from the important, but often more tractable, Aslde ‘problem of prediction of transport properties, the fundamental question in physical separation processes is the prediction of phase equilibria. Regardless of the nature of the process, be it extraction; ordinary, extractive, and/or azeotropic distillation, extractive or fractional crystallization, etc., its design requires accurate knowledge of the equilibrium distribution of components between the contacting phases, Le., of component separation factors. In a thermodynamicsense, design requires detailed knowledge of component activity coefficients in the equilibrium phases. The predictions of these quantities from a minimum of experimental data is the broad scope of this series of two articles. In summary, extensive correlations are outlined for the prediction of separation factors of a wide range of substances for use in physical separation process applications. The 6rat type of correlations provides estimates of limiting activity codficients of solutes in pure solvent phases and of their dependence on temperature. These correlations are based largely on empirical relationships between molecular structure and nonideality of components in solutions and form a major aspect of this first article. The second type of correlations provides means for estimating compositional effects on the values of such limiting quantities, in liquid or vapor phase, and so translates them for direct use in actual multicomponent system. While these are somewhat further introduced below, the second article of this two-part series will describe these correlations in detail (Industrial and Engineering Chemistry, September 1963). By definition, activity coefficients are a measure of the deviation of a mixture and of its components from ideal behavior. The latter is in turn rigorously defined by the properties of the pure components in their standard states. (For convenience, the standard state in the liquid phase is defined as that of the pure component under its own saturation pressure; in the gas phase, that of the pure component at a pressure of one atmosphere; in the solid phase, that of the pure solid at the atmospheric melting point.) In the standard state the activity codfieient is unity by definition. Mixtures are ideal, and corresponding activity coefficients are therefore unity, when the behavior of their components can be rigorously derived from their properties in their standard states by the usual ideal solution laws, for example, Raoult’s law. Correspondingly, the behavior of any mixture can be resolved into that of an ideal part, and of a nonideal or “activity coefficient” part. In regards to the ideal part of solution behavior, its systematics are in many cases reasonably well in hand. Although the subject is outside the scope of this paper, a brief summary of its status is pertinent. In general, standard property values are available for many compounds. When not, they can be calculated fairly accurately by analogy from the corresponding property values of compounds of similar structure. For example, the thermodynamic properties as well as many of the transport properties of mmt organic gaseous compounds 40
INDUSTRIAL AND ENGINEERING C H S M I S T R Y
svstemalic seoaralion--
-
~
PREDICTION OF
~
I
FACTORS
SCREENING ESTIMATES Part 1 CLINE BLACK E. L . D E R R M. N. PAPADOPOULOS
y, . .. :, ..;.?;1 c ,.\\, y .
\
h ,
\
\\
-4”
-
can be so calculated. Similarly, many of the properties of organic liquids can be calculated, for example, vapor pressures, heats and entropies of vaporization, heat capacities, and molal volumes. For solids, only the beginnings of property correlations have been made, and these for organic molecular crystals only; yet there is adequate hope that this class too may yield to similar systematic correlation. Much more complex is the situation regarding the nonideality of solution behavior, the subject proper of these articles. Most important, therange of nonideality is enormous. Even when one confines the field to that of mixtures of organic nonelectrolytes, activity coefficients of components may range over several powers of ten in magnitude. It is of course just this range of behavior which gives rise to almost an infinite number of separation possibilities. Yet, for a long time our knowledge of the systematics of n o n i d d i t y was unsatisfactory. Systematics based on knowledge of the properties of the standard state alone (for example, Scatchard's cohesive energy densities or Hddebrand's solubility parameters) have been very useful, but often give estimates too crude for practical process purposes. A somewhat different but quite successful approach to the problem is presented here. I t is largely based on empirical rules obtained from the observed systematics of nonideality in structurally similar systems. Its application for the present has been conhed to mixtures composed of nonelectrolytes, mostly organic. However, there is considerable hope of its successful future application to other systems as well. Much of the subject matter is the result of the efforts during thc last fifteen years by a group in our Physical Chemistry Department, and has appeared as several papers in the p u b l i e d literature OVR this p m o d (26). Rather than give an exhaustive review of accumulated correlations, this paper instead attempts to give the reader a working insight into the methods used in our laboratories to define, tackle, and solve physical separation process problems encountered primarily in the petroleum and petrochemical indus-
of interest is usually present at zero concentration, that is, at infinite dilution. As will appear in later discussion, the choice of infinite dilution is a convenient reference point. At this dilution the nonidealities of components have their maximum values. The empirical rules which govern the dependence of nonideality on concentration are best formulated by making use of infinite dilution parameters. As a further simplification, the nonideality of vapor phase is neglected in screening. Approximate as it must be, screening is by no means qualitative. Although often screening uses but a few experimental correlation parametem, it can represent reasonably accurately the nonidealities of very large numbers or classes of compounds. Thus, with but three parameters, the limiting activity coefficients in a given solvent of mentially any hydrocarbon can be represented to about twenty percent, although the value
tries.
The subject has been divided for convenience in two parts--screening and design. The emphasis in both is on vapor-liquid systems. However, the methods are fairly duectly extensible to liquid-liquid systems, and i n some cases to solid-liquid situations as well. I n general, systems in which compound formation occurs have been excluded, although cognizance has been taken of hydrogen-bonded or weakly associating systems. The 6rst or screening part provides the general tools for narmwiug down the selection of the solvent system or systems and of the approximate range of process temperatures; for defining the approximate magnitudes of activity coefficients of the various components to be separated once such a d e c t i o n has been made; for delineating the limits of feasibility of the separations envisioned; and for providing guidance for the ensuing minimum experimentationnecessary for design in detail. In general, the screening is done with simpWed liquid systems in which the component or dass of components
of the coefficients often spans a range of several powers of ten. More or less exact predictions can be made for other systems, depending largely on the amount of experimental information available on their standard states and on their simple mixtures. I n its essence, screening utilizes an economic representation of large numbers of systems with a minimum of empirical or semiempirical parameters. The second or design part finishes the job. It also utilizes an economic representation of the effect of the important process variables on the magnitude of the separation factors, but to the high accuracy required for actual design. This part establishes in detail the effects of component concentration and mixture composition on activity coefficients in multicomponent systems; it also provides the methods for checking the consistency of VOL 5 5
NO. 8
AUGUST 1963
41
and for making maximum use of the experimental data which are available or can be obtained on systems of process interest. I n addition, the second part gives a complete treatment of vapor phase nonidealities. Specifically, by the use of suitable empirical structural parameters and equations of state, this section makes it possible to predict accurate values of the critical constants for a very large number of organic compounds. It establishes the effects of mixture composition and nature of the components on the magnitude of component nonidealities over a broad range of the reduced critical variables in multicomponent gas mixtures. Further, it quantitatively
defines the effect of gas phase total pressure on liquid phase free energies. Obviously, in the final step of making the actual design calculations (for example, the calculation of yields and purities of products in multistage operations), one can and does make use of modern computational techniques. I n fact, even prior to this step, both the data reduction and the actual calculation of the pertinent parameters in simpler laboratory systems have been so mechanized in many cases. Description of such techniques actually lies outside the scope of these articles, since their choice often depends on the nature of the process and of the available computational equipment.
SCREENING EST1MATES General tools for narrowing down selection of separation conditions The basic factor in the consideration of separating components by distillation is the relative volatility, a. Neglecting for the moment vapor phase imperfections, this a for key components i, j is given hy 7 , P r " / y P j o , i.e., in terms of the components' activity coefficients y and saturation vapor pressures Po. A convenient picture for the representation of the volatilities yPo is a plot of the logarithm of this product against the inverse of the absolute temperature (Figure 1). For screening purposes in all varieties of distillation, thii volatility factor can be considered alterable primarily through changes in they values. In any distillation operation the pertinent activity coefficient may vary between the value y = 1 for the environment of the pure compound of interest and a value y = yo, the limiting or infinite dilution activity coefficient for an environment composed solely of other compounds of the mixture or of the material employed as a solvent. Thus, volatilities can be considered embraced in bands defined by these two extreme environmental limits. The job of screening is the conspuction of such bands. The principal task of conspucting the volatility bands reduces to that of estimating the pertinent activity coefficients. Vapor pressures are generally available, certainly for hydrocarbons. When not, they can be estimated from values of homologous or otherwise related compounds, with boilii points and heats of vaporization as the bases. Heats of vaporization in turn may be calculated using the systematic correlations of Bondi (6)or from Hildebrand's or Trouton's rules. The use of activity CoeRicients as the screening parameters has of course the inherent value that these thermodynamic quantities can all be calculated from three types of phase equilibria (liquid-vapor, liquid-liquid, 42
INDUSTRIAL AND ENGINEERING CHEMISTRY
and liquid-solid) and are hence available from a wide range of data. Particularly, the use of limiting or infinite dilution activity coefficientsis most suitable for systematic correlations, because these quantities not only represent convenient common points, but in general represent the maximum deviations from ideality and therefore possess maximum sensitivity to structural factor changes. However, for proper utilization of structural correlations it is necessary that available experimental data be readily convertible to limiting gammas at the temperature of interest. While the details for such conversion of the data are fully treated in the design article of this series, some mention of the simplified techniques used for screening purposes may be pertinent here. Preferably, isothermal phase equilibrium data should be used for simple binary systems in which the component of interest is present at a low concentration level. The finite-concentration activity coefficients can then be approximately derived from the measurements, e.g., (1) liquid-vapor, yt = (yP)/(xlP1°), whereyl, x1 are mole fractions in the vapor and liquid, and Pis the total pressure; (2) liquid-liquid, y1 = yl'xl'/xl, where the primes refer to the second liquid phase; and (3) liquidsolid, y1 = xid-,/xl, where the ideal solubility xidal is a function of temperature and heat of fusion. The translation to the infinite dilution values can be d e c t e d by using the simple unmodified van Laar expression log y o u = (log
rid
(1
+ R Xi/x3'
Here, the ratio R = log y'1Jlog y0s1can be assumed to he unity or assigned a value based on more extended data. For nonisothermal data obtained with simple binary systems, small interpolations or extrapolations often
suffice to bring the data to the temperature of interest. Otherwise, approximate temperature effects may be estimated, for example, by assuming the system to obey the regular solution form of temperature dependence, Le., that log y o is proportional to 1 / T . As discussed later, in many cases the limiting heat of solution may be estimated from structural correlations and so furnish a more exact basis for temperature extrapolation. Structural Correlations
c
As noted earlier, solution theory does not yet permit reliable estimates of activity coefficients to be made on the basis of the properties of pure compounds alone. However, it has been possible from a minimum of data on solutions to establish the empirical correlations below which allow satisfactory predictions of these quantities to be made over a broad range of systems by simple use or" available data for structurally related compounds. Although these correlations emphasize hydrocarbons and organic nonelectrolytes, the continuously increasing fund of literature data on other systems may well provide the basis for extension of these or similar correlations to a broader area. Structural parallelisms based on observed changes of the limiting activity coefficient with molecular weight, molecular configuration, and functional group type form the basis of the correlations. As the details and range of such relationships have been presented in previous papers, we shall emphasize here the simplicity and utility of these structural patterns for screening purposes. I n general, the purpose of the correlations is to define properties at a desired point in a field in terms of known properties at another point in the same field, as pictured in Figure 2. Let us imagine, for example, that Figure 2 portrays the activity coefficients of a given series of solutes, say,
paraffins, in a given series of solvents, say, aliphatic alcohols. T h e choice is deliberately simple in that only two functional groups are represented-the paraffin or methylene group and the hydroxyl group. I n such a case, a family of lines describes the system, each line representing the activity coefficients of paraffins in a given alcohol. The slope of each line, B, is a property of the particular solvent. Since the lines are approximately straight, two points will determine the behavior of paraffins in that solvent. In fact, in many cases each line may be determined by a single point, since the 7) B is generally valid. relationship log y o l = (nl Moreover, if one were to choose a solute series other than paraffins, say, aliphatic acids, one would obtain a similar pattern of lines, which would in addition have the same slopes as the paraffin solute series. In other words, the carbon number or methylene addition effect on the activity coefficient of any homologous solute series, i.e., the constant, B, is a property of the particular solvent. Small deviations from strict methylene group additivity may occur in first members of a homologous series, particularly if the series contains a strong polar group. However, such deviations turn out to be Characteristic of the particular solute series only, and, once determined, can be applied to any solvent environment. Similarly, as Figure 2 suggests, simple and approximately additive relations define the effect of solvent methylation on the level of the activity coefficients of the solute series. Deviations from additivity of these relationships are similarly uniquely characteristic of the solvent series.
+
Fixed Solvent Environments
The fixed solvent environment situation, given analytically by log 71' = K Bnl C/nl
+
+
Figure 2. Correlation grid. Such a plot enables us to dejne properties at a desiredpoint in afield in terms of known properties at another point
CARBON NUMBER OF SOLUTE
VOL. 5 5
NO. 0
AUGUST 1963
43
Correlations based on molecular structure extend experimental data.
presents perhaps the simplest and yet technologically most important structural correlation. It has been particularly useful for the description of the nonideality of a large number of solute homologous series in water, as well as for that of all hydrocarbon solute series in a great number of polar organic solvents. In view of the importance of hydrocarbon separations, let us consider how the foregoing simple relation may be applied to the screening evaluation of extractive distillation solvents with a minimum experimental effort. We shall regard all hydrocarbon solutes (paraffins, olefins, alkyl benzenes, alkyl cyclanes, etc.) as methylated series of differing characteristic groups, for example, double bond (olefins), saturated ring (cyclanes), and unsaturated ring (aromatics). I n a given solvent, the effect of methylation or alkyl addition is the same constant B, characteristic of the solvent alone. The constant C is characteristic of the particular functional group in the various hydrocarbon series, and is solvent-independent. The constant K is a function both of the solvent and the particular hydrocarbon solute series. However, further simplification of this pattern occurs, particularly if the pattern of the hydrocarbon activity coefficients is available for a single solvent, which then may be chosen as the reference for screening any other solvent at all. As discussed in a previous paper (70), with heptane solvent as the known reference, any solvent of interest may be screened by measuring the activity coefficients of just three hydrocarbon solutes, from the values of which the activity coefficients of any hydrocarbon type and molecular weight are determined :
I n this equation, r and s refer to the two solvents, of which r is the reference solvent, K,, and B,, are exclusively solvent parameters, and z is proportional to the hydrogen deficiency of the hydrocarbon solute of interest. In other words, the important parameters that govern hydrocarbon separations by the use of selective solvents are two-size and hydrogen deficiency. Incidentally, the foregoing formulation is directly applicable to liquidliquid extraction: The left hand side of the expression is simply the limiting distribution coefficient of the hydrocarbon solute between the two solvent phases-the reference phase r which may be either a hydrocarbon mixture itself or a polar solvent, and the extracting solvent phase. I n spite of the simplicity of this relationship, its representation of experimental data is remarkably good, as shown in Figure 3. Refinements are of course possible. As shown in Figure 4, such minor structural factors as the position of the double bond in olefins can be accurately predicted by observing simple counting procedures which are independent of the solvent system. 44
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
It is clear that from the precision standpoint all such grids should be constructed with the base-compound experimental points taken for hydrocarbons widely different in molecular weight and in unsaturation. Especially dangerous of course are values extrapolated from two points closely spaced in carbon number. It should be emphasized also that hydrocarbon data for a wide range of solvent structures such as are summarized in reference (26) can be very useful in estimating the molecular weight sensitivity B for similarly constituted organic solvents. Such B values, once estimated, are of course applicable also to methylated solute series other than hydrocarbons. An idea of the truly broad spectrum of solvent selectivities and capacities for hydrocarbons may be obtained from the summary Figure 5 . This plot depicts over thirty different solvents with regard to their type and selectivity for hydrocarbons (expressed as the hexane/ benzene ratio in the ordinate) and their solvency for the least extractable-least hydrogen deficient-paraffin series (expressed as the hexane gamma in the abscissa). The selectivity-capacity range encorr-passes two to three logarithmic cycles in magnitude, therefore the possibilities of solvent choice are numerically almost overwhelming. Yet some systematics in solvent groups are already discernible ; for example, type selectivities at given capacity are maximum for sulfones, lower for nitriles, lowest for hydrogen-bonded hydroxyl solvents. Varying Solvent Environments
Structural parallelisms can be drawn for situations where the solvent environment is varied homologously. The analytical expression employed for this case is:
for the behavior of a component of carbon number nl in solvent n2. As the carbon number of the solvent changes from 722 to n’2, say, by methylation, the relative behavior of component 1 in these two homologous solvents is given by
The B constant is the same as the B described previously and expresses the molecular weight selectivity of the solvent homologous series. The F-term is characteristic of the functional (polar) group in the solvent series of interest. Like the C-term for the solute series, it may be estimated from two members of the same or a similar solvent series, or (particularly at moderate solvent molecular weights) it may be simply ignored. A convenient solute for determining F in a homologous solvent series is one having no hydrocarbon grouping, e.g., water, so that the B term can be ignored. The C- and F -
0 Normal paraffins D Naphtheno.arornatnr
Figwe 4. OlcJFn cmrclafion. Conridnalion of shrctwol factors rc&s accuracy of tlu cwrclotion
11111PENIANE
DMf
I
36
20 SOLUTE CARBON WUMBIR Figurc 3. Thee-poinf rcpcsmfation of hydrocurbom in dicthylrm glycol‘bptanpt,,rolvmts. A l t h q h such d plot is bared on = vny simple relation&@, it repcsmts expmhmtnl daro quirt well
F i p e 5. Selecfiuitv-solvemy for hexme-bnunu. This m m n r y shows thd wide mngc of pnfomnccpossiblc with &&mzt soluents. Sulfones me s h o w a( solid circles, nifriles ar sgumcr, hydrogm-boded hydro.$ solnenfs a( opm circles
i
i
F i p t 7. Correlation of w a t n in alcohols
Solution theory does not yet permit the estimation of activity constants are typified by the correlation of normal alcohols in water and water in alcohols in Figures 6 and 7. Variable Solvent and Solute Environments
The more general situation of simultaneous variation of both solute and solvent structures is represented analytically by log 7’1 = A
+ ( C / d + ( B / n z ) n ~+ ( F / n z ) + D(n1 -
~ 2 2 ) ~
Here A is a single constant uniquely applicable to a particular “homologous binary,” as a binary series of monobasic aliphatic acids and aliphatic alcohols. Once determined, A is used directly for all combinations of members of the two homologous series. As discussed previously, C and F are deviation factors characteristic of the two series, and are thought to arise from nonadditive interactions in the immediate vicinity of a substituted polar group. The B factor, as stated, reflects
of activity coefficients. This method is currently being modified to handle polyfunctional group situations, although its validity in such situations has not been fully tested as yet. The method utilizes the full concentration range gamma data for a binary, for example paraffin-alcohol, which can be reduced to a binary solution of hydroxyl and methylene groups, independent of the sizes of the molecules to which these groups are attached. Thus, with the data from a single such binary, the activity coefficients of a wide variety of alcohols, polyols, water, and paraffin compounds may be reasonably well represented, as shown in Table 1. Other group combinations such as methylene-nitrile, methylene carbonyl. etc., have been similarly correlated. The details of “solutions of groups” calculations are given elsewhere ( 7 I ) , but a summary of the method may be pertinent here. Briefly, the measured molecular activity coefficients are broken into entropic and interactional contributions. For componentj in the mixture:
1% TABLE
1.
ACTIVITY
COEFFICIENT GROUP METHOD
PREDICTION-
Basis: Data for a single paraffin/alcohol binary system
Solute Octanol Octanol Water Heptane
Solvent Water Propanol-52 mole 70 Octane-20.7 mole yo Water-27.2 mole yo Decyl Alcohol Ethylene Glycol
Log y o of Solute Ex$. Calc. 3.97 3.85 0.08 0.00 0.63 0.69 0.52 0.59 0.63 0.79 2.84 2.72”
molecular weight selectivity, i.e., the change of activity coefficient of the solute with increasing methylation. The small D-term on the other hand is completely systemindependent and has the function of adjusting for the decrease in gamma observed when the size difference between solvent and solute molecules becomes large; it thus may be regarded as an entropy term. The use of the general expression is no different from that of the “fixed-solvent” or “homologously changing solvent-fixed solute” more restricted cases, except that since more constants have to be determined the parallelisms are less direct and possibly less precise. Group Method for Varying Solvent-Solute Environments
An extension of the foregoing methods toward a broader systematics of structural parallelisms is represented by the “solution of groups” method ( 7 7). This method, especially useful for mixtures of two functional groups, shows promise in further reducing the number of empirical parameters required for screening estimates 46
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
71 =
(1%
’Y3)S
+ (1%
YJ)G
The entropy portion is calculated by an expression analogous to that of Flory-Huggins, in which the volumes of all atomic groups in the molecule have been assigned the same arbitrary value except hydrogen, which is ignored :
where v and x refer to the number and mole fraction of such groups, respectively. The interaction portion is calculated as a sum of group where rk activity coefficient differences, (Pi,- I?&*), is the activity coefficient of group k in the environment of interest and rk* is that in the standard state group environment. The resulting expression is
where u t , is the number of groups k in moleculej. Thus expressed, the group parameter Fx is assumed to be a function only of the relative concentration of groups k in the mixture, regardless of the particular molecular configurations these groups may be attached to. Of course the predictive accuracy of so broad a method is not expected to be as great as that afforded by the somewhat more restrictive correlations presented earlier. Particularly, its accuracy probably suffers from the somewhat arbitrary-and inadequate-choice of representation of entropic contributions. Yet by carrying the concept of structural additivity to its natural extreme, namely by considering the group building blocks apart from their aggregates in molecules, the method can and does utilize data other than those at infinite dilution to advantage.
coefficients from the properties of pure materials alone TABLE
2. ACTIVITY COEFFICIENT PREDICTIONS, SCATCHARD-HILDEBRAND RELATION
Solute
*
Hexane Benzene Benzene Ethylbenzene Hexane Sulfolane Hexane Cetane Propionitrile Acetonitrile Water n-Propyl alcohol
1
Solvent Benzene Hexane Cetane Heptane Sulfolane Hexane Sulfolane. Sulfolane. Heptane Heptane n-Propyl alcohol Water
log y o , 25’ C. Calc Ex$.
.
0.332 0.224 0.087 0.163 2.93 2.12 1.86 2.95 0.52 0.77 1.96 8.16
0.308 0.187 0.060 0.212 1.86 2.79 1.86 3.25 1.09 1.41 0.56 1.07
a The solubility parameter for sulfolane has been empirically determined from the hexane/binary experimental data, as shown.
50
40
30
Estimates of Temperature Dependence
T h e prediction of heats of mixing and of the associated partial molal heat contents of components in solution is useful per se, but particularly so in the determination of the change in activity coefficients with temperature :
b log y & ( l / T )
= H,“/2.3
R
I n the special case of regular solutions the heat of solution represents the entire nonideality in the mixture. For such a case the utility of predictions of excess heats is obvious. For the general case of nonregular solutions, excess heat correlations can beneficially augment the correlations for excess free energy, that is for activity coefficients, even without the parallel development of excess entropy systematic relationships. Intuitively one might expect that excess heat correlations, which by definition exclude such nonlinear effects as the entropic ones of molecular size and shape, are probably more directly related to the “building block” interactions which form the basis of the free energy systematics. Hence, a systematics of group excess heats is probably simpler in form and requires fewer parameters in its formulation. Although such systematics have been only partly developed (28), a number of very simple relationships have been already obtained. For example, excess heats of paraffins in polar solvents are well represented by the single-constant relationship H: = J n l . Conversely, the excess heats of polar solvents in paraffins are independent of paraffin size H: = J n 2 = constant. Similar relationships yield the excess heats of other homologous hydrocarbon series in polar solvents and vice-versa. The Scatchard-Hildebrand Method
As mentioned earlier, the Scatchard-Hildebrand relationship (18) presents the only practical means for estimating solution behavior exclusively from pure component physical properties :
20
log
10
~~~
20 40 60 80 PERCENT AROMATIC CARBON ATOMS Figure 8. 2 5 O C.
~
~
V1 (61 - 6 ~ ) ~ / 2 RT .3
where VI is the molal volume, and 61, the solubility parameter, is given in terms of the heat of vaporization and the molal volume by
1(
Estimating activity coej’icient of ethanol in butylbenzene at
Cline Black is an engineer with Shell Development Co., Emeryville, Calif., and E. L. Deir is a chemist with the same company. M . N . Papadopoulos, a research supervisor with Shell Development when this article was prepared, is now a senior technologist at Shell Oil Co.5 Norco, La., refinery. AUTHOR
71 =
This classical relationship continues to contribute much to the understanding of solution behavior. However, it is important that its limitations be recognized in the estimation of activity coefficients even for screening purposes. I n general, as shown in Table 2, predictions are satisfactory for mixtures where small, nondirected interactions are involved, e.g., in hydrocarbon-hydrocarbon solutions. T h e behavior of polar substances in nonpolar media is represented erratically. Water in paraffins (78) is estimated surprisingly well, but sulfolane, acetonitrile, and propionitrile, all in paraffin solvents, VOL. 5 5
NO. 8
AUGUST 1 9 6 3
47
are predicted to not much better than two- to fivefold. Hydrocarbons, both paraffins and aromatics, are predicted even less well in polar solvents. Even when a n arbitrary solubility parameter has been established for the polar solvent, no generally satisfactory basis may be formulated for prediction by structural analogy. Thus, cetane in sulfolane is poorly estimated even when the solubility parameter for sulfolane is empirically obtained from parallel data on hexanesulfolane. A more general picture of the predictability of hydrocarbon behavior in polar solvents by the S-H relationship is shown in Figure 5. An S-H calculated curve is shown as a black curve, which was obtained by using experimentally determined solubility parameters for all solvents in terms of solvent-hexane available data. It is interesting that the S-H line roughly coincides with the experimental selectivity-capacity envelope formed by the more type-selective solvents. T h e greatest deviations are observed with hydrogen-bondcd solvents and solvents which may form weak complexes with the aromatics, but not with the paraffins. Clearly it cannot be expected that such chemical effects should be predictable by any theory which is based solely on physical properties of pure materials.
104
1 03 'L
102
O+
10
30
10
I n contrast to the fair success of excess free energy and excess heat correlations, correlations for excess entropies are in their infancy. T h e fairly restricted FloryHuggins expression for the excess entropy in binary solutions of liquids is essentially the only equation available for estimating these quantities, and then only in terms of the relative sizes (molal volumes) of the molecules in solution. T h a t such a representation is generally a n inadequate one is not surprising since this expression does not take into account the effects of spatial configuration of molecules. T h a t spatial configuration as well as molecular size and packing density are important factors in elucidating this problem has been demonstrated by Bondi in his correlation of entropies of vaporization of hydrocarbons and some of their polar homologs (6). Undoubtedly, this or a similar approach may be found useful in treating excess entropies in liquid solutions.
90
Figure 9. Volatility inversion in but~lbenzene-ethanol-water system. Temperature is plotted on a scale of rec$rocal of absolute temperature
~5
0
Excess Entropies
70
50
TEMPERATURE, "C.
*
1 -
0.1
TABLE 3.
0 50 75
A 1
A2
N
y 3 A3
A 4 100 (Azeotrope 0
-
P(4
EXAMPLE:
Solvent
- -
3.8 11.5 25
-
12 )
h
EXTRACTIVE DISTILLATION, 100' c.
Yo
yo
Ethanol
Water
Ethylene Glycol Dimethyl Formamide
5
1
0.7
1
1
a , Ethanol/ Water
11 1.6 0.83 0.33
3.5
50 Examples of Screening Applications
As a n illustration of the application of the foregoing, let us consider the solvent possibilities for the separation of ethanol from water by extractive distillation. We observe that the problem is essentially reducible to the separation of a pure hydroxyl group (water) from a mixed methylene-hydroxyl group (ethanol), I n general, solvents which possess reasonable selectivity for either one of these two group types, and a t the same time possess reasonable capacity for both, should be considered first. Let us now look at the tabulation of limiting activity coefficients of these two compounds in various solvents, Table 3 . All values have been calculated by using the 48
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Solvent
Butyl Benzene Ethylene Glycol Water
Ethanol/
j
y o Ethanol
y o Water
Watera
1
23
420 1 1
15.6 16.1
CY,
-
3.5 3.4
~-
appropriate screening procedures. For example, the value shown for ethanol in dimethyl formamide was estimated from trade literature data on the solubility of a C, alcohol in this solvent, coupled with available paraffin-dimethyl formamide data for the molecular weight effect. T h e values for ethanol and water in octyl alcohol were estimated from already available homologous correlations (26). T h e value for ethanol in butylbenzene was estimated in terms of a crude aromaticparaffin group concentration treatment as shown in Figure 8. T h e values for both water and ethanol in ethylene glycol were available in the literature, but they also could have been estimated from the alcohol correlations (with rules for polyfunctionality) since the same types of binary groups-methylene and hydroxylappear in both systems. It is evident from the magnitudes of the calculated ethanol/water a-values that ethylene glycol and dimethyl formamide would yield ethanol as a n overhead product. T h e nonpolar solvents, butylbenzene and octyl alcohol, would instead produce water overhead. I t is also clear that the solvents dimethyl formamide and octyl alcohol would provide no practical separation of the two compounds of interest. T h e rather dramatic volatility inversion produced by butylbenzene is pictured in Figure 9. I n pursuing this separation example further, we may examine possibilities other than extractive distillation, e.g., liquid-liquid extraction and extractive crystallization. First liquid-liquid extraction considered, it is easy to show that with the same activity coefficients estimated for extractive distillation in Table 3, a n ethanol/water relative distribution factor of 15 may be calculated using butyl benzene as the nonpolar extractant and either water or ethylene glycol as the polai. counterextractant, Table 4. Regarding extractive crystallization, the possibilities of dehydrating ethanol by freezing are illustrated in Figure 10, a plot of the solubility of ice in various ethanolsolvent environments as functions of temperature. Recalling that the solubility of any solid in a n environment with which the solid freezes out as a pure compound is given by the ratio of its ideal solubility (approximately calculable from its heat of fusion and melting point) over its activity coefficient in the liquid environment, one may ,reduce the concentration of soluble water in the ethanol liquid solution simply by lowering the temperature. However, as shown in Figure 10, even a t -74’ C . the calculated concentration of water in ethanol is still 20% higher than in the normally boiling ethanoI/water azeotrope. By adding ethyl ether to the liquid phase the activity coefficient of water is increased (and its solubility correspondingly decreased) so much that at high ether concentrations the water/ethanol ratio can be reduced to 0.1%. I n making these estimates, the pertinent activity coefficients were estimated from- ambient temperature homologous correlations using a 1/ T temperature extrapolation.
Nomenclature
relative volatility activity coefficient y mole fraction in vapor x mole fraction in liquid y o = limiting, infinite dilution y r = group activity coefficient T = absolute temperature R = gas low constant P = total pressure Po = vapor pressure of pure component V = molal volume He = excess partial molal heat content AHv = molal heat of vaporization 6 = solubility parameter n = number of carbon atoms v = number of atomic groups not including hydrogen A , B, C, F, D,K = homologous (Pierotti) correlation constants J = excess heat correlation constant G, S = subscripts denoting interaction and entropy effects a: y
=
= = =
LITERATURE CITED (6) Bondi, A., Simkin, D. J., A.Z.C.h.E.J. 3,No. 4,473 (1957). (10) Deal, C. H., Derr, E. L., Papadopoulos, M. N., Znd. Eng. Chem. Fundamentals 1,17 (1962). (11) Deal, C. H., Wilson, G. M., Zbid., 20 (1962). (18) Hildebrand, J. H., Scott, R. L., “Solubility of Nonelectrolytes,” Reinhold, 1953. (26) Pierotti, G. J., Deal, C. H., Derr, E. L., TND. ENG.CHEM.51, 95 (1959). (28) Redlich, O., Derr, E. L., Pierotti, G. J., J . Am. Chem. Soc. 81, 2283 (1959); Papadopoulos, M. N., Derr, E. L., Zbid., 2285 (1959).
N O T E : The above references are cited in this article. A complete bibliography will be included in Part 2, IIEC September 1963.
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