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The esterification of tartaric acid with ethanol: Kinetics and shifting the equilibrium by means of pervaporation
Pergamon
Chemical Engineering Science, Vol. 49, No. 24A, pp. 4681-.4689, 1994 Copyright ~) 1995 Elsevier Science Ltd Printed in Great Britain, All rights reserved 000%2509/94 $7.00 + 0.00
0009-2509(94)00365-3
THE ESTERIFICATION OF T A R T A R I C ACID WITH ETHANOL: KINETICS AND SHIFTING THE E Q U I L I B R I U M BY MEANS OF P E R V A P O R A T I O N J. T. F. K E U R E N T J E S , G. H. R. J A N S S E N and J_ J. G O R I S S E N Akzo Nobel Central Research, Dept. CRP, PO Box 9300, 6800 SB Arnhem, The Netherlands
(Received 10 May 1994; accepted for publication 4 October 1994)
Abstract--In this study the kinetic parameters have been established for the esterification of tartaric acid with ethanol. Both concentration-based as well as activity-based reaction rate constants and equilibrium constants have been determined. The activity-based data have been determined using UNIFAC activity coefficient estimations. It can be concluded that reaction rate constants determined in dilute solutions are capable of describing the reaction in a concentrated environment. This applies both for the activity-based description as well as for the concentration-based description. Although the activity coefficients involved differ significantly from unity, the effects of the individual activity coefficients are mutually compensated. Therefore, it is also possible to predict the reaction correctly when the concentration-based parameters are used. When pervaporation is used to remove the water produced in this reaction, the equilibrium composition can be shifted significantly towards the formation of the final product diethyltartrate. The membrane surface area to be installed has a clear optimum: when A/V is chosen too low the water removal is too slow and when A/V is chosen too high, too much of the ethanol is removed also.
INTRODUCTION
Esterifications represent a significant group of the reactions c o m m o n l y found in the chemical industry. H o w e v e r , kinetic data on h o m o g e n e o u s esterifications are relatively scarce in literature (Bart et al., 1994). For the description of the reaction it is c o m m o n practice to determine the required kinetic and t h e r m o d y n a m i c parameters on the basis of concentrations occurring in the reaction mixture. The data thus obtained can be considered as apparent constants (Chang, 1981) and their use is limited to the concentration range investigated. T h e r e f o r e , a more general approach is the determination of these parameters on the basis of activities of the components involved (Denbigh, 1981). Generally, activity data will not be available, however, using group contribution methods such as U N I F A C (Fredenslund et al., 1977) activities can be estimated with reasonable accuracy. D u e to the fact that esterifications are equilibrium reactions, high yields can be obtained when a large excess of one of the starting reagents is used. A n example is the production of perfumes and ester-waxes, for which a large excess of lower alcohols is used to achieve a 95% esterification of the acid ( O k a m o t o et al., 1993). H o w e v e r , this results in a relatively inefficient use of reactor space, and an efficient separation is required afterwards. Alternatively, the reaction can be forced towards completion by the removal of one of the reaction products. For esterifications the most logical c o m p o n e n t to r e m o v e is water. Distillation seems to be the most appropriate technique for the
removal of water; however, azeotrope formation can be prohibitive for the design of an efficient process_ Examples are the distillative removal of water from low-boiling alcohols. Also, due to large reflux ratios, energy consumption can be significant. In the case of the production of temperature-sensitive products or using biocatalytic conversions, the application of distillation can be impossible due to temperature constraints (Van der Padt et al_, 1993). To avoid the above-mentioned problems, m e m b r a n e separations can be considered as a viable alternative. For the removal of water from organic streams, pervaporation (PV) seems to be the appropriate m e m b r a n e technique (Rautenbach and Albrecht, 1989). Selective m e m b r a n e s are available for the dehydration of alcohols, carboxylic acids, amines and many other liquids. D u e to the fact that only the heat of vaporization of the permeating components has to be supplied, pervaporation is considered to be more energy-efficient than distillation. In the present study the esterification of tartaric acid with ethanol is investigated. A general framework is presented for the description of esterification kinetics. Also, parameters of importance to coupling of the reaction with the selective removal of water from the reaction mixture using pervaporation are discussed. THEORY
The reaction of tartaric acid with ethanol is catalyzed by methanesulfonic acid and is a two-step esterification:
4681
4682
J. T. F_ KEURENTJESet al.
0
OH
0
C-C-C--C HO /
I OH
O
OH
1 OH
--C-C---C
/
~OH
I
HO
OH
\
+ H20 OEt
% ?.o
O
C-C-C-C HO /
~)H//o + EtOH
+ EtOH NOE t
C-C--C--C
/
tEO
I
OH
\
+ H20 OEt
This can be represented schematically as: A+B~__C+D
dCE /'2 = - -
C+B,~_E+D
dt
with A = tartaric acid, B = ethanol, C = ethyltartrate, D = water and E = diethyltartrate. Due to the fact that the catalyst is a strong acid, dissociation of tartaric acid can be neglected. In dilute solutions most esterifications are first-order reactions in all components (Morrisson and Boyd, 1987). Assuming a constant reaction volume, the following rate equations can then be written for the two consecutive reactions:
=
k~f'ac" an- aeat -
k~b
"aE" ao" aca,
(2b)
The reaction rate constants k / a n d k b are replaced by ~ and k/~, so that k l / = k { f ' y A ' y S • Y c a t and klb = k[b" 7C" YD • %~,, respectively. ~ and k~ are now expected to be "true constants". The activity coefficient of component i, 3% is written as rli
3'~ = - -
dCa
(3)
Ci
r I = --__
dt
= klf" CA" Ca' C=a, - klb" Cc" CD" Cca, r2 m
(la)
dee
The activity coefficient depends on the composition of the mixture and on temperature and pressure: (4)
Vi = f ( C A , C B , C c , C o , C E , Cca,, T, P )
dt = k2f" C c ' CB" C c a t - k2b" C E " C D • Ccat
(lb)
in which klf , k l b , kEf and k2b a r e the forward and backward reaction rate constants for the first and the second reaction, respectively. For this particular esterification, dilute solutions can be obtained when a large excess of ethanol is used. However, when high yields per volume are to be achieved, the initial excess of ethanol will be relatively small. This implies that the concentrations of the different components involved will vary significantly during the reaction. Therefore, it is expected that variations in the activity coefficients will have to be taken into account, since these variations account for variations in apparent reactivities. This implies that the validity of eq. (1) cannot be taken for granted. A more general approach is to describe the reaction rate based on activities, as is done in eq. (2):
According to eq. (4), activity coefficients for each component will have to be calculated at every occurring combination of concentrations. In this paper this is done using the U N I F A C group contribution method (Fredenslund et al., 1977)• In order to model the reaction the following mass balances for each component are used:
dCA
r1 = - _ _
= k{i' VA C a ' ~'B CB" ~ , , C~,,
dt
- k{b" 7 c C c " Yo Co" ')teat Ceat
(5a)
dC~
r2 = - dt
= k~f. ~ c C c . ~ B C B . "Ycatfcat
- k~b" YECE" 7 o C o " ~'¢,,Cc,t
(5b)
dCa =
- r x - r2
(5c)
dt dCc
dCa
dt
dt
dCn = k{f. a a . a o • ac,, - k[b- ac- an" aca,
(2a)
dt
= rl - r2
(5d)
= rl + 1"2
(5e)
The esterification of tartaric acid with ethanol It is assumed that the volume of the reaction mixture is constant during the reaction: dV
--=
dt
0
(6)
This set of differential equations is solved simultaneously using a fourth-order Runge-Kutta procedure. During each iteration all activity coefficients are calculated using UNIFAC. The removal of components from the reaction mixture by means of pervaporation is usually described on the basis of the permeability coefficients (P~) and activities in the liquid (Rautenbach and Albrecht, 1989): Jt
=
Pi . a i
(7)
in which Ji is the flux of component i through the membrane. It has to be noted, however, that eq. (7) only applies when concentrations inside the membrane are low, and coupling of component flows can be neglected. The selectivity of the membrane is then defined as the ratio of the permeability coefficients (amem = Pi/Pj)- Subsequently, the water removal rate can be introduced in the water production rate equation [eq. (5e)] as follows:
rva p ~---
- Po" ao" A
V
(8)
in which A is the membrane surface area and V the volume of the reaction mixture, respectively.
4683
Table I. Initial compositions of the reaction mixture Component
Diluted
Concentrated
Ethanol Tartaric acid Methanesulfonic acid
15 mole 1.07 mole 3.6 g
10.35 mole 4.60 mole 3.6 g
0.1 N H 2 S O 4 flowing at 0.8 ml/min. UV detection at 210 nm was used. RESULTS AND DISCUSSION
Determination of kinetic parameters Activity coefficients are calculated using the UNIFAC group contribution method, using groupinteraction parameters derived from vapor-liquid equilibrium data (Rasmussen and Fredenslund, 1982). It is not always possible to apply UNIFAC to molecules having more than two functionalities (such as tartaric acid); however, distribution equilibria for tartaric acid over water and isobutanol (Collander, 1950) have been calculated and appear to be predicted correctly. Since it is difficult to assign an activity coefficient to the catalyzing acid, the reaction rate constants have been defined slightly different from those in eq. (2). Due to the fact that the concentration of the catalyst is very low, the catalyst will not influence the activities of the other components involved in the reaction. Also, it is assumed that its activity will not vary during the reaction. Although it seems plausible that the catalyst's activity even equals unity, the reaction rate constants are now defined as: k" = ")/cat" k '
EXPERIMENTAL
Reactions were carried out in a glass i-liter reaction vessel fitted with a total reflux condenser to prevent losses of product. The vessel was thermostatted and the reaction mixture was stirred at 1,000 rpm. The ethanol used was of 99.8% purity. All other reagents used were analytical grade and were purchased from Janssen Chimica (Belgium). Prior to the addition of catalyst, tartaric acid and ethanol were heated and mixed in the vessel. Experiments for the determination of kinetic data were performed at 45, 60 and 70°C, respectively, using dilute solutions (a molar ratio ethanol/tartaric acid of 14). Experiments in a concentrated system were performed using an ethanol/tartaric acid ratio of 2.25. The initial composition of the reaction mixture is given in Table 1 for both diluted and concentrated systems. The reaction mixture was analyzed for its water content by means of an automated Karl Fisher titration apparatus (Metrohm 701 KF Titrino). Concentrations of tartaric acid, ethyltartrate and diethyltartrate were determined on an Aminex HPX-87H HPLC column at 60"C. The eluent was
(9)
Reactions in diluted solutions have been performed at different temperatures. The values of k~, k2~-, /~, and k'~ are determined from the initial conversion rates and equilibrium constants. The equilibrium constants are defined as follows: aC . aD
Kto = - -
,
aA "aB
Cc" Co Ca" Ca '
K~c = - -
aE - a o
K~ = - -
(10a)
ac " aa
Ce" Co Cc'CB
K2~ - - -
(10b)
The concentration-based equilibrium constants (Klc and K2c) are usually considered as apparent constants, whereas the activity-based constants (K~o and K2o) are regarded as "true" constants. The results for both activity-based and concentrationbased constants are given in Table 2. From Table 2 it can be concluded that the deviation between k and k" values can be almost a factor of 3. The largest deviation can be found for the backward rate constants of the second reaction (k~ is much larger than /~,). The same applies for the equilibrium constants of the second reaction. This is due
J. T. F. KEumsrcrms et al.
4684
Table 2. Reaction rate constants (in 10-' m6/mole 2 . s -1) and equilibrium constants (dimensionless) at different temperatures
45 60 70
45 60 70
45 60 70
to the fact that (3'E3'O)/(YC3'B) deviates more from unity as compared to (3,c'ro)/('r,~ "/~). The forward reaction rate values of Table 2 are in the range of the values commonly found for esterifications. David et al. (1991) reported k values
2.0 4.5 9.1
0.87 1.2 1.7
0.40 1_3 2.7
0.85
.of 1 . 9 × 1 0 -3 and 2 . 6 × - 4 m 6 . m o l e - 2 . s - l for the
1.1
kv
klb
k2f
k2b
1.7 3.8 7_7
0.77 1.0 1.5
0.62 2.2 2.8
2_0 2_9
Kin
Kit
K2~
K~
esterification of propionic acid with 1-propanol and 2-propanol, respectively (T = 70°C). Okamoto et al. (1993) obtained a value of 6.6 x 10 -5 m 6. mole -2. s - l for the esterification of oleic acid with ethanol at 70 °C. By plotting In(R) versus 1/T, an Arrhenius plot is obtained [Figs l(a) and (b)]. From these plots the activation energies and frequency factors can be derived, according to
2.28 3.78 5.30
2.16 3.62 5.18
0.46 1.15 1.05
0.31
+
-7
In k l f "
2.6
4_1
0.69
/x
k = ~exp
In k l b "
o
In k2f"
+
-
In k2b"
I
-0
-0
-10 0.21
0.30
0.31
lfr
+
In k l f
In k l b
A
0.32 (S-2)
(l/K)
o
In k2f
+
In k2b
-7
-8
-0
-10 o.2e
o.3o
o.3~
1/T (IlK)
o.32
(s.21
Fig. 1. Arrhenius plot for the determination of activation energies and frequency factors: (a) activity-based; (b) concentration-based.
(11)
4685
The estefification of tartaric acid with ethanol +
A
A
E
O
C
+
D
5 4
i
,
~
,
~
,
I
0
O
.
.
0
.
.
50
0
0
+
4-
I
,
,
*
100
0
0
,
I
i
i
0
0
i
150
i
I
0
0
I
I
200
I
I
I
'
0
0
'
'
250
'
I
'
I
I
300
I
350
time (mln)
+
6
.
A
a
.
.
E
.
o
.
C
.
.
+
D
. 4.
4.
5 4 3 2
0
0
50
100
160
200
260
300
350
time (rain)
Fig. 2. Experimental results and (a) activity-based and (b) concentration-based predictions of the reaction with initial ethanol/tartaric acid ratio of 2.25.
in which Ea is the reaction activation energy and k ° the frequency factor. The results are given in Table 3 from which it is obvious that, similar to the reaction rate constants, the largest deviation between concentration-based and activity-based activation energies can be found for the backward second reaction. Reaction in concentrated mixtures
Once the reaction rate constants have been determined, reactions in concentrated solutions have been carried out. The excess of ethanol is such that initially a heterogeneous mixture exists. Solid tartaric acid is present and dissolves during the first part of the reaction. This results in an increase of the reaction volume during which the tartaric acid concentration is observed to remain constant.
Therefore, the volume increase is approximately linear and eq. (5c) is now expanded as follows: dCB
CB .
dt
.
.
.
V
dV .
dt
r! -- r 2
(12)
in which d V / d t is taken constant until all tartaric acid is dissolved. Equations similar to eq. (12) can be written for components C, D and E, whereas the concentration of component A is kept constant. In Figs 2(a) and (b) the experimental results for reactions at 70 °C are given. The solid lines in Fig. 2(a) are the model predictions using the activitybased data, whereas in Fig. 2(b) the concentrationbased data are used. Comparing Figs 2(a) and (b) it can be concluded that both approaches give acceptable predictions, although the concentration-based
J. T. F_ KEURENTJESet al.
4686 1 .eO
B 1.4o
/
~D
/
1.20
~E
1.00
~A 0 . 8 0
~'~C
o.eo
,
i
i
.
i
.
.
.
50
.
J
.
.
.
100
.
i
.
.
.
150
.
i
.
.
.
.
200
i
.
.
.
250
.
i
.
.
.
300
.
.... 350 400 t
time (mln) 1.80
1.40
i
~x~
A*B
D*E
1.20 1.00
C*D EO
1O0
B*C 150
200
2 EO
300
380
400
Ume (mln)
Fig. 3_ (a) Activity coefficients of all components during the reaction. (b) Products of activity coefficients involved.
Table 3. Activation energy E (kJ/mole) and frequency factor k° (m6/mole2. s -~) as derived from Figs l(a) and (b)
a-based c-based
Elf
Etb
E2y
E2I
~/
60.1 59.6
26.4 25.5
71.4 65.3
40.6 27.4
1.37 × 1.00 ×
predictions seem to fit the experimental data somewhat better. Although the activity coefficients of the different components deviate significantly from unity [Fig. 3(a)], this effect is partly compensated by the fact that the products of activity coefficients involved [YAYB, YCYO, YCYB and YeYo; Fig. 3(b)] are more close to unity. One of the differences between Figs 2(a) and (b) is the time required for dissolving tartaric acid. A possible explanation is that the activity coefficient of tartaric acid as calculated by U N I F A C is overestimated as compared to the real activity coefficient, possibly as a result of dimerization of the acid. When simulations are performed in which the value of aA is reduced, the description of the experimental results is improved indeed.
~b 10 6 10 6
1.84 1.12
I~,_/ 2.34 X 1 0 7 3.32 X 106
Ic°2b 357 630
Reaction combined with pervaporation The commonly used membrane for dehydrations is a polyvinylalcohol-based composite membrane. This membrane was found to be stable in an environment similar to the one used in this study (esterification of 2-propanol with propionic acid in the presence of 8 wt% paratoluene sulphonic acid) (David et al., 1991). For the combination of pervaporation with this reaction system, calculations have been performed using literature data for water/ethanol separation. Data are abundant (Mulder et al., 1985; Spitzen, 1988; Rautenbach and Albrecht, 1989; Rhim and Huang, 1992; Will and Lichtenthaler, 1992; Okamoto et al., 1993), and typical values for Po and P s are in the order of 10 -6 and 10 -8 m/s, respectively. For the model
The estefification of tartaric acid with ethanol
4687
200
180
160
140 o E =
Y
120
100
8O 60
, 0
,
,
,
i 50
,
,
,
,
i
,
,
,
,
1 O0
i
I
I
,
150
,
I
i
i
200
,
,
250
AN (l/m) Fig, 4. Required reaction time for 95% conversion at different A/V.
_.;iL'
B
E
C
50
D
timo
60
70
80
(h)
Fig. 5_ Concentrations of all components during the reaction combined with PV at A/V is 100 m -I.
calculations, values for Po and PB of 1.2 x 10-6 and 1.4 x 10 -8 m/s, respectively, are used. Starting with an initial tartaric acid/ethanol ratio of 2.25, 95% of the initial amount of tartaric acid has to be converted into diethyltartrate. The time required to come to this conversion is taken as the variable to be optimized. In Fig. 4 the reaction time is plotted versus the ratio of the membrane surface area to reaction volume (m2/m3). At low A / V the water removal rate is too low, resulting in long reaction times. At A / V = 100m -1 the required reaction time is at a minimum value of 70.5 h. For this situation the concentration profiles of all components are depicted in Fig. 5. However, when A / V is chosen too high, a significant amount of ethanol will be removed, also resulting in decreased forward reaction rates (Fig. 6). Shorter reaction times with increased membrane area are of course possible if the initial ethanol content of the batch is increased or ethanol is added in a fed batch mode during the reaction.
When Figs 2 and 5 are compared, it is obvious that the equilibrium can be shifted towards the formation of diethyltartrate. In Fig. 2 the equilibrium concentration of ethyltartrate still exceeds the concentration of diethyltartrate. Effectively removing the water produced during the reaction yields a product which contains more than 95% of diethyltartrate. CONCLUSIONS Kinetic parameters have been determined for the esterification of tartaric acid with ethanol. From this study it can be concluded that reaction rate constants determined in dilute solutions are capable of describing the reaction in a concentrated environment. This applies both for the activity-based description using UNIFAC as well as for the concentration-based description. Although the activity coefficients involved differ significantly from unity, the effects of the individual activity coefficients are mutually compensated. For this
J. T. F. KEURENTJESet al.
4688 e
A
B
5
!
E
v
s 2
C ~ D
~ 0
10
,
,
,
20
$0
40
50
80
70
80
time (h)
Fig. 6. Concentration of all components during the reaction combined with PV at A/V is 400 m- i. reason it is also possible to predict the reaction correctly when the concentration-based parameters are used. When pervaporation is used to remove the water produced in this reaction, the equilibrium composition can be shifted significantly towards the formation of the final product diethyltartrate. The m e m b r a n e surface area to be installed has a clear optimum: when the A / V chosen is too low the water removal is too slow and when the A / V chosen is too high, too much of the ethanol is removed also. Acknowledgement--The authors wish to thank H. M. van Sonsbeek for the development of the UNIFAC computer program.
Q
A C Ea J k ko K P r
V
NOTATION activity, mole/liter m e m b r a n e surface area, m 2 concentration, mole/liter activation energy, J/mole flux, mole/(m 2_ s) reaction rate constant, m6/(mole 2. s) frequency factor, m6/(mole 2. s) equilibrium constant permeability coefficient, m/s reaction rate, mole/(m 3 . s) volume, m 3
Greek letters m e m b r a n e selectivity ~, activity coefficient Subscripts and superscripts 1 reaction 1 2 reaction 2 a activity based A component A (tartaric acid) b backward B component B (ethanol) c concentration based cat catalyst C component C (ethyltartrate)
D E f i vap ' "
component D (water) component E (diethyltartrate) forward component pervaporation activity based activity based, excluding catalyst
REFERENCES Bart, H. J., Reidetschl~iger, J., Schatka, K. and Lehmann, A., 1994, Kinetics of esterification of levulinic acid with n-butanol by homogeneous catalysis. Ind. Eng. Chem. 33, 21-25_ Chang, R_, 1981, Physical Chemistry with Applications to Biological Systems, 2nd edn. Macmillan, New York. Collander, R., 1950, The distribution of organic compounds between iso-butanol and water. Acta Chim. Scandinavica 4, 1085-1098. David, M.-O., Gref, R., Nguyen, T. Q. and Neel, J., 1991, Pervaporation-esterification coupling: Part I. Basic kinetic model_ Trans. Inst. Chem. Eng. 69A, 335-340. Denbigh, K., 1981, The Principles of Chemical Equilibrium, 4th edn. Cambridge University Press, Cambridge. Fredenslund, A., Gmehling, J_ and Rasmussen, P_, 1977, Vapour-Liquid Equilibria using UNIFAC. Elsevier, Amsterdam. Morrison, R. T. and Boyd, R, N., 1987, Organic Chemistry, 5th edn. Allyn and Bacon, Newton, Mass, Mulder, M. H. V., Franken, A. C. M. and Smolders, C. A., 1985, On the mechanism of separation of ethanol/ water mixtures by pervaporation II. Experimental concentration profiles. J. Membrane Sci. 23, 41-58. Okamoto, K_, Yamamoto, M., Otoshi, Y., Semoto, T., Yano, M., Tanaka, K. and Kita, H., 1993, Pervaporation-aided esterification of oleic acid. J. Chem. Eng. Japan 26, 475--481. Rasmussen, P. and Fredenslund, A., 1982, Vapor-liquid equilibria by UNIFAC group contribution, revision and extension. Ind. Eng. Chem, Proc. Des. Dev. 21, 118--127. Rautenbach, R. and Albrecht, R., 1989, Membrane Processes. John Wiley, Chichester. Rhim, J. W. and Huang, Y. M., 1992, Prediction of pervaporation separation characteristics for the ethanol-water-nylon-4 membrane system. J. Membrane Sci. 70, 105-118.
The esterification of tartaric acid with ethanol Spitzen, J., 1988, Pervaporation membranes and models for the dyhydration of ethanol. Thesis Twente University of Technology. Van der Padt, A., Sewalt, J. J. W. and van 't Riet, K., 1993, On-line water removal during enzymatic triacylglycerol synthesis by means of pervaporation. J. Membrane Sci_ 80, 199-208.
4689
Will, B. and Lichtenthaler, R. N., 1992, Comparison of the separation of mixtures by vapor permeation and by pervaporation using PVA composite membranes. I_ Binary alcohol-water systems. J. Membrane Sci. 68, 119-125.
Chemical Engineering Science, Vol. 49, No. 24A, pp. 4681-.4689, 1994 Copyright ~) 1995 Elsevier Science Ltd Printed in Great Britain, All rights reserved 000%2509/94 $7.00 + 0.00
0009-2509(94)00365-3
THE ESTERIFICATION OF T A R T A R I C ACID WITH ETHANOL: KINETICS AND SHIFTING THE E Q U I L I B R I U M BY MEANS OF P E R V A P O R A T I O N J. T. F. K E U R E N T J E S , G. H. R. J A N S S E N and J_ J. G O R I S S E N Akzo Nobel Central Research, Dept. CRP, PO Box 9300, 6800 SB Arnhem, The Netherlands
(Received 10 May 1994; accepted for publication 4 October 1994)
Abstract--In this study the kinetic parameters have been established for the esterification of tartaric acid with ethanol. Both concentration-based as well as activity-based reaction rate constants and equilibrium constants have been determined. The activity-based data have been determined using UNIFAC activity coefficient estimations. It can be concluded that reaction rate constants determined in dilute solutions are capable of describing the reaction in a concentrated environment. This applies both for the activity-based description as well as for the concentration-based description. Although the activity coefficients involved differ significantly from unity, the effects of the individual activity coefficients are mutually compensated. Therefore, it is also possible to predict the reaction correctly when the concentration-based parameters are used. When pervaporation is used to remove the water produced in this reaction, the equilibrium composition can be shifted significantly towards the formation of the final product diethyltartrate. The membrane surface area to be installed has a clear optimum: when A/V is chosen too low the water removal is too slow and when A/V is chosen too high, too much of the ethanol is removed also.
INTRODUCTION
Esterifications represent a significant group of the reactions c o m m o n l y found in the chemical industry. H o w e v e r , kinetic data on h o m o g e n e o u s esterifications are relatively scarce in literature (Bart et al., 1994). For the description of the reaction it is c o m m o n practice to determine the required kinetic and t h e r m o d y n a m i c parameters on the basis of concentrations occurring in the reaction mixture. The data thus obtained can be considered as apparent constants (Chang, 1981) and their use is limited to the concentration range investigated. T h e r e f o r e , a more general approach is the determination of these parameters on the basis of activities of the components involved (Denbigh, 1981). Generally, activity data will not be available, however, using group contribution methods such as U N I F A C (Fredenslund et al., 1977) activities can be estimated with reasonable accuracy. D u e to the fact that esterifications are equilibrium reactions, high yields can be obtained when a large excess of one of the starting reagents is used. A n example is the production of perfumes and ester-waxes, for which a large excess of lower alcohols is used to achieve a 95% esterification of the acid ( O k a m o t o et al., 1993). H o w e v e r , this results in a relatively inefficient use of reactor space, and an efficient separation is required afterwards. Alternatively, the reaction can be forced towards completion by the removal of one of the reaction products. For esterifications the most logical c o m p o n e n t to r e m o v e is water. Distillation seems to be the most appropriate technique for the
removal of water; however, azeotrope formation can be prohibitive for the design of an efficient process_ Examples are the distillative removal of water from low-boiling alcohols. Also, due to large reflux ratios, energy consumption can be significant. In the case of the production of temperature-sensitive products or using biocatalytic conversions, the application of distillation can be impossible due to temperature constraints (Van der Padt et al_, 1993). To avoid the above-mentioned problems, m e m b r a n e separations can be considered as a viable alternative. For the removal of water from organic streams, pervaporation (PV) seems to be the appropriate m e m b r a n e technique (Rautenbach and Albrecht, 1989). Selective m e m b r a n e s are available for the dehydration of alcohols, carboxylic acids, amines and many other liquids. D u e to the fact that only the heat of vaporization of the permeating components has to be supplied, pervaporation is considered to be more energy-efficient than distillation. In the present study the esterification of tartaric acid with ethanol is investigated. A general framework is presented for the description of esterification kinetics. Also, parameters of importance to coupling of the reaction with the selective removal of water from the reaction mixture using pervaporation are discussed. THEORY
The reaction of tartaric acid with ethanol is catalyzed by methanesulfonic acid and is a two-step esterification:
4681
4682
J. T. F_ KEURENTJESet al.
0
OH
0
C-C-C--C HO /
I OH
O
OH
1 OH
--C-C---C
/
~OH
I
HO
OH
\
+ H20 OEt
% ?.o
O
C-C-C-C HO /
~)H//o + EtOH
+ EtOH NOE t
C-C--C--C
/
tEO
I
OH
\
+ H20 OEt
This can be represented schematically as: A+B~__C+D
dCE /'2 = - -
C+B,~_E+D
dt
with A = tartaric acid, B = ethanol, C = ethyltartrate, D = water and E = diethyltartrate. Due to the fact that the catalyst is a strong acid, dissociation of tartaric acid can be neglected. In dilute solutions most esterifications are first-order reactions in all components (Morrisson and Boyd, 1987). Assuming a constant reaction volume, the following rate equations can then be written for the two consecutive reactions:
=
k~f'ac" an- aeat -
k~b
"aE" ao" aca,
(2b)
The reaction rate constants k / a n d k b are replaced by ~ and k/~, so that k l / = k { f ' y A ' y S • Y c a t and klb = k[b" 7C" YD • %~,, respectively. ~ and k~ are now expected to be "true constants". The activity coefficient of component i, 3% is written as rli
3'~ = - -
dCa
(3)
Ci
r I = --__
dt
= klf" CA" Ca' C=a, - klb" Cc" CD" Cca, r2 m
(la)
dee
The activity coefficient depends on the composition of the mixture and on temperature and pressure: (4)
Vi = f ( C A , C B , C c , C o , C E , Cca,, T, P )
dt = k2f" C c ' CB" C c a t - k2b" C E " C D • Ccat
(lb)
in which klf , k l b , kEf and k2b a r e the forward and backward reaction rate constants for the first and the second reaction, respectively. For this particular esterification, dilute solutions can be obtained when a large excess of ethanol is used. However, when high yields per volume are to be achieved, the initial excess of ethanol will be relatively small. This implies that the concentrations of the different components involved will vary significantly during the reaction. Therefore, it is expected that variations in the activity coefficients will have to be taken into account, since these variations account for variations in apparent reactivities. This implies that the validity of eq. (1) cannot be taken for granted. A more general approach is to describe the reaction rate based on activities, as is done in eq. (2):
According to eq. (4), activity coefficients for each component will have to be calculated at every occurring combination of concentrations. In this paper this is done using the U N I F A C group contribution method (Fredenslund et al., 1977)• In order to model the reaction the following mass balances for each component are used:
dCA
r1 = - _ _
= k{i' VA C a ' ~'B CB" ~ , , C~,,
dt
- k{b" 7 c C c " Yo Co" ')teat Ceat
(5a)
dC~
r2 = - dt
= k~f. ~ c C c . ~ B C B . "Ycatfcat
- k~b" YECE" 7 o C o " ~'¢,,Cc,t
(5b)
dCa =
- r x - r2
(5c)
dt dCc
dCa
dt
dt
dCn = k{f. a a . a o • ac,, - k[b- ac- an" aca,
(2a)
dt
= rl - r2
(5d)
= rl + 1"2
(5e)
The esterification of tartaric acid with ethanol It is assumed that the volume of the reaction mixture is constant during the reaction: dV
--=
dt
0
(6)
This set of differential equations is solved simultaneously using a fourth-order Runge-Kutta procedure. During each iteration all activity coefficients are calculated using UNIFAC. The removal of components from the reaction mixture by means of pervaporation is usually described on the basis of the permeability coefficients (P~) and activities in the liquid (Rautenbach and Albrecht, 1989): Jt
=
Pi . a i
(7)
in which Ji is the flux of component i through the membrane. It has to be noted, however, that eq. (7) only applies when concentrations inside the membrane are low, and coupling of component flows can be neglected. The selectivity of the membrane is then defined as the ratio of the permeability coefficients (amem = Pi/Pj)- Subsequently, the water removal rate can be introduced in the water production rate equation [eq. (5e)] as follows:
rva p ~---
- Po" ao" A
V
(8)
in which A is the membrane surface area and V the volume of the reaction mixture, respectively.
4683
Table I. Initial compositions of the reaction mixture Component
Diluted
Concentrated
Ethanol Tartaric acid Methanesulfonic acid
15 mole 1.07 mole 3.6 g
10.35 mole 4.60 mole 3.6 g
0.1 N H 2 S O 4 flowing at 0.8 ml/min. UV detection at 210 nm was used. RESULTS AND DISCUSSION
Determination of kinetic parameters Activity coefficients are calculated using the UNIFAC group contribution method, using groupinteraction parameters derived from vapor-liquid equilibrium data (Rasmussen and Fredenslund, 1982). It is not always possible to apply UNIFAC to molecules having more than two functionalities (such as tartaric acid); however, distribution equilibria for tartaric acid over water and isobutanol (Collander, 1950) have been calculated and appear to be predicted correctly. Since it is difficult to assign an activity coefficient to the catalyzing acid, the reaction rate constants have been defined slightly different from those in eq. (2). Due to the fact that the concentration of the catalyst is very low, the catalyst will not influence the activities of the other components involved in the reaction. Also, it is assumed that its activity will not vary during the reaction. Although it seems plausible that the catalyst's activity even equals unity, the reaction rate constants are now defined as: k" = ")/cat" k '
EXPERIMENTAL
Reactions were carried out in a glass i-liter reaction vessel fitted with a total reflux condenser to prevent losses of product. The vessel was thermostatted and the reaction mixture was stirred at 1,000 rpm. The ethanol used was of 99.8% purity. All other reagents used were analytical grade and were purchased from Janssen Chimica (Belgium). Prior to the addition of catalyst, tartaric acid and ethanol were heated and mixed in the vessel. Experiments for the determination of kinetic data were performed at 45, 60 and 70°C, respectively, using dilute solutions (a molar ratio ethanol/tartaric acid of 14). Experiments in a concentrated system were performed using an ethanol/tartaric acid ratio of 2.25. The initial composition of the reaction mixture is given in Table 1 for both diluted and concentrated systems. The reaction mixture was analyzed for its water content by means of an automated Karl Fisher titration apparatus (Metrohm 701 KF Titrino). Concentrations of tartaric acid, ethyltartrate and diethyltartrate were determined on an Aminex HPX-87H HPLC column at 60"C. The eluent was
(9)
Reactions in diluted solutions have been performed at different temperatures. The values of k~, k2~-, /~, and k'~ are determined from the initial conversion rates and equilibrium constants. The equilibrium constants are defined as follows: aC . aD
Kto = - -
,
aA "aB
Cc" Co Ca" Ca '
K~c = - -
aE - a o
K~ = - -
(10a)
ac " aa
Ce" Co Cc'CB
K2~ - - -
(10b)
The concentration-based equilibrium constants (Klc and K2c) are usually considered as apparent constants, whereas the activity-based constants (K~o and K2o) are regarded as "true" constants. The results for both activity-based and concentrationbased constants are given in Table 2. From Table 2 it can be concluded that the deviation between k and k" values can be almost a factor of 3. The largest deviation can be found for the backward rate constants of the second reaction (k~ is much larger than /~,). The same applies for the equilibrium constants of the second reaction. This is due
J. T. F. KEumsrcrms et al.
4684
Table 2. Reaction rate constants (in 10-' m6/mole 2 . s -1) and equilibrium constants (dimensionless) at different temperatures
45 60 70
45 60 70
45 60 70
to the fact that (3'E3'O)/(YC3'B) deviates more from unity as compared to (3,c'ro)/('r,~ "/~). The forward reaction rate values of Table 2 are in the range of the values commonly found for esterifications. David et al. (1991) reported k values
2.0 4.5 9.1
0.87 1.2 1.7
0.40 1_3 2.7
0.85
.of 1 . 9 × 1 0 -3 and 2 . 6 × - 4 m 6 . m o l e - 2 . s - l for the
1.1
kv
klb
k2f
k2b
1.7 3.8 7_7
0.77 1.0 1.5
0.62 2.2 2.8
2_0 2_9
Kin
Kit
K2~
K~
esterification of propionic acid with 1-propanol and 2-propanol, respectively (T = 70°C). Okamoto et al. (1993) obtained a value of 6.6 x 10 -5 m 6. mole -2. s - l for the esterification of oleic acid with ethanol at 70 °C. By plotting In(R) versus 1/T, an Arrhenius plot is obtained [Figs l(a) and (b)]. From these plots the activation energies and frequency factors can be derived, according to
2.28 3.78 5.30
2.16 3.62 5.18
0.46 1.15 1.05
0.31
+
-7
In k l f "
2.6
4_1
0.69
/x
k = ~exp
In k l b "
o
In k2f"
+
-
In k2b"
I
-0
-0
-10 0.21
0.30
0.31
lfr
+
In k l f
In k l b
A
0.32 (S-2)
(l/K)
o
In k2f
+
In k2b
-7
-8
-0
-10 o.2e
o.3o
o.3~
1/T (IlK)
o.32
(s.21
Fig. 1. Arrhenius plot for the determination of activation energies and frequency factors: (a) activity-based; (b) concentration-based.
(11)
4685
The estefification of tartaric acid with ethanol +
A
A
E
O
C
+
D
5 4
i
,
~
,
~
,
I
0
O
.
.
0
.
.
50
0
0
+
4-
I
,
,
*
100
0
0
,
I
i
i
0
0
i
150
i
I
0
0
I
I
200
I
I
I
'
0
0
'
'
250
'
I
'
I
I
300
I
350
time (mln)
+
6
.
A
a
.
.
E
.
o
.
C
.
.
+
D
. 4.
4.
5 4 3 2
0
0
50
100
160
200
260
300
350
time (rain)
Fig. 2. Experimental results and (a) activity-based and (b) concentration-based predictions of the reaction with initial ethanol/tartaric acid ratio of 2.25.
in which Ea is the reaction activation energy and k ° the frequency factor. The results are given in Table 3 from which it is obvious that, similar to the reaction rate constants, the largest deviation between concentration-based and activity-based activation energies can be found for the backward second reaction. Reaction in concentrated mixtures
Once the reaction rate constants have been determined, reactions in concentrated solutions have been carried out. The excess of ethanol is such that initially a heterogeneous mixture exists. Solid tartaric acid is present and dissolves during the first part of the reaction. This results in an increase of the reaction volume during which the tartaric acid concentration is observed to remain constant.
Therefore, the volume increase is approximately linear and eq. (5c) is now expanded as follows: dCB
CB .
dt
.
.
.
V
dV .
dt
r! -- r 2
(12)
in which d V / d t is taken constant until all tartaric acid is dissolved. Equations similar to eq. (12) can be written for components C, D and E, whereas the concentration of component A is kept constant. In Figs 2(a) and (b) the experimental results for reactions at 70 °C are given. The solid lines in Fig. 2(a) are the model predictions using the activitybased data, whereas in Fig. 2(b) the concentrationbased data are used. Comparing Figs 2(a) and (b) it can be concluded that both approaches give acceptable predictions, although the concentration-based
J. T. F_ KEURENTJESet al.
4686 1 .eO
B 1.4o
/
~D
/
1.20
~E
1.00
~A 0 . 8 0
~'~C
o.eo
,
i
i
.
i
.
.
.
50
.
J
.
.
.
100
.
i
.
.
.
150
.
i
.
.
.
.
200
i
.
.
.
250
.
i
.
.
.
300
.
.... 350 400 t
time (mln) 1.80
1.40
i
~x~
A*B
D*E
1.20 1.00
C*D EO
1O0
B*C 150
200
2 EO
300
380
400
Ume (mln)
Fig. 3_ (a) Activity coefficients of all components during the reaction. (b) Products of activity coefficients involved.
Table 3. Activation energy E (kJ/mole) and frequency factor k° (m6/mole2. s -~) as derived from Figs l(a) and (b)
a-based c-based
Elf
Etb
E2y
E2I
~/
60.1 59.6
26.4 25.5
71.4 65.3
40.6 27.4
1.37 × 1.00 ×
predictions seem to fit the experimental data somewhat better. Although the activity coefficients of the different components deviate significantly from unity [Fig. 3(a)], this effect is partly compensated by the fact that the products of activity coefficients involved [YAYB, YCYO, YCYB and YeYo; Fig. 3(b)] are more close to unity. One of the differences between Figs 2(a) and (b) is the time required for dissolving tartaric acid. A possible explanation is that the activity coefficient of tartaric acid as calculated by U N I F A C is overestimated as compared to the real activity coefficient, possibly as a result of dimerization of the acid. When simulations are performed in which the value of aA is reduced, the description of the experimental results is improved indeed.
~b 10 6 10 6
1.84 1.12
I~,_/ 2.34 X 1 0 7 3.32 X 106
Ic°2b 357 630
Reaction combined with pervaporation The commonly used membrane for dehydrations is a polyvinylalcohol-based composite membrane. This membrane was found to be stable in an environment similar to the one used in this study (esterification of 2-propanol with propionic acid in the presence of 8 wt% paratoluene sulphonic acid) (David et al., 1991). For the combination of pervaporation with this reaction system, calculations have been performed using literature data for water/ethanol separation. Data are abundant (Mulder et al., 1985; Spitzen, 1988; Rautenbach and Albrecht, 1989; Rhim and Huang, 1992; Will and Lichtenthaler, 1992; Okamoto et al., 1993), and typical values for Po and P s are in the order of 10 -6 and 10 -8 m/s, respectively. For the model
The estefification of tartaric acid with ethanol
4687
200
180
160
140 o E =
Y
120
100
8O 60
, 0
,
,
,
i 50
,
,
,
,
i
,
,
,
,
1 O0
i
I
I
,
150
,
I
i
i
200
,
,
250
AN (l/m) Fig, 4. Required reaction time for 95% conversion at different A/V.
_.;iL'
B
E
C
50
D
timo
60
70
80
(h)
Fig. 5_ Concentrations of all components during the reaction combined with PV at A/V is 100 m -I.
calculations, values for Po and PB of 1.2 x 10-6 and 1.4 x 10 -8 m/s, respectively, are used. Starting with an initial tartaric acid/ethanol ratio of 2.25, 95% of the initial amount of tartaric acid has to be converted into diethyltartrate. The time required to come to this conversion is taken as the variable to be optimized. In Fig. 4 the reaction time is plotted versus the ratio of the membrane surface area to reaction volume (m2/m3). At low A / V the water removal rate is too low, resulting in long reaction times. At A / V = 100m -1 the required reaction time is at a minimum value of 70.5 h. For this situation the concentration profiles of all components are depicted in Fig. 5. However, when A / V is chosen too high, a significant amount of ethanol will be removed, also resulting in decreased forward reaction rates (Fig. 6). Shorter reaction times with increased membrane area are of course possible if the initial ethanol content of the batch is increased or ethanol is added in a fed batch mode during the reaction.
When Figs 2 and 5 are compared, it is obvious that the equilibrium can be shifted towards the formation of diethyltartrate. In Fig. 2 the equilibrium concentration of ethyltartrate still exceeds the concentration of diethyltartrate. Effectively removing the water produced during the reaction yields a product which contains more than 95% of diethyltartrate. CONCLUSIONS Kinetic parameters have been determined for the esterification of tartaric acid with ethanol. From this study it can be concluded that reaction rate constants determined in dilute solutions are capable of describing the reaction in a concentrated environment. This applies both for the activity-based description using UNIFAC as well as for the concentration-based description. Although the activity coefficients involved differ significantly from unity, the effects of the individual activity coefficients are mutually compensated. For this
J. T. F. KEURENTJESet al.
4688 e
A
B
5
!
E
v
s 2
C ~ D
~ 0
10
,
,
,
20
$0
40
50
80
70
80
time (h)
Fig. 6. Concentration of all components during the reaction combined with PV at A/V is 400 m- i. reason it is also possible to predict the reaction correctly when the concentration-based parameters are used. When pervaporation is used to remove the water produced in this reaction, the equilibrium composition can be shifted significantly towards the formation of the final product diethyltartrate. The m e m b r a n e surface area to be installed has a clear optimum: when the A / V chosen is too low the water removal is too slow and when the A / V chosen is too high, too much of the ethanol is removed also. Acknowledgement--The authors wish to thank H. M. van Sonsbeek for the development of the UNIFAC computer program.
Q
A C Ea J k ko K P r
V
NOTATION activity, mole/liter m e m b r a n e surface area, m 2 concentration, mole/liter activation energy, J/mole flux, mole/(m 2_ s) reaction rate constant, m6/(mole 2. s) frequency factor, m6/(mole 2. s) equilibrium constant permeability coefficient, m/s reaction rate, mole/(m 3 . s) volume, m 3
Greek letters m e m b r a n e selectivity ~, activity coefficient Subscripts and superscripts 1 reaction 1 2 reaction 2 a activity based A component A (tartaric acid) b backward B component B (ethanol) c concentration based cat catalyst C component C (ethyltartrate)
D E f i vap ' "
component D (water) component E (diethyltartrate) forward component pervaporation activity based activity based, excluding catalyst
REFERENCES Bart, H. J., Reidetschl~iger, J., Schatka, K. and Lehmann, A., 1994, Kinetics of esterification of levulinic acid with n-butanol by homogeneous catalysis. Ind. Eng. Chem. 33, 21-25_ Chang, R_, 1981, Physical Chemistry with Applications to Biological Systems, 2nd edn. Macmillan, New York. Collander, R., 1950, The distribution of organic compounds between iso-butanol and water. Acta Chim. Scandinavica 4, 1085-1098. David, M.-O., Gref, R., Nguyen, T. Q. and Neel, J., 1991, Pervaporation-esterification coupling: Part I. Basic kinetic model_ Trans. Inst. Chem. Eng. 69A, 335-340. Denbigh, K., 1981, The Principles of Chemical Equilibrium, 4th edn. Cambridge University Press, Cambridge. Fredenslund, A., Gmehling, J_ and Rasmussen, P_, 1977, Vapour-Liquid Equilibria using UNIFAC. Elsevier, Amsterdam. Morrison, R. T. and Boyd, R, N., 1987, Organic Chemistry, 5th edn. Allyn and Bacon, Newton, Mass, Mulder, M. H. V., Franken, A. C. M. and Smolders, C. A., 1985, On the mechanism of separation of ethanol/ water mixtures by pervaporation II. Experimental concentration profiles. J. Membrane Sci. 23, 41-58. Okamoto, K_, Yamamoto, M., Otoshi, Y., Semoto, T., Yano, M., Tanaka, K. and Kita, H., 1993, Pervaporation-aided esterification of oleic acid. J. Chem. Eng. Japan 26, 475--481. Rasmussen, P. and Fredenslund, A., 1982, Vapor-liquid equilibria by UNIFAC group contribution, revision and extension. Ind. Eng. Chem, Proc. Des. Dev. 21, 118--127. Rautenbach, R. and Albrecht, R., 1989, Membrane Processes. John Wiley, Chichester. Rhim, J. W. and Huang, Y. M., 1992, Prediction of pervaporation separation characteristics for the ethanol-water-nylon-4 membrane system. J. Membrane Sci. 70, 105-118.
The esterification of tartaric acid with ethanol Spitzen, J., 1988, Pervaporation membranes and models for the dyhydration of ethanol. Thesis Twente University of Technology. Van der Padt, A., Sewalt, J. J. W. and van 't Riet, K., 1993, On-line water removal during enzymatic triacylglycerol synthesis by means of pervaporation. J. Membrane Sci_ 80, 199-208.
4689
Will, B. and Lichtenthaler, R. N., 1992, Comparison of the separation of mixtures by vapor permeation and by pervaporation using PVA composite membranes. I_ Binary alcohol-water systems. J. Membrane Sci. 68, 119-125.