Products from Hydrocarbon - American Chemical Society

(7) Kressman, T. R. E., and Kitchener, J. A,, J. Chem. SOC., 1949,. 1190. (8) lbid., p. 1208. (9) Kunin, R., and Barry, R. E., IND. ENG. CHEM., 41, 12...
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INDUSTRIAL AND ENGINEERING CHEMISTRY

Gregor, H. P., J . Am. Chem. SOC., 70, 1293 (1948). l b i d . , 73, 643 (1951). Gregor, H. P., and Bregman, J. I., J . Colloid Sci., 6, 323 (1961). Kressman, T. R. E., and Kitchener, J. A , , J . Chem. SOC.,1949,

1190. ( 8 ) l b i d . , p. 1208. (9) Kunin, R., and

Barry, R. E., IND. ENG.CHEM.,41, 1269 (1949). (lo) Report of Comm., Int. Union of Chem., IND.ENO. CHEM., NEWSED., 15, 278 (1937). ‘(11 ) Sandell, E. B., “Colorimetric Analysis of Traces of Metals,” New York, Interscience Publishers, 1944. (12) Schwarzenbach, G., and Ackerman, H., Helv. Chim. Acta, 30, 1798 (1947). (13) Shriner, R. L., and Fuson, R. C., “Systematic Identifieation

of Organic Compounds,” 3rd ed., New York, John Wiley &

Sons, 1948. (14) Skogseid, A., “New Derivatives of Polystyrene and Their Use as Ion Exchangers,” Oslo, Aas and Wahls, 1948.

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(15) Snell, F. D., “Colorimetric Methods of Analysis,” New York, D. Van Nostrand Co., 1936. (16) Sussman, S., Nachod, F. C., and Wood, W., IND. ENG.CHEM., 37, 618 (1945). (17) Welcher, F. J., “Organic Analytical Reagents,” New York, D. Van Nostrand Co., 1947. (18) Yoe, J. H., and Sarver, L. A., “Organic Analytical Reagents,” New York, John Wiley & Sons, 1941. (19) Zimmerman, J., and Knyrim, M., Ber., 15, 518 (1882); 16, 514 (1883). RECEIVED for review May 9, 1952. ACCEPTED September 9, 1952. Presented as part of the Symposium on Specificity of Adsorbents before the Division of Colloid Chemistry at the 117th Meeting of the AMERICAN CHEMICAL SOCIETY, Houston, Tex., Maroh 1950. Taken in part from the thesis of Mark Taifer, submitted in partial fulfillment of the requirements for the degree of Master of Science in Chemistry, Polytechnic Institute of Brooklyn, New York, June 1950.

Products from Hydrocarbon Synthesis C. E. MORRELL, C. S. CARLSON, J. H. McATEER, R. F. ROBEY, AND P. V. SMITH, JR. Esso Laboratories, Standard Oil Development Co., Linden, N . J.

T

HE accelerated development of the carbon monoxide hydro-

genation process for the production of gasoline during the years immediately following World War 11, will have, perhaps in the immediate future, more significance for the aliphatic chemical industry than the petroleum industry. It is not generally anticipated t h a t this process, or for t h a t matter, other types of synthesis processes will be required or extensively utilized in the foreseeable future for t h e production of liquid fuels. On the other hand, realization of the potential economic importance (9) of the by-product aliphatic oxygenated chemicals simultaneously produced has resulted in a n extensive study and development of recovery methods, analytical procedures, and purification processes applicable to complex mixtures of oxygenated compounds similar in some respects t o those now commercially available from other processes, such as, for example, hydrocarbon oxidation. The present paper has a twofold purpose. The first is t o provide a summary of the work carried out in these laboratories on the recovery, analysis, and purification of the oxygenated compounds produced by the hydrocarbon synthesis process. The second is t o serve as background for a more detailed presentation of certain phases of t h e work relating t o t h e separation and purification of oxygenated compounds obtained in the synthesis products. HYDROCARBON SYNTHESIS PROCESS AND PRODUCTS

Numerous discussions of the hydrocarbon synthesis process have already appeared in the literature ( 1 , 5 - 7 ) . Figure 1 shows schematically the major steps involved. Natural gas or coal is converted by partial oxidation to synthesis feed comprising, predominantly, hydrogen and carbon monoxide. The synthesis feed is contacted with a finely divided iron catalyst maintained as a fluid bed. Reaction temperatures of the order of 350’ t o 650” F. and pressures generally in the range of 250 t o 600 pounds per square inch gage are used to produce B complex mixture of hydrocarbons and oxygenated compounds. This mixture is condensed t o form a n aqueous liquid phase, a liquid hydroearbon phase, and residue gas. The residue gas is normally recycled in part to the reactor, the remainder being bled off. Hydrocarbon products are distributed between t h e liquid hydrocarbon and gas

phases; oxygenated chemicals are distributed in all three phases. The hydrocarbons and oxygenated Chemicals consist of mixtures of aliphatic compounds extending over a wide range of molecular weight and comprising olefins, paraffins, alcohols, aldehydes, ketones, acids, esters, and acetals. As shown by Figure 2, the distribution of products with increasing molecular weight (or more exactly t h e number of carbon atoms per molecule) follows a regular pattern for both bhe hydrocarbons and oxygenated chemicals, t h e sole departure from which is the remarkably small amount of C1 oxygenated compounds found in t h e products. The pattern suggests, of course, a relationship between the relative yields of C, hydrocarbon and C,+ 1 oxygenated chemicals. From the foregoing, it is not surprising t o observe t h a t t h e lower molecular weight oxygenated chemicals, particularly those having 5 or less carbon atoms per molecule, are distributed in all three product phases although, with the exception of acetaldehyde, these compounds are found largely in the aqueous phase, The hydrocarbon phase contains in addition t o a portion of t h e water-soluble oxygenated compounds nearly all of the oxygenated compounds of more than 5 carbon atoms per molecule. As indicated above, part of the noncondensable gas is recycled t o the synthesis reactor and part, tho so-called tail gas, is withdrawn as a purge. Highly volatile oxygenated conipounds, such as acetaldehyde, may be scrubbed from either or both of t h w e gas streams for later purification. Some of the oxygenated compounds are preferably removed from the oil phase t o make the latter suitable for use as a motor fuel. This may be accomplished by thermal or chemical decomposition of the oxygenated compounds or recovery of these substances for chemical uses. The water phase containing a dilute mixture of organic acids, alcohols, esters, kebones, aldehydes, and their reaction products can be processed for chemicals recovery. WATER-PHASE CHEMICALS

Although t h e detailed composition of t h e water phase realized in commercial plant operation depends upon the synthesis conditions employed (S), the average composition of aqueous phases studied t o date from experimental synthesis units is given in Table I.

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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

Vol. 44, No. 12

different volatilities and relative volatilities from those existing in the absence of the solvent. In extractive distillation, a rionideal liquid vapor system is deliberately created t o facilitate distillation separat,ions. Some of the factors affecting Corcrrrn*rro the separation may be better understood ALcoWoLa ETC. from the theoretical treatment given below: In a binary mixture the relationship Iietlveen equilibrium liquid and vapor compositions is given by the equation YlIY2 = (crlz)(zl/za) (1) where y and z refer t'o vapor and liquid concentrations, subscripts 1 and 2 refcr to Figure 1. Flow- Sheet for Hydrocarbon Synthesis the more volatile and less volatile components, respectively, and a is the relative volatility of component' I referred to component 2. I n an ideal TABLEI. -4VERAGE COXIPOSITIOS O F AQUEOCS PHASE solution, therelativevolatilityisequalto the ratio of the vapor prcsCoinooneiit Vieieht ~. % suros of the constituents a t the temperature of the boiling niisture CAa

Rcrcioi

Pionucl R L C O V Z ~ Y

91.3

7~-propyI,n-butyl, isobutyl,

5.1 0.6 0.9 0.3 1.8

=

a12

+

P,:'P,

(2)

n-here P is the vapor prcssurc.

-

The oxygenated materials were concentrated by fractional dist'illation of the total water phase. Redistillation of the neutral oxygenated distillate obtained in this manner results in five major fractions as s h o m in Figure 3. These may be loosely termed the aldehyde ( A ) , acetone ( B ) , ethanol (C), n-propyl alcohol (D), and higher alcohol ( E ) cuts. The represent,ative data given in Table I1 show t h a t this classification is an oversimplification of a very complex situation and hints a t t,he manifold analytical problems involved in clarifying the constitut,ion of these various fractions. Both chemical and spectrographic methods of analysis were employed in arriving at the values set forth in this table. The major product distribution given in Table I11 is typical of neutral oxygenated mixtures from the water phase. Ethanol is t h e most abundant ETHANOL CUT COMPOSITION. compound present. For this reason the ethanol cut was examined in initial separation studies. The composition of a typical anhydrous ethanol cut is given in Table IV. Repeated fractional distillation of such an ethanol cut failed t o give a product of purity comparable with coinmercial ethanol; the cut differed noticeably in isopropyl alcohol and carbonyl concentrations. The difficulties encountered in purification by straight fractional distillation can be better appreciated by reference t o Table V where some of the known azeotropes and boiling points are listed. EXTRACTIVEDISTILLAT~ON. An alternate approach t o the problem involved the use of extractive distillation where the separations obtainable generally depend upon maintaining a high solvent concentration in the liquid phase during distillation (10). Gnder these circumstances the components to be separated have

-

:! 20

DISTRIBUTION

10

Boiling Range, O

c.

22-39 39-56 56-68 65-77 77-86 86-88 88-92 92-99 HzO phase Alcohol phase

TVt. % Of Charge

4.3 2.3 7.0 8.2 34.3 1.3 7.6 32.2

2.9

Hn0,

Wt. 470 2.0 T o t detd. 1.6 6.9 9.6 27.6 25.9

93.0 13.6

Wt. % Alcohol as 1.8-C1 2.2-G 1.2-ci 53.5-cz 75,542 71.0-Ca 67.3-Ca 61:2&

HYDROCARBONS

-

n

i

5-

---

A

a

G

O

+

.

0 Y

OlSTRlBUTlON OF OXYGENATED COMPOUNDS

_I

i

10

i

5

O

I.

Figure 2.

2

4 5 6 7 B 9 1 0 NUMBER OF CARBON ATOMS PER MOLECULE

3

1

1

I

Product Distribution as a Function of Kumher of Carbon Atoms

TABLE11. ANALYSESO F FRACTIONS FROM HYDROCARBON SYNTHESIS \I-ATER Acid as HOBO, Wt. %

OF

15-

PHASE

CRUDE ALCOHOLS

Acetal, Wt.

Wt. % Aldehydes as

Wt. % Ketones as

Wt.%

2.0 0.9 1.0 0.2 0.1 0.0 0.1

Wt. % Ester as 4.24 1.5-Ca 1.3-Ca 3.O-Ca 0.3-Ca 0.5-cs 1.0-cs

0.0 0.0 0.0 0.0 0.0 0.9

0.0

68.2-Cn 38,3-Ca 8.l-Cs 7.9-Ca 2,2-ca 0.1-cj 0.7-c:

10.0-cs 47.1-cs fi4.5-cz 23.8-Ca 0.0 1 ,O-Cs 1.0-cs

90.0 77.7 98.3 87.7 101.1 96.0

1.9 11.6

0.0 3.9-c7

0.0 0.0

0.0 3.7-ce

0.0 4,2-c7

94.9 98.2

Total, 88.2

~

INDUSTRIAL AND ENGINEERING CHEMISTRY

December 1952

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TABLE111. MAJOR PRODUCT DISTRIBUTION OF NEUTRAL SYNTHESIS OXYGENATEDCOMPOUNDSFROM HYDROCARBON WATERPHASE (ANHYDROUS BASIS) Alcohols Methanol, Ethanol includes isopropyl alo. and tert-butyl a h . calculated as ethAnol n-Propyl alcohol includes sec-butyl alc., isobutyl alo., and tert-pentyl alc. 'calculated as n-propyl alc. n-Butyl alcohol Includes sec-pentyl a h . , isopentyl alo., and %-Pentylalcohol) tert-hexyl alc. Aldehydes Acetaldeh de Propionadeh de But raldeh Higler ydes Ketones Acetone Methyl ethyl ketone Hiaher ketones Mixe;d esters

Weight % 0.45 56.7 11.6 3.3 5.5 2.9 2.6 0.3

aide%&

TABLEIV.

TABLE V.

Y

;BO

10.9 3.7 0.4 1.6

A

COMPOSITION OF A TYPICAL CRUDEETHANOL CUT FROM HYDROCARBON SYNTHESIS Compound Weight 9%

Ethanol 2 ; ~ ~ o p jalcohol l ehy es as C4 Ketones as methyl ethyl ketone Esters as ethyl acetate Hydrocarbon Acetal Acids Unknown

condition, ethanol is more volatile than isopropyl alcohol (01ethanol/ isopropyl alcohol = 1.15). T h u s , with increasing water di-

B

E40 2

tility of the iso-

85.0 2.5 1.8 4.3 2.2 1.7 0.0 Trace 2.5

SOMEPOSSIBLE AZEOTROPES OCCURRING IN ETHANOL CUT Boiling Pt.,

Components

O

Ethanol-water a e t h y l ethyl ketone-water Methyl ethyl ketone-ethanol Methyl ethyl ketone-ethanol-water Isopropyl alcohol-water Isopropyl alcohol-water-methyl ethyl ketone-ethanol Isopropyl alcohol-methyl ethyl ketone Ethvl acetate-water Ethyl acetate-ethanol Ethyl acetate-isopropyl alcohol Ethyl acetate-ethanol-water

c.

78.1 73.4 74.8 73-74 80.8 78-79 77.3 70.4 71.8 74.8 70.3

In nonideal solutions where abnormal relative volatilities exist, the partial pressures of the individual components deviate from Raoult's law but may be calculated with the aid of activity coefficientb, y Pl =

YlPlZl

(3)

and

Y1

= YlPlXl/.rr

where p is the partial pressure and Also

r

(4)

is the total pressure.

From this it is clear t h a t in nonideal systems a12

= YlPl/Y2P2

(6)

The activity coefficient varies with t h e concentration, as can be seen from Figure 4 where the activity coefficient for ethanol in water ( 4 ) is plotted as a function of ethanol concentration. The activity coefficient is a maximum (6, 6) at the lowest ethanol concentration but decreases t o one a t x = 1.0. A similar curve can be plotted for isopropyl alcohol-water ( 9 ) where the activity coefficient is 11.8 at x = 0. In extractive distillation where a solvent is present as B third component, the solvent concentration is maintained at such a level t h a t the other two components are both present in low concentrations. As a result, they have high activity coefficients, and hence an appreciable change in relative volatility is realized.

I

0.0

0.2

1 0.4

0.6

I

MOLE FRACTION ETHANOL IN WATER

Figure 4. Activity Coefficient of Ethyl Alcohol in Water

Vol. 44, No. 12

INDUSTRIAL AND ENGINEERING CHEMISTRY

87.5 MOLE PER CENT W

0.2

0

0.4

0.6

0.8

1.0

MOLE FRACTION ISOPROPANOL IN ETHANOL

(BINARY BASIS)

Figure 5. Vapor-Liquid Equilibria of Isopropyl AlcoholEthyl Alcohol i n the Presence of Water as a Solvent

taining equimolar quantities of ethanol and isopropyl alcohol and 80 weight yo of a white oil, an alpha (ethanol/isopropyl alcohol) of 1.46 is realized instead of the normal alpha of 1.15 for this binary alcohol mixture. Numerous solvents such as phenol, sulfolane, cellosolves, carbitols, esters, and diphenyl ether-diphenyl oxide mixtures behave in a similar manner. CHEMICALREACTIONS. In choosing the most satisfactory separation process for use on oxygenated compound mixtures, consideration must be given t o the chemical reactivities and stabilitiera of the constituents. These chemical factors may limit the ultimate purification reached or they may, with proper choice of conditions, actually be used t o facilitate the separation. Some of the potential reactions are illustrated. For example, aldehydes combine with themselves t o form aldol condensation products in a reversible reaction which is catalyzed by caustic RCHzCHO

+ R’CHzCHO e RCH2CHOHCH(R’)CHO

(7)

T h e alcohol condensation products can dehydrate and polymerize further. I n addition, aldehydes form higher molecular weight polymers nRCHO

+ (RCHO),

(8)

They also react in a reversible manner with alcohols t o form acetals, particularly in the presence of acid RCHO

+ 2R’CHzOH

RCH(OCH2R’)z

+ HzO

(9)

Acids and alcohols form esters which under appropriate conditions hydrolyze t o liberate t h e original acids and alcohols RCHeOH

+ R’COOH e R’COOCHZR + H20

be substantially complete and rapid. One disadvantage of this technique is that valuable products may be destroyed. Hydrogenation has also been suggested as a means of eliminating reactive compounds. By this means, aldehydes would be converted t o normal alcohols, thus increasing the yields of these products, but ketones would be converted into secondary alcohols, thereby aggravating the separation problems in the production of high purity normal alcohols. For example, in virtually every hydrocarbon synthesis run explored t o date there has been a high yield of acetone amounting t o approximately 10% of the total neutral organic material in the water phase. Converting this to isopropyl alcohol would appreciably increase the difficulties in purifying the ethanol cut where isopropyl alcohol is the most difficult impurity t o eliminate. Many of these difficulties arising from the combination of simple oxygenated compounds are dependent upon such factors as concentration of reactive component, concentration of water in the oxygenated compound mixture, and history of a particular oxygenated compound mixture as regards method and degree of dehydration. For instance, distillations resulting in extensive removal of water from the oxygenated compounds ahvays resulted in increased chemical interaction. The rate and extent of these reactions were dependent upon temperature and holdup time in the column. Even during storage, it R-as observed that the rate of chemical reaction increased in partially dehydrated samples. Therefore, laboratory continuous distillation of the water phase as well as aqueous extractive distillation of the total water phase were investigated t o ascertain the feasibility of preferentially separating the reactive components prior t o subsequent purification of the alcohols. Both of these methods have been shown to be successful in continuous, pilot scale experiments.

(10)

Considerable evidence for reactions of this type was noted during distillations of the neutral oxygenated compounds from the original synthesis water phases and also during distillation of the concentrated oxygenated compound mixtures. For instance, acetaldehyde was often recovered as the trimer in the %-propyl alcohol fraction. Also, when considerable removal of water was effected by simple distillation, the amounts of acetals and esters were observed t o increase. ALTERNATE RECOVERY METHODS. Caustic treatment has been suggested as a means of minimizing or eliminating chemically reactive compounds by polymerizing aldehydes, saponifying esters, .and neutralizing acids. To be effective, however, reaction must

z

0 0 c 4

E Y

ESTERS

0

c z

W

0

a

w n

5

0

c I ‘3

I

ACIDS (RCOOH)

4-

I

I

0 A L C O H O L S (ROHI

IO

CARBOWYL COMPOUNDS

b

c01

0

I

I

10

20

I-

WEIGHT PER C E N T

Figure 6.

l 40

30

OF

l

. 50



ORIGINAL O I L

Oxygenated Compound Distribution in Hydrocarbon Synthesis Oil Product

INDUSTRIAL AND ENGINEERING CHEMISTRY

December 1952

AQUEOUSACID COMPOSITION.After the neutral oxygenated compounds have been distilled from the water layer, a residual aqueous mixture of organic acids is obtained. The concentration may range from less than 1 t o 5% or more. Although traces of formic acid have been identified, the bulk of the acids present fall within the range of 2 t o 5 carbon atoms, as is shown by the distribution figures for a typical acid bottoms mixture given in Table VI, Inasmuch as these acids would necessitate a neutralization treatment of the waste water prior t o its disposal, it was of interest t o investigate the possibility of their recovery in a salable condition. The extremely dilute solutions involved make t h e economic recovery of these materials difficult despite the fact t h a t large tonnages of organic acids are present. Of the methods investigated t o date, solvent extraction appears t o be the most promising.

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P

w 0

a E

60

X W

II

0 W

K W P

/

40

W

0

z

TABLEVI. DISTRIBUTION OF ACIDS I N HYDROCARBON SYNTHESIS AQUEOUS PHASE (ANHYDROUS BASIS) Volume %

Acid Acetic acid Propionic acid Butyric acid Valeric acid Higher acids

48 18 14 11 9

1

I

I

20

40

I 60

I 80

VOLUME PER CENT METHANOL I N SOLVENT

Solvent Capacity for Oxygenated Compounds as a Function of Methanol Concentration

Figure 7. OIL-PHASE CHEMICALS

.

A major problem in connection with the chemicals in the oil layer was the isolation of these materials in sufficient amounts and purity to permit a reliable determination of their nature, structure, and properties. The initial approach t o t h e problem was to fractionate a typical hydrocarbon synthesis oil layer product produced over synthetic ammonia catalyst into 20” C. boiling range cuts. The results of chemical-type analyses of these cuts are shown graphically in Figure 6 where certain trends can be seen. The weight per cent esters and acids increase with increasing boiling point (molecular weight) of t h e fraction. The weight per cent alcohols and carbonyls (aldehydes and ketones) present decrease with increasing boiling point (molecular weight) of the fraction. The curve for the total weight concentration of oxygenated compounds as a function of the boiling point of the fraction shows a fairly uniform level. The acids in another oil layer sample were isolated as a group by extraction with dilute aqueous caustic. The mixed acids so obtained were liberated, dried, and fractionally distilled. The detailed component analysis so obtained is given in Table VII.

boric acid or phthalic anhydride. The unesterified material was distilled away from t h e ester, after which the esters were hydrolyzed t o regenerate the alcohols. Extraction with water a t elevated temperatures was effective in removing a major part of the alcohols and acids from the oil. Water fortified with a low molecular weight alcohol such as methanol was an effective extractant at room temperature for all the oxygenated compounds present in the oil. The efficiency of this method in a single stage extraction is a function of methanol concentration in the solvent. This is illustrated graphically in Figure 7. If free acids are present, an appreciable amount of t h e methanol will be converted t o esters. By means of multistage extraction with aqueous methanol, virtually 100% recovery of oxygenated compounds should be possible. Free acids can be removed by aqueous caustic as mentioned above. Complete removal of oxygenated compounds from the oil can be achieved by extraction with 65y0sulfuric acid or 85% phosphoric acid. ACKNOWLEDGMENT

The authors of this paper are indebted t o the management of Standard Oil Development Co. for permission t o publish this TABLEVII. ACID CONSTITUENTS FROM HYDROCARBON work. They also wish t o express their appreciation t o t h e many SYNTHESIS OIL LAYER members of t h e laboratory staff who assisted in various phases of Assumed Estimated this project. The assistance of Esso Laboratories (Louisiana Boiling Range, Identity Purity of Wt: % ’ of. Fraction C. (1 Atm.) of Acid Cut Original Oil Divison) in making synthesis products available for study is Acetic 76 0.08 1 70-125 gratefully acknowledged. Propionic 83 0.22 125-145 2 O

3 4 5 6 7 8 9

145-165 165-194 192-21l5 211-225Q 225-240a 240-2540 254-270Q Above 270a

Butyric Valeric Caproic Heptyljc Caprylic Pelargonic Capric

96 86 87 87 91 87 80

.

0.64 1.01 0.51 0.46 0.52 0.51 0.36 1.23

... .. Bottoms Distillation was carried out at 50 mm. of mercury pressure; temperatures were corrected to atmospheric pressure. a

Valeric acid was found t o be present in the highest concentration with yields decreasing for lower and higher molecular weight acids. Acids containing more than 10 carbon atoms are present in the oil layer but in low concentrations. OIL PHASEPURIFICATION METHODS. A number of methods for the recovery of oxygenated compounds from synthesis oils have been investigated. Alcohols have been isolated from cuts of narrow boiling range by the formation of nonvolatile esters of

LITERATURE CITED

(1) Arnold, J. H., and Keith, P. C., Advances in Chem. Series, 5, 120 (1951). (2) Brunjes, A. S., and Bogart, M. J. P., IND.ENG.CHEM., 35, 255 (1943). (3) Eliot, T. Q., Goddin, C. S., Jr., and Pace, B. S., Chem. Eng. Progress, 45, 532 (1949). (4) Jones, C . A., Schoenborn, E. M., and Colburn, A. P., IND. ENG. CHEM.,35, 666 (1943). (5) Keith, P. C., Oil Gas J., 45, No. 6, 102 (1946). (6) Murphree, E. V., Ibid., 46, No. 49, 66 (1948). (7) Pichler, H., “Synthesis of Hydrocarbons from Carbon Monoxide and Hydrogen,” U. S. Bur. Mines, Spec. Rept. trans. by R. Brinkley (1947). (8) Sherwood, P. W., Chem. Eng., 56, No. 9, 9 9 (1949). (9) Sullivan, F. W., Jr., Chem. Eng. Progress, 43, No. 12, 13 (1947). (10) Weissberger, A., ed., “Distillation,” p. 317, New York, Interscience Publishers, 1951.

RECEWED for review March 14, 1952.

ACCEPTED August 12, 1952.