Ind. Eng. Chem. Res. 1998, 37, 1917-1928
1917
SEPARATIONS Measurement of Residue Curve Maps and Heterogeneous Kinetics in Methyl Acetate Synthesis Wei Song,† Ganesh Venimadhavan, Jason M. Manning, Michael F. Malone, and Michael F. Doherty* Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003
Kinetically controlled reactive distillation is a bridge between the two limiting cases of nonreactive and equilibrium reactive distillation. In this paper, we study the influence of heterogeneous catalysis on the transition from the nonreactive to the equilibrium reactive limits for the esterification of acetic acid with methanol. A Langmuir-Hinshelwood/Hougen-Watson rate model was developed to represent the reaction kinetics. Since reactive distillation is carried out at the boiling temperature of the liquid, the pressure of the system plays an important role in determining the product composition. Higher operating pressures imply higher temperatures and faster rates of reaction but could also lower equilibrium conversions (for exothermic systems) and trigger unwanted side reactions. To study the importance of side reactions and the effect of pressure on product selectivity, we also include the reaction kinetics for methanol dehydration. Isothermal batch kinetic experiments were performed using a heterogeneous (Amberlyst 15W) catalyst at various temperatures and catalyst concentrations. Independent binary adsorption experiments were also performed to estimate the adsorption equilibrium constants. As a test of the kinetic model, independent equilibrium reactive open-evaporation experiments were performed and the model prediction was found to be in good agreement with the experimental residue curve measurements. The model was also used to predict the behavior of the system in the kinetically controlled regime. Residue curves for the kinetically controlled cases are qualitatively similar to that of the equilibrium case, showing that the production of methyl acetate can be carried out using reactive distillation in both the equilibrium and the kinetically controlled regimes. Introduction Reactive distillation is an important hybrid separation process (e.g., Agreda and Partin, 1984; Agreda et al., 1990; DeGarmo et al., 1992; Doherty and Buzad, 1992; Smith, 1981, 1984, 1990). A useful tool for the synthesis and analysis of both nonreactive and reactive distillation systems is the simple distillation residue curve map (RCM) (e.g., Fidkowski et al., 1993; Foucher et al., 1991; Wahnschafft et al., 1992; Venimadhavan et al., 1994). The structure of the residue curve map is determined by the number of singular points in the mixture together with their temperature and composition. For a nonreactive mixture, these singular points are the pure components and azeotropes; however, their number, temperature, and composition may change with the introduction of chemical reaction. Reactive distillation systems are bounded by two limiting cases: (1) the equilibrium reactive case where there is simultaneous vapor-liquid and reaction equilibrium (Barbosa and Doherty, 1988; Ung and Doherty, 1995a-d) and (2) the nonreactive case where no reaction occurs. To under* To whom correspondence should be addressed. † Present address: Pennzoil Products Company, 1520 Lake Front Circle (77380), P.O. Box 7569, The Woodlands, TX 77387.
stand the transition from the nonreactive to the equilibrium reactive distillation system, we need to know the kinetics of the reaction (Venimadhavan et al., 1994; Rev, 1994; Rehfinger and Hoffmann, 1990; Sundmacher and Hoffmann, 1994). In this paper, we study the influence of heterogeneous catalysis on the transition from the nonreactive to the equilibrium reactive limits. We report the related simple distillation experiments for the reactive mixture. Methyl acetate can be made by the liquid-phase reaction of acetic acid (HOAc) and methanol (MeOH) catalyzed by sulfuric acid or a sulfonic acid ion-exchange resin in the temperature range of 310-325 K and at a pressure of 1 atm. The reaction is
acetic acid + methanol S methyl acetate + water (H2O) (HOAc) (MeOH) (MeOAc) (1) This is a classic example in reactive distillation (Agreda et al., 1984, 1990; Siirola, 1995). The simple distillation experiment is an easy way of studying the feasibility of continuous and batch distillation processes (Bernot et al., 1991; Fidkowski et al., 1993; Wahnschafft et al., 1992). For reactive systems, the limiting case of simultaneous vapor-liquid and
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1918 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998
reaction equilibrium is now well understood theoretically (Barbosa and Doherty, 1988; Ung and Doherty, 1995a-d, Espinosa et al., 1995). However, in many applications, conditions of reaction equilibrium may not be approached because of limited rates of reaction and residence times. Furthermore, in systems where the main product is an intermediate that reacts further with the reactants or with other products, it is undesirable to let the system reach reaction equilibrium. The behavior of a system near reaction equilibrium may be quite different from conditions where the reaction is kinetically controlled, and we must have a good understanding of the reaction kinetics to examine the behavior. Kinetic rate expressions used in reactive distillation models are best written in terms of activities as opposed to the more familiar concentration-based rate expressions (e.g., Venimadhavan et al., 1994; Rehfinger and Hoffmann, 1990; Sundmacher and Hoffmann, 1994). For the methyl acetate system the rate expression in terms of activities is strongly preferred because the high polarity of water and methanol compared to methyl acetate leads to strongly nonideal solution behavior. Earlier works on the kinetics of this system have reported preexponentials and the activation energies for the concentration-based rate expressions for the esterification kinetics of different alcohols (Smith, 1939) or have not addressed the range of species and catalyst concentrations of interest for reactive distillation space (Neumann and Sasson, 1984; Xu and Chuang, 1996). In this paper we report the results of batch kinetic experiments for the methyl acetate system over a range of molar feed ratios more typical of reactive distillation conditions. A macroreticular ion-exchange resin such as Amberlyst 15W is an ensemble of microspheres. More than 95% of all functional groups (the protons) are inside the microspheres and are only accessible to substances which are able to penetrate the network of cross-linked polymer chains. Consequently, adsorption effects must be taken into account in order to describe reactions catalyzed by ion-exchange resins, e.g., Oost and Hoffmann (1996). Therefore, we developed a heterogeneous Langmuir-Hinshelwood/Hougen-Watson (LHHW) type rate expression. The LHHW model has three types of parameters, the forward reaction rate constant, the reaction equilibrium constant, and the individual component adsorption equilibrium constants. To decouple the reaction and adsorption phenomena, we performed independent isothermal binary adsorption experiments for the nonreactive binary pairs. Since reactive distillation is carried out at the boiling temperature of the liquid, the pressure of the system plays an important role in determining the product composition. Higher operating pressures imply higher temperatures and faster rates of reaction. Faster reaction rates give higher conversions and/or smaller residence times and hence smaller equipment. However, higher temperatures could also lead to triggering of unwanted side reactions with higher activation energies and, in the case of exothermic reactions, lower equilibrium conversions. Higher temperatures also require more expensive materials of construction since acetic acid/water mixtures are corrosive at elevated temperatures. To study the importance of side reactions and the effect of pressure on product selectivity, we also include the reaction kinetics of the methanol dehydra-
Figure 1. Experimental setup for the measurement of residue curve maps.
tion reaction at different temperatures. This reaction is
2MeOH S DME + H2O
(2)
We developed a LHHW model for this reaction also. In the next section, we describe the details of the apparatus, the experimental conditions, and the data acquisition for the kinetic and adsorption experiments. Experiments Materials. Methanol (purity > 99.9 wt %), acetic acid (purity > 99.7 wt %), methyl acetate (purity > 99.5 wt %), and ethylene glycol dimethyl ether (anhydrous, water < 0.005 wt %) were purchased from Aldrich. The catalyst was a strongly acidic macroporous resin (Amberlyst 15 wet, moisture content 53 wt %) purchased from Rohm & Haas Co. The concentration of acid sites, the average pore diameter, and the surface area of the dry catalyst were 4.9 mmol/g, 250 Å, and 45 m2/g, respectively, as reported by the manufacturer. Apparatus. A 500-mL, three-neck glass flask was used for kinetic and adsorption experiments. One neck was connected to a thermometer and another to a condenser with a pressure release on top, and the third was sealed with a septum cap. The flask was immersed in a stainless steel tank filled with a 1:1 mixture of ethylene glycol and water as the heating fluid. The contents were stirred by a magnetic stirrer (Thermolyne SP18400) positioned underneath the bath. A desired constant temperature in the bath was obtained by a digital circulator (HAAKE, DC3) which ensures a temperature constancy of (0.1 °C. The cooling water circulation for the condenser was achieved by a circulator (NESLAB RTE-111). Figure 1 shows a schematic of the experimental setup for the residue curve measurements. A 500-mL, threeneck glass flask was connected to a thermometer, a custom-made distillation head, and a septum cap. The heating was controlled by a voltage controller (Ace Glass 12088) and heating mantles. A magnetic stirrer was used to mix the reactants. The distillation head and the reaction flask were insulated with glass wool to minimize heat loss to the surroundings and to prevent condensation of vapor and reflux back to the liquid mixture.
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1919
Composition Analysis. An HP 5890 series II gas chromatograph (thermal conductivity detector) equipped with 7673 Automatic Injector and 3365 Chemstation Software was used to analyze the composition of samples from the liquid phase of the reactive mixture. The sample size for GC was 1 µL. Both injection port and detector temperatures were set to be 230 °C. A 30 m × 530 µm × 1 µm HP INNOWax column (HP 19095N123) was used to separate methanol, acetic acid, methyl acetate, water, and ethylene glycol dimethyl ether (solvent used to dilute the sample). The column temperature was programmed to rise from an initial value of 50 to 80 °C at 30 °C/min, followed by a 60 °C/min ramp up to 130 °C, and then held constant at 130 °C for an additional 1.5 min. High-purity helium gas (Merriam Graves 1071-300) with a minimum purity of 99.997% was used as a carrier gas. The flow rate of the carrier gas was 17 mL/min, and a complete GC run took 3.33 min. All four components were calibrated for their individual GC responses, and the calibrations were verified by mixtures of the components. Procedure. For kinetic studies, the catalyst was airdried for roughly 2 weeks until the weight remained constant (within 0.5 wt %). For the kinetic experiments, two 500-mL flasks, one charged with a measured amount of methanol and the other charged with measured amounts of acetic acid and the air-dried catalyst, were first kept in the constant-temperature bath for about 1 h to reach the desired temperature. Then the reactants and catalyst were mixed together, and timing was started. The total volume of liquid was 306 mL. Periodically, a 0.1-mL sample was taken from the liquid phase using a 1-mL syringe and immediately diluted with 20 mL of anhydrous ethylene glycol dimethyl ether in a sample vial. Subsequently, 1 µL of the diluted sample was injected into the GC for analysis. At the beginning of the experiment samples were taken at ∼10min intervals; the sampling intervals were increased as the experiment progressed. A kinetic experiment was stopped when the compositions leveled off, which was judged to happen when the difference between three consecutive measurements taken at 1-h intervals were within instrument error (5%). Typically, about 20 samples were taken for one run. For residue curve measurements, the flask was charged with 306 mL of liquid mixture of desired initial compositions along with a measured amount of air-dried catalyst. While valve A of the distillation head was open and valve B was closed (see Figure 1), a constant heat input (117 W) was supplied and the liquid was totally refluxed until temperatures of both liquid and vapor phases of the mixture were stabilized. Then valve A was closed and valve B was opened, and the vapor phase was removed continuously and condensed into a separate collection flask. During the distillation process, liquid samples were taken periodically and measured for their composition. Eventually, the amount of liquid residue in the reaction flask was small enough to preclude sampling, and the experiment was stopped. A typical experimental run took around 1 h to stabilize and could be run for 2 and 3 h (depending on the initial conditions) to collect the equilibrium RCM data before the still ran dry. Subsequent runs, beginning at compositions as close as possible to the measured end point of the previous experiment, were necessary in most cases to get a significant portion of each residue curve.
Figure 2. Adsorption equilibrium diagrams for the three nonreactive pairs at 45 °C.
Adsorption Experiments. Binary adsorption parameters are needed for the kinetic models (described in the next section). Among the four components in the methyl acetate reaction, it is possible to carry out three independent binary adsorption experiments. Of the four nonreactive binary pairs, we investigated (1) acetic acid with water, (2) methanol with methyl acetate, and (3) methanol with water. These pairs were picked to maximize the expected adsorption strength difference in order to increase experimental accuracy. The experimental setup for the adsorption experiments was similar to that for the kinetic experiments. The flask was immersed in a constant-temperature bath maintained at 45 °C. The Amberlyst 15 catalyst was dried under vacuum (500-635 mmHg) at 80 °C for 8 h and then under vacuum at room temperature for another 12 h. Thirty grams of the vacuum-dried catalyst were used in all adsorption experiments. A binary liquid mixture was prepared with a total volume of ∼100 mL and a composition of 10 mol % of the stronger adsorbing species. The mixture was heated in the constant-temperature bath for 40 min before the vacuum-dried Amberlyst 15 catalyst was added. In preliminary experiments, the composition of the mixture became constant within ca. 10 min after the addition of the catalyst. To ensure a close approach to adsorption equilibrium, a liquid sample was taken 20 min after the addition of the catalyst. The composition of the sample was then determined by GC. The relative adsorption strengths for the components were determined from literature (Mazzotti et al., 1997).
1920 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998
Model and Data Analysis
Table 1. Summary of the Kinetic Studies for Methyl Acetate mol of H+ initial initial run temp catalyst (from catalyst/ moles of moles of no. (°C) (g) mol of mixture HOAc MeOH
total time (h)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
23.16 23.00 23.50 23.00 23.50 23.00 5.50 22.00 21.00 23.92 11.00 5.50 23.00 12.00
40 40 40 45 45 45 50 50 50 50 50 50 50 50
24 48 48 48 24 48 24 48 48 12 48 24 24 48
0.009 86 0.019 72 0.029 58 0.019 72 0.009 86 0.029 58 0.009 86 0.019 72 0.029 58 0.004 93 0.019 72 0.014 79 0.009 86 0.019 77
1.87 1.87 1.87 1.87 1.87 1.87 1.87 1.87 1.87 1.87 3.74 1.87 1.87 2.80
3.74 3.74 1.87 3.74 3.74 1.87 3.74 3.74 1.87 3.74 1.87 1.87 3.74 2.80
Table 2. Experimental Data for the Methyl Acetate System Run No. 1: Measured Liquid-Phase Mole Fractions vs Time time (min)
MeOAc
MeOH
H2O
HOAc
1.5 20 40 60 90 120 150 180 240 300 360 420 450 540 600 660 720 810 900 1390
0.0053 0.0551 0.0917 0.1163 0.1477 0.1682 0.1826 0.1958 0.2143 0.2276 0.2391 0.2453 0.2462 0.2513 0.2525 0.2523 0.2560 0.2578 0.2563 0.2572
0.6005 0.5402 0.5074 0.4746 0.4559 0.4356 0.4189 0.4096 0.3893 0.3794 0.3749 0.3680 0.3647 0.3583 0.3534 0.3499 0.3513 0.3489 0.3484 0.3441
0.1063 0.1550 0.1884 0.2258 0.2371 0.2638 0.2809 0.2889 0.3117 0.3213 0.3230 0.3316 0.3323 0.3405 0.3480 0.3512 0.3477 0.3516 0.3531 0.3582
0.2879 0.2497 0.2125 0.1833 0.1593 0.1323 0.1176 0.1057 0.0848 0.0716 0.0631 0.0551 0.0568 0.0499 0.0461 0.0466 0.0450 0.0418 0.0421 0.0404
Water is adsorbed most strongly, followed in decreasing order of adsorption strength by methanol, acetic acid, and methyl acetate. The next data point was obtained by adding more of the stronger adsorbing component to the previous mixture in order to study the adsorption over the entire range of liquid compositions. To limit the accumulation of error, measurements were stopped when the total volume of the liquid in the flask reached ∼300 mL. A subsequent run was then started at a composition close to the last data point of the previous run, and this process was continued until the entire composition range was investigated. Figure 2 shows the adsorption curves obtained for the three binary pairs. Results Fourteen sets of kinetic experiments were performed at different molar ratios of reactants, catalyst concentrations, and temperatures; Table 1 gives the conditions. A typical data set for one of the kinetic experiments is given in Table 2. These data were regressed as described below. The model fit for the data in Table 2 is given in Figure 5. The remaining data sets for the methyl acetate kinetics are provided in the Supporting Information (Tables S1-01-S1-13). The experimental data and the model fits for the adsorption experiments are given in Figure 2.
The LHHW Model. The batch kinetic data were in the form of data sets for mole fraction of the components as a function of time. Since the reactions were carried out in the presence of a heterogeneous catalyst, we used a heterogeneous LHHW model. The assumptions are as follows: (1) the adsorption sites are uniformly energetic; (2) there is a monolayer coverage (typical of chemisorption); (3) a molecule on site 1 does not influence what attaches onto a nearby site 2; (4) a dual-site mechanism is used for the reaction; and (5) the surface reaction is the rate-controlling step. A possible mechanism for the esterification reaction is as follows (Froment and Bischoff, 1990):
HOAc + S S HOAc-S MeOH + S S MeOH-S HOAc-S + MeOH-S S MeOAc-S + H2O-S MeOAc-S S MeOAc + S H2O-S S H2O + S
(3)
The resulting LHHW model is rMeOAc )
(
kS,1KHOAcKMeOH aHOAcaMeOH -
)
aMeOAcaH2O Keq1
(1 + KHOAcaHOAc + KMeOHaMeOH + KMeOAcaMeOAc + KH2OaH2O)2 (4)
where S represents an active site and kS,1 is the forward reaction rate constant for the surface reaction defined as follows:
kS,1 ) kS0,1WeE/RT
(5)
W is the catalyst concentration (mol of H+ ions/mol of mixture) and E is the activation energy for the surface reaction (kcal/mol). Ki are adsorption equilibrium constants, ai are the liquid-phase activities and Keq1 is the thermodynamic equilibrium constant for reaction 1. Lumping some of the constants in the numerator, we get rMeOAc )
(
k′S,1 aHOAcaMeOH -
)
aMeOAcaH2O Keq1
(1 + KHOAcaHOAc + KMeOHaMeOH + KMeOAcaMeOAc + KH2OaH2O)2 (6)
where k′S,1 can be written as
k′S,1 ) k′S0,1WeEAPP/RT
(7)
k′S0,1 is the preexponential factor, and EAPP is the apparent activation energy in kcal/mol. If we assume that the adsorption equilibrium constants are independent of temperature (i.e., that their heats of adsorption are small), then the apparent activation energy, EAPP, will be equal to the activation energy of the reaction, E. The model has seven parameters: the preexponential factor, the activation energy, the thermodynamic equilibrium constant, and the four adsorption equilib-
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1921
rium constants. Regression of all the coefficients in the LHHW model from the reaction kinetics experiments alone is problematic due to the correlation of parameters, giving rise to convergence difficulties (e.g., Parra et al., 1994). As an alternative, we need independent binary nonreactive adsorption experiments to obtain the adsorption equilibrium constants relative to a reference component (methyl acetate). The next section describes the development of the required adsorption model. Modeling the Adsorption Experiments. For a nonreactive binary adsorption experiment with two components 1 and 2, an overall material balance gives the composite isotherm (Kipling, 1965; p 28)
adsorbed on the surface must be independent of surface composition. Therefore,
n0∆x ) nS1 x2 - nS2 x1 m
with a similar expression for nS2 . Substituting these expressions in eq 8 gives the composite isotherm
(8)
where n0 is the total initial number of moles in the liquid phase, ∆x is the change in the mole fraction in the liquid phase, m is the mass of the catalyst, and nS1 and nS2 are the number of moles of 1 and 2 transferred onto the surface of unit mass of catalyst. The quantities n0, x1, x2, ∆x, and m can all be measured, leaving two unknowns in eq 8, nS1 and nS2 . To get an expression relating the number of moles of each species adsorbed (nSi ) and the activities of the components in the two phases, we consider the chemisorption process as a reaction of the following form:
1(l) + 2(s) S 1(s) + 2(l)
(9)
We make the following assumptions about the nature of the adsorbed layer: (1) The adsorbed layer is confined to a single molecular layer, (2) the adsorption sites are all equivalent, (3) the two components of the binary mixture have the same molecular area in the adsorbed phase, and (4) the fraction of sites occupied is constant for all binary pairs at all compositions. If we also assume that the liquid phase is nonideal and the solid phase is ideal, the equilibrium constant for reaction 9 is
xS1 a2 xS2 a1
) K2,1
(10)
K2,1 can be thought of as a ratio of the equilibrium constants for two independent adsorption processes of the form
1(l) + s S 1(s)
K1 (xS1 ) K1a1)
(11a)
2(l) + s S 2(s)
K2 (xS2 ) K2a2)
(11b)
Equation 9 can be obtained by subtracting eq 11b from eq 11a and, hence, K2,1 is the ratio of K2 to K1
K2,1 ) K2/K1
(12)
Since xS2 ) 1 - xS1 , it follows that
xS1 )
K2,1a1 K2,1a1 + a2
(13)
Because the total number of occupied sites is a constant and all molecules occupy the same number of sites (have the same molecular area), the total number of moles
nS1 + nS2 ) nS
(14)
where nS is the constant total number of moles which can be accommodated in the adsorbed phase by unit mass of solid. Since xS1 ) nS1 /nS, eq 13 can be rewritten as
nS1 )
K2,1nSa1 K2,1a1 + a2
n0∆x nS(K2,1a1x2 - a2x1) ) m K2,1a1 + a2
(15)
(16)
There are two parameters in this model, K2,1 and nS, which are found by nonlinear regression of the experimental adsorption data. There are four pairs of components for which adsorption experiments could be performed (the other pairs are reactive). Only three of these pairs are independent (the fourth ratio can be used as a consistency check). Hence, we have three ratios of adsorption equilibrium constants, and we can choose one of the Ki’s as a reference component and relate all the others to it. We chose the adsorption equilibrium constant of methyl acetate as the reference and related the other adsorption coefficients to it through these experimentally determined ratios:
KHOAc ) K1,3KMeOAc KMeOH ) K2,3KMeOAc KH2O ) K4,3KMeOAc
(17)
The adsorption experiments were performed at 45 °C. The denominator of the LHHW rate expression can be written in terms of the reference component, and then the kinetic model has only two adjustable parameters, namely, the forward reaction rate constant k′S,1 and the adsorption equilibrium constant for the reference component KMeOAc. The ratios of the adsorption equilibrium constants obtained from the adsorption experiments and the value of KMeOAc obtained from the kinetic data fitting at 45 °C were assumed to be independent of temperature. The Equilibrium Constant. The reaction equilibrium constant Keq1 was obtained as follows. The kinetic experiments were run to long times until the composition (mole fraction) vs time curves were essentially flat. To determine whether the reaction had truly reached equilibrium, we performed the following test. The relative error of the GC was less than 5%. We performed an error propagation analysis to get the error in the measured mole fractions, and at long times we checked the change in mole fractions between three successive pairs of measurements. If the change in the mole fraction was less than the error in the measurement for these three successive pairs, we considered all points after the third pair to be at equilibrium. These data points were then used to get a value of Kx
1922 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 Table 3. Thermodynamic Data for the Methyl Acetate/DME System Antoine Coefficients component
A
B
C
Vi (m3/mol)
acetic acid (1) methanol (2) methyl acetate (3) water (4) DME (5)
22.1001 22.4999 21.1520 23.2256 21.2303
-3654.62 -3643.3136 -2662.78 -3835.18 -2164.85
-45.392 -33.434 -53.460 -45.343 -25.344
57.54 44.44 79.84 18.07 69.07
A11 ) 0.0 A21 ) -547.5248 A31 ) -696.5031 A41 ) 658.0266 A51 ) 96.7797
Wilson Parameters A13 ) 1123.1444 A23 ) 813.1843 A33 ) 0.0 A43 ) 1918.232 A53 ) -21.2317
A12 ) 2535.2019 A22 ) 0.0 A32 ) -31.1932 A42 ) 469.5509 A52 ) -418.6490
ln Psat ) A +
B T+C
∑
A15 ) -96.6698 A25 ) 900.9358 A35 ) -17.2412 A45 ) 703.3566 A55 ) 0.0
Psat [Pa], T [K]
C
ln γi ) 1 - ln(
A14 ) 237.5248 A24 ) 107.3832 A34 ) 645.7225 A44 ) 0.0 A54 ) 522.2653
C
xjΛij) -
j)1
∑ k)1
( ) xkΛki
C
∑x Λ j
kj
j)1
where
Λij )
( )
Vj -Aij exp Vi RT
Vj[m3/mol],
Aij [cal/mol]
Aij ) 0 implies ideality The dimerization constant in the vapor phase for acetic acid is
log(KD) ) -12.5454 +
3166.0 T
Table 4. Minimum-Error Estimate of the Equilibrium Constant for the Methyl Acetate Reaction temp (°C)
Keq
temp (°C)
Keq
40 45
30.2 27.4
50
24.0
()xMeOAcxH2O/xHOAcxMeOH). The liquid-phase activity coefficients for each point were obtained using the Wilson model with the parameters given in Table 3. Thethermodynamic equilibrium constant for that point is found from
Keq1 )
aMeOAcaH2O aHOAcaMeOH
) KxKγ
(18)
The thermodynamic equilibrium constant is only a function of temperature. The value of Keq at a particular temperature was obtained by adjusting Keq to minimize the squared error between calculated and measured equilibrium compositions of all the data points (with different molar ratios and catalyst concentrations). A detailed listing of the point values of Kx, Kγ, and Keq for the equilibrium composition data points and the minimum-error estimate of the equilibrium constant at the three experimental temperatures is given in the Supporting Information (Table S3). Table 4 gives the minimum-error estimate of the equilibrium constant at the three different temperatures. An independent method for estimating Keq is from free energies of formation (i.e., Keq ) e∆G°/RT). However, the free energies of formation are large and their difference (∆G°) is small. The result, therefore, has a large uncertainty, and we did not find this method reliable.
KD [1/Pa],
T [K]
Figure 3 shows a plot of the logarithm of the value of the thermodynamic equilibrium constants of all the experimentally determined data points (at the three different temperatures of 40, 45, and 50 °C (Table S3)) and one point at 154 °C from Menschutkin (1879) as a function of reciprocal temperature. From the plot, the following expression was obtained for the thermodynamic equilibrium constant as a function of temperature (T in K)
ln(Keq1) ) 0.839 83 + 782.98/T
(19)
From this expression, we estimate the free energy of the reaction (∆G°) to be -1.55 kcal/mol. In the temperature range of interest (40-120 °C), the value of Keq1 ranges from 28.2 to 17.0, which is slightly higher than the value quoted by earlier workers (Agreda et al., 1990; Barbosa and Doherty, 1988). They used a value of Kx ) 5.2 at 154 °C from Menschutkin (1879). Then using a UNIFAC estimate for the liquid-phase activity coefficients γι and the fact that Keq ) KxKγ, they estimated the value for Keq1 to be 14.7. If the Menschutkin data point is removed from Figure 3, the slope of the curve increases and the new expression for Keq1 is ln(Keq1) ) -0.8226 + 1309.8/T. In this case, ∆G° ) -2.6 kcal/mol, and the value of Keq1 varies from 28.8 to 12.3 over the temperature range of 40120 °C. This does not affect our results significantly since the change in Keq1 over the 40-50 °C range (over which the kinetic experiments were performed) is minor. The value of Keq1 from these two correlations is significantly different at the higher temperature end, but we believe that inclusion of the Menchutkin data point (at 154 °C) would give a better estimate of the equilibrium
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1923 Table 5. Results of the Regression for the Methyl Acetate/DME System Reaction Equilibrium Constant for Methyl Acetate Keq1 ) 2.32e782.98/T Adsorption Equilibrium Constants KH2O ) 10.50 KMeOH ) 4.95 KHOAc ) 3.18 KMeOAc ) 0.82 Forward Reaction Rate Constants k′S,1 ) e(24.64-(6287.7/T)) k′S,2 ) e(27.4-(10654.0/T))
Figure 3. Temperature dependence of the reaction equilibrium constant for the methyl acetate reaction: ln(Keq) vs 1/T. Open symbols represent the individual data points; filled symbols are the minimum-error estimates.
constant at higher temperatures in comparison to a correlation that is purely based on equilibrium constant values at much lower temperatures. Regression of Kinetic Data. A summary of the kinetic experiments performed is given in Table 1. At 45 °C, the LHHW model has two parameters that need to be estimated from the kinetic data fit, namely, the forward reaction rate constant k′S,1 and the adsorption equilibrium constant of the reference component (methyl acetate). These were obtained by minimizing the following objective function: total time 4
min f(x) )
∑ ∑ time)0 j)1
(xj,expt - xj,model)2
(20)
where xj’s represent the mole fractions of the four species, namely, acetic acid, methanol, methyl acetate, and water. The minimization was done using a modified Levenberg-Marquardt algorithm (the IMSL routine DBCLSF (IMSL MATH/LIBRARY, 1987)) embedded within the LSODES integrator (Hindmarsh, 1983). Once the adsorption equilibrium constants are determined at 45 °C, only one parameter, namely, the forward reaction rate constant k′S,1, remains to be fitted using the kinetic experiments at the other two temperatures. This is because we have assumed that the value of the adsorption equilibrium constant for methyl acetate and the ratios of the adsorption equilibrium constants for the other components are independent of temperature. The rate constants were obtained by minimizing the objective function in eq 20. The results are given in Table 5. Figure 4 shows the logarithm of the forward reaction rate constant k′S,1 as a function of reciprocal temperature for the methyl acetate reaction. The slope of the curve gives an apparent activation energy of 12.49 kcal/mol, and the intercept gives a preexponential factor of 5.02 × 1010 (mol of mixture) (mol of H+ ions)-1 min-1. From the plot, we get the following Arrhenius expression for the forward reaction rate constant as a function of temperature:
Figure 4. Logarithm of the forward reaction rate constant for the MeOAc reaction as a function of reciprocal temperature.
ln(k′S,1) ) 24.64 -
6287.7 T (K)
(21)
Figure 5 shows a typical fit of the mole fraction for each component as a function of time using the LHHW model. As can be seen, the model does a very good job of predicting the mole fraction profiles as a function of time. The DME Reaction. One of the side reactions in the methyl acetate system is the dehydration of methanol to dimethyl ether and water (eq 2). An increase in pressure leads to an increase in the boiling points of the components and hence the operating temperature in reactive distillation. This leads to higher rates of reaction and smaller equipment, leading to a savings of investment costs. On the other hand, an increase in temperature leads to a decrease in the equilibrium constant (and hence the equilibrium conversion) and could potentially trigger unwanted side reactions such as the methanol dehydration reaction. Eleven sets of high-pressure experiments were carried out with an initial charge of pure methanol both with and without the catalyst to measure the extent of the dehydration reaction. A second apparatus similar to the one described in Figure 1 was built out of stainless steel using a Parr reactor (model 4521 constructed from T316 stainless steel with a volume of 1000 mL) with a maximum working pressure of 700 psig. The details of the high-pressure equipment are given in Venimadhavan (1998).
1924 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 Table 6. Summary of the Kinetic Studies for the DME Reaction mol of H+ initial initial total run temp catalyst (from catalyst)/ moles of moles of time no. (°C) (g) mol of mixture MeOH H2O (h) 1 2 3 4 5 6 7 8 9 10 11
100 100 100 100 100 100 100 100 100 115 85
25.0 49.0 71.0 0.0 72.0 72.0 130.0 82.4 72.9 71.0 72.0
0.009 65 0.018 60 0.028 31 0.000 00 0.028 29 0.028 55 0.015 26 0.027 21 0.028 27 0.028 61 0.028 56
9.88 9.88 9.88 9.84 9.88 9.88 9.88 9.88 9.88 9.88 9.88
0.280 0.659 0.610 0.140 0.688 0.590 9.880 1.190 0.660 0.570 0.590
12.0 12.5 12.0 12.0 12.0 12.0 12.0 12.6 12.0 12.0 12.0
Table 7. Experimental Data for the Kinetic Study of the DME System (Run No. 10): Measured Liquid Mole Fractions vs Time
Figure 5. Methyl acetate system: isothermal batch kinetic data and model fit. The dots represent experimental data, and the solid line represents the heterogeneous (LHHW) model (T ) 40 °C, catalyst concentration ) 0.009 mol of H+/mol of mixture).
The reaction was not significant at low temperatures (pressures) even with high catalyst concentrations and large liquid holdups. However, at higher pressures and catalyst concentrations (8.41-15.69 atm and 61 g of catalyst for a 400-mL methanol charge), significant amounts of DME were formed. The LHHW model for the methanol dehydration reaction is
(
kS,2KMeOH2 aMeOH2 rDME )
)
aDMEaH2O Keq2
(1 + KMeOHaMeOH + KDMEaDME + KH2OaH2O)2 (22)
where kS,2 is the forward reaction rate constant for the surface reaction, ai’s are the liquid-phase activities computed using the Wilson model with the parameters given in Table 3, Ki’s are the adsorption equilibrium constants, and Keq2 is the thermodynamic equilibrium constant for reaction 2. DME is the lightest boiling component in the mixture, with a boiling point of 44.68 °C at 10 atm pressure. Isothermal batch kinetic experiments were performed at various temperatures in the range 85-115 °C. If most of the DME is in the vapor phase and if we lump the constants in the numerator together, eq 22 can be simplified to
(
k′S,2 aMeOH2 rDME )
)
aDMEaH2O Keq2
(1 + KMeOHaMeOH + KH2OaH2O)2
(
(23)
∆G° , RT ∆G° ) -2.4634 1.5167 × 10-3T (K) (24)
)
MeOH
H2O
DME
5 120 240 360 480 600 720
0.9361 0.8829 0.8213 0.7710 0.7230 0.7020 0.6625
0.0627 0.0856 0.1230 0.1534 0.1739 0.1968 0.2272
0.0012 0.0315 0.0557 0.0757 0.1031 0.1012 0.1103
where ∆G° is in kcal/mol and R ) 0.001 987 kcal/mol‚K. In the experimental temperature range (85-115 °C), the value for the thermodynamic equilibrium constant for the methanol dehydration reaction ranges from 68.4 to 52.3. It was assumed that the amount of DME adsorbed was small and that the adsorption equilibrium constants for methanol and water had the same values as those from the methyl acetate data fit. This leaves only one parameter, namely, the forward reaction rate constant, to be estimated from the kinetic data for the DME reaction. The kinetic data from the methanol dehydration reaction were regressed in a manner similar to that for the methyl acetate reaction. Table 6 is a summary of the kinetic experiments performed for the DME reaction. Table 7 gives the measured data from one of the experimental runs (at 85 °C and a catalyst concentration of 72 g of catalyst in ∼400 mL of methanol). The data for the remainder of the experimental runs are given in the Supporting Information (Tables S2-01-S2-10). Figure 6 shows a plot of the logarithm of the forward reaction rate constant (k′S,2) as a function of the reciprocal temperature. From this graph, we find an apparent activation energy of 21.17 kcal/mol and a preexponential factor of 7.9 × 1011 (mol of mixture) (mol of H+ ions)-1 min-1, giving the following Arrhenius rate expression
ln(k′S,2) ) 27.40 -
The thermodynamic equilibrium constant for the methanol dehydration reaction was taken from Nisoli et al. (1997):
Keq2 ) exp -
time (min)
10654.0 T (K)
(25)
Figure 7 shows a sample fit of the mole fraction for each component as a function of time for the methanol dehydration data given in Table 7. The solid line is the computed value while the dots are the experimental data points. Our results indicated that the amount of DME formed was quite small at lower temperatures (40-50 °C) but became significant at higher temperatures (85-115 °C). Residue Curve Maps. As mentioned earlier, a useful tool for the synthesis and analysis of both
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1925
is the reference forward reaction rate constant (defined at a convenient temperature such as the lowest boiling temperature in the mixture), W is the normalized weight of catalyst in moles of H+ ions per moles of mixture, and V0 is the initial rate of the vapor leaving the still. The model for a kinetically controlled reactive distillation system is given below (for the detailed derivation of the model; see Venimadhavan et al., 1994).
dxi
H V0 N (νi,j - νT,jxi)Ri ) xi - yi + Da dξ H0 V j)1 (i ) 1, ..., (R + P - 1)) (27)
∑
where xi and yi are the liquid and vapor phase mole fractions, respectively, dξ is a “warped” time variable defined by dξ ) (V/H) dt, V is the instantaneous vapor rate, H is the instantaneous liquid holdup in the still, t is the clock time, νi,j is the stoichiometric coefficient of species i in reaction j, νT,j is the sum of the stoichiometric coefficients in reaction j, and
Ri ) rj/k′S,1,ref (j ) 1, ..., N) Figure 6. Logarithm of the forward reaction rate constant for the DME reaction as a function of reciprocal temperature.
(28)
where Ri is the normalized reaction vector, rj is the rate of an individual reaction, and k′S,1,ref is the reference surface reaction rate constant of the first reaction. The i’s correspond to the five species, namely, acetic acid, methanol, methyl acetate, water, and DME. The rj’s are rMeOAc and rDME which were determined earlier using the data from the kinetic and adsorption experiments. The reference reaction rate constant is chosen as the value for the methyl acetate reaction at the boiling point of DME at 1 atm which is -24.72 °C (the lowest point on the boiling surface). The matrix νi,j and the vector νT,j in eq 27 are respectively
y)
(
-1 -1 1 1 0 0 -2 0 1 1
)
(29)
and
yT ) Figure 7. DME system: Isothermal batch kinetic data fit. The dots represent experimental data, and the solid line represents the heterogeneous (LHHW) model (T ) 85 °C, catalyst concentration ) 0.028 mol of H+/mol of mixture).
nonreactive and reactive distillation systems is the residue curve map (e.g., Fidkowski et al., 1993; Foucher et al., 1991; Wahnschafft et al., 1992; Venimadhavan et al., 1994). An important parameter in the study of the kinetically controlled reactive distillation system is a Damkohler number defined by the ratio of a characteristic residence time to a characteristic reaction time (Venimadhavan et al., 1994). The Damkohler number can be thought of as a dimensionless holdup in the system or a dimensionless rate of reaction. For a heterogeneous system, the Damkohler number can be redefined to explicitly show its dependence on a normalized catalyst concentration as follows:
Da )
H0/V0 1/k′S,1,refW
(26)
where H0 is the initial molar holdup in the still, k′S,1,ref
() 0 0
(30)
A limiting case that is well-understood is the case of equilibrium reactive distillation where simultaneous vapor-liquid and reaction equilibrium prevail. The assumption of reaction equilibrium allows us to define certain transformed composition variables which make the analysis of the equilibrium reactive residue curve maps easier (Barbosa and Doherty, 1988; Ung and Doherty, 1995a-d). As a test of our model at the equilibrium limit, we performed independent equilibrium open-evaporation experiments. One way of ensuring that the system reaches equilibrium rapidly is to have a large amount of catalyst present in the reactor. We ensured that there was a sufficiently large amount of catalyst present by performing several experiments starting with the same number of moles of acetic acid and methanol but with increasing amounts of catalyst on successive runs. For each run, we plotted the data on a transformed mole fraction diagram until a further increase in the amount of catalyst did not result in any appreciable shift in the RCM (Figure 8). We then concluded that, under the given conditions, the reaction could not proceed any faster and thus we had achieved almost instantaneous reaction and phase equilibrium. Earlier calculations
1926 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998
Figure 8. Effect of the mass of catalyst for simultaneous reaction and phase equilibrium.
(Figure 8) showed that, for all values of Da > 80, the structure of the residue curve map was indistinguishable from that at simultaneous vapor-liquid and reaction equilibrium (Da f ∞). The residue curves computed from our model at Da ) 99 (chosen well above the minimum required to model equilibrium behavior) were compared to the experimentally obtained residue curves (Figure 9a). Figure 9b gives the curves computed by Barbosa and Doherty (1988). The qualitative agreement between their diagram and the experimental data is good considering the fact that they had obtained the value of Kx ) 5.2 from Menschutkin (1879) and estimated the value of Kγ ≈ 2.83 using the UNIFAC method to get an overall value of Keq ≈ 14.7 (independent of temperature). This value is somewhat lower than the range of values that we obtained from the experimental data in this work (Keq in the range of 20-30). The solid lines in Figure 9a show the computed curves, while the symbols show the measurements. The agreement is good, especially considering that none of the parameters in the model were adjusted to fit the measurements. The good agreement appears to validate the modeling approach and provides confidence in applying our kinetic and VLE models to reactive distillation systems of commercial interest. We used the model to predict residue curve maps at lower values of Da in the kinetically controlled regime. Figure 10 shows the results at Da ) 1, 10, and 50. The model predicts that the lightest boiler is always the methyl acetate-methanol azeotrope, that the heaviest boiler is always pure acetic acid, and that methyl acetate, methanol, and water are always intermediate boilers for all values of Da. Since the structure of the residue curve map is qualitatively the same for all the values of Da, we predict that methyl acetate can be successfully produced by reactive distillation in both the equilibrium-controlled and the kinetically controlled regimes. Conclusions Analysis of kinetically controlled reactive distillation systems requires knowledge of the chemical kinetics. Rate expressions for reactive distillation systems are
Figure 9. (a) Comparison of computed (solid line) and experimentally measured equilibrium reactive RCM for the methyl acetate system at P ) 1 atm. (b) RCM for the methyl acetate system at vapor-liquid and reaction equilibrium computed by Barbosa and Doherty (1988).
usually written in terms of the liquid-phase activities of the components rather than the more common concentration-based rate expressions used in reaction engineering. The methyl acetate synthesis is a classic problem for the application of reactive distillation, but there is a lack of kinetic rate data/expressions in the range of interest for this system. We performed kinetic experiments on a solid sulfonic acid resin catalyst (Amberlyst 15W) for the methyl acetate reaction as well as for an unwanted side reactionsthe dehydration of methanol to dimethyl ether and water. We developed a heterogeneous (LHHW) model for the reaction kinetics for these two reactions. To decouple the reaction and the adsorption phenomena, we performed independent nonreactive binary adsorption experiments. These experiments gave estimates of the three independent ratios of the adsorption equilibrium constants. The remaining parameters of the LHHW model were fitted from the kinetic data. The resulting kinetic models fit the experimental data quite well. These rate expressions are applicable over a wide range of catalyst concentrations and molar ratios of reactants. To test the equilibrium limit of the model, we performed independent equilibrium reactive open-evaporation ex-
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1927
Acknowledgment We are grateful for the financial support provided by the National Science Foundation (CTS-9613489) and the National Environmental Technology Institute. We are also grateful to Ms. Pamela Stephan for preparing the illustrations. Supporting Information Available: Tables of experimental data for kinetic study of the methyl acetate and the DME systems for several runs and equilibrium constants for the methyl acetate reaction (26 pages). Ordering information is given on any current masthead page. Notation
Figure 10. RCMs at Da ) 1, 10, and 50 on transformed coordinates for the methyl acetate reaction.
periments. The experimental residue curves were compared to the predictions generated by the model, and the agreement was found to be very good considering that none of the parameters in the model were adjusted to fit the simple distillation data. The good agreement appears to validate our vapor-liquid equilibrium and kinetic models and gives us confidence in applying these models to the reactive distillation of systems of commercial interest.
ai ) activity of component i Da ) Damkohler number ()(H0/V0)/(1/kS,1,refW)) E ) activation energy (kcal/mol) EAPP ) apparent activation energy (kcal/mol) ∆G° ) change in free energy (kcal/mol) H ) liquid holdup (mol) H0 ) initial liquid holdup (mol) kf ) forward reaction rate constant for a homogeneous reaction (1/time) kS,j ) forward reaction rate constant for surface reaction j (1/time) k′S,j ) apparent forward reaction rate constant for surface reaction j (1/time) k′S,j,ref ) reference apparent reaction rate constant for the surface reaction (1/time) Keqj ) thermodynamic equilibrium constant for reaction j Ki ) adsorption equilibrium constant for component i Ki,j ) ratio of the adsorption equilibrium constants for components i and j Kx ) reaction equilibrium constant based on mole fractions Kγ ) ratio of the activity coefficients of the products to those of the reactants m ) mass of catalyst for the adsorption experiments mol ) gmol nSi ) number of moles of species i transferred onto the surface of unit mass of catalyst n0 ) total initial number of moles in the liquid phase rj ) rate of reaction for reaction j (1/time) R ) universal gas constant (1.987 cal/mol‚K) Rj ) normalized reaction vector defined as rj/k′S,1,ref S ) active site on the catalyst t ) time (min) T ) temperature (K) V ) vapor rate (mol/time) V0 ) initial vapor rate (mol/time) W ) normalized catalyst concentration (mol of H+ ions/ mol of mixture) ∆x ) change in the liquid-phase mole fraction for the adsorption experiments xi ) liquid-phase mole fraction for component i xSi ) mole fraction on the catalyst for component i yi ) vapor phase mole fraction for component i Greek Symbols ξ ) “warped” time νi,j ) stoichiometric coefficient of component i in reaction j νT,j ) sum of the stoichiometric coefficients for reaction j
1928 Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 Subscripts i ) component i 0 ) initial value
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Received for review December 1, 1997 Revised manuscript received February 4, 1998 Accepted February 5, 1998 IE9708790
