An initial study of the calculation of the extractive distillation of trimethylamine from a mixture of water, mono-, di-, and trimethylamine

(1)

Verslag behorende

bij het

fabrieksvo~rontwerp

van

JOSEF FRENKEL .

... ...

' ... .,.

...

_

...

'

.

onderwerp:

. . . -<""~ ... _ . . . .. )' .1i - , . ' , : ..

DISTILLATION OF TRIMETmAMINE' FROM A MIXTURE OF ', .. • "f),. ~ J 'J

..

WA::J;1~;2..s.,M.9.~Qi~.~X::-

...

~

..

::ç~~r.~~~.~

...

.':

....

.

adres:

Koornmarkt 9

opdrachtdatum :

Ju1y 1973

verslagdatum:

June 1974 Delft

(2)

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An Initial Study of the Calculation of the Extractive Distillation of Trimethyl@nine from a Mixture of Water, Mono-, Di- and Trimethylamine.

June, 1974 Process-Design Project

Josef F'renkel Koornmarkt

9

(4)

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To strive, to seek, to find and not to yield.

Front "Ulysses"

(5)

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-1-List of contents Topic Summary I. 11. III. IV. V.

Conclusions and Recommendations Introduction

Theory and literature research Calculational procedure

VI. Results and discussion VII. Figures

VIII. Nomenclature IX. Literature cited X. Appendices 2 3

4

6

10 22 37

45

47

49

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-2--I. Summary

---The core of the problem was to describe the vapor-liquid equilibria

of the multicomponent system, composed of: (a) Monomethylamine (r-1MA);

(b) Dimethylamine (DMA); (c) Trimethylamine (TMA); (d) Hater (H).

Based on this description a distillation column was supposed to be

designed "hich would separate TMA from the system by means of extractive

distillation.

The problem was attacked by selecting, aftel' an extensive literature study, the Wilson equation which seemed to be the most applicable

equation to this type of system composed of highly polar nonideal

components. The Hilson constants of the binary system DMA-H were regular

in their trend; while those of the binaries: (a) I1MA-H, (b) TMA-H exhibited some anomalous results. An atternpt ,-laS made to clarify these phenomena.

The attempts to design the distiIIation column were not successful. The program was run many times with different reflux ratios and rates of extracti ve '-later. Unfortunately, no optimal solution was found. It

lS very weIl possible that the Vlilson equation cannot be applied to the

system under discussion because of incomplete miscibility. It is suggested to check this point experiffientally, and in any case, to try to appIy the Renon equation.

In order to check the whole calculational procedure of the Wilson constants and the incorporation of the latter in a design of a distillation column, it is suggested to apply it to a system for which the Vlilson constants are known in the literature.

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-3-11. Conclusions and Recommendations

1. The Wilson constants for the binary system (a) DMA-water exhibited regular behaviour, while those for thc binary systems (b) },flvlA.-water

and(c) TMA-water exhibited some anomalies. The cause(s) of this irregular behaviour may lie in one or more of the following factors: (a) tbe occurrence of immiscibility;

(b) data over an insufficiently wide range;

(c)

inaccuracies in the data.

2. It is suggested to determine experimentally whether the binary

mixtures of water and the respective amines and the multiconrponent system under discussion are completely miscible.

3. It is recommended to try to apply Renon's equation to the system

under discussion for the description of its vapor-liquid equilibria.

4.

It is suggested to check the calculational procedure concerning the Wilson ccnstants and the distillation column for a system, whose

Wilson parameters and distillation' s design are knovn from literature.

5. It is suggested to develop a more efficient computer program for the design of a distillation column for nonideal systems.

(8)

,-

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-4-111. Introduction 1. General

t1ono-, di- and trimethylamines , CH

3NH2, (CH3) 2NH anel (CH3) 3N

are manufactured in a continuous process (the Leonard process) from technical grade anhydrous ammonia and methanol (1). The flowsheet

is described in Fig. 1. Accordingly, e.rnmonia, methanol and recycle

liquid are fed continuously at controlled rates through a vapor1zer, heat exchanger and superheater into an amination catalyst packed converter. Part of the exothermic reaction heat 1S used in the feed preheater. The crude product is fed to a series of fOUT distillation columns. The first column separates excess ammon1a and part of the TMA-ammonia azeotrope which is recycled. Bottoms go to the TMP. column, where T~ffi is separated by means of extractive distillation and goes

over-head. Bottoms are fed to the MMA column where pure NMA goes over-head to storage or recycle. MMA-column bottoms go to the DMA-column where pure DMA goes over-he ad to product storage or recycle with water

drained from the bottom to waste. The reaction system is in perfect equilibrium and any amount of tri-, mono-,or dimethylamine can be taken off as product with any amount of unwanted product recycled which suppresses formation of an equivalent amount of that material. All the products-are

99%

pure.

The overall yield of both ammon1a and methanol is above

95%.

Raw materials used per

100

Ibs. of anhydrous product are as follows:

MMA

Methanol

108.7

Ammonia, anhydrous

57.7

Utility consumptions per

100

Stearn Water Electricity

1300.

Ibs

13250.

ltr.

9.

KWh DMA TMA

149.7

171.3

39.8

30.3

Ibs. of anhydrous product

Operator Labor: one operator per shift

(9)

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-5-Capital cost: For a 20-million-lbs/yr. plant for 5 DMA / 3 ~WA / 2 TMA product ratio including tvlO .. reeks raw material storage for methanol, and two weeks storage for all anhydrous products, complete battery limits process plant, cost is $ 1.6 million based on current labor and material costs in

u.s.

(valid for November 1973).

Commercial installations: sixteen companies in 11 different countries use the process. Estimated total tonnage produced using the process in 1973 was 150-200.000 tons/yr.

2. Extractive distillation and its application in this project. When a system contains components of similar boiling points

separation by means of ordinary distillation lS of ten neither easily achieved due to the low relative volatility nor economically

attractive, because equipment and operating costs are usually very high. In such a case a modified distillation procedure is used; this procedure entails adding an extraneous liquid which changes the

relative volatilities of the original components and thus facilitates their separation. If the extraneous material is less volatile than the feed, it is called a solvent, and the operation is called extractive distillation. To be effective the concentration of the solvent ln the liquid phase must be at least 40 mole-%, and it is usually much higher.

A flowsheet of an extractive distillation column lS shown in Fig. 2. Accordingly the solvent lS charged to the top of an extractive-distil-lation column, the bulk of the solvent passing downwards being with-drawn from the bottom together with the component(s) whose volatilities are least affected by the solvent. The latter is required to improve the relative volatilities of some component(s) over the entire height of the column, so that they would pass overhead.

Separation of the bottom product from the solvent lS easy, because the volatility of the pure solvent is always substantially .lower than the former.

The extraneous agent ln the case of separation of aIDlneS lS

water. It is charged to the column in a rate which is equal to 1.65 times the mole rate of the feed. The relative volatility of TMA is increased significantly, and hence it passes overhead, while water, MMA and DMA pass through the bottom of the column to uridergo further separation.

(10)

r }

L

r .,

.1

l

I .

·-6-1. The concept of a real solution

The simplest 'tray to describe the properties of a liquid

solution is due to Raoult's law. Viz., the partial pressure of any component in a liquid mixture lS equal to the product of its

vapor pressure, as pure component at the temperature of the system and its mole fraction in the liquid phase (2).

However, Raoult's law holds only in simple cases in which the

components are chemically similar and becomes exact when they are

almost identical e.g., homologous compounds. It fails to represent actual behaviour of liquid solutions because of differences in molecular size and intermolecular forces of the pure components. It appears logical, therefore, to use Raoult's relation as a reference and to express observed behaviour of real solutions as

deviations from the behaviour calculated by Raoult's law.

A thermodynamic model can be developed by means of which, the

solution can be described. vfuatever this model is, it incorporates

the activity coefficients. The latter are thermodynamic functions which describe the deviations from ideal solutio:1.

2. Activity and activity coefficients

2.1. The activity of component i at some temperature, pressure and

composition is defined as the ratio of the fugacity of i at these

conditions to the fugacity of 1 1n the standard state, ,{hich is

a state at the same temperature as that of the mixture and at

some specified conditions of pressure and composition

(3):

a. (T, P, x) 1

=

1n which: activity a. 1 f. fugacity 1 f<? ₁ fugacity f.(T,P,X) 1 of the 1 .th component of the component 1n of the component 1n (Iv-1) [dimensionless]

the given state [atm. ]

(11)

r , I LJ r .

L~

L

r ' r ' , l _ r ' I ' , I I I , , , • I

n

r

-7-arbitrary specified pressure ln a standard state [atm. ]

arbitrary specified composition in a standard

state [mole fraction; dimensionless].

The fugacity is defined as follows:

~.

=

RT In f. + B(T)

l l

(rV-2)

ln which:

~.

l - chemical potentialof the i th

component [cal/gmol]

R - Universal gas constant [cal/gmol KO]

B(T) - Integration coefficient which lS a function of temperature only [cal/gmol].

On combining o ~. ~. l l Equations

(rV-1)

and

(rV-2)

f.

=

RT ln(--l-)

=

RT In a. f.o l l it follows:

(IV-3)

which means that the activity lS a measure of the difference of the chemical potentials in the given and the standard states. Obviously, the numerical value of the activity depends among other things on the choice of the standard state. If the standard state is chosen such that it lS that of the pure component at the temperature and pressure of the system, it follows that for a pure substance the activity is always equal to unity,

=

f.o l

(Iv-4)

and the activity of a component ln an ideal solution lS equal to its mole fraction, viz.,

f. l

=

al =

x.

(12)

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l , f '

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f'

l _

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l .

( , , I ' r , l , r ., , -, , J

i

, J

l

• J

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-8-2.2. The activity coefficient y. is the ratio of the activity of 1 1

te some convenient measure of the concentration of i, which lS usually taken to be the mole fraction:

y. 1

=

al

x.

1 (Iv-6) On comparison between Equatiens (IV-5) and (Iv-6) it follows that for an ideal solution the activity coefficient is equal to unity:

ai

x.

1

y.

₌

1

x.

(IV-7)

1 1

Another way of describing deviations from ideal solution, by using the activity coefficient lS as follows:

K.

=

y. K.O

1 1 1 (Iv-8)

ln which:

K. equilibrium constant which equals Y/X [dimensionlessJ

1

ln which:

TI

equilibrium constant ln an ideal system which equals pO/TI [dimensionless].

vapor pressure of the pure component at the tempera-ture of the system [atm.]

total pressure of the system [atm.]

3.

Estimation of multicomponent vapor liguid eguilibria

3.1. As pointed out above, the core of the problem of describing a

real multicomponent system is to estimate the vapor-liquid equilibria. In most of the cases the required experimental data are almost never available. In order to make the best possible estimate with a minimum of experimental data it is efficient and useful to express the problem in thermodynamic terms which would consolidate the basis for a molecular model. Because the activity coefficients are exactly defined thermodynamic quantities it is possible in terms of them to describe real systems in equilibrium under various conditions.

(13)

r l r '

L

f '

l . I l , r ' r ' , 1

1 ~l

~l

I ,

-9-The useful thermodynamic concept for efficiently expressing the E nonideálity of a liquid mixture is the excess Gibbs energy g ,

which ",as originálly introduced by Scatchard (12). I t is defined as follows (3): E g 1n which:

=

_{g(actual solution)} at T, Pand X

g(ideal solutio~ at) same T, Pand X

E

g Excess Gibbs energy of the solution ~alJ g Gibbs energy of the solution [cal.]

H'

(IV-9)

By means of the function g'" it is possible to derive an expreSS10n

for the activity coefficient Y

K for any component K in the system.

d . E (

nTg )

=

dOK T,P all n. (i;lK)

1

(IV-l0)

1n which:

n. number of moles of component 1

1

total number of moles.

3.2. There are several thermodynamic techniques for the calculation of

multicomponent solution properties. The latter are based on the

concept of excess Gibbs energy. Examples are the van Laar-type

(4, 5,

6,

7),

the Margules-type

(8, 9,

10, 11) and the Wohl-type

(13, 14) equations.

The van Laar equation for a binary system lS as follows:

A ln Y₁

=

[1

+ A X1

1

2

13

X₂

J

(IV-11)

B In Y 2

=

[ 1 + - -B X2

f

A Xl

(IV-J2)

(14)

.. ' r~ L • ( , I I L,

..

. L ~ r , , j

,l

J

~l

n

r

l . ln 'lhich:

-10-mole fractions of component No. rèspectively [dimensionless].

and No. 2

A and B constants which dep end on pressure and

temperature but are independent of composition [dimensionless] •

The Margules equation for a binary system lS as follows:

(IV-13)

=

Xl 2 (2A-B) + 2X₁3 (B-A) (IV-14)

Note that Vli th systems for ,-,hich A=B. both the van Laa.r and Margu.les equations further simplify to the common form:

In Yl =

=

AX 2 2 AX 2 1 (IV-15) (IV-16) Another procedure to calculate the activity coefficient Vlas

suggested by Wohl (13. 14). The excess Gibbs energy is expyessed as a polynomial series in the mole fractions (or volume fyactions) of the components in the mixture. It is a.s follOYls:

E g RTLq.X. . 1 1 1 in which: q. 1 Z. 1

=

+ L Z.Z.a .. + 1 J lJ lJ L Z. Z . Zka . . k + "k 1 J . lJ-lJ • L Z,Z,ZkZla . 'kl + ... ijkl 1 J lJ ( IV-17)

a constant which Wohl called the effective molar volume of the component.

effective volume fraction of the component.

The effective volumetrie fraction of any component is defined by the relation:

(15)

[ L... r 1 1

l

n

z.

=

1 n q.X. 1 1 L q.X. j=1 J J

-11-(IV-18)

Volumetrie fractions like mole fractions are related by the condition

L:Z. =

j J

(IV-19)

Second-power terms in this series represent deviations from ideal

behaviour due to interaction between two molecules; third-power

terms, those due to interaction between three molecules; and so on.

Thus, one of the advantages of this method is that some approximate

significance can be assigned to the parameters which appear in the

equation.

3.3. The methods cited above have some inadequacies which must be kept

in mj:'1d while calculating the activity coefficients. The constants

which appear in these equations are a function of temperature and

pressure but are not dependent on the composition. Concerning the

pressure, the dependence is not great; at low and moderate pressures

it can be neglected. However, the temperature usually plays a role ln determining the values of the constants. Only in one case is the

temperature effect on the constants zero. This occurs when the

solution is athermal, viz., I"hen the solution process of the com-ponents occurs isothermically, isobarically and with ~H

=

O.

For practical applications it is assumed that the dependence of the

activity constants on temperature at a modest range of the latter can be neglected.

Another problem embodied in the polynomial serles of Whol lS that in principle, binary data are not sufficient to describe multicomponent behaviour unless the series is truncated af ter the

second power term. The reason is that ternary, quaternary etc., data are necessary in order to calculate the higher order terms. Thus, this fact greatly complicates the experimental procedure and makes it less attractive.

(16)

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L. I . j • J

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-12-Many ot her methods are available ln the literature for calculating the activity coefficients. These methods usually require ternary

data and are not always applica1üe to polar systems. Therefore they are not described in this ·paper. The reader is referred to Prausnitz

(3) for further literature survey.

A completely different expression for the excess Gibbs energy has been proposed by Hilson (15). Accordingly, gE is "ritten as a

logarithmic function of the liquid composition. It has some very useful advantages:

(a) buÏ1t-in temperature dependence;

(b) accurate representation of data with only a few parameters (hro

constants for a binary system;

(c) prediction of multicomponent properties from binary data without any additivity assumptions;

(d) a semi-theoretical interpretation of the parameters.

For systems which exhibit incomplete miscibility, Hilson's equation

is not applicable.

Wilson's equation was tested by Professor J.M. Prausnitz and his

co-workers at the University of California (Berl~eley) for various

binary and multicomponent systems, including polar, highly nonideal cases, and they concluded that the equation is a good method for

describing multicomponent vapor-liquid equilibria with only binary

(17)

r 1

L

( ,

I

,

. r ' , ) , 1 I , J

l

n

, I

n

-13-4.

The Wilson Equation

Wilson's equation is a semitheoretical extension of the

theoretical equation of Flory (1'7) and Huggins (18) which lS used

for the thermodynamic description of mixtures with macromolecuJar

components, viz., polymer solutions (for full derivation see Appendix A). By means of this equation it is possiblè to find a

relation between the mole fractions of the components ln the liquid

phase and the respective activity coefficients. This relation is

made using thc Wilson constants, which are defined as follows:

Aij

₌

Aji

₌

in which: L v. - L L v. l L v. l L v. J Aij, Aji v L v.L i ' J

Àij, Àji, Àii, Àjj

(IV-20)

(IV-21)

Wilson constants [dimensionless].

liquid molar volumes of components l, j

respectively [cm3/gmol].

energy coefficient of interaction between

the respective pair of molecules [cal/grool].

Note that, whereas Àij

=

Àji, in general Aij

#

Aji.

An ideal solution lS one where A

12 = 1\21 = 1; thi s deviation

of the parameters fr om unity is an indication of the nonideality of

the solution. If both A

12 and 1\21 are greater than unity, the solution

exhibits negative deviations from ideality (gE < 0), whereas if they

are both less than unity, positive deviations from ideality (gE> 0) results. If one parameter is greater than unity and the other one lS less, than the deviations from ideality are not large.

(18)

I .

l

• 1 , J

J

n

--

14-In general, the relation between the excess Gibbs energy and the activity coefficient lS as follows: E g

=

n RT L i=l x.lny. l l (IV-22) By introducing Wilson's equation into Equation IV-22, one gets: E g

=

-RT n _L _x_._ln[ n _L _{xJ' Al'J'J}

1

. 1 l . 1 l= J=

from which it follovTs for any component k,

=

-In

[~

x. A .] + 1 -

~

j=l J kJ i=l X. l n L j=l (IV-23) (IV-24) x. A •. J lJ

For a binary sOlution, the activity coefficients are as follows:

lnYl = _{-ln(x l} + _{A12x2 )} + _{x2 [Xl} +

A

12 _A2l _]

A

12x2

A

21xl + x2 lnY2 -ln(x 2 +

A

21xl) - xl _[Xl A₁₂ A2l ] = +

A

12x2 A2lxl + x2

4.2. The Hilson equation has two remarkable advantages which make it

(r

V

-

2 S)

(IV-26)

very useful for engineering applications. Firstly~it has a built-in temperature dependence, which is introduced in the IV'ilson constants; the former has at least an approximate theoretical significance.

Furthermore, the differences of the energy coefficients of interaction, viz., (À •• - À •• ) and (À •• - À •• ) may be, approximately, considered

lJ I I lJ JJ

independent of temperature, at least over a modest interval. This means that parameters obtained from data at one temperature may be used

reliably to calculate activity coefficients at another temperature not too far away. Secondly, Wilson's model for a multicomponent solution requires only parameters which can be obtained from data for the pure components and for the individual binary systems. The relative simplicity of the

experim

e

n

~

al

determination of binary data as contrasted to multi-component data is a basic advantage. The extension of Wilson's equation

(19)

L

( ,

l.

4.3. [

:

r '

L . • 1

-1

• 1

n

-15-from the binary to the multicomponent case requires no additional

assumptions.

There are blO disadvantages of Hilson' s equation which must be

taken into consideration. Firstly, it lS not applicable to systems which exhibit incomplete miscibility. In this case another equation,

which is a modification of Hilson's,can be applied; the former is Renon's equation (30). This equation, which is named the NRTL (Hon-Random, Two-Liquid) equation is applicable to partially miscible as weIl as completely miscible systems. Renon's equation for the excess Gibbs energy is as follows:

n E n _j~1L T •• _{J1 J1 J}G .. X. iL ₌ _I _x. RT i=1 1 n L _GR,iXR, R.=1

(IV-27)

where (g ..

_-

g .. ) J1 11 (g .. g .. ) T ••

=

J1 _RT Jl 1J

(rv-28)

G ..

₌

exp( -ex •• T .. ) (ex ..

₌

ex .. )

J1 J1 J1 J1 1J

(IV-29)

The significance of g .. is similar to that of A .. in Wilson's

1J 1J

equation; g .. is a (Gibbs) energy parameter characteristic of "the 1J

i-j interaction; the parameter a .. is related to the nonr~ndomness

1J in the mixture.

A

second disadvantage lS that Wilson's equation lS not applicable for systems where the logarithms of the activity coefficients, when plotted against xl~ exhibit maxima or minima. Such systems, however, are not common. Mixtures of chloroform with alcohols do exhibit that

phenomenon; still an approximate prediction can be obtained for the activity coefficients over almost the whole range of compositions.

(20)

,

, I ' L r '

l,

[ , ( , I ,

~1

:

1 ~1

n

r

-16-V. Calculational Procedure 1. General

In order to design the distillation coluum it was necessary to

calculate some parameters concerning the pure component properties and

the multicomponent system.

These parameters were calculated by means of computer programs which

are specified in the book "Computer Calculations for multicomponent

Vapor-Liquid Equilibria" by Prausnitz, Eckert, Orye and O'Connell (19).

The .design of the column lS based on a computer program for nonideal

distillation. The latter appears in the book "Computation of Multistage

Separation Processes" by Hanson, Duffin and Somerville (20). Originally

the program was written with a subroutine based on the Margules equation

to calculate the activity coefficients. This subroutine was replaced by

another one based on the Wilson equation.

2. Calculation of Parameters

2.1. Liquid Molar Volume

It is necessary for a rigorous thermodynamic description of

binary-and multicomponent-phase equilibria to have information on the

temperature dependence of the pure-component liquid molar volume.

The molar volume of a component at any temperature T may be calculated when required ln the computer programs as:

L

v = a + bT + CT2

(V-1)

The constants are (T 3-T1) L L L L (T 2-T1) (v -v ) -₂ ₁ _(v3-v 1 ) c =

_(v.,.2L

(T 2_T2) 2 1 (T3-T1) -

(T

2_T2 ) 3 1 (T2-T1) L' L ₂ ₂ (v 2-v 1 ) - c(T₂-T 1)

"

b = T₂-T₁ v L 2 a = _{- bT 1 - cT 1} 1

(V-3)

(21)

r'

r '

L

( ,

L

r . - 1 , )

~l

n

r - ,

I

-17-Tl' T

2 and T3 are the temperatures at which the pure component liquid

L L L

molar volumes v l' v 2 and v 3 are available.

A computer program for this purpose - VMOL - described ln Appendix B.

The data was taken from Gallant (21).

2.2. Constants for the Vapor Pressure Equation

The vapor preSSlITe of the pure component as a function of ternperature

is written as follOi-ls:

lnP~(atm. )

l

=

Cl' C₂, C

₄

and C

₆

are constants.

(v-4)

The program according to which these constants are calculated lS

named VAPFIF and is described in Appendix C.

The data for BHA Here taken frorn Felsing (22). The data for TMA

were taken from Felsing (23). The data for DMA were taken from

Jordan (24). The equation for i-later was taken frcm Prausnitz (19).

The equations cited above are intended to represent very precisely

the vapor pressure dependence on temperature, but they cannot be

transformed to the more convenient form for interpolation, viz., a linear equation.

A modified equation which has recently become very popular lS the

Antoine equation. It has the form:

B lnP~(atm.)

=

A +

-l

(V-5)

The advantages of this equation are that it is sufficiently preClse

and at the same time still permits the representation of dependence of the vapor pressure on temperature by a simple equation.

This form of equation was used in the design of the distillation column.

The equations for ~1A and DMA were taken froID the Handbook of Chemistry

(22)

( ) l ~ r ' l ,

r'

L • ( . r ' I l . { , ' l , i

n

r

-18-The equation for TMA was taken from Felsing (23). The equation for vlater was taken from Bijwaard (26).

The constants are listed in Table V-1.

Table V-1: Constants fOT the vapor pressure equation of MMA, TMA,

DMA and water.

Component A B Range 0 C

MMA

-

5859.4 12.048890

_-

95.8

..

144.6

TMA - 4983.9 10.066016 60 .;. 130

DMA - 6031.9 11.780227 - 87.7 .;. 162.6

Water - 8585.1 12.809286 0

..

150

2.3. The Hilson Constants - Calculations of Binary-Interaction Parameters

For mixtures of components i and j, the two parameters /tij and 1\ji can be obtained from vapor-liquid equilibria data. In principle, only one experiment al point (X, Y, T or p) lS required, and sometimes it

is possible to obtain a good estimate of the parametersmerely from azeotropic composition and boiling point. In general, however, it lS

necessary to have a series of data points, either isothermal or isobaric.

The method of Barker (27), for reducing experiment al binary data to thermodynamic parameters, was adopted. According to this procedure total pressures are measured as a function of the composition of one of the phases (usually the liquid phase), and no measurements are made of the composition of the other ph~se. Instead, the composition of the other phase is calculated from the total-pressure data with the help of the Gibbs-Dubem equation:

n

I:

i=1

X.dlny.

l l

= o

(at constant Pand T)

(v-6)

From such information it is possible to obtain the parameters 1\12 and A

21 of Equation IV-23, or the parameters of any other equation chosen to represent the activity coefficient as a function of composition.

(23)

( ) L~ I •

L. l:

r' r ' I

l

r '

I l. (

.

I

l . r l l )

n

-î9-Further, the data reduction method requlres information on the

volumetric properties of' the gas-phase mixtures in order to correct

for vapor-phase nonidealities. At low and moderate pressures these

corrections can be calculated from the virial equation of state:

ln which:

z

v B C etc. Pv == RT B C + - + v + •••

compressibility factor [dimensionless]

molar volume [cm3/gmol]

the second virial coefficient [cm3/gmolj

• • • • • [ f

3/

)2]

the thlrd vlrlal coefflclent ,-cm gmol

rrhis equation of state was utilized together .Ti th a correlation of

pure and mixed virial coefficients prepared by O'Connell (19).

A complete computer program ~ IHLS - for the calculation of 11. •• and 1\ ..

;iJ J l

is described in Appendix D. The data was taken froill Rohm and Haas Co.

(28),

and Gallant

(21).

2.4.

Design of an Extractive Distillation Col~~.

The distillat ion colliEr! for which the following progran has been

designed is that with a total condenser. It is taking into consideration the fact that the system is nonideal and the composition effect on the

equilibrium constants is here expressed by means of the activity

coefficients as follows:

(K)modified

=

y(K)'d _l _eaI

(v-8)

where the values of gamma (activity coefficient) are determined by

the i-lilson equation for multicomponent systems.

The y values are determined in a subroutine - ACTCO - and are stored in a two dimensional array for use by the main program. The y values are used in bubble-point calculation, and a special bubble-point subroutine BUBPTG has been written for this purpose.

(24)

( 1 I ' I L~

r:

r :

r ' I l . I ' l . r ' I •

r :

rl

I

I l J

[1

n

-2C-Since the system is nonidcal the competing effects on the composition

map of first temperature and second composition dependent activity coefficients of ten result in 8. severe oscillation of the composi tion map from iteration to iteration, with little or no tendency to

converge.

An iterative scheme named thc method of succeSSlve flashes, which approaches convergence in an asymptotic fashion but with less tendency to oscillate, was applied here (see Appendix E).

In the use of this method i t vras necessary to asswne all stage

temperatures and set all vapor and liquid flows. The pressure and

number of stages was set too. In this program no heat balance lS

used and no correct ion to flows is made. Thus, the initial values of

flovTs assumed are used throughout the calculation. It is assumed that

the liquid flow is constant for all plates d01m to the point of feed

introduction. The liquid flmv from all plates below the point of feed

introduction is assumed to be the sum of reflux plus feed.

In addition the starting composition on every stage must be assumed.

It 15 not necessary to have accurate compositions, since the

steady-state Golution is independent of any starting compositions. A simple way of starting is to fill every stage with feed liquid at its

bubble-point while the vapor is in equilibrium.

The equilibrium constants (derived from vapor pressures) can be

represented by the equation:

A

InK

=

+ B

(TOF)

+

460

The constants are listed ln Table" V-2

Table V-2: The equilibrium constant for ~ffi, TMA, DMA and water

Component A B IvIMA

-

5859.4

9.805907

TMA.

- 4983.9

7.823033

DMA

-6031.9

9.537244

Water

-

8585.1

]0.568466

/j

(25)

I , r ' I I l .

[

:

r ' l . r ~1 r 1 \ J

]

f1

fl

-21-Note: The constant B lS taking into consideration the pressure 1n the

column of TI

=

9.4

atm.

Three error limits are required by the calculation: SillvlliRR, the accuracy to which all vapor and liquid mole fraction summations must approach unity; RFERR, the accuracy to which the top and the

bottom recovery fractions of a component must approach unity; and

BPERR, the accuracy of the bubble point calculation. These error

limits have been given the values Sill1ERR = 0.001, RFERR = 0.001,

and BPERR

=

0.0001.

(26)

[

:

r~

l.

[

:

,

' I l . f ' l • r ' I r -, l ,

n

r

I

-22-VI. Results and Discussion

1. Liquid molar volume

The dependence of the pure-component liquid molar volume on the

temperature lS as follmvs:

=

a + (VI-l )

The constants are listed in Talbe VI-l.

These values,like the rest of the values discussed in this chapter,

were calculated using procedures described in chapter V.

Table Vl-l: Constants of MMA, TMA, DMA and Water ln the liquid

molar eguation.

Component a[cm3/gmol] . b[cm /3 grnol TK] c[cm3/gmol

101 _-1.413

_'*

101 _3.830 _4 MMA _5.537

_*

*

10 TMA 7.964

*

101 -9.633 3i 102 4.9118

*

104 DMA 8.239

*

101 -2.155

*

101 5.800 i i 104 Hater 2.288

*

101 -3.6112

*

10-2 6.856

*

104 2. Vapor pressure (ToK)2]

The vapor pressure of the pure component as a function of temperature is written as follows:

lnP~ [atm.]

=

Cl +

---The constants are listed ln Table VI-2.

Table VI-2: Constants of MMA, TMA, DMA and water ln the vapor pressure equation

I

(27)

, 1

[

:

[

:

[

:

r ' I

l.

r'

I I, • r' l • , I l • ,1

i

I _, l ' r 1

f1

D

o

n

r

1

-23--Table VI-2: Constants of MMA, TMA, DMA and Water ln the vapor pressure

equation. Component _Cl C 2 C3 C4 Range ° C MMA 8.5512*10 2 -2.995067*10 4 1.859*1-1 0 -1.420*10 2 80~Î40 TMA 4.3780*10 1 -3.-(15630*103 8.818*lÖ 3 -5.821*10 0 60-i-11fO 1 4 -1 _'₁_-"'-3 ₁₀₂ 81

7

139 DHA 9.4267*10 -3.333743*10 I ₂_.₀_11*1₀ - .)0 * . 1 3

I

6

-3 _° Water 7.0430*10 -7.362690*10 -.950*10 -9.000*10

o

.:;125 3. Wilson constants 3.1. Results

The Hilson constants vere calculated for the following binary systems:

(a) M.r-1A-water; (b) TJ"IA-water; (c) DMA-.. rater. The calculation .. ras carried

out at temperatures between 70 to 140°C in intervals of 10°C. The

results are listed in Tables VI-3, VI-4 and VI-5.

Table VI-3: Hilson constants for the binary system r-.-R-1A-water Note: the component lS no. (1)

water (W) lS no. (2) tOe A 12 A21 70 5.4647 0.0000 80 4.9892 90 4.4315 100 4.0338 (see Fig. 3) 110 3.6300

1

120 3.2716 130 3.0000 140 2.7143 ,/ / I

(28)

f 1

L~

l,

l •

rl

fl

o

fl

n

~

-24-Table VI-4: Wilson constants for the binary system TMA-water tOe Á 12 Á21 70 0.0801 0.7502 80 0.0835 0.6623 90 0.0890 0.5628 100 0.0950 0.4702 (see Fig. 4,5) 110 0.0969 0.4114 120 0.1009 0.3474 130 0.0000 1.4387

Table VI-5: Hilson constants for the binary system D~1A-Ylater tOe Á 12 Á21 70 0.2418 1 .7253 80 0.2603 1 .5802 90 0.3560 1.2178 100 0.3031 1 .2854 110 0.3198 1 • 1520 (see E'ig.

6,

7) 120 0.3289 1.0233 130 0.3342 0.9193 140 0.3167 0.8599

The characteristic ener~T differences (À . . -À .. ) and

• lJ II

calculated for the binary systems mentioned above at 70 to 140o

e.

The results are listed in Table VI-6.

(À •. -À .. ) were

lJ JJ

(29)

( ,

L

r •

L.

l J

[1

n

-25-Table VI-6: Energy coefficients of interaction (À .. -À .. ) and (À . . -À .. )

lJ II J-J JJ

for the binary systems:

(a) HMA-H; (b) TMA-W; (c) DMA-W.

tOe syste::l _P12-À₁₁₎ cal.

(À 12-À22) cal. gmol gmol ]·IIifA-H - 1865. 23108. 70 TMA-H 534. 1382. DMA-H

_-

0.22 596. MMA-W - 1868. 22888. 80 TMA-\\T 509. 1522. DMA-W

_-

63. 687. W\1A-H - 1848. 12688. 90 TMA-W 465. 1694. DMA-W

_-

303. 871. MMA-Vl - 181

n.

_21720. 100 TMA-Vl 417 . 1887. DMA-I{

-

204. 903. MMA-W - 1826. 20466. 110 TMA-W 401. 1023. DMA-W

_-

263. 2051. MMA-W - 1806. 26057. 120 TMA-W 368. 2249. DMA-W

-

304. 1155. MMA-W - 1797. 24520. 130 TMA-W 27630. 1180. DMA-W

-

337. 1283. MMA-W - 1774. 24180. 140 TMA-W DMA-IV

_-

314. 1381.

(30)

, ) r ' r~ \ . r ' l . r ' j ,

n

L J

r

-26-3.2. Discussion

The scope of this paragraph is: (a) to discuss the method according

to whjch, the Hilson equation was applied to the various binaries which compose the r:mlticor.'lponent syst.em under discussion ; (b) to

clarify some points concerning the computer progrrun (see Appendix

C),

by means of .rhich the Hilson parruneters are obtained; (c) to analyse

the values obtained for the paramet.ers; (d) to discuss some other

methods for the calculation of the activity coefficients.

The approach of attack to the problem was the following: Since there

was no information available concerning the G-L equilibria of the

binary systems (a) MMA-DHA, (b) r-1MA-'l'l'fJil., (c) TMA-DMA; and since these

are binary systems composed of nearly homologous compounds they were

treated as ideal systemS:the Hilson constants were set equal to 1.0.

Therefore, the problem ,-laS focused on caleulati!1g the parameters for the

the binary systems: (a) HHA-W, (b) TVlA-H, (e) DMA-H for vlhieh only

bubble-point behaviour was available in the range 70 ~ T ~ 1400

c

and

a eoncentration range of 0.0 to ea. 40.0 mole-% of the respeetive

am1ne.

As it was discussed 1n Chapter V, the parruneters were ealeulated by

means of a computer progrrun (see Appendix C) whieh was described by

Prausnitz

(19).

This progrrua ineorporates a eertain subroutine nruned

LSQ. The latter lS a nonlinear multiple-regression subroutine whieh

adjusts the parameters of a function being fitted to data in sueh a

manner as to yield a least-square fit. The Wilson parameters are

obtained according to the optimal fit of the total pressure. The

sub-routine LSQ was not deseribed in the program, and therefore another

subroutine nruned

oppm"

replaced it. The latter has been used at the

T.H. Delft and gave good results for ealeulating the minimum sum of squares and thus finding the best fit between a eertain function and given data.

In order to check the entire progrrun (including the new subroutine),

an example whieh appeared in Prausnitz

((19),

p.

155)

was programmed

and run on the computer. To the writer's surprise the Wilson parrur.eters

whieh were obtained differed up to

15

%, as compared with the results

(31)

( , L ,

r:

, , r ,

r-I

I ,

~l

n

-27-In the light of these results it was suspected that a mistake was

made vrhile punehing the program on eards. The listing .TaS earefully

eheeked several times but no mistakes eould be found. The only two reasons whieh might eause the disagreement in the results eould be

the following:

(a) subroutine LSQ is more effieient 1n ealculating and minimizing

the sum of the squares .,hile fitting a function to data in comparison

vrith subroutine OPPOW;

(b) there is amistake either 1n the original program or ln the exan!ple

1n Prausnitz.

It might be a good idea to try and get the subroutine LSQ and make a

test-run with the original progrmn and the example whieh appears in the book. Because, however, the difference was not too large (~ 15%) and beeause no error in the program eould be found, it was nevertheless decided to carry on the calculational procedure using the modified program with subroutine OPPOH.

eoncerning the calculated Wilson constants , the system DM.4.( 1 )-H( 2) exhibited normal behaviour ln its variation of

A

12 and

A

21 with tempe -rature. The rate of change of

A

12 and

A

21 is regular and indeed the parameters do not vary mueh over a modest range of temperature. At 700e

A

12 = 0.2418 and

A

21

=

1.7253; at 140 0 e

A

12 has increased to 0.3167; while

A

21 has decreased to 0.8599.

For the binary systems TMA(1)-H(2) and MHA.(1)-W(2), however, anomalous

behaviour is found. For the former system the change in the values of

A

12 and

A

21 with temperature from 70 to 120

0 e is normal. At 700e,

A

12 =.D.0801 and

A

21 = 0.7502; at 120 0 e

A

12 has increased to 0.1009 and

A

21 has decreased to 0.3474. This rate of change is regular. But at 1300e there is an abrupt change in the trend of the values of the

parameters.

A

12 decreases to 0.0 and

A

21 increases to 1.4387.

The constants of the binary system MMA(1)-W(2) vary too much in a small range of t emperatures; e.g., at 700e A

12

=

5.4647, while at 90

0

e A

12

=

4.4135. A21 remains constant through the whole range of tempera-tures 70 ~ T ~ 1400e and is equal to

o.o.

Bearing in mind the fact that these constants are not supposed to vary much over such a temperature range (the difference lS usually in the order of a few tenths), this trend seems strange.

(32)

r 1 I L~

I

.

l

~

I l J l , r ' r '

l

.

n

l;

-28-The values obtained for the energy coefficients (1..

12-1..11) and

(1..

12-1..22) raised some questions, namely:

(a) the trend in the values of (1..

12-1..11) and (1..12-1..22) of the binary

system TMA(l )-H(2) suddenly rcverses in direction at 1300C (keep in

mind the abrupt change in

A

12 and

A

21 for this system mentioned above).

o ( , /

Up to 130 C, 1..

12-1..11 ) lS 1n the order of a few hundreds cal. gmol.

At 130°C, (1..

12-1..11 ) lS equal to 27630.cal./gmol. This jump seems

strange;

(b) the results for the binary systems at 800

e

are, for example:

Component ( 1 ) _{( 1..} 12-",1) cal. (1..₁₂-"22) cal. gmol gmol TMA 509. 1522. DMJI.

_-

63. 687. MMA

_-

1886. 22888.

Note: water(W) l S no.(2).

Based on these resul ts the following statements can be "rri tten, in which r = energy of interaction in cal. /gmol. Recall the fact that

1..

12,1..1..11 and "22 are ah.rays less than zero.

1 . r(THA-W) < I(TMA-TMA) 2. r(DHA-\v) > r (DMA-m,1A) 3.

r(MMA-Vl)

> r (MMA-MI.1A)

4. r(TMA-H)

< r(w-w) 5. r(DMA-W) < I(\<l-W) 6. r(MMA-W) < r(W-H) and: (>.. -À )

. 12 22 ('l'MA-W) À 22 (DMA-W) )

=

835. cal/gmol

7.

r(D~ffi-W) > r(TMA-W)

( À - L )

12 'ë2 (THA-W) (1..12

-À )

(33)

r ' I I L •

L

r '

l.

r , I ' ( ,

l ,

n

-29-8.

I (TMA-H) > 1 (HMA-H)

Thus, combination of 7 and 8 gives:

9. I(DMA-W) > 1 (THA-iv) > IU-1tvfA-1;.,r)

It must be born in mind that the lflilson equation is a semitheoretical equation, and applying theoretical significance to the parameters is

only an approximation. In any case, statement no. 1 seems incorrect.

From the standpoint of organic chemistry (see belOW) the interaction

of water and TMA must obviously be greater than the interaction of

two TMA molecules due to the polari ty of \-later, viz.,

r

1 1 t., r 1 2

I

L ~ H - 0 CH 3 - N - CH3 CH 3 ?H3 CH 3

- n

- eH3 eH 3

- N

- eH3 CH 3 H TMA-I'l interact.ion .J ï

TMA-TMA interaction

...

Concerning the other statemen~ it lS difficult to say defineteiy whether

they are correct or not, since two opposing effects must be taken into consideration; these are: while substituting methyl groups for hydrogen atoms in ammonia two effects occur:

(a) the basicity is' increased,' thus. increasing the solubility in water; (b) hydrophobia is increased since methyl groups have no affinity for water; thus)the solubility in water is decreased.

Because the writer, af ter much thought and consultation, could not

explain the cause of all these ancmalous results obtained for the Hilson

parameters a letter was sent to Professor J.H. Prausnitz of the University of California, Berkeley (see Appendix G). Professor Prausnitz is a world authority in the entire area of molecular thermodynamics and the writer

(34)

· 1 r ' L _

[

:

r '

[

~

[1-n

n

answer lS given ln Appendix H). In his lette~ Professor Prausnitz

mentioned a few points which are very important when applying the Hilson equation, namely:

(a) Wilson equation is applicable only to completely miscible systems,

and immiscibility may occur in the system (8) under discussion;

(b) Wilson equation is a semitheoretical equation;

(c) the data necessary to calculate the parameters must be very accurate;

(d) various sets of parameters can be obtained for varlOUS sets of data;

(d) the parameters obtained depend on the reduction method of the data,

viz., the fit of vapor composition data, or the fit of total pressure

data.

Concerning point (a), as pointed out earlier one of the disadvantages of

the model is its inability to describe immiscible systems. When Vlilson's

equation is substituted in the equations of thermodynamic stability for

a binary system (see Prausnitz (3), p. 233),

A

12 and

A

21 cannot indicate

the existence of two stable liquid phases. This is a cardinal point and

must be absolutely clear. Concerning the binary systems treated above and

the multicomponent system of t&4A, TMA, DMA and Water, it is not certain

that these mixtures are completely miscible, especially at high tempera-tures. If indeed they are not,another model may be applicable.

The latter is Renon's equation which, unlike Vlilson's is applicable to partially miscible systems. Since there was no information about the

miscibility of these systems, it would seem wise to check this point

experimentally. In any case, it is recommended to try to apply the Renon's

equation to this problem.

Concerning points,

(c)

and (d), the data used to calculate the parameters were taken from graphs published by Rohm and Haas Co. (28) and Gallant

(21). No tables were found with TI vs.T for the binary system under dis-cussion. Because the data for TI appeared on a logarithmic scale it was difficult to read it accurately • . On top of that the graphs of TI vs.T

covered only the concentration range from 0.0 up to approximately 40 mole-%. Thus, it is very well possible that if more data were available and if it were more accurate another set of parameters could have been obtained.

(35)

L-I i . L _

[

:

I '

l .

l , r ' I l !

n

r

_!

-3'-Because of some uncertain values of the Wilson constants it was decided

to try and calculate the activity coefficients for the multicomponent system under discussion by means of the three suffix Margules equation.

Some methods are described in Hála ((2), p. 41), from which it is

possible to calculate the constants A and B in the Margules equation

without a knol-Jledge of the equilibrium G-L composition of the binary

systems; only a knowledge of the bubble-point behaviour is required.

However, these methods cited above could not be successfully applied.

One method, suggested by Carlson and Colburn (29), is based on the fact

tnat in those cases where the vapor phase can be treated as an ideal

one, then: (a) the fugacity of the component in the system can be replaced

by the partial pressure; (b) Dalton's lm'J holds for the vapor phase.

Then by definition for a binary system:

TI - y₂P0 ₂X 2 Y

,

=

(VI-3)

0 P,X, TI - y,p,X, 0 Y2

=

0 P 2X2

(vI-4)

As X

2 ~ '.0, Y2 ~ '.0 so that an apparent activity coefficient can be calculated for component' by assuming Y

2

=

'.0. By plotting these apparent activity coefficicnts on semilog paper vs.X, an extrapolation may be made to find the terminal values of the activity coefficients, whose logarithms are the constants in the Margules equation.

Unfortunately the assumption of an ideal vapor phase seems to be incorrect in this case because of the polarity of the components.

Furthermore, when substituting Y,

=

'.0 into equation

v-4,

a negative value is obtained ln some cases for the apparent activity, making it im-possible to continue with the calculations:

Another method to obtain the constants A and B is by plotting log TI vs.X and drawing tangents to the curve at X

=

0.0 and X

=

'.0. Based on these data and some mathematical manipulations the constants can be calculated. But the data for the binary systems and the respective amines cover only concentrations range up to approximately 40.0 mole-%. Therefore a tangent

(36)

r:

I '

r

n

-32-to the curve at X

=

1.0 could not be dravrn, and. thus the method could not be applied.

Summing up, the values obtained for the Wilson parameters exhibit different trends for the various binary systems under discussion. The parameters cannot be rega.rded as reliaole until certain points viz., miscibility, range of data and its accuracy can be clarified. In any case it is reasonable to try to apply Renon's equation.

4.

Extractive Distillation Column

The column was supposed to be designed by means of a computer program which was vrritten especially for nonideal distillation (see Appendix F). The deviations from ideality were expressed by means of the activity

coefficients) vhich vtere calculated in a special subroutine. Originally

the calculation was carried out with the three suffix Margules equation.

Fo!' reasons already indicated a new subroutine, based on the Hilson

equation, was introduced in the program.

The program v;as punched on cards and a test-run vTaS made wi th the example

which appeared in Hanson's book (20)~ however, no solution vas obtained.

The program was checked several times and according to the writer, there

are two mistakes in it, namely:

(a) statement no. 23 is written as follows:

23 DO

24

J

=

1,JC

it should be written:

23 DO

24

J=1,JD;

(b) the statement following statement no. 25 1S written as follows:

DO

26

J

=

1,JC

it should be vTri tten:

(37)

I ' Î l _

! '

[

:

r ' I I . r ' i I , r ' I 1

n

-

33--Af ter correcting these statements, a sOlution, identical with the one which appeared in the book, .Tas obtained.

The Wilson parameters \.,rhich were used in the calculations "Tere as follows: For the binary systems MMA(1 )-DMA(2), MI,1A(1)-TMA(2) and DMA(1)-T.t..1A(2), the parameters were set equal to 1.0. For the ot her binary systems viz.,

MMA ( 1 ) -We 2), DMA ( 1 ) -H( 2) and TMA ( 1 ) -Vl( 2) the parameters .Tere the averages

o 4 0

of t heir respcctive values between 70 C and l OC. They are listed in Table VI-7.

Table VI-7: Average Wilson parameters for the systems: (a) MMA(1)-W(2) (b) TI.1A(1)-Vl(2); (c) DMA(l )-W(2), in the temperature range 700C 140oC.

·~

i

, I MMA( 1 )-vl( 2) TMA(1)-H(2)

I

DMA( 1 )-Vl(2)

A

I

I I

l

1\12 3.9418 0.0909 0.3076

I

i

1\21 0.0000 0.53110 I 1.2279

I

Note: ln the case of the binary system TMA(1)-W(2) the anomalous values at 1300C were neglected in the calculation of the average.

The reason for averaging of the parameters was that an actual column, which separated TMA from the system under discussion by means of extractive

distillation, was operating at about the same temperature range. By using average values the parameters are less accurate for the whole temperature range, but this procedure is areasonabIe approximation for a first design. The next step would certainIy be to rewrite subroutine ACTCO (for y's), in such a manner that it would read a new set of parameters for about each 100C and caIcuIate accordingly the activity coefficients. Thus the built-in temperature dependence of the Hilson parameters would play its proper role in calculating the activity coefficients.

(38)

, 1 r ' I I l , r' I

l.

[

:

( , , , r' i l , l )

[1

r

1 [1

n

-34-Many trials were made vrith vanous reflux ratios

(0.5

R .:

2.0

R) and various rates of extractive "Tater

(0.75

F :.

1.

65

F in kgmol/hr). Unfortunately, none provided an optimal desigr... All of them exhibited an -anomalolB change of temperatures along the column and an insufficient separatioll of TMA. As for example SOL V:ccE N,-,-T_~ F

=

142.8

kgmol/hr

r

22 .4

1

20.3

18.4 \..81.6

F

=

233.3

kgmol/hr W

2

OVERHEAD

.D

---'~~-PR 0 D uCT SOLVENT PLUS

S

eorrOM PRODUCT kgmol/hr MMA 11 TMA

"

DMA

"

w

The column consists of

60

plates, and the feed lS introduced above the

th th

50

plate. The extractive water is introduced above the

55

plate.

L

The reflux ratio is set equal to

1.0,

thus R

=

D

= 1.0.

The results obtained af ter

93

iterations are listed 1n Table

VI-8.

Note the following order of the components, viz.;

(1) MMA

(2) TMA

(3 ) DMA

(39)

~ '--:1 p, )-'. en c+ )-'. f-' f-' Pl c+ )-'~ 0 ::s en () 0 ::s p, )-'. ei -)-'. 0 ::s en ~ CD >-j-CD en "d CD () )-'. H:l )-'. CD P, ~ 0

<

_CD ~ :. \::

:=J

en

«

_en c+ CD S

~

_J

~

_J t::J ~ J ~ 1-3 ~ f-' CD <: H J CP ~ CD en ~ f-' c+ en ,0 H:l CD >< c+ >-j Pl () c+ )-'. < CD P, )-'. en c+ )-'. f-' f-' ~ )-'. o ::s o H:l

~

~ o S c+ ::r CD

.

::=J

l

.---, ..---, ---" r - ~ , r-

-

'

[

~ ~

,.

" PROBlEM NO.

~

11ERATION

NO.

=

93 MOLE FRACTrONS LISTED AS COMPONENTS

PCR

PL~T~

BOTTCM

P~ODUCT (t) O.62077902E-01 (2) O.124825<J13!:-C'1 RE88ILEI\

VAPOR

0.22443ó28E

ro

O.22587490F.

nn

Rf FLUX

O.15ó7C86oE-Ol TOP

PROfJUC

T O.15670866E-Ol Oo7~313231~ CO O.7H:H32.31F 00

BorTOM PRODUCT RECOVERY

rR~CTrGNS

O.0S57ó367E 00 O.21765nOOE 00

TOP PRODUCT RECOVERY FRACTIONS

0.14271677E-01 0.7~313226E 00

SUft'MATION OF

R.ECI)VERY

fRACTIUNS

0.lCOC0353E 01 O.lO(')782')E I)!.

HOLES OF

Fé~D

ANO PRODUCTS

(3)O.4~~SJ2i2~-Ol () .2:l6262tnE ;')11 ,l.lH328154E rIJ \~.11nL(H')41: 'Ir) '1.d6C)CH4J::3[ 00 fl. LH 1391'5 E >') (1 \I • l('\{) 0 1 5 1 6 E iJl I . ~4' O.8J~40160E

na

:) • 2 G ) 3 ',I ~ 12 E 00 J.gFt':ÏC',)69[-Ol "I.13245CSb'}E-01 Cl. C1_94:i'ltZ5E ₀₀ 0. 5341J~73E-02 l:".:) j09U2S5E ClJ

COMPONENT

FEED

~OTTC\I r~o;)uc

T

r ;) P P ;~ IJ uU C T

MMA

1 O. 2239t:l9 q1t[ 02 O .. 22!l!.l1100[ l'2 O. J 1 'V) 8 " ") 2 F () '.)

"'~1A

2 O.203S9994E 02

o

• '

+

1+ ~t J () ') F 1 C (l 1 ( ) 0 1 5 ') 7 ? 8 q lt t= ;) 2

nMR

3

o

•

1 i3 3') ) 9 ') 4

r:

0 l () .. 1 ':) g B S ~p~ 'i [ r) 2 ~'). 2 4 1 2 9 It 1 ,)

r

ei i

\vATER

4 0.31't80<)<]I)[ 03 n.JIJIU72,sE ()3 ') • 1 6 'H 9 9 (~ ó I-: () 1

O.37r,OQ)85F 03 !) ,. :3 S

c

,

u

<; :L~ Id--

():>

n • Z 0 3 '1 n I. ~ < I [ : ) 2 --- -- - --- .. .~ _. --- ?-~--

-

---_.~----_ ... -. . '"---.. _----.-_._ -I W V1 I I

(40)

(

.

I I ~

r

l ,

r-'

I I ( I r ' r -, l J

f1

n

-36-The change and rate of change of the temperatures along the column are very strange, namely:

(a) the temperature of the "reboiler lS equal to 131oC; (b) the temperature of the lst plate l S equal to 118°C;

(c) the temperature of the 2nd plate l S equal to 117°C;

(d) the temperature of the 50th plate is equal to 112oC;

(e) the temperature of the 51st plate (above the introducticn of the feed to the column) lS equal to 1320C (!) ,.,hich is physically impossible;

(f) the temperature 1ncreases up to 1520C at the 56th plate (above the introduction of the extractive water to the column);

(g) the temperature of the 60th plate lS equal to 97°C; (h) the temperature of the distillate lS equal to 82oC.

One of the causes of this anomalous behaviour may be that no heat balance is incorporated in the program. Thus, there is no correction of the mass flows, and they are assumed to remain constant throughout the calculation. This may be too rough an approximation for the present system.

Another reason may be connected with the Wilson parameters, some of which exhibited irregularities. This point has been discussed previously

and i t is very well possible that the Hilson equation is not applicable

in this case. In any case, before trying to clarify the anomalous results concerning the temperature gradient in the column, and the insufficient separation of TMA, the question concerning the Wilson parameters must definitely be clarified.

As a general remark it should be said that it is worthwhile to develop a more comprehensive, efficient program for. nonideal distillation which would incorporate heat balance and would converge more quickly af ter a

small number of iterations. A basis for such a program can be found in an article written by Naphthali and Sandholm (31), which describes new calculational methods for distillation,