## Z

Ooi 0.2 03 0.4- 0.5 0.6 0.7 0.& 0.9 KG Mol. Fraction of Benzene Fig. 11-8. Operation of benzene-toluene column. results are shown in Fig. 11-9. The amount of xylenes was small so that a large proportion of toluene was present on the bottom plate. The highest concentration of toluene occurred on the fifth plate, this component thus tending to segregate in the column. Under ordinary conditions, a column would be operated at a lower temperature level so that the benzene at the top would have...

## Y

The effects of various values of p are shown in Fig. 7-4 for a given slope of the operating line above the feed. Thus, if p 0, the mols of overflow above and below the feed are equal, and the operating lines must intersect in a horizontal line through the diagonal at zF. A value of p 1, i.e., Vf - F -would put the intersection on a vertical line at zf. The value of p is best obtained by an enthalpy balance around the feed plate. However, when the molal enthalpy of...

## X

Thus if (In y ) x is plotted vs. x2, and (In y x is plotted against 0.5 + Xi, they will both give a line of slope c and intercept b. Such a plot facilitates the evaluation of the constants. The constants in the Margules equation are a function of temperature thus, if one experimental point is used to evaluate them, then assuming the equation to apply, they should be suitable for other compositions at the same temperature. A generalized relationship for the effect of temperature on the activity...

## Oir

Correlated were for essentially standard caps and plate arrangements, and the relation should be used with caution for plate layouts that differ significantly. It will be noted for Fig. 16-7 that ' is essentially inversely proportional to the value of Re'. Combining this relationship with the fact that for large plates 2L0 is small in comparison with b gives This relation would indicate that the hydraulic gradient is directly proportional to the liquid flow rate per foot of plate width and to...

## 1

Much more suitable for extrapolation in the design of large-scale bubble-plate towers than those obtained in packed towers. These small columns give plate efficiencies that are comparable to those of large towers, and their effectiveness is not a major function of the wetting characteristics of the liquid as it is in a packed tower. The one major remaining advantage of the packed tower is low pressure drop even in this case, new types of columns are being developed which give definite and...

## Www

5- -rr + -J L-rr + -rr + -1 (12-33) au < f> aB ao 4> In many cases, the use of these equations is complicated by the fact that a trial-and-error procedure is involved. If the terminal compositions are known, the trial-and-error operation involves matching at the feed plate. Usually the terminal conditions are not completely known, and additional trial and error may be required. In most cases a three-component problem can be solved just as rapidly by the usual stepwise procedure, and...

## W

These equations are similar to Eqs. (7-16) and (7-17), and the same considerations relative to the constancy of molal rates of vapor and overflow apply in this case. 3. General Case. The derivations given in the two previous sections were for the case with no side streams, but the general case is similar. In the system shown in Fig. 7-15, the over-all and component material balances above plate a are where Va vapor rate to plate a + 1 Oa+1 - overflow rate from plate a + 1 N net mols leaving...

## W 0 V r

R ahk , t w i un x ' i a (See nomenclature at the end of this chapter.) These equations should not be applied to mixtures having minimum reflux ratios determined by a tangent contact in one section of the tower only. It is customary to use relative volatility values corresponding to approximately the feed-plate temperature. Actually some of the values correspond to the pinched-in region above the feed and the others to the lower section, but usually this refinement is not made although it can...

## Vax

Product ' f Tl m Hsl fl9 1 Product composition as fractions 11 and 15. Samples 20, 21, and 22 can be redistilled in the same manner, and by a repetition of the procedure essentially all of the material will be given the desired separation. The method outlined in the preceding paragraph can be made continuous. Thus by regulating the fractions vaporized in the various distillations it is possible to have fractions 5 and 13 of the same composition as the original mixture, and fresh feed can be...

## Vapor Pressures Of Completely Miscible Liquid Mixtures At Constant Temperature

Whenjj& e liquid is dissolved in another, the partial pressure of each is decreased. Assume two liquids, the molecules of which are the same size and which mix without the complicating effects of molecular association, chemical combination, and the like. In an equimolecular mixture of two such liquids, each unit of surface area of the liquid mixture will have in its surface half as many molecules of each component as exist in the liquid surface of that component in the pure...

## Vapor Phase

Pure gases or gaseous mixtures approach agreement with the perfect-gas law if the pressures are low enough.1 Under these conditions, the volume of the gaseous mixture is so large that the volume of the mole-, cules is a negligible percentage of the total, and the molecules on the 1 The reduction to zero pressure may cause a change in species. Thus, if the pressure on pure Cl2 gas is reduced, the gas may never obey the perfect-gas law since, before exact agreement is reached, the CI2 will...

## Vacuum Distillation

Reduced pressures are frequently used in distillation processes for the purpose of lowering the temperature required. This is frequently important in the distillation of organic substances that are thermally unstable and would decompose if boiled at normal pressures. In addition to the reduced thermal degradation, the lower temperature often modifies the relative volatility or the degree of separation involved. In the design methods considered in the preceding chapters, vapor-liquid equilibrium...

## Ujf

Operating line to the other must therefore occur at some value of x between the values corresponding to c and e, and a change at any value within this range will give an operable design. In general, for a given reflux ratio, it is desired to carry out the rectification with as few plates as possible in order to reduce the plant costs i.e., the minimum number of steps from a to d between the equilibrium curve and the operating line is desired. This minimum number of steps for the design...

## Rdv

qVW + m-l + Sm-lSm-2 + ' * Assuming S is a constant and letting Nm equal the number of theoretical plates below feed, xf S yw - ( yw x ) (I + S + S* + + S ) (12-23) Xf-Zi** XiS(l + S + S2+ + - yw (1 + S + 2 + + S *-1) Multiplying the numerator and denominator of the right-hand side by 1 S gives A similar analysis above the feed plate gives y - Vt AN +l - A yf - KtXr An +1 - 1 where Xr composition of reflux to top of tower A O KV Equation (12-26) is applied to the heavy key component above the...

## F[ 1 a2 lxF

If XF > 7w-- -i t V 1 inin < Vi min Split Tower. Figure 7-25 shows a split-tower system which partly separates the feed in one fractionating column and completes the fractionation in the second column. It is similar to the previous case except that a fractionating column with reflux is employed instead of the stripping column. This system can be adjusted so that the two towers are in heat balance. The feed is shown entering the high-pressure tower. This makes relatively pure bottoms but...

## U

Vacuum distillation, 113,236,393,396 Van Laar equation, 50, 56-59, 63, 98 for azeotropic distillation, 286 evaluation of, 62 example of use, 65 for extractive distillation, 286 for multicomponent mixtures, 73 Van der Waals equation, 57 Vapor, distribution of, 418 enthalpy of, 140 velocity allowable, 430 Vapor-liquid composition diagram, 16 Vapor-liquid equilibria, 3, 18 calculation of, 26 data on, 22-24 determination of, 3 experimental determination of, 3 presentation of, 16 Vapor phase, 34...

## Tt

0.998(835) (0.796) Vl -76 - S 0'8'1 0.685(725)(0.204) _ Q yi + yi - 1.004 The fact that the sum of the mol fractions is greater than 1.0 indicates the assumed temperature is too high, but the relative volatility is nearly constant with small temperature changes, and Other results are tabulated as follows

## T

Tar acid fractionation, 236 Temperature-composition diagram, 16 for acetone-carbon disulfide, 19 for acetone-chloroform, 19 for benzene-toluene, 19 for carbon tetrachloride-carbon disulfide, 17 for isobutanol-water, 19 Theoretical plate, 119,122 height equivalent to, 187 Thermal efficiency, methods of increasing, 167 in molecular distillation, 401 Thermodynamic relations, 32 Thiele and Geddes method, 336 Total reflux, 128, 147, 243, 270, 292, 321, 376, 384 analytical equation for, 174 Transfer...

## T C

0.2 0.4 06 08 Mol fraction phenol in liquid, xp Fig. 3-3. Calculated vapor-liquid equilibria for system phenol o-cresol. Basic Thermodynamic Relations. Most mixtures are not ideal, and the deviations from Raoult's law are large in all but a limited number of cases. For such mixtures, the basic thermodynamic relations can be employed to formulate expressions for the equilibria involved. It is not the purpose of this text to consider in detail the thermodynamics of solutions, but an appreciation...

## Summary

The Lewis and Matheson method appears to be the most satisfactory method of handling the general multicomponent design problem. In most cases, it requires relatively little trial and error and will handle cases of normal and abnormal vapor-liquid equilibria. It is especially well suited to the cases in which the reflux ratio and the separation of the key components are specified and the problem is to determine the number of theoretical plates and the component concentrations in the column. In...

## Special Binary Mixtures

This chapter covers special fractional distillation systems for binary mixtures. The examples illustrate the flexibility of the fractional distillation process and the broad applicability of the design methods. The first section will consider operating conditions that lead to unusual operating lines, and the last section will consider the separation of binary azeotropic mixtures. Special Operating Lines. The operating lines so far considered intersected the y x line at values between x 0 and x...

## S

Form Fig. 14-3 the relation between xD, xl, and the slope of the operating line, dO dV, can be obtained and Eq. (14-4) integrated to give the vapor requirement. The use of these methods will be illustrated by the following example. Batch Fractionation of a Binary Mixture. An equimolal mixture of A and B is to be fractionated in a batch column equivalent to three theoretical plates plus a Still. The still will operate at atmospheric pressure, with a total condenser, and the holdup in the column...

## RTdlnfvdp37

T absolute temperature fugacity v molal volume, i.e., volume of 1 mol of substance under consideration partial molal volume for a component in a mixture p pressure For mixtures that obey the perfect-gas law this relationship makes the fugacity of a component in the vapor proportional to the partial pressure of the component, i.e., the mol fraction of the component times the total pressure. It is customary to define the standard state for fugacity such that it is numerically equal to the...

## Presentation Of Vaporliquid Equilibrium Data

It is usually desirable to present the experimental vapor-liquid equilibrium data graphically. A number of methods of presentation have been developed, but the most important are the temperature-composition and the vapor-liquid composition diagrams. Phase Rule. The method of presentation must be consistent with the number of variables involved. For equilibrium conditions the number of independent variables can be obtained from the phase rule which states that the number of phases < f> plus...

## Preface To The Fourth Edition

The first ditipn,of-this book and the early revisions were the result of the efforts of Professor Robinson, and he took an active part in guiding the revision of the previous edition. His death made it necessary to prepare this edition without his helpful guidanoe and counsel. The present revision differs extensively from the previous edition. The material has been modified to bring it more closely into line with the graduate instruction in distillation at Massachusetts Institute of Technology....

## Platetype Columns

Plate Efficiency Definitions and Relations. Over-all Column Efficiency. The relation between the performance of actual and theoretical plates is expressed as plate efficiencies. A number of different plate efficiencies have been proposed, but the two most commonly used are the over-all column efficiency which was proposed by Lewis (Ref. 20) and plate or point efficiencies suggested by Murphree (Ref. 24). The over-all column efficiency, E , is the number of theoretical plates necessary for a...

## Platetoplate Methods

In addition to the Lewis and Matheson, and Lewis and Cope methods given in Chap. 9, plate-to-plate procedures have been given by Thiele and Geddes (Ref. 14) and Hummel (Ref. 9). The Thiele and Geddes method is a stepwise procedure based on using a ratio of the concentration of a component to its terminal concentration. Starting at the top of the column, for any component, Thus, if the values of the equilibrium constants and the ratios of 0 V are known for each plate, it is possible to calculate...

## Pl

The right-hand side of Eq. (16-23) would be constant for all parts of the plate on the basis of the assumptions made, and if the value of iz, varies across the plate, then the vapor flow per cap must vary. This relation indicates that a given cap will become inactive when hL at that point is equal to hp 0.12(7 pl) i.e., when the liquid head over a slot becomes equal to the total pressure drop minus the pressure drop necessary to initiate bubbling against the surface tension. Consider the case...

## Pi Vm33

Where y is the mol fraction of component 1 in the vapor. This is the most commonly used form of Dalton's law. For the prediction of vapor-liquid equilibria, it is usually combined with Raoult's law to give Fia. 3-2. Schematic diagram for Henry's law. Fia. 3-2. Schematic diagram for Henry's law. This combination gives the composition of vapor as a function of the composition in the liquid with the total pressure and vapor pressure as proportionality constants. Thus, fixing the temperature and...

## P

Packed towers, 183 allowable gas and liquid velocities, 439 design of, 184, 466 efficiency of, 464 example, 466 flooding velocity, 440 pressure drop in, 437 Partial condensation, 115 equilibrium of, 116 differential of, 116 Partial condenser, 116 Partial pressure, 26 (jrtially miscible systems, 14, 21, 88, 197 rforated plate, 431 tase rule, 16, 81, 216 enol-water fractionation, 197 me efficiency, 105, 445 Iborrelations, 457 Iquation for, 462, 463 l ample, 463 Experimental data, 455 flte-design...

## Os 135

This is close enough to the value of 2.26 employed so that no recalculation is necessary. In other cases, such as an all vapor feed, the value of < f> varies much more with the reflux ratio. 3. If, in the preceding example, the feed condition had been such that 0 Om, a higher reflux ratio would have been required. As a first assumption, (O D) will be taken as 7.0

## Ooooooooo oooooooo ooooooo

Down flow pipe from plate above Fig. 16-13. Layout of bubble-cap plate. Hydraulic Gradient. The section with the bubble caps approximates a rectangular section, and Eq. (16-16) will be employed for the calculation of the hydraulic gradient. The average foam velocity by Eq. (16-19) is 3(480) (92) 3600(53) (0.5) (4.6) 0.30 f.p.s. The value of b 4.6 feet was taken as the average of the diameter of the column md the width at the first row of caps. By Eq. (16-17), ind from Eq. (16-18), using the...

## Oo

Relatively independent of the reflux ratio. These results are plotted in Fig. 7-6. It will be noted that the total of these costs passes through a minimum at a reflux ratio, O V, equal to about 0.43, (O D 0.75). This is very close to the minimum reflux ratio, 0.65 and is a result of the fact that the heating and cooling costs are large and increase rapidly with the reflux ratio. The calculated economic reflux ratio for most cases is so close to the minimum reflux ratio that the accuracy of the...

## Od

Efficiency of Supplying and Removing Energy from a Distillation Tower, In a simple distillation tower, the greatest inefficiency usually results from the methods employed in supplying energy to the system rather than in the separation process. For example, consider the benzene-toluene mixture of Table 7-6. Even allowing for the actual reflux ratio being greater than the minimum reflux ratio, a thermodynamic efficiency of 50 per cent or greater would be obtained over a wide range of feed...

## N

Exit weir 2' _ Water rate 25gpm per. foot of piate width Superficial air velocity c 2.6 ft sec. 1 23456789 10 Number of rows of caps in direction of liquid flow Diagram B Fig. 16-6. Higher air rates or foaming agents increased the apparent liquid height, but static pressure probes indicated that for these cases the density was approximately one-third that of the liquid for the main region of fluid flow just above the plate and on top of this layer there was a light froth containing essentially...

## Ml

Where pL normal density of liquid, lbs. per cu. ft. iih normal viscosity of liquid, lbs. per f.p.s. h0 hydrostatic head in outlet calming section, ft. Klein found that the value of f was a function of the exit-weir height relative to height of the slot and used an empirical relation to allow for this effect. He correlated ' L J as a function of Re', where h8p height of top of slot above plate.

## Methods Of Increasing Efficiency

One method of reducing the irreversibility in the fractionating tower is to make the vapor stream entering a plate more nearly in equilibrium with the liquid on the plate. The extreme in this case is for this vapor and the liquid to be in equilibrium, but this obviously means no enrichment per plate. To accomplish this condition throughout the tower requires that the operating line coincide with the equilibrium curve, and this in turn involves a different reflux ratio for...

## M

That this simplified method is not very satisfactory. In fact it would indicate that water was more volatile than phenol at all compositions and that no azeotrope was formed. The results obtained would not be of much utility and would actually be very misleading. Thus, if water containing a low concentration of phenol were to be distilled, the calculations based on Raoult's and Henry's laws would indicate that water was the more volatile component, while the actual data indicate that phenol is...

## Lnfe Ft1

W< > V lA Ja I - X2 P2 For convenience in plotting, this equation was rearranged to eA i WJV) y (yJP )a 2 J(Vi Pi> )a (1 n P Y W The integration of this equation requires a knowledge of the variations of Pf with temperature. Equation (3-26) indicates that the variation of the pressure with the temperature could be calculated if the heat of vaporization of 1 mol of the component from the solution into a vacuum were known. This heat of vaporiza tion differs from the true heat of...

## Liquid Phase

Deviations from ideal solution laws are more important for the liquid phase than those for the vapor phase because they are encountered even at low pressures, and in general their magnitudes are greater. The densities of the liquids are such that the volume of the molecules and the forces between them are always significant. Deviations for the liquid phase are of at least two main types (1) Those due to the fact that the vapor does not obey the perfect-gas law. Thus, if one tries to define the...

## LavJrhlpir Ja

The right-hand side of this equation requires graphical integration. At the low pressures involved the variation in the values of p* and p* will be neglected. In order to reduce the variation in the groups involved, the equation was rearranged to The values utilized for preparing the graphical integration plot are given in the first five columns of Table 3-5. As a basis for calculations, propanol was taken as component 1 and benzene as component 2. As the check point, the value for the partial...

## L

These equations are the same as some of those presented in Chap. 12, page 341, for the approximate design of contiguous columns. Using an average value of a ( gives XB )D & v XB L For the average value it is possible to use either or the ratio of (aav av) calculated as Equation (14-25) is analogous to Eq. (14-18) and the resulting integrated form is equivalent to Eq. (14-20) except that a is replaced by (a P). The evaluation of 3l requires a trial-and-error procedure that can be best...

## L oxi Jr LJt

Where d in pf is the fractional change in effective pressure of component 1 due to the change in total pressure on the liquid. It is calculated by Eq. (3-7). where t total pressure on liquid phase V partial molal volume of component 1 R gas law constant T absolute temperature The value of d In is calculated in the same manner with v2 instead of V . In most cases these corrections at constant temperature are small in comparison to the change in fugacity due to the change in composition for this...

## Introduction

Definition of Fractional Distillation. By the expression fractional distillation was originally meant the process of separating so far as it may be feasible a mixture of two or more volatile substances into its components, by causing the mixture to vaporize by suitable application of heat, condensing the vapors in such a way that fractions of varying boiling points are obtained, re vaporizing these fractions and separating their vapors into similar fractions, combining fractions of similar...

## Info

0.209(100) 0.98D -f 0.001(100 - D) D 21.25 and W 78.75 An enthalpy balance on the exchanger between the bottoms and the feed is Fig. 7-20. Flowsheet for ammonia-water example. Fig. 7-20. Flowsheet for ammonia-water example. Fig. 7-20a. Enthalpy-composition diagram for ammonia-water example. Fig. 7-20a. Enthalpy-composition diagram for ammonia-water example. where ts ** temperature in reboiler 211.2 C. hp enthalpy of feed entering tower Cv - heat capacity of bottoms 19.0 cal. per g. mol C. (used...

## I

0.001 0.002 0.004 0.006 0008001 0.02 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1.0 results for the same design conditions as Fig. 9-10, except that O D was 7 instead of 10. The number of plates increases from 26 to 35. It is to be noted that the asymptotic values of the concentrations of the heavier components in the lower part of the column also increase this results from the fact that there is less overflow in this section of Minimum Theoretical Plates at Total Reflux. The minimum number of...

## Rwh

Diagram of instrumentation for continuous rectification system. Fig. 18-1. Diagram of instrumentation for continuous rectification system. and runs to a reflux drum accumulator, and a portion of the condensate is pumped back to the column for reflux. The excess condensate is the overhead product and is removed from the drum by the liquid level controller. The reflux rate is regulated by the reflux-flow controller which attempts to hold the temperature near the top of the column at a...

## Hno3h2o

Glycerine Acetone, furfural Acetone, furfural Acetone Phenol Water means, such as extraction, must be employed to separate the agent. The bottoms from the tower are treated to separate the agent and the bottoms product. Occasionally, a portion of the agent is added with the feed in order to maintain its concentration essentially the same above and below the feed. Fig. 10-1. Schematic diagram of extractive distillation system. Fig. 10-1. Schematic diagram of extractive distillation system. The...

## Heat Economy

In the section on the Optimum Reflux Ratio it was pointed out that the operating costs, i.e., the heating and cooling charges, were frequently the major cost of a distillation process and that fixed charges on the equipment were small. In such cases, it would appear desirable to decrease the heating and cooling requirement at the expense of additional equipment, and this section will consider a number of methods of accomplishing that result. From a thermodynamic viewpoint the inefficiencies of...

## G

In many cases there are considerable differences in the compositions of the liquids at various points on a plate, and the conditions assumed in the derivation are not satisfied for the whole plate. However, for convenience, the value of the Murphree plate efficiency is defined as where yi, y0 average composition of vapor entering and leaving plate, respectively ' ' y* composition of vapor in equilibrium witji liquid flowing to plate below Equations (17-3) and (17-4) appear similar, but the...

## Fvi yifi315

Where fvi fugacity of component in vapor y mol fraction in vapor fvl fugacity of pure component at same temperature and pressure as mixture The value of f* can be estimated from the fugacity plots, and this fugacity rule has been widely used in vapor-liquid and other equilibrium calculations. It can be shown that this is true if the vapor mixture obeys Amagat's law, which states that the volume of a mixture is equal to the sum of the volumes of the pure components when these are measured at the...

## Fig 912

The same limitations as to the constancy of relative volatility would apply as for the binary mixtures* Feed-plate Location. The criterion for the optimum location of the feed plate is that the relative enrichment of the key components should be a maximum. As with binary mixtures, the feed plate corresponds to the step that passes from one operating line to the other. The change from one operating line to the other should be made just as soon as it will give a...

## Fib VbXa

Owing to the utility of the mol fraction ratio given in Eq. (3-5) for distillation calculations, the group will be used as the definition of the relative volatility for all cases whether or not Dalton's law applies. Thus, in this text the relative volatilities of any two components in a mixture will bedefinedas the ratio of revalues for the two components. In any constant-boiling homogeneous liquid mixture the composition of the liquid is identical with that of the vapor in equilibrium with it,...

## D

Dalton's law, 28, 46 Dal ton's and Raoult's law, 28, 44 Definitions, of fractional distillation, 1 of plate efficiency, 445 of theoretical plate, 119, 122 Degrees of freedom in distillation system, 215 for rectifying column, 216 Determination of vapor-liquid equilibria, 3 7, 8, 79 Diagrams, Henry's law, 28 Raoult's law, 27 temperature-composition, 16 vapor-liquid, 16 Differential distillation, 107 Distillation, A.S.T.M., 325 azeotropic, 285 batch, 108, 118, 370 continuous, 118 degrees of...

## Contents

Preface to the Fourth Edition . v Preface to the First Edition vii 1. Determination of Vapor-Liquid Equilibria. . . .3 2. Presentation of Vapor-Liquid Equilibrium Data 16 3. Calculation of Vapor-Liquid Equilibria . . .26 4. Calculation of Vapor-Liquid Equilibria (Continued) . . .79 5. General Methods of Fractionation . .101 6. Simple Distillation and Condensation. 107 7. Rectification of Binary Mixtures. . 118 8. Special Binary Mixtures 192 Rectification of Multicomponent Mixtures . 214 10....

## Combined Gas Law And Solution Deviation

In the preceding discussion the deviations of the vapor-liquid equilibria due to gas law and solution abnormalities have been treated separately however, such deviations frequently occur simultaneously. In such cases, the factors are combined into a single equation as follows In many cases, by combining the Van Laar and Margules equations with the fugacity corrections, it is possible to correlate vapor-liquid equilibrium data up to high pressure. At very high pressures, it is probable that the...

## Rectification Of Complex Mixtures

The design methods considered for multicomponent mixtures in Chap. 9 were based on a limited number of definitely known components. In some cases, the mixtures are so complex that the composition with reference to the pure component is not known. This is particularly true of the petroleum naphthas and oils which are mixtures of many series of hydrocarbons, many of the substances present having boiling points so close together that it is practically impossible to separate them into the pure...

## Extractive And Azeotropic Distillation

The design engineer frequently must separate mixtures for which normal distillation methods are not practical due either to the formation of azeotropes or to a very low relative volatility over a wide concentration region. In the first case he separation is impossible unless some special method of by-passing the azeotrope is employed (page 196), an3 in the second case excessive heat consumption and equipment size are involved. For a large number of such mixtures, it has been found possible to...

## Bubblecap Plates

The bubble-cap plate is the most common vapor-liquid contacting device employed for fractional distillation. Its purpose is to bring the vapor and liquid into intimate contact so that the necessary mass transfer can be effected. This requires means for bringing the liquid down the column from plate to plate, across the plates, and into contact with the vapor. The design of such a unit involves obtaining the desired flow conditions of the liquid and vapor and the contact between the two. Figure...

## B

Graphical correlation for design calculation. polating plate-to-plate calculations. In this latter case, if only one plate-to-plate result is available at a reflux ratio from 1.1 to 2.0 times (O D)min, this point can be plotted on the diagram and a curve of similar shape to the correlation curve fitted to it. Such a method should give good results for other reflux ratios, assuming the values of Sm and (O D)min are reasonably accurate. Use of Graphical Correlation for...

## Analytical Equations

Exact mathematical equations for the case of constant molal overflow rate and constant relative volatilities have been presented by Harbert (Ref. 7) and Underwood (Ref. 16). Underwood's equation for a three-component mixture can be arranged as follows Xpi __ f < t> i M1 XFx XD 2 Xpt Xd Similar ratio equations can be written for any two components of a multicomponent mixture where oia < pi aB (pi QLc 91 xD distillate composition Id,, XDs XDl with fa replaced by < 2 and respectively Xf XD...

## Alternate Design Methods For Multicomponent Mixtures

In Chap. 9 the Lewis and Matheson procedure for SorePs plate-to-plate method was presented. Many other design methods have been proposed based on alternate methods of analysis or approximations. None of them illustrates the phenomena involved in multicomponent rectification so well as the Lewis and Matheson ihethod. A number of the methods require less effort to obtain certain design factors than the stepwise procedure and are useful in cases where similar systems are to be analyzed repeatedly....

## AhkXMJ ss y aixDl

An ahk ahk Li al ahk) This equation requires no trial and error for F Vm. The first bracket again corresponds to the binary mixture case for the same and ratio of key components in the distillate. Equations (9-20) and (9-22) are given for Case I, and for Case II the last term involving Xwh is eliminated. Similar equations can be derived by equating the ratio of key components below the feed plate to < > . Thus,

## A12 A22

In the case of more than three components, the relationship is obtained by the same procedure, but it is relatively easy to write the activity coefficient equations simply by inspection. Returning to the three component equations, Eq. (3-58), it is noted that the denominator is always the same and simply involves the square of the sum of the mol fraction times the a for the term in question relative to some given base component. In the equations given, component 2 is used as the base, and a 22...

## A

Using this value, the steps corresponding to theoretical plates are stepped off. In this manner the lines on Fig. 7-20a were constructed for the top seven plates giving the vapor entering the T 6 plate equal to 0.073. Below this value the diagram becomes difficult to use, and the calculations were completed by the use of Eq. (7-31), using Hm 8,400, and hm+1 -20. ' Mw hm+l 1 2.92xm+i - 1.92(0.001)

## Molecular Distillation

This type of operation has been applied to the distillation of materials that have very low vapor pressures at the maximum operating temperature. The available pressure drops in such cases would be too low to obtain practical production rates in conventional equipment, but by operating such that the rate of distillation is approximately equal to the absolute evaporation rate of the liquid reasonable capacities can be obtained. The most common method of obtaining the molecular distillation...

## Fractionating Column Design

The design calculations given in the previous chapters involved the mathematical problem of determining the number of theoretical plates and did not consider whether or not such performance could be obtained. This chapter will consider the mechanical design problems encountered in attempting to attain the desired degree of contact between the vapor and liquid and the necessary fluid and vapor flow. The fractionating column must bring the liquid and vapor into counter-current contact (or some...

## Rectification Of Multicomponent Mixtures

Multicomponent mixtures are those containing more than two components in significant amounts. In commercial operations, they are encountered more generally than are binary mixtures, and as with binary mixtures, they can be treated in batch or continuous operations, in bubble-plate or packed towers. Since the continuous operation is much more amenable to mathematical analysis, owing to the steady conditions of concentration and operation, it will be considered first. Fundamentally, the...

## General Methods Of Fractionation

There are several methods by which fractionation can be obtained. The more important among them are (1) successive distillation of condensed distillate, (2) fractional condensation, and (3) rectification. Successive Distillation. The first method, successive distillation of the condensed distillate, can be shown best by referring to Fig. 2-1. Starting with a large amount of liquid of the composition x& which boils at 760 mm. pressure, temperature U, a small amount of vapor of the composition...

## Fractionating Column Performance

The design calculations considered in the preceding chapters were based on theoretical plates. In order to complete the design, it is necessary to have the relationship between these idealized values and the actual performance of the contacting device. The vapor and liquid brought into contact with each other in the tower are not at equilibrium, and the rate of mass transfer determines the effectiveness of the unit. This chapter will consider the methods of predicting the effectiveness of the...

## Preface To The First Edition

The subject of fractional distillation has received but scant attention from writers in the English language since Sidney Young published his book Fractional Distillation in 1903 (London). French and German authors have, on the other hand, produced a number of books on the subject, among the more important of which are the following La Rectification et les colonnes rectificatriccs en distillerie, E. Barbet, Paris, 1890 2d ed., 1895. Der Wirkungsweise der Rectificir und Dcstillir Apparate, E....

## Rectification Of Binary Mixtures

The separation of two liquids from each other by fractional distillation may be accomplished in two general ways (1) the batch, or intermittent, method and (2) the continuous method. In the former, the composition and temperature at any point in the system are changing continually in the latter, conditions at any point are constant. It will be recalled that a fractionating column consists of a system up through which vapors are passing and down through which a liquid is running, countercurrent...

## Efficiency Of Packed Towers

The efficiency of packed towers is generally expressed as the height equivalent to a theoretical plate. Most of the reported values of H.E.T.P.'s are for small laboratory columns, since this is one of the largest uses of packed columns. H.E.T.P. is a function of the packing dimension and construction, tower size, vapor velocity, and system being rectified. The efficiency of packed towers may be seriously impaired by the liquid's tending to pass down one side while the vapor flows up the other....

## Relative Volatility Using Partial Pressure

Using T7 31G.4 K., xwp 0.74, and a , 0.9775 gives six equations with six unknown quantities which can be solved to give A 0.206 and B 238. With these constants, the vapor-liquid equilibria were calculated for the system phenol and water at a temperature of 43.4 , and the calculated results are given in Figs. 4-13 and 4-14, labeled Van Laar. It will be noted in this case that the agreement with the experimental results is satisfactory and would be of great utility for actual distillation...

## Vacuum And Steam Distillation

Hg abs., the distillation operation can be carried out in a manner similar to those at higher pressures, and the problems relate to reducing the pressure drop for vapor flow through conventional equipment. The pressure drop of bubble-cap plates can be reduced to the order of 2 mm. Hg per plate (see page 404), and special spray-type plates can give pressure drops as low as 0.5 mm. Hg per plate. With such contacting units it is obvious that even a few plates will...

## K

In cases where the value of the bracketed term is small, the pressure drop for a plate with caps just becoming inactive is equal to approximately twice the pressure drop for the same plate with the same total vapor load uniformly distributed. If the last terms are not small, the pressure drop will be increased by a factor less than 2.0. This increased pressure drop is one of the objections to hydraulic gradient. The relations given in Eqs. (16-24) to (16-32) were based on the condition that the...

## Geometric Average For Relative Volatility

And at total reflux the operating-line equation gives yw Xi, giving In some cases the relative volatility does not vary widely, and an average value for the entire column can be used, giving where N is the number of plates in the column. This can be changed to N log x> x)N x xf)w If a total condenser is employed, this becomes N + 1 g(x' x)D(x'7 U (7.53) or, if a partial condenser equivalent to one theoretical plate is employed, N + 2 log These equations offer a simple and rapid means of...

## Binary Mixtures

The batch distillation of binary mixtures will be considered fpr the cases of 1 no rectification, 2 rectification without liquid holdup in the column, and 3 rectification with holdup. No Rectification, Batch distillation without rectification corresponds to the simple distillations of Chap. 6, and the calculations of the concentrations as a function of the amount distilled can be made by Eqs. 6-3 and 6-7 . Rectification without Liquid Holdup in Column. Finite Reflux Ratio. In this case, it is...

## Other Types Of Plates

Bubble-cap plates are the most common plate type of contacting device, but other arrangements are used. Perforated or sieve plates are effective vapor-liquid contacting devices and are frequently used for liquids containing suspended solids, such as the beer mashes in alcohol production. At their rated capacity, their efficiency is equal to that of bubble-cap plates, but they have two disadvantages that have limited their utility. 1 Because the pressure drop through the openings of the...

## E

Or reflux from condenser before solvent is added at top Xds, Xrs mol fraction of solvent in distillate and total liquid added to the top of tower, including reflux and solvent Fs solvent added with feed a, a relative volatilities for solvent concentrations above and below feed, respectively If the feed is binary mixture, the terms involving Xdi and xwh are dropped. For certain special cases, simpler equations can be employed. For example, if solvent is added with the feed such that its...

## Liquid Volatility Pa Pb

Assuming that none are reflected, Eq. 15-2 can be used to calculate the. rate of evaporation from a liquid at equilibrium with a vapor. The same relation has been used to predict the rate of evaporation from a liquid even when the vapor is not in equilibrium with a liquid. This may be approximately true for the nonequilibrium case, but there is undoubtedly some interference of the molecules in the vapor with those evaporating, and the use of Eq. 15-3 to calculate the absolute rate of...

## HTU fjj

The transfer unit consists of a step on the operating line such that the change in y or x is equal to the average difference between the equilibrium curve and the operating line over the region of the step. If the equilibrium and operating lines are parallel, the step will be exactly equal to that for a theoretical plate, and the H.T.U. value will equal the H.E.T.P. value. If the slope of the equilibrium curve is less than that of the operating line, the two curves will tend to converge with...

## What The Relative Volatility Of Acetic Acid

Between y and x are known, both the vapor and the liquid compositions can be calculated. In order to determine the equilibrium relationships either the temperature or the total pressure must be known. Given either of these, the other can be determined from the equilibrium relationship for all the components involved. Differential Distillation. This type of distillation is usually carried out as a batch operation although continuous units may also-operate in this manner. Considering first a...

## Modified Equilibrium Curves And Operating Lines

Several methods have been given which treat a multicomponent mixture as a modified binary mixture of the key components that can be analyzed graphically on a y,x type diagram. Jenny Ref. 10 published a graphical method for multicomponent design calculation. A few plate-to-plate calculations are made at the top and bottom of the column and above and below the feed plate. For the section below the feed plate, a y x diagram is made for the light key component using the calculated values to place...

## Snd

These equations reduce to Eqs. 7-14 , 7-17 , 7-27 , and 7-31 for the special cases considered. Method of Ponchon and Savarit. Ponchon Ref. 14 and Savarit Ref. 15 showed that Eqs. 7-13 and 7-27 , or in general any equation Fia. 7-16. Enthalpy-composition diagram. Fia. 7-16. Enthalpy-composition diagram. of this type, could be easily solved by plotting the enthalpy or other property of the saturated vapor and liquid vs. the mol fraction. For example, in Fig. 7-16, if the value Md for the upper...

## Multicomponent Systems

The ideal solution laws such as Raoult's law and Raoult's law corrected for gas law deviation are applicable to binary or multicompo-nent systems. They treat each component independently of any other component present i.e., the relationship between the mol fraction in the vapor and in the liquid for a given component depends only on the temperature and total pressure. In many cases, these simplified rules are not applicable, and there is interreaction between the various components. It would be...

## Vb w

Rp , CM 12 VB7l X A 32 VB zY V I m 72 -7r 1- A 2- I O-05 XiAn x2 xzAwY x A 12 y B X2 B32 2 X1A12 X2 X3A32 2 In the above equations, the values of A and b are similar to those given for a binary, but in this case, considerable care must be exercised with respect to the subscripts. Thus A12 is equal to amp 1 amp 2, -432 is equal to 63 62, and similarly for other subscripts. It should be pointed out that for a ternary mixture, there are only two independent A terms. Any other A terms can be...

## KA Jyy y y kA xxw x X

Where x'ff y'f are the liquid and vapor compositions in the tower at the level at which the feed is introduced, and x'w is the liquid concentration at the bottom of the packed section. A material balance above the feed gives By assuming values of y, values of x can be calculated by Eq. 7-82 , and these used in Eq. 7-80 together with equilibrium data to evaluate the integrals. A similar material balance below the feed can be used with Eq. 7-81 . The equilibrium curve and the material-balance...

## A 1[2 a 2XF

This arrangement is very similar to that employed in the so-called double towers for the separation of oxygen and nitrogen. In this case the feed is relatively rich in the lower boiling component, nitrogen, and the first tower is used to produce an overhead that contains a high concentration of nitrogen and an impure bottoms containing 40 to 50 per cent oxygen. The liquid nitrogen overhead product from the high-pressure tower is added to the top of the low-pressure tower and serves as the only...

## Ammonia And Water Relative Volatility

Oxygen-Nitrogen and Ammonia-Water Example. Tables 7-3 and 7-4 give similar comparisons for other systems. In Table 7-3 the comparison is for the oxygen-nitrogen system at 10 atm., and again the agreement between the two methods is good. The other data are for ammonia-water at 10 atm., and even in this case the two methods are in fair agreement. Ammonia-Water Example. In order to illustrate the fact that the assumption of constant molal overflow rate is not always justified, consider the...

## Relative Volatility Of Co2

0.4 06 08 Mol fraction COg in liquid 0.4 06 08 Mol fraction COg in liquid 0.2 0.4 06 OB 1.0 Mol fraction COg In liquid Fig. 4-4. a. Vapor-liquid equilibria for CO2-SO2 at constant pressure. 6. Vapor-liquid equilibria for CO2-SO2 at constant temperature. same temperature, but at different total pressures. This is shown in Fig. 4-4 which gives the vapor-liquid equilibrium data for the system carbon dioxide-sulfur dioxide. In general, it is found that the relative volatility decreases as the total...

## F C 221

In the usual vapor-liquid equilibria two phases are involved liquid and vapor. Plowever, in some systems more than one liquid phase may be encountered. For the two-phase system the phase rule states that the degrees of freedom or variance are equal to the number of components. Thus a binary system has two degrees of freedom and can be represented by two variables on rectangular coordinates. Three-component systems involve three degrees of freedom and are usually presented on triangular...