## 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...

## O

Chromatogram for stepwise elution of bovine serum albumin on a Vistec diethyl aminoethyl cellulose ion-exchanger, using stepwise increases in sodium chloride concentration in the mobile phase to achieve selective desorption. Proteins 1, serum fraction not adsorbed by column (includes y-gobulin) 2,3, transferrin, and so on 4,5 albumin1-57-1 For large-scale separations, a further operational change is commonly adopted. Maximum production requires that the width of the protein band...

## 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...

## 131 General characteristics

The properties of solids in bulk are a function of the properties of the individual particles including their shapes and sizes and size distribution, and of the way in which the particles interact with one another. By the very nature of a particulate material, it is always interspersed with a fluid, generally air, and the interaction between the fluid and the particles may have a considerable effect on the behaviour of the bulk material. Particulate solids present considerably greater problems...

## 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...

## Sieving 50 m

Sieve analysis may be carried out using a nest of sieves, each lower sieve being of smaller aperture size. Generally, sieve series are arranged so that the ratio of aperture sizes on consecutive sieves is 2, 21 2 or 21 4 according to the closeness of sizing that is required. The sieves may either be mounted on a vibrator, which should be designed to give a degree of vertical movement in addition to the horizontal vibration, or may be hand shaken. Whether or not a particle passes through an...

## Solution

Taking a material balance for the whole throughput and for the ammonia gives D + W 1.0 0.995D + 0.1 W (1.0 x 0.3) Thus D 0.22 kg s The enthalpy-composition chart for this system is shown in Figure 11.29. It is assumed that the feed F and the bottom product W are both liquids at their boiling points. Nm for minimum reflux is found by drawing a tie-line through F, representing the feed, to cut the line x 0.995 at Nm. length AL (1952 - 1547) (1547 - 295) Figure 11.29. Enthalpy-composition diagram...

## 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...

## 1762 Pore sizes

Having obtained a measure of surface area, a mean pore size may be calculated by simplifying the pore system into np cylindrical pores per unit mass of adsorbent, of mean length Lp and mean pore radius rp. Hence Pore volume Vp npnr2Lp This expression has been generalised by Everett and Stone(8) for any shape of capillary by including a shape factor y which takes a value that depends on the geometry of the capillary. This is unity for parallel sided fissures as well as for cylindrical pores....

## 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

## Info

Column with multiple feeds and sidestreams Figure 11.21. Column with multiple feeds and sidestreams F1 and F2 are separate feed streams to the column. Sidestreams are most often removed with multicomponent systems, although they may be used with binary mixtures. A binary system is now considered, with one sidestream, as shown in Figure 11.22. S' represents the rate of removal of the sidestream and xs its composition. Assuming constant molar overflow, then for the part of the...

## 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...

## 1931 Plate height

In a hypothetical ideal column, a solute band would retain its initial profile unaltered as it migrated along the column. In a real, non-ideal, column an initially narrow band broadens by dispersion as it migrates. The band width is proportional to the square root of the distance travelled along the column. The rate at which the band broadens depends on the inefficiency of the column. This is more precisely defined as the height equivalent to a theoretical plate (HETP), discussed in detail in...

## 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...

## 136 Flow of solids through orifices

The discharge rate of solid particles is usually controlled by the size of the orifice or the aperture at the base of the hopper, though sometimes screw feeders or rotating table feeders may be incorporated to encourage an even flowrate. The flow of solids through an orifice depends on the ability of the particles to dilate in the region of the aperture. Flow will occur if the shear force exerted by the superincumbent material exceeds the shear strength of the powder near the outlet. The rate...

## 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

## 152 Crystallisation Fundamentals

In evaluating a crystallisation operation, data on phase equilibria are important as this indicates the composition of product which might be anticipated and the degree of supersaturation gives some idea of the driving force available. The rates of nuclei formation and crystal growth are equally important as these determine the residence time in, and the capacity of a crystalliser. These parameters also enable estimates to be made of crystal sizes, essential for the specification of liquor...

## 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...

## 1862 Fixed beds

Most ion exchange operations are carried out in fixed beds of resin contained in vertical cylindrical columns. The resin is supported on a grid fine enough to retain the pellets of resin, but sufficiently open so as not to hinder liquid flow. Sizes range from laboratory scale to industrial units 1-3 m in diameter and height. Liquid is fed to the top of the column through a distributor carefully designed and fitted to ensure an even flow over the whole cross-section of the bed. A mass transfer...

## Precoat filters

All the filters described previously have been in the category of cake filters for they all rely on the solids present in the feed slurry having properties which are suitable for them to act as the actual filter medium and to form cakes which are relatively easily discharged. Applications arise where extremely thin filter cakes, perhaps only a fraction of a millimetre thick, have to be discharged, where extremely good filtrate clarity is essential, or where a particularly blinding substance is...

## 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...

## 2

If za is the value of z0 which corresponds to the position where the free surface is at the axis of rotation (r0 0), then Equations 9.1 and 9.2 correspond with equations 2.80 and 2.79 in Volume 1, Chapter 2. Taking the base of the bowl as the origin for the measurement of z0, positive values of za correspond to conditions where the whole of the bottom of the bowl is covered by liquid. Negative values of za imply that the paraboloid of revolution describing the free surface would cut the axis of...

## 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...

## 421 Darcys law and permeability

The first experimental work on the subject was carried out by Darcy1 in 1830 in Dijon when he examined the rate of flow of water from the local fountains through beds of sand of various thicknesses. It was shown that the average velocity, as measured over the whole area of the bed, was directly proportional to the driving pressure and inversely proportional to the thickness of the bed. This relation, often termed Darcy's law, has subsequently been confirmed by a number of workers and can be...

## 35

0.12 -T- Resin particles 0.1 0.08 -0.06-0.04 -0.02 0 o 2.23 Hz (134 rpm) 2.5 Hz (150 rpm) x 8.0 Hz (180 rpm) 3.3 Hz (200 rpm) a 4.2 Hz (250 rpm) Figure 20.15. Experiment flooding data obtained in the low-g rotor with nozzle discharge(20> Figure 20.15. Experiment flooding data obtained in the low-g rotor with nozzle discharge(20> the nozzle discharge, the results for flooding conditions obtained from the tests are shown in Figure 20.15 in which uL is the superficial liquid velocity, uS is...

## 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...

## 1163 Operation at constant reflux ratio

If the same column is operated at a constant reflux ratio R, the concentration of the more volatile component in the top product will continuously fall. Over a small interval of time di, the top-product composition with respect to the more volatile component will change from xd to xd + dxd, where dxd is negative for the more volatile component. If in this time the amount of product obtained is dDb, then a material balance on the more volatile component gives More volatile component removed in...

## 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...

## 129 Other Equipment For Gas Absorption 1291 The use of vessels with agitators

A gas may be dissolved in a liquid by dispersing it through holes in a pipe immersed in the liquid which is stirred with some form of agitator, as shown in Figure 12.29. Although this type of equipment will give only one theoretical stage per unit, but it often provides a useful method of saturating a liquid with a gas. Cooper et al.(58) have studied the absorption of oxygen from air in an aqueous solution of sodium sulphite using simple vessels of 0.15 to 2.44 m diameter fitted with four...

## Example 117

A mixture of benzene and toluene containing 40 mole per cent benzene is to be separated to give a product containing 90 mole per cent benzene at the top, and a bottom product containing not more than 10 mole per cent benzene. The feed enters the column at its boiling point, and the vapour leaving the column which is condensed but not cooled, provides reflux and product. It is proposed to operate the unit with a reflux ratio of 3 kmol kmol product. It is required to find the number of...

## 11102 Factors determining column performance

The performance of a column may be judged in relation to two separate but related criteria. First, if the vapour and liquid leaving a tray are in equilibrium this constitutes a theoretical tray and provides a standard of performance. Secondly, the relative performance of, say, two columns of the same diameter must be considered in relation to their capacity for liquid and vapour flow. The main features are (a) Liquid and vapour velocities. (b) Physical properties of the liquid and vapour. (c)...

## 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...

## Overall coefficients

In order to obtain a direct measurement of the values of kL and kG the measurement of the concentration at the interface would be necessary. These values can only be obtained in very special circumstances, and it has been found of considerable value to use two overall coefficients KG and KL defined by Kg and Kl are known as the overall gas and liquid phase coefficients, respectively.

## Drum filter

Area of filtering surface (0.6 x 0.6n) 0.36n m2 (0.125 1000) 1.25 x 10 4 m3 s of filtrate 1 kg or 10 3 m3 water is associated with 0.2 kg of solids 0.2 (3 x 103) 6.67 x 10 5 m3 of solids in the slurry. Since the cake porosity is 0.5, 6.67 x 10 5 m3 of water is held in the filter cake and (10 3 6.67 x 10 5) 9.33 x 10 4 m3 appears as filtrate, per kg of total water in the slurry. Volume of cake deposited by unit volume of filtrate, v (6.67 x 10 5 x 2) (9.33 x 10 4) 0.143. Volumetric rate of...

## 533 Solids flux in batch sedimentation

In a sedimenting suspension, the sedimentation velocity uc is a function of fractional volumetric concentration C, and the volumetric rate of sedimentation per unit area or flux f is equal to the product ucC. Thus f ucC uc(1 e) (5.88) Then, if the relation between settling velocity and concentration can be expressed in terms of a terminal falling velocity (u0) for the particles, substituting for u0 using equation 5.71 From the form of the function, it is seen that f should have a maximum at...

## 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...

## Example 154

What is the yield of sodium acetate crystals (CH3C00Na.3H20) obtainable from a vacuum crystalliser operating at 1.33 kN m2 when it is supplied with 0.56 kg s of a 40 per cent aqueous solution of the salt at 353 K The boiling point elevation of the solution is 11.5 deg K. Heat of crystallisation, q 144 kJ kg trihydrate Heat capacity of the solution, Cp 3.5 kJ kg deg K Latent heat of water at 1.33 kN m2, X 2.46 MJ kg Boiling point of water at 1.33 kN m2 290.7 K Solubility of sodium acetate at...

## Dc dc 1 dcs dc

Equation 17.75 is important as it illustrates, for the equilibrium case, a principle that applies also to the non-equilibrium cases more commonly encountered. The principle concerns the way in which the shape of the adsorption wave changes as it moves along the bed. If an isotherm is concave to the fluid concentration axis it is termed favourable, and points of high concentration in the adsorption wave move more rapidly than points of low concentration. Since it is physically impossible for...

## 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,...

## 2013 The role of the chemical engineer

In a further paper, Edwards(6) classifies the processes and operations which occur in the manufacture and supply of products using an appropriate length scale as follows Chemical engineers are well versed in the design and sizing of unit operations such as reactors, mixing vessels, heat exchangers and separation units, operating on a length scale appropriate to the equipment of around 1 metre. Chemical engineers are also able to integrate individual operations to create an entire plant or...

## Inclusions in crystals

Inclusions are small pockets of solid, liquid, or gaseous impurities trapped in crystals that usually occur randomly although a regular pattern may be sometimes observed. As described by Mullin(3) , a simple technique for observing inclusions is to immerse the crystal in an inert liquid of similar refractive index or, alternatively, in its own saturated solution when, if the inclusion is a liquid, concentration streamlines will be seen as the two fluids meet and, if it is a vapour, a bubble...

## 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)....

## Xl

1 Xtt is strongly dependent on the mass fraction of vapour y. The density and viscosity terms give a quantitative correction for the effect of pressure in the absence of nucleate boiling. Eighty-five per cent of the purely convective data for two-phase flow were correlated to within 20 per cent by the expression Similar results for a range of organic liquids are reported by Guerrieri and Talty(10), though, in this work, hL is based on the point mass flowrate of the unvaporised part of the...

## 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...

## Filter press

Using a filter press with n frames of thickness b m, the total time, for one complete cycle of the press (if + 120n + 240) s, where if is the time during which filtration is occurring. Overall rate of filtration --- 1.25 x 1CT4 m3 s where Vf is the total volume of filtrate per cycle. The volume of frames volume of cake deposited by unit volume of filtrate, v, is given by But Vf (3.38 x 10-10) x (1.75 x 105)(2n x 0.3 x 0.3)2if (from equation 7.11) That is 25.8b2 + 0.015n + 0.030 0.629nb n is a...

## 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...

## Constant rate period

During the constant rate period, it is assumed that drying takes place from a saturated surface of the material by diffusion of the water vapour through a stationary air film into the air stream. Gilliland(8) has shown that the rates of drying of a variety of materials in this stage are substantially the same as shown in Table 16.1. Table 16.1. Evaporation rates for various materials under constant conditions'-8-1 Table 16.1. Evaporation rates for various materials under constant...

## Plate efficiency in terms of liquid concentrations

With the same concept for tray layout as in Figure 11.55, relations for Eml and EMl may be derived. Assuming that the vapour concentration does not change in a horizontal plane, a similar analysis to that above gives Emi 1 exp( N0l) (11.134) The efficiencies Emv and Eml may be related by using the relation between N0G and Nol given in equation 11.130 to give ln(1 Emi) e ln(1 Emv) (11.135)

## 0105

From equation 11.103 ln(Sj S2) 1.1 and (S1 S2) 3.0. Product obtained, Db S1 S2 (100 100 3) 66.7 kmol. Amount of ethanol in product xjSj x2S2 (0.55 x 100) (0.105 x 33.3) 51.5 kmol Thus average composition of product (51.5 66.7) 0.77 mole fraction ethanol. The heat required to provide the reflux (4000 x 2.1 x 66.7) 560,380 kJ. Heat required to provide reflux per kmol of product (560,380 66.7) 8400 kJ. Thus in Example 11.12 the total heat required per kmol of product is (5320 + 4000) 9320 kJ and...

## 422 Specific surface and voidage

The general structure of a bed of particles can often be characterised by the specific surface area of the bed SB and the fractional voidage of the bed e. SB is the surface area presented to the fluid per unit volume of bed when the particles are packed in a bed. Its units are (length)-1. e is the fraction of the volume of the bed not occupied by solid material and is termed the fractional voidage, voidage, or porosity. It is dimensionless. Thus the fractional volume of the bed occupied by...

## 815 Further Reading

Belfort, G. (ed.) Synthetic Membrane Processes (Academic Press, Orlando, 1984). Cheryan, M. Ultrafiltration Handbook (Technomic Publishing Company, Pennsylvania, 1998). Rautenbach, R. and Albrecht, R. Membrane Processes (Wiley, 1989). Schweitzer, P. A., (ed.) Handbook of Separation Techniques for Chemical Engineers, 2nd edn. (McGraw Hill, New York, 1988). Zeman, L. J. and Zydney, A. L., Microfiltration and Ultrafiltration. Principles and Applications (Marcel Dekker, New York, 1996).

## 425

The solid is usually in contact with the hot metal for 6-15 s, short enough to prevent significant decomposition of heat sensitive materials, and heat transfer coefficients are 1-2 kW m2 K. When the temperature of the drying material must be kept as low as possible, vacuum drying is used, and one form of vacuum dryer is shown in Figure 16.18. The dried material is collected in two screw conveyors and carried usually to two receivers so that one can be filled while the other is emptied.

## 1342 Cocurrent contact with immiscible solvents

In this case, which is illustrated in Figure 13.12, triangular diagrams are not required. If the initial solution contains a mass A of solvent A with a mass ratio Xf of solute, then the selective solvent to be added will be a mass S of solvent S. On mixing and separating, a raffinate is obtained with the solvent A containing a mass ratio X1 of solute, and an extract with the solvent S containing a mass ratio Y1 of solute. A material balance on the solute gives

## 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...

## 334 Rising velocities of light particles

Although there appears to be no problem in using the standard relations between drag coefficient and particle Reynolds number for the calculation of terminal falling velocities of particles denser than the liquid, Karamanev, Chavarie and Mayer(12) have shown experimentally that, for light particles rising in a denser liquid, an overestimate of the terminal rising velocity may result. This can occur in the Newton's law region and may be associated with an increase in the drag coefficient CD'...

## 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...

## 721 Introduction

Equations are given in Chapter 4 for the calculation of the rate of flow of a fluid through a bed of granular material, and these are now applied to the flow of filtrate through a filter cake. Some differences in general behaviour may be expected, however, because the cases so far considered relate to uniform fixed beds, whereas in filtration the bed is steadily growing in thickness. Thus, if the filtration pressure is constant, the rate of flow progressively diminishes whereas, if the flowrate...

## 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...

## 155 Crystallisation From Vapours 1551 Introduction

The term sublimation strictly refers to the phase change solid vapour, with no intervention of a liquid phase. in industrial applications, however, the term usually includes the reverse process of condensation or desublimation solid vapour solid. In practice, it is sometimes desirable to vaporise a substance from the liquid state and hence the complete series of phase changes is then solid liquid vapour solid, and, on the condensation side of the process, with the supersaturated vapour...

## 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...

## 2014 Green chemistry

Increasing concern for the need to conserve and to use effectively world reserves of raw materials and, at the same time, to reduce the quantities of waste materials which are likely to have an adverse effect on the environment has led to pressure for the increased use of renewable resources and so-called 'green chemistry'. The principles of green chemistry have been enunciated by Hamley and Poliakoff1-7 as follows molecular level micro level unit operations factory supply chain Length (m) lO-l...

## 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...

## Simple and vacuum sublimation

Simple sublimation is a batch-wise process in which the solid material is vaporised and then diffuses towards a condenser under the action of a driving force attributable to difference in partial pressures at the vaporising and condensing surfaces. The vapour path between the vaporiser and the condenser should be as short as possible in order to reduce masstransfer resistance. simple sublimation has been used for centuries, often in very crude equipment, for the commercial production of...

## Expressions for plate efficiency related to mass transfer

By assuming that the vapour issuing from slots is in the form of spherical bubbles, Chu(66), Geddes(67), and Bakowski(68) derived methods for expressing the efficiency E in terms of transfer coefficients, kg, kl and tray parameters such as the slot dimensions. These methods have proved very difficult to use because of the unreliability of data for calculating transfer coefficients, and the greater problem of calculating the interfacial areas. Probably the most successful analysis for...

## 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.

## 1123 Relative volatility

The relationship between the composition of the vapour yA and of the liquid xA in equilibrium may also be expressed in a way, which is particularly useful in distillation calculations. If the ratio of the partial pressure to the mole fraction in the liquid is defined as the volatility, then Volatility of A and volatility of B The ratio of these two volatilities is known as the relative volatility a given by Substituting PyA for PA, and PyB for PB This gives a relation between the ratio of A and...

## 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...

## Forcedcirculation crystallisers

A Swenson forced-circulation crystalliser operating at reduced pressure is shown in Figure 15.15. A high recirculation rate through the external heat exchanger is used to provide good heat transfer with minimal encrustation. The crystal magma is circulated from the lower conical section of the evaporator body, through the vertical tubular heat exchanger, and reintroduced tangentially into the evaporator below the liquor level to create a swirling action and prevent flashing. Feed-stock enters...

## 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...

## 93 Centrifugal Pressure

A force balance on a sector of fluid in the rotating bowl, carried out as in Volume 1, Chapter 2, gives the pressure gradient at a radius r Unlike the vertical pressure gradient in a column of liquid which is constant at all heights, the centrifugal pressure gradient is a function of radius of rotation r, and increases towards the wall of the basket. Integration of equation 9.3 at a given height gives the pressure P exerted by the liquid on the walls of the bowl of radius R when the radius of...

## 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 -...

## 1861 Staged operations

In the simple batch process, conservation of counter-ions leaving the liquid may be written as V(Co - C) Rv(CS - Cso) (18.24) where V and Rv refer to initial volumes of liquid and resin. If the batch process behaves as an equilibrium stage, the phases in contact will achieve equilibrium. If the equilibrium relationship is known, then and equations 18.25 and 18.26 may be solved. In Figure 18.5 it is assumed that V and Rv remain constant. It is sometimes convenient to use the fractional...

## 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...