Research Collection

Doctoral Thesis

Determination of film coefficients in liquid extraction

Author(s): Morgan, Arthur Ivarson

Publication Date: 1953

Permanent Link: https://doi.org/10.3929/ethz-a-000150957

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Determination of Film Coefficients

in Liquid Extraction

Thesis presented to the

Swiss Federal Institute of Technology, Zurich

for the Degree of

Doctor of Technical Science

by

Arthur I. Morgan Jr.

Master of Science of Berkeley, California U. S. A.

Citizen of the United States of America

Accepted on the Recommendation of

Prof. Dr. A. Guyer and Prof. Dr. G. Triimpler

ZURICH (SWITZERLAND) 1953

PRINTED BY KOPP-TANNER SOHNE

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To Professor Dr. A. Guyer

am I indebted for advise and counsel and under whose leadership

this work became possible.

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Table of Contents

Introduction............. 7

A. THEORETICAL WOEK 9

1. Extraction Equipment 9

a. Stagewise Equipment 9

b. Continuous Equipment ......... 10

2. Theoretical Considerations 12

a. Equilibrium Data 12

b. Two Film Theory 13

c. Eate Coefficients 15

d. Practical Coefficients 17

e. Variation of Coefficients 19

3. Experimental Bate Factors 22

a. Tower Types 22

b. Miscellaneous Performtnce Data 23

c. Techniques Used 24

d. Measurement of Overall Coefficients on a Volume Basis . . 25

e. Measurement of Overall Coefficients 27

f. Measurement of Film Coefficients on a Volume Basis. .

28

g. Wetted Wall Towers 30

h. Extraction in Wetted Wall Towers 33

B. PRACTICAL WOEK 39

1. Apparatus ............ 39

%. Measurement of Wall Layer Thickness ...... 43

3. Butanol Water System 46

4. Water-Butanol-Benzene System 55

C. COEEELATION AND EVALUATION 70

1. Butanol-Water Results 70

2. Separation of the Film Coefficients 71

3. Final Correlation 80

Summation 87

Tables and Figures 90

Bibliography 91

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Introduction

Liquid extraction as a chemical engineering operation has been

recognized for over fifty years. The important advantages and possi¬bilities it entails have been widely known only since the 1930's.

Developing from a laboratory procedure, extraction has been in¬

creasingly utilized in industry. First mainly in petroleum refining,it is now fairly widely spread over all the branches of the chemical

industry. Of late, particular interest has been shown in the

possibilities of the process for the practical separation of inorganicsubstances. This arose from the realization of the selectivity of cer¬

tain organic solvents for these solutes. The new uses of extraction

are reviewed in the yearly symposia on the subject begun by Elgin23and continued by Treybal.73Liquid extraction is supplementary to fractional distillation. The

separation of a solute from solution, which is the purpose of the pro¬

cess, may usually be accomplished either by extraction with another

liquid solvent or by distillation or evaporation in the case of a

non volatile solute. The circumstances of the case dictate the more

advantageous method. Liquid extraction may be indicated where the

solute differs chemically from its solution but only a slight volatilitydifference exists. Another common case is a high boiling solute in a

dilute solution of a low boiling solvent, likewise a high boiling so¬

lute which suffers degradation at the boiling point of the solvent.

This selection of method was reviewed by Souders.67 In any event

extraction is now recognized as an often invaluable alternative to the

older separation processes.

Extraction may by defined as the process of removal of one or

more components of a solution or mixture by contacting the solu¬

tion with another solvent in which the desired component is prefer¬entially dissolved. The added solvent must be more or less immis¬

cible with other components of solution so as to form a separate

phase allowing its simple removal. Obviously, the resulting new

phase must be such as to permit subsequent evaporation resulting in

solute and solvent recovery. Three operations may then be distin¬

guished; contacting, separation, and solvent recovery. The first two

are often carried out in the same piece of equipment. The third stepis not part of the unit operation known as liquid extraction, beingclearly an example of distillation or evaporation. Contacting may be

carried out by bringing discrete amounts of solvents together in a

vessel, usually with mechanical or jet stirring, and then allowingthem to separate. An amount of solution may be treated several

times in this way using fresh solvent and thus extracting more of the

solute than would be possible with the one stage. This may also be

done by contacting the already solute-poor solution with fresh sol¬

vent and the original solute rich solution by the resulting solute-

7

containing solvent. This is often extended over a number of con¬

tactings and is known as countercurrent multistage extraction. Most

analytic and preparative laboratory equipment is of this type. The

above methods have in common the mixing of given amounts of so¬

lutions, allowing them to come to the equilibrium solute distribution,and then separating them. They are called batchwise operations.In contrast to the above, continuous liquid extraction has been

developed. In this form, a stream of solution is brought into contact

with a stream of solvent and the resulting extract and raffinate are

continuously removed. The theoretical efficiency in this, as in anycountercurrent continuous operation, is higher than a batchwise

operation. The throughput capacity is naurally greater here for com¬

parable equipment size. The cost of operation, particularly in regardssupervision, is less, although the installation cost may be greater.

Continuous liquid extraction apparata of a variety of types havebeen developed. These include stirred columns with alternate calm¬

ing sections, bubble cap and baffle columns, spray towers, packedcolumns and wetted wall equipment. Each of these constructions hasbeen characterized in the literature and some of the properties ofeach measured. These are summarized by Morello and Poffenberger53and Treybal.72

In any system of liquid extraction, the primary requirement isaccurate data on the equilibrium distribution of the solute betweenthe solution and the possible extracting solvents. With this infor¬mation the choice of solvent may be fixed. The type of equipmentand operating conditions are then decided by a study of the desiredrate of solute transfer from one phase to the other. That this is a

complex problem in continuous equipment arises from the fact that

equilibrium conditions are not achieved at any point in such ap¬paratus. In a given column a balance must be struck between a

satisfactory solute recovery and a desired throughput capacity. Thetotal area over which the phases are in contact with each other con¬

trols the rate of extraction for a given set of conditions and thisoften dictates the tower construction. In addition to this factor, thestate of flow and physical properties of each liquid affect the rateof solute transfer.

Very little experimental information is available on the impor¬tance of the various isolated factors involved in continuous liquidextraction. It is particularly desirable to separate the influences ofthe liquid flow conditions from those of changing interfacial area.

Further utility could be achieved by separating the influences on

each of the liquid phases in the tower. Experimenters have naturallyconcentrated on certain systems which possess properties leading tounusual simplification of the process. Measurement of a more aver¬

age case might be enlightening. It is with these thoughts the presentwork was undertaken.

8

A. Theoretical Work

1. Extraction Equipment

a. Stagewise Equipment

A number of different types of extraction equipment have been

proposed or investigated. From the standpoint of the present work,they may be differentiated on the basis of those requiring con¬

tinuous and those requiring stepwise operation.For stepwise equipment, the two essential parts of extraction lis¬

ted in the introduction, mixing and separating, may occur in dif¬

ferent pieces of equipment. Stepwise extractors in industrial use

usually consist of a tank with a central mechanical agitator or a

chamber, usually smaller, into which one component is pumpedthrough a jet. The latter method appears to produce better mixingfor an equal power consumption. Also, a smaller hold up of material

is possible with the latter type. A variation of the latter method is

to pump the two components together through an oriface, the tur-

bulance of which accomplishes the contacting. For the latter type of

equipment an independent separator must be provided. This may be

a simple settling vessel or one equipped with horizontal calmingbaffles. Where emulsions of some stability are formed, the problemis greater. These may be centrifuged or passed through a filter

which is preferentially wet by one phase.The above equipment was listed together but two separate distinc¬

tions may be made in the methods of operation. The first is between

batch and continuous use. Any of the above types of apparata may

be so constructed that continuous operation is possible. The two

streams may be introduced at rates corresponding to the optimumproportion as obtained from solubility and tie line data as outlined

in the Chemical Engineers Handbook.55 Virtually complete attain¬

ment of equilibrium conditions may be assumed with adequate con¬

tacting apparatus and a reasonable holdup. A suitable continuous

separator must be supplied in such cases. Such suparators are norm¬

ally of the baffle type. Needless to say, equipment such as the agi¬tated chamber may be operated batehwise by introducing discrete

amounts of each component, contacting, and subsequently separat¬ing. For such operation, contacting and separating may well be car¬

ried out in the same piece of apparatus. This may be the best systemwhere capacity and labor costs are not important.The other distinction to be made in the operation of this class of

equipment is as to single or multistage contacting. When discrete

9

amounts or rates of each solvent are mixed and separated, the pro¬

portion of solute transferred between phases is limited by the distri¬

bution equilibrium relation and the relative amounts of each solvent.

To attain the desired recovery, enormous amounts of solvent may

be required with high attendent solvent recovery costs. This may be

improved by treating the solution several times successively with

fresh solvent, permitting a higher degree of extraction without a

large holdup. Similarly, multistage countercurrent operation may be

used. This entails first contacting the solution with a solvent phase

already laden with some solute. The separated, partially extracted

solution is then contacted in a second stage with less heavily laden

solvent and further extracted. The solvent phase separated in this

stage is that which was used for the first contacting mentioned

above. In this way the solution and solvent phases are passed coun¬

tercurrent through as many stages as desired until the last stage is

reached where the now largely solute-exhausted solution is contacted

with the fresh solvent. Such multistage operation permits a very

high degree of solute recovery, entire recovery requiring an infinite

number of perfect stages. The equipment costs are high for such

operation and the capacity is not normally large but the degree of

recovery may become economically the determining factor in favor

of such a system. Of incidental interest here are the laboratoryextractors of this type. These are used to separate fractions in

analysis, complementing the chromatogram particularly in the field

of natural products. These apparata are such that a large number of

stages may be included in one piece of equipment. Craig describes

such an extractor.18 29 He also reviewed the laboratory uses of such

apparata.19 Such a process may, like the single stage equipment, be

operated continuously if the separators are so designed. This is a

commonly used system in the petroleum industry. An interestinglaboratory example of this method is described by Johnson and Tal¬

bot,40 using air lifts to pump the components from each separatorto the next mixer.

In the foregoing, it was pointed out that the short-comings of the

simple batch process are: limited degree of theoretical solute re¬

covery, large holdup of material, and expensive operation. In con¬

tinuous operation, costs may be less but the limiting degree of re¬

covery may also decrease. For the multistage process, recovery is

improved but costs and capacity are worsened.

o. Continuous Equipment

The highest degree of theoretical solute recovery is to be attained

in the continuous countercurrent extractor with which we are here

concerned. It may be regarded as a combination of the continuous

10

contactor combined with the multistage countercurrent type. It is, in

fact, a multistage apparatus which may be built so as to correspondwith any desired number of stages and dispensing with separation of

the phases between stages, all incorporated into one piece of equip¬ment. In addition to the high theoretical recovery rate, due to the

countercurrent principle, continuous countercurrent extraction

shows certain other advantages over the previous methods. Labor

and other operating costs are usually lower and the capacity is far

greater. An economic compromise must be made in any extraction

process between rate of operation and extent of solute recovery. In

this regard, the continuous countercurrent method shows a greater

flexibility to accomodate the current requirements. However, a

scheme of countercurrent stagewise extraction offering most of the

advantages of continuous operation has been suggested by Compereand Ryland

18together with a system of computation for it.

A hybrid type of equipment should be mentioned at this time.

While no separation of the phases between stages may be thought of

as a characteristic of continuous countercurrent apparata, there is

a variation in use in which this does partially occur. An example is

the early laboratory column of Cornish et al.17 This is a tilted tower

which is a series of mixing and separating sections in the same pieceof equipment. There is a central shaft with agitators in the mixingsections which alternate with separation chambers which are fitted

with wire gauze to calm the liquids. There are'several others of this

type, such as the Scheibelai tower. The entire distinction is, perhaps,conventional since separation of phases occurs in perforated platecolumns and, in fact, true dispersion does not occur at all in wetted

wall towers and but slightly in baffle columns.

The purpose of this but partially successful attempt to distinguishstepwise extractors from continuous countercurrent lies in the dif¬

ferent nature of the information required to operate each type. In

a stepwise extractor, even though it be continuously operated, ex¬

traction may often be considered to procede to equilibrium in each

stage. The correctness or incorrectness of this assumption is pro¬

bably a better criterion than construction differences in classifyingextractors. Thus in continuous countercurrent apparatus, definitely

incomplete solute transfer prevails at every point in the equipment.That means that the process is carried out at such a rate that

throughout the extraction, insufficient time of contact has been

allowed for the optimum amount of solute to redistribute at any

given point. Thus the central problem for such equipment is the

rate of transfer. The rate of transfer determines the relation between

capacity and extent of solute recovery. It is obvious that the rate of

transfer is directly proportional to the interphase area considered.

It would appear also to be some function of the extent to which

conditions fall short of optimum distribution. Furthermore the rate

11

should depend on the physical properties of the two phases and

those of the solute. Lastly it would seem reasonable to assume that

the dynamic condition of the components control the rate to some

extent. The relation of these factors have been the subject of theoryand experiments and are the questions dealt with in this work. Due

to the enumerated advantages of continuous countercurrent ex¬

traction, its basic problem of rate becomes increasingly worthy of in¬

vestigation.

2. Theoretical Considerations for Extraction

a. Equilibrium Data

Of primary importance in regard to any extraction process are the

equilibrium data. These include both solubility and distribution in¬

formation. Pressure is not a factor and the process is usually iso¬

thermal. The data used must, obviously, apply very closely to the

temperature prevailing since strong temperature dependence is an

outstanding characteristic of these properties. For a binary liquid-liquid system, the only necessary facts are the mutual solubilities.

For a ternary system, however, these must be supplemented by the

socalled tie line data which indicate the compositions of phases in

equilibrium with each other. Solubilities of ternary systems are

usually portrayed on equilateral triangle graphs, the apices of which

represent the pure components. One and two phase regions are then

represented by the areas enclosed by the appropriately drawn

solubility curves within the triangle. The tie lines are straight, but

usually not parallel lines which connect points on the solubilitycurves which represent the compositions of coexisting phases.An alternative to the tie line presentation is a rectangular plot of

the concentration of one component in one phase against the same

component's concentration in the other phase. This adequately repre¬

sents the system since the phase rule shows there is but one degreeof freedom at constant temperature and pressure. The system, then,is uniquely fixed by defining the solute concentration in one phase.This is analogous to the concentration in liquid versus concentration

in vapor charts used in distillation. This plot would result in a

straight line if the solute distributed proportionately between the

phases regardless of concentration. This is the case only for ex¬

tremely dilute solutions. The activities of the solute in each phasemust be proportionate at equilibrium. If there is no association with

the solvent or change of molecular species in either phase as is the

case in the dilute solution, the concentrations are proportionate to

12

the activities and hence the distribution is linear. When polymole-cules of solute are formed in one solvent, the corresponding root of

the solute activity in that phase is proportionate to that activiy in

the other phase. This is Nernst's Law.54 These activities may be ex¬

pressed as mole fractions for nearly perfect solutions.

Equilibrium data are obtained in several ways. An advantageousmethod is described by Bogin

7whereby a prepared binary solution

is titrated to turbidity with the third component. Tie line inform¬

ation is found by analyzing conjugate phases. A good list of the

ternary systems for which tie line data have been published has been

made by Smith.65 66 Certain generalized correlations are described

by Treybal.72

b. Two Film Theory

The mechanism of extraction is to be explained on the basis of the

two film theory. This theory was advanced by Whitman78 in 1923.

It has been very successfully applied to heat transfer and gas ab¬

sorption poblems. It is extended to liquid extraction by analogy to

the latter although confirmation of the physical bases in extraction

is conspicuously lacking. The theory postulates regions of stationaryor laminar flow on either side of an interphase boundary, each ex¬

tending a certain distance into the otherwise turbulent main stream

of each phase. Film thicknesses in adjacent phases are not neces¬

sarily equal, of course. Conditions directly on the phase boundaryare assumed to be in physical equilibrium states with each other. The

term laminar as applied to flow conditions implies streamline move¬

ment. That is, each particle of fluid moves only in the direction of

flow. Differential sections of the flow column may slip when a velo¬

city gradient exists but may not have a transverse component of

motion. The consequence of this theory is that through a region in

each phase, mass transfer can occur only by means of the relativelyslow mechanism of molecular diffusion. Material is brought up to

this ficticious beginning point of laminar flow by the efficient

means of eddy currents.

The basis of transfer by diffusion was laid by Maxwell50 with the

equation,

dcA = —b cA cb (va — vB) dl (1)

A definition of all symbols and units is to be found in Table 6.

Equation (1) states that the resistance to diffusion is proportionateto the distance of transfer, the relative velocity of the diffusingmolecules, and the number of all molecules in the path of diffusion.

Implicit in this statement, is the very important concept that the

13

concentration gradient is proportionate to the resistance to mass

transfer. This is analagous to the familiar current equal to potentialdifference divided by resistance of electricity. The principle is per¬

vasive but somewhat obscured in the cases of heat and mass transfer

by the use of coefficients of reciprocal resistance corresponding to

conductivities. Equation (1) has been inegrated for a number of

different circumstances and solved for the rate of diffusion.

The integrated forms of equation (1) are not of practical interest

at present since the laminar film thickness enters into their solution.

This film thickness is hypothetical and too complex to use.

These integrations of equation (1) lead, however, to the definition

of diffusivity,

DAB = -rj-^r-T (2)

o (cA + cB)

which is a temperature dependent intensive property of solutions.

No statement of a mass transfer problem is complete without the

diffusivity. The variation and prediction of diffusivtiy in gases have

been worked been worked out as discussed by Sherwood.62 For liquiddiffusivities, the data are fewer. A useful recent correlation has been

made by Wilke.79 Based partly on theoretical consideration, he pos¬

tulates a quantityT

F=nV (3)

which may be determined from the solvent and the molal volume of

the solute. This latter is the sum of the atomic contributions as givenby LeBas.47 The variation of F with concentration is given by Powell,

as,

(f).din

(I) ~(h) z>+&) <4>VF'B<, \F'a„ vF/a„

The divisor of the first term may be found as the slope of a

logarithmic plot of the solute activity against solute mole fraction.

This variation has been treated differently by Hartley and Crank30

with about the equivalent result.

In fact, although ignored by the two film theory, in addition to

the resistance to molecular diffusion in the laminar film, a further

resistance to eddy transfer in the turbulent region exists. Very little

work has been done bearing directly on this question. Obviously the

two resistances, if individually known, would be additive. The eddydiffusion is an unknown function of the flow conditions and

14

properties of the solution. This factor may be expressed as the eddydiffusivity. The eddy diffusivity has not been correlated due to the

difficulty in separating the two stages of mass transfer experimen¬tally. The entire question of the two forms of transfer is problem¬atical. There is good evidence that the eddy region changes imper-ceptably into the laminar or diffusion region without any discrete

boundary for any given set of conditions. There is, in fact, some

reason to believe that there is only a very thin laminar film indeed

under certain cireumstances. This has been suggested by Higbie.32 It

is to be remembered, however, that the fact that a velocity gradientacross a flow path ends in a stagnant layer at a boundary has been

very well established and repeatedly documented. Any work on

hydraulics may be cited on this point, Walker et al.,75 chapter 2 for

example. Likewise Danckwerts 22 has developed a theory on the more

realistic assumption that the surface of the liquid is being constantlyrenewed. His conclusion on this basis was that the equations usingthe mass transfer coefficient are still valid when no chemical reaction

at the surface is involved.

c. Rate Coefficients

The assumption of the two film theory regardless of the validityof its premises has led to certain simlifications which are the onlyuseful methods at present in practical extraction calculations. If the

total resistance to mass transfer is assumed to lie in the diffusion

film, this film thickness must be correspondingly adjusted to ac¬

count for the eddy resistance as well as its own. The previouslymentioned simple integration of equation (1) is now carried out.62

Assume the following: the rate of transfer of substance A is

constant; the solvent B does not diffuse, and the diffusivity is

constant at the point in question. The rate of solute transfer between

points 1 and 2 is,

XTDab 5 C , , ._.

NA =— (c'A - c"A) (5)

where

C B C B

CBta""_7~c'B (fi)In —

c B

and

c = cA + cB (7)

and 1 is the ficticious laminar film thickness. A coefficient is now

defined,

15

Dab c

Equation (5) then becomes

NA = k S (cA> - ca») (9)

where NA is the moles of A transferred per second. This result is

the basis of all practical investigations of extraction operations. The

factors of the mass transfer coefficient, k, are the following. The

diffusivity and its constituent factors have been discussed, the total

molal concentration, c, and the log mean solvent concentration, cBlm)are dependent on the composition of the solution and its variation

along the path of diffusion. They are not strongly variable, however,where the solution is moderately dilute since they are determined

by the density and mean molecular weight of the phase. The assum-

med film thickness, then, is the factor of primary importance. It is

dependent on flow conditions and physical properties of the solution

involved.

The foregoing discussion dealt with the resistance to mass transfer

in one phase. That in the other phase may be similarly dealt with.

The use of weight fractions in place of the molar concentrations is

justified in solvent extraction by the liquid character of the two

phases. It should be emphasized, however, that the units expressingconcentration gradient must be weight fraction and not the more

convenient weight solute per weight solvent. This arises from the

Maxwell concept which states that all molecules, not just solvent

molecules, in the path of diffusion present a restistence to mass

transfer. Naturally this substitution involves introducing a cor¬

recting constant into the definition of k, equation (8). This cor¬

rection is the density of the solution divided by the molecular weightof the solute. The density may be considered constant across

SGC

virtually any liquid film. The factor 3600 ,—- is included to obtainhour

k in grams, A, transferred per hour. The result is

NA=kwS(y-yi) (10)

and for the other phase,

NA = kc S (x, - x) (11)

where x and y are the weight fraction of solute A and the subscripti indicates the phase boundary conditions. The assumed situation

is then shown by figure 1.

16

It is desirable to write an expression for the total resistance

suffered by the solute in crossing from the body of one phase to that

of the other. This is possible in two forms

NA=KwS(y-y*) (12)

NA = Kc S (x* - x) (13)

where Kw and Kc are called the overall coefficients and y* is the

ficticious concentration in phase w which would be in equilibriumwith the actual concentration, x, in phase c. Similarly, x* is the

ficticious concentration in phase c which would be in equilibriumwith that obtaining phase w. These relations are shown in figure 9.

Certain simple relations exist between the various coefficients of

mass transfer when the equilibrium line in x, y coordinates is

straight. These are developed by Walker, et al.75 chapter 14. In

general, it is instructive to note the reciprocal resistance or con¬

ductance nature of the mass transfer coefficients. Thus the overall

resistances are each the result of the two film resistances in series.

The overall concentration potential may be measured either in terms

of concentrations in one phase or in the other. That is, either hori¬

zontally or vertically on the x, y diagram. Thus the individual film

resistances must be considered to partake of the nature of capacitiveor inductive impedences. The significance of these concepts will be

developed in a later section.

d. Practical Coefficients

In order to use the coefficients of mass transfer, they must be

arranged to include an entire extraction apparatus. The known or

required quantities are normally the rates of flow of the solvent

streams and the bulk or average concentrations of solute in each in¬

coming and outgoing solution. This bulk concentration of one phaseat any given point in the extractor is a mean between the concen¬

tration in the turbulent region and that directly at the interface.

The turbulent area in any cross section of the apparatus is obviouslygreater than the laminar and enormously greater than the actual

interphase boundary region. For this reason, the bulk concentration

may be equated with the turbulent concentrations, x and y, of

figure 1. Thus equation (10) is differentiated with regard to areas,

perpendicular to the diffusion path giving

dNA = k. (y - y,) dS (14)

and equation (11) may similarly be transformed. The overall

17

equations are also so treated. To find a solution for an entire ap¬

paratus, equation (14) must be integrated over the total interfacial

area. In order to connect the amount of solute transferred with the

bulk entry and exit concentrations, a material balance is written.'

Thus, in a differential length of the column containing the inter¬

facial area dS, the amount of solute leaving phase c is GdX where

G is the weight rate of flow of solvent alone and X is the amount of

solute in unit amount of solvent only. This amount is equal to that

entering phase W or

dNA = GdX = LdY (15)

and if steady conditions are predicated, and points 1 and 2 are the

top and bottom of the extractor,

G(X1~Xi) = L(Yi-Y1) = NA (16)

•u-

Direction of solute transfer

Figure 1. Sketch of Two Film Condition

18

By combining equations (14) and (15),

GdX = LdY = k. (y - yt) dS (17)

Similar equations may be written for the other film coefficient

and the two overall coefficients, using the corresponding concen¬

tration differences. These are naturally equivalent since the rate of

transfer across one film is the same as that across the other for a

particular solute. This is the basic equation used in all further cal¬

culations. In many practical cases, the total interphase area is un¬

known. This may be handled by introducing a factor, a, which is the

interfacial area per unit of tower volume. The factor dS then ap¬

pears for integration as

dS = a 4 n dh (18)

if the tower is round in cross section. Variation in the mass transfer

coefficients is then lumped together with that of the factor, a, which

has a strong dependence on the flow rates for a given tower cons¬

truction and packing. The basic equations then take this form

GdX = LdY = kw a ~ n (y - y,) dh (19)

KaTo facilitate comparison, the factor —=— is often grouped together

Jj

and called the number of transfer units. This was developed byChilton and Colburn12 in order to reduce the variation with flow

rates. The height of the transfer unit (HTU) is the height of

the extractor divided by the number of transfer units found. This

is, then, a method of comparing tower constructions.

e. Variation of Coefficients

An analysis of the transfer coefficient may be made by com¬

parison with the heat transfer coefficient. As shown by equation(8), this coefficient is determined largely by the ratio of the diffus-

ivity to the effective film thickness. For reasonably dilute solutions

this becomes entirely the case. This is, the same definition used

in heat transfer involving a flowing fluid having a laminar film

through which heat must pass by conduction alone. The effective

19

film thickness, 1, is assumed to be a function of fluid velocity, kine¬

matic viscosity, diffusivity, and some characteristic linear dimension

of the system, such as diameter. By dimensional analysis these

factors may be divided into two dimensionless groups each with an

unknown exponent. The product of these groups and the diameter

is proportionate to the film thickness. If combined with the relation

of diffusivitiy to film thickness mentioned above, the result is

where $ is an unknown function. This was first applied to extraction

by Hunter and Nash.36 These groups are similar to those used with

great success in fluid and heat transfer problems. The first group

was developed by Reynolds and has been successfully used to des¬

cribe fluid flow conditions in innumerable instances. It appears in

the dimensional analysis of friction in steady flow of fluids in cir¬

cular pipes called the Fanning Equation. This group has been gen¬eralized as a parameter of turbulent flow by using four times the

hydraulic radius for d where the hydraulic radius is the cross section

of flow divided by the wetted perimeter. Another use of this group

was in the problem of mass transfer to a gas by Sherwood82, chapter2. The Reynolds number has been modified in various ways to

describe the particular conditions involved. Primarily it has been

defined as a shape factor times linear velocity divided by kinematic

viscosity. The second group called the Schmidt Number (Sc) is the

mass transfer analogue of the Prandtl Number, (Pr), which is the

heat capacity times the viscosity divided by the heat conductivity.This correspondence was shown by Arnold2 by assuming the effective

laminar film in mass transfer has the same thickness as that in heat

transfer. Another use of the Schmidt Number is that by Colburn13in an expression derived by analogy to fluid friction for mass trans¬

fer in turbulent gas streams. The origin of the group on the left side

of equation (20) has been pointed out above. This group correspondsto the Nusselt Number, (Nu), which is the heat transfer coefficient

times the diameter divided by the heat conductivity. It should be

noted that the necessary dimensions of k are length per unit time.

This means that k is expressed as grams per cm2 sec/grams per cm3

or in other words, the units of concentration difference used in

equations (10) and (11) should be grams per cm3. In order to use

weight fraction, the left hand term of equation (20) must be divided

by p, the density of the solution. The dynamic similarity of the

various factors in fluid flow, heat, and mass transfer are carefullydeveloped by Chilton and Colburn.11 The underlying basis of the

treatment is dimensional analysis. This subject is discussed byBridgman in Perry's Handbook55, page 341. The various groups are

20

analyzed by Mc Adams52, chapter 4. The method of grouping is

simple and reliable if the prior assumptions are correct. That is, all

the factors entering into a solution must be known although how

they enter does not matter. If some property which controls mass

transfer has been overlooked, dimensional analysis fails to providean adequate expression. In connection with equation (20); it is im¬

portant to note that all the properties involved have values corres¬

ponding to those in the presumed laminar film. This is of particularrelevance in case of the velocity, v, which is taken as the average

velocity in the film and may well differ considerably from the aver¬

age bulk velocity of the fluid. Since a solute concentration gradientexists through the film, the other properties may significantly differ

from the stream average as well. In practice, the film conditions are

unknown and the only method possible is to use the bulk properties.When this is done, equation (20) is unlikely to be adequate since

other factors not considered in the analysis affect the bulk

properties. Certain adjustments may be possible as will be men¬

tioned.

The foregoing has dealt with the description of k, the film coef¬

ficient of mass transfer. If a description of K, the overall coefficient,defined by equations (12) and (13), is desired, the situation becomes

more complicated. The overall coefficient is determined by the cond¬

itions in each film and the relative importance of each. In line with

the comparison to series conductances, the relation is

t=4+*(!) <21>

where f is some function corresponding to the weight to be given the

film resistace in phase C. Hence,

(22)

1 1

K„ d,. /Vwdpw\" / pv \P

+ V1

»-*(^)"Q

where the proporties are still to be construed as those of the

films only. Since the development of equation (20) was general, it is

deemed justified to use the same function and exponents for the two

film resistances. Theoretical considerations have led to the above

results but experimental evidence is required to ascertain their vali¬

dity and the values of the exponents and the nature of the unknown

functions which involve unknown constants. What changes are neces¬

sary from the use of bulk rather than film properties is likewise

unknown.

21

3. Experimental Bate Factors

a. Tower Types

The rate of extraction in continuous equipment and the factors

affecting it have been studied for a number of different types of

equipment. In many cases, the investigations have been carried out

to test and demonstrate the capabilities of a particular construction.

Other workers have intended to ascertain optimum operating con¬

ditions for a given class of equipment. In view of this, such re¬

searches may reasonably be classified on the basis of the type of

equipment measured. For the purposes of this work, data may best

be oriented by virtue of the type of information obtained. It has

been decided to arrange them under the following headings: data on

factors other than rate of extraction; data on overall coefficients on

a volume basis, K, or heights of the overall transfer unit, HTU0;on overall coefficients, K; on film coefficients on a volume basis, ka,or heights of the film transfer unit, HTUf; or finally on film coef¬

ficients, k. The continuous countercurrent systems of major interest

are the following. In the spray tower one phase is introduced into

the extraction chamber through a jet or collection of jets and as

droplets passes through the chamber which is completely filled bythe other phase. The droplets rise or fall depending on which phaseis the denser. Thus in spray, as in packed and perforated platecolumns, one liquid is spoken of as the dispersed and the other as the

continuous phase. In the packed tower the liquids are introduced at

opposite ends of a tower filled with a packing which is usuallypreferentially wetted by one phase. Thus one liquid passes throughthe extractor by flowing over the packing and the other by fillingthe intervening spaces. In the perforated plate column the lighterliquid enters at the bottom and passes upward through the heavier

liquid by passing through transverse perforated plates which are

placed at intervals up the column. The heavier phase descends con¬

tinuously, passing the plates by means of downcomer tubes which

penetrate the plates and extend below the level of lighter liquidwhich accumulates underneath each, due to the resistance of the per¬forations. This may be varied by inserting riser tubes instead of

downcomers on some plates thus allowing the lighter phase to passand forcing the heavier to flow through the perforations. The ap¬

paratus may be further refined by placing bubble caps on the per¬

forations, as is done in distillation columns. In baffle towers one

liquid fills the apparatus while the other flows along the surface of

a horizontal baffle to the opening provided, and then verticallythrough the other phase to the next baffle. The baffles may have

central or side openings and alternate baffles may vary in form.

22

Often baffles are turned into trays by adding a lip over or under

which the liquid flows as over a weir. In the wetted wall tower, one

liquid flows along the tower wall while the other moves in the un¬

obstructed center as a core. In practice the heavier liquid has been

made to flow down the wall and the lighter to rise as the core. In the

wetted wall and baffle columns, both phases may be thought of as

continuous. There are several other variations of special purpose or

as yet unknown importance. Treybal72 describe the various types of

installations.

b. Miscellaneous Performance Data

The non-rate data for many systems have been reported. This

consists mainly of capacity information. The rate of operation of a

tower is limited by the phenomenon of flooding which preventsfurther satisfactory extraction. Flooding involves an excessive

holdup of one phase in the tower due to the friction exerted on it bythe high relative velocity. This large holdup causes the liquid to be

swept into the exit stream of the other. In other words, flooding

prevents proper separation of the phases. A milder flooding effect

is the coalescense of the dispersed phase when one is present, with

a great attendant diminution of the interfacial area. A lower limit

of operation is set by channeling in many types of apparatus. This

effect is the breaking up of a continuous film into rivulets due to an

insufficient flow of liquid. This depends strongly on the wettingproperties of each phase. The minimum flows are not of industrial

interest, naturally, and only incidentally observed. Relative to tower

volume, the absolute throughput capacity of the towers is, in de-

creading order; wetted wall, baffle, spray, perforated plate, and

packed columns. This has very little importance in view of the limit¬

ing rates of transfer. The upper limit or flooding rates have been

systematically studied for spray and packed columns. For spray

extractors, the flooding velocities are known to depend on proper

tower construction. With a diffuse condition of dispersed phaseentry and calm continuous phase entry, flooding depends on the

relation between the linear velocities of the two phases and the den¬

sity difference prevailing. Velocities of 2 cm/sec for the continuous

and 1 cm/sec for the discontinuous phase appear to be the highestreported. In packed columns, an excellent correlation has been made

by Breckenfeld and Wilke.8 They showed a constant relation to exist

between the two linear velocities, the density difference, the inter¬

facial tension, the density and viscosity of the continuous phase and

two simple characteristics of the packing. The form of this cor¬

relation has been improved by Crawford and Wilke.21 Continuous

phase velocity of 0.5 cm/sec seems to be very high with a corres-

23

pondingly smaller discountinuous phase velocity. In the above, it is

to be understood that the linear velocities are relative to the wall and

refer to the gross trower gross sectional area. For wetted wall towers,

the reported values,9 1B 74including those of the present work, range

from 0.1 to 4.1 cm/sec for the wall fluid and from 0.04 to 5.5 cm/sec

for the core liquid. These figures correspond to the actual linear ve¬

locities of 2.8 ta21 cm/sec for the wall and from 0.032 to 4.9 for the

core based on computed flow cross sections. For one reported use of

a horizontal column analogous to the wetted wall type,5 both phaseswere varied between 0.5 and 10 cm/sec, actual velocity. There has

been no previous comparison of these figures and it would not appear

worthwhile to attempt any generalization. Each of the workers

achieved approximately the same range which is not surprising as

the systems were very similar. It is sufficient to note that they are

very high in relation to other types of construction. The conclusion

may be drawn that a much smaller diameter wetted wall column maybe used for a given job than any other ordinary type but it must be

much higher due to the small interfacial area. Special types of wetted

wall columns using a spinning tower have been developed29 31 5e

with claims to very good extraction rates as well as the high capa¬

city. These have not yet been well tested.

c. Techniques Used

In the foregoing experiments and those to be described later, the

technique was about the same. A round straight tube of desired

construction was prepared. These tubes were almost entirely of glassand ranged from 2 to 10 cm in diameter. The great majority were of

2—3 cm size. With one exception,5 they were installed vertically. The

heavier solvent, almost invariably water, was stored in a reservoir

from which it passed at metered rates to the top of the column. The

lighter solvent, usually a hydrocarbon, would flow from its reservoir

to the bottom of the column. The feeds were usually separatelypumped but gravity flow and air pressure were also used. The

solute, of course, was introduced into one of the reservoirs at a

known concentration. Since the two liquids could not be pumped pasteach other in the tube, relative motion continued by virtue of densitydifference alone. The pressure produced by the heavier liquid pumpat the entry point at the upper end of the tube had to be less than

that produced by the lighter liquid pump at the bottom of the tube

by the amount of hydrostatic head due to the height of column and

the friction loss. Likewise, the back pressure at the lower exit had to

exceed that at the upper by the same amount. This was usually ac¬

complished by forming a loop in the lower exit line of a height equalto the tower. The position of the standing interface either at the top

24

or bottom was then regulated by a valve increasing or decreasing the

resistance in the lower exit line. In some cases, this was accomplishedby varying the height of the lower exit line loop. The two exit streams

were then fed into their separate collectors with some provision for

taking instantaneous samples. The temperature at one or several

points was normally measured and, in some cases, thermostats were

used for heating or cooling the fluids. In some instances, also, both

the entry and the exit streams were metered or weighed while in

others only side was measured. The entry fixtures of each phasewere so arranged as to the desired effect. This might be an even dis¬

tribution across the tube area or a calming and steamlining effect.

Various operating techniques were developed but all with the pur¬

pose of completely filling the tube with the two phases and maint¬

aining the desired flow conditions throughout a run. Tests were

made to determine when steady conditions prevailed before the

tabulated results were recorded.

d. Measurement of Overall Coefficients on a Volume Basis

and Heights of the Overall Transfer Unit

Turning to actual rate of extraction data, overall coefficients on a

volume basis, Ka and heights of the overall transfer unit, HTU„,measurements are to be mentioned first. It should be understood that

these two functions are equivalent. In the simplest case with the prop¬

er units, HTU„ may be converted to Ka by dividing it into the mass

rate of flow. In general, results on comparable systems show the best

transfer rates are obtained in packed columns with perforated platecolumns nearly identical. Spray towers are next, and wetted wall,the poorest. This comparison refers to the height of each type of ap¬

paratus required to do a comparable job. This does not mean that for

a specific system a spray column may not be preferable to a packedtower. The results are highly dependent on construction factors. For

example, Johnson and Bliss 39 showed that both shape and size, and

number and distribution of inlet nozzles for the dispersed phase in

a spray tower are critical factors for extraction rate. Likewise for

packed columns, the size and shape of packing are important factors

as shown by Hou and Franke35 in work with very fine packingwhich gave very high rates. Nonetheless, packing size and shapewithin the limits of ordinary commercial packings does not appear

to be critical.1 The dispersed phase entry nozzles also play a small

role in packed towers. The material and texture of the packing is

important insofar as it affects the preferential wetting by one or the

other phase. This was demonstrated by Sherwood, Evans and Lon-

eor63 in the extraction of acetic acid from water by benzene in a

9 cm packed tower.

25

The influence of direction of solute transfer and flow rates requirea more general consideration. In the above works and others, a majordifficulty has been to separate the effects of influences on the two

films as postulated by the two film theory. In gas absorption, the

concept of the controlling film has been found effective. This as¬

sumption is that the greater part of the resistance to transfer lies in

one of the films and hence variables which affect that so called con¬

trolling film will have the major effect on the results. Contrarywise,the factors affecting the film which allows the solute to pass more

easily will not appear as important in the overall results. In many

gas absorption cases, optimum conditions can be predicted by a mere

consideration of the nature of the two phases. In liquid extraction,where no difference in state exists, the concept has been less re¬

warding. However, the flow rates of one phase or the other have been

found in the overall coefficient experiments to have the greater

bearing on the results. For example, Row, Koffolt and Withrow59

and a number of others working with packed towers found that the

velocity of the dispersed phase has very little effect on the overall

coefficients and the continuous phase film may be said to control.

This seems to be a general conclusion for packed towers. In spray

towers, there seem to be many exceptions and the range of coeffi¬

cients with both flow rates is very large in most cases. Most of the

above can be correlated by empirical equations which are valid onlywithin the range of values tested and for a particular tower and

system. These correlations may be made by plotting the overall coef¬

ficients (or HTUo) against the ratio of the linear velocities of each

phase based on the superficial tower cross section on double loga¬rithmic coordinates. When the result is a straight line, as it usuallyis, this may be taken as a vague confirmation of equation (21) and

the two film theory.A very important consideration enters into all this class of results.

That is that the difference in overall rates of extraction with any

particular change in conditions may be due in part to the changedfluid conditions and in part to an unknown alteration in total inter-

facial area attendent on the change. "When we consider any of the

above experiments, we see that this factor is implicit in the measured

variable. The nature of the packing, for example, affects both dis¬

persion of the phases by preferential wetting and the actual linear

velocity of each phase by the diminution of the free flow cross

section. The alteration of the flow rates in packed towers clearlyaffects the interfactial area critically and thus the Ka or HTU„values. This is shown by the data of Sherwood et al.63 where thetransfer coefficient increased with the velocity of the continuous

phase as holdup of the discontinuous increased and then decreased

abruptly with a further increase due to the coalescense of the dro¬

plets of the dispersed phase. That this is proof of the above is based

26

on the observed fact that holdup of the dispersed phase, that is, the

volume of that phase present in the tower under steady conditions,is proportional to the size of the droplets into which it is dispersedand thus to the interfacial area. That this should roughly be so is

obvious from the fact that the holdup is proportionate to the re-

latiue velocity of the dispersed particles. This in turn depends on the

difference between the net density and the retarding force on the

drop. The retarding force is some function of the drop size depend¬ing on the deformation. This is further demonstrated by Johnson

and Bliss39 who also measured the holdup in their spray tower with

the system methyl isobutylketone-acetic acid-water. They found the

holdup values paralleled the overall coefficient values very closely.Appel and Elgin * also made this observation. It may then be as¬

sumed safely that variations in the true overall transfer coefficient

are very largely masked in this class of experiment by the variations

in the factor, a, namely the interphase area per unit tower volume.

e. Measurement of Overall Coefficients

One method which has been used to circumvent this difficultywith the area is the measurement of extraction from single drops, the

area of which may be estimated. This has been done by Sherwood et

al.,63 West et al.,77 and Licht and Conway.48 They all extracted acetic

acid from several solvents with water by letting one drop of known

volume rise or fall through a still column of the other phase. The

results were values of Kd but it was not found possible to divide the

results into those of the two films. It was shown, however, that the

so called end effects are of major importance in spray towers to

which the circumstances of these experiments correspond. The end

effects are the extraction which takes place as the droplet forms at

the nozzle or inlet and that which occurs as it leaves the column and

coalesces with the stationary interface at the other end. These effects

were believed to amount to over half of the extraction taking place. A

very considerable discrepeney exists between the results of Sherwood

et al. and West et al. on the work with the same system and compar¬able apparatus and methods. These effects have been qualitatively con¬

firmed by others using the spray tower to be of great importance.26An ingenious method of estimating the volume factor, a, has been

employed for gas absorption in packed towers. Mayo, Hunter and

Nash B1 used packing made of paper and placed dye in the water

phase. After operation, the packing was dried and the colored area

measured. The tower wall itself was also lined with paper. The

wetted packing surface fell off markedly below the inlet and was

better near the wall than in the center of the tower. The appli¬cability of the results to a condensed system is unknown.

27

/. Measurement of Film Coefficients on a Volume Basis

and Heights of the Film Transfer Unit

The next class of experiments to be discussed are those which re¬

sulted in measurements of the film coefficients on a volume basis,ka or heights of the film transfer unit, HTUf. These separations of

the film coefficients are very few. The precursor of these was the

classic experiment on gas absorption by Gilliland and Sherwood.27

They built a wetted wall absorber of 2.67 cm diameter down the

inner wall of which various pure liquids were made to flow. Air was

pumped countercurrently as a moving core. The liquids were recir¬

culated and the amount vaporized into the air stream was measured

by decrease in the total volume of circulating liquid as shown by the

fall in the level of the reservoir. From this and the air rate, the

partial pressure of the liquid in the exit air could be calculated.

With the known vapor pressures, the partial pressure difference or

driving potential could be reckoned. Since pure liquids were used,no liquid resistance existed and the gas film thickness at varyingrates and different solutes could be calculated. This was correlated

by the following expression,

f- 0.023 (^r^44 (23)

This was derived in the same fashion as equation (20) and is entirelyanalogous. As previously mentioned, the film thickness, 1, is, by the

two film theory, the equivalent of the diffusivity divided by the

mass transfer coefficient. The heat transfer film, incidentally, is

defined by the same assumptions as the thermal conductivity divided

by the heat transfer coefficient. Thus three groups, —, —, and ——

are eqivalent and amount to the ratio of the diameter to the film

thickness.

This technique of using pure liquids in place of solutions in orderto eliminate one film and thus measure the other directly, was

extended to extraction by Colburn and Welsh.14 They used a 9.4 cm

glass column packed to a depth of 54 cm with 1.25 cm clay Raschigrings. Water and isobutanol were the two liquids used as both the

continuous and dispersd phase. Room temperature prevailed through¬out. The results were expressed in HTUd and HTUC calculated

using the log mean of the upper and lower differences between the

prevailing concentration and the saturated value. This use of the logmean was continued by Laddha and Smith44 and in the presentwork largely because of the successful results achieved with it byGilliand and Sherwood. The theoretical basis for it rather than any

28

other mean seems doubtful. This mean has gained reknown in heat

transfer and diffusion operations because it is so defined that it

simplifies a certain type of integrated relation. When one quantityis linear in a second and the differential of the latter is a direct

function of the first, the log mean of the values of the first taken

at the limits of integration may be used to write the relation as a

linear equation. For heat and mass transfer potentials, the first

quantity in question is usually the difference between two other

quantities, both of which may be linear in the second, hence their

difference is likewise linear in such cases. Thus if the operating and

equilibrium lines are both linear within the applicable limits and the

entry and exit concentrations are in such units that they are directlyproportional to the extraction rate, the coefficient being considered

constant, the log mean concentration difference is rigorously cor¬

rect. Actually the equilibrium line becomes a point in a binarysystem. The log mean may be a valid representation of this situation

or it may not be. In any event, Colburn and Welsh were able to cor¬

relate their results by the HTUd and HTUC regardless of which

component was discontinuous. They found the HTUd a constant for

each component and HTUC an exponential function of the ratio of

the weight rates of flow of the continuous to the discontinuous

phase. The results could not be generalized with the fluid properties.Therefore different constants must be used for each fluid. Laddha

and Smith 44 used the same method. They measured the HTUC and

HTUd for the systems water-3 pentanol and water-isobutyraldehydein a 5 cm glass tube used as a spray tower and as a column packedfirst with 0.64 em and later with 0.94 cm Rashig rings. The tem¬

perature was not controlled. Three of the four exit stream concen¬

trations were measured but the conjugate of water in isobutyralde-hyde, they were unable to analyze. The velocity range for both

phases was from 0.05 to 0.40 cm/sec. No difference in performancewas found when the spray inlet was mildly altered. The results sup¬

ported those of Colburn and Welsh in general. In each case the HTUdwas constant and independent of the flow rates, although differingfrom one system and construction to the next and as to which phasewas discontinuous. The continuous phase transfer unit was againcorrelated by an equation of the type

HTUC = b (£)" (24)

where c and D are the inlet weight rates of the continuous and dis¬

continuous phases and b and <* are constants, b varied with the

system, tower construction and as to which liquid was continuous.

a varied with the system but remained substantially constant with

the tower construction and the identity of the continuous phase. No

29

correction was mentioned for the considerable variation of the mass

rate of flow from inlet to exit due to the portion of one liquid which

dissolved in the other. The results showed a better rate of extraction

(i. e. a shorter transfer unit) of the continuous phase in the packedthan in the spray tower and with decreasing packing size. The re¬

sults for the discontinuous phase are not conclusive in this respect.Comparison of one system with another does not reveal any con¬

nection with the fluid properties and it is assumed that variations

in total interfaeial area are the effective cause in variation of ex¬

traction rates with flow. Presumably this area variation could be

studied by using a large number of differing systems in one type of

tower and comparing the generally constant values of the HTUd.This is not likely to "occur soon as experimenters show a very under¬

standable reluctance to use many different systems as new equili¬brium and other physical data would be required for each as well as

new analysis methods, not to mention separate purification proce¬dures.

g. Wetted Wall Towers

The difficulty with the complicated area problem has resulted in

the use of the wetted wall column in which the interfaeial area is

known from the simple geometry of the system. This began in 1934

with the work by Sherwood and Gilliand in gas absorption which has

been mentioned. In the same year Fallah, Hunter, and Nash24 des¬

cribed the hydraulics of such a column but with a liquid rather than

gas core. This was extended by Strang, Hunter and Nash71 later.

They described the construction and operation of the first wetted

wall liquid extraction column. A mathematical analysis of the fluid

friction in the wall layer when in isothermal laminar flow was made

and a function was arrived at which if plotted against the thickness

of the wall layer, m, would give an insight into the velocity distri¬

bution of the layer. This expression assumes no slippage directly at

the wall and is valid if the diameter of the tower is great enough to

be treated as a very long flat plane. This equation is

tMfr(i-g-)g'i°w (Pw —pc)_

(25)

where r is the mass rate of flow per unit length of tower peripheryand Vi is the velocity at the interface with the core. Since 'V, is not

easily measured, various assumptions of the velocity gradient were

made and the relations corresponding to them were developped in

30

terms of fluid properties, T and m by substitution in equation (25).The tower was then operated with water as the wall liquid and air,kerosene and several lubricating oils as the cores. The flows were

suddenly stopped and the volume of water collecting in the tower

was used to calculate the wall layer thickness, m. It was found that

an expression corresponding to the assumption of a semi-parabolicvelocity distribution in the wall layer with the maximum wall velo¬

city at the core interface best described the results within a lower

range of flow rates with a low viscosity core. This assumption of ever

increasing velocity in the wall layer as the inter face is approachedresults in the following modification of equation (25).

m =(—*p*-\ 1 (26)vgjow (pw- Pcy

Thus when the experimental values of m were plotted on double

logarithmic coordinates against the right hand side of equation (26)without the numerical constants, the results with the low viscositykerosene cores produced a straight line of slope 1/3 and with

an intercept corresponding to 3. This would be otherwise if the

assumption of maximum velocity at the interface were incorrect.

This section of the plot is terminated by an abrupt discontinuitywhich is taken to be the point at which turbulent wall flow sets in.

Beyond this point the function continues with an altered slope. As

cores of higher velocity were measured, the intercepts changed and

the results no longer could be represented by equation (26) but

rather by other relations based on assumptions of maximum wall

velocity at points farther from the interface and toward the to¬

wer surface within the wall layer. These relations involve other

values than the 3 in equation (26). Likewise the point of discon¬

tinuity changed with the different cores. No relation was worked

out but it seems proved that in laminar wall flow, the interfacial

velocity is the maximum wall velocity for highly fluid cores and

decreases to very low values with high viscosity cores. This is emin¬

ently reasonable as, in the extreme case, the core would be a solid.

In such an event, the well established flow patterns in any conduit

would call for a completely stagnant layer directly at such a solid

boundary.For turbulent flow, as distinguished from the discussion above

which is relative to laminar flow only, the situation is much less

clear. However, it has been proved many times that the turbulent

flow relations may be described by a dimensionless group known as

a Reynolds number or a modification of the Eeynolds number. This

group has also been found to be the sole parameter of the point at

which turbulence begins. This group may be shown to require the

31

addition of a second dimensionless group in the present case to cor¬

rect for the liquid core. The development is by dimensional analysiscorresponding entirely to the steps involved in forming the originalfamous Panning equation. With this correction and using the

generalized form of the Reynolds number to accommodate the non

circular cross section of the wall layer, the following simple steps are

shown,

Re.w = Re (Ml) = r~AP?-\(PzilPe.) = (27)

4rvW|ow/ ,oWlow\_

4 f (pw—pc/fwPvA

Pvi ' f^w |Ow

where r is called the hydraulic radius and is equal to the ratio of the

area of flow cross section to the wetted perimeter. This is derived

by deduction from the original Fanning equation and is used to re¬

place the diameter when the cross section is not circular. The friction

factor for the wall film which is a function of the Reynolds number

has the usual form in this development,

r-2mVg.(28)

ft

It should be noted that the density term becomes virtually unitywith a gaseous core so that Re'w reverts to the usual form for gas

absorption operations.The results of Fallah et al. in the turbulent region are inconclusive

but it may be that Re'w alone is insufficient to mesure wall friction

loss. It would appear that the nature of the core is of some influence.

This point has not been elucidated and later workers have obviouslybeen confused as to the meaning of these results. The conclusions as

to laminar flow have been applied falsely to turbulent flow. For

fluid flow in general, the analytical approach, which equation (26)represents, has been worthless in the turbulent region whereas the

dimensional methods of equation (27) have been successful. Thus, the

transition to turbulent flow and the conditions thereafter have been

found a unique function of Re'w. The work of Fallah et al. shows

that the transition point, at least, is dependent on the properties of

the core as well as Re'w but only general conclusions are drawn. The

onset of wall layer turbulence occurs at much lower values of Re'wfor a liquid than a gas core and sooner with highly viscous core than

with a very fluid one. The transition for a given core took place at

a definite value of Re'w. The bulk velocity of the core did not affect

the transition point for the wall liquid, at least to their experimental

32

limit of vc= 2.5 cm/sec. The conditions at the interface beyond tran¬

sition would probably be faithfully represented by Re'w if the

values of the properties directly at this interface could be used in

determining Re'w. This is, unfortunately, obviously impossible.The problem of representing the flow conditions in the core are

even more poorly formulated than those for the wall liquid. Since

the cross section of the core is circular, the linear parameter of the

Reynolds number would seem to be simply diameter of the tower less

twice the thickness of wall layer. Thus, the grouping is

Rec =.MfiL (29)

where d is understood to be the reduced diameter of the core. The

core linear velocity, vc, might be evaluated relative to the movingwall layer if the interfacial velocity were not unknown. Correlations

using this velocity relative to the average wall velocity have giveninferior results compared to evaluation relative to the tower wall.9 27

Hence the former will be used hereafter. The results of Fallah et al,throw some doubts on the adequacy of equation (29). They dealt

with core conditions only in a superficial way and were largely con¬

cerned with stationary cores. But by the use of the colored band

method of Reynolds, the onset of turbulence was observed. Theyfound it began in stationary kerosene cores (/ic = 0.018 g/sec cm) at

the Re'w value of 70. This odd result is due to the downward drag

on the core by the wall liquid which must be restored by an opposite

upward movement at the center of the core. For vc of 1 to 2 cm/sec,the turbulence began at Re"w of 35. Stationary oil cores (/xc = 0.34 g/sec cm) remained streamline for all wall rates up to the maximum of

Re'w = 100. Thus the wall rate affects the flow condition of the core

but with a given core liquid, the contrary does not seem to be the

ease.

h. Extraction in Wetted Wall Towers

In three publications,25 38 70 Fallah, Strang, Hunter and Nash

report on their extraction as distinguished from hydraulic

experiments with the wetted wall tower. They extracted phenol from

kerosene with water, the latter being the wall fluid. All the results

were at one of two wall rates of Re'w of 100 or 140. The core rates

were varied from Rec of 40 to 500. Thus, turbulent flow probably

prevailed throught. The distribution coefficients were believed suf¬

ficiently constant to use a log mean concentration difference. No

effect on the extraction rate by the wall flow within these narrow

33

limits was observed. By assuming all variation in the overall ex¬

traction coefficient to be due to changes in the core film coefficient,this value was determined as a function of the Reynolds and

Schmidt numbers. Experiments were carried out at several tem¬

peratures to obtain a variation in liquid properties. It was finallyfound impossible to correlate the results with the Schmidt number

but the following equation was developed,

kc d_

/ VcdjOc \ 0.83

DT=

bW—7(30)

No information was collected on the wall film coefficient. An

exponent for the Schmidt number was originally proposed but was

later withdrawn as unjustified. Some doubt has been cast on equation(30) by the fact that the wall rate was varied so little that its in¬

fluence could not be excluded. The method of the separation of the

film coefficients seems questionable. This method will be discussed

more fully below.

Comings and Briggs16 measured the extraction of three solutes,benzoic acid, aniline, and acetic acid, between benzene and water in

four different wetted wall columns and four packed columns. Hydro¬chloric acid was used in the water phase in some runs to assist the

extraction of aniline from the benzene and in others sodium hydro¬xide or potassium carbonate water solutions were used with benzoic

or acetic acid benzene solutions. Benzoic acid in 20% sucrose water

solution were extracted by benzene. The wetted wall towers were

2.16 cm in diameter by 74 cm long, 2.16 cm by 118 cm, 1.60 cm by70 cm, and 1.19 cm by 70 cm. The results in the packed columns are

expressed in overall coefficients on a volume basis and do not differ

appreciably from this class of results previously mentioned. The

logarithmic mean calculation method was used although equilibriumcurves justifying it were not presented. All runs were made at room

temperature. The values of the overall transfer coefficients were cor¬

related with the superficial velocity of the phase in which the majorresistance was believed to lie, based on the distribution coefficients.

The results were rather incoherent due to the short range of rate

variation and the very small number of runs made in each category.When base or acid was added to the supposed controlling phasewhich was invariably the wall liquid, it was assumed that this vir¬

tually eliminated the influence of the resistance in this phase and

revealed the importance of the other. This was assumed from the

fact that the resulting chemical reaction with the solute in the in¬

dicated phase would minimize the necessity for transport of the ori¬

ginal molecular species of the solute in that phase. The results

showed a large increase in the transfer coefficient but the effect of

34

the flow rate of the wall phase remained strong. This was inter¬

preted to mean that the wall liquid influenced the coefficient of the

core. In the extraction with the aqueous sucrose solution, the presence

of the sucrose was ignored in the calculations and the decreased coef¬

ficients found were ascribed to the doubling of the water viscositydue to the sugar. This is in accord with the inverse effect of visco¬

sity on the Reynolds number. By these results, the assiimption was

made that the film coefficients could be reconciled by the equation

ka = b vw vc (31)

where the constants appear to differ for every situation but /? is very

small for the wall film coefficients. It would seem that the method

does not take into account a large number of influences. For example,what of the introduced acid or base extracted from the water into

the benzene phase which then reacts with the solute there even before

it itself has been extracted by the water? Likewise the resistance to

the removal of the reaction products in the water film would appear

to constitute a reason that the influence of that phase does not dis¬

appear. The fact that K2 CO3 in the water gave different results

than NaOH gives weight to these two objections. In his work on

liquid film «controlled» absorption theory, Danckwerts22 has

recently thrown doubt on the applicability of transfer coefficients

when a chemical reaction occurs in one phase. The full data of

Comings and Briggs might well be reviewed in light of Danckwerts'

report.

Treybal and Work 74 extracted acetic acid solutions in water with

acetic acid solutions in benzene in a wetted wall tower. The column

was 2.60 cm in diameter and 152 cm long but the effective lengthwas not given. Use of the log mean method in calculating Kc seems

justified by the low solute concentrations used which were not zero,

however, at any point in either phase. Values of the film thickness,

m, were measured and fitted a variation of equation (26). The wall

flow was very low and it was presumed that it was at all times

streamline. The values of Re'w varied from 3 to 30 and Re'c from

100 to 1000. The method used in attempting to separate the film

resistances is typical of this class of experiment. It is based on the

previously mentioned relation existing if the two film theory is valid

and if a fixed solute distribution holds over the concentrations in¬

volved. This is both the crux and the weakest point in this manner

of attack. In short, equation (21) becomes

&-w kw kc

35

where H is the distribution constant in the relation,

y= Hx (33)

so that H is the slope of the equilibrium curve. Now the assumptionmade for equation (20) was that the Schmidt and Eeynolds numbers

for each film were calculated from the actual values obtaining in the

film. If the average bulk properties are used, it seems likely that the

groups for both phases may affect both films. This is born out by the

observations of Pallah et al.56 with the wetted wall column. Thus,equation (31) may be written

Dw=

1_ 1

Kw d b Rewa Re^ b' Rewy Re/

if one system and one temperature is postulated, thus making the

Schmidt group constant. In order to separate the variables in

equation (34) various simplifications have been tried. In some cases,

one film resistance has been considered so predominant that one or

the other right hand terms could be written as zero. This method has

been shown to be an oversimplification. Another method is to assume

that one of the terms remains constant when one fluid rate is held

constant. In this way by assuming that the core coefficient is unaf¬

fected by the wall rate the last term is constant at constant core rate

and the reciprocal of Eew may be plotted against the left hand term

and the value of a determined graphically. This method was used

by Treybal and Work and no correlation could be achieved. Bythe use of various similar graphical approaches, they felt that a

relation at least as complex as equation (34) was required to describe

the data. They concluded that each flow rate affected each film

coefficient. They also tried using the core velocity relative to the

calculated interfacial velocity of the film in their Reynolds numbers

and found it inferior to the velocity relative to the tube wall. It is

to be noted that they used very low velocities only, due to their de¬

pendence on gravity flow, and virtually all of their results are in the

range of wall rates which Pallah et al. considered to be on the

boundary between turbulent and streamline flow in this type of

system. This might explain their failure to obtain sufficiently con¬

sistent results.

Bergelin, Lockhart and Brown 5 built a very interesting horizontal

extractor which belongs in the wetted wall family. The extractor was

a 300 cm long, 5 cm diameter tube. The heavy phase flowed in the

lower half toward the left and the light phase in the upper half

toward the right. They extracted tetrachlorethylene solutions of iso-

propyl alcohol with water. They used the log mean concentration

36

difference although their own equilibrium data does not justify it

since the distribution is by no means linear. They concluded from

observation that the flow of each phase is affected by that of the

other. No correlation was found possible. One additional reason for

this was their observation of how foreign matter, impurities, etc.

collected at the horizontal interface and impeded extraction. For this

reason, this eonsrtuetion was deemed impractical although a wide

and independent variation of the flow rates was possible.Brinsmade and Bliss 9 extracted acetic acid from methyl isobutyl-

ketone with water in a 2.15 cm wetted wall tower of 30 and 113 cm

lengths. The tower was operated at 25° and 45° C. The distribution

coefficient of the acetic acid between the two solvents was measured

and was found to decrease quite definitely as the concentrations de¬

creased. Since the water entered the system in every case at zero acid

concentration, this casts grave doubts on the validity of the mean

concentration difference which was subsequently used. By the use of

a system in which H approaches unity in order of magnitude (about0.5 for their system), the results showed that each extraction coef¬

ficient was influenced only by its own flow for their apparatuswhich was operated entirely in what may be assumed to be the

turbulent region for each phase. They showed this independence by

plotting — against -— for runs with constant core rate and con-

kc Rew

tersely for runs with constant wall rate. The extrapolation of the

lines to infinite fluid rates did not give infinite values of Kc which

would have been the case if either /? or y in equation (34) were

other than zero. Then by trial and error choice of constants for the

term which was made constant by constant fluid rate, the exponentsa and 8 were determined graphically. It is to be noted this separationmethod applied exclusively to systems showing a constant solute

distribution ratio. By inserting the values of the Schmidt group for

each temperature and solving for the exponent, the final correlations

were achieved. These are

^ = 1.07 Rec 0.67 (^-°-62) (35)Dc \oc Dc /

D^ \^Tg) 3 = 135 X 10-3 Re,w (_s-) (36)

where kc and kw are the core and wall film coefficients and D, /*,

and 9 are the diffusivity, viscosity and density of the core or wall

fluids. These correspond to the forms developed by dimensional

analysis shown in equation (20). The diameter must be replaced bythe layer thickness for the wall coefficient in equation (36). For a

37

general solution, the layer thickness may be resolved into the group

shown and the Reynolds number already appearing in the equation.This may be done by dimensionless regrouping through the relation

of the friction factor for film flow as given in equation (28). These

relations, equations (35) and (36), represent one system at two

temperatures. The separation of variables depends primarily on the

extrapolation of curved lines which is uncertain. These are the sole

general relations ever published concerning the variation of film

coefficients in liquid extraction. They were made using the mass

rates of flow rather than the Reynolds numbers themselves, and

ignore the wall layer thickness in the calculation of this rate and in

the use of the tube diameter. They stand in contrast to the ob¬

servations of Treybal and Work 74 and Comings and Briggs15 who

found both film rates affected by both fluid rates. The objections to

the methods of these two workers have been noted previously. Bythe use of the Brinsmade and Bliss plotting method, it has been pos¬

sible to reconcile some of the results of Comings and Briggs qua¬

litatively and justify the Brinsmade relation as to form, at least in

the turbulent region which is of greater importance in practice than

the laminar. It is hoped that by the technique to be given hereafter

and the data on a different liquid system, the present work may

throw some light on this very important fundamental problem.

38

B. Practical Work

1. Apparatus

In order to measure extraction rates where the interfacial area is

known, it was decided to construct a wetted wall column. Certain

general considerations had to be met in the design. As great a range

of flow rates as the liquid system within the tower was capable of

carrying, should be available. The supply and removal of the fluids

should be as regular as possible, without either short or long range

fluctuation. The system should be capable of running steadily for as

long as required. The control of the apparatus by one person should

be quick and simple so that unduly large quantities of solvent are

not wasted in uneven operation.The apparatus is diagramed in figure 2 and listed in table 1. Glass

vessels and piping with solvent resistant flexible tubing were used

throughout except inside the thermostat where lead tubes were pre¬

ferred for their higher heat conductivity. The liquid containers were

all ten liter bottles. Distilled water for the wall liquid could be drawn

from the steam cabinet into either overhead reservoir, B or C, byvacuum. The core liquid was sucked into reservoir A from lower

reservoir D where it was accumulated and stored. All the overhead

reservoirs were about three meters above the laboratory floor. The

water could flow to the extractor by gravity, by positive air pres¬

sure in the reservoir or through the centrifugal pump, H, with

its bypass. The core liquid flowed by air pressure or gravity alone.

The spaces over the liquids in the reservoirs were closed and the air

to replace the flowing liquids entered through tubes immersed in the

liquids and ending at the level of the fluid outlets.

TABLE I

List of apparatus parts shown in fiure 2

A. Core Liquid Upper Reservoir

B, C. Wall Liquid Upper Reservoirs

D. Core Liquid Lower Reservoir

E. Drying Tower

P. Hg Column Pressure RegulatorGr. Water Column Pressure RegulatorH. Centrifugal Pump with Bypass

39

J. Flowmeters

K. Main Regulatory Valves

L. Thermostat

M. Vents

N. Calming Piece

0. Drains

P. Thermometer

Q. Extraction Tube

R. Free Fall

S. Sample Cutoffs

T. Core Liquid Collector

U. Cleaning Solution Reservoir

V. Adjustable ReceptacleW. Wall Liquid Collector

Y. One Way Valves

The air pressure in these tubes was maintained constant by al¬

lowing a steady exhaust through the mercury and water columns,F and G. Thus the pressure at the levels of the outlets was alwaysthat of the air applied regardless of the hydrostatic head of the

stored liquids above. In this way a slow change of flow was avoided.

One way valves, Y, were placed in these air lines so that they would

close when suction was applied. The drying tower, E, was placed in

the line to the core liquid reservoir to prevent wet air from reachingthe liquid. The water reservoirs were so arranged that one could be

filled while the other was being emptied. The air and vacuum control

valves and the liquid cut-offs were grouped together for simultan¬

eous shifting of the flow path. The two fluids passed through the

control valves, K, and the flow meters, J. These were interchangeableorifaces, the pressure drops across which were measured by the dis¬

placements of mercury columns in U tubes. These tubes were mounted

in a convenient position and connected to the taps by glass tubing.The liquids then passed through the thermostat, L. This was a ten

liter pan filled with water agitated by an electric stirrer. Two im¬

mersion heaters were controlled by a microrelay thermometer. A

cooling water coil of lead tubing was also installed. It was later

found convenient to use the water leaving this coil for the refracto-

meter and viscosimeter, either directly or through a heat exchangermade of a laboratory condenser. The distilled water leaving the

thermostat entered the column, Q, through the upper fixture and the

core liquid through the axially centered tube below. The upper fix¬

ture consisted of a 9 cm by 15 cm long glass tube attached to the

column by a resistant rubber stopper through which passed the

column, the water inlet line, and the drain, 0. Through the similar-

stopper above, passed the vent, M, and the glass calming piece, N.

Thus, as the water filled the end piece, the air was driven out of the

40

Apparatus

of

Diagram

2.

Figure

T—wr

xHs

bl

ft

vent. When water had risen sufficiently, it flowed under the end of

the calming piece and over the upper end of the column and down

the walls. The clearance between the inner surface of the calmingpiece and the outer surface of the column was about 3 mm. It was

found very important to center these pieces quite exactly so that the

annular space was as regular as possible. To assist in doing this,aluminium plates were fitted over and under the rubber holdingstoppers and connected by rigid bolts. Through these plates were

bored carefully placed holes through which passed the calming pieceand vent above, and the column, water inlet, and drain below. A

similar set of plates and bolts were used on the lower fixture. Prom

below into the lower fixture, entered the core inlet line and the water

outlet which latter was fitted with a drain, 0, to empty the column.

The core inlet was of adjustable length so that any desired level of

the lower phase interface could be achieved without altering the

system. Through the upper stopper of the lower end piece, passeda thermometer, P, which was removable so as to act as a vent as well.

The inlet for the cleaning solution entered here also. This solution

was kept in reservoir, U, and could be forced into the empty column

by air pressure when desired. The water left the column below and

flowed into the open ended adjustable receptacle, V, through flexible

tubing. This receptacle was suspended by a cord which ran over a

set of pulleys to a conveniently located, hand-operated spool. The

receptacle could be located anywhere from well above to well below

the ends of the column. A suitable counter-weight was provided. It

was found desirable to use as the adjustable receptacle a vessel of

appreciable volume to avoid spillage during adjustment of the flow

rates. This receptacle ran along taut guide wires to insure vertical

rise and descent despite the torque of the tubing. The water leavingthe movable receptacle through flexible tubing, passed the tap, S,for the taking of samples for analysis, and was collected in the re¬

ceiver, W. A gentle vacuum was applied to W to prevent an

undue hold up in the adjustable receptacle and hence a varyinghydrostatic back pressure. A lower drain was used in the receiver, M.As the core liquid rose and filled the column, it passed up into the

calming piece, N, the displaced air leaving through the central vent,M. The lighter liquid could not pass down into the body of the upperend piece due to the higher pressure there of the water. When the

core liquid level in the calming piece had risen sufficiently it passedoff through the large diameter side spout to the free fall, E. To

reduce the head and thus prevent the core liquid from entering the

water channel below, this side spout was located as short a distance

as possible above the end of the column. The side spout was of such

a diameter that it was never entirely filled and thus a siphon effect

was prevented. The free fall had the same purpose. The core liquidthen flowed past the sample tap, S, and into the receiver, T. This

42

last was a two liter separatory funnel with vent. M. Since during ad¬

justment, water occasionally was carried over, it was found advisable

to use a separatory funnel rather than a bottle. It was found necessary

to build a rigid metal skeleton to hold the column and pulley arrange¬

ment. This was because the liquid system was often very delicate and

had to be protected from vibration. The column itself was attached

to this skeleton only by two clamps at right angles to each other but

at different heighs so that it could easily be aligned vertically with

the help of a plumb line which could be hung inside the glass column.

The tube forming the extraction column was 117.99 cm long and had

an average diameter of 2.340 cm. The upper end was ground smooth

at right angles and then the outer edge was beveled slightly so as to

provide a regular and not unduly sharp weir over which the water

could flow.

Certain calibrations of the equipment were necessary. The average

diameter of the column at various points was measured by weighingthe water contained and comparing with the filled heights. A small

variation of several tenths of a millimeter were found and this cor¬

rection was applied to all later computations. Several orifaces for

each flow meter were calibrated by weighing the liquid delivered at

the operating temperature of 25° C for varying mercury column

deviations. By using several orifaces, smooth curves were achieved

for overlapping ranges of flow. This was necessary since a discontin¬

uity intruded at a given point for a certain oriface. No appreciabledifference was found in calibrating the core liquid oriface with n-

butanol and benzene although theory would relate the head differ¬

ences as the square root of the ratio of densities which varied byseven percent. This may have been due to compensation by the other

physical properties.

2. Measurement of Wall Layer Thickness

In order to calculate the interfacial area in the wetted wall ex¬

tractor, it was desirable to know the extent to which the column dia¬

meter was reduced by the layer of water flowing down the inner

wall. This thickness is also an indicator of the state of flow in the

wall layer. To make this measurement, it was necessary to bringthe column into steady operation, instantly stop the incoming and

outgoing flows of each component, and compare the horizontal

level of the interface after the wall liquid has entirely drained

down with that obtaining during steady operation. From this the

volume of the liquid on the wall may be computed, and hence the

layer thickness, m.

43

The system used was that of benzene-water so that no separationof solvents would be necessary later. Both water reservoirs, B and

C, were filled by suction from the distilled water supply and reser¬

voir, A from the benzene holder, D. The suction was then removed

and the air supply to all three reservoirs was opened. The pressure

was so regulated that a constant air stream was allowed to flow

through the closed mercury column, F, and then to escape throughthe open water column, G. The pressure at the outlets of the reser¬

voirs was thus a constant value amounting to the combined lengthsof mercury and water. The outlet of the water reservoir B was

opened, permitting a moderate flow at first, later reduced to

a minimum of about 1 kg/hr regulated by valve K as measured bythe manometer. It passed through the thermostat, L, and filled the

"6

1j

s/.

y^/*

Wall Bate (kgrhr)

2 1 * i 10 30 30 40 50 100 J00

Figure 3. Wall layer thickness versus wall rate af flow

upper end piece. As the water flowed down the wall, the lower end

piece was filled by allowing the air to escape by removing the thermo¬

meter, P, for a moment. The standing level of water at the lower end

of the column was adjusted to a point just below the end of the cen¬

tral core inlet tube by raising or lowering receptacle, V. "When this

was steady, the benzene line was opened and a very slow flow of

benzene of 1 kg/hr was set by valve K. This then filled the spaceinside the down flowing water in the column and eventually flowed

out through the side spout at the top. As the level of the core rose,it was necessary to raise receptacle V to keep the lower interface

steady. If this was not carefully done, bubbles of benzene surrounded

by water were formed which could not be eliminated without drain¬

ing the system. The benzene was first introduced into the tube at a

44

moderate rate so that the swiftly falling water at the bottom did not

have time to break up the cylindrical body of benzene before enoughwas present to retard the water. For the same reason the water rate

was kept as low as would cover the entire wall. Then as the tube

filled, the benzene rate was much reduced so that, its tendency to

tear the water away from the wall was reduced. If this latter oc-

cured, the water would shower down through the benzene and the

process would have to be begun again. By the time the core liquidhad filled the column and was spilling out the spout above, the

adjustable respectable had been raised to the height of the overflow

spout, less a distance corresponding to the fluid friction which

depended on the rates of flow. The adjustment was quite delicate

and it was later found advisable to let the lower interface seek its

own level within limits, which accounts for the varying column

lengths used later in the extraction series of runs. After the column

was filled, the desired flow rates were set. When the lower interface

was steady, it was marked and inlet and outlet of both streams were

simultaneously cut off at points as near the column as possible. The

best method tried for this was the rather primitive one of four

people closing the four streams by clamping sections of flexible

tubing with their fingers at a verbal signal.The theoretical relation (equation 26) based on isothermal stream¬

line flow has been used as a basis of the correlation. There should be

a variation with the core liquid used but the variation between the

sets of physical properties for benzene and n-butanol, the proposedcore fluids, is insufficient to be manifest within the experimentalerror. Two runs were made using butanol and the rest with benzene,no variation being apparent. The water rate was varied from the

minimum of 2.5 to the maximum of 80 kg/hr while the core rate was

held constant at about 10 kg/hr. The resulting curve is shown in

Figure 3 with film thickness plotted against weight rate of flow of

the water. The results agree in form with previous works but this

system has not been previously measured in this range. The repro¬

ducibility for the results was poor. The investigation was not ex¬

tended to varying core rates. The point of transition from laminar

to turbulent flow appears to be near 10 kg/hr but the data is not very

extensive so no conclusions may be drawn. The predicted line for

turbulent flow is shown and from the similarity of slope, it is as¬

sumed that the points lie almost entirely in the turbulent region. In

any event, the range of wall rates to be used in the extraction runs

which is narrower than the above may be thought entirely turbulent.

The slope to be expected of laminar flow is shown. This is the result

of both theory and experiment as previously discussed, and would

appear to lie outside the experimental error, albeit large. Eegardless,the results are clearly accurate enough to be used to modify the

diameter in the extraction series.

45

3. Butanol-Water System

In selecting a binary system for determination of extraction coef¬

ficients, a number of factors were considered. The heavy liquid was

fixed as water for obvious reasons of its importance as a solvent,availability, and physical properties. Use of another liquid as the

high rate stream would involve enormous separation and recovery

problems. For the other liquid, certain factors were of primary im¬

portance. It should wet glass less readily than water and have an

appreciably lower density. It must be moderately water soluble and

vice versa. It should be easily analyzed both as solute and solvent. It

should be non corrosive. It should show as high an interfacial tension

with water as possible. It should be common enough that many of its

properties be already measured and that it be available in largequantities in the pure form. It should also be capable of easy se¬

paration from water for recovery. Normal butanol was fixed on as

possessing these characteristics except that of high interfacial

tension against water. It was found that this property is extremelyrare in moderately water soluble substances, so a compromise was

necessary. It is a limiting but not prohibitive objection.Distilled water was used from a steam cabinet since tap water in

Zurich is very hard. Nearly all other investigators have used tapwater. Commereial n-butanol was distilled over CaCb and a fraction

boiling between 117.0 and 117.8° C was used throughout. The method

of Lund and Bjerrum49 with magnesium and iodine was tried but

found too slow for the quantities involved. In the recovery of the

butanol by distillation, an azeotrope is formed at 92°. This azeotropeis 58% butanol and thus is made up two phases which may be se¬

parated and each redistilled. In this way most of the butanol may

be removed from water solution without evaporating all the water.

The butanol remaining in the water after the temperature reaches

95° may be discarded. In the same way,the majority of the water in

butanol solution may be eliminated by the separation of the phasesin the azeotropie distillate. Calcium chloride may then added and

the remaining butanol distilled.

Several methods of analysis of the two binary solutions were in¬

vestigated. The most rapid method is the use of the index refraction.

Known concentrations of water in butanol and butanol in water were

measured by a Zeiss refractometer for sodium D wave length. Aconstant temperature of 20° was maintained with water from a

thermostat. The results were straight lines with some curvature at

very low solute concentrations. This is in accord with the form of

the results of Berner 6 for the aqueus solutions although the absolute

values showed a small difference, probably due to impurity. It is

interesting to note that the observed refractive indices were checked

46

at several points on each curve and coincided within less than one

twentieth of one percent with the values predicted from the com¬

position and the molar refractivities of the pure components. This

regularity is not reflected in other properties. The range of values

was fairly short, the maximum nj difference being 0.0084. The rangefor the butanol rich solutions was slightly longer. Prom the nature

of the operation, a greater accuracy was desired in the water-rich

solutions than in the butanol analyses. For this reason other methods

of analysis for the former were sought. Various titration schemes

were tried based on the general principle of Bogin.7 A number of

° ' 1 1 1x|l" 1 3500 1 400 1 4500 1 5000 n0 BuOH ,n C,H6 u

!\c

I \N

X 20-9 \ \ 0

CD*

\ \ / a*

\ \ / 70 —

\ \ /\ \ /\\\\

\ /

15-

\ / HjO in BuOH— 5

\ \ / BuOH ,n HjO

-. y\ BuOH in C,H,

50 —

10 —

- 330 —

5 —

X

qCD

~'

13950 1 3975 \ \l4000

10 —£

On„ HjO in BuOH 1 3925 , X*

1 / 1 1 1 \f «

n0 BuOH in H,0 1 3325 I 3350 1 3375 1 3400

Figure 4. Index of refraction versus solute concentration at 20° C.

third solvent titrations to turbid end points were ried including of

the Lazzari48 method of adding a benzene, acetone mixture and

titrating with water. These proved no worthwhile improvement on

the index of refraction since end point uncertainty cancelled the

greater theoretical accuracy. The surface tensions of standardized

solutions were measured in a stalagmometer at 25°. This was found

a very sensitive gauge for dilute solutions but useless for more con¬

centrated. The results were slightly different from those of Bartell

and Davis 4 when corrected for the temperature difference but the

literature shows agreement on surface and interfacial tensions to be

47

quite exceptional. Reproducibility was poor so the index of refraction

methods was fixed on for both solutions with the surface tension

method reserved for special cases. Figure 4 shows the curves of

solute concentration versus index of refraction used. Since a givensolution gave the same index to four places after the decimal pointon repeated tries, the accuracy of analysis may be seen to be +

0.0004 and ± 0.0005 weight fraction solute for the water and butanol

rich solutions respectively.Because of disagreement in the literature and the discrepencies

noted above, certain already cited physical properties and others

\0 610

10 320 0 630

10 840 p HjO in BuOH

o

~ \\ H,0 in BuOH

«

o\

in \ BuOH m H,0c 60—

o.\ BuOH m C.H,

l"\

M \\

\

-!0

K— 15 / *

^ \

/ \— 10

S^

\s\

— 5

^

^^ Density -^

,

cm'

1-x 0 870

1 1 \l

S 19 BuOH ,.C.h\ 0 840 . 0850 0660 X,-x

0965 0990 0995 1000 O BuOH in Hp

Figure 5. Density versus solute concentration at 25° C.

previously unmentioned were measured. The mutual solubilities weremeasured by titration in the thermostat at 25°. The turbid end pointcould be detected after some experiment by using reflected lightonly. The point was approached from two directions by titratingboth to clarity and turbidity. The water in butanol solutions were

particularly well adapted to this method. Glass stoppered flasks were

used and agitation was manual. The results showed no appreciablevariation from the values of Hill and Malisoff33 who used sealed

tubes. The accepted values were 0.0735 weight fraction butanol in

water and 0.2027 weight fraction water in butanol. The density of

solutions of varying strengths of each binary are given in the Inter¬

national Critical Tables.38 The values were checked by experiment at

48

several points and found to agree within the limits of the method.

Beaurettes of 50 ml volume were filled at 25° in the thermostat from

prepared solutions and weighed. The curves of density versus com¬

position appear in figure 5.

The viscosity of various water-butanol and butanol-water solutions

was measured in a Hoppler Viscosimeter at 25°. The value of the

pure butanol agreed well with the Jones and Christian42 value of

2.605 centipoises. Particular attention was paid to constancy of tem¬

perature. Each value used was the average of eight measurements

which is necessary with fluids of low viscosity in this type of ap-

H,0 in BuOH

BuOH n H;0 X^u

BuOH " C.H,X

qCQ

-20

/

/

/

,-'''.,--

-15

/

1 t

eo-

60 —

-101

11

1 -^/

/

40 —

-5

1^"7| ">

1

j

0 80

I

0901

:20-

1 1L^/

1 1 '/iBuOH , n CtHa cenlipo se 0 40 1 00 1 60 2 20

1 <-''l 1 1 1 1 1

2 70 2 90 it H,0 in BuOH cenlipoise

Figure 6. Viscosity versus solute concentration at 25° C.

paratus. The results are shown in figure 6 with viscosity plottedagainst composition. It may be noted here that a large negative de¬

viation from ideal behavior is shown by both sets of solutions, indi¬

cating a strong hydrogen bond formation in the mixture. That is to

say, the observed viscosities are far greater than those calculated

from Kendall's equation28 which states that in ideal mixtures, the

sum of the mole fractions times the logarithms of the fluidities of the

pure components is the logarithm of the fluidity of the mixture. This

lowering of the activity of the components by solvent bonding is

further substantiated by other properties.The procedure used in the binary extraction runs has been largely

described under wall layer thickness measurement. The purified al-

49

cohol was sucked into the core liquid reservoir and the process was

begun as indicated. After the desired flow rates for each phase had

been set, samples were periodically taken from the taps to de¬

termine when steady conditions were attained. It was found that

when about a liter of the slower moving core had passed through,values were constant. This amounts to about twice the holdup of the

tower. During the operation five or six samples of each exit liquidwere taken. The temperature of the system was continously observed

but this proved to be very constant and offered no difficulty once

lead tubing had been installed in the thermostat. The constancy of

the two flow rates was observed by the manometers and the level of

the lower interface as previously described. The calibration of both

the manometers with the orifaces was checked from time to time

throughout the entire experiment against the weight of fluid del¬

ivered in order to check any error from slowly accumulating fouling.The lower interface level was marked with wax pencil during each

run and the extraction length was later measured with the help of a

number of previously etched marks at known intervals along the

tube. It was found impossible to alter the flow rates to the next

desired value without draining the tube because the liquid systemwas quite precarious. Thus after a run, the core liquid supply was

cut off and the adjustable receptacle raised still higher so that water

forced the alcohol out the spout. As soon as the core completelydrained off, the water supply was cut and the receptacle lowered

below the bottom of the extractor so that the water drained out. The

tube was then flushed with tap water. The water was then shut off

and the upper end fixture drained. The tube was then entirely filled

with chromic acid from reservoir, U, by the use of air pressure. This

solution was composed of a 5 °/o solution of CrOs in 10 normal

H2SO4. This solution stood at least 20 minutes in the tower before it

was drained back into its reservoir. The tube was then washed with

tap water for at least 10 minutes before the next run was attempted.These were found to be the minimum precautions possible due to the

great sensitivity of the system. The experimental plan used was to

vary the core rate at several fixed water rates and then vary the

water at several fixed core rates. The limiting flow rates of the water

were 4 to 9 cm/sec and 0.2 to 1.3 cm/sec for the core. These are actual

not superficial velocities. Above and below these limits, breakdown

occurred. Many failures were encountered with the attendent delayof repurifying the alcohol wasted. The system broke down in two

ways. Occasionally a large bubble of water would form in the core

and the alcohol streaming up around it would prevent it from sink¬

ing on down to the lower water interface, and it would thus rise, or

more often be held steady in the core. Much more frequently, the

water layer would form waves of such amplitude that the rising core

would tear of the wave tips and small drops of water would shower

50

down within the core. This effect was much more pronounced at

higher wall rates. It would usually occur toward the lower end of the

tube and could thus be much reduced by shortening the tube. Both

effects were very strongly influenced by any uncleanliness of the

glass wall which hindered regular wetting by the water. Vibration

was found to be very important, and a specially redesigned support¬ing frame aided enormously. This effect was evidenced by the fact

that tapping the tube, particularly at the top, with the finger would

start wave formation. Contrary to previous investigations, the wave

formation was found to have other causes, as mentioned above, than

the flow rates alone. Experiencce would suggest, in fact, that for

ideal conditions, waves would not be formed even at moderately highflows. If once begun, howewer, they increase alarmingly with the wall

flow, the length of the extractor, and, as later shown, with inter-

facial tension. No effect of the core rate on waves was observed

within the limits used. A very careful and standard procedure in

starting the tube in operation was also of primary importance in

avoiding these effects.

The analyses were carried out immediately when possible. The

samples were collected in stoppered bottles. Three readings of the

refractive index were taken of each sample using different portionseach time. In all runs used, the last three samples taken agreed com¬

pletely in n<j. This seems a severe requirement but was found sur¬

prisingly easy to attain. The results were calculated in the followingmanner. The total area of extraction was

S = (d-2m)*rh (37)

This ignores the increase due to waves which was too indefinite to

include. An approximate correction for this error may be possiblewhen the results of an experiment on this subject which is under¬

stood to be underway are published. As shown by Walker et al.,75the potential for mass transfer in extraction may properly be ex¬

pressed in weight fractions. Hence the log mean of the end concen¬

tration differences are

(38)

and

(xs

-y,)-

lnVys

— x2) -

(ys-

-yi

-3'i

~x2

y2) =

-*!> =

y2jy\m —

Inys

ys-

xi

y2

4Y\m —

Inxs

Xs-in

xs ~X1 xi

(39)

51

Subscripts 1 and 2 stand for the top and bottom of the extractor.

Since the liquids enter in the pure state, yi and x% disappear. The

use of the log mean has been sanctioned by experience altoughlacking in theoretical basis. The total amount of butanol transferred

to the water, and vice versa, is calculated in the following way. Byequation (15), the solute per unit solvent in the leaving fluid, less

the solute per unit solvent in the entering, times the weight rate of

flow of the solvent alone is equal to the solute transferred. Since the

weight rate of each pure solvent entering was measured, this must be

reduced by the amount dissolving in the other phase to express the

weight of solvent alone leaving. Thus the following expressions were

developped for the weight rate of solute leaving in each solvent, as

infinite geometric progressions.

tvtWY2 - Xi Y2 B

Nw=

1-XtY,~ (40)

nc = Mlz^w (41)1 — Ai Y2

Where Nw and Nc are the solute rates in the wall and core liquidsand "W and B are the weight rates of pure water and butanol enter¬

ing. Solute per unit solvent, X and Y, may be computed from the

measured weight fractions as follows

Y = T^- ; X =-^— (42)

1 — y 1 — x

The film coefficients may be calculated from the integrated form

of equation (14) by

kw = ^V- (43)SUy) lm

kc = ^^V~ WSUx) lm

Implicit in this method is the assumption that all resistance to the

transfer of a liquid from a nearly pure state where it is a solvent to

52

a second phase where it is a solute occurs inside the second phase.The measure of resistance to transfer is the concentration gradientrequired to overcome it. When a nearly pure liquid is in contact with

another in which it is but sparingly soluble, the maximum concen¬

tration gradient possible within the first is that from the pure bulk

of the liquid to the interface where a small amount of the second

liquid is in solution. This would be very small in comparison with

the gradient at the other side of the interface where the first liquidexists in the form of a dilute solute. It must be acknowledged,however, that the resistance in the phase, in which the liquid in¬

volved is the solvent, is not zero. This consideration is one of those

which later made desirable a calculation method of the film coef¬

ficients for the ternary system which was independent of the results

of the binary. It may be observed that this source of error is more

important for the butanol, or core, coefficient than for the wall, or

water, coefficient since the wall phase at the boundary is 93% water

wheres the core phase is but 80% butanol.

An actual calculation for run B3 is given. The leaving alcohol had

an index of 1.3955 at 20° hence, by figure 4, it contained a weightfraction of 0.1004 water. The leaving water solution had an index of

refraction of 1.3398 and thus the butanol weight fraction was 0.0644.

By equation (42) the weights solute per unit solvent were:

X,x 0.1004 ^0;1117gwater

1 - x, 1 - 0,1004'

e butanol

W^- o,o687 e^1^1

1 — y8 1 — 0,0644'

g water

The incoming streams were measured as 13,400 —,and 4,900

hour

.Thus by equations (40) and (41), the transfer rates

hour

were

M -

WY* — X, Y, B_

920 - 38_

g butanol transferredNw~

1 - X, Y,~

0,992~

hour

BX, - X, Ya W 547 - 103„ „„ g water transferred

1 - X. Y, 0,992 hour

53

The log mean potentials based on the previously determined satur¬

ation values given on page 69 were

, , x, 0.1004U/X)lm

(Jy) lm

InXs

Xs—

Xi

„ ,0.2027

*"' '"s 0.2027 - 0.1004

.

„ .„ g water

0.147 :—

g Bu OH solution

_

y» 0.0644

Inys

ys —y2

" 3 lo»°-°735

* 80.0735 - 0.0644

« „„rBu OH0.0309 -

7—.

g water solution

The value of the wall layer thickness read from figure 3 for 13,400

g water

—; is m = .045 cm. The area by equation (37) ishour

S = (2.31 — .09) 7T (63.0) = 439 cm2

where the average diameter for the length in question was 2.31 cm.

Then the coefficients by equations (43) and (44) are

k -

M§= 6

95 g water

Kc0.147 (439)

°,VDhour cm2

890=

gBu OH

0.0309 (439) hour cm2

The results are given in Table 2 together with the Reynolds numbers

as calculated by equations (27) and (29). The film coefficientsdivided by a function of the physical properties of the solutions are

plotted against Reynolds number in figures 12 and 13. The functionsof the physical properties were derived from equations (35) and

(36) with the help of the ternary results as later described.

54

TABLE 2

Binary System Results

Xj ya B W S Rec Rew kc kw

Run wt. fract. wt. fract.e e

cm"S s

hr hr hr cm2 hr cm'

Bl .0962 .0635 5100 18100 364 29.6 46.6 7.61 103

2 .0918 .0635 5300 8600 370 30.4 22.2 8.54 46.7

3 .1004 .0644 4900 13400 439 28.2 34.6 6.95 65.6

4 .0983 .0644 5000 17200 420 29.0 44.4 6.70 88.5

5 .0962 .0635 5000 26800 346 29.3 69.1 6.60 163

6 .1004 .0644 4900 22700 361 28.5 58.5 7.05 138

7 .1049 .0625 4200 23200 358 24.6 59.9 6.10 129

8 .1027 .0652 3500 10600 370 20.1 27.3 5.90 64.5

9 .0596 .0644 16000 11100 398 92.2 29.4 14.3 57.0

10 .0744 .0644 9500 10500 362 54.5 27.4 12.0 60.8

11 .1091 .0644 3250 10500 417 18.7 27.1 5.35 54.3

12 .0918 .0625 4600 10700 345 26.4 27.6 7.52 60.6

13 .1350 .0644 1600 11000 374 9.17 27.8 2.92 64.5

14 .0637 .0635 12200 10700 400 70.5 28.2 11.6 53.0

15 .1672 .0706 3450 25100 643 19.8 61.8 5.10 135

16 .1263 .0706 6720 24400 711 38.8 61.5 7.80 116

17 .1091 .0706 10110 25000 720 59.1 63.9 11.8 137

18 .0443 .0527 10700 15600 221 62.3 43.4 11.6 91.0

19 .0466 .0491 10200 8900 215 59.3 24.7 12.4 45.9

20 .0443 .0500 10800 7800 220 62.3 21.7 12.3 39.9

21 .0466 .0455 10400 29100 197 61.3 81.6 12.6 147

22 .0723 .0463 2950 20100 188 17.1 55.5 5.02 110

23 .0446 .0473 7100 20200 185 41.5 56.0 9.11 116

24 .0357 .0508 15900 19700 193 93.5 54.6 15.4 123

25 .0336 .0508 20100 19800 206 118 55.0 17.5 115

4. Water-Butanol-Benzene System

A binary extraction system is not of any direct practical interest.

The only purpose it serves is to elucidate the mechanism and cal¬

culation of more complicated systems. For this reason, it was decided

to measure a ternary system in the same aparatus used for the binary

and attempt to correlate the results of one with the help of the

other. For this purpose, it was necessary to keep one film in the

ternary system identical with one of the films in the binary. Thus if

the wall liquid remains water for practical reasons, the solute must

be n-butanol. In selecting the other solvent, the following consider¬

ations were enterained. The solvent must show a density moderately

less than water. It must be as nearly insoluble in water as possible.

55

Normal butanol must be partially or completely soluble in it. A highinterfacial tension between the solvent and water should prevail. It

should be easily available and be common enough that some im¬

portance be attached to its performance. As many of its physicalproperties as possible should be known. Benzene fits these speci¬fications quite well. The commercial benzene obtained was considered

satisfactory without further treatment. It boiled at 79.5° to 80.5°

and had a refractive index of 1.5003. This is clearly not pure benzene

but it was considered to be satisfactory for the non-chemical use as

a solvent for which it was intended.

The solubility limits of the ternary system, water-n-butanol-

benzene was determined by the Bogin titration method. In this case,

binary solutions of various strengths were made up and titrated to

turbidity or clarity with the third solvent. The weights were de¬

termined from the previously known densities. It was of primaryimportance here to approach the end point from both directions

before accepting it. All titrations were carried out at 25°. The

solubility of benzene in water and water in benzene were taken from

the literature 45as 0.0015 and 0.0007 by weight fraction respectively.

The benzene and butanol are soluble in each other in all proportions.Thus the situation is two pairs of partially miscible liquids and the

usual isothermal triangular diagram would show a large two phasearea separating a very small one phase area at the water apex and

a thin one phase area along the butanol-benzene axis which widens

at the butanol end somewhat. No plait point is involved in such a

system. This diagram would give only a general idea of the solubil¬

ities. A more exact representation was found to be a rectangular plotof the weight fraction water against the weight fraction butanol,the difference of the sum for any point from unity being understood

as the benzene weight fraction. The amount of benzene dissolving in

water solutions of butanol was very small, rising from 0.0015 in pure

water to about 0.0030 weight fraction and falling off to zero in water

saturated with butanol. This system was measured at the same tem¬

perature by Washburn and Standskov76 and Stavely, Johns and

Moore68 and their results as to solubility agree extremely well with

the present ones. Figure 7 shows these results. The curve was

analyzed and expressed for less than 50% butanol solutions as

follows,

H2O = 0.167xs + 0.016x (45)

In the above solubility measurements, a sample of each saturated

solution at the clear end point was taken and the index of refraction

measured. These curves of n,j against butanol concentration are

shown in figure 4 and are intended for analyses of the ternary

system products. The weight fraction of butanol in the benzene and

56

water rich solutions are designated as x and y in analogy to the

binary solutions. It is to be observed that these refraction values

hold only for solutions lying on the solubility curve. Thus when the

refractive index versus butanol percent curve for water free benzene

solutions was drawn for another purpose, the values showed a de¬cided difference from those shown. However, the very small amounts

of benzene dissolving in the water solutions, a maximum of 0.5%,did not alter the indices so that the same curve was obtained for both

the binary and ternary system analyses in this case. These refractionresults also show very close agreement with the calculated values

Figure 7. Water content versus butanol content in benzene solutions at 25° C.

from the molar refractivities of the pure components. As may be

seen, the accuracy here remains ± 0.0004 weight fraction for the

butanol in benzene.

Of major importance for this experiment were the tie line or

distribution data. This was collected as follows. A series of bottles

containing equal amounts of water and benzene and varyingquantities of butanol was prepared. They were kept in the ther¬

mostat at 25° for 72 hours with periodic agitation. Samples were

withdrawn from each layer while still at 25° and analyzed with the

refractometer. As a control on loss, the amount of butanol added

was checked against the concentrations found in analysis. A second

series of solutions were agitated continuously for 8 hours and Avere

found to check with the previous results. The butanol was added to

57

the water and then the benzene added in half the tries and in the

other half the butanol was added to the two solvents together so that

it first entered the top benzene layer. Thus the distribution of

the solute took place in opposite directions in each half of the

experiments. No variation in results was obtained from this cause.

The results are plotted as the familiar x, y diagram in figure 8 and

listed in table 3. Washburn and Stranskov obtained somewhat lower

y values for the corresponding x. On the other hand, agreement with

the values of Hutchinson 37 is almost perfect. The former measured

mainly high concentration distribution and the latter only low. The

0X

c

X

o3to

— 7

•

"— S

WnUun

— 5

Mofgan

III

1 a

1SO '5

1 1% BuOH ,n QH4

Figure 8. Butanol content in water versus butanol content in Benzene in ad¬

jacent phases at 25° C.

lower region is of far greater importance at present, in any event.

This region may be best seen in figure 9. Difference in reagents mayaccount for the discrepency. The present results were certainlyhighly reproducible. Methods of correlating distribution data par¬

ticularly for double immiscible pair systems are poorly developed.However, Bachman3 suggested that a plot of the fraction of one

solvent in the phase in which it predominates against the ratio of

this same weight fraction with the weight fraction of the other

solvent in the phase in which it predominates on rectangular coor¬

dinates would be straight for the normal case. This has proved use¬

ful for systems of the single partially miseible solvent pair type.Brown10 suggested that by the proper choice of solvents to be plot-

58

TABLE 3

Conjugate Solutions at Equilibrium at 25°

Weight Fraction Butanol Weight Fraction Butanol

„rin equilibrium with

.

m Water Phase in Benzene Phase

.0000 .0000

.0111 .0042

.0147 .0092

.0214 .0220

.0309 .0520

.0400 .1241

.0427 .1820

.0481 .2838

.0481 .3740

.0517 .4387

.0572 .5293

.0017 .6349

.0652 .6942

.0679 .7351

ted, the method may be applied to the double partially miscible pairtype, of which very few examples have been studied. This has been

done with the present system. An excellent correlation is found byplotting the weight fraction benzene in the benzene phase againstthe fraction benzene in benzene divided by the fraction water in the

water phase. A straight line results with a small curvature of

increasing slope at very low solute concentrations. The formula of

the straight portion of the line is

.

fraction benzene in benzene

(fraction benzene in benzene = 0.964 : : 0.90fraction water in water

(46)

As previously mentioned, the water solutions of butaol show

properties suggestive of H-bond formation. Likewise the benzene-

butanol solutions are imperfect. If the x, y values are converted to

mole fractions, the most nearly constant ratio involves the cube root

of the solute mole fraction in benzene so that approximately

-^^55 (47)Zy

If the activities as estimated from vapor pressure measurements are

used in place of mole fractions, the ratio is even more constant.

59

According to the partition law, this indicated that butanol exists in

benzene solutions as a triple molecule. It was found that Kreuzer

and Mecke43 deduced a triple butanol molecule in carbon tetra¬

chloride and Hoffmann 34 the same in carbon disulphide and phenol,both from spectroscopic data. An anomaly in the heats of dilution

as measured by Stavely et al.68 for the alcohol series in water-

benzene mixtures appears first for butanol. It may be concluded

that n-butanol forms a triple molecule in benzene and that it is

probably the lowest member of the aliphatic series to do so.

The density of the benzene solutions were measured at several

points. The solutions of butanol in benzene were made up and then

— 4

0I*

I

q

-3

.—-" 1

ope rating line

equilibrium line

a

+ Hufchinsori

& Washburn

_2I''""

v^iz^>^(v-vX"1* p^'

<^y y,L

"'/

O Morgan

% BuOH in C6H6

/ 1 2

1 1

3 4

1 15 6

i 1

Figure 9. Portion of equilibrium line with operating line T-34

saturated with water. The measurement was carried out at 25° in

weighing beaurettes as before. The results are plotted in figure 5

as density versus weight fraction butanol. The results differ onlyslightly from the densities of dry butanol-benzene solutions as

measured by Jones, Bowden, Yarnold and Jones.41

The viscosity of water-butanol solutions when saturated with

benzene were found to be identical with those previously measured

for benzene-free solutions. The measurements were carried out as

before in a Hoppler falling sphere viscosimeter. The viscosity of

water saturated butanol-benzene solutions were checked at several

points and were found to agree substantially with the water free

values of Jones et al. which were accepted. The results are plotted in

figure 6 as viscosity versus composition.

60

The method of operation of the extractor for the ternary systemwas exactly that previously described for the wall layer thickness

and binary series of runs. The solutions were prepared analyticallyand checked by index of refraction before use. The benzene solutions

used were always previously saturated with water and the water

with benzene. This reduced the exchange between the solvents

themselves although some still occurred. This was due to the fact

that the mutual solubility varied as the butanol concentration in

each changed during the extraction. Subsequent calculations are car¬

ried out on the basis of universal saturation of each solvent with the

other. The operating difficulties were much reduced in the ternary

% BuOH in HjO

l \i \ Aga nsl air

V \ Against Benzene

\ \ D Aoamst Butanol

\ \\ \\ \

-» \ \\ \\ \\ \

\ >s, dynes»0 20 v 40 SO 60v— 80 (X ~^ZT

i i X. I i i ^-. i 1

Figure 10. Boundary tension versus butanol content in water at 25° C.

system due to the much greater interfacial tension prevailing. In

this connection it may be noted that the interfacial tension between

n-butanol and water was measured by Silbereisen 84by the capillary

rise method at 25° as 1.57 dynes/cm. The interfacial tension for va¬

rious concentrations of n-butanol at the benzene-water interface was

measured at 25° by Bartell and Davis 4 by the pendant drop method,allowing each drop of benzene to come to complete equilibrium with

the large volume of aqueous alcohol before measurement. The results

are a parabolic curve of tension decreasing with butanol concen¬

tration between 34 dynes/cm for zero alcohol to 2 dynes/cm for water

saturated with butanol. This is shown in figure 10 as surface tension

versus butanol concentration. In other words, with increasing al-

61

cohol concentration, the boundary finally assumes the character of a

butanol-water interface at saturation. As predicted from this result,the difficulty in maintaining the wetted wall system depended on

the final aqueous concentration of butanol. The range of flows was

greater than with the binary system although still disappointinglylimited. The actual velocities in this case were from 4 to 20 cm/secfor the wall liquid and from 0.25 to 2.25 cm/sec for the core.

The scheme of the experiment was as follows. For each pair of

original solutions, the water velocity was varied as widely as pos¬sible at constant benzene rate. The benzene rate was then varied at

several constant water rates. This was repeated for each pair of

solutions used. The solution pairs were varied so that benzene sol¬

utions of increasing initial alcohol concentration were extracted bywater and then water solutions of increasing initial butanol concen¬

tration were extracted by benzene. Thus the pairs used were 10, 20,and 50 weight percent butanol in benzene with water, and 0.75, 2.36,and 6.50 percent butanol in water with benzene. In some series,various tube lengths were used so that this effect could be studied.In this way, wall rate, core rate, initial concentration, direction of

transfer, and tube length were each individually studied. All runs

were carried out at 25°. It was hoped that the different initial con¬

centrations and directions of transfer would produce results varyingwith the several physical properties so that the effects of these couldbe studied in connection with the binary results.

The results of the extraction runs were checked by a materialbalance on the amount of butanol transferred from one solvent to

the other. This had been impractical with the binary series. Thus the

amount of alcohol per hour lost by one solvent was compared withthat gained by the other. This is a much more severe check than

comparing the total amount of butanol in the inlet solutions againstthat in exit streams. This latter balance is that reported by most

previous workers. In one case, Treybal and Work 74, this more severe

type of type of balance was made and 20% deviation was considered

satisfactory due to the fact that the process involves the subtractionof large numbers of the same order of magnitude. The results in the

present work show deviation of less than 12% with an average of4%. This was possible because of the relatively larger amounts ofsolute being transferred. The deviation is due to the analytical in¬

accuracy since large percent errors appear where the flows are largeand the concentrations low. A study of the material balance de¬viations show them dependent wholly on the previously designatedlimits of the analysis. "Where this was not the case, the runs were

discarded. A very important criterion was the arithmetical value ofthe error. The experiment was in this respect satisfactory in that the

negative and positive errors occurred at random and without trends.An example of the balance is given for run T 34 where the initial

62

solutions were benzene and 2.36% butanol in water. The core inlet

rate was 3.05 kg/hr which was pure benzene. The wall fluid inlet was

2.36% butanol in water. Prom figure 7, the benzene content was

negligible. The wall inlet rate was 7.30 kg/hr. The rate of pure water

entering was

L = 7,300 (1 — 0.0236) = 7,120g wa1fr °nly

The leaving wall fluid refractive index was 1.3344 so it contained

1.56% butanol, yz, and a negligible amount of benzene. The leavingcore index was 1.4979 so it was 1.65% butanol (xi) and from figure7, water content of 0.08%. Hence the weight butanol per unit solvent

are

v n v°-0165 ft„„0gBuOH

Xa= ° : Xl =

1^(03165 + 0.0008)= °-°168

gCTHTIn other words

gBuOH

g Bu OH g solution

g Ce H6 g Ce H6

g solution

and

Yl_ <y»* MM2t*i2H1 — 0.0236 g water

Yl_ «L«»- 0.01591^°!1

1 — 0.0156 g water

then by equation (16)

Nw = L (Ya - Yi) = (7120) (0.0159 - 0.0242) =

g Bu OH transferred

hour

Nc = G (Xi - X2) = (3050) (0.0168 - 0) =

, ~* « £ Bu OH transferred+51.2 &-

hour

The deviation from the mean of 55.2 is then —7.2% on the basis of

Nc. This is quite high due to the particularly low concentration

involved. The deviation is given in table 4 for all runs.

The results may be calculated in terms of the overall coefficients

Kw or Kc in the following manner. Equation (17), if written for

the overall condition reads,

GdX = LdY = Kw (y—y*) dS = Kc (x*—x)dS (48)

83

TABLE 4

Ternary System Results

Run x, x2 y, ya S B W error Kc Kw

J_ A A. e_ cm„ _e_ _s_ »/o _g g__

g g g g hour hour hr cm2 hr cm1

Tl .0513 .0980 0 .0191 610 7700 21600 —4.7 9.09 28.0

1 .0236 .0980 0 .0156 741 7900 34500 4.9 15.8 30.6

3 .0569 .0980 0 .0236 603 7900 12600 6.1 8.43 22.8

4 .0695 .0980 0 .0165 612 8000 15600 —3.2 5.14 15.7

5 .0243 .0980 0 .0139 625 7900 42400 0.0 18.2 38.0

6 .0151 .0980 0 .0111 785 6100 51000 —5.0 14.6 28.9

7 .0289 .0980 0 .0156 655 4300 18100 3.4 8.48 17.7

8 .0748 .0980 0 .0200 604 13400 18100 —4.5 7.01 23.9

9 .0803 .0980 0 .0200 592 19200 18600 —0.8 7.60 24.8

10 .0237 .0980 0 .0120 750 7700 45200 3.5 15.1 28.3

11 .0609 .0980 0 .0227 585 7800 12500 2.7 7.42 21.4

12 .0546 .0980 0 .0120 280 7700 26100 5.3 17.3 39.2

13 .0406 .0980 0 .0094 309 7700 44400 4.5 23.2 47.2

14 .0482 .0980 0 .0075 305 7600 54700 —2.0 18.8 43.8

15 .0850 .0980 0 .0111 285 8000 8100 11.8 4.55 10.1

16 .0328 .0980 0 .0075 381 7800 63300 4.6 23.4 42.4

17 .1660 .2000 0 .0120 205 7800 27600 —1.8 8.66 44.5

18 .1451 .2000 0 .0120 235 7700 45300 —4.7 12.5 64.5

20 .1763 .2000 0 .0218 203 8100 9300 6.3 6.33 32.6

21 .1180 .2000 0 .0236 614 7900 24600 11.1 8.01 33.6

22 .1130 .2000 0 .0218 604 7900 34900 0.1 8.69 43.0

23 .1584 .2000 0 .0236 586 7900 14400 3.2 3.88 20.2

24 .1771 .2000 0 .0318 552 7700 6500 2.3 2.29 16.1

25 .1502 .2000 0 .0236 622 7700 19600 —1.3 4.44 25.9

26 .1022 .2000 0 .0218 614 7800 37200 —1.6 9.20 45.7

27 .4061 .4660 0 .0336 715 7300 28400 —2.4 3.24 42.5

28 .4260 .4660 0 .0381 512 8600 16500 0.5 3.08 43.1

29 .4429 .4660 0 .0418 627 8500 8000 3.7 1.50 20.8

30 .3861 .4660 0 .0373 550 8900 31700 —0.1 5.65 76.1

31 .3548 .4660 0 .0336 537 9100 42200 5.8 7.94 86.8

32 .4570 .4660 0 .0427 561 9100 3200 4.0 0.750 9.69

33 .0200 0 .0236 .0183 781 3050 15200 —13.3 7.37 17.5

34 .0165 0 .0236 .0156 814 3050 7300 —7.2 6.30 12.2

35 .0288 0 .0236 .0210 801 3020 29100 4.6 23.8 33.0

36 .0258 0 .0236 .0210 811 3050 24900 8.6 13.6 24.4

37 .0288 0 .0236 .0218 784 3020 42000 5.6, 23.6 52.8

38 .0288 0 .0236 .0218 761 3050 60500 —12.1 24.6 78.3

39 .0212 0 .0236 .0191 796 6850 22000 21.3 17.6 22.5

40 .0150 0 .0236 .0147 809 9500 22200 —16.2 17.9 39.2

41 .0103 0 .0236 .0147 807 15500 22100 —11.1 17.1 30.4

42 .0090 0 .0236 .0147 800 20300 21900 —3.6 18.4 27.4

43 .0072 0 .0236 .0165 714 37000 23300 7.6 18.1 21.9

44 .0288 0 .0236 .0218 760 4000 71200 —6.5 32.3 111.0

45 .1250 0 .0650 .0372 724 3200 15400 1.3 2.64 30.8

64

Run x, x2 y,

J_ iL JL

g g g

46 .0870 0 .0650

47 .1621 0 .0650

48 .1922 0 .0650

49 .2490 0 .0650

50 .0780 0 .0650

51 .0552 0 .0650

52 .0451 0 .0650

53 .0429 0 .0650

54 .0381 0 .0650

55 .2020 0 .0650

66 .0178 .0980 0

67 .0460 .0980 0

68 .0619 .0980 0

69 .0802 .0980 0

70 .0780 .0980 0

71 .0853 .0980 0

72 .0127 .2000 0

73 .0507 .2000 0

74 .0650 .2000 0

75 .0719 .2000 0

76 .0757 .2000 0

77 .0749 .2000 0

78 .1540 .2000 0

79 .1781 .2000 0

80 .1808 .2000 0

88 .4350 .4660 0

81 .1821 .2000 0

82 .0109 .2000 0

83 .1231 .2000 0

84 .1484 .2000 0

85 .1658 .2000 0

86 .1723 .2000 0

87 .3521 .4660 0

89 .4491 .4660 0

90 .4500 .4660 0

91 .4521 .4660 0

92 .2482 .4660 0

93 .3938 .4660 0

94 .4279 .4660 0

95 .4400 .4660 0

96 .4410 .4660 0

97 .0142 0 .0236

98 .0102 0 .0236

99 .0072 0 .0236

100 .0058 0 .0236

101 .0950 0 .0650

102 .0351 0 .0650

103 .0267 0 .0650

104 .0181 0 .0650

y, S B

g hour

.0300 721 3200

0418 733 3850

.0426 747 3900

.0482 650 3300

.0354 699 10200

.0318 740 15700

.0318 721 19800

.0308 795 23400

.0308 801 26700

.0490 552 3900

.0214 700 3050

.0255 619 6100

.0282 630 10200

.0309 635 15700

.0318 641 20900

.0318 622 28100

0111 691 3100

0183 650 10100

.0210 561 16000

.0237 535 21100

.0245 595 26600

.0345 622 3100

.0381 670 9350

.0391 654 17100

.0400 710 22900

.0455 677 9600

.0418 826 26400

.0255 700 3100

.0318 529 10300

.0364 641 17600

.0381 669 23600

.0381 698 27800

.0436 635 3050

.0463 650 16000

.0463 666 21100

.0482 791 26400

.0345 642 3000

.0400 505 8700

.0418 511 17100

.0436 533 22200

.0436 596 27300

.0200 618 3100

.0147 765 10700

.0129 771 19400

.0129 789 26800

.0373 790 3100

.0308 712 11000

.0264 795 19900

.0336 600 25500

W error Kc Kw

-J_ •/. _* I—hour hr cm' hr cm2

7300 4.0 2.62 17.6

29100 2.6 3.17 50.2

38300 2.3 4.03 67.9

57700 4.5 4.46 90.0

28400 —0.5 5.62 51.9

28300 —2.9 8.10 51.3

28200 —1.6 7.41 48.9

27700 3.6 8.54 45.0

27800 3.8 8.06 43.8

57600 1.5 3.72 85.6

12100 —3.1 8.18 17.2

12800 —0.3 8.85 26.6

13100 2.1 '9.59 31.2

11200 —7.2 7.07 31.8

13500 2.4 10.9 4o.9

12000 —1.8 9.05 37.1

25700 —3.6 9.57 15.9

26400 1.0 11.3 3o.4

25ooo 2.9 13.5 38.8

26100 —2.8 14.7 51.3

25100 1.6 13.9 46.8

13600 —6.8 6.27 39.8

12800 1.3 5.43 41.5

12400 —3.5 4.88 44.5

131oo 0.8 5.65 47.5

12100 0.8 2.46 37.0

12200 6.0 6.01 47.0

25200 —5.3 12.1 49.o

26100 3.3 11.6 69.5

25500 6.1 11.5 76.0

25700 —1.5 9.80 83.6

25700 —4.5 8.60 78.8

14000 —6.2 2.65 42.5

12100 —4.8 2.36 40.3

13200 0.0 2.70 43.0

12400 5.1 3.52 39.5

27500 —4.5 4.29 50.2

25000 2.9 5.64 75.4

25000 5.9 6.15 80.5

27100 —4.9 5.53 92.3

26400 2.8 5.77 80.6

12500 —5.9 4.65 9.0;

12500 —1.8 12.1 17.9

11900 4.4 15.3 19.3

13200 4.6 17.6 19.7

12100 —3.0 1.65 19.o

12400 —4.5 3.24 22.6

12500 4.8 5.54 22.7

13100 5.1 4.55 21.2

65

Then if the negligible benzene content in the water solution is

ignored,

then by substitution in equation (48)

Kw dS dyL (l-y)My-y*)

y

-/

ya

Kw S f dy

(l-y)My-y*)

yi

(50)

(51)

For Kc, where the water content may not be ignored, using equation(45)

dX = d (l-(x+ H.6j) = d (l^(x + 0.167x2+0.016x)) (52)

dX =(l + 0.167x2)dx

(l-l.016x-0.167x2)2

and thus (53)

xi

KCS C (l+0.167x2)dx

"JVG J (l-1.016x-0.167x2J2 (x*-x)

X2

In order to solve equations (51) and (53), the differences (y—y*)and (x*—x) must be known at the various points along the ex¬

traction column. If the bulk concentrations are known at every pointin the tube, the difference from the equilibrium values may be read.

Thus it is necessary to plot the bulk concentration of butanol in the

water phase against that in benzene phase at each point in the ex¬

tractor. This is called the operating line in absorption problems.From equation (16) it may be seen that X is linear in Y if steadyconditions prevail. The entry and exit values, xi, X2, and yi, y2 are

known from analyses and, as shown above, the quantities Xi, X2 and

Yi, Y2 may be calculated by the use of figure 7. On a plot of X ver¬

sus Y, the points Xi, Yi and X2, Y2 may be connected by a straightline which gives the coordinates of every point in the extractor as

demonstrated by equation (16). The coordinates of as many points

66

as desired may be read and each transposed back into x, y values.

These may be plotted on the x, y diagram and give the operatingline. Thus for run T34, the line connecting the end concentration of

butanol per gram solvent 0,0.0159, and 0.0168, 0.0242 is drawn and

three intermediate points 0.0050, 0.0203: 0.0100, 0.0216: and 0.0150,0.0230 are noted. These points may be converted to the desired x, y

coordinates in the following manner derived from equation (42),

X(1-H2Q) Yx = -T+x—and Y = I+y

(54)

The fraction water at a given X value may be most easily read from

an auxilliary chart constructed from figure 7 in which the x coordi¬

nate is replaced by the corresponding X. Thus the x, y values of the

points, expressed in grams butanol per gram solution, are found to

be 0.0050, 0.0180: 0.0099, 0.0204: and 0.0148, 0.0227. These pointstogether with the top and bottom ordinary weight fraction concentra¬

tions are located on figure 9 and the resulting slightly curved opera¬

ting line is drawn. The curvature for other runs was far greater where

higher concentrations prevail. This line shows the coexisting bulk con¬

centrations as one passes down the tube. It should be born in mind,however, that unit lenght along this line does not show the variation

of conditions along unit length of the extractor. Equations (51) and

(53) may now be integrated graphically. As many points on the

1he quantities x or y and

l + 0.167x2 1

(l-i.6i6x-0.i67x2)2 (x*-x)or(l-y)2(y-y*)

are calculated. Thus for position 1, four intermediate points, and

position 2, the y values are 0.0156, 0.0168, 0.0192, 0.0205, 0.0229, and

0.0236. The values of the fraction -, are then 1.032, 1.034, 1.039,d-y)

1.042, 1.047 and 1.049. These may be most conveniently read, par¬

ticularly for the complex x term, from a graph constructed in

advance, of the fraction versus x or y. The values of the difference

y-y* for each point are read from figure 9 as the vertical distance

to the equilibrium line. They are 0.0156, 0.0083, 0.0059, 0.0054, 0.0048

and 0.0047. For this operation, many runs required the use of a

smaller scale chart showing the equilibrium line at higher concen¬

trations. In fact, five different scales of this diagram were used in

all. The values of the complex fraction divided by the y-y* values

are 66.1, 125, 176, 193, 218, and 223. If these values are plotted

against y, a smooth but complex curve results. The area bounded by

67

this curve, the yi and y2 values, and the y axis may be measured

with a planimeter. By referring to equation (51), it will be seen that

this area is the value of the integral. Thus for run T34,

^ = 1.390 and ^ = 1.680

The effective length of the column was 115.1 cm and the wall layerthickness from figure 3 was 0.041 cm. Then by equation (37) the

interfacial area was

S = (2.33 - 0.08) n (115.1) = 814 cm2

The overall coefficients are

_

1.390 (7120) gw~

814~ lU

hour cm2

and

814 hour cm

Also, if desired, the height of the overall transfer units may be cal¬

culated,

HTU0W =>¥r-A = 1^_ 82.7 cm (55)

f(l-y)a(y-y*)YiJ

HTUoc — 7z—;—. „ ^_—sr—: < ,„„— 68.5 cm

(l + 0.167x2) dx 1.680

/ (l-l.016x-0.167x2)2 (x*-y)

(56)

It may be noted at this point, that the HTU0 values for the other

runs do not differ from these values by any great amounts. Thus it

may be seen that the efficiency of the wetted wall tower is much less

than comparably large spray or packed towers which often show

HTUo values as low as 30 cm.

The values of Kw and Kc are collected in table 4. It is interestingto note the discrepency produced when the logarithmic mean con¬

centration difference is used. As mentioned in reviewing the litera¬

ture, that was the method used, without exception, previously. By

68

this method the coefficient would be calculated as the average rate

of solute transferred divided by the area times the log mean of the

top and bottom concentration differences from equilibrium. Hence,

(J.(y-v*)2-(y-y*h 0.0156-0.0047

( y)lm~,

(y-y*)2~,,.

0.0156"°-0091

and

(y-y*)i 0.0047

,. (x*-x)i-(x*-x)2 0.0108-0.0108nnin_

(z,x)lm = Tl^xK=

,,,0.0107= °-0107

ln(^r^ 2-31oSo:oTo7

so

KW = ^V- =^IL^

= 7.45

and

S (^y)im 814 (0.0091)"

hour cm2

KXNm OD.Z/'or

c==

r. / A \==

»i . /rv Ai A-\— O.OD

S(^x)in, 814(0.0107) hour cm2

The error in Kw by using the log mean method in this ease

would have been about 40% although the positive error in Kc would

have been very small. This error is not constant in size or sign but

varies with the concentrations and flows. The error has two causes.

First, the operating line is erroneously considered straight. Second,the equilibrium line is assumed straight, even at low concentrations

where it is doubtful if this is ever the case. Due to the irregularnature of the present system, the error is probably greater than in

the more perfect (and unusual) cases often studied. However, the

log mean has been used in the past even in the face of a considerablyvarying distribution constant. It is of interest, that the curves used

for the graphical integrations were of a large variety of shapes, and

complexity, showing at times several maxima. This is evidence of

the great difficulty attending a mathematical solution, all attemptsat which failed. The mathematical method of Scheibel and Othmer60

was tried but found to entail so many steps for correction in this

particular case as to make its usefulness over the graphical method

doubtful since it is an approximate method which is designed to

shorten the work of computation.

C. Correlation and Evaluation

1. Butanol-Water Results

The correlation of the results was envisaged in advance in the

following way. The results of the binary system extractions would

result in a correlation of the physical properties and the rates with

the film coefficients, since the latter could be directly measured in

the binary system. The overall coefficients of the ternary extractions

would then be divided into film coefficients, since a relation for the

coefficients of a film identical with one of the two present in the

ternary system would have already been elaborated. This film which

occurred in both experiments was that of the water with butan¬

ol diffusing through it. As previously stated, this was the film,the coefficient of which was the more reliably determined in the

binary runs since the water solutions were more dilute than the

butanol. The other film coefficient so isolated would serve as a check

for a general correlation. This plan failed for two reasons. First, the

range of the flow rates in the low interfacial tension binary systemwas disappointingly small. Secondly, the actual relation of the film

to the overall coefficients proved more complex than had been

thought previously.The correlation desired was of the form of equation (35) and (36)

which had been dictated by dimensional analysis alone. The first

step, then, was the computation of the wall and core Reynoldsnumbers as defined by equations (27) and (29). This could be done

with the information in the solute concentration versus density and

viscosity graphs. For lack of better, the concentrations used to enter

the curves, were the arithmetic averages of the entering and leavingbulk concentrations. The Reynolds values appear in tables 2 and 4.

The next step was to plot the binary values of kw versus Rew and kcversus Rec. The results fell on roughly straight lines but the rangewas very short. The lines could equally well be called the flatter

portion of a curved function. The physical properties of the solutions

did not offer sufficient variation for any conclusions. This had also

been the fate of the results of most previous workers. It did seem

fairly clear that the effect of each flow rate was limited to its own

film coefficient within the range studied. This appeared an im¬

portant conclusion.

70

2. Separation of the Film Coefficients

in the Water-Butanol-Benzene System

The problem of separating the film coefficients in the more ex¬

tensive ternary system runs remained. A variety of mathematical

systems were attempted. These were based on the relations of the

film to the overall coefficients as shown in equation (21). It may be

seen from the x, y diagram of figure 9 that the concentration dif¬

ferences used for the overall coefficients and those for the films are

related by the slope of the equilibrium line. Consequently from

equations (10), (11), (12), and (13) the reciprocals of the coef¬

ficients are so related. This flows directly from the potential-resistance concept. Thus for a known transfer rate, N

Y"=

T- +(slope) ~V~ (59)

^-= -^- +(slope)-^- (60)

It may be seen by inspection that the slopes involved are between

different points for equations (59) and (60) and so the same slopewould not apply to both. This situation is most clearly seen from a

study of figure 9. Where there is a changing slope in the present

case, two difficulties intrude. First, which of all the possible po¬

sitions on the operating line should be used to determine the portionof the equilibrium line whose slope is valid? Secondly, for any givenportion of the line, what sort of average of the slopes occuring within

the limits of the portion should be used? Several assumptions were

tried to settle the matter mathematically but it appeared that the

ordinary averages were not valid and some sort of complex solution

was called for. The data was such that various assumption could be

tested by using them to calculate the water film coefficient, kw,within the range of values measured in the binary system. For some

attempts the correlation was adequate for kw but no resolution of

kc occurred which could be considered rational. Thus the mathe¬

matical solution was discarded and a graphical method attempted.The first difficulty of finding the decisive point on the operating

line was attacked as follows. If the rate of solute transfer is divided

by the area of contact and the overall coefficient found by graphicalintegration, the result will be an indicative value of the overall con¬

centration difference. This may be easily seen from equations (57)and (58). This was calculated for all runs. This difference may be

set on dividers in the scale appropriate to the graph used, and a

71

point may be found on the operating line corresponding to this

difference. This is done by holding the dividers vertically when the

(y-y*)w distance is set and horizontally when the (x-x)c distance is

set. One point is then moved along the operating line and the co¬

ordinates recorded when the other point falls exactly on the equili¬brium line. The result in most cases was one point for each run usingthe (y-y*)w value and another for the (x*-x)c value. In some cases,

two points fitted for one or each orientation. In these cases, one

point was usually so close to one end of the operating line that it

could be discarded as giving a measure of the run £s whole. In a few

cases, no elimination by estimate could be made. It is of importance,however, that in no case did the decisive points for the horizontal

and vertical alignments coincide. Furthermore in nearly all runs, the

separation was considerable. The great majority of the points based

on the overall wall coefficients were at higher concentrations than

those based on the overal core coefficients when the direction of

transfer was from the core to the wall while the reverse was usuallytrue for the opposite direction. Thus for run T34 the decisive overall

concentration differences were

«*-*-T£r--sTO--M10°

When the (y-y*)w value was set on the dividers, only the point on

the operating line for run T34 having the coordinates .0070, .0190

allowed the dividers to touch both the operating and equilibriumlines when held vertically. When the (x*-x)c value was applied, two

points, 0.0128, 0.0218, and 0.0039, 0.0175 were found to fit with the

horizontal orientation. Of these latter two, the first point would

appear more reasonable as it is closer to the center of the line, but

no definite decision could be made for this particular run at this

time. Whichever of the indicative core points be considered, a

notable separation from the single wall point exists. It may be noted,that the transfer rate calculated from the final wall concentrations

is used for the wall point and the rate from the final core concen¬

trations for the core point. Since the balance on the transfer rates

was poor for this run, it may be argued that this accounts for the

separation of the indicative points. This is not the case since

originally the average transfer rates were used for both points and

the separation was equally definite. It was later found that a better

correlation of results occurred when self-consistent measurements

72

were used for each. That is, for separation of the film coefficients,all calculations for each should be based only on the concentrations

measured for each. Thus if the characteristic error in measuringfinal water concentration affects the calculation of the core coef¬

ficient, a false appearance of interdependence is created. The ar¬

gument is further supported by the undiminished point separationobserved in a number of runs in which the extraction rates cal¬

culated from each end solution happened to agree completely. The

coordinates for the decisive points from the overall core coefficient

(xc, yc) and from the wall coefficient (xw, yw) are listed in table 5.

Only the points which later proved correct when referred to the

final correlation curve are listed.

This non-coincidence of the points based on each overall coef¬

ficient may be discussed as follows. On the basis of the two film

theory, a constant is assumed which is inversely proportional to the

resistance to mass transfer. If the resistance is assumed to lie entirelyin one phase, the coefficient is called the overall coefficient based on

that phase. This implies that there is a concentration gradient in this

so called controlling phase corresponding to the produced extraction

rate and no concentration gradient at all in the other phase which

thus offers no resistance to transfer. The overall coefficient of mass

transfer may then be calculated by the graphical integration method

described above. This integration became necessary because the bulk

concentration for each stream required for the calculation of the

concentration differences may be measured only at the top and

bottom of the column. Since it is desired to express the overall

coefficient as one applying to the entire apparatus rather than one

point in it only, the operating and equilibrium lines were drawn and

the values of the bulk concentrations, and their distance from equili¬brium according to any desired assumption could be read for as

many points along the column as wished. Thus the concentration

difference based on the water phase is large at the bottom of the

tube and small at the top when the butanol is being transferred from

the water to the benzene as in run T34. Since the overall coefficient

based on the water phase was calculated taking proper account of the

variation of this concentration difference along the column by the

integration method, the concentration difference, (y-y*)w> found bydividing the observed transfer rate by the coefficient and the area

is a decisive one. It is less than the large lower value and greaterthan the small upper value and is the weighted average of all the

values along the tube. Thus the concentration differences at least

one point in the column are those which produced the observed

extraction rate when multiplied by the overall coefficient and the

area. In short, this point may be termed typical of the tower per¬

formance for the given assumption of controlling film. The con¬

ditions at another height are those of the average fulfilling the as-

73

TABLE 5

Correlated Ternary System Results

Run Rec Re'w Xc yc Xw yw kc kw

— —

JL

s

g_

S

J_

S

g S

hr cm2 hr cm2

Tl 198 44.4 .0707 .0076 .0783 .0109 10.5 92.02 208 71.0 .0523 .0060 .0766 .0110 13.5 175.3 201 25.6 .0701 .0071 .0815 .0136 10.4 47.24 204 32.4 .0790 .0056 .0809 .0092 5.59 91.35 212 87.5 .0532 .0050 .0856 .0113 15.3 222.6 165 106. .0452 .0038 .0440 .0036 15.9 320.7 111 37.4 .0566 .0060 .0322 .0011 10.9 88.18 342 37.3 .0988 .0200 .0874 .0111 8.78 80.69 490 38.4 .0953 .0164 .0901 .0112 9.50 69.5

10 207 93.8 .0528 .0045 .0480 .0036 15.6 251.11 199 25.6 .0714 .0064 .0827 .0129 8.70 51.512 202 55.0 .0743 .0054 .0775 .0063 17.8 144.13 208 94.0 .0649 .0038 .0910 .0082 19.8 242.14 206 117. .0705 .0031 .0750 .0039 19.0 304.15 202 17.3 .0881 .0025 .0919 .0057 4.27 45.016 215 135. .0596 .0027 .0620 .0030 22.2 364.17 192 61.6 .1842 .0065 .1821 .0060 9.53 141.18 196 100. .1714 .0055 .1741 .0061 13.8 229.20 189 20.3 .1925 .0140 .1891 .0121 14.7 41.521 195 52.4 .1551 .0104 .1656 .0133 7.91 111.22 198 74.5 .1476 .0082 .1621 .0119 9.16 173.23 185 31.0 .1755 .0096 .1834 .0134 4.05 62.524 182 13.8 .1886 .0160 .1915 .0192 3.60 22.025 190 42.2 .1725 .0102 .1788 .0130 4.97 78.426 186 79.0 .1449 .0089 .1596 .0123 9.73 172.27 158 65.5 .4626 .0317 .4418 .0199 3.66 147.28 149 37.8 .4560 .0280 .4504 .0233 17.0 56.129 143 18.1 .4599 .0321 .4561 .0261 2.41 37.630 163 72.1 .4572 .0330 .4363 .0225 8.00 157.31 172 96.6 .3891 .0093 .4267 .0192 8.16 177.32 150 7.26 .4648 .0376 .4621 .0269 4.56 15.133 80.0 28.6 .0111 .0215 .0105 .0213 11.6 67.034 79.0 13.7 .0128 .0218 .0070 .0190 11.7 33.835 81.0 53.7 .0213 .0230 .0184 .0228 28.8 122.36 81.6 46.0 .0181 .0229 .0172 .0227 16.9 107.37 82.6 77.4 .0211 .0230 .0211 .0230 36.2 159.38 85.5 111. .0211 .0230 .0211 .0230 43.6 230.39 182 40.7 .0123 .0219 .0114 .0217 19.6 110.40 253 41.5 .0082 .0197 .0051 .0178 33.4 121.41 412 41.4 .0048 .0190 .0028 .0171 28.7 116.42 537 40.7 .0045 .0191 .0017 .0165 31.2 108.43 719 43.4 .0037 .0201 .0019 .0185 27.5 91.444 113 131. .0210 .0230 .0221 .0230 60.0 273.45 83.0 25.8 .0508 .0480 .0940 .0574 9.88 47.546 81.9 12.2 .0310 .0429 .0501 .0511 12.2 29.2

Run Rec ReV

47 102 48.6

48 105 64.5

49 91.4 97.5

50 271 47.0

51 416 46.8

52 525 46.5

53 620 45.6

54 709 45.9

55 108 95.9

66 77.7 25.0

67 155 26.5

68 260 27.1

69 400 23.2

70 533 27.9

71 716 24.8

72 82.0 53.1

73 267 54.5

74 423 51.7

75 557 54.0

76 704 52.0

77 74.6 29.5

89 278 28.1

78 226 27.8

79 412 26.9

80 552 28.4

81 636 26.4

82 76.9 54.6

83 256 56.5

84 436 55.3

85 585 55.6

86 690 55.6

87 53.0 32.4

88 167 28.1

95 394 62.9

96 485 61.2

89 278 28.1

90 366 30.6

91 459 28.8

92 53.1 63.7

93 154 58.0

94 303 58.0

97 81.0 23.4

98 279 23.4

99 506 22.2

100 700 24.7

101 80.0 20.2

102 284 20.7

103 515 20.8

104 659 21.9

xc yc xw

JL JL JL

s g g

.0527 .0484 .1242

.0566 .0480 .1460

.1636 .0580 .2160

.0294 .0463 .0520

.0181 .0424 .0320

.0157 .0434 .0250

.0144 .0424 .0240

.0134 .0427 .0200

.2010 .0650 .1940

.0448 .0066 .0573

.0623 .0066 .0794

.0917 .0232 .0841

.0933 .0226 .0917

.0931 .0233 .0910

.0948 .0239 .0941

.0410 .0032 .0537

.0702 .0071 .0778

.0762 .0067 .0841

.0937 .0195 .0877

.0945 .0201 .0896

.1088 .0070 .1620

.4638 .0394 .4602

.1904 .0299 .1848

.1950 .0300 .1930

.1962 .0320 .1941

.1977 .0348 .1953

.0716 .0060 .1920

.1947 .0294 .1713

.1891 .0284 .1824

.1919 .0285 .1889

.1931 .0276 .1913

.4560 .0396 .4250

.4620 .0389 .4508

.4612 .0363 .4571

.4620 .0373 .4568

.4638 .0394 .4602

.4639 .0393 .4610

.4641 .0407 .4623

.3310 .0113 .3689

.4561 .0340 .4400

.4588 .0339 .4531

.0071 .0218 .0067

.0054 .0193 .0097

.0037 .0186 .0045

.0024 .0175 .0032

.0400 .0481 .0143

.0127 .0431 .0149

.0100 .0404 .0123

.0053 .0427 .0074

yw kc kw

JL g g

g hr cm2 hr cm2

.0588 11.4 86.6

.0587 14.3 114.

.0620 8.20 156.

.0550 18.2 88.0

.0508 20.4 117.

.0502 24.3 108.

.0496 33.4 88.5

.0485 32.6 89.2

.0640 7.81 135.

.0099 8.70 63.3

.0153 11.0 55.2

.0171 16.2 60.4

.0198 16.4 46.5

.0204 26.3 61.4

.0204 25.1 52.0

.0050 8.86 139.

.0101 11.9 133.

.0119 14.9 120.

.0137 21.4 112.

.0155 21.3 103.

.0222 8.11 52.4

.0307 15.8 57.3

.0249 13.6 60.0

.0262 22.2 57.3

.0274 29.2 61.5

.0300 26.9 68.8

.0241 8.59 132.

.0192 20.0 130.

.0232 22.1 121.

.0254 24.4 114.

.0250 28.6 96.1

.0274 7.56 67.0

.0299 13.6 57.6

.0278 21.2 130.

.0280 24.1 126.

.0307 15.8 57.3

.0308 18.5 62.5

.0331 20.4 55.8

.0177 4.66 121.

.0246 14.4 123.

.0262 19.9 121.

.0217 6.72 40.9

.0232 17.3 53.0

.0194 24.3 55.7

.0186 28.5 58.0

.0408 8.90 40.6

.0451 17.9 40.6

.0440 26.4 41.9

.0466 25.4 41.2

75

sumption that the resistance is entirely in the opposite phase. These

point concentration differences are those which would produce the

observed transfer rate if they prevailed throughout the system for

the particular phase assumed controlling.At least two sets of alternatives may be seen from this situation.

First, either the relative importance of each film resistance to the

other varies appreciably with the variation of concentrations up the

column in a given run, or the variation is unimportant. Secondly,either the individual film coefficients for a given run vary appre¬

ciably as the concentrations vary along the column, or they remain

approximately constant and thus reasonably independent of the con¬

centrations at which they are evaluated within the limits of expe¬

rimental error.

For the first question, it appears inevitable that the relative

importance of each film differs for each point on the operating line

since the portion of the equilibrium curve whose slope is the combin¬

ing factor varies as the point moves. This is shown in equations (59)and (60). By examination of the curve in figure 9 this influence

should appear in both film results at least for some cases. The second

question is more complex. If end effects may be ignored or con¬

trolled, the film coefficients are thought to vary only as the vis¬

cosity, density and diffusivity change due to the concentration

change along the tube, since the state of flow for a given ran oughtto bo constant at all points. These physical properties suffer only a

small change between inlet and outlet concentrations in one phasefor one run. Some idea of the end effects may be gained by varyingthe length of the extractor so that in a long tube their importance is

reduced. This was one factor observed and it was tentatively con¬

cluded from the results that end effects are of not serious con¬

sequence for the wetted wall system. This may be seen by comparingthe points on figures 12 and 13 prodiiced by runs B-l to B-14 with

those form B-15 to B-17 and from B-18 to B25. The points are seen

to lie on the same curve although the lengths used were about 50,

100, and 30 cm respectively.These considerations lead to the following procedure. If the film

coefficients are to be considered constant along the tube, the concen¬

tration difference from the bulk to the interface across the wall film

(y-yi) must be identical for each of the two decisive points and the

same must be true for the gradient in core film, (x-ix), if the

relative importance of each film does not appreciably change, since

at these points the concentrations are indicative of the prevailingtransfer rate. This is because the observed transfer rate for the run

must be the product of the assumed constant film transfer coef¬

ficient, the film concentration gradient, and the interfacial area.

These rather unlikely assumptions may be checked by solving for

(y-yi) in the following

76

V [yw - (y - y.)] - xw = W [yc - (y - yi)] _ Xc (61)

where W is the function, x = W (y) of the equilibrium curve and

xw, yw and xc, yc are the two previously determined decisive pointson the operating line. Thus the quantities within the brackets are

the values of yf which the function f transforms then to x1 values

since the interface is always assumed at equilibrium. This equationmay be solved through trial and error by assuming values of y-yi

and solving by the use of the equilibrium curve.

Thus for run T34 W [0.0190-(y-y,)] -0.0070 = <F [0.0218-(y-y,)]-0.0218. By trial and error choice of (y-yt), it is found that for the

value 0.0012, W [0.0178-0.0070] = ^[0.0206] -0.0128. Then by re¬

ferring to the equilibrium curve to convert the functions to xit

0.0144-0.0070 = 0.0200-0.0128 = 0.0072 = (x,-x). Hence if these

are the points corresponding to the transfer rate,

59.1 g

814(0.0012) hrcm2

(62)

51-2= s 7,

g

814(0.0072) hrcm2

The results of this method were hopeful at first but provedultimately to be a failure. No rational alignment of results could be

achieved. This was to be expected from the overly broad assumptionsused. Based on the previously reasoned alternatives, the very sim¬

plest conclusion from this failure was that the relative importanceof the films vary appreciably with the position in the tube. Ac-

cordingsy, it was assumed that the wall film gradients, (y-yi)w and

(y-Vj)c, at the two points are related to each other as the two overall

wall gradients, (y-y*)w and (y-y*)c, are related. One of the latter

being calculated from the overall coefficients as above and the other

obtained from the diagram, figure 9. The same was assumed for the

two core film gradients. This leads to the equation

<P [yw - (y-y,)w] - xw = j§^jf (63)

[*(*-£E&fr-»>.HEquation (63) is a statement that the overall concentration gradientsat the points were all resistance may be considered in one phase or

the other are related as the film gradients at these points. The

kw —

kc =

Nw

S (y —yi)

Nc

S(xi-x)

77

various quantities are shown in figure 9. This method is supportedby the following considerations. At point W the water overall con¬

centration difference is decisive, and at point C where water overall

concentration is less than at point W, the same water overall coef¬

ficient is assumed to apply. The change in the overall concentration

differences must then be due to the changed importance of the two

films since the extraction rate for the run was constant. This changeof relative importance between the two films along the column must

be reflected by the film concentration gradients since they are the

expression of the real physical situation prevailing. Thus if the

overall concentration gradients are related at the two points as are

the importances of the two films, the film concentration gradientsmust be related according to the same proportion. The theoretical

difficulty here is the use of a point on the operating line found to

fit the assumption of one film controlling to measure the concen¬

tration gradient based on the assumption that the opposite film con¬

trols. There does not appear to be any organic importance of that

particular point for the second assumption. To this excent is the

development empirical. Equation (63) may be solved by trial and

error choice of the wall film gradient at point W with the help of

the equilibrium curve when, as in the present case, the equilibriumand operating lines are curved so that a unique solution is possible.Thus for T34

V [0.0190 -(y-jr,)w] - 0.0070 = °^r,r, / 0.00500

, a "1

|JP (0.0218- TO^(y-yi))-o.0128Jby trial and error, the value of (y —yi)w is chosen as 0.0022

W(0.0168)-0.0070 = 0.950 [*P (0.0218 -0.845 [0.0022])-0.0128]0.0056 = 0.950 (0.0059) = 0.0056

henee (y-yi)w = 0.0022 (0.845) = 0.0018

(y-yi)c = 0.0022

(xi-x)w = 0.0056

(xi-x)c = 0.0059

Now the point at which the film gradients correspond to the actualtransfer rate should be between the points found by assuming first

one phase and then other offers the entire resistance. This is probablesince each film does in fact contribute to the resistance regardless ofwhat convention is adopted. Thus the points for the two extreme as¬

sumptions should lie on either side of the points at which the indivi¬dual film gradients produce the observed transfer rate. It need not

78

be the same point for each film, however. Several sorts of weightedaverages were tried for each of the two films but the experimentalaccuracy was not found sufficient to support any such refinements.

As a result, the simple arithmetical average of each of the two

gradients was assumed to represent the facts sufficiently well for the

calculation of the film coefficients. Hence

y-yi= 'A (0.0022 f 0.0018) = 0.0020

x,-x = '/s (0.0056 + 0.0059) = 0.0058

and so by equations (62) and (63)

v59.1 g

w

814(0.0020)",0

hour cm2

k __5L?___117_JL_c

814 (0.0058)'

hour cm2

The film coefficients calculated in this manner gave a promisingcorrelation with the flow rates and thus were used to form the final

result. It must be emphasized that no claim of theoretical perfectionattaches to the method. In particular, the use of the average of the

two film gradients is indefensible. A weighted average using the

ratio of the two overall coefficients as a combining factor might be

a refinement possible with results of a different order of magnitude.Furthermore, the trial and error solution of equation (63) is quiteinaccurate in many cases and thus a large number of experimentalruns at varying concentration ranges are required to achieve a

significant trend in the film coefficients. In over 10% of the runs

made, a solution was impossible due to an insufficient variation in

the key concentration values or the portion of the equilibrium curve

in question was too flat. In practice, these runs were evaluated byassuming a wall coefficient on the basis of the curve formed from the

other results and then solving for the core film gradient by equation(63). This method in no way detracts from the value of the inform¬

ation and is made necessary only by the geometric limitations of the

method of separation used. It is seen that the entire method is made

possible by the curvature of the equilibrium line. If a straightrelation of the distribution constant type prevailed, all points would

fit the requirements and no discrete values would result. The

greatest imperfection of the separation method, however, lies in the

use of a point on the operating line found typical of one assumptionto measure the concentration gradient pertaining to the other as¬

sumption. For this reason, mainly, the method may be found

restricted to the present system or to very similar ones. Further

experiments may elucidate this point. Despite its shortcomings, this

79

method may offer a possibility of separating the film effects for the

most general possible case of liquid extraction, consistent with the

assumptions. The test of the results was made partly by the results

of the binary investigation but the method itself is quite independentof any such sources outside the ternary system. The film coefficients

so calculated are listed in table 5 with the Reynolds number for

each run used.

3. Final Correlation

For the final correlation, the diffusivities of the solutes in the

several solvents must be known in addition to the density, viscosityand Reynolds numbers already calculated. Using the atomic volumes

at the boiling points, the generalized graph given by Wilke 79 of this

quanty versus F shows the values of F for the systems of butanol in

water and water in butanol. For the value for butanol in benzene,the graph was entered with the assumption previously explainedthat the solute molecule is a trimer. These values are 3.27X107,

0.96 X107, and 4.67 X107 ^^ centipoise respectively. The lastcm

would be 2.33 X107 if the monomer were assumed. The first value,that of butanol in water, is well supported by experimental results

of 3.25 X107 and 3.12X107 based on single values of D found in the

literature.38 45 The second value is unconfirmed. The third systemhas been measured but the results were expressed without the dif¬

fusion area so that the constant of diffusivity cannot be calculated

from the results.37 The above values are for negligible solute con¬

centrations. Equation (4) shows the correction for concentration

which was applied to the above constants. The correction for ir¬

regular solute activity is the fraction. ,

-. The compositions of thed In /,

vapor in equilibrium with liquid solutions of butanol in water and

water in butanol at one atmosphere are given by Stockhardt and

Hull69. The mole fraction of the solute in the liquid was plottedagainst its mole fraction in the vapor on double logarithmic coor¬

dinates and the slope at various points was read. Since the mole

fraction in the vapor is the partial pressure and the partial pressure

is roughly equal to the activity, the slope of the curve described was

regarded as approximately the desired correction for the irregularsolute activity. As expected from the hydrogen bonding of the

systems, which caused large irregularities in all properties men¬

tioned above, this correction was quite large and as a result, the dif¬

fusivities at high concentrations are considerably less than the un¬

corrected values since the correction is a divisor of F in equation (4).The vapor pressure data on butanol in benzene is sparse, but the

80

activity term was believed unimportant if the trimer concept is

correct and the corresponding values for the concentration cor¬

rection are applied. The results of all this were values of the diffu-

sivities at various concentrations for butanol in water, water in bu-

tanol in benzene, all at 25°. These curves appear in figure 11.

To achieve the final correlation of all the values of the film

coefficients, the average concentration of solute in each phase for

each run was recorded as the arithmetic mean of the inlet and outlet

values. From these concentration means, the values of the physical

properties of density, viscosity and diffusivity were listed for each

phase. Possibly some other mean than arithmetic would have been

q.i*

X

\

H,0 <n BuOH u ^q

\ c

ca * - BuOH m H,0 X~

<#x oQ

— 7 1

\

\

(BuOH), m C6Ht

30 —

— 5r

N\\

\

\20 —

— 3 \\

Kv.

\

Diffusivity —sec

10 —

10'

0 20

I

0 40

1o<so— —

1

—.

.

oso

1 _\ i

I 20

Figure 11. Diffusivity versus solute concentration at 25° C.

better but no theoretical basis could be seen for it. An improvementwould certainly have been the use of the average values of the con¬

centration estimated at the interface but this was highly impracticalfor comparison purposes only.As previously stated, the film coefficients for the binary system

were found approximately linear with their corresponding Reynoldsnumbers on double logarithmic coordinates. This was a test used

during the search for a proper method of separating the film

coefficients in the ternary system. Having achieved a separation, the

wall film coefficients for both the binary and ternary systems were

plotted together and a satisfactory line of slope equal to unity could

be drawn through the points. One hundred and thirty runs were

completed but the series of eleven using 0.75% butanol in water were

81

discarded due to poor material balances, stemming from the low

concentrations involved. Two others were discarded for the same

reason. The remaining 117 runs were plotted and fell in a moderatelyscattered manner around the line of unity slope. There were con¬

siderable divergences but the total number of points was so highthat the line was considered established. As before, no consistant

evidence was present of an influence of the core flow on the wall

coefficients. This is shown by the series at varying core rates with

constant wall rates. It is true that this alone would be insufficient

evidence of the relation since it was one of the criteria used in

evaluating the separation methods tried. However, the separationmethod was independently developed and the results show an

alignment in harmony with the results of the binary system for

which no separation of film coefficients was necessary. Since this

was true for both the wall and core films, it was considered a con¬

firmation of the method of sufficient validity to free it from the bias

in its original conception. The general applicability of the method

remains open to question, however, due to the similarity of the two

systems compared.The core film coefficients f. the binary and ternary runs were plot¬

ted against core Eeynolds number producing approximately straightlines for the various series of runs. In some cases a slight curvature

could be recognized but the general impression was linearity. The

cross plots of the core coefficients at constant core rate against the

varying wall rates suggested an influence of the wall rate in some

cases but the points were so scattered as to be considered random

within the rather low accuracy limits of the results after so many

operations had been performed on them. It cannot be said with

certainty that the wall rate does not affect the core coefficients, but

within the range studied, the influence must have been small. Consi¬

derable attention was given this question; and for the experiment as a

whole, it was definitely decided that the best alignment results from

exclusion of the wall rate from the expression for core coefficient. A

plot of the film coefficients against length of the extraction column

showed an utterly random pattern. This factor was considered

definitely excluded from the final correlation. This would not be

the case for an extractor with significant end effects. The various

lines of kc versus Rec on log coordinates had an average slope of

0.52.

The problem resolved itself now to introducing the physical pro¬

perties of the solutions in such a way that the correlation of kwversus Rec 0.52 become one continuous for the different cores. This

was done by gathering together the concentration dependent terms

of equations (35) and (36). These equations depend only on dimens¬

ional analysis and the previously determined effects of flow rates.

Thus

82

kcd=b(Recp2(-^r (64)

PcDc \pcD,

kw_ (jj _\ I= b, Re,w /_J^_ „

(65);OwDw \pw*g) \pwD

For equations (35) and (36), the concentration gradients are ex¬

pressed on a volume basis. That is, the units of kw, for example, are

grams BuOH transferred

,gBuOH

sec cm e—:—r——cm solution

so that the dimensions are cm/sec. This is the coefficient defined byequation (9). These overall dimensions must be maintained so that

the left hand terms remain dimensionless. If the concentration

gradients are kept as weight fractions as defined by equation (10)the density of the solution must be introduced in the denominator.

Hence the units of —— are

Pw

g BuOH_

cm

o g BuOH g solution sec

sec cm :— :—

g solution cm8 solution

If the customary units of g/hrcm'2 are used, the constant of

3600 sec/hr must be included. Then by rearranging

dkc = b(Rec)°-520(xm) (66)

kw = b'Re'w «P(ym) (67)

where 0 and W are functions of the average solute concentrations

only. These functions were

0 (xm) = 3600 pc Dc M-)a

(68)

3600 pw Dw\Pw JJw/

V (ym) = rVTTT (69)3

/°w2gThe wall function, equation (69), was plotted for the various con¬

centrations of butanol in water using various values of from 0.3 to

1.30. The same was done for equation (68), first for the water in

butanol and then for the butanol in benzene solutions. The various

83

5 10 20 30 40 SO '00 200

Figure 12. Wall Beynolds number versus function of wall film coefficient

curves for different values of were tested in equations (66) and (67)to find the value producing the best straight line on log-log co¬

ordinates. The wall coefficients were not of great help in this since

the Schmidt group varied only from 900 for zero butanol to 4470for water saturated with butanol and the average wall concentrations

did not differ very widely. The same group for the core varied from650 for zero butanol to 1740 for 50% butanol in benzene and from2750 for zero water to 43500 for butanol saturated with water. In

this case, the average concentrations also underwent a largervariation. By trial and error, the best value for was found to be 0.50

which produced the relatively straight lines of figures 12 and 13. In

these figures, the final correlations are shown by plotting -^°—r ver-

sus Rec and;r.

,w versus Re'w wherein the value a=0.50 is* (ym)

84

coefficient

film

core

of

function

versus

number

Eeynolds

Core

13.

Figure

1000

500

400

300

200

100

50

40

30

20

10

S

Re,

°sS^

oy01^

++

X

X

4

+

a9

D

o'

»,

-ouO

+

+

+

X

X+

*"

50%

6A

^4.

D

VHjO

..

36%

2V

,.

.60%

46

0

++

_a

*„

DHiV

V

C6H6

in

BuOH

00%

10

+

.cm

30

..

©

.cm

100

..

»

tube

cm

50

with

Bina

ryO

used. It may be noted that while the points as a whole are scattered,the different types of points each representing a series under similar

conditions are equally scattered so that no serious constant error in

the generalization intrudes. This was considered more importantthan a tighter grouping of an indiscriminate majority of the points.The inaccuracy of the method when one film exerts very little in¬

fluence on the overall resistance, as does the core film in certain runs

due to the preference of the butanol for benzene, is shown by certain

regions of scattering in figure 13. This may be seen to be

unavoidable for the system used. The final equations may be written

by measuring the intercepts and slopes of these figures as

V A / II \0-5°

-^- = 8660 (Rec)0-52 M£-) (70)Pc Dc \ pc Do I

_JE^_ fltaL) t = 40.0 Re'w (-^-)°'5°

(71)pw Dw \Pw g/ \PwDwJ

Where all quantities have their usual units as stated in table 6.

This correlation is to be accepted with caution in several respects.The method of establishing the value of the Schmidt number ex¬

ponent is very approximate and the range of values is not very

great. This value is also dependent on the explained method of cor¬

recting the diffusivities which in itself is not well founded in

experimental results. The question as to the error in area measure¬

ment due to waves has been left unsolved. Whether the wall flow

exerts an influence on the core coefficients is not perfectly clear as

explained. The evidence supports the that view such influence does not

play a substantial role as was maintained by Brinsmade and Bliss 9

in contradiction to Treybal and Work.74 A moderate difference

exists in all respects between the present results and those of Brins¬

made and Bliss, the only other comparable experiment reported. For

purposes of this comparison, equations (70) and (71) may be con¬

verted into the somewhat less useful form and units used in equations(35) and (36) and then appear

*g - "2 Ota*" (-fa) TO

It may be seen that the use of a lower power of the last group, the

Schmidt number, has produced a lower value of the numerical

constants in each case.

86

Summation

It was desired to measure the film coefficients and their variation

with flow rates and physical properties in a liquid extraction systemof the most general type. In order to avoid an indeterminate inter¬

phase area, the wetted wall type of column was adopted. In order to

measure the film coefficients, a binary system, water and normal

butyl alcohol, was first to be used. Accepting the Two Film Theory,the results would give directly an approximation of the affect of the

fluid rates on the film coefficients within a limited range of flows.

The extraction rates of the ternary system, water-butanol-benzene

were to be measured under various conditions. It was desired to

elaborate a method of separating the film coefficients in the ternarysystem and to deduce a relation for the film coefficients covering the

results of both systems. The following was done:

1. The thickness of the wall layer in a wetted wall extraction

column of 2.31 cm diameter at varying rates of flow was measured

so that the area of extraction could be calculated. The results agreedwith previous works and were interpreted as showing that in the

subsequent extraction runs, the wall liquid was in turbulent flow.

2. The solubility, tie line data, and physical properties of the

binary and ternary systems were measured as preliminaries to the

extraction runs.

3. Butanol and water were passed continuously and counter-

currently through a wetted wall extractor at 25° at various water

and butanol rates and lengths of tube used. The exit streams of each

phase were analyzed. Approximate film coefficients for each solvent

were calculated from the results using the log mean concentration

differences.

4. The ternary system was passed through the extractor at 25° with

varying rates of flow of each phase, composition of each phase,direction of solute transfer, and length of tube used. The compositionof the exit streams were measured.

5. The overall coefficients based on each phase were computed bygraphical integration from the operating line for each run which was

drawn by means of continuity and material balances.

6. A graphical method of separating the film coefficients was

developed, independent of the binary system results. This method

exploited the fact that the operating and equilibrium lines were

considerably curved in the pertinent regions as they would be in

many cases in practice. Thus, concentrations at a single point in each

run corresponded to one film considered controlling and those at

another to the other film controlling. Since the overall coefficients

are applicable to the run as a whole, the difference in the overall

concentration gradients between the two indicative points must be

87

proportionate to the differing relative importance of the two films,hence the film gradients themselves. Using this proportion, the film

gradients and thus the film coefficients were solved for by trial

and error. The use of each point typical of one film assumed con¬

trolling for the measurement of the concentration gradient pertain¬ing to the opposite assumption may cause this method to be of res¬

tricted utility.7. The film coefficients of both the binary and ternary system for

each film were correlated by single relations which involved the

fluid rates and the fluid properties. The rate of each phase affected

only its own film coefficient within the range studied. The exponentof the Schmidt number was determined by trial and error choice

although the range of values for this factor was rather short. The

particulars of the final relations are somewhat uncertain but the

method was developed in a general manner. This method, when

tested on other liquid systems, is intended to be an aid in similar

situations where the more direct methods fail due to the irregularityof the solutions.

TABLE 6

Meanings and units of symbols and subscripts

a interfacial area per unit tower volume.1

cm

a' activity —

B weight rate of core flowg

hour

b,b' constants

c concentrationg mols

cm3

D diffusivityem2

sec

a differential operator or diameter cm

F parameter of diffusivityoK sec

em2 centipoise

G weight rate of solvent flow in light phaseg

hour

8 acceleration of gravitycm

see2

H slope of equilibrium line —

h effective height of tower cm

2 overall transfer coefficientg

]j film transfer coefficient

hour cm2

g

hour cm2

88

phaseheavyinsolventweightunitinsoluteweightT

wpointatgradientfilmcorex)w—(xi

cpointatgradientfilmcorex)c—(xi

phaseheavyinyw

fractionweightwithequilibriuminbewould

whichphaselightinsolutefractionweightx*w

w)(point

coefficientwalloverallonbasedlineoperatingonpointdecisiveofcoordinatexxw

phaselightinvaluesexitandentrybetweensolutefractionweightaveragexm

interface

atphaselightinsolutefractionweightxi

phaseheavyinyc

fractionweightwithequilibriuminbewould

whichphaselightinsolutefractionweightx*c

c)(point

coefficientcoreoverallonbasedlineoperatingonpointdecisiveofcoordinatexxc

phaseheavyiny

fractionweightwithequilibriuminbewould

whichphaselightinsolutefractionweightx*

phaselightinsolventweighunitinsoluteweightX

hour

gflowofratewallW

sec

cm

velocitylinearactualV

see

em

sectioncross

towergrossonbasedvelocitysuperficialu

oKtemperatureabsoluteT

cm2areainterfacials

Mc

—-—£-£=numberEeynoldscoremodifiedEec

t^l5lj?=numberEeynoldswallmodifiedEe'w'lw^

——

=numberivnolds

—numberReynoldsEe

hour——transfersoluteofrateN

—refractionofindexn<i

—integerann

cmthicknesslayerwallaveragem

hour

—^—phaseheavyinflowsolventofrateweightL

—logarithmnaturalIn

cmthicknessfilmeffective1

cmunittransferofheightHTTJ

y weight fraction solute in heavy phase

y*» yc, y*c yu ym, yw, y*w, (y-yOc, (y-yi)wsee corresponding definitions for x values

z mole fraction —

0/oH20 weight fraction water in benzene rich

solutions

affySr

exponents

weight rate of wall flow per unit lengthperiphery

g

hour cm

m viscosityg

cm sec

viscosityratio of circle circumference to diameter

centipoise

P densityg

cm8

I summation —

a

0. W

surface tension

functions

dynescm

Subscripts

A, B refer to pure substances, A and B

AO, BO» „ infinitely dilute solution of A in B,

B in A

AB„ „

A in solution of B

Cn „

continuous phasec

» „core liquid or core overall decisive

pointD

ii „discontinuous phase

iii „

interface

1mii „ logarithmic mean value

Mii „ average value

0ii „

overall value

OCit „

overall core or continuous

ODii „

overall discontinuous

OWii „

overall wall

wii „

wall liquid or wall overall decisive

point1,2 it „ top and bottom of tower

Index of Figures

1. Sketch of Two Film Situation.

2. Diagram of Wetted Wall Apparatus.3. Wall Layer Thickness versus Wall Rate of Flow.

4. Index of Refraction versus Butanol Content in Water and in Water Sa¬

turated Benzene and versus Water Content in Butanol at 20°.

90

5. Density versus Butanol Content in Water and in Water Saturated Benzene

and versus Water Content in Butanol at 25°.

6. Viscosity versus Butanol Content in Water and in Water Saturated Benzene

and versus Water Content in Butanol at 25°.

7. Water Content versus Butanol Content in Water Saturated Benzene Solut¬

ions at 25°

8. Butanol Content in Water versus Butanol Content in Benzene at Equilibriumat 25°.

9. Portion of Equilibrium Curve Showing Operating line T34.

10. Surface Tension versus Butanol Content in Water at 25°.

11. Diffusivity versus Butanol Content in Water and in Water Saturated

Benzene and versus Water Content in Butanol at 25°.

kcd12. versus Bec Final Correlation

9 (xm)k

13. —— versus Ee'w Final Correlation

Index of Tables

1. Parts of Apparatus.2. Binary System Eesults Giving xi, y2, W, B, 8, Bew> Bec, kw, and kc.3. Butanol Distribution Concentrations Between Water and Benzene at 25°.

4. Ternary System Eesults Giving xi, X2, yi, y2, percent imbalance, W, B, S,KWi and Kc.

5. Calculated Ternary Eesults Giving EeCi Rew> xw, yw, xc, yc, kw, kc.6. Symbols and Their Units.

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92

BIOGRAPHY

I was born May 21, 1923 in Berkeley, California U. S. A.,

the son of Arthur I. Morgan of Kansas and Agnes Fay Morgan

of Illinois. I attended grammar school and high school in Ber¬

keley, California, and entered the University of California in

Fall, 1940. I received the degree Bachelor of Science in Che¬

mistry in Fall, 1943. After three years service in the U. S. Navy,

I returned to the University of California in Fall, 1946 and

received the degree of Master of Science in Chemical Engineer¬

ing in Spring, 1948. In Summer, 1948 I entered the present

study under Professor Dr. A. Guyer of the Swiss Federal In¬

stitute of Technology in Zurich.