow of filtrate of dV dt out of the filter, the rate of flow of slurry into the vessel must also be dV dt and the corresponding influx of solids is (1 e0) dV...

1536 Batch and continuous crystallisation

Continuous, steady-state operation is not always the ideal mode for the operation of crystallisation processes, and batch operation often offers considerable advantages such as simplicity of equipment and reduced encrustation on heat-exchanger surfaces. Whilst only a batch crystalliser can, in certain cases, produce the required crystal form, size distribution, or purity, the operating costs can be significantly higher than those of a comparable continuous unit, and problems of product...

Example 146

For the concentration of fruit juice by evaporation it is proposed to use a falling-film evaporator and to incorporate a heat pump cycle with ammonia as the medium. The ammonia in vapour form will enter the evaporator at 312 K and the water will be evaporated from the juices at 287 K. The ammonia in the vapour-liquid mixture will enter the condenser at 278 K and the vapour will then pass to the compressor. It is estimated that the work for compressing the ammonia will be 150 kJ kg of ammonia...

1144 Location of feed point in a continuous still

From Figure 11.20 it may be seen that, when stepping off plates down the top operating line AB, the bottom operating line CE cannot be used until the value of xn on any plate is less than xe. Again it is essential to pass to the lower line CE by the time xn xb. The best conditions are those where the minimum number of plates is used. From the geometry of the figure, the largest steps in the enriching section occur down to the point of intersection of the operating lines at x xq. Below this...

44 Heat Transfer In Packed Beds

For heat and mass transfer through a stationary or streamline fluid to a single spherical particle, it has been shown in Volume 1, Chapter 9, that the heat and mass transfer coefficients reach limiting low values given by where Nu'( hd k) and Sh'( hDd D) are the Nusselt and Sherwood numbers with respect to the fluid, respectively. Kramers(41) has shown that, for conditions of forced convection, the heat transfer coefficient can be represented by Nu' 2.0 + 1.3Pr015 + 0.66Pr 31Ref5 (4.42) where...

522 Flocculation Introduction

The behaviour of suspensions of fine particles is very considerably influenced by whether the particles flocculate. The overall effect of flocculation is to create large conglomerations of elementary particles with occluded liquid. The flocs, which easily become distorted, are effectively enlarged particles of a density intermediate between that of the constituent particles and the liquid. The tendency of the particulate phase of colloidal dispersions to aggregate is an important physical...

162 General Principles

The moisture content of a material is usually expressed in terms of its water content as a percentage of the mass of the dry material, though moisture content is sometimes expressed on a wet basis, as in Example 16.3. If a material is exposed to air at a given temperature and humidity, the material will either lose or gain water until an equilibrium condition is established. This equilibrium moisture content varies widely with the moisture content and the temperature of the air, as shown in...

91 Introduction

There is now a wide range of situations where centrifugal force is used in place of the gravitational force in order to effect separations. The resulting accelerations may be several thousand times that attributable to gravity. Some of the benefits include far greater rates of separation the possibility of achieving separations which are either not practically feasible, or actually impossible, in the gravitational field and a substantial reduction of the size of the equipment. Recent...

3360 4000 4760

The efficiency of screening is defined as the ratio of the mass of material which passes the screen to that which is capable of passing. This will differ according to the size of the material. It may be assumed that the rate of passage 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...

E

Fixed bearing whereas the other has an adjustable spring-loaded bearing. Since the rollers rotate at different speeds, size reduction is effected by a combination of compressive and shear forces. The roller mill is extensively used in the flour milling industry and for the manufacture of pigments for paints.

1382 Aqueous twophase systems

The possibility of a three component system consisting of water and two organic components separating into two phases has been known for some time, though it is only since biochemical processes, including fermentation, have been used for the production of expensive highly complex molecules that it has assumed such a great industrial importance. Two-phase aqueous systems are now extensively used for the separation of product from the associated cell debris. Essentially, the addition of a...

1943Liquid chromatography LC

Many forms of liquid chromatography have been developed in order to separate different types of compound, as shown in Table 19.2. Bonded-phase chromatography (BPC) is an improved form of the now virtually extinct liquid-liquid chromatography. The problem of mutual dissolution of the two liquid phases, and hence progressive loss of stationary phase during service, is solved by chemically bonding the stationary liquid as a monomolecular layer to the surface of a solid support. The support is...

11105 Plate efficiency

The number of ideal stages required for a desired separation may be calculated by one of the methods discussed previously, although in practice more trays are required than ideal stages. The ratio n np of the number of ideal stages n to the number of actual trays np represents the overall efficiency E of the column, which may be 30-100 per cent1-4). The main reason for loss in efficiency is that the kinetics for the rate of approach to equilibrium, and the flow pattern on the plate, may not...

1277 The operating line and graphical integration for the height of a column

Taking a material balance on the solute from the bottom of the column to any plane where the mole ratios are Y and X gives for unit area of cross-section Gm(Yj Y) Lm(Xj X) (12.55) or Yl-Y (X1-X) (12.56) This is the equation of a straight line of slope Lm Gm, which passes through the point (X 1 Y1). It may be seen by making a material balance over the whole column that the same line passes through the point (X2, Y2). This line, known as the operating line,

222 Mechanism of size reduction

Whilst the mechanism of the process of size reduction is extremely complex, in recent years a number of attempts have been made at a more detailed analysis of the problem. If a single lump of material is subjected to a sudden impact, it will generally break so as to yield a few relatively large particles and a number of fine particles, with relatively few particles of intermediate size. If the energy in the blow is increased, the larger particles will be of a rather smaller size and more...

1522 Solubility and saturation

A solution that is in thermodynamic equilibrium with the solid phase of its solute at a given temperature is a saturated solution, and a solution containing more dissolved solute than that given by the equilibrium saturation value is said to be supersaturated. The degree of supersaturation may be expressed by where c and c* are the solution concentration and the equilibrium saturation value respectively. The supersaturation ratio, S, and the relative supersaturation, p are then and p Ac c* S -...

Plate efficiency in terms of transfer units

The process of mass transfer across a phase boundary is discussed in Volume 1, Chapter 10. A resistance to mass transfer exists within the fluid on each side of the interface, and the overall transfer rate of a component in a mixture depends on the sum of these resistances and the total driving force. The concept of a transfer unit for a countercurrent mass transfer process, introduced in Volume 1, is developed further for distillation in packed columns in Section 11.11. The number of transfer...

L L

Concentration of adsorbate in equilibrium with C s Specific heat capacity of the gas phase Specific heat capacity of the adsorbent with adsorbate Specific heat capacity of the wall Diffusivity Average diffusivity Effective diffusivity Knudsen diffusivity Longitudinal diffusivity Molecular diffusivity Surface diffusivity Surface diffusivity in standard conditions Total diffusivity Bed diameter Pellet diameter Energy of activation in surface diffusion Energy of activation of desorption from empty...

17 Further Reading

Particle Size Measurement, Volumes 1 and 2. 5th edn. (Chapman and Hall, London, 1997) Beddow, J. K. Particle Characterization inTechnology, Vol 1 Application and Micro-analysis, Vol 2 Morphological Analysis. (CRC Press, Boca Raton, FL, 1984) Bohren, C. F. and Huffman, D. R. Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983) Bradley, D. The Hydrocyclone. (Pergamon Press, Oxford, 1965) Clarke, A. N. and Wilson, D. J. Foam Flotation, Theory and Applications....

65 Heat Transfer To A Boundary Surface 651 Mechanisms involved

The good heat transfer properties of fluidised systems have led to their adoption in circumstances where close control of temperature is required. The presence of the particles in a fluidised system results in an increase of up to one-hundredfold in the heat transfer coefficient, as compared with the value obtained with a gas alone at the same velocity. In a liquid-fluidised system the increase is not so marked. Many investigations of heat transfer between a gas-fluidised system and a heat...

95 Sedimentation In A Centrifugal Field

Centrifuges are extensively used for separating fine solids from suspension in a liquid. As a result of the far greater separating power compared with that available using gravity, fine solids and even colloids may be separated. Furthermore, it is possible to break down emulsions and to separate dispersions of fine liquid droplets, though in this case the suspended phase is in the form of liquid droplets which will coalesce following separation. Centrifuges may be used for batch operation when...

828

(Dryer inlet 700 K, dryer outlet 365 K) (Dryer inlet 700 K, dryer outlet 365 K) In these systems, the total collection efficiencies of the dry product are 85 per cent for the drying vessel, 90 per cent for the cyclone collector and 98 per cent for the scrubber-condenser. The net efficiency of the system may be as high as 99.97 per cent if the scrubber effluent is considered as product. All the runs are based on 1.25 kg s product and 0.75 kg s evaporation at an elevation of 300 m above sea...

86 Ultrafiltration

Ultrafiltration is one of the most widely used of the pressure-driven membrane separation processes. The solutes retained or rejected by ultrafiltration membranes are those with molecular weights of 103 or greater, depending mostly on the MWCO of the membrane chosen. The process liquid, dissolved salts and low molecular weight organic molecules (500-1000 kg kmol) generally pass through the membrane. The pressure difference applied across the membrane is usually in the range 0.1-0.7 MN m2 and...

243 Size enlargement processes

Processes commonly used for size enlargement are listed in Table 2.4, taken from Perry(30). For comprehensive overall reviews, reference may be made to Perry and to the work of Browning(31). (a) Spray drying (as discussed in Chapter 16). In this case, particle size is largely determined by the size of the droplet of liquid or suspension, which may be controlled by a suitably designed spray nozzle. The aggregates of dried material are held together as a result of the deposition of small amounts...

83 The Nature Of Synthetic Membranes

Membranes used for the pressure-driven separation processes, microfiltration, ultrafiltration and reverse osmosis, as well as those used for dialysis, are most commonly made of polymeric materials'1. Initially most such membranes were cellulosic in nature. These are now being replaced by polyamide, polysulphone, polycarbonate and a number of other advanced polymers. These synthetic polymers have improved chemical stability and better resistance to microbial degradation. Membranes have most...

The mechanical classifier

Several forms of classifier exist in which the material of lower settling velocity is carried away in a liquid overflow, and the material of higher settling velocity is deposited on the bottom of the equipment and is dragged upwards against the flow of the liquid, by some mechanical means. During the course of the raking action, the solids are turned over so that any small particles trapped under larger ones are brought to the top again. The mechanical classifier is extensively used where it is...

45 Packed Columns

Since packed columns consist of shaped particles contained within a column, their behaviour will in many ways be similar to that of packed beds which have already been considered. There are, however, several important differences which make the direct application of the equations for pressure gradient difficult. First, the size of the packing elements in the column will generally be very much larger and the Reynolds number will therefore be such that the flow is turbulent. secondly, the packing...

82 Classification Of Membrane Processes

Industrial membrane processes may be classified according to the size range of materials which they are to separate and the driving force used in separation. There is always a degree of arbitrariness about such classifications, and the distinctions which are typically drawn are shown in Table 8.1. This chapter is primarily concerned with the pressure driven processes, microfiltration (MF), ultrafiltration (UF), nanofiltration (NF) and reverse osmosis (RO). These are already well-established...

1954 Process design and optimisation

The design of a production chromatograph is a complex exercise because of the many process variables involved. Some of the published work on optimisation proceeds from the unsatisfactory notion that a large-scale chromatograph is little more than a scaled-up analytical one into which large samples are injected. Thus the sample size is commonly chosen as the largest which does not excessively degrade resolution. While this approach simplifies scale-up in preparative work, it does not lead to...

2957

A still is operated at 18 kN m2 and steam is blown continuously into it. Estimate the temperature of the boiling liquid and the composition of the distillate if liquid water is present in the still. 11.9. The following values represent the equilibrium conditions in terms of mole fraction of benzene in benzene-toluene mixtures at their boiling-point Liquid 0.51 0.38 0.26 0.15 Vapour 0.72 0.60 0.45 0.30 If the liquid compositions on four adjacent plates in a column are 0.18, 0.28, 0.41 and 0.57...

134Angles of repose and of friction

A rapid method of assessing the behaviour of a particulate mass is to measure its angle of repose. if solid is poured from a nozzle on to a plane surface, it will form an approximately conical heap and the angle between the sloping side of the cone and the horizontal is the angle of repose. When this is determined in this manner it is sometimes referred to as the dynamic angle of repose or the poured angle. In practice, the heap will not be exactly conical and there will be irregularities in...

2022 Principles and advantages of process intensification

Process intensification, pioneered by Ramshaw(8) in the 1980's, may be defined as a strategy which aims to achieve process miniaturisation, reduction in capital cost, improved inherent safety and energy efficiency, and often improved product quality. In recent years, process intensification has been seen to provide processing flexibility, just-in-time manufacturing capabilities and opportunities for distributed manufacturing. In order to develop a fully intensified process plant, it is...

114 The Fractionating Column 1141 The fractionating process

Fractionating Process

The operation of a typical fractionating column may be followed by reference to Figure 11.11. The column consists of a cylindrical structure divided into sections by Figure 11.11. Continuous fractionating column with rectifying and stripping sections Figure 11.11. Continuous fractionating column with rectifying and stripping sections a series of perforated trays which permit the upward flow of vapour. The liquid reflux flows across each tray, over a weir and down a downcomer to the tray below....

The gyratory crusher

The gyratory crusher shown in Figure 2.6 employs a crushing head, in the form of a truncated cone, mounted on a shaft, the upper end of which is held in a flexible bearing, whilst the lower end is driven eccentrically so as to describe a circle. The crushing action takes place round the whole of the cone and, since the maximum movement is at the bottom, the characteristics of the machine are similar to those of the Stag crusher. As the crusher is continuous in action, the fluctuations in the...

682 Fluidised Bed Catalytic Cracking

The existence of a large surplus of high boiling material after the distillation of crude oil led to the introduction of a cracking process to convert these materials into compounds of lower molecular weight and lower boiling point in particular into petroleum spirit. The cracking was initially carried out using a fixed catalyst, although local variations in temperature in the bed led to a relatively inefficient process, and the deposition of carbon on the surface of the catalyst particles...

1523 Crystal nucleation

Nucleation, the creation of crystalline bodies within a supersaturated fluid, is a complex event, since nuclei may be generated by many different mechanisms. Most nucleation classification schemes distinguish between primary nucleation - in the absence of crystals and secondary nucleation - in the presence of crystals. Strickland-Constable(27) and Kashchiev(28) have reviewed nucleation, and Garside and Davey(29) have considered secondary nucleation in particular. Classical theories of primary...

102 Mass Transfer In Leaching Operations

Mass transfer rates within the porous residue are difficult to assess because it is impossible to define the shape of the channels through which transfer must take place. It is possible, however, to obtain an approximate indication of the rate of transfer from the particles to the bulk of the liquid. Using the concept of a thin film as providing the resistance to transfer, the equation for mass transfer may be written as where A is the area of the solid-liquid interface, b is the effective...

Dc d2c

Net accumulation rate due to diffusion from boundaries in axial direction Diffusion in radial direction at radius r Corresponding rate at radius r + 8r Net accumulation rate due to diffusion from boundaries in radial direction - 2itr8l e DR + 2ic(r + Sr)Sl e DR + 8r dr V or dr2 8r+r8r + (8r)2 dr dr2 dr2 Thus, from equations 4.33, 4.30, 4.31 and 4.32 (2nr8r8l)e -uc(2nr8r) 81 + 2nr8re)DL -8l+2n8leDR dt dl dl2 --h uc Dl - + -Dr r Longitudinal dispersion coefficients can be readily obtained by...

173 Adsorption Equilibria

Much of the early work on the nature of adsorbents sought to explain the equilibrium capacity and the molecular forces involved. Adsorption equilibrium is a dynamic concept achieved when the rate at which molecules adsorb on to a surface is equal to the rate at which they desorb. The physical chemistry involved may be complex and no single theory of adsorption has been put forward which satisfactorily explains all systems. Fortunately for the engineer, what is needed is an accurate...

811 Reverse Osmosis Water Treatment Plant

The largest scale applications of membrane separation processes are those which form the key step in the desalination, or more generally demineralisation, of brackish water in the production of drinking water. In this section an outline is given of such a plant capable of producing 70,000 m3 day of drinking water for a large city in the Middle East, as described by Finlay and Ferguson(25) . The water to be processed is obtained from a deep well with a total dissolved solids (TDS) content of 1.4...

233 293 386

Adiabatic conditions may be assumed and heat transfer between phases neglected. 12.16. A bubble-cap column with 30 plates is to be used to remove n-pentane from solvent oil by means of steam stripping. The inlet oil contains 6 kmol of n-pentane 100 kmol of pure oil and it is desired to reduce the solute content of 0.1 kmol 100 kmol of solvent. Assuming isothermal operation and an overall plate efficiency of 30 per cent, what is the specific steam consumption, that is kmol of steam required kmol...

224 Methods of operating crushers

Diagram Close Circuit Grinding

There are two distinct methods of feeding material to a crusher. The first, known as free crushing, involves feeding the material at a comparatively low rate so that the product can readily escape. Its residence time in the machine is therefore short and the production of appreciable quantities of undersize material is avoided. The second method is known as choke feeding. In this case, the machine is kept full of material and discharge of the product is impeded so that the material remains in...

52 Sedimentation Of Fine Particles 521 Experimental studies

The sedimentation of metallurgical slimes has been studied by Coe and Clevenger , who concluded that a concentrated suspension may settle in one of two different ways. Figure 5.1. Sedimentation of concentrated suspensions (a) Type 1 settling (b) Type 2 settling Figure 5.1. Sedimentation of concentrated suspensions (a) Type 1 settling (b) Type 2 settling In the first, after an initial brief acceleration period, the interface between the clear liquid and the suspension moves downwards at a...

62 Liquidsolids Systems 621 Bed expansion

Liquid-fluidised systems are generally characterised by the regular expansion of the bed that takes place as the velocity increases from the minimum fluidisation velocity to the terminal falling velocity of the particles. The general relation between velocity and volumetric concentration or voidage is found to be similar to that between sedimentation velocity and concentration for particles in a suspension. The two systems are hydrody-namically similar in that in the fluidised bed the particles...

2VMalv cos AA

Equation 17.44 is known as the Kelvin equation, and is considered to be valid for desorption. Figure 17.10. The capillary condensation equation applied to a cylindrical pore (a) for desorption (b) for Figure 17.10. The capillary condensation equation applied to a cylindrical pore (a) for desorption (b) for For adsorption on to existing layers of adsorbate on the cylindrical surface of the pores dV d n(rp - r2)Lp -2nrLp dr dA d 2nrLp 2nLp dr where r'p is the net radius of the pore. Equation...

Selection of economic reflux ratio

Optimum Reflux Ratio

The cost of a distillation unit includes the capital cost of the column, determined largely by the number and diameter of the plates, and the operating costs, determined by the steam and cooling water requirements. The depreciation charges may be taken as a percentage of the capital cost, and the two together taken as the overall charges. The steam required will be proportional to Vm, which may be taken as Vn where the feed is liquid at its boiling point. From a material balance over the top...

Dt dc JH

In general, the concentration of particles will be a function of position and time and thus Conditions of constant concentration are therefore defined by Substituting in equation 5.34 gives the following relation for constant concentration Since equation 5.36 refers to a constant concentration, df dC is constant and uw( dH dt) is therefore also constant for any given concentration and is the velocity of propagation of a zone of constant concentration C. Thus lines of constant slope, on a plot...

105 Calculation Of The Number Of Stages

The solid residue obtained from a batch leaching process may be washed by mixing it with liquid, allowing the mixture to settle, and then decanting the solution. This process can then be repeated until the solid is adequately washed. Suppose that, in each decantation operation, the ratio R' of the amount of solvent decanted to that remaining in association with insoluble solid is a constant and independent of the concentration of the solution, then, after the first washing, the fraction of the...

66 Mass And Heat Transfer Between Fluid And Particles

The calculation of coefficients for the transfer of heat or mass between the particles and the fluid stream requires a knowledge of the heat or mass flow, the interfacial area, and the driving force expressed either as a temperature or a concentration difference. Many early investigations are unsatisfactory in that one or more of these variables was inaccurately determined. This applies particularly to the driving force, which was frequently based on completely erroneous assumptions about the...

E Electrostatic precipitators

Electrostatic Precipitator Figure

Electrostatic precipitators, such as that shown in Figure 1.63, are capable of collecting very fine particles, < 2 m, at high efficiencies. Their capital and operating costs are high, however, and electrostatic precipitation should only be considered in place of alternative processes, such as filtration, where the gases are hot or corrosive. Electrostatic precipitators are used extensively in the metallurgical, cement and electrical power industries. Their main application is in the removal...

104 Countercurrent Washing Of Solids

Where the residual solid after separation is still mixed with an appreciable amount of solution, it is generally desirable to pass it through a battery of washers, arranged to give countercurrent flow of the solids and the solvent as shown in Figure 10.10. If the solids are relatively coarse a number of classifiers may be used and, with the more usual case of fine solids, thickeners are generally employed. In each unit a liquid, referred to as the overflow, and a mixture of insoluble residue...

Drying of a granular material according to the capillary theory

Pipe Fitting Formula Bend Deflection

If a bed of uniform spheres, initially saturated, is to be surface dried in a current of air of constant temperature, velocity and humidity, then the rate of drying is given by where Pw0 is the saturation partial pressure of water vapour at the wet bulb temperature of the air, and Pw is the partial pressure of the water vapour in the air stream. This rate of drying will remain constant so long as the inner surface of the stationary air film remains saturated. As evaporation proceeds, the water...

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

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...