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...

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...

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...

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...

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....

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...

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...

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...

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...

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...

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...

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...

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...

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...

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,

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 -...

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...

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...

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...

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...

1641 Diffusion theory of drying

In the general form of the curve for the rate of drying of a solid shown in Figure 16.2, there are two and sometimes three distinct sections. During the constant-rate period, moisture vaporises into the air stream and the controlling factor is the transfer coefficient for diffusion across the gas film. It is important to understand how the moisture moves to the drying surface during the falling-rate period, and two models have been used to describe the physical nature of this process, the...

5

What power would be required to crush 1 kg s of a material of compressive strength 45 MN m2 from a feed of minus 45 mm, plus 40 mm to a product of 0.50 mm average size 2.3. A crusher reducing limestone of crushing strength 70 MN m2 from 6 mm diameter average size to 0.1 mm diameter average size, requires 9 kW. The same machine is used to crush dolomite at the same output from 6 mm diameter average size to a product consisting of 20 per cent with an average diameter of 0.25 mm, 60 per cent with...

Mno

Whilst the Schildknecht column is essentially a laboratory-scale unit, a melt-crystalliser of the wash-column type was developed by Phillips Petroleum Company in the 1960s for large-scale production of -xylene. The key features of this Phillips pulsed-column crystalliser, as described by McKay etal. 88 , are shown in Figure 15.27. A cold slurry Figure 15.27. Phillips pulsed-column crystalliser1-88-1 Figure 15.27. Phillips pulsed-column crystalliser1-88-1 feed, produced in a scraped-surface...

1473 Natural circulation evaporators

Basket Type Vertical Evaporator Figure

Whilst each of the previous types of evaporator is of considerable importance in a given industry, it is the steam-heated evaporator that is the most widely used unit in the process industries and this is now considered in detail. In Chapter 9 of Volume 1, it is shown that the movement of the liquid over the heating surface has a marked influence on the rate of heat transfer, and it is thus convenient to classify evaporators according to the method of agitation or the nature of the circulation...

1

A bed consists of uniform spherical particles of diameter 3 mm and density 4200 kg m3. What will be the minimum fluidising velocity in a liquid of viscosity 3 mNs m2 and density 1100 kg m3 Galileo number, Ga d3p ps p g 2 3 x 10 3 3 x 1100 x 4200 1100 x 9.81 3 x 10 3 2 1.003 x 105 Assuming a value of 0.4 for emf, equation 6.14 gives Remf 25.7 V 1 5.53 x 10 5 1.003 x 105 1 40 and umf 40 x 3 x 10-3 3 x 10-3 x 1100 0.0364 m s or 36.4 mm s Oil, of density 900 kg m3 and viscosity 3 mNs m2, is passed...

Centrifugal attrition mills

Figure Attrition Mill

This mill shown in Figure 2.19, consists of a series of pushers which cause heavy cast iron balls to rotate against a bull ring like a ball race, with the pressure of the balls on the bull ring being produced by a loading applied from above. Material fed into the mill falls on the bull ring, and the product is continuously removed in an upward stream of air which carries the ground material between the blades of the classifier, which is shown towards the top of the photograph....

Batch type vacuum filters

Batch vacuum filters were developed from gravity filters and, in essence, Buchner funnels as used in laboratories and Nutsche type filters as used in industry are similar to gravity filters, except that they feature a vacuum pump or some other vacuum generating equipment to reduce the pressure under the filter medium, thereby increasing the driving force across the filter medium. Simple filters operating in this manner are often referred to as pan filters, and they incorporate certain features...

Horizontal continuous filters

One way of limiting still further cyclic variations is to use vacuum filters of the horizontal continuous type, and many designs have been developed which in the main consist of pans arranged in line or in a circle so that each in turn goes through the same cycle of operations, namely feeding, dewatering, washing, drying, automatic solids discharge and cloth washing. The pans move past the stationary feed and wash areas where the feed and wash liquors are continuously introduced to the filter....

2025 Twophase flow in a centrifugal field Introduction

As described by Bisschops et al. 20'21 centrifugal technology, using countercurrent contact of the process liquid with micrometer-range adsorbent particles constitutes a new technique for carrying out adsorption and ion-exchange processes in a centrifugal field. Because the use of very small particles results in large interfacial areas and short distances for diffusion, the mass-transfer rates are extremely fast, and centrifugal adsorption equipment is usually much more compact than that used...

1642 Capillary theory of drying Principles of the theory

The capillary theory of drying has been proposed in order to explain the movement of moisture in the bed during surface drying. The basic importance of the pore space between granular particles was first pointed out by Slichter 16 in connection with the movement of moisture in soils, and this work has been modified and considerably expanded by Haines 17 . The principles are now outlined and applied to the problem of drying. Considering a systematic packing of uniform spherical particles, these...

178 Adsorption Equipment

The scale and complexity of an adsorption unit varies from a laboratory chromatographic column a few millimeters in diameter, as used for analysis, to a fluidised bed several metres in diameter, used for the recovery of solvent vapours, from a simple container in which an adsorbent and a liquid to be clarified are mixed, to a highly-automated moving-bed of solids in plug-flow. All such units have one feature in common in that in all cases the adsorbent becomes saturated as the operation...

1659 Turboshelf dryers

Simple Figure Turbo Type Dryer

The handling of sticky materials can present difficulties, and one type of dryer which is useful for this type of material is the turbo-dryer. As shown in Figure 16.30, wet solid is fed in a thin layer to the top member of a series of annular shelves each made of a number of segmental plates with slots between them. These shelves rotate and, by means of suitably placed arms, the material is pushed through a slot on to a shelf below. After repeated movements, the solid leaves at the bottom of...

1279 The transfer unit

The group f dy ye y , which is used in Chapter 11, has been defined by Chilton and Colburn 52 as the number of overall gas transfer units N0G. The concept of the transfer unit is also introduced in Volume 1, Chapter 10. The application of this group to the countercurrent conditions in the absorption tower is now considered. Over a small height dZ, the partial pressure of the diffusing component A will change by an amount dPAG. Then the moles of A transferred are given by change in mole fraction...

Design considerations

Many of the design problems associated with rotary dryers have been discussed by Friedman and Marshall 24 , by Prutton et al. 25 and by Miller et al. 26 . Heat from the air stream passes to the solid material during its fall through the air stream, and also from the hot walls of the shell, although the first mechanism is much the more important. The heat transfer equation may be written as where Q is the rate of heat transfer, U is the overall heat transfer coefficient, V is the volume of the...

734 Delayed cake filtration

In the filtration of a slurry, the resistance of the filter cake progressively increases and consequently, in a constant pressure operation, the rate of filtration falls. If the build-up of solids can be reduced, the effective cake thickness will be less and the rate of flow of filtrate will be increased. In practice, it is sometimes possible to incorporate moving blades in the filter equipment so that the thickness of the cake is limited to the clearance between the filter medium and the...

Fluid energy mills

Another form of mill which does not give quite such a fine product is the jet pulveriser, in which the solid is pulverised in jets of high pressure superheated steam or compressed air, supplied at pressures up to 3.5 MN m2 35 bar . The pulverising takes place in a shallow cylindrical chamber with a number of jets arranged tangentially at equal intervals around the circumference. The solid is thrown to the outside walls of the chamber, and the fine particles are formed by the shearing action...

1211 References

Eng. 29 1923 147. The two-film theory of absorption. 2. Higbie, R. Trans. Am. Inst. Chem. Eng. 31 1935 365. The rate of absorption of pure gas into a still liquid during short periods of exposure. 3. Danckwerts, P. V. Ind. Eng. Chem. 43 1951 1460. Significance of liquid-film coefficients in gas absorption. 4. Danckwerts, P. V. and Kennedy, A. M. Trans. Inst. Chem. Eng. 32 1954 S49. Kinetics of liquid-film processes in gas absorption. 5. Lynn, S., Straatemeier, J....

85 Crossflow Microfiltration

The solids-liquid separation of slurries containing particles below 10 m is difficult by conventional filtration techniques. A conventional approach would be to use a slurry thickener in which the formation of a filter cake is restricted and the product is discharged continuously as a concentrated slurry. Such filters use filter cloths as the filtration medium Membrane flux is denoted by J, the usual symbol in the literature on membranes. It corresponds with uc, as used in Chapters 4 and 7 for...

Nab

Bed inversion a Complete segregation b Complete and partial segregation' The relative rates at which the bed densities change as the fluidising velocity is increased may be obtained by differentiating equations 6.42a and 6.42b with respect to uc, and dividing to give _ dpbH j _ dpbL _ dpbH _ psH - p uql_ V n _ PsH - P eH As eH gt eL and psH gt psL, then from equation 6.44, r, which is independent of fluidising velocity, must be greater than unity. It is thus the bed of heavy...

610 References

Chem. Eng. Prog. 44 1948 201. Fluidization of solid particles. 2. Jackson, R. Trans. Inst. Chem. Eng. 41 1963 13, 22. The mechanisms of fluidised beds. Part 1. The stability of the state of uniform fluidisation. Part 2. The motion of fully developed bubbles. 3. Murray, J. D. J. Fluid Mech. 21 1965 465 22 1965 57. On the mathematics of fluidization. Part 1. Fundamental equations and wave propagation. Part 2. Steady motion of fully developed bubbles. 4. Leva, M.,...

1510 References

W. 'Crystallization' in Kirk-Othmer Encyclopedia of Chemical Technology, Volume 7, 3rd. edition John Wiley amp Sons, New York, 1979 2. Mullin, J. W. 'Crystallization and Precipitation' in Ullmann's Encyclopedia of Industrial Chemistry, Volume B2 VCH Verlagsgesellschaft mbH, Weinheim, 1988 3. Mullin, J. W. Crystallization 4th. edn. Butterworth-Heinemann, Oxford, 2001 4. Feilchenfeld, H. and Sarig, S. Ind. Eng. Chem. Process. Prod. Res. Dev. 24 1985 130-133. Calcium chloride...

1113 References

R. Elements of Fractional Distillation, 4th edn. McGraw-Hill, New York, 1950 . 2. Thornton, J. D. and Garner, F. H. J. Appl. Chem. Suppl. 1 1951 61. Vapour-liquid equilibria in hydrocarbon-non-hydrocarbon systems. 1 The system benzene-cyclohexane-furfuraldehyde. 3. Antoine, C. Comptes Rendus 107 1888 681, 836. Tensions des vapeurs nouvelle relation entre les tensions et les temperatures. 4. Boublik, T., Fried, V. and Hala, E. The Vapour Pressure of Pure...

The hydraulic jig

Denver Jig

The hydraulic jig operates by allowing material to settle for brief periods so that the particles do not attain their terminal falling velocities, and is therefore suitable for separating materials of wide size range into their constituents. The material to be separated is fed dry, or more usually in suspension, over a screen and is subjected to a pulsating action by liquid which is set in oscillation by means of a reciprocating plunger. The particles on the screen constitute a suspension of...

The Dodge jaw crusher

Dodge Crusher

In the Dodge crusher, shown in Figure 2.5, the moving jaw is pivoted at the bottom. The minimum movement is thus at the bottom and a more uniform product is obtained, although the crusher is less widely used because of its tendency to choke. The large opening at the top enables it to take very large feed and to effect a large size reduction. This crusher is usually made in smaller sizes than the Stag crusher, because of the high fluctuating stresses that are produced in the members of the...

Working Of Stag Jaw Crusher

Fixed Jaw Face Swing Jaw Face Swing Jaw Stock Toggle Seating Front Toggle Plate Toggle Seating Back Toggle Plate Springs and Cups Swing Jaw Shaft Eccentric Shaft 14. Flywheel grooved for V rope drive 19. Cheek Plates top 19A. Cheek Plates bottom 21. Swing Jaw Shaft Bearing Caps 22. Eccentric Shaft Bearing Caps 27. Eccentric Shaft Bearing Bush bottom 28. Eccentric Shaft Bearing Bush top Figure 2.4. Typical cross-section of Stag jaw crusher Stag crushers are made with jaw widths varying from...

The Denver DR flotation machine

Denver Sub Aeration Mechanism

The Denver DR flotation machine, which is an example of a typical froth flotation unit used in the mining industry, is illustrated in Figure 1.47. The pulp is introduced through a feed box and is distributed over the entire width of the first cell. Circulation of the pulp through each cell is such that, as the pulp comes into contact with the impeller, it is subjected to intense agitation and aeration. Low pressure air for this purpose is introduced down the standpipe surrounding the shaft and...

Electronic particle counters

Electronic Particle Counters

A suspension of particles in an electrolyte is drawn through a small orifice on either side of which is positioned an electrode. A constant electrical current supply is connected to the electrodes and the electrolyte within the orifice constitutes the main resistive component of the circuit. As particles enter the orifice they displace an equivalent volume of electrolyte, thereby producing a change in the electrical resistance of the circuit, the magnitude of which is related to the displaced...

154 The hydrocyclone or liquid cyclone

In the hydrocyclone, or hydraulic cyclone, which is discussed extensively in the literature1-29-35-1, separation is effected in the centrifugal field generated as a result of introducing the feed at a high tangential velocity into the separator. The hydrocyclone may be used for a separating particles suspended in a liquid of lower density by size or density, or more generally, by terminal falling velocity Figure 1.36. NEI Delta sizer ultrafine classifier Figure 1.36. NEI Delta sizer ultrafine...

Solution

Assuming the galena and quartz particles are of similar shapes, then from equation 1.42, the required density of fluid when Stokes' law applies is given by 0.065 _ 7500 p 0'5 0.015 2650 p The required density of fluid when Newton's law applies is given by 0.065 _ 7500 p 10 0.015 2650 p Thus, the required density of the fluid is between 1196 and 2377 kg m3. 1.5.2. Gravity settling The settling tank Material is introduced in suspension into a tank containing a relatively large volume of water...

12 Particle Characterisation 121 Single particles

The simplest shape of a particle is the sphere in that, because of its symmetry, any question of orientation does not have to be considered, since the particle looks exactly the same from whatever direction it is viewed and behaves in the same manner in a fluid, irrespective of its orientation. No other particle has this characteristic. Frequently, the size of a particle of irregular shape is defined in terms of the size of an equivalent sphere although the particle is represented by a sphere...