Nomenclature
dimensionless tracer concentration, C’IQ coiicent,ration of injected tracer particles if uniformly distributed throughout the miser C(s) = residence-time distribution function E = apparent dispersion coefficient, in.2/sec F ( 0 ) = cumulative distribution function or step response L = length of the miser, in. Pe = Peclet number, uL/E t’ = time, see f = mean residence time, sec u = apparent linear velocity in the miser, in. ‘see z = dimensionless distance c
co
= =
GREEKLETTERS 0
=
diniensionless time,
t’l
f
Literature Cited
Armeniade?, C. D., Johnson, W.C., Raphael, T. (to Arthur D. Little, Inc. j, C.S. Patent 3,286,992 (November 29, 196.5). Brenner, H., Chem. Eng. Sci., 17, 229 (1962). Chen, S.J., Fan, L. T., Chung, I). S., Watson, C. A., J . Food S a . , 3 6 , 688 (1971). Fan, L. T., Ahn, Y. K., A p p l . Sei. Res., Sect. A . , 10,465 (1961). Fan, L. T., Ahn, Y. K., Ind. Eng. Chem. Process Des. Develop., 1, 190 (1962).
Fan, L. T., Chen, S. J., Watson, C. A, “Annual Reviews of Industrial and Engineering Chemistry, 1970,’ V. W. Weekman, Jr., Ed., pp 22-56, American Chemical Society, Washington, D.C., 1972. Fan, L. T., Chen, S. J., Watson, C. A., Ind. Eng. Chern., 62, 53 (1970). Levenspiel, O., Bischoff, K. B., “Patterns of Flow in Chemical Process Vessels,” in “Advances in Chemical Engineering,” Vol 4, T. B. Drew, J. W. Hoopes, Jr., and T. Vermeulen, Eds., Academic Press, Kew York, N.Y., 1963. hIuchi, I., PhD thesis, Nagaya University, Nagaya, Japan, 1461
hIuEhi,’I., Mukaie, S.,Kamo, S., Okamoto, M., Kagaku Kogaku, 2 5 . 757 11961). Pattison, D. A., Chern. Eng., 11, 94 (1969). Rutgers, R., Chern. Eng. Sci., 20, 1079 (1965). Sugimoto, ll., Endoh, K., Tanaka, T., Kagakzi Kogaku, 31, 145 (1967). Van der Lann, E. T., Chern. Eng. Sa.,7, 187 (19%). Wen, C. Y., Fan, L. T., “Models for Flow Chemical Reactors,’’ to be Dublished. Black and Teach. Sew York. N.Y.. 1972. Williams, J . C., Rahman, 11. .4.,presented at the Symposium on Powders organized by the Pharm. Soc. of Ireland and the Soc. of Cosmetic Chemists of Great Britian at Dublin, Ireland, April 1969. Yagi, S., lliyauchi, T., Kagaku Kogaku, 17, 382 (1933).
RECEIVED for review December 17, 1971 ACCEPTED October 5 , 1972 Work supported by the JIarket Quality Research Division, Agricult,ural Research Service, U.S. Department of Agriculture.
Process for Extracting High-Molecular-Weight Hydrocarbons from Solid Phase in Equilibrium with Liquid Hydrocarbon Phase Daryll J. Cordeiro, Kraemer D. Luks,’ and James P. Kohn Department of Chemical Engineering, 17niversity of Sotre Dame, Sotre Dame, Ind. 46666
Methane pressurization of a liquid hydrocarbon phase in equilibrium with a solid hydrocarbon phase is demonstrated as a method to extract high-molecular-weight paraffins from the solid phase.
T h i s paper proposes a process for extracting high-molecularweight hydrocarbons from a solid phase in equilibrium with a liquid hydrocarbon phase using methane pressurization. An application for this process could be the removal of highmolecular-weight hydrocarbons from a reservior on which primary and secondary recovery procedures have been performed. The initial experimental study of this process has attended to the solubility behavior of a reasonably well-defined highmolecular-weight paraffin in liquid n-decane as affected by methane pressurization. Future work d l focus on aromatic high-molecular-n-eight materials in a similar vein. At t h a t time, some statement will be made concerning the selectivity of the process for aliphatic vs. aromatic high molecular weight materials.
Thermodynamics and Model
The prototype three-phase (S-LG) system selected for study consisted of methane (gas), n-dotriacontane (solid), both of which are soluble in liquid n-decane. n-Dotriacontane (n-CarHss)n’as chosen for the study since it is a \Tell-defined high-mo1eculz.r-weight paraffin-i.e., it can be obtained in reasonably piire form and should be representative of highmolecular-weight paraffins in general. It was assumed that the gas phase consisted of only niet’hane a t the temperatures imposed and that the solid phase consisted of pur3 n-dotriacontane since t,he large difference in molar volumes between n-decane and n-dotriacontane makes the possibility of solid solution remote. Equilibrium thermodynamics demands that, a t pressure P and temperature T ,
To whoni correspondence should he addressed. Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 1, 1973
47
Table 1. Smoothed Values of Methane Pressure, Methane liquid Mole Fraction, and liquid Phase Molar Volume for Vapor-liquid 70°C Isotherm for Methanen-Dotriacontane System (The methane liquid mole fractions listed under "Flory-Huggins" are those achieved by a least-squares fit to the FloryHuggins model and agree with experimental with a standard deviation of h0.0026) Pressure, atm
Methane liquid mole froction Experimental Flory-Hugginr
15.85 20.25 24.75 29.60 34.80 40,40 46.30 52.50 59.00 65.50
0.1000 0,1250 0.1500 0.1750 0.2000 0.2250 0.2500 0.2750 0.3000 0.3250
pig(T,P )
0.1023 0.1270 0.1509 0.1762 0,1997 0.2246 0,2490 0,2730 0,2965 0,3186
=
521,5 508.3 495.1 481,9 468.7 455.4 442.2 428.9 415.5 402.2
pi'(T, P , xi, 2 3 2 )
(2)
The chemical potentials can be espressed as:
+ RT In ( y j x j )
(6)
where OpjZ ( T , P ) is the chemical potential of pure liquid j (perhaps hypot'hetical) and y I = y j ( T , P , x l , 2 3 4 is the activity coffiecientof speciesj in the liquid phase. Use of Equation 6 in Equations 3 and 4, followed by division by dP and elimination of either (bxl/dp)T or (dXQZ/dP)T will lead, respectively, to expressions for (bx32/bP)T and ( d ~ l / b P ) TFor . esample,
A -B
c - D
where
48
[4 (XdXl@)
T
f l
where v3' is molar volume of species 3 in phase i, and t,is the partial molar volume of species j in the liquid phase defined by
T
=
where i\rj denotes bhe moles of species j in the liquid phase. t1 determines whether n-dotriacontane dissolves or precipitates upon methane pressurization-Le.,
(3)
@pj'(T,P )
€1
M o l a r vol, cm3/g mol
where p3' is the chemical potential of species j in phase i, arid X I and 2 3 2 are the mole fractions of methane and n-dotriacontane in the liquid phase. Taking differentials of the above equations a t constant T , one gets
pj' =
The process derivatives (bx32/bP)T and ( b x ~ / d Pare ) ~used to evaluate two important process functions:
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 1, 1973
(7)
> 0 4 dissolution of n-CZzH66 < 0 +- precipitation of nn-C32H66
Furthermore, the favorability of either behavior increases with the magnitude of €1. It should be noted that, because 7a2> ~ 3 2 9 ,pressure alone will cause precipitation of n-dotriacontane. As will be shown, t'he presence of methane in the liquid solution will cause ( 1 to be positive. Also, it should be noted that since methane does dissolve in the liquid phase, a negative value of (bx32/dP)T does not necessarily mean that blie n-dotriacontane precipitates. Consequently, one needs to consider a function like l1in which the amount of n-decane in the liquid phase, which is fixed, serves as a basis. f 2 measures how much n-dotriacontane is dissolved per mole of methane. & h a s the same significance as E 1 with respect to sign. A high positive value of f z is, of course, desirable, from the viewpoint of yield. The presence of methane under pressure will not only increase dissolution of solid n-dotriacontane but also reduce the viscosity of the liquid phase substantially through its dissolution in the liquid phase. With methane as the extractive agent in this process, the process is further aided by the fact that the methane in solution can be easily outgassed and recovered once the liquid phase is removed from the system. The nonideality of a liquid misture is frequently expressed in terms of the thermodynamic escess Gibbs energy GE. This function can be related to the activity coefficients of a binary solution of species i andj:
RT
111
yz =
(E) b*yt
P ,T , N ,
great deal of attention has been directed toward expressing the proper composition dependence of GE. The equations derived generally involve the use of one or more adjustable parameters which have to be determined from experiment. Kohn and eo-workers (1962, 1964, 1966, 1968) have shown that the model proposed by Flory (1941, 1942) and Huggins (1942) is a reasonably accurate representation of the Gibbs free energy data for a large number of hydrocarbon systems, particularly paraffins. The Flory-Huggins model was found to be superior to other one-parameter correlations in correlating the activity coefficient of n-dotriacontane in solution with n-decane. The data employed for this determination were freezing point data of mixtures of n-dotriacontane and ndecane, from which activity coefficients were computed via the well-known van't Hoff isochore. See Equation 15. Table S1 of the supplementary material placed with the -4merican Chemical Society Microfilm Depository Service presents the
results. The Flory-Huggins model fitted the experimental activity coefficients with a standard deviation of j=0.0055 down to 2 3 2 = 0.65. This correlative success, combined with the above-cited success of correlating mixtures of methane with higher paraffins achieved by Kohn and eo-workers encouraged us to employ the Flory-Huggins model to correlate all the data relating to the study of our prototype system of methane-n-decane-n-dotriacontane. However, the author's goal is not model testing but rather describing a process, the data of which they have attempted to correlate in as simple a manner as possible. I n passing, it should be noted that subst'antial amounts of n-decane cause only modest depressions in the melting point of mixtures of n-dotriacontane and n-decane. This fact esplains why the narrow range of 330-40'K was chosen to esamine the methane pressurization process. The Flory-Huggins model proposes the following espression for GE of a binary misture:
GE
=
RT [xi In ( $ < / x i )
+
xj
iAL'tj [ V / (Pip,)11z]4i$j (11)
In
($j/xj)]
+
where V = x f v i zjpj, @ i= z i p i / V , and where AUij is a weakly temperature-dependent parameter called the interchange energy of species i arid 3 . T h e activity coefficients are
(12) I n this study the temperature dependence of the interchange energies has been neglected since the temperature range explored is fairly narrow. The analogs to Equations 11 and 12 for a ternary system of species i,j , k are :
G E = RT
a=i,j,k
Experiments Performed
+
[x, In
E
t h a t the ternary composition of the liquid phase is always known during methane pressurization. Establishing the locus of the ternary three-phase surface is accomplished by varying state conditions in the ternary two-phase system until a single crystal appears (presumed to be n-dotriacontane for reasons stated earlier). The appearance of this small amount of solid is assumed not to alter the liquid phase composition and amount to a n y significant degree. I n this manner, the ternary three-phase surface can be mapped out. d point concerning the relationship of our laboratory experiments with the ternary three-phase systems to the earlier stated isothermal experiments (e.g., see Equation 7) is warranted here. An isotherm would be a curve on the ternary three-phase surface. I n the laboratory we fix the ratio of ndecane and n-dotriacontane prior to pressurization. Consequently the curve we get is on the same surface but not isothermal. We performed enough of these "constant ratio" experiments, however, so that the isothermal curves could be reasonably located. Further comments on this point will be confined to the section on Results. Temperatures were measured with a platinum resistance thermometer believed t o be accurate to +O.O2"C. Pressures were measured with Bourdon tube gauges frequently calibrated against a n accurate deadiveight gauge. The maximum error in measuring pressures was estimated to be *0.07 atm. Liquid volumes were measured by calibrated marks on the glass equilibrium cell and judged to be accurate to d~0.02 ml . The methane and n-decane were pure-grade chemicals purchased from the Phillips Petroleum Co. and were stated to have a minimum purity of 99 mol yo.The n-dotriacontane was purchased from the Humphrey Chemical Co. and was stated to be of 97 mol yominimum purity.
A C a , [ ~ / ( ~ a ~ , ) 1 1 2 1(13) 4a$~
(a,P ) = ( i , j ) ,
(i, k),(j,k )
and
(14) where the activity coefficients for the ternary mixture are expressed in terms of binary parameters-Le., are determined solely from binary solution information. We shall support this approsirnation a posteriori in the results-Le., its use in the correlation of ternary data. Finally, the composition dependence of the partial molar volumes was small; these volumes consequently were correlated only with respect to temperature. Experimental Method
The equipment and experimental techniques used have been described b y Kohn and Kurata (1956). Briefly, the esperimental procedure involves the quantitative addition of methane to a calibrated 10-ml glass equilibrium cell containing a kiiown amount of n-decane and n-dotriacontane. The glass cell is visible, yields liquid volumetric data, and the rest of the apparatus is calibrated, volumetrically speaking, so
The following experiments were performed t o arrive a t a description of the methane pressurization process-Le., the ternary three-phase system, which data were correlated with the Flory-Huggins equations presented in the section on "Thermodynamics and Model" : (a) The depression in the freezing point of n-dotriacontane upon addition of n-decane was measured a t several compositions. The liquid phase activity coefficients of n-dotriacontane were calculated using the van't Hoff isochore equation
where AH32m is the heat of fusion for n-dotriacontane, R is the gas constant, and T , is the temperature of melting for ndolriacontane. The heat of fusion was taken to be 18,750 cal/g mol. The interchange energy AU,o, 32 between n-decane and n-dotriacontane was obtained by fitting the FloryHuggins equation (Equation 12) to the activity coefficients obtained using a least-squares method. (b) ,4 vapor-liquid isotherm was measured for the methanen-dotriacontane system a t 7OoC, with methane pressures up to 70 a t m being employed. These data supplied VI and 7 3 2 in the liquid phase and enabled the determination of A1;1,32 by the same method of analysis as (a). The data are presented in Table I. (e) Data on the methane-n-decane system obtained by Beaudoin and Kohn (1967) was analyzed to get A l ' l , IO. (d) The partial molar volumes and the interchange energies obtained for the binary systems were used to test the allplicability of the Flory-Huggins ternary model on three Ind. Eng. Chem. Process Der. Develop., Vol. 12, No. 1, 1973
49
Table II. liquid Phsse Composition and Coefficients & and 5 2 (see Equations 8 and 9 ) as Function of Pressure at T 340°K for Ternary Three-phase Prototype System of Methane-n-Decane-n-Dotriacontane
=
P, xaz
XI
0 5 10 15 20 25 30
0 000 0 0323 0 0631 0 0926 0 1208 0 1477 0 1734
atm-‘
0 0 0 0 1 2 12
8412 8362 8310 8258 0 8206 0 8154 0 8103 0 0 0 0
1887 2465 3594 5724 0463 5005 1909
t2
4 4 4 4 4 4 4
3091 2640 2267 1980 1810 1634 1579
~~~~
Table 111. Liquid Phase Composition and Coefficients l1 and $,% (see Equations 8 and 9 ) as Function of Pressure at T 335°K for Ternary Three-phase Prototype System of Methane-n-Decane-n-Dotriacontane
=
Ex
P, atm
0 5 10 20 30 40 50 60 TO 80 90 100
Xl
0 0 0 0 0 0 0 0 0 0 0 0
0 0286 0559 1068 1534 1961 2353 2712 3042 3346 3626 3886
x32
0 0 0 0 0 0 0 0 0 0 0 0
5622 5584 5543 5455 5367 5279 6192 5107 5022 4940 4859 4780
t
atm-’
0 0 0 0 0 0 0 0 0 0 0 0
0131 0135 0141 0154 0171 0190 0214 0239 0270 0305 0349 0399
E2
0 0 0 0 0 0 0 0 0 0 0 0
9205 9503 9147 8770 8475 8225 8001 7793 7600 7421 7255 7096
different ternary vapor-liquid isotherms. See Equations 13 and 14. Tables S2-S4 of the supplementary material compare the experimental compositions of the ternary two-phase systems Ivith those achieved by the Flory-Huggins correlations a t three different ratios of ( ~ 1 0 / ~ 3 2 ) ,The Flory-Huggins fit is shown to be more than adequate for describing these three ternary systems. (e) The freeziiig point’ elevat’ioii of pure n-dotriacontane by pressure was measured up to a pressure of 1500 a t m and was used to determine the volume change upon fusion of n-dotriacoiitane via the Clausius-Clapeyron equation. An equation fitting the data is presented in the section on “Results.” (f) Pressure-composition data were taken in the manner described in t,he section of “Esperimental Prlethod” to locate the ternary three-phase surface, upon which our prototype process operates, These data are discussed in the sect’ion on “Results.” Experiment (a) in the preceding section yielded a n interchange energy A r l o , 32 = 250 cal/g mol. The experimental and calculated ti.@.)Flory-Huggins) activity coefficients agreed with a standard deviation of +0.0055. The data taken are in excellent agreement x i t h those reported by Seyer (1938). Experiment (b) yielded a n interchange energy AVI, 32 = 3058.4 cal/g mol with a standard deviation of +0.0026 between esperimental and calculated composition data. Analysis of the data of Beaudoin and Kohii (1967) produced AL-I , l o = 1264.5 cal/g mol with a standard deviation of +0.0023 bet\\ een experimental and calculated composition data. The partial molar volumes of the three component’s were espressed simply as temperature-dependent functions in the 50
=
P,
E1 I
atm
Table IV. liquid Phase Composition and Coefficients (1 and (2 (see Equations 8 and 9 ) as Function of Pressure at T 330°K for Ternary Three-phase Prototype System of Methane-n-Decane-n-Dotriacontane
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 1, 1973
€1r
otm
x1
0 5 10 20 30 40 50 60 70 80 90 100
0.0 0.0263 0.0515 0.0986 0.1419 0.1817 0.2184 0.2522 0.2835 0.3123 0.3390 0.3638
0.3457 0.3443 0.3425 0.3383 0.3337 0.3290 0.3241 0.3192 0.3142 0.3093 0.3043 0.2994
b
atm-’
x82
0,003591 0.003684 0.003532 0.003557 0.003578 0.003599 0.003626 0.003619 0.003626 0.003623 0.003591 0.003560
0.4413 0.4226 0.4042 0.3832 0.3647 0.3481 0.3336 0.3189 0.3062 0.2939 0.2814 0.2701
Table V. Variation with Pressure of Number of Moles of Methane and n-Dotriacontane in Liquid Phase (Based on lo00 Mol of Solution at Zero Pressure) Along the Isotherm 340” K on Ternary Three-phase Surface P, atm
Moles of methane in solution
Moles of n-dotriacontane
0 39.0 94.7 180.1 326.8 634.7 1689.1
841.2 1009.6 1246.4 1606.0 2220.2 3504.3 7894,l
0 5 10 15 20 25 30
in solution
narrow range of temperature studied : ?I f1,
T32
+ 6.65 = 0.18T + 143.93 = -385.0 + 2.8T =
0.122‘
where 7 1is in cc/g mol and T is OK. These binary experimental data have been shown to describe ternary vapor-liquid systems using the Flory-Huggins correlation, Equations 13 and 14. See Tables S2-S4 of the supplementary material. The freezing curve of pure n-dotriacontane was fitted to a second degree equation, suggested by Babb (1963) :
P
=
194.68 T - 0.205 T2
- 42,574.4
(19)
where P is atm and Tis OK. See Experiment (e). The ClausiusClapeyron equation yielded the following espression for the volume change upon fusion for n-dotriacontane: AV3zrn = (AHaz”/T) [41,298/(194.68
-
0.41T)I
(20)
where A V 3 P is cc/g mol and T i s OK. Tables S5-S8 of the supplementary material are curves of constant ( X ~ O / X ~taken ~ ) in the laboratory for the ternary three-phase surface, The data are compared n i t h FloryHuggins predictions; the adequacy of the model is again apparent. It is on this surface that the thermodynamic process takes place. .Ispointed out earlier, the process path of interest on the surface is that of the isotherm (along which X ~ O / X would not be constant). Using the Flory-Huggins model with the binary parameters, one could choose several ways (equiv-
~
alerit in principle) to predict such a n isot'herm, the goal being to see how well the Flory-Huggins model, up to now adequate, can represent the ternary three-phase methane pressurization process. Because of the availability of state data on methane, the best scheme to comput'e the isotherms consisted of using Equation 7 : ( d 2 3 2 / d P ) T = f(z1, 2 3 2 ,
T)
(21)
and the relationship
PI'(T,P) = PI'(T, TI,
232)
@a)
where the left-hand side (LHS) of Equation 2a is computed with the aid of existing methane fugacity data and the righthand side (RHS)is, of course, a Flory-Huggins expression. The pressure dependence of the R H S is suppressed since no significant pressure dependence was found in t'he data employed. .lfter Equation 21 is used to compute a new x 3 2 value, Equatioii 2a is used to compute x1 via trial arid error. The method used to integrate Equation 7 was Hammings method as described by Cariiahan et al. (1969). The met'haiie gas data were obt'aiiied from hIichels and Kederbragt (1936), M a t t h e n s and Hurd (1946), Kvalnes and Gaddy (1931), Tester (1961), Caiijar (1956), Keyes and I3urke (1927), and Reamer et al. (1942). Enough isotherms ivere generated via the above coniputatiotial d i e m e to test the adequacy of the Flory-Huggins model against the esperimeiit'al data in Tables S5-S8 of the supplementary material. The values of composition yielded by the Flory-Huggins correlation are labeled as such in those tables. Discussion
Trusting the Flory-Huggiiis model t'o describe adequately the ternary three-phase behavior of the prototype system in the laboratory, the authors used the model to calculate three isotherms which would be representative of a met'harie pressurization process. Since a decreasing value of xs2 in the liquid phtrse does not necessarily mean precipitot'iori of n-dotriacontane, the process fuiiction El is tabulated iii Tables 11-IT' aloiig with compositioiis z1 and 2 3 2 . The process fuiiction E2, which liav some ecoiioniic import, is tabulated also. The zero-pressure compositioiis were obtained as a function of temperature nsing the data of Step (a). One fact that had to be taken into account in this analysis is that n-dotriacoiitaiie undergoes a solid phase traiisitiori a feiv degrees below its freezing point, as studied by Garner (1931) and Rozenthal (1936). The temperature of the solid phase traiisition was taken to be 6 3 5 ° C and the heat, of transition taken to be 9770 cal/g mol in our analysis. The transition state was verified in a n approximate manlier by differential thermal analysis experiments in our laboratory. The potential of methane pressurization as an extractive process for high-molecular-weight paraffins is easily assessed upon examination of t,heprocess tables. For example, a t 340°K, a substantial amount of n-dotriacontane can be dissolved with a moderate pressurization, say t o 20 atm. Starting with 1000 lb mol of liquid phase a t zero-methane pressure (1.59 Ib mol of n-decane and 841 Ib mol of n-dotriacontane), one gets a t 20 a t m a liyuid phase containing 159 Ib mol of n-decane, 327 Ib mol of methane, arid 2220 Ib mol of n-dotriacoiitaiie. Of the three isotherms tabulated here, the one a t 340°K is the most favorable for methane pressurization and is, as Ivell, closest to the melting point of n-dotriacoiitaiie. Table T' describes the methane pressurization iii terms of moles of methaiie and n-dot riacoiitaiie a t 330" B.
.Ilthough lower temperatures are less favorable, it should be recognized that recovery of the methane is very simple, accomplished by depressurization of the liquid phase after i t is removed from contact with the solid phase. This removal of the liquid phase Jvould be aided b y the substantially decreased liquid phase viscosity caused by the presence of the methane in solution. Fut,ure work in our laboratory will focus on the effect of methane pressurization on the solubility of high-molecularweight aromatic substances. h significant difference in behavior of the solubility of various groups of high-molecularweight materials could suggest additional separat'ion techniques. Nomenclature
f
"function of" thermodynamic excess Gibbs energy AHs2" = heat of fusion of n-dotriacontane -Yj = moles of speciesj P = pressure R = molar gas constant T = temperature A rij = Flory-Huggins interchange energy paramet'er bet'ween species i and j V j a = molar volume of species j in phase i 7, = partial molar volume of species j in liquid phase AV3Zrn = volume change upon fusion of n-dotriacontane z j = mole fraction of species j in liquid phase GE
=
=
GREEKLETTERS y t = liquid phase activity coefficient of species i IJ,~ = chemical potential of species j in phase i op,' = chemical potent'ial of pure liquid j El = a process derivative (Equation 8) €2 = a process derivative (Equation 9) 4i = liquid volume fraction of species i literature Cited
Babb, S. E., Rev. M o d . Phys., 35, 400 (1963). Beaudoin, J. ll.,Kohn, J. P., J . Chem. Eng. Data, 12, 189 (1967). Canjar, L. X., ihid., 3, 185 (1958). Carnahan, Luther, Wilkes, "Applied Sumerical Methods," pp 391-402, Wiley, Sew York, N.Y., 1969. Flory, P. J., J . Chem. Phys., 9, 660 (1941). Flory, P. J., ibid., 10, 5 (1942). Garner, W.E., Van Bibber, K.. King. A . 11..J . Chem. SOC.. 1931, p 1533. Humins. 11.L.. Ann. T . Y . Acad. Sci.. 43. 1 (19421. Kef&, F. G., Burke, H. G., J . Amer. Chem. Soc., 49, 403 (1927). Kohn, J. P., Bradish, W. F., J . Chem. Eng. Data, 9, 5 (1964). Kohn, J. P., Kurata, F., Petrol. Processes, 1 1 , 57 (1956). Kvalnes. H. ll.,Gaddv. V. L.. J . Amer. Chem. floc.. 53, 394 (1931). llatthews, C. S., Hurd, C. O., Trans. Am. Inst. Chem. Eng., 42, 55 (1946). llichels, A., Kederbragt, G. W., Physica, 3, 569 (1936). Reamer, H. H., Olds, R. H., Sage, B. H., Lacey, W.S.., Ind. Eng. Chem., 34, 1526 (1942). Rodriaues. A . B. J.. LlcCaffrev. D . S.. Kohn. J. P.. J . Chem. ' Ena: Data. 13. I64 11968). Rozeithal, h., hull. Soc. Chem. Belg., 45, 485 (1936). Seyer, W.F., J . Amer. Chem. Soc., 60, 827 (1938). Shim, J., Kohn, J. P., J . Chem. Eng. Datu, 7, 3 (1962). Shipman, L. &I., Kohn, J. P., ibzd., 1 1 , 176 (1966). Tester, H. E., "Thermodynamic Functions of Gases," F. Din, Ed.,'pp 1-71, Butterworths, 1961 RECEIVED for review December 23, 1971 ACCEPTED August 7, 1972 Data comprise part of the PhD dissertation of Daryll J. Cordeiro. Work supported by the American Petroleum Institute (Research Project 135). Eight supplementary tables will appear following these pages in the microfilm edition of this volume of the Journal. Single copies may be obtained from the Business Operations Office, Books and Journals Division, A4merican Chemical Society, 1155 Sixteenth St., ?J.JV'., Washington, D.C. 20036. Refer to the following code number: PROC-73-47. Remit by check or money order $3.00 for photocopy or 32.00 for microfiche. I
"
I
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 1 , 1973
51
