I n d . Eng. Chem. Res. 1995,34, 4092-4098
4092
Ethylene Oxide Solubility and Ethoxylation Kinetics in the Synthesis of Nonionic Surfactants M. Di SerioJ R. TesserJ F. Felippone? and E. Santacesaria*v+ Dipartimento di Chimica, dell'Uniuersita Federico II di Napoli, Via Mezzocannone 4, (80134)Napoli, Italy, and Pressindustria SPA, Biassono (MI), Italy
Solubility data from different sources of ethylene oxide i n nonylphenol, dodecanol, dodecanoic acid, and their related ethoxylated derivatives have been interpreted by the authors with the UNIFAC, NRTL (nonrandom two-liquid theory), and Wilson methods. The results obtained with these methods have been compared. The two parameters of the NRTL and Wilson equations have been correlated with the mean number of the ethylene oxide adducts of the hydrophilic chain by applying quadratic polynomials. The Wilson equation give the best performances. The role of ethylene oxide solubility in ethoxylation kinetics and mass transfer will be stressed. Kinetic and mass-transfer parameters are clearly correlated with the ethylene oxide concentration. Therefore, the availability of more reliable solubility data or the use of a different method to represent these data requires the recalculation of kinetic parameters. This has been done for the three different substrates considered by applying the solubility data calculated with the Wilson equations. Small differences are observed in the kinetic parameters for dodecanol and dodecanoic acid with respect to previously published data, while remarkable differences are observed for nonylphenol as a consequence of the acquisition of more precise solubility data.
Introduction Ethoxylated nonionic surfactants are produced in industry by reacting ethylene oxide with an organic molecule containing a mobile hydrogen such as fatty alcohols, alkylphenols, or fatty acids. The reaction occurs in the liquid phase, at 150-180 "C and 2-5 atm, in the presence of an alkaline catalyst, that is, KOH or NaOH. Ethylene oxide is partitioned between the liquid and vapor phase, and the partition coefficient changes according to the organic substrate used, temperature, pressure, and extent of the reaction. Reaction products are oligomers of different molecular weights whose distributions are normally of the type suggested by Weibull and Nycander (1954); that is, the reaction environment gradually turns from hydrophobic to hydrophilic and ethylene oxide solubility changes as a consequence. It is of great importance, therefore, to know the ethylene oxide solubility in the reaction mixture at any time because the reaction rate directly depends on the ethylene oxide concentration in the liquid phase (Santacesaria et al., 1990; Hall and Agrawall, 1990; Santacesaria et al., 1992a; Di Serio et al., 1994) and because the reaction is strongly exothermic and an accumulation of ethylene oxide in the liquid phase could be the origin of reactor instability. Despite the importance of the argument, very few papers report data on the vapor-liquid equilibria of ethylene oxide in admixture with organic substrates of fundamental industrial interest such as, for example, nonylphenol and ethoxylated derivatives (Santacesaria et al., 1990; Pate1 and Young, 19931, dodecanol and ethoxylated derivatives (Hall and Agrawall, 1990; Santacesaria et al., 19921, and ethoxylated derivatives of lauric acid (Di Serio et al., 1993). In this paper, all the data existing in the literature for ethylene oxide solubility in the mentioned organic substrates as well as other data we collected in further measurements have been reported and elaborated with
* Dell'UniversitA
Federico I1 di Napoli. Pressindustria SPA.
three different methods: UNIFAC (Fredeslund et al., 1977),Wilson (19641,and two parameters NRTL (Renon and Prausnitz, 1968). In all the cases, the mixture of ethoxylated oligomers has been considered as a unique component with averaged molecular weight. We considered, therefore, vapor-liquid equilibria of the binary mixtures of ethylene oxide with nonylphenol, dodecanol, and their ethoxylated derivatives, respectively, with different mean molecular weights. Binary mixtures of ethylene oxide with ethoxylated derivatives of lauric acid have been considered too, while binary mixtures with lauric acid cannot be achieved because the system is very reactive, even in the absence of the catalyst (Di Serio et al., 1993). All equilibrium data have been subjected to statistical regression analysis to evaluate the optimal NRTL and Wilson parameters. We observed that these parameters simply depend on the mean number of ethylene oxide adducts in the ethoxylated component; relations for this dependence will be presented. The performances of the three abovementioned methods will be compared. The predictive UNIFAC method gives rise to large errors, mainly for ethylene oxide solubility in nonylphenol ethoxylated derivatives. The Wilson methods gave the best results. A correct interpretation of the ethylene oxide solubility data with a reliable vapor-liquid equilibrium model becomes very important when the industrial reactor conditions need to be extrapolated. Another important aspect treated in this paper concerns the general observation that, in a gas-liquid reaction, the solubility of the gaseous reactant and the kinetic parameters are normally strictly correlated. As a consequence, when new and more reliable solubility data are available, kinetic parameters must be recalculated, as has been done in this paper for the ethoxylation of the three substrates considered.
Experimental Section (a)Apparatus and Methods. Ethylene oxide solubility runs were carried out in thermostated autoclaves by introducing a weighed amount of the organic sub-
Q888-5885/95f2634-4092$09.00/0 @ 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 4093 Table 1. Relationships Giving Density as a Function of Both Temperature and Mean Number of Ethylene Oxide Adducts per Mole of the Hydrophobic Substrate" substrate nonylphenol nEO dodecanol + nEO dodecanoic acid + nEO
+
d =A
c
B
A 0.95 0.86 0.93
2.33 x 2.50 x 3.29 x
-5.33 10-4 -4.76 x 10-4 3.20 x 10-3
PEO(atm) PEO(atm) 110°C 130°C XEO 90°C 110°C 130°C Nonylphenol 0.70 0.99 0.473 4.23 0.99 1.41 0.514 3.52 5.08 7.33 8.18 1.97 2.54 0.548 3.95 5.92 3.24 Nonylphenol 4 E 0
XEO
90°C
0.130 0.185 0.281 0.418
0.42 0.70 1.13
0.200 0.295
0.99 1.69
1.55 2.54
0.240 0.514
0.99 2.82
1.41 3.95
0.425 0.500 0.651
0.57 1.14 1.57
+
2.26 3.52
0.493 0.700
3.52 6.14
5.22 8.88
7.05 12.5
7.05 9.16
9.87 12.69
4.57 7.00 10.0
6.71 9.72 14.3
+
0.065 0.081 0.121 0.129 0.165 0.185 0.228 0.241 0.251
Nonylphenol 9EO 1.97 0.700 4.93 5.55 0.774 6.06 Nonylphenol 40E0 1.00 1.43 0.795 3.14 1.57 2.14 0.870 4.50 2.43 3.42 0.925 6.72
+
PEO(atm) PEO(atm) 120°C 140°C 160°C XEO 120°C 140°C 160°C Nonylphenol 1.01 0.285 5.07 1.01 0.308 4.05 2.03 0.313 3.04 1.01 0.333 6.08 2.03 0.357 5.07 3.04 0.377 4.05 3.04 0.403 6.08 4.05 0.438 5.07 2.03 0.495 6.08 Nonylphenol lOEO 1.01 0.407 4.15 1.01 0.408 3.04 1.01 0.444 5.07 2.03 0.487 5.07 2.03 0.488 4.05 3.04 0.489 6.08 2.03 0.516 6.08 3.04 0.542 5.07 4.05 0.602 6.08
+
0.114 0.146 0.186 0.223 0.238 0.294 0.300 0.327 0.385
XEO
0.202 0.218 0.263 0.270 0.286 0.306 0.313
nmax 10 15 4
-6.5 10-4 -7.7 x 10-4 -8.0 x 10-4
+ Bn + Cn2 + Dn3 + ET (g/cm3)(2' "C).
Table 2. Ethylene Oxide Partition Data at Different Temperatures in Nonylphenol and Ethoxylated Nonylphenol with Different Average Numbers of Ethylene Oxide Adducts
XEO
E
D -6.38 x 10-5 -2.69 x 10-5 -1.02 x 10-3
PEO(atm) PEO(atm) 100°C 125°C XEO 100°C 125°C Nonylphenol 2.23 0.333 2.53 2.76 0.355 2.99 2.94 0.378 3.14 2.03 0.405 3.45 Nonylphenol lOEO 2.84 0.360 2.48 3.19 0.383 2.72 2.13 0.406 2.96
+
Table 3. Ethylene Oxide Partition Data at Different Temperatures in 1-Dodecanol and Ethoxylated Dodecanol with Different Average Numbers of Ethylene Oxide Adducts PEO(atm) PEO(atm) XEO 70°C 99°C 150°C XEO 70°C 99°C 150°C Dodecanol 0.036 0.55 0.248 1.15 0.039 0.33 0.278 1.95 0.059 0.35 0.295 1.35 0.072 0.90 0.310 2.25 0.077 0.54 0.338 1.55 0.105 1.31 0.347 2.55 0.112 0.73 0.375 1.71 0.130 0.68 0.386 2.70 0.136 1.70 0.409 1.90 0.161 1.01 0.417 3.15 0.165 2.07 0.439 2.07 0.193 0.90 2.42 0.467 2.21 0.204 1.34 0.492 2.37 0.231 2.94 0.521 2.5 0.242 1.65 Dodecanol 4.3EO 0.72 0.336 1.40 0.094 2.80 0.40 0.355 0.102 1.58 0.370 0.134 0.43 1.03 0.381 1.08 0.154 0.73 0.399 1.80 0.187 1.38 0.426 2.00 0.203 0.434 1.24 0.237 0.64 1.70 0.478 1.40 0.248 1.00 0.515 1.55 0.259 2.08 0.542 1.68 0.287 1.20 0.567 1.81 0.300 0.589 1.95 0.317 0.89 2.45 0.600 2.00 0.323 Dodecanol 15E0 0.47 1.17 0.520 0.200 0.24 4.00 0.70 2.00 0.600 1.06 0.300 2.35 1.06 2.70 0.400 0.47 0.800 2.35
+
+
perature, and equilibrium pressures were measured by a pressure transducer. The vapor phase had been considered ideal in calculations, because we observed a negligible effect of nonideality in that phase. Ethylene oxide densities in the liquid phase were estimated with the Yeen and Woods correlation (19661, while the densities of organic substrates were measured by a picnometer. Relationships giving density as a function of both the temperature and the mean number of ethylene oxide adducts per mole of the hydrophobic substrate were observed and reported in Table 1. (b) Fundamental Equations for the NRTL and Wilson Methods. The Wilson equations for calculating the activity coefficients are the following:
0.330 3.45 0.430 3.09 a Data from Pate1 and Young (1993). * Data from Felippone and Gaia (1991). Data from Santacesaria et al. (1990).
In y1 = -ln(x,
strate, i.e., either nonylphenol or its ethoxylated derivatives, dodecanol or its ethoxylated derivatives, and ethoxylated derivatives of lauric acid. Weighed amounts of ethylene oxide were then added at a prefured tem-
In
+ x2A12)+ x2[A12/(xl+ x2A12)A2143t1A21
72
= -1n(x1A21
+
- xl[Ald(xl
x2A12)
+ 2211 -
+
A214~1A21 x2)l
The two interaction parameters
A12
and
(1)
1\21
(2)
were
4094 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 Table 5. Average Percent Errors Obtained for the Different Binaries Applyng the UNIFAC, Wilson, and NRTL Methods
Table 4. Ethylene Oxide Partition Data at 120 "C in Ethoxylated Dodecanoic Acid (EDA) with Different Average Number of Ethylene Oxide Adducts
XEO
0.060 0.079 0.089 0.098 0.144 0.154 0.200 0.211 0.262
XEO
0.292 0.298 0.302 0.317 0.351 0.403 0.410 0.420
1.82
1.50 1.94
mean error (%)
PEO(atm)
PEO(atm) E D A f EDA+ EDA+ 1EO 2.5EO 3.7EO 0.48 0.53 0.60 0.78 1.30 1.00 0.93 1.34
EDA+ EDA+ EDA+ 1EO 2.5EO 3.7EO 1.98 2.98 2.34 2.62 2.54 4.42 3.81 3.30
considered dependent on the mean number of ethylene oxide adducts in the component other than ethylene oxide according t o the following relations: A12
=
+ B12nE0 + C12nE0
A21
=
-k
+ C21nE0
B21nE0
2
(3)
2
(4)
The dependence of these parameters on the temperature has been found negligible. The NRTL equation for a binary system can be written as
5
Tl2G21 = x1x2[xl x2G2, x 2
+
+ +
+ +
G12= exp(-aT12) G2, = exp(-aT,,)
(7)
where gu is an energy parameter characteristic of the i-j interaction. The activity coefficient can be determined from eq 5 and result
analysis of the experimental data by finding the minimum of the objective function (Buzzi Ferraris, 1968):
where Pci, the calculated pressure, was determined by considering the vapor phase ideal: Pci
2[
(
(13)
Results Ethylene oxide partition data, at different temperatures, in nonylphenol and ethoxylated nonylphenol with different average numbers of ethylene oxide adducts, collected by Santacesaria et al. (1990), Felippone and Gaia (1991), and Patel and Young (1993), respectively, are reported in Table 2. As it can be seen, data are available for a wide range of temperatures and compositions. In Table 3, solubility data collected at different temperatures for ethylene oxide in dodecanol and in
14 2
G12
r12 x1 +
= PYEC+EO
The vapor pressure of ethylene oxide was determined with the following h t o i n e equation (Prausnitz and Anderson, 1980):
16
=1 '
8 17 6 5 19 16 7 3 3 6
18 43 18 16 20 9 8 20
18 35 10 4 3 8
+ +
Wilson
Po= expf16.74 - 2568/(T - 29.01)1/760 (14)
and
Y2
NRTL 7 24
+
where the two binary adjustable constants are linked to the energy parameters according t o the relations:
In
UNIFAC 8 33 33 28
substrate nonylphenol nonylphenol 4 E 0 nonylphenol 9EO noniylphenol + 40E0 dodecanol dodecanol 4.3EO dodecanol 15EO dodecanoic acid 1.OEO dodecanoic acid + 2.5EO dodecanoic acid 3.7EO
2
G
r21G21 2] 12)
+
(x2 +xlG2,)
(9)
a, the parameter of randomness, has been assumed
P calc., atm
, 1
Santacesaria et al. data X
0
0/'
/
Felippone and Gaia data Patel and Young data
t
l2
10
c
constant and equal t o 0.3 after optimation in the range 0.1-0.4 (Renon and Prausnitz, 1968). Again, the two interaction parameters have been considered dependent on the mean number of ethylene oxide adducts in the molecule of the component other than ethylene oxide, with the same polynomial relations: r12
=
+ B12nE0 + C12nE0
'21
=
+ B21nE0 + '21nE0
2
(10)
2
(11)
"he dependence of these parameters on the temperature has been found negligible. The parameters of the two models, i.e., A12, A21, B12, Bzl, Clz, and CZI,were determined through regression
0
2
4
6
8 10 P exp, atm
. 12
14
16
Figure 1. Perfomance of the Wilson method in predicting the equilibrium pressures for the respective binary systems EOnonylphenol and EO-ethoxylated nonylphenol with different numbers of EO adducts and different temperatures.
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 4095 Table 6. Wilson Equation Parameters Obtained by Regression substrate nonylphenol nEO dodecanol nEO dodecanoic acid + nEO
+
+
Biz
Aiz 4.010 13.00 5.917
ClZ 1.351 x -1.967 x lo-' 1.584 x
1.797 x lo-' 9.611 x lo-' 1.042
Azi 8.987 x lo-' -4.069 x lo-' 8.678 x
Bzi
CZl
-4.423 x 4.714 x -4.272 x
5.329 x -1.340 x -4.200 x
Table 7. NRTL Equation Parameters Obtained by Regression substrate nonylphenol nEO dodecanol nEO dodecanoic acid + nEO
+
+
Biz
Ai2 -2.468 x 10-1 3.713 -2.283
-9.829 -3.387 x lo-' -1.006 x lo-'
ClZ -1.694 1.748 x lo-' 1.993 x
B2i
Azi -1.429 -2.394 3.228
C2l -1.000 x 3.800 x -7.530 x lo-'
-8.340 x -1.453 x lo-' 1.473
P calc., atm
P calc.,atm I
I 1
/O
4.
1
dodecanol
-A
Ok 3 P exp, atm
4
5
Figure 2. Perfomance of the Wilson method in predicting the equilibrium pressures for the respective binary systems EOdodecanol and EO-ethoxylated dodecanol with different numbers of EO adducts and different temperatures.
ethoxylated dodecanol with different average numbers of ethylene oxide adducts are reported. These data have partially been interpreted by use of Henry's law in a previous paper (Santacesaria et al., 1990; Santacesaria et al., 1992). Solubility data are reported in Table 4, at 120 "C, for ethylene oxide in ethoxylated dodecanoic acid with 1,2.5, and 3.7 ethylene oxide adducts, respectively (Di Serio et al., 1993). All the experimental data have been subjected to statistical regression analysis. Table 5 shows the average percent errors obtained for the different examined binaries applying the UNIFAC, Wilson, and NRTL methods, respectively. As can be seen, the predictive method UNIFAC gives poor results for both ethoxylated nonylphenol and dodecanol probably because these binaries are characterized from different size molecules. NRTL gives poor results, too, while the Wilson method proved the best. In the case of ethoxylated dodecanoic acid with more than one ethylene oxide adduct, the assumption of the ethoxylated compound as a single component is rather rough; it is well-known (Di Serio et al., 1993), in fact, that during the ethoxylation transesterification reactions occur with the formation of diesters and polyglycols, according to the equilibria RCOO(EO),H
+ RCOO(EO),H
-
RCOO(EO),OOCR
+ HO(EO),H
Thus, we have mixtures of oligomers of three different types. Despite the great approximation introduced, the experimental data are well interpreted by all the
0
I
dodecanoic acid
P
2 3 P exp, atm
1
4
5
Figure 3. Perfomance of the Wilson method in predicting the equilibrium pressures for the binary systems EO-ethoxylated dodecanoic acid at 120 "C. Table 8. Comparison of Experimental Data of Hall and Agrawall(1990) for Dodecanol at High Temperature with Those Calculated with the Wilson Equations and the Parameters of Table 6 P (atm) 2.07 2.07 1.38 0.69 2.07 2.07
T ("C)
[EO], (mol/L) expt calcd
171.1 190.6 162.8 162.8 148.8 123.8
0.41 0.30 0.35 0.19 0.59 0.96
0.55 0.43 0.43 0.22 0.79 1.20
Table 9. Comparison of Experimental Data of Pate1 and Young (1993) for Nonylphenol at High Temperature with Those Calculated with the Wilson Equation and the Parameters of Table 6 PEO (atm) XEO
T ("C)
expt
calcd
0.20 0.29 0.38
193 188 188
4.55 7.72 11.10
4.96 7.61 11.34
methods applied. As the experimental data are not available for dodecanoic acid, in order t o obtain the approximated parameters for the Wilson and NRTL methods, partition data were generated by UNIFAC. The values obtained were then submitted to statistical regression analysis together with the experimental data related with the ethoxylated mixtures. Table 6 reports all the Wilson equations parameters, obtained by regression, while Table 7 reports the corresponding NRTL parameters. By using the Wilson equation parametres of Table 6, EO equilibrium pressures have been calcu-
4096 Ind. Eng. Chem. Res., Vol. 34,No. 11, 1995 molar % I--
40
~
O ~
3-
nonylphenol
30 35:
/ /
I
nonylphenol dodecanol
i 25
I
R
0- 0
-
1
1 2 3 4
Time, minutes
~
_-%k&.+
5 6 7 8 91012131415 n EO
Figure 4. Comparison of the EO consumption per mole of
Figure 6. Comparison of the oligomer distribution at EOEtOH
substrate as a function of time for, respectively, 1-dodecanol and nonylphenol. The simulation was performed at T = 130 "C, PEO= 3 atm, and catalyst concentration = 1 mole %.
= 3 for, respectively, 1-dodecanoland nonylphenol. The simulation was performed at T = 130 "C,PEO = 3 atm, and catalyst concentration of 1 mole %.
dodecanol
dodecanoic acid
1
I
I
II
I ! I
0 L--J 0
60
120
180 240 TIME, minutes
300
360
mentioned, fatty alcohols, alkylphenols, and fatty acids are ethoxylated in industry a t 150-180 "C,2-5 atm, in the presence of an alkaline catalyst such as KOH or NaOH. The kinetic behavior shown by the three substrates is absolutely different, as it can be seen in Figures 4 and 5, where the ethylene oxide consumption, referred to the initial concentration of the substrate as a function of time, is plotted. Also the evolution with time of the oligomer distribution is different as shown in Figure 6 for dodecanol and nonylphenol, respectively. Fatty acids in particular give rise t o secondary transesterification reactions (Di Serio et al., 1993) with the formation of diesters and polyglycols. All the phenomena observed have previously been explained and interpreted (Santacesaria et al. 1990, 1992a,b; Di Serio et al., 1993) on the basis of the following reaction mechanism:
(A) in situ catalyst formation B'OH-
+ RXH
Figure 5. Comparison of the EO consumption per mole of substrate as a function of time for, respectively, 1-dodecanol and dodecanoic acid. The simulation was performed at T = 130 "C, PEO= 4 atm, and catalyst concentration of 1 mole %.
lated and compared with the experimental data reported in Tables 2-4. The agreement is very satisfactory, as can be seen in Figure 1 for nonylphenol with different EOhubstrate ratios. A satisfactory agreement has also been obtained for dodecanol and derivatives as reported in Figure 2. In Figure 3, the agreement obtained for ethoxylated dodecaonoic acid with different EO/substrate ratios can be appreciated. The reliability in the use of the Wilson equation by extrapolating at high temperatures has been verified on the data reported by Hall and Agrawal (1990) for dodecanol and in those of Patel and Young (1993) for nonylphenol. In Table 8, the experimental data of Hall and Agrawal(1990) are compared with those calculated with the Wilson equation and the parameters of Table 6. In Table 9, the same comparison has been made for the data on nonylphenol reported by Patel and Young (1993). Effect of Ethylene Oxide Solubility on Both Ethogylation Kinetics and Mass Transfer. As
-
RX-B'
+ H,Ot
(B) initiation reactions (a) catalyzed
RX-B'
+ EO !!. RX(EO)-B'
(b) uncatalyzed (predominant for acid substrates)
RXH + EO
!. RX(E0)H
(C) propagation reaction
+
RX(EO)-~B+ EO 5 RX(EO)-~+~B+ (D) proton transfer RX(EO),.H
+ RX-B+
keg
RX(EO),B+
+ RXH
In the case of fatty acids, we have also transesterification reactions, such as RCOO(EO),H
+ RCOO(EO),H
+
RCOO(EO),OOCR HO(EO),H occurring with two mechanisms, one catalyzed by the
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 4097 Table 10. Kinetic and Equilibrium Constants for the Ethoxylation of Dodecanol, Nonylphenol, and Dodecanoic Acid Recalculated by Using the Wilson Equation with the Parameters Reported in Table 6 Ethoxylation Constants
ko ki k, substrate In A (moVcm3s-l) E (kcal/mol) In A (moVcm3s-l) E (kcaVmo1) 1nA (moVcm3s-l) E (kcaVmo1) Ke 1 nonylphenol 26.0 f 0.3 18.2 f 0 . 5 28.7 f 0 . 2 19.4 k0.4 0.5 f 0.1" dodecanol 20.2 f 0.3 13.2 f 0.3 20.2 f 0.3 13.2 f 0.3 4.1 f 0.5 17.5 f 0.6 22.9 f 0.7 19.6 f 0.5 20.6 f 0.4 12.5 f 0.5 (2.5 f 0.4) x dodecanoic acid 19.9 j, 0.6 Transesterification Constants
kto substrate dodecanoic acid a
T
