SHARPNESS OF SEPARATION IN BATCH DISTILLATION OF TERNARY MIXTURES

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The Pennsylvania State College The Graduate School Department of Chemical Engineering

SHARPNESS OF SEPARATION IN BATCH DISTILLATION OF TERNARY MIXTURES

A Thesis by Victor Jo O'Brien, Jr.

Submitted in partial fulfillment of the

requirements for the degree of Doctor of Philosophy

September 1950

Approved:

-t-y cXjL'' S

ACKNOWLEDGMENT The author wishes to express his sincere appreciation to Dr. Arthur Rose for his con­ tinued interest and able direction of this in­ vestigation; and to the Shell Oil Company for the fellowship which largely made this investi­ gation possible. The author is also indebted to Miss Joan S hilk

and Mr. Charles Dix for their assistance

in many phases of this investigation.

*

TABLE OF CONTENTS Page Summary I II III

i

Introduction

1

Literature Survey

3

Theoretical Analysis

7

General Batch Distillation Equations

IV

V

VI VII

7

Batch Distillation Equations When Holdup Is Negligible

13

Equations of Performance for Continuous Multicomponent Distillation

15

Integration of Negligible Holdup Differ­ ential Equations

19

Conclusions from Theoretical Analysis

24

Apparatus

25

Still Pot and Rotameter

25

Rectifying Section

27

Condenser and Reflux Divider

29

Column Control

31

Column Characteristics and Operating Variables

34

Flooding Technique

34

Column Adiabaticity

35

Pressure Drop-Throughput

35

Column Holdup

39

Number of Theoretical Plates at Total Reflux

56

Batch Distillation Procedure

59

Results

62

Methods of Expressing and Comparing Results

64

TABLE OF CONTENTS (Continued) Page VIII IX

X XI

Reproducibility

102

Discussion of Results

109

Comparison of Binary and Ternary Dis­ tillations

109

Absolute and Effective Holdup

113

Effect of Holdup upon Sharpness of Separation in Ternary Experiments

114

Effect of Reflux Ratio

124

Comparison of Experimental and Calculated Curves

127

Conclusions

135

Appendix

133

A.

Relative Volatility Equations

138

B.

Integration of Rayleigh Equation at Total Reflux

139

Calibration of Rotameter

141

Calibration of Reflux Divider

145

D.

Purification of Test Mixtures

148

E.

Nomenclature

149

C.

XII

Bibliography

151

LIST OF FIGURES Figure

Page

1

Schematic Diagram, Batch Distillation Column

2

Batch Distillation Column

26

3

Column Rotameter and Support Disc

28

4

Column Condenser and Reflux Divider

30

5

Pressure Drop vs Throughput

38

6

Holdup-Pressure Drop-Throughput

41

7-10 11

Holdup Batch Distillations Determination of Efficiency Index

8

44-47 65

12-13

Batch Distillation Efficiency Indices

14-18

Duplicate Batch Distillations

103-107

19-20

Comparison of Binary and Ternary Ex­ perimental Distillations

110-111

Effect of Holdup upon Sharpness of Separation

116-122

21-27 28 29-32

Effect of Reflux Ratio at High Percent Holdup Comparison of Calculated Binary and Ex­ perimental Ternary Batch Distillation Curves

68-69

126

130-133

33

Calibration Apparatus for Column Rotameter

142

34

Column Rotameter Calibration Curve

143

35

Calibration Curve for Reflux Divider

146

LIST OF TABLES Table

Page

1

Adiabaticity-Pressure Drop-Throughput

36

2

Holdup-Throughput-Pressure Drop Data

42

3-6

Holdup Batch Distillations

48-55

7

Number of Theoretical Plates at Total Reflux

58

8

Summary of Batch Distillations

70

9-33 54-37

Ternary Batch Distillations

72-96

Binary Batch Distillations

97-100

38

Batch Distillation Efficiency Indices

101

39

Calibration of Rotameter

144

40

Calibration of Reflux Divider

147

SUMMARY Amost no reference to the important subject of multicomponent batch distillation can be found in the literature. The obvious need for study of this subject was the basis for this investigation and a theoretical and experimental program was undertaken. It was the purpose of this investigation to obtain ex­ perimental data indicating the effect of the more important variables in multicomponent batch distillation as well as to review and study various methods of calculating the course of such distillations.

In addition it was of interest to

determine whether the generalizations deduced from prior binary studies were applicable to multicomponent systems. A theoretical analysis was made of possible methods of calculating multicomponent batch distillations under con­ ditions of both appreciable and negligible holdup.

It was

concluded from this analysis that the only practical means available is the numerical procedure of Rose, Johnson, and Williams (17) regardless of whether holdup is appreciable or negligible.

The differential equations applicable to multi-

component batch distillation for the case of negligible holdup and finite reflux ratio and number of theoretical plates were examined.

But there is little reason to believe

that algebraic solutions of these will be possible. The experimental studies were limited to the system nheptane-methylcyclohexane-toluene.

Complete vapor-liquid

ii equilibria were available and a method of analysis perfected by Kirk (ll).

In order to study the batch distillation of

this mixture a laboratory size column was constructed.

It

had an internal diameter of 1/2" and was packed with 1/16" 36 ga. stainless steel helices to a height of five feet. The packing holdup was approximately 60 cc and the charge capacity was 5 liters so that the ratio of holdup to charge (usually expressed as a percent and called percent holdup or simply holdup) could be varied from 1-1/2$ to any desired value by varying the size of the charge.

The column was

tested with the mixture n-heptane-raethylcyclohexane and was found to have about 82 theoretical plates near the maximum throughput of 400 cc of methylcyclohexane per hour. rate was used in this investigation.

This

Column holdup was

determined under conditions closely approximating the ternary distillations of this work.

This was done by adding non­

volatile di-octyl pthalate to a ternary charge and determining holdup throughout the course of a batch distillation by means of material balances.

The results of four of these holdup

distillations showed that the column holdup could be considered to be substantially constant raolal holdup for the column and components of this work. Twenty-five ternary batch distillations and four binary batch distillations were conducted. positions were used:

Two ternary charge com­

7-21.7-71.3 and 30-20-50 mole percent

n-heptane, methylcyclohexane, and toluene respectively. Reflux ratios were varied from 7.5/1 to 60/1 and the ratio of

iii

holdup to ternary charge from 4.5 to 18$. runs were duplicate runs.

Five of the ternary

These check runs showed that small

discrepancies in distillate mole fraction and break point were present from run to run.

But in no runs were the discrepancies

large enough to seriously affect the interpretations of the results of the work reported herein. A comparison of the batch distillation curves of the ternary runs and binary runs conducted under identical con­ ditions of reflux ratio and absolute charge of each component showed that the separation between the two components of the binary was similar to the separation of these two components in the ternary, provided that only these two components were present in the ternary distillate in appreciable quantity. These binary-ternary comparisons also indicated that the sharpness of separation between two components must be governed by the effective holdup, that is, the percent holdup based upon the absolute amount of the two components under consideration in the initial ternary charge.

Since

two components may constitute a small portion of a multicom­ ponent charge, large effective holdups and consequently large effects on separation can be expected to be regularly present in multicomponent batch distillation. A number of binary batch distillation curves were calcu­ lated for the systems n-heptane-methylcyclohexane and methyl­ cyclohexane- toluene assuming negligible holdup.

These curves

were compared with the corresponding experimental ternary

iv cases in which all variables were the same except percent holdup.

When the effective holdup of n-heptane-methylcyclo­

hexane in the experimental ternary distillations was 9$, the experimental curves agreed well with the binary curves calcu­ lated at reflux ratios of 15, 30, and 60/1.

However the ex­

perimental curves of methylcyclohexane-toluene in which the effective holdup was 6% did not agree with the binary calcu­ lated curves at reflux ratios of 7.5 and 15/1. The general effects of holdup in ternary batch dis­ tillation were the same as observed for binary systems (4) (14)(19).

The effect of increasing percent holdup was found

to be beneficial, detrimental, or of no effect upon the sharp­ ness of separation between components of a ternary batch dis­ tillation, depending upon the reflux ratio.

The effect of

holdup was also complicated by total reflux startup.

When

total reflux startup effects are present, the distillate com­ position at the start of the batch distillation is much higher in the most volatile component than would occur if the column were operating at the reflux ratio to be used throughout the distillation.

In such a case the mole fraction of the most

volatile component tends to drop sharply and percent holdup has a pronounced effect upon the shape of the batch dis­ tillation curve.

In the presence of this effect it was

found that increasing holdup was beneficial to the sharpness of separation between n-heptane and methylcyclohexane in the ternary mixture at reflux ratios of 7.5, 15, and 30/1.

V

In the absence of total reflux startup effects it was found that holdup was beneficial at reflux ratios of 7.5 and 15/1, detrimental at R = 60/1 and exerted no effect when the reflux ratio was 30/1.

This was true of the separation of

both n-heptane-methylcyclohexane (a -- 1.08 - 1.15) and methylcyclohexane-toluene (a = 1.10 - 1.60).

The reflux

ratio of 30/1, then, was the critical reflux ratio as defined by Prevost (15) for this column of 82 theoretical plates and the data of this thesis indicated that it depends only upon the number of theoretical plates of the column.

I INTRODUCTION Batch distillation is a unit operation suitable for the separation of liquid mixtures which might be difficult to re­ solve by other methods.

Consequently it would be desirable

from an economic standpoint to be able to predict the optimum conditions for conducting batch distillations.

However, this

has been difficult since there are a number of operating variables such as theoretical plates, reflux ratio, holdup, and charge composition which Influence the course of a batch fractionation; and the relationships between these variables are complex largely because of the unsteady state nature of the process. A number of experimental and theoretical investigations have been made in the field of binary batch distillation.

The

few investigations of multicomponent batch distillation which have been reported in the literature are entirely of a highly theoretical nature.

The obvious need for further study of

the problem of multicomponent batch distillation was the basis for the theoretical and experimental program described herein. The objectives of the investigation were threefold: (1)

To obtain experimental data indicating the effect of the more important variables in multicomponent batch distillation.

(2)

To review and study various methods of calculating the course of multicomponent batch distillations.

2 (3)

To determine whether the generalizations deduced from prior binary studies were applicable to multicomponent systems, particularly when holdup was appreciable.

In order to simplify the problem, the experimental work and most of the theoretical considerations were limited to ternary studies.

The experimental data were obtained ex­

clusively with the system n-heptane-methylcyclohexane-toluene. This system was chosen because complete vapor-liouid equilibrium data were determined and a method of analysis perfected by Kirk (ll)

1

II LITERATURE SURVEY Early investigations of batch distillation simplified the problem by considering only binary systems and neglecting column holdup (l)(21)(16)(12).

Under these conditions the

Rayleigh equation is applicable: dS S

dxs

(1)

Smoker and Rose (21) used this equation and continuous distillate-still relationships such as McCabe-Thiele procedure to obtain batch distillation curves (plots of distillate com­ position versus percent of initial charge distilled) at finite reflux ratio and they obtained experimental confirmation for two systems when holdup was 1-2 % of the initial charge. Similarly, 0 TBrien (12) showed that there was fair agreement between calculated no-holdup curves and experimental curves where the column holdup was about 5 %. studied and four comparisons were made.

Two systems were Bogart (l) formulated

equations to calculate the time required and the yield fraction for a batch distillation conducted under conditions of varying reflux ratio and constant distillate composition. Eventually it was recognized that relationships derived on the assumption of negligible column holdup would not predict correctly the course of a up was appreciable.

batch fractionation when column hold­

Rose (18) investigated the problem and de­

rived an equation that included holdup as a variable:

S

fh (xs) dxs (xj3 - xs)eY‘

4 where XD - XS

(?)

However the equation could not be integrated to yield a numerical solution,

Colburn and Stearns (4) derived a

similar equation which they were unable to integrate:

They used the equation as a guide in predicting that high percent holdup could be either beneficial or detrimental to the sharpness of separation.

Their experiments showed a

beneficial effect of holdup when compared with curves calculated on the assumption of negligible holdup.

The experiments of

Rose, Williams, and Prevost (19) demonstrated experimentally that increasing holdup could be either beneficial, detrimental, or without effect.

In addition this work suggested the concept

of a critical reflux ratio in batch distillation.

At the

critical reflux ratio increasing holdup had no effect upon the sharpness of separation.

Above the critical reflux ratio

holdup was detrimental while below the critical value holdup was beneficial. In an attempt to determine appreciable holdup, binary batch distillation curves analytically, Pigford, Tepe, and Garahan (14) studied the mathematical relationships for plate columns.

They obtained differential equations for the change

of composition with time on each plate but were unable to obtain algebraic solutions.

Instead numerical solutions were

5 obtained through the use of a differential analyser. (10) also derived similar equations.

Johnson

He concluded that an

algebraic solution of the differential equations was' hopeless. Rose, Johnson, and Williams (17) used numerical methods for the solution of the differential equations and obtained good experimental checks of the results.

Their calculations were

made for a five plate column and the labor involved was greatly reduced through the use of an I.B.M. machine calculator. An extensive discussion of the application of I.B.M. computers to batch distillation calculations was given by Williams (24). Bogart’s work (l) concerning the yield fraction of batch dis­ tillations conducted at constant distillate composition and varying reflux ratio at negligible holdup was extended by Edgeworth-Johnstone (6) (7) and Chu (3) for the case of appreciable column holdup and for multicomponent systems.

Un­

fortunately their equations were derived with the aid of math­ ematical relationships applicable only in continuous distilla­ tion or in batch distillation with negligible holdup.

There­

fore the value of the derived equations is questionable. With the exception of the last two references, the above work considered only binary batch rectification.

Actually,

it is probable that most batch distillations are multicomponent so that this field should be more important than the binary counterpart.

In spite of this, few investigations of either

a theoretical or experimental nature have been undertaken in this field.

The literature contains "numerous articles on con­

tinuous multicomponent distillation but these have little

6 bearing on the subject of batch distillation, because of the essential difference between steady and unsteady state processes.

Crosley (5) derived equations enabling the calcu­

lation of multicomponent batch distillations at total reflux, constant relative volatility, and negligible holdup.

He

described a method of calculation for the condition of negligible holdup and finite reflux ratio.

It was necessary

to assume the rectification was so conducted that only the two most volatile components appeared in the distillate at one time.

The procedure consisted of finding the number of

plates at a probable operable reflux ratio which would give the same separation as a column of fewer plates operated at total reflux.

No experimental data were given to support

the calculations. The theory of batch distillation of an indefinite number of components was studied by Bowman (2).

Equations were derived

for total reflux and minimum reflux (infinite number of plates) at negligible holdup.

These equations can be applied to a

finite number of components but apparently no derivation was possible for the more useful condition of finite reflux and negligible holdup.

III.

THEORETICAL ANALYSIS

Theoretical analysis is particularly desirable in connec­ tion with multicomponent batch distillation because of the difficulties inherent in the experimental approach.

It was

not expected that theoretical analysis would be straightfor­ ward and productive of immediate conclusions, since the theory of binary batch distillation is so complex.

As the analysis

progressed it became clear that the mathematical problems of multicomponent batch theory were very complicated indeed, even when simplifying assumptions are valid. One portion of the analysis dealt with cases where holdup was appreciable, and a second portion with the cases where holdup could be considered to be negligible.

These two cases

are discussed in turn. General Batch Distillation Equations The best approach to the study of the effect of column operating variables upon the course of a batch distillation is through the use of differential material balances together with such simplifying assumptions as are necessary and justified Batch fractionations are conducted in plate and packed columns. The differential equations are of a somewhat different form for the two types and only plate columns will be discussed here. There is evidence that the final relations will be similar regardless of the approach.

(2a)(17)

The differential equations applicable to batch distilla­ tions with appreciable column holdup and conducted at constant

8 reflux ratio were derived by Pigford (14) and Johnson (10). Johnson’s treatment was for binary systems but will be briefly presented here since it is basic to the discussion for multicomponent mixtures.

Consider the batch distillation column

of N theoretical plates diagrammed below,

(Figure l) the

column operating under the following assumptions: (1)

The usual simplifying assumptions of continuous distillation prevail.

(2)

There is equal molal vaporization V and overflow L at each plate.

(3)

Each plate acts as a perfect plate with constant molal holdup, h.

(4)

Vapor holdup is negligible.

(5)

The pot acts as a perfect plate containing S moles of liquid.

(6)

The condenser is a total condenser with negligible holdup.

D, x ht t x t

/ / // /,

r~

\

r

1

1

Li* *n '

Li //

Fig. 1

S, xs

D

A differential material balance around the top plate for component A of a mixture yields dX

At d&

h.

V>At-l

"

LXAt

DXAD

(5)

The n th plate and still pot equations are dx An

=

dd

a (*AS S> d 6

1

V(yAn-l - yAn) +

L (xAn+l

xAn)

(6)

n

^ A l ' VyAS

(7)

There are corresponding equations for each component of the mixture being distilled.

Thus, for a column of N theoretical

plates and C components there are a total of (N + l)C simul­ taneous differential equations which must be solved although the number can be reduced by N + 1 through the use of the relationships ^ x = 1, ^ y = 1.

Neither Johnson nor Pigford

(14) were able to obtain analytical solutions of these equations for binary systems and series solutions were found to be too laborious due to poor conversion.

Therefore no attempt was

made to solve multicomponent systems of these equations in this investigation.

Solutions are possible if an adequate

differential analyser similar to that employed by Pigford is available.

Unfortunately, not only are there few machines of

this type but the capacity of the present machines is limited to a few plates with the simpler binary system and would be less for a multicomponent system.

10 Another means of solving systems of ordinary simultaneous differential equations is through the use of the numerical methods of approximation discussed in most mathematics texts. The most basic of these was employed by Rose, Johnson, and Williams (17) in order to make a number of binary calculations and their procedure is equally applicable for multicomponent calculations.

The method consists of computing an x increment

for a small O increment in an equation of the type

i t = f (x,* ) When the increment in O is small, dx de constant so that

will remain nearly

(8 ) For example equation (6) representing the n th

plate of

a column becomes

xAnx

XAn0 + hn

V ^yA(n-l)0" ^ o ^

+ L (xA(n+l)o“ xAno)

(0i“ 0o) (9)

An increment in x is computed by substituting initial numerical values into the equation and calculating the value of

at the end of the time interval.

Similar computations

are made over the first interval utilizing the finite difference equations of the other plates as well as the still pot equation. The new values are substituted into the equations and another increment is calculated.

(Values of y are obtained from values

11 of x and a knowledge of vapor-liquid equilibria.)

The compu­

tations are continued until the desired solution is obtained. Errors inherent in this method had not been thoroughly studied and were therefore reviewed from the point of view of multicomponent distillation. One source of error of the method that might prove serious in multicomponent distillation is the assumption of constant dx . This is only an approximation so that cumulative d© errors are introduced with each calculated interval. In order to minimize the errors it is necessary to choose small inter­ vals and even then it is difficult to ascertain the magnitude of the errors at any point during the computation.

However,

it is assuring to know that any desired degree of accuracy can be obtained by successive reduction of the interval size.

It

is necessary to emphasize that the terms error and accuracy are used here in connection with the computational operations themselves and not in connection with any comparison of calcu­ lated and experimental results. The accuracy of the calculation for a given size of interval can be increased by using better approximation methods than those used by Rose, Johnson and Williams, even though such methods increase the amount of computation per interval.

Among those available are the modified Euler,

Milne, and Runge-Kutta methods.

(See Sherwood and Reed (20)

or any book of differential equations.)

A number of such

calculations were made during this investigation and these

12 calculations indicated that the Runge-Kutta method gives the most accurate results for a given interval size. it is very cumbersome.

However,

The modified Euler and Milne methods

are particularly advantageous in that they indicate whether the proper interval size was chosen for the computation. A disadvantage of all the numerical approximation methods is that they are very laborious.

This is particularly true if

the number of plates and components is large.

Rose, Johnson

and Williams solved this problem by performing the calculations on an electronic digital computer manufactured by the Inter­ national Business Machines Corporation.

Williams (24) has

discussed the application of these machines to binary batch and continuous distillation calculations and to continuous ternary distillation, all under circumstances where simpli­ fying assumptions are applicable.

Some approaches to the

more complex cases have been outlined by Rose and Williams (18a) .

An example of these more complex cases is the

variable relative volatility characteristic of the ternary mixture n-heptane, methylcyclohexane, toluene used in the experimental part of this investigation.

The necessary

supplementary equations for this specific case, expressing relative volatilities as a function of concentration, were derived, and details of these are given in Appendix A. These make possible the execution of the IBM calculations by the above mentioned procedures. It was concluded that these predictions of batch dis­ tillation operations with appreciable holdup had best be

13 made by the method of Rose, Johnson and Williams, using IBM machines, but that interval size and extent of errors should be estimated and controlled by also doing some calculations by the Milne or Euler methods. Batch Distillation Equations When Holdup Is Negligible. It Is unlikely that anything except numerical solutions will be possible for the equations of batch distillation con­ ducted with appreciable holdup.

Therefore negligible holdup

multicomponent relationships were examined in this investigation for possible algebraic solutions.

The assumption of negligible

holdup may be a serious limitation but equations derived upon this assumption had some utility for the binary case and it might be expected that this utility would extend to multicom­ ponent distillations. When holdup is negligible a differential material balance around a batch distillation column reveals that distillate out­ put must equal still pot depletion since there can be no accumulation in the rectifying section.

Under these conditions

the Rayleigh equation is applicable and a material balance for each component of a multicomponent mixture gives

as = xs The equations for the other components of the mixture are similar LBD

=

aBi (^ + l)

-

^

LBS,

etc.

(14b)

ax