1366
INDUSTRIAL AND ENGINEERING CHEMISTRY
becomes the extrapolated liquid density since benzene is solid a t this temperature. I n the same way since ethylbenzene boils at 136.2", any compound with a higher boiling point has a vapor density less than 1 in the fifth decimal place at 0 " C. and above this temperature a becomes the liquid density a t 0" C. to five decimal places. The equation for the evaluation of the vapor density only holds for nonassociated liquids. However, if determined vapor densities are available for associated liquids the amount of association can be obtained by comparing the determined value with that calculated for the monomolecular value.
Vol. 41, No. 7
LITERATLRE CITED (1) Antoine, C., Compt. rend., 107, 1143-5 (1888).
( 2 ) Dreisbach, R. R., and Spencer, R. S., IXD. ENG.CHEW,41, 1i(i (1949). (3)
Goionoski, E. J., Aniick, E. H., and Hixon,
H., Ibid., 39, 134h
(1947).
(4) Lange, N. A , ed., "Handbook of Chemistry," 3rd ed., Sandusk? Ohio,Handbook Publishas, Inc., 1939. (5) Schmidt, A . J . chim. phys., 15, 97-153 (1917). (6) Thomson, G. W., Chem. Reus., 38, 1-39 (1946). (7) Thomson, G. W., private communication. R m s r v a n Junr 11,1948.
Separation of Hydrocar ons by Solvent Extrac RELATION OF DISTILLATION, VAPOR-LIQUID EXTRACTION, AND LIQUID-LIQUID EXTRACTION HENRY J. HlBSH3IAX ESSO Laboratories, Standard Oil Development Compuny, Elizabeth, S . J . Equations relating the separation selectivities, a , for distillation; 8, for liquid-liquid extraction; and y, for vapor-liquid extraction are derived thermodynamically. For separation of components w-hich follow approximately the perfect solution and gas laws (such as hydrocarbons) the relationship 01 X p = y is approximately true w-hen the proper definitions of CY, 6, and y are used.
T
consideration of the tR-0 equilibrium liquid phases involvcd ili liquid-liquid extraction and t,heir equilibrium vapor. I n such H t,hree-phase system the liquid extract, phase with the ve,por phase constitutes a simple vapor-liquid extraction system which must be related thermodynamically to the simple liquid-liquid extraction system formed by the two liquid phases. The components A and B to be separated are chosen such that the following relation exists between their activities, a , as solutw a t infinite dilution in the solvent a t t.he temperature involvcd:
HIS article presents equations relating the separation selectivities, CY, for distillat,ion; p, for liquid-liquid extraction ;
and -1, for vapor-liquid extract'ion. These relationships are useful in two principal respects. First, they show the fundamental interrelation and the relative limitations and advantages of the t,hree methods of separation. Secondly, they indicate that a broad survey of the possibility of separating a large number of compounds from each other by these three met,hods can be made with a small amount of experimental data. While the first part of this article is confined t o the derivation of 'the selectivity interrelations, the second part will present the results of a broad survey of the possihilitiea of separating hydrocarbons by solvent extraction. The selectivity factors--a, p? and y---have bee11 used in the past for the design of separation processes by methods adequately covered in the literature (3-6). Although two r tors (2, 8) have implied that a, relationship exists among these factors, it has usually bren customary to define them in an arbitrary manner such that each w i s greatw than unity. This practice is adequate nhen considering N separation by one DloCess at a time, but tetlds to obscure aIlv lnterlelatlorl amollA the three processes such as the simple relationship a X p = 7, which is subsequently deiived Cor h>dr ocltrboii separations In the following derivation, redefinition of components for calculating p , and is essential for arriving at a u~liversalrelationship among the separation selectivities and in a few instances, results in selrctivities which are reciprocals of the selectivities obtained by the usual definitions. I n many cases no changr in U , 6, or y reaultr. The definition ~ n arrived s at bv x
> a,H
aA
(1)
which, where the vapors behave as perfect gases is sirnpl?,
for equiniolar solutions of A and B in the solvent a t concentratioils There Henry's law applies. The term vapor-liquid is used herein in the broadest sense embracing the processes often referred to ns azeotr opic and extractive distillation which differ only in that the proximity of the volatilities of the feed and solvent used in azeotropic distillation results in formation of a constant boiling mixture between the solvent and one or more feed components. The only assumption made in the following derivation is that the vapors behave as perfect gases. Under conditions such that the. deviations are appreciable, fugacities may be used directlv. DEFINING
a,
8, AND
y IN
TERMS OF ACTIVITY
F O R 4 L I Q W ~AND D A FT.4P0R P H ~xuLEQT'ILIBRII v The. wntional volatilitv of e given voniponent i i drfinrtl v =
the relati.vr volatlhtv ( C Y ) ot
c,
{YJII-
(2)
A\
co1~lpoll~~~t* PE
& . = % " ' =s/ A VB 1LT R
July 1949
INDUSTRIAL AND ENGINEERING CHEMISTRY
1367
Activity (relative fugacity) is defined
(4) where f " refers to the standard state (defined as the vapor of the component above its pure liquid phase a t the temperature involved). For perfect gases
(5)
P =.f
and, Equation 4 becomes
and
(7) Then suhstitutiiig in Equation 3,
%AKA .-
FORA LIBRIUN.
SYSTEM OF Two IMMISCIBLE LIQUIDPHASESIN EQUIBy definition
The relative volatility (Equation 8) may also be expressed in terms of activity coefficients
Equations 17, 18, and 19 are all rigorously derived on the basis of thermodynamics and are universally applicable when fugacities are used in place of activitics. The activity coefficients may be determined by a variety of methods as discussed by Colburn ( 1 ) . When the actual partial pressure of a component is divided by Raoult's law, the pressure differs from the activity coefficient only to the extent that the system deviates from the perfect gas laws and in this laboratory is distinguished from the activity coefficient by giving i t the designation J factor. This designation also avoids confusing the activity coefficient with the vaporliquid selectivity factor, y, which would otherwise often appear in the same equations subsequently developed. The foregoing equations may be modified by application of certain limiting assumptions to produce simpler and more useful equations for specific uses. For example, when components A and B obey perfect solution and gas laws, their activity coefficients are both unity and Equation 8 reduces to the familiar distillation equation
(9)
Considering two liquid phases (extract X and raffinate R ) and a vapor phase in equilibrium a t the boiling point, a relative volatilitv exists or each liquid phase: & L A(
However, where a selective solvent is used, the activity coefficients of the components to be separated are not both equal to unity and i t is convenient to designate the relative volatility of Equation 8 as y.
(10) and
But since the same vapor is in equilibrium with both liquids w~hichare in equilibrium with each other UAX
=
aAR
(12)
Another particularly useful case is liquid-liquid extraction of components such as hydrocarbons which in the absence of a solvent satisfy Equation 20 reasonably well. I n this case when the system is sufficiently below the critical solution temperature to make extraction practical, the solvent content of the raffinate is usually sufficiently low that the activity coefficients of both components in the raffinate phase are essentially equal to unity and Equation 18 reduces to
p =
JAX* JBX
&Ild
(13)
CCBX = a B R
Let these-be designated by
UA
P E A=
and
U B , respectively.
Then since
K
Equations 10 and 11 may be written
It is enlightening to consider Equation 17 for the special case where the components to be separated satisfy Equation 20 reasonably well (typical of hydrocarbon systems) and the solvent is nonvolatile and insoluble in the liquid raffinate phase (typical of certain glycol type solvents with hydrocarbons). Then O I R becomes CY and ax becomes y, from which . CYXP=r*
and
Dividing 15 by 16 and simplifying, a particularly significant equation is obtained
By utilizing the relationship that, the activity coefficient (y) is equal t o a/N, Equation 15 divided by 16 reduces t o
(23)
This is a particularly significant equation because it shows clearly the definite relationship of distillation, vapor-liquid extraction, and liquid-liquid extraction. Even with the other limiting assumptions removed, i t should be directionally correct when applied to the separation of components which form reasonably perfect solutions with each other. If either a liquid-liquid or vapor-liquid selectivity is known, the other may be estimated by use of this equation if CY can be estimated, as is usually the case where vapor pressure data are available. The J factor, which is often difficult to determine where multicomponent solutions are involved, is easily measured for many solvent hydrocarbon binary mixtures. J factors determined in binary solutions may be substituted in the foregoing equations
INDUSTRIAL AND ENGINEERING CHEMISTRY
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Vol. 41, No. 7
I n estimation of the liquid-liquid selectivity, p, at some practical solubility, Equation 17 is used as a basis. This equatiorl states that for any solubility, p =
Figure 1. Phase Diagram Illustrating Relationship of Distillation Vapor-Liquid and Liquid-Liquid Solvent Extraction
to calculate the multicomponent selectivity provided the tot.al solute concentration in the solvent is low enough that perfect solution laws apply for all the solute components and that the J factor was determined a t a correspondingly lorn concent'ration. I n the event that select,ivities a t highcr, more practical solubilities are dcsired, the following empirical mcthods of calculation have been found to be fairly reliable. Assume that components A and B are present in solvent S a t equimolar concentration XI (the total hydrocarbon concentration X T = N A f - 1 ' ~= 2 L V ~ ) I. n the range of infinite dilution, i t is reasonable to expect on the basis of dilute solution laws that each hydrocarbon will exhibit the same partial pressure it would if the other hydrocarbon were absent. When this is the case, the relative volatility, y , is t.he ratio the partial pressures A and B would have if each were present alone in the solvent a t '/z the total hydrocarbon concentration, - V T : ~ ,
I-'rooess
OX
and
Ycslod. = (YNT)~\'T
f ( ~ I V Z ' , ~ )-( ~JvT)
(26)
However, in those cases where the hydrocarbons in the absence of any solvent exhibit deviations from Raoult's law i t is necessary t o correct Y x T by adding to it the factor C , 1%-hichis obtained from equilibrium data on the pure hydrocarbons with the following equation,
Ca
= ~ N c
ao.5
(27)
where O ( N is ~ OL for the hydrocarbon mixture present in the solvent and is a! for an equimolar mixture of the two hydrocarbons. The equation for calculating y then becomes
are the
O T RAT -OiV R T
Liquid-liquid extraction Vapor-liquid extraction
OL
by
p
y =
OT E 4
L-
O.\
ET
and simplifying, the desired equatiori
ACKKOWLEDGMENT
The author wishes to express his appreciation for suggestions from Robert H. Lafferty which resulted in appreciable simplification of the derivations. NOMENCLATURE
For intermediate concentrations the relative volatility would obviously fall between these two extremes. It has been found for the hydrocarbon systems investigated that the actual relative volatility over the entire concentration range is reproduced within experimental accuracy by a weighted average of the two y's
O(R
Eelectirity a =
Distillation
hlultiplying rcsults:
At the other extreme of concentration, as the solvent concentration approaches zero, the relative volatility, y, approaches a , the well-known relative volatility for distillation, which is the ratio of the vapor pressures of the pure hydrocarbons when perfect solution laws are followed. This is equivalent to saying that the relative volatility in concentrated hydrocarbon solutions can b r expressed by the ratio of the vapor pressures of the hydrocarbons at the total hydrocarbon concentration, N T ,
-where CYR
vapor-liquid selectivities for the extract and raffinate phases, respectively, and are calculated by the foregoing equations. It is significant that CYR is nearly equal to (Y in solutions COIIt,aining considerable solvent. As a result, the equation a x p = 7, rigorously true only a t infinite dilution, may be used to approximate p when complete data are lacking. I n view of the utility and significance of the relation UI X p = y , its derivation from the geometry of phase diagrams is also present'ed. Figure 1 shows a ternary phase diagram typical of one which might be encountered in the separation of a more soluble component, T , from a less soluble component, N , by extraction with a solvent, S . The equilibrium compositions on a solvent-free basis of a rafinate phase A, extract phase B, and vapor phase C are represent,ed by the respective points R, E , and 0 located on line N T by projection (dotted) from point S through points A , B, and C. For solvents of identical selectivity, expressed as p or y, as t,he volatility of the solvent decreases the point C progressively approachos 0 along the line SCO, and as the solubility of the solvent in the raffinate decreases the point A progressively approaches R along the line SAR. I n the limiting case of a raffinate-insoluble, nonvolatile solvent the raffinatc phase and vapor phase const,itute a siinple distillation system. The extract and vapor phascs constitute a simple vapor-liquid cxtraction system. Sinw on triangular diagrams distances are proportional to compositions, the following selectivities then rsist,:
24)
=
components to be separated
BJ H = absence of solvent J = J factor as defined herein
-1- = mole fraction P = vapor pressure of a pnre substance R = raffinate phase solvent 7 ' = summation (or lotal concentration) v = vapor phase extract phase a = activity, Lewis and Randall ( 7 ) c = constant fugacity, Lewis and Randall ( 7 ) f = partial pressure P = t = temperature v = volatility coefficient 1 z activity equation limited by indicated assumptions
s =
x =
July 1949
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
1369
(6) , , Hunter. T . G.. and Nash. A. W.. J. SOC.Chem. I n d . . LIII,
LITERATURE CITED
(1) Carlson, H. C., and Colburn, A. P., IND.ENG.CHEM.,34,581-9
95T (1934).
(2) Colburn, A. P., and Sohoenborn, E. M., Trans. Am. Inst. Chem. Enars.. 41. 422 (1945).
(7) Lewis and Randall, “Thermodynamics,” 1st ed., p. 255, New York and London, McGraw-Hill Book Co., 1923. (8) White, R. R., Trans. Am. Inst. Chem. Engrs., 41, 551 (1945).
270-7 (1937). (4) Gilliland, E.R., Ibid., 32,1229 (1940). (5) Hibshman, H. J., Ibid., 32,988-91 (1940).
RDCEIVED August 23, 1947. Presented before the Division of Petroleum Chemistry at the 111th Meeting of the AMERICAN CHEMICAL SOCIETY, Atlrtntio City, N. J.
(1942).
(3) Fenske, M. R., and Varteressian, K. A , , IND.ENG.CHEM.,29,
(Separation of Hydrocarbons by Solvent Extraction)
SEPARATION BY CHEMICAL TYPE AND MOLECULAR WEIGHT HENRY J. HIBSHMAN Esso Laboratories, Standard Oil Development Company, Elizabeth, N . J . Selectivities for separating hydrocarbons by vaporliquid and liquid-liquid extraction processes were calculated from partial pressure data of pure hydrocarbons above a typical selective solvent, dimethyl phthalate. It was found that the boiling range of a mixture separable by a liquid-liquid process is roughly three times that separable by a vapor-liquid process and that the selectivities for separating hydrocarbons of equal boiling point according to chemical type increase with boiling point, and result in extraction in the following order: unsubstituted aromatics (benzene, naphthalene, etc.), alkylsubstituted aromatics, naphthenes, and paraffins.
M
ANY new commercial extraction processes both of the
pressure measurements of solutions of individual hydrocarbons in dimethyl phthalate, a typical selective solvent. This particular solvent was chosen for this study on the basis of its low vapor pressure which in most cases made the directly measured total pressure equal t o the hydrocarbon partial pressure. Other unpublished data indicate its selectivity for separating toluene and normal heptane to be of the same order of magnitude as the commercially used physical solvents with the exception of sulfur dioxide. EQUIPMENT AND EXPERIMENTAL PROCEDURE
In determining partial pressure data Rayleigh distillations (7‘) were used. The essential features of the still are shown in Figure 1.
liquid-liquid and vapor-liquid types have resulted from the necessity for production of war materials. Some examples pertaining to the petroleum industry are as follows:
The Pyrex flask of 500- or 1000-ml. capacity was surrounded by a constant temperature bath. The flask was equipped with a steel bar stirrer driven by a magnetic activator placed beneath the bath. The heater on the exposed portion of the still prevented condenTOLUENE PRODUCTION FOR TNT. Liquid phase extraction ussation of vapors and return of reflux. The condensed vapors from ing sulfur dioxide as a solvent. Vapor phase extractions using the still passed into a receiver equipped with a vacuum source phenol, methyl ethyl ketone-water, and methyl alcohol-water as and manometer. The majority of isothermal data were detersolvents. mined on nonvolatile solvents for which the total pressure was the SEPARATION OF n - B U T Y L E N E S FOR DEHYDROGENATION TO hydrocarbon partial pressure. I n this case the flask was charged BUTADIENE. Vapor phase extractions using furfural and acetonewith known amounts of solvent and hydrocarbon, the bath was water as solvents. PURIFICATION OF BUTADIENE FOR RUBBERPRODUCTION.brought to temperature, and the flask pressure reduced slowly and recorded along with the volume of hydrocarbon collected in Liquid phase and vapor phase extractions using ammoniacal the receiver. cuprous acetate as a solvent. Vapor phase extractions using furfural as solvent. SEPARATION OF ISOPRENE FOR RUBBER PRODUCTION. Vapor HEATING phase extraction using aqueous acetone. GO ND,ENSER
The design of both liquid-liquid and vapor-liquid extraction processes from batch equilibrium data is well advanced and is adequately covered in the literature (1, 3-6). However, as a first step in determining the feasibility of achieving a new separation or in evaluating the relative efficiencies obtainable by vaporliquid extraction and liquid-liquid extraction it usually has been customary in the past t o obtain batch data on mixtures of the solvent and components involved. This necessitated analysis of the phases, often requiring development of special procedures. Hydrocarbon critical solution temperatures when plotted against molecular weight follow separate smooth curves for each hydrocarbon type ( 6 ) and have been used to evaluate solvent selectivities in terms of an arbitrary number for separation of hydrocarbons ( 2 ) . However, so far no rigorous quantitative relationship of selectivity with this property has been found. The present evaluation of solvent extraction methods for separation of hydrocarbons has been obtained from simple vapor
Figure 1.
Rayleigh Still
The partial pressure of wax in dimethyl phthalate was estimated from solubility data. For systems such as this with very low solubility, the partial pressure of a solute in the solvent must be nearly equal to the vapor pressure of the pure solute, a slight correction exists for solvent solubility in the pure solute. I n the case of volatile solvents four t o six small cuts were taken and analyzed. The partial pressures above the charge were then
