2626
Ind. Eng. Chem. Res. 1997, 36, 2626-2633
Catalytic Hydrogenation in Supercritical CO2: Kinetic Measurements in a Gradientless Internal-Recycle Reactor Alberto Bertucco,* Paolo Canu, and Luca Devetta Istituto di Impianti Chimici, Universita´ di Padova, via Marzolo 9, I-35131 Padova PD, Italy
Andreas G. Zwahlen F. Hoffmann La-Roche AG, CH-4070 Basel, Switzerland
Catalytic hydrogenation in supercritical carbon dioxide has been studied. Experimental results and theoretical calculations are presented, attempting to elucidate the effects of temperature, pressure, and CO2 concentration on the rate of reaction. An effort has been made to develop a procedure to test catalytic reactions in supercritical fluids in view of future industrial applications. Hydrogenation rates of the two double bonds of an unsaturated ketone on a commercial aluminasupported palladium catalyst were measured in a continuous gradientless internal-recycle reactor at different temperatures, pressures, and CO2-to-feed ratios. A Berty-type reactor has been suitably modified for use with supercritical solvents. The accurate control of the organic, carbon dioxide, and hydrogen feed flow rates and of the temperature and pressure inside the reactor provided reproducible values of the product stream compositions, which were measured on-line after separation of the gaseous components. In order to develop a kinetic model, vapor-liquid equilibrium calculations were carried out through a Peng-Robinson equation of state, tuned on binary high-pressure vapor-liquid equilibrium data. Compositions in the liquid phase inside the reactor were predicted, starting from the on-line analysis after depressurization. A simplified power law kinetic equation is shown to provide a good description of the experimental data. Introduction Reactions in supercritical fluids (SCFs) are an innovative and challenging field of research, which offers a number of important advantages in the development of new technologies for the chemical and biochemical process industries. A first review of this topic was published by Subramaniam and McHugh (1986), when its development was still in the early stages. Recently, a comprehensive review by Savage et al. (1995) provided a thorough overview of the state-of-the-art, which actually needs to be continuously updated, owing to the number of researchers presently involved in this area. Among other reactions under supercritical conditions, a topic of current interest is the production of chemicals and pharmaceuticals using a SCF as a solvent. The fluids most frequently considered are water and CO2. This is also the case for our work, where the hydrogenation of organics on a supported metal catalyst in the presence of supercritical CO2 (ScCO2) is studied. The potential advantages of carrying out heterogeneous reactions with ScCO2 as a solvent are well-known. Among them, we emphasize the unusual properties of high-pressure vapor-liquid equilibria with ScCO2, which allow us either to homogenize multiphase reactors or to enhance dissolution of reactants (in this case hydrogen) in the phase where the reaction takes place (cf. Jessop et al., 1995); in this way, it is possible to exploit new solutions for integrating reaction and separation units of the same process, owing to the equilibrium sensitivity on pressure and CO2 content. Also, favorable effects are ensured by the reduction of interphase transport limitations, which produces higher effectiveness factors (cf. Clifford, 1994) and by the possibility of * Author to whom correspondence should be addressed. E-mail:
[email protected]. Phone: [+39] (49) 8275457. Fax: [+39] (49) 8275461. S0888-5885(96)00369-7 CCC: $14.00
using CO2 as a heat carrier, to dampen thermal effects and reduce heat duties. At present, the development of a continuous hydrogenation process with ScCO2 is a task of strong interest, especially in the pharmaceutical industry. For the design, simulation, and optimization of such a plant, it is essential to provide tools suitable to represent correctly both phase equilibria and reaction rates; while equation-of-state-based models sufficient for this scope are already available and allow quantitative predictions of multicomponent behavior from binary equilibrium data, the reaction kinetics must be determined experimentally for any specific case. As summarized in a review by Mills et al. (1992), several hydrogenations of interest to the fine chemicals and pharmaceuticals industries have already been studied, at low to ambient pressure, mostly in slurry reactors. Kinetic models range from simple first-order to detailed Langmuir-Hinshelwood expressions. Also mass-transfer limitations have been frequently addressed, due to the crucial role played in detailedmechanism-based models. On the other hand, there is little kinetic information published for reactions in supercritical solvents; among hydrogenation and dehydrogenation reactions, only few works are reported (Savage et al., 1995) and mainly refer to gas-gas reactions involving the solvent, like the FischerTropsch synthesis (Yokota and Fujimoto, 1991) and the CO2 hydrogenation (Jessop et al., 1994). Apparently, there are no open data on hydrogenation in ScCO2 as a solvent. In this work, experimental reaction rates will be presented for a specific case. Measured kinetic data are correlated through a power-law model in terms of liquid molar fractions, the values of which are provided by a vapor-liquid equilibrium (VLE) model. As already suggested by Subramaniam and McHugh (1986), the importance of performing a precise vapor-liquid equi© 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2627
Figure 1. Laboratory setup used for kinetic experiments.
librium calculation in order to corrrectly describe the kinetic data is confirmed. Experimental Section Materials. The hydrogenation reaction involves both double bonds of an unsaturated ketone (identified in the following as component A), whose generic structure is R1sCHdCdCHsC(dO)sR2, to produce the corresponding saturated ketone (referred to as component C). The feed mixture (from Hoffmann-La Roche) includes the main reactant A and three of its isomers, here considered together as a unique pseudocomponent (named as D). Some of the main product C is also present in the feed, as well as semihydrogenated species with only one double bond (named as E, indiscriminately). The average composition of the feed mixtures used is 0.71-0.79 (A), 0.23-0.26 (D), 0.005-0.02 (E), and 0.015-0.025 (C); units are weight fractions. The catalyst is based on Pd (1 wt %) supported on alumina (Engelhart): egg-shell pellets of 3 mm nominal size were used. Apparatus. The experiments were carried out in the laboratory apparatus schematically represented in Figure 1. We adopted an internal-recycle reactor (Berty, 1979 and 1984), of about 0.3 L total volume, modified by Zwahlen in the internal fluid path, mainly for hightemperature and high-pressure reactions (Zwahlen and Agnew, 1987 and 1992). Tracer experiments confirmed that it closely matches ideal mixing conditions. Recycle reactors operating at very high internal recycle ratios approximate quite well differential conditions on the catalyst bed (Berty, 1984), even though inlet and outlet streams have significantly different composition; moreover, it can be regarded as a perfectly mixed reactor. Such a reactor allows direct and accurate determination of the reaction rate from reliable composition measurement of the inlet and outlet streams.
The temperature and pressure inside the reactor and the flow rates of all of the three feeds (liquid organic mixture, carbon dioxide, and hydrogen) were continuously acquired and controlled by a Eurotherm TC S1000 process control unit. The organic liquid feed was supplied by a membrane-metering pump (Lewa) and monitored through a mass flow meter (Rheonik); the CO2 mass flow meter was also by Rheonik. The flow rates were controlled through a pneumatic valve (Kammer) for CO2 and by a mass flow controller (Bronkhorst) for H2. After the reactor, the product stream was flashed to ambient pressure; a cyclon-type separator was inserted after the pressure reduction valve to recover completely the condensable components and to remove CO2 and the unreacted hydrogen. The analysis of the liquid products was done on-line by a Perkin-Elmer 6020 gas chromatographer with a flame ionization detector. A 15m-long capillary column in fused silica was used, with DB17 as a stationary phase. The working temperatures of the gas chromatographer were as follows: column (isothermal), 170 °C; injector, 250 °C; FID, 330 °C. Experimental Runs. Preliminary tests were performed to ascertain the influence of external mass transfer resistances in the whole range of the investigated variables. When the recycle ratio through the internal turbine tap speed is progressively increased, the outlet concentration varies accordingly, as shown in Figure 2 for species C, thus indicating an external diffusion-controlled regime. Above 1800 rpm the reaction rate becomes independent of the speed of the mixer for any of its values; note that two extreme values of T and P are reported in the figure. Therefore, all experimental runs were performed at 1900 rpm, where the reaction rate is not affected by external mass-transfer effects.
2628 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 Table 1. Summary of Experimental Results Together with Operating Variablesa run
T (K)
P (bar)
F (g/min)
FCO2 (g/min)
F H2 (nL/min)
wC (wt %)
wA (wt %)
wD (wt %)
wE (wt %)
-rA [mol/(h gcat)]
-rD [mol/(h gcat)]
rC [mol/(h gcat)]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
448 448 448 448 448 448 423 423 423 448 448 448 423 423 423 473 473 423 423 423 473 473 473 473 473 473 473
120 150 175 120 150 175 120 150 175 120 150 175 120 150 175 175 175 120 150 175 120 150 120 150 120 150 175
28.48 28.48 28.48 28.68 28.68 28.68 28.42 28.42 28.42 28.52 28.52 28.52 28.60 28.60 28.60 28.45 28.45 28.72 28.72 28.72 28.53 28.53 28.53 28.53 28.46 28.46 28.46
68.84 68.84 68.84 28.89 28.89 28.89 13.79 13.79 13.79 13.89 13.89 13.89 28.76 28.76 28.76 13.97 68.88 68.79 68.79 68.79 68.82 68.82 13.78 13.78 28.79 28.79 28.79
6.63 6.63 6.63 6.62 6.62 6.62 6.62 6.62 6.62 6.63 6.63 6.63 6.62 6.62 6.62 6.61 6.61 6.60 6.60 6.60 6.64 6.64 6.64 6.64 6.61 6.61 6.61
21.21 23.65 26.61 28.86 29.81 33.55 27.59 30.54 32.29 29.51 32.47 34.95 25.21 28.60 30.45 41.22 30.12 22.21 24.92 22.86 24.71 27.73 31.16 33.74 33.47 36.33 36.45
11.34 9.16 8.87 11.16 8.99 7.34 16.78 14.21 13.31 14.44 11.39 9.61 15.77 13.30 12.44 12.78 12.58 15.47 13.37 13.56 14.63 13.18 12.36 10.90 12.08 10.29 9.68
3.85 2.93 3.31 3.48 2.78 1.79 8.12 6.88 6.56 6.54 4.95 3.69 7.42 6.29 5.80 5.64 5.77 5.66 5.36 6.04 5.82 6.23 5.96 4.99 4.49 4.00 3.87
63.60 64.25 61.22 58.50 58.43 57.40 47.51 48.38 47.83 49.52 51.20 51.75 51.60 51.82 51.30 40.37 51.53 56.66 56.35 57.55 54.84 52.87 50.52 50.34 49.97 49.45 50.01
0.361 0.376 0.377 0.365 0.379 0.390 0.326 0.312 0.348 0.342 0.362 0.373 0.334 0.350 0.356 0.352 0.353 0.338 0.351 0.350 0.341 0.350 0.355 0.365 0.356 0.368 0.372
0.179 0.185 0.183 0.183 0.187 0.194 0.151 0.159 0.161 0.162 0.172 0.180 0.157 0.164 0.167 0.167 0.167 0.169 0.171 0.166 0.167 0.164 0.166 0.172 0.175 0.178 0.179
0.131 0.146 0.165 0.168 0.188 0.211 0.171 0.190 0.201 0.184 0.203 0.218 0.157 0.178 0.190 0.258 0.187 0.138 0.156 0.142 0.153 0.172 0.194 0.211 0.209 0.227 0.228
a
Note that organic species mass fractions refer to the organic feed stream.
Figure 2. Influence of the turbine speed on the outlet composition of product C: Reaction conditions: T ) 473 K and P ) 160 bar (0); T ) 423 K and P ) 100 bar (O).
The start-up procedure was completely automated, allowing for a high level of reproducibility. Temperature and pressure set points are attained with pure CO2 both to minimize disturbances as the remaining inlet stream is switched on and to keep the catalyst clean, in order to avoid coke accumulation into the pores during the subcritical phase of reactor start up (cf. Saim and Subramaniam, 1991). A typical experimental session provided three data points, at three pressure levels, while temperature and feed flow rate were kept constant throughout the experiment. Such a procedure allows us to collect a larger number of data points more efficiently, since the time delays required to reach a new steady state are largely reduced. Moreover, data collected in the same session are related to the same catalyst activity, provided no deactivation occurs during the time of the experiment (nearly 5 h); thus, irreproducibilities due to actual catalyst conditions could be minimized. Up to five gas chromatographic (GC) measurements were taken at each pressure level, either to assess the steady-state conditions or to provide a representative sample of data; data points were obtained by averaging the different measurements. The reproducibility was very high, due to the accuracy of the control system, as is shown in Figure 3, where the composition of the product stream during a run at T ) 423 K and P ) 20 MPa is reported.
Figure 3. Profile of the monitored composition of the product stream for components A (dashed line) and C (full line). Reaction conditions: T ) 423 K, P ) 200 bar.
The experimental design was based on a full factorial at three levels over three variables, namely the temperature, the pressure, and the ratio between CO2 and organic feed flow rates. Overall results of 27 runs are reported in Table 1. The experimental error variance of the measured production rate of C, σ2C, evaluates to 3 × 10-6, giving a 95% confidence interval of (2%. Similar or better results have been calculated for the rate of production of the other species A, D, and E. Thermodynamic and Kinetic Models In order to describe the reacting system, both the vapor-liquid equilibrium at high pressure and reaction kinetic models need to be developed. Indeed, the compositions of reactants and products in the phase where the reaction takes place appear as variables in every model which can be proposed, and their values depend on the equilibrium behavior of all components of the system (including inerts, such as CO2). Vapor-Liquid Equilibrium. In the system investigated, six components were considered: H2, CO2, and four organic species (A, C, D, and E). Performing accurate calculation of their partitioning between the two phases means being able to simulate high-pressure vapor-liquid equilibria in the presence of compounds at a supercritical state. This implies the use of an equation-of-state approach. At the present state of
Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2629 Table 2. Physical Properties of Components Considered property
A
C
molecular weight (kg/kmol) normal boiling temp (K) critical temp (K) critical pressure (bar) acentric factor liquid density at 20 °C (kg/m3)
264.44 566.5 739.6 14.3 0.8 861
268.48 577.5 693.2 13.0 1.37 832
knowledge, no quantitatively correct predictive models are available in this respect; therefore, it was convenient to apply a cubic equation of state with parameters adjusted to binary data. The well-known Peng-Robinson equation of state was used, where the attractive and repulsive parameters a and b were calculated through the classical random mixing rules:
a)
∑i ∑j xixj(1 - ki,j)(aiaj)1/2
(1)
∑j xjbj
(2)
b)
In eq 1, ki,j indicates the binary interaction parameter (one adjustable parameter per pair of components). The pure component parameters aj and bj were calculated through the usual equations. The temperature dependence of parameter aj (R function of component j) is expressed by
Rj(T) ) [1 + mj(1 - xT/Tc,j)]2
(3a)
where Tc,j is the critical temperature of species j, T is the temperature, and m is a component-dependent parameter. Equation 3a is used for all components except H2, for which the Boston-Mathias equation (Boston and Mathias, 1980) was preferred:
{(
Rj(T) ) exp
)
Figure 4. Comparison between experimental and calculated values of the vapor-liquid equilibrium for the binary system C-CO2 (equilibrium pressure in part a and liquid mass fraction in part b). Data are from Tiegs, 1994.
}
0.5mj [1 - (T/Tc,j)1+0.5mj] 1 + 0.5mj
(3b)
The value of the parameter mj in eqs 3a and 3b was evaluated by the usual correlation:
mj ) 0.374 64 + 1.542 26ωj - 0.269 92ω2j
(4)
where ωj is the acentric factor of species j. Critical and acentric factor values needed for the calculation are summarized in Table 2, together with other relevant properties; due to the similarity of components D and A, the same values were assumed for both of them, while those of component E were averaged between A and C. Note that, except for H2 and CO2, the values were estimated by group contributions according to Reid et al., 1986. Except for the system H2-CO2, whose behavior is well-known (Tsang and Streett, 1981), there are no references in the open literature to binary systems regarding the species of our interest; luckily, some unpublished experimental values of the VLE close to the reaction conditions could be used to estimate the binary interaction coefficients ki,j. Available data were limited to the systems H2-C and C-CO2 (Tiegs, 1994);
Figure 5. Comparison between experimental and calculated values of the vapor-liquid equilibrium: liquid mass fraction for the binary system H2-C. Data are from Tiegs, 1994.
the behavior of unsaturated (A and D) and semihydrogenated (E) species was assumed to be comparable to the one of C, so that the ki,j’s of the binaries H2-A (and A-CO2), H2-D (and D-CO2), and H2-E (and E-CO2) were set equal to the corresponding parameters obtained for H2-C (and C-CO2). As can be checked in Figure 4, the Peng-Robinson equation of state provides a good data fitting, both for the pressure (Figure 4a) and for the liquid composition (Figure 4b) of the system C-CO2. A larger scatter (errors up to 15%) was detected for vapor phase compositions; however, it was noted that the experimental procedure adopted results in intrinsically less reliable data for the vapor phase. Similar conclusions were drawn for the system H2-C (liquid composition parity plot of Figure 5). Some results are also shown in Figure 6, where the bubble- and dew-point-calculated curves of C-CO2 are compared to data points, with satisfactory agreement. With the values of binary interaction coefficients derived on the basis of binary systems, ternary and multicomponent equilibria were predicted; since a few data of this kind were also available from the same source, they were used to confirm the accuracy of the thermodynamic model. As can be seen in Table 3, the agreement between calculated and experimental liquid compositions is acceptable for the system C-H2-CO2. It was concluded that the Peng-Robinson equation of state with interaction parameters fitted for binary data (one parameter per pair) ensures a satisfactory descrip-
2630 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997
of the main reactants A and D. Accordingly, stoichiometry dictates the following reactions:
Figure 6. Binary isothermal vapor-liquid equilibrium curves in the range of experimental temperatures: T ) 473 K (b); T ) 398 K (O); T ) 353 K (2); T ) 343 K (]); T ) 333 K (9). Data are from Tiegs, 1994.
(1)
A + H2 f E
(2)
D + H2 f E
(3)
E + H2 f C
As pointed out by Mills et al. (1992), most hydrogenation reactions with palladium-on-alumina catalyst are simply described as irreversible power-law models. Following this suggestion, a kinetic model was formulated as follows:
Table 3. Liquid Phase C Composition in the Ternary Systems C-H2-CO2 at C/H2 Molar Ratios of 1/2 (a) and 1/1 (b) T (K) 398 398 398 423 423 423 473 473 473 523 523 523 398 398 398 423 423 423 473 473 473 523 523 523
β2 R1 ) k1xβA1xH 2
(6a)
% error
β4 R2 ) k2xβD3xH 2
(6b)
120 140 160 120 140 160 120 140 160 120 140 160
(a) Molar Ratio 1/2 0.8003 0.8153 0.7730 0.7743 0.7275 0.7294 0.8269 0.8413 0.8065 0.8064 0.7602 0.7684 0.8653 0.8655 0.8350 0.8359 0.8126 0.8035 0.8636 0.8694 0.8450 0.8397 0.8240 0.8065
1.87 0.17 0.26 1.74 -0.01 1.08 0.02 0.11 -1.12 0.67 -0.63 -2.12
β6 R3 ) k3xβE5xH 2
(6c)
120 140 160 120 140 160 120 140 160 120 140 160
(b) Molar Ratio 1/1 0.7898 0.8294 0.7482 0.7932 0.7259 0.7546 0.8246 0.8521 0.7976 0.8209 0.7595 0.7873 0.8483 0.8737 0.8228 0.8467 0.7901 0.8174 0.8666 0.8770 0.8490 0.8497 0.8133 0.8194
5.01 6.01 3.95 3.33 2.92 3.66 2.99 2.90 3.46 1.20 0.08 0.75
P (bar)
wC,exp (wt %)
wC,cal (wt %)
tion of the liquid phase, while more data would be needed to check the vapor phase. Reaction Rate. The reaction rate enhancement typically encountered in reactions with SCFs can be ascribed to the sum of two effects (Subramaniam and McHugh, 1986): the pressure dependence of the rate constant and the change of reactant composition due to the high pressure. According to the transition state theory and classical thermodynamic concepts (Van Eldik et al., 1989), one can obtain the variation of the reaction rate constant kx with pressure as
(
)
∂ ln kx ∂P
T
)-
∆V+ RT
where xj are the mole fractions in the liquid phase, which is supposed to be the sole reaction locus. The rate constants of reaction i depend upon temperature and pressure according to the following Arrhenius-like expression:
( ) (
ki ) k0,i exp
)
-Ea,i -∆Vi+P exp RT RT
(7)
where k0,i is the preexponential factor and Ea,i is the activation energy; note that the activation volume is supposed to be independent of both temperature and pressure, due to the relatively limited experimental range investigated for these variables. According to the CSTR behavior of the recycle reactor, compositions of different species inside the reactor are equal to those measured at the outlet, with the same vapor-liquid distribution. GC measurements on the outlet liquid stream, after a flash depressurization, are used to estimate the composition of the liquid phase inside the reactor: actual values at the reactor T and P conditions are evaluated according to an adiabatic equilibrium-flash model of the throttling valve, as those values that agree with the measured composition of the resulting liquid; CO2 and H2 amounts were determined from flow measurements and stoichiometry, respectively. Parameters in the kinetic equations, namely k0,i, Ea,i, ∆V+i and βi, have been estimated through standard numerical optimization techniques. Fitting results and, specifically, the precision of the parameter estimates, suffer somehow from the relatively little number of experimental data available, with respect to the number of parameters.
(5)
where ∆V+ is the activation volume. On the basis of the simplified chemistry outlined in the Experimental Section above, a first attempt was developed to model the reaction kinetics, in order to account for both temperature and pressure dependencies. Following the proposed scheme, all different isomers were given the same reactivity and they were treated as single pseudocomponents, with the exception
Results and Discussion From the mass balance, the production rate of each organic reactant j can be calculated by
rj )
F (w - wjF)/MWj Wc j
(8)
with F ) organic feed mass flow rate; Wc ) mass of catalyst; wj, wjF ) weight fraction of component j in the outlet and inlet organic streams, respectively; MWj )
Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2631 Table 4. Calculated Liquid Phase Mole Fractions at the Experimental Conditions
Figure 7. Production rate of component C as a function of pressure at T ) 448 K, at different organic feed-to-CO2 flow rate ratios, rr: rr ) 0.7 w/w (O); rr ) 0.5 w/w (9); rr ) 0.3 w/w (4).
Figure 8. Production rate of component C as a function of temperature at P ) 175 bar, at different organic feed-to-CO2 flow rate ratios, rr: rr ) 0.7 w/w (O); rr ) 0.5 w/w (9); rr ) 0.3 w/w (4).
Figure 9. Production rate of component C as a function of pressure at T ) 473 K, at different organic feed-to-CO2 flow rate ratios, rr: rr ) 0.7 w/w (O); rr ) 0.5 w/w (9); rr ) 0.3 w/w (4).
molecular weight of component j; and rj ) production rate of component j. Experimental values of production rate are reported in Table 1. Reaction rates for the postulated mechanism are readily derived from species production rates as R1 ) -rA; R2 ) -rD; and R3 ) rC. The influence of the operating variables T, P, and CO2 inlet flow rate on the experimental rate of production of C is plotted, for instance, in Figures 7-9. The positive influence of the pressure on the reaction kinetics is clearly shown in Figure 7, where the rate at which the desired product is obtained is reported at different total pressure values. Data are taken at the same temperature (448 K), and three levels of CO2 are investigated. Besides the evidence that total pressure increases the rate of formation of the product C, it is also clear that the amount of CO2 in the system is a limiting factor. According to the VLE calculations, such an effect is a consequence of a monophase system (liquid) in which CO2 has already dissolved the organic species, so that additional CO2 just lowers the reactant concentration. The same results are shown in terms of temperature, at 17.5 MPa, in Figure 8. An increase of the system temperature favors the production rate of C. Again, the limitation of an excess of CO2 beyond the minimum dissolution of the organic phase can be noticed. The key role of the vapor-liquid equilibrium leads to the unusual behavior depicted in Figure 9. Here, the high temperature (473 K) causes the formation of a significant vapor fraction as long as the pressure remains limited. As a consequence, an increase of CO2 in the system leads to a maximum in the production rate, while values around such an optimum cause a
run
xA (mol/mol)
xD (mol/mol)
xC (mol/mol)
xE (mol/mol)
x H2 (mol/mol)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
0.059 86 0.040 83 0.034 15 0.042 19 0.044 46 0.032 09 0.103 30 0.077 94 0.066 64 0.090 50 0.063 63 0.048 81 0.087 01 0.063 28 0.052 41 0.065 42 0.050 63 0.077 61 0.056 02 0.048 85 0.079 72 0.061 07 0.078 24 0.061 61 0.070 30 0.052 01 0.043 56
0.020 32 0.013 06 0.012 75 0.062 36 0.013 75 0.007 83 0.049 96 0.037 74 0.032 85 0.040 99 0.027 65 0.018 74 0.040 94 0.029 93 0.024 44 0.028 87 0.023 22 0.028 40 0.022 46 0.021 76 0.031 72 0.028 87 0.033 73 0.028 80 0.026 13 0.020 22 0.017 41
0.1115 0.1053 0.1027 0.1596 0.1459 0.1453 0.1674 0.1652 0.1595 0.1825 0.1790 0.1752 0.1374 0.1346 0.1270 0.2082 0.1210 0.1108 0.1042 0.0825 0.1340 0.1281 0.1946 0.1882 0.1926 0.1817 0.1623
0.3364 0.2878 0.2376 0.3256 0.2880 0.2503 0.2904 0.2636 0.2380 0.3085 0.2843 0.2613 0.2832 0.2455 0.2154 0.2055 0.2091 0.2842 0.2368 0.2086 0.3000 0.2465 0.3180 0.2830 0.2899 0.2493 0.2245
0.021 54 0.027 00 0.031 96 0.042 19 0.052 85 0.061 03 0.067 30 0.083 33 0.097 22 0.070 14 0.086 09 0.099 17 0.042 08 0.052 60 0.062 08 0.105 20 0.033 93 0.021 10 0.026 86 0.033 02 0.023 12 0.028 96 0.074 58 0.091 85 0.044 68 0.055 34 0.065 13
limitation in the production kinetics. Note that higher pressures turn the system back in the case of Figures 7 and 8. The accurate description of such a behavior can be clearly achieved only if the component distribution in the liquid phase is accounted for correctly; i.e., a good calculation of phase equilibrium is necessary in order to develop a kinetic model able to simulate experimental results. According to the results discussed in the previous section, the Peng-Robinson equation of state was applied for calculating the concentrations under the experimental conditions: they are tabulated for the liquid phase in Table 4. These values were then used to calculate rj and thus to estimate the adaptive parameters of the kinetic equations (eqs 6). Note that even a simple model, like the one adopted here, introduces 15 parameters (12, if the activation volumes are neglected), whose numerical determination based on 27 experimental data points (Table 1) is quite cumbersome; this is true even though each data point provides three responses, namely the three rates of reaction of the postulated mechanism. Moreover, the inlet composition of the organic species is almost constant, so that apparent reaction orders are difficult to establish. Nevertheless, the simple model proposed, although based on an empirical rate law, showed quite a good representation of experimental rate data, as can be seen in Figure 10. Here, experimental and calculated values of rA, rD, and rC are shown; optimal parameter values are reported in Table 5, together with the average percent error for the consumption or production rate. Note that the reaction order with respect to H2 has been set to zero for the production rates of A and D, since their values appeared extremely low after a preliminary data reduction. Note also that frequency factors, activation energies, and activation volumes make sense, but there are some apparent orders that exhibit a negative value. Such a behavior, which is typical of heterogeneous reactions, where surface coverage somehow limits the reaction rate, suggests the development of a Langmuir-Hin-
2632 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997
Figure 11. Predicted (continuous lines) vs experimental data points of the species C production rate at T ) 448 K, at different organic feed-to-CO2 flow rate ratios, rr: rr ) 0.7 w/w (O); rr ) 0.5 w/w (0); rr ) 0.3 w/w (4).
Conclusions
Figure 10. Predicted vs experimental values of species consumption (A and D) and production (C) rates; dashed lines indicate (10% error. Table 5. Results of the Regression of Experimental Kinetic Dataa parameter preexponential factor (mol cm h gcat) activation energy (kJ/mol) activation volume (cm3/mol) reaction order exponent of hydrogen average percent error on rj a
A (consumption)
D (consumption)
C (production)
0.283
0.125
1.112
0.46
0.45
5.60
16.7
21.4
17.6
-0.15 0 0.24
-0.14 0 0.32
-0.39 0.25 3.05
Consumption and production rates are in [mol/(h gcat)].
shelwood mechanism; however, this type of model would introduce additional parameters for the adsorption and desorption steps, thus calling for a significantly more extensive experimental data collection. It is interesting to observe that positive values of the activation volume lead to a negative influence of pressure on the kinetics; indeed, this so-called indirect effect on the reaction rate is small except in the vicinity of the mixture critical point (Randolph and Carlier, 1992; Johnston and Haynes, 1987). On the other hand, the positive effect of pressure on the rate of reaction, shown clearly in Figures 7-9, is explained by the favorable change in the vapor-liquid equilibrium, which increases the hydrogen dissolved in the liquid phase. The values of the activation volumes are similar to those of comparable high-pressure kinetic studies in liquid solutions (Van Eldik et al., 1989). Finally, in Figure 11 a comparison between experimental kinetics (data points) and curves calculated with the proposed model is presented. The model is clearly able to represent the actual behavior in the considered ranges of temperature, pressure, and CO2-to-liquid feed ratio: also the unusual CO2 effect can be accounted for. We recall once more that a precise evaluation of liquid composition under the reaction conditions was essential to obtain such a good result in the modeling of kinetic data.
In this work the effect of supercritical CO2 on a hydrogenation reaction catalyzed by supported Pd was measured. Accurate kinetic data were obtained with a modified internal-recycle reactor at pressures between 12 and 17.5 MPa and temperatures between 423 and 473 K for the hydrogenation of the two double bonds of an unsaturated ketone with a 1% Pd on alumina industrial catalyst. A simple homogeneous kinetic model was developed to interpret experimental results. To apply this model to the multiphase reacting system under investigation, the calculation of high-pressure phase equilibria is required. A Peng-Robinson equation of state with mixture parameters tuned on experimental binary data provided a satisfactory interpretation of all binary and ternary VLE data available and was extended to multicomponent calculations. The kinetic model was able to reproduce the experimental results on the basis of the calculated compositions in the liquid phase, which are the reaction locus. The influence of the VLE on the reaction kinetics accounts for some apparently unexplainable behavior. Acknowledgment The authors are very grateful to Dr. Kurt Steiner for supporting this research project and to Mr. Thomas Kircher of Hoffmann-La Roche for the patience and help demonstrated during the experiments. Nomenclature a ) attractive parameter of the Peng-Robinson EOS b ) repulsive parameter of the Peng-Robinson EOS Ea,i ) activation energy of reaction i F ) feed mass flow rate k ) reaction rate constant k0 ) preexponential factor ki,j ) binary interaction parameter of the Peng-Robinson EOS between components i and j m ) parameter of eq 3 MW ) molecular weight P ) pressure rj ) production rate of component j [mol/(h gcat)] Ri ) rate of reaction i [mol/(h gcat)] R ) universal gas constant T ) temperature ∆V+ i ) activation volume of reaction i x ) mole fraction w ) mass fraction Wc ) mass of catalyst Greek Symbols R ) temperature dependence function of the Peng-Robinson EOS parameter a β ) exponents in eqs 6
Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2633 σ ) experimental error variance ω ) acentric factor Subscripts and Superscripts c ) critical condition F ) feed stream
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Received for review July 1, 1996 Revised manuscript received November 27, 1996 Accepted January 3, 1997X IE960369Q
X Abstract published in Advance ACS Abstracts, May 1, 1997.
