Ind. Eng. Chem. Process Des. Dev. 1980, 19, 174-179
174 TI
= integral controller constant
derivative controller constant T d = dead time w = frequency Literature Cited TD
=
Box, M. J., Comput. J., 8(l), 42-52 (1965). Cooley, J. W., Tukey, J. W., Math. Comput., 19(90), 297-301 (1965). Cumming, I.G., "Proceedings of the 2nd IFAC Symposium on Identification and Process Parameter Estimation", Prague, Paper 7.8, June 1970. Cusset, B. F., Mellichamp, D. A,, Ind. Eng. Chem. Process Des. Dev.. 14. 359-368 (1975). Gallier, P. W., ISA Trans., 13(1), 50-58 (1974).
Gustavsson, I., Automatica, 11(1), 3-24 (1975). Harris, S.L., Ph.D. Thesis, University of California, Santa Barbara, Calif., 1978. Johnson, P. C., Mellichamp, D. A., Ind. Eng. Chem. Process Des. D e v . , 11, 203-212 119721. Nieman, R. E., Fisher, D.G., Seborg, D. E., Int. J . Control, 13(2), 209-264 (1971). Van den Bos, A.. "Proceedings of the 3rd IFAC Symposium on Identification and System Parameter Estimation", The Hague, Paper TT-3, June 1973. Van den Bos, A., "Proceedings of the 1st IFAC Symposium on Identification in Automatic Control Systems", Prague, Paper 4.6, June 1967.
Receiued for reuieu September 6, 1978 Accepted August 27, 1979
Studies on Thermal Degradation of Synthetic Polymers. 12. Kinetic Approach to Intensity Function Concerning Pyrolysis Condition for Polyethylene Low Polymer Takashl Sawaguchi, Tatsuo Inami, Takeshi Kuroki, and Tadashl Ikemura Department of Industrial Chemistry, College of Science and Technology, Nihon University, Kandasurugadai, Chiyoda-ku, Tokyo, Japan
A kinetic equation for the pyrolysis gasification reaction of polyethylene low polymers has been established. On the basis of this equation, the intensity function IF = Toa (K.sa) concerning the severity of decomposition conditions, conventionally considered as an important parameter regarding product yield, is clarified theoretically from a kinetic point of view. IF is supported by this point of view and the value of the exponent a of IF can be calculated quantitatively from the kinetic parameters by the following equation: a = -In (1 - RT/Eln @/In 8. It is found that the value of a decreases with increasing activation energy. From the kinetic parameters in this experiment, the value of a is a proximated as 0.032. The calculation method of the product yield from the Arrhenius equation, k = 9.9 X 10' ;Pexp(-53.7 X 103/RI,), for the IF standard is better in terms of convenience and practicality. Since the exponent a is clarified theoretically, the concept of IF has universal acceptance.
Introduction From the point of view of energy deversification and chemical resources, attention is paid not only to coal and heavy oils of the petroleum group, but also to plastic waste matter and recovery of resources by pyrolysis. The most suitable control method of recovery by pyrolysis requires development of a way for estimating product yield corresponding to decomposition conditions. In the case of petroleum hydrocarbons, it is known that the parameter expressing the degree of severity of the decomposition conditions, i.e., the intensity function (1, = TP), has a good correlation with the product yield. From experience, 0.06 is used as the value for the exponent a (Davis and Farrell, 1973), and this value is also applied for the pyrolysis of crude petroleum (Kunugi et al., 1975). The authors (1977a,b, 1976a,b) introduced the concept of I F for polymers and in cases where property values differ completely from naphtha, crude petroleum etc., an experimental induction method for the value of a was established. It was made clear that IF has a good correlation with the product yield. Moreover, the authors (1977a) found out that the value of a for polymers differs from 0.06 for petroleum hydrocarbons, and they suggested that the value of a is dependent on the molecular structure of the sample and that it is correlated with the kinetic parameter (activation energy). IF is useful as a means for estimating product yield, and it is clear that the value of a depends considerably on the pyrolysis reaction according to the type of material. In order to use the concept of IFfor the pyrolysis reaction with a wide range of hydrocarbons, it is necessary 0019-7882/80/1119-0174$01.00/0
to elucidate the value of a still further theoretically. Davis and Farrell (1973) have recently indicated a definition of IF(IFcorresponds to the temperature required to obtain an optional conversion ratio x in a residence time of 1 s) and established an IF standard kinetic equation using a = 0.062. They have used this value for the decomposition reaction of kerosene, light oil, etc. It is noteworthy as a first attempt that elucidation of the relation between IF and kinetics was made from the definition of IF. In this study, the empirical parameter IF,which has been used up until now, is clarified theoretically on the basis of this kinetic consideration. A useful means for estimating the product yield from IFon the basis of the kinetic parameter, which quantitatively reflects the pyrolysis reaction, is developed. Theoretical Relation between IFand Kinetics. The relationships between the value for the exponent a on IF and the kinetic parameters is described below. The intensity function equation, first-order reaction velocity equation, and Arrhenius equation are shown as follows I F = T8" da = k ( l
d8
-
(1) x)
or k = [In (1 - x)-']/8
k = A exp(-E/RT) 0 1979
American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 1, 1980
175
where IF= intensity function (K.s"), T = reaction temperature (K), 0 = residence time (s), a = constant, x = conversion ratio (gasification ratio), k = reaction velocity constant (s-l), A = frequency factor (s-l), E = activation energy (cal/mol), and R = gas constant (cal/mol.K). From eq 2 and 3, the reaction temperature is expressed by the following equation.
T=
-
R[ln A
E
+ In 0 - In In (1- x)-']
(4)
Equations 5 and 6 are obtained when the above definition of I F (Davis and Farrell, 1973) is introduced into eq 2 and 3. kIF = In (1- x ) - l (5)
k~~ = AI, exP(-EI,/RIF)
(6)
with kIF = IFstandard reaction velocity constant (s-l), AI = I F standard frequency factor (s-'), and E, = I F standard activation energy (cal/mol). Equation 7 is obtained from eq 5 and 6.
El, IF= R[ln AI, - In In (1 - x)-1]
(7)
As is clearly shown by comparison of eq 4 and 7, E = El, and A = AI, are established for 6' = 1, so that IF can be expressed as follows from eq 4 and 7. IF
=
T 1 - R T / E In 6'
(8)
By comparison of eq 1 and 8, the mutual exchangeability of TB", i.e., the reaction temperature and the residence time, is equivalent to right side of eq 8, and the value of a can be expressed by the following equation. -In (1 - R T / E In 0) a = (9) In 6' For 0 = 1, eq 9 becomes the limit function of eq 10. RT lim a 0-1 = (10)
E
Equation 10 shows that the value of a decreases with an increase in E. Equations 8 and 9 hold in the range 0 = 1, but whether those equations hold in the whole range 6' for the reaction restricted to E and A depends on whether or not E = ET, and A = AI, hold in the variable range of 0 # 1. If these conditions are satisfied, theoretically or experimentally, eq 8 and 9 become general formulas, and it is found that the value of a can be expressed by a function having the variables E , T, and 0, and the definition range is specified by A and x. Whether or not E = El, and A = AI hold in the variable range 6' # 1 can be experimentally cgecked by comparison of eq 3 and 6. The evaluation of the value of a obtained from eq 9 by kinetic considerations is performed as follows. According to eq 1, combinations (Tl, O1), (T,, 0,) ... (T,, 0,) of the decomposition conditions giving an optional conversion ratio x exist, and their mutual relationships are expressed by the following equations. Tiel" = T202" = ... = T,8," (11) k101 = k202 = ... = k,0, (12) In the case of TIOl and T2&, eq 11 and 12 take on, respectively, the form of eq 13 and 14. 0, = 0,(Tl/T2)'/" 02 = 01 exp[E/R(1/T2
-
(13)
l/T1)l
(14)
Figure 1. Flow diagram of experimental apparatus: 1, N2 bomb; 2, H 2 0 capillary feeder; 3, pre-heater; 4, steam generator; 5 , reactor; 6, melter; 7 , ice cooler; 8, separator; 9, water cooler; 10, gas tank; 11, orifice meter; 12, manometer; 13, thermocouple; 14, electric furnace.
Comparison of eq 13 and 14 permits evaluation of the value of a by kinetic consideration. Computation of the product yield on the basis of I F is carried out by transformation of eq 7. x = l -
1
exP[A exp(-E/RI~)l
(15)
Theoretical analysis for second- and third-order reactions can be achieved in the same manner as for the first-order reaction, and consequently, eq 8 and 9 can be determined.
Experimental Section Sample. The polyethylene used was the commercial "low polymer", which was dried under vacuum and used following removal of the moisture. The molecular weights are as follows: M , = 1.0 x io3; M , = 3.7 x lo2;M,/M, = 2.7. Apparatus and Procedure. The flow diagram of the experimental apparatus is shown in Figure 1 and the details of the reaction part are shown in Figure 2. The samples were melted in a melter according to the reaction conditions a t 80 " C by constant electric heating, and fixed sample amounts were introduced, in pulse, into the reactor. T o avoid thermal influence on the sample supply nozzle from the electric furnace of the reactor as much as possible, the temperature was controlled with water. The water serving as the heat agent was passed from the capillary feeder through the preheater and introduced into the steam generator. The reactor had an inner diameter of 21 mm, a total length of 1040 mm, and was made of SUS 310s. To maintain a uniform flow of the sample gas, the inside of the reactor had the shape of an empty cylinder. The outside was heated electrically by a heater subdivided into five blocks, and the temperature was adjusted as the outer wall of the reaction tube. The temperature distribution in the axial direction inside the reactor was measured by a movable alumel-chromel thermocouple installed a t the reactor center, and the temperature gradient was compensated by the effective reactor volume obtained by the method of Haugen and Watson (1947). The separation product escaped from the top of the reactor, was cooled by water or ice, and was separated into gas and liquid. The liquid product was separated from water by a separator. During the period required for attaining a specified tem-
176
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 1, 1980 Thermocouple-4 rolysis products
C
S ,og M
Polymer
Figure 3. Molecular weight distribution change for polyethylene low polymer: 1, original polymer; 2, the reprecipitate from the residue in the polymer supply nozzle (x = 0.07); 3, the reprecipitate from pyrolysis products (x = 0.07).
T
t -
Coolant, Polymer
E
E
measuring point (SV)(K), and E = 55 X l o 3 cal/mol is used. The yield for each gaseous product is calculated by the following equations
0
8
Y
(19)
Thermocouple
Figure 2. Details of reaction part.
perature, the air in the reactor was replaced by nitrogen. A definite amount of steam was then passed into the reactor and following the stabilizing of conditions for reaction, 10 g of sample was delivered into the reactor in a pulse a t a rate of 200 mg/2.5 min, and the pyrolysis reaction was carried out. Analysis. The gaseous product was analyzed by a Shimadzu 4B-PT gas chromatograph (thermal conduction type detector). The conditions for the analysis of each object have already been reported (Kuroki et al., 1976a). The C4 fraction was analyzed by benzyl cyanide + 30% AgN03 on a Uniport C (60/80 mesh) 10-m column. The liquid product was analyzed by a Shimadzu IR-400 spectral unit and measurement was carried out with a NaCl cell by the capillary method. The average molecular weight and molecular weight distribution were measured by gel permeation chromatography using a Waters Associates Model 200 GPC. The calibration line was produced by standard polystyrene, and N.P.L. standard polypropylene was used for Q factor authorization. Definition of Terms. The residence time is calculated from the following equation (Kunugi et al., 1973). 8=
-
VR
x 10-3
with V, = effective reactor volume with compensation for the temperature gradient in the axial direction inside the reactor (mL), Q1 = diluent supply amount at normal conditions (L), Qz = gaseous product volume a t normal conditions (L), and T = reaction period (min). V, is calculated from the following equation (Haugen and Watson, 1947).
VR =
Vr.e-E/RTe.eE/RT
(17)
with Te = effective reactor temperature (K), VR = reactor volume (mL), Ti = temperature in the reactor a t the
YG = EyGi
(20)
x = YG/100
(21)
with YG, = yield of the gaseous product i for the sample (wt YO),P G = ~ concentration of the component i in the gaseous product (vol YO), MGl= molecular weight of the gaseous component i, YG = total gas yield for the sample (wt YO), W = sample weight (g), and x = gasification ratio. The definitions for the dilution ratios etc. are the same as already reported (Sawaguchi et al., 1977a). Results and Discussion Effect of Reaction Temperature on Gasification. The residual polymer in the supply nozzle and the liquid product, both occurring in a low gasification ratio range, were each treated with hot xylene-methyl alcohol, giving their respective reprecipitates whose molecular weight distributions are given in Figure 3. A low molecular weight is observed prior to gasification. The IR spectra for liquid products obtained under conditions of differing gasification ratios are shown in Figure 4. Up to the vicinity of a gasification ratio of a 0.5, the main constituent in these liquid products is formed by aliphatic olefins such as those reported on by Iida et al. (1973),who investigated pyrolysis of high density polyethylene in detail. For these aliphatic olefins there are the terminal vinyl (990, 910 cm-l) and trans-vinylene (965 cm-') types. It is thought that the formation of the trans-vinylene type olefin is caused by an intermolecular radical transfer reaction suggested by Slovoklotova et al. (1964) [RCHCH2R + R. RCH==CHR RH]. With a gasification ratio of 0.5 or more, aromatics (1600,1500 cm-' etc.) can be observed, and their absorption appears stronger with an increase in the gasification ratio. Figure 5 shows the composition of the gaseous products for the gasification ratio. With a gasification ratio near 0.5, the product gas composition shows a constant ratio. With a gasification ratio of 0.5 or more, it is believed that secondary reactions come about such as the redecomposition of olefins which are the initial products of the gasification reaction and the formation of aromatics by condensation, etc. The change in composition occurring at a gasification ratio of 0.1 or less is thought to be caused by the initial polymer reaction with low molecularization. For the gasification reaction, two reaction ranges can be observed: the first stage reaction occurs within a range
+
--
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 1, 1980
11
12
177
13
l O O O I T , *K-l
Figure 6. Arrhenius plot for k . 0
1
-
: -2 G
x-
-3
-4 13
12
I1
1 O O C l IF
Figure 7. Arrhenius plot for k I F , IC
2000
000
1230 Wave r ~ m Q P l cm-'
Figure 4. IR spectra of pyrolysis products from polyethylene low polymer.
-
/*0
0
A
04
0 2
k = 9.9
X
10l2 exp(-53.7
X
103/RT)
(23)
06
X
Figure 5. Composition of gaseous products corresponding to the gasification ratio.
with a gasification ratio of up to 0.5, where the gas composition is formed with a fixed ratio, and the second stage reaction occurs within a range with a gasification ratio of 0.5 or up, where the secondary reactions of the product gas are caused. For the first stage reaction range, the following quantitative chemical equation is obtained. [polymer] [depolymerized polymer] 0.18CH4 + 0.44CZH4 + 0.04CzH6 + 0.17C3H6 + 0.01C3H, + 0.05C4H, + 0.12H2 (22)
-
fraction in the gaseous products. Kinetics of Gasification and IF.The product yield is hardly influenced by the steam dilution ratio (Sawaguchi et al., 1977a), and the reaction has no relation to the initial concentration of the sample polymer. As shown in eq 2 and 22, these experiments are governed by overall firstorder reaction kinetics in regard to the depolymerized polymer concentration for the complicated gasification reaction, and the gasification velocity is analyzed. A linear relation is established for the plot of -In (1x ) vs. 6' in the range of short residence times. For long residence times, the above mentioned secondary reaction of olefins occurs and linearity is lost. The various reaction velocity constants of the first stage reaction range are obtained from the slope of the straight line, and they are shown in the Arrhenius equation (Figure 6) as
-
with the coefficients of each components expressed by mole
The value of the exponent a in eq 1 is obtained by the experimental induction method already reported in detail (Sawaguchi et al., 1977a). Based on the methane yield, the value of a in the range from 525 to 575 "C (first stage reaction range) is averaged arithmetically and approximated a t 0.03. From this result, the following experimental equation is obtained. IF = (24) kzFand I F under various conditions are obtained from eq 5 and 24. Figure 7 shows the In kI vs. l / I F in eq 6. Since this shows good linearity, the Arrgenius equation for the I F standard is expressed as kzF = 9.7 x 10l2exp(-53.6 X 103/RTF) (25)
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Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 1, 1980
1
1 700
800
500 T
1000
'K
Figure 8. Change range for the value of a in eq 9. 12, 'K
Figure 10. Comparison of eq 13 and 14. 20
N
m
b x
04
02
12
'K 0
Figure 9. Comparison of eq 13 and 14.
800
900
'F
Comparison of eq 23 and 25 clearly shows good coincidence for E and El, as well as A and A,. This means that k = kl,. Accordingly, it is found that IF can be treated as a temperature for the whole range of 0 for the reaction restricted to E and A , and the definition of IF represented above is supported by kinetic considerations. A theoretical relationship between the value of a and the kinetic parameters is expressed in the general formula of eq 9, and as a result, it becomes clear that the value of a can be calculated by the kinetic parameters as shown in eq 9. Figure 8 shows the change range corresponding to the experimental conditions for the value of a in eq 9. Since the change range for the value of a is determined by the residence time, reaction temperature, activation energy, frequency factor, and conversion ratio (gasification ratio), an approximation value can be obtained in the range of the experimental conditions when the kinetic parameters are definite. Since the value of a obtained from the kinetic parameters in this experiment changes in the shaded part (0.030 to 0.035) in the figure, it is approximated as a = 0.032. Evaluation of the value of a obtained from the kinetic parameters is determined by comparison of eq 13 and 14. Figure 9 shows the change for T2and O2 for TI = 810 K and 0, = 10 s, while Figure 10 shows the change for T , = 850 K and O1 = 10 s. For both figures, eq 13, using a = 0.032 as obtained from the kinetic parameters for this experiment, and eq 14 using E = 53.7 x lo3 cal/mol show good coincidence. These figures also show considerable dependency of the value of a on the activation energy. Figure 11 shows the comparison of the experimental values with the calculated values for the various product yields based on I F , as shown in eq 15. The calculated values and experimental values show good coincidence up to a gasification ratio near 0.5 (first stage reaction range).
Figure 11. Comparison of the experimental values with the calculated values for the various product yields based on IF.
On the basis of standard kinetics, the product yield can be calculated from the following equation. 1I
x = l - exp[AO exp(-E/Rn]
(26)
Since eq 26 has two variables on the right side, the combination of T and 0 must be chosen from a three-dimensional function (x-T-0). The calculation of the product yield on the basis of I F as shown in eq 15 directly performed from only one variable IF, but the combination of T and 0 can be arbitrarily chosen from eq 1. Moreover, as mentioned above, the value of a can be calculated exactly from the kinetic parameters. Thus, this method of calculation is shown to be both more practical and convenient. Conclusion A pyrolysis gasification reaction was carried out for polyethylene low polymer. The reaction model used was simplified as much as possible. Then, a gasification kinetic equation was established, and on the basis of this, a kinetic investigation of I F was carried out. As a result, the following conclusions were obtained. (1)Since overall first-order reaction kinetics applied for the depolymerized polymer concentration, the Arrhenius equation, k = 9.9 X 10l2exp(43.7 X 103/RT), could be obtained. (2) On the basis of the experimental equation IF = T80.O3, obtained from the methane yield, the Arrhenius equation, kIF = 9.7 X 10" exp(-53.6 X 103/RIF),for the IFstandard was obtained. (3) k = k l , is established, and IFcan be treated as temperature for the whole range of 0 for the reaction restricted
Ind. Eng. Chem. Process Des. Dev. 1980, 19, 179-185
to E and A , and the definition of IF mentioned above is supported by kinetic considerations. Accordingly, the value of a can be calculated quantitatively from eq 9 on the basis of the kinetic parameters. It becomes clear that the value of a decreases with an increase in E. The value of a obtained from the kinetic parameters (0.032 in this experiment) is evaluated by comparison of eq 13 and 14. (4) The calculation of the product yield from the I F standard gasification kinetic equation is shown to be simpler and to have abundant applicability. As shown above, the theoretical side of IF, conventionally treated as a simple experimental parameter for the estimation of the product yield, is clarified from the point of view of the reaction kinetics. As a result, the concept of IF has universal acceptance.
179
work and also to express their gratitude to Mr. Suganami of the Goi plant of Chisso Petrochemical Co., Ltd., for GPC measurements of samples and decomposition products. Literature Cited Davis, H. G.,Farrell, T. J., Ind. Eng. Chern. Process Des. Dev., 12, 171 (1973). Kunugi, T., Kunii. D.. Tominaga, H., Sakai, T., Mabuchi. S., Takeshige, K., Bull. Jpn. Pet. Inst., 17(1), 43 (1975). Sawaguchi, T., Kuroki, T., Ikemura, T., Bull. Jpn. Pet. Insf.,19(2),124 (1977). Sawaguchi, T., Kuroki, T., Isono, T., Ikemura, T.,Nippon Kagaku Kaishi, 565
(1977). Kuroki, T., Sawaguchi, T., Hashirna, T., Kawashima, T., Ikemura, T., Nippon Kagaku Kaishi, 322 (1976). Kuroki, T., Sawaguchi, T., Sekiguchi, Y., Ogawa, T., Kubo, T.,Ikemura, T., Nippon Kagaku Kaishi, 328 (1976). Haugen, 0. A., Watson, K. M., "Chemical Process Principles", Part 111, p 884. Wilev. New York. 1947. Kunugi, T . , Kunii, D., Tominaga, H., Sakai, T., Mabuchi, S.,Takeshige, K., Sekiyu Gakkai Shi, 16(3).232 (1973). Iida, T. A., Honda, K., Nozaki, H., Bull. Chem. SOC.Jpn., 46, 1480 (1973). Slovoklotova, N. A,, Margupov, M. A,, Kargin, V. A,, Vysokomol. Soedin., 6,
Acknowledgment
1974 (1964).
The authors wish to thank Mr. Fukuoka and Mr. Ishikawa for their assistance throughout this experimental
Receiued f o r review October 3, 1978 Accepted July 20, 1979
Isothermal Vapor-Liquid Equilibria for the Water-Formaldehyde System. A Predictive Thermodynamic Model V. Brandani," G. Di Giacomo, and P. U. Foscolo Isfifuto di Chirnica Applicata e Industriale, Universiti de' L 'Aquila, 67100 L ' Aqulla, Ifaly
Vapor-liquid equilibrium data have been measured for the water-formaldehyde system at six temperatures and in the concentration range between 0 % and 50% by weight of the second component. The system exhibits large deviations from ideal behavior. Because of strong associations, the usual equations for the activity coefficients are inadequate in correlating the experimental results. A new model, which takes only chemical forces into account, is presented. This model describes with a good approximation the vapor-liquid equilibrium for the water-formaldehyde system in the examined ranges of temperature and composition.
Introduction
The water-formaldehyde system, which is very often applied in chemical processes (polyoxymethylene manufacture for instance), has been studied intensively, and there is a wealth of literature on the subject (Walker, 1975, and references cited therein). Nevertheless, the problem of characterizing its vaporliquid equilibrium is to date open as far as experimental measurements are concerned and the definition of a satisfactory theoretical model capable of predicting vaporliquid equilibrium for wide ranges of temperature and composition. Particularly, we can recognize in the experimental data reported in the literature contradictions which may derive from the different experimental techniques employed and, probably, from the differing purity grades of the solutions used. Examining the various experimental data in the literature, the existence of "apparent azeotropes" for the water-formaldehyde system remains doubtful. In fact, concerning the data obtained a t atmospheric pressure, while Auerbach and Barschall (1905) and Piret and Hall (1948) deny the existence of the azeotrope, other authors including Ledbury and Blair (1925), Pyle and Lane (1950), Olevsky and Golubev (1954), Green and Vener (1955), and Tsochev and Petrov (1973) find an apparent azeotrope even though they do not agree on the value of azeotropic 0019-7882/80/1119-0179$01.00/0
composition. A greater uncertainty, also deriving from the experimental data of which there are less available, exists in the range of lower pressures. In this case, while Pyle and Lane (1950) find that a t a pressure of 460 mmHg vapor composition is always less rich in formaldehyde than liquid, Olevsky and Golubev (1954) find an azeotrope also a t 350 mmHg. In trying to clarify our ideas on this matter, we have deemed it suitable to carry out new measurements on the vapor-liquid equilibrium for the water-formaldehyde system and particularly we have measured the total pressure while varying the temperature and composition. This type of measurement allows us to establish the existence of the apparent azeotropes and to identify their range of existence to a good approximation. Experimental Section M a t e r i a l s . Aqueous solutions of formaldehyde purchased from Merck and containing 10 wt % methanol were
employed. Before use the solutions were distilled, under vacuum, a t a high reflux ratio until chromatographic analysis on the residue failed to show any significant amount of methanol. In this way a stock solution containing 30 wt % formaldehyde and less than 0.01 wt 70 methanol was obtained and stored in a dark bottle, maintained in an isothermal bath at 25 "C. The mixtures for the VLE study were made from the stock solution by 0 1979 American Chemical Society
