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Ind. Eng. Chem. Res. 1997, 36, 2066-2074
Influence of the Thermodynamic State on Cyclohexane Oxidation Kinetics in Carbon Dioxide Medium Palakodaty Srinivas† and Mamata Mukhopadhyay* Indian Institute of Technology, Powai, Bombay, India
Cyclohexane has been oxidized in supercritical carbon dioxide (SC CO2) medium in the presence of oxygen to give the main products, cyclohexanone and cyclohexanol. Kinetic studies have been performed to study the effects of the proximity to the plait point, nature of the phase and initial feed concentration on the product profiles, selectivities, and rates of product formation. The initial reaction conditions have been chosen to be at different regions of space on the ternaryphase diagram of the initial reaction mixture comprising cyclohexane, oxygen, and carbon dioxide. These conditions encompass different thermodynamic phases such as (i) the homogeneous subcritical (mixture) phase rich in SC CO2, (ii) the homogeneous supercritical (mixture) phase, (iii) the SC CO2-rich vapor-liquid two phase, and (iv) the CO2 dissolved liquid phase. It has been observed that the density and the proximity to the plait point of the reaction mixture influence the reaction conversion, rates, and pathways. The first-order rate constants are observed to be dependent on the thermodynamics state of the feed. Introduction Supercritical fluids as reaction media have several advantages over conventional solvents, particularly when one studies the effects of solvent parameters on the reaction. As the physical properties of these solvents are sensitive to pressure and temperature, a single SCF solvent can provide a means of studying the effect of different parameters on the reaction. Chemical reactions are well-known to be influenced by solvent effects (Caralp et al., 1993). The reaction products can be made to condense by adjusting the operating conditions in the vicinity of the mixture critical point, with a view to circumventing the side reactions. In our earlier work, we have reported the results of the cyclohexane oxidation reaction in supercritical carbon dioxide medium starting with a homogeneous mixture comprising 10 mol % C6H12, 10 mole % O2, and 80 mol % CO2 (Srinivas and Mukhopadhyay, 1994a). The work was targeted at understanding the effects of temperature and pressure on the product profile, selectivities, and reaction rates. It was demonstrated that these parameters have significant effects on the reaction rates and conversions. In the present study, another dimension is added to the problem, that is, the study on the effects of the proximity to the mixture critical point, nature of the phase, concentration, and density of the initial reaction mixture on the reaction pathways, conversion, and rates. Reaction Conditions The reaction mixture consists initially of three components, namely, cyclohexane, oxygen, and carbon dioxide. As the reaction is initiated, the products cyclohexanone, cyclohexanol, and water are formed. Measurements of the phase equilibrium data with oxygen are not feasible with cyclohexane, as it initiates the reaction at temperatures above 390 K. Hence, the phase equilibrium behavior with nitrogen has been * Author for correspondence. Present address: Chemical Engineering Department, Indian Institute of Technology, Bombay, India. † Present address: Postgraduate Studies in Pharmaceutical Technoloy, School of Pharmacy, University of Bradford, Bradford BD7 1DP, U.K. S0888-5885(96)00530-1 CCC: $14.00
Figure 1. Predicted phase envelope of the ternary system N2CO2-C6H12 at 410 K based on the reported binary data (Shibata and Sandler, 1989). (2) Plait point; (shaded area) supercritical region; (O) experimental reaction conditions for feed I.
Figure 2. Predicted phase envelope of the ternary system N2CO2-C6H12 at 423 K based on the reported binary data (Shibata and Sandler, 1989). (2) Plait point; (shaded area) supercritical region; (O) experimental reaction conditions for feed I.
considered for the present study. The phase equilibrium diagram of the ternary system of carbon dioxidecyclohexane-nitrogen has been predicted using the P-R equation (Peng and Robinson, 1976) of state with quadratic mixing rule at the desired conditions of temperature and pressure (Srinivas, 1994). Figures 1, 2, and 3 show the phase envelopes of this ternary system at 410, 423, and 433 K and 170 and 205 bar, respectively. Also shown in these figures are the conditions of the initial reaction mixture. The five feed compositions and the different reaction conditions at which the kinetic experiments have been performed are given in Table 1. The location in the vicinity of the mixture’s critical point (from here onwards referred to © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2067
(iii) Single Liquid Phase. Feed V corresponds to the liquid-phase composition in feed IV and thus lies on the saturated liquid-phase boundary at 433 K and 170 bar. This liquid phase has the advantage of reduced viscosity of CO2 dissolved in it. Experimental Section
Figure 3. Predicted phase envelope of the ternary system N2CO2-C6H12 at 433 K based on the reported binary data (Shibata and Sandler, 1989). (2) Plait point; (shaded area) supercritical region; experimental reaction conditions: (O) feed I; (0) feed II; (4) feed III; (b) feed IV; (9) feed V.
as the plait point), termed the mixture critical region, exhibits similar unique physical properties to that in the vicinity of the critical point of a pure SC solvent and is discussed below with respect to their thermodynamic states. (i) Single Fluid Phase. The single fluid phase encompasses two distinct homogeneous regions, namely, the subcritical SC CO2-rich vapor phase and the SCF phase with respect to the mixture’s critical point. These can be characterized by the location of the plait point at the specific conditions of temperature and pressure. As can be seen from the location of the plait point in the phase diagrams, Figure 1, feed I is in the SC CO2rich vapor phase at 170 bar, while it is in the mixture critical region at 205 bar. As the temperature is increased to 423 and 433 K, the phase envelope of the ternary mixture reduces. Thus, this feed composition falls closer to the mixture critical region even at the lower pressure of 170 bar at higher temperatures. The other homogeneous feed composition at 433 K, i.e., feed II, is close to the plait point at both 170 and 205 bar. Feed III, at 433 K and 205 bar, corresponds to the SC CO2-rich saturated vapor phase as it lies on the boundary of the two-phase region. (ii) Two (Fluid-Liquid) Phase. In order to study the effect of phase behavior on reaction performance, a feed composition such as in feed IV is chosen at 433 K and 170 bar. This mixture is in the two-phase region of coexisting vapor and liquid, one rich in SC CO2 and the other rich in cyclohexane, respectively. The SC CO2rich vapor phase composition is identical to the composition of feed III and the CO2-dissolved liquid phase is identical to the composition in feed V.
The experimental setup and procedure are described elsewhere (Srinivas and Mukhopadhyay, 1994a,b). Kinetic experiments have been performed in a 316-L stainless steel microreactor fitted with a movable piston in order that the volume can be varied from 18 to 5 cm3 while maintaining the pressure and temperature constant in the reactor. Since the reaction involves free radicals, it is ensured that the reactor is absolutely clean and reagents are highly (99.9%) pure (analytical grade). The reaction conditions can be attained in about an hour, and the time of reaction is considered from this instant onwards. A separate feed mixture having the same composition and number of moles is charged for each kinetic run and experimental point. The analysis of the samples is carried out using an elaborate and standardized procedure of GC analysis on a 10% supelcowax-fused silica glass capillary column, with an accuracy of (0.0001 mole fraction. Results and Discussion Reaction Pathways. Oxidation of cyclohexane in a supercritical solvent (CO2) medium is believed to follow the free-radical mechanism consisting of elementary steps of initiation, propagation, and termination. However, after a sufficient amount of intermediates accumulate, free radicals are formed by degenerate chain branching. After an initial induction period, the rate increases steadily, with the chain branching taking over with an increase in the concentration of radicals. The reaction mechanism is essentially similar to the one presented in our earlier paper (Srinivas and Mukhopadhyay, 1994a) and described in Figure 4. The chain branching is proposed to be responsible for the formation of the desired products, namely, cyclohexanone and cyclohexanol. The different pathways for the formation of these products are shown schematically in Figure 5. Only two products, namely, cyclohexanone and cyclohexanol, have been detected in the present studies. The reaction has been stopped when side products begin to form. Cyclohexanone may be formed via two pathways,
Table 1. Experimental Reaction Conditions for the Cyclohexane Oxidation Kinetic Experiments SCF phase
SC CO2-rich vapor phase
SCF liquid two phase
CO2 dissolved liquid phase
feed I CO2, 80 mol % C6H12, 10 mol % O2, 10 mol % temp 410, 423, 433 K pressure 170, 205 bar feed II
feed III CO2, 52 mol % C6H12, 16 mol % O2, 32 mol % temp 433 K pressure 205 bar
feed IV CO2, 52 mol % C6H12, 16 mol % O2, 32 mol % temp 433 K pressure 170 bar split vapor, 94% CO2, 52 mol % C6H12, 15 mol % O2, 33 mol % liquid, 6% CO2, 35 mol % C6H12, 50 mol % O2, 15 mol %
feed V CO2, 35 mol % C6H12, 50 mol % O2, 15 mol % temp 433 K pressure 170 bar
CO2, 70 mol % C6H12, 25 mol % O2, 5 mol % temp 433 K pressure 170, 205 bar
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Figure 4. Reaction mechanism of the formation of cyclohexanone and cyclohexanol by cyclohexane oxidation in SC CO2 medium.
Figure 6. Effect of pressure on the (a, top) cyclohexanone and (b, bottom) cyclohexanol formation in SCF phase at 433 K for feed II.
Figure 5. (a) Pathways and (b) sequential steps for the formation of cyclohexanone and cyclohexanol.
namely, (R1) f (R4) and (R1) f (R2) f (R3) f (R4), whereas cyclohexanol by one pathway, namely, (R1) f (R2) f (R3) f (R5), as shown sequentially in Figures 4 and 5. Another important observation made was the appearance of a visual aberration or haziness on the glass window of the reactor at the end of induction period. Water is formed by (R3), (R4), and (R6), and the phase equilibrium studies of the reacting multicomponent system (Srinivas and Mukhopadhyay, 1994b) substantiate that water is the only product which condenses out until the conversion is about 6-7%. Effects of Temperature and Pressure. The effect of temperature on the product formation has been studied for feed I and the effect of pressure for both feed
I and feed II. The product profiles for the other feeds are discussed with respect to the nature of the phase of the feed or its proximity to the plait point. (a) Feed I. The product profiles obtained for feed I have been reported in detail in our earlier paper (Srinivas and Mukhopadhyay, 1994a) and are only briefly described here in light of the reaction pathways. The maximum cyclohexanone formed at any pressure increases with temperature. These observations are in conformity with the ones reported in the literature for liquid-phase oxidation (Berezin et al., 1966). However, this is not the case with cyclohexanol formation. The maximum amount of cyclohexanol formed (which also includes cyclohexyl hydroperoxide) is less at 433 K than at 423 K. This may be attributed to the formation of C6H11O2* radical in larger proportion than C6H11O* radical, which subsequently gives rise to the products cyclohexanone and cyclohexanol, respectively. In other words, the pathway (R1) f (R4) is presumably preferred to (R1) f (R2) f (R3) f (R4). Thus, it is noted that reaction R4 is preferred to (R2) for consuming C6H11O2*, or degenerate chain branching is preferred to the propagation step after accumulation of free radicals from the initiation step.
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2069
Figure 7. Effect of phase behavior on the (a, top) cyclohexanone and (b, bottom) cyclohexanol formation at 433 K.
The maximum amount of cyclohexanone formed increases with pressure at each of the three temperatures. On the other hand, the maximum amount of cyclohexanol formed increases less significantly with pressure. This may be attributed to the suppression of reaction R2 relative to (R4) at higher pressures, which would have otherwise resulted in a similar increase in both products. This is due to accumulation of C6H11O2* radicals produced by (R1) and resistance to the formation of the same radicals by (R3) in conformity with the Le Chatelier principle. The cyclohexanol formation passes through a maximum at 205 bar and 433 K. This is due to subsequent conversion of cyclohexanol at higher times and higher temperatures by reaction R6. (b) Feed II. This feed is close to the plait point at 433 K and at 170 and 205 bar and is in the supercritical region. Though the concentration of oxygen is halved (as compared to feed I), it is expected not to alter the reaction mechanism, as the products are assumed to be formed by the degenerate chain-branching step where oxygen does not take part in the reaction. Oxygen is only required for the free-radical initiation as shown in reaction mechanism step (R1). The product profiles as shown in Figure 6 are not very much different from the ones observed for feed I, in which cyclohexane and oxygen are in a 1:1 ratio in the feed mixture. Cyclohexanone and cyclohexanol concentrations increase with
Figure 8. Effect of cyclohexane concentration on the (a, top) cyclohexanone and (b, bottom) cyclohexanol formation at 433 K and 205 bar of pressure.
pressure. Cyclohexanol concentration passes through a maximum, which indicates that at higher concentrations, it is reacting further to give C6H10O by (R6). At higher conversions, C6H11O2* is depleted more by the degenerate chain-branching step (R4) rather than by propagation step (R2). As a result, cyclohexanol formation is always less than that of cyclohexanone. Effect of the Nature of the Phase. The effect of phase condition of the initial reaction mixture has been interpreted by comparing the product formation in the SC CO2-rich vapor phase (feed III), SC CO2-rich vaporliquid two phase (feed IV), and CO2 dissolved liquid phase (feed V). Parts a and b of Figure 7 show the formation of cyclohexanone and cyclohexanol, respectively. At 433 K and 170 bar, the feed composition of feed IV splits into 94% vapor, with composition corresponding to that of feed V. As can be seen, the product formation decreases with a change in phase from two phase (fluid-liquid) to a single vapor phase. Moreover, the vapor phase composition of feed IV, being the same as that of feed III and the conversion of feed III at 205 bar being much less, it can be concluded that the reaction in feed IV occurs mainly in the cyclohexanerich liquid phase. This confirms the fact that the product formation increases on going from two phase to a single liquid phase.
2070 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
Figure 10. Effect of the cyclohexane-to-O2 ratio on the selectivity of C6H10 O with respect to C6H11OH at 433 K after 3 h (for feed IV, the ratio is in the initial feed).
Figure 9. Effect of cyclohexane-to-CO2 ratio on the (a, top) cyclohexanone and (b, bottom) cyclohexanol formation at 433 K after 3 h (for feed IV, the ratio is in the initial feed).
The maximum conversion of cyclohexane of 5% has been observed for feed V and the minimum of 1% for feed III. At feed conditions close to the plait point as in feed II, conversions comparable to those obtained in the SC CO2-dissolved liquid phase can be achieved because of increased local concentrations in the cluster or cage. Effect of Concentration. The effect of cyclohexane concentration on the product formation is shown in parts a and b of Figure 8 at 433 K and 205 bar for cyclohexanone and cyclohexanol, respectively. The product formation is more with increased concentration of cyclohexane in feed II as compared to that of feed I in the SCF phase. In the case of feed III, which lies on the saturated vapor curve, the product formation is much lower as compared to that observed in feed I and feed II. A similar effect is shown in parts a and b of Figure 9 for the formation of cyclohexanone and cyclohexanol, respectively, for all the five feeds mentioned above. As can be seen, except for the SC CO2-rich feed III, the formation of both products cyclohexanone and cyclohexanol is more when the cyclohexane-toCO2 concentration is higher in the feed. This is at-
tributed to the fact that feed III is neither in the supercritical phase nor in the liquid phase where the cage effect is pronounced, thereby altering the reaction pathways. Selectivity. As shown in Figure 10, the selectivity of cyclohexanone to cyclohexanol is the highest for feed IV and the lowest for feed V (at 2 h of time when the selectivity and conversion are highest), which is more or less at the same level for feed III. This implies that, with the formation of the products in the liquid phase of feed IV, the products are transferred to the vapor phase (up to a mole fraction of 0.06) as per our multicomponent solubility studies (Srinivas and Mukhopadhyay, 1997). This improves the overall selectivity, justifying that a higher conversion takes place in the liquid phase. The selectivity increases with the cyclohexane-to-oxygen ratio for the homogeneous SCF feeds I and II at 170 bar and the SC CO2-rich feed III at 205 bar. But the ratio decreases with the cyclohexane-tooxygen ratio on going from two phase (feed IV) to the single liquid phase (feed V) or with SCF feeds I and II at 205 bar. Cyclohexanol formation is more favored in the liquid feed or with higher cyclohexane concentration. The selectivity ratio for feed II is higher than that for homogeneous liquid-phase feed V at 2 h for a higher cyclohexane-to-oxygen ratio. The selectivity toward cyclohexanone has been observed to be better for feed II compared to feed V, because the oxygen ratio is less in the SCF phase, which reduces the formation of side products. Kinetic Data Analysis. In the SC CO2 medium, the formation of the free radicals is favored by the presence of oxygen. From the analysis of the product profiles, it can be seen that the products are formed by different pathways. In the low-conversion range as obtained in the present study, it can be reasonably assumed that the majority of the conversion of cyclohexane takes place by the degenerate chain-branching steps, namely, (R4) and (R5), as the products formed are mainly cyclohexanone and cyclohexanol. Hence, reactions R1, R4, and R5 are of interest for the kinetic data analysis. Rate Equations. The rate of oxidation becomes independent of oxygen concentrations at sufficiently high concentrations of free radicals and can be sche-
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2071
matically represented as
Table 2. Density (G) and Isothermal Compressibility (β) of the Initial Reaction Mixtures at Different Reaction Conditions
k HC
401 K
P* a
feed
where HC represents cyclohexane, P* represents C6H11O2*, k represents C6H10O, and a represents C6H11OH. Therefore, the overall rate of reaction, in the presence of sufficiently high concentration of free radicals, can be written as (Berezin et al., 1966)
-rc ) -
dCA 1 dNA )) koCAn dt V dt
( )
II III IV
(1)
where CA is the concentration of cyclohexane in mol/ cm3, ko is the overall rate constant, NA is the number of moles of cyclohexane reactant at any given time, V is the total volume of the reactor, and n is the order of reaction. In the low-conversion ranges as in the present study, it is reasonable to assume n equal to one. Thus, after integration, with the moles of reactant changing from NA0 at the start of the reaction to NA at any instant of time, the above equation reduces to
NA - ln ) kot NA0
I
The rate of formation of individual products cyclohexanone and cyclohexanol via reactions R4 and R5, respectively, can be written as
I II
IV V
where rk and ra are the rates of formation of cyclohexanone and cyclohexanol respectively, and kk and ka are their respective rate constants. Here again, the reactions are assumed to be first order in cyclohexane concentration in the low-conversion range. In the following paragraphs, this assumption is validated by the experimental results. With this mechanism, the overall rate of reaction may be written as
ro ) (kk + ka)CA ) koCA
(5)
Dividing (3) by (4) gives
dNk kk ) dNa ka
(6)
Integrating between the limits of initial concentration of the products at time zero to the final concentrations Nk and Na of cyclohexanone and cyclohexanol, respectively, at time t, eq 6 reduces to
Nk - Nk0 kk ) Na - Na0 ka
(7)
Thus, from the overall rate constants, the individual constants have been determined at different conditions of temperature and pressure. The effects of reaction conditions on these constants as well as on the reaction
170 bar
205 bar
170 bar
205 bar
7.11 6.43
8.50 4.69
6.46 6.41
7.92 4.81
6.09 6.39 7.84 5.13
7.35 4.86 9.07 3.37 7.27 4.66
5.94 6.15 9.38 1.73 9.38 1.73
410 K
(3)
(4)
205 bar
Table 3. First-Order Reaction Rate Constants of Cyclohexane Oxidation in SC CO2 Medium
and
1 dNa ra ) ) kaCA V dt
170 bar
103 F, mol/cm3 103 β, bar-1
III
1 dNk rk ) ) kkCA V dt
103, F mol/cm3 103 β, bar-1 103 F, mol/cm3 103 β, bar-1 103 F, mol/cm3 103 β, bar-1 Vapor 103 F, mol/cm3 103 β, bar-1 liquid 103 F, mol/cm3 103 β, bar-1
433 K
V
feed
(2)
property
423 K
423 K
433 K
rate const × 103, h-1
170 bar
205 bar
170 bar
205 bar
170 bar
205 bar
ko kk ka ko kk ka ko kk ka ko kk ka ko kk ka
1.95 1.15 0.80
1.50 0.95 0.55
2.30 1.37 0.93
2.28 1.38 0.89
3.61 2.52 1.09 16.69 10.68 6.01
6.13 4.38 1.75 19.95 13.48 6.47 3.33 2.05 1.28
22.06 16.16 5.89 41.59 26.52 15.07
pathways have been interpreted in terms of the thermodynamic state of the system utilizing the following thermodynamic properties which have been calculated (Reid et al., 1987) as below and given in Table 2:
(i) isothermal compressibility (β) as calculated from
β)-
1 ∂ν ν ∂P T,x
( )
(8)
and (ii) density, F, of the initial feed mixture as calculated using the P-R EOS. Rate Constants. Feed I. The behavior of the conversion data with time for the homogeneous kinetic experiments with feed I has been presented in our earlier paper (Srinivas and Mukhopadhyay, 1994a). The values of ko at six conditions are given in Table 3. The individual reaction rate constant kk and ka for all six conditions are also given in Table 3. For a 76% change in isothermal compressibility with an increase in pressure from 170 to 205 bar, the overall rate constant increases by 70%. Feed II. The kinetic data of the experiments with feed II, in the homogeneous SC phase at 433 K, have been similarly analyzed and fitted to the first-order rate equation. Here again, as in the case of feed I, the data above conversion levels of 0.1% are only considered in the analysis. The values of ko along with the individual
2072 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
rate constants kk and ka are given in Table 3. The change in isothermal compressibility (as shown in Table 2) is 66% with an increase in pressure from 170 to 205 bar, and there is only a 20% increase in the overall rate constant with pressure, unlike a 70% increase as in the case of feed I. Feeds III, IV, and V. The above three cases are clubbed together because the compositions of feed III and feed V resemble those of the vapor and liquid phases of feed IV, respectively. Unlike in the previous two cases where the reaction mixture is in a single SCF phase, the conversions are very low at 205 bar for feed III where the reaction mixture is in the SC CO2-rich vapor phase. The rate constants are given in Table 3. The kinetic data for feed IV, consisting of two phases at the reaction condition, result in a higher rate constant as compared to that of feed III at 205 bar, where the reaction mixture is in the homogeneous single SCF-rich phase. Out of all the cases, the reaction is fastest in the liquid phase. As can be seen from these three conditions, the overall rate constant increases from 3.33 × 10-3 h-1 in the SC CO2-rich vapor phase to 22.06 × 10-3 h-1 in the fluid-liquid two-phase region. The change in the thermodynamic state has been caused by a decrease in pressure from 205 to 170 bar for the same initial feed composition. For the liquid-phase reaction as in feed V, the overall rate constant is 41.59 × 10-3 h-1. This means that the reaction is favorable in the liquid phase where the concentration of the cyclohexane is higher as compared to that in the SCF phase. Proximity to the Plait Point. The reaction rate constants obtained in the present study are found to be dependent on the thermodynamic state of the feed. As the reaction feed in the SCF region is moved toward the plait point as in feed II, the rate constants obtained are comparable to that in feed IV. For feed V, a saturated liquid, the rate constants are 2-fold higher than those observed for feeds II, III, and IV. The rate constants for feed III are of the same order of magnitude as for feed I but less than feed II, as both are slightly away from the plait point, though all are in the homogeneous phase. With the 20% increase in pressure, the change in isotherml compressibility is 66% for feed II, while it is 76% for feed I at 433 K. An 8-fold increase in kk and 5-fold increase in ka are observed with changing the thermodynamic state of the system from a single (SCF rich) phase to two (fluid-liquid) phase. Effect of Density. Figure 11 shows the variation of the overall reaction rate constant with the density of the feed mixture, depending on the thermodynamic state. It is observed that the density of the reaction mixture has a considerable effect on the rate constant. While the rate constants for feed I increase with an increase in density of the reaction mixture at 433 K in the SCF region, they remain invariant at 410 and 423 K where the thermodynamic state is away from the plait point. At 433 K, for a 20% increase in pressure, (i) a 74% increase in kk and 60% increase in ka for feed I and (ii) a 26% increase in kk and 8% increase in ka for feed II are observed. A similar behavior of a 3-fold increase in the rate constant is found in the literature (Dooley et al., 1987) for a 3-fold increase in pressure at far beyond the critical point of the mixture. At 423 K, for feed I, the trend is different, with the rate constant being
Figure 11. Variation of the overall first-order rate constants with density. Table 4. Experimental Pressure Coefficient Values for Reaction Step R1 at Average Pressure feed
410 K
423 K
433 K
I II
-7.5 × 10-3
-2.4 × 10-3
1.5 × 10-3 5.1 × 10-3
almost invariant with pressure, whereas at 410 K, ka decreases. The sign of the experimentally observed pressure coefficient as calculated from the overall reaction rate constants, as shown in Table 4, changes from negative to positive on going closer to the plait point, i.e., changing the temperature from 410 to 433 K. This elucidates the reaction mechanism, changing on approaching the plait point near the critical region for a feed composition as that of feed I. This corroborates that different reaction mechanisms may be followed at different conditions and that the rate constants essentially depend on the local compositions in the cluster or solvent cage. Activation Energy. The Arrhenius plots for the rate constants kk are shown in parts a and b of Figure 12 at 170 and 205 bar, respectively, and that for ka are shown in parts a and b of Figure 13 for the homogeneous SCF reaction of feed I. Thus, the temperature dependence on the rate constant, RR, can be expressed as
kk ) 1.56 × 103 exp(-11.5/RT) at 170 bar (9) and
kk ) 8.80 × 108 exp(-22.5/RT) at 205 bar
(10)
and on ka, can be expressed as
ka ) 0.25 exp(-4.68/RT) at 170 bar
(11)
and
ka ) 9.97 × 105 exp(-17.4/RT) at 205 bar
(12)
with an activation energy of 11.5 kcal/mol at 170 bar for reaction R4. These values compare well with the reported value of 13 kcal/mol (Berezin et al., 1966) for reaction R2 between the C6H11O2* radical and the C6H12 molecule to give cyclohexyl hydroperoxide and cyclo-
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2073
Figure 12. Arrhenius plot of cyclohexanone formation in the SCF phase (feed I) at (a, top) 170 and (b, bottom) 205 bar.
Figure 13. Arrhenius plot of cyclohexanol formation in the SCF phase (feed I) at (a, top) 170 bar and (b, bottom) 205 bar.
hexyl radical. Reactions in dilute gases are characterized by successive collisions between reacting species, not all encounters possessing sufficient energy for reaction and thus remaining “activation controlled”. The increase in activation energy with increase in pressure is attributed to an increase in viscosity due to which the collisions between the free radicals and cyclohexane are slowed down. As explained earlier (Srinivas and Mukhopadhyay, 1994a) the increase in activation energy with increase in P is attributed to the reduction of cage effects. The solvent clustering being more at a lower pressure in the vicinity of the mixture critical point can move the energy levels of the reactants and/ or activated complex, lowering the activation energy. Lower values of preexponential factor for reaction R5 as compared to reaction R4 indicate that the concentration of C6H11O* radicals is lower than the C6H11O2* radicals. This is in conformity with the reaction mechanism proposed according to which the C6H11O2* radical is formed both in the initiation steps (R1) and the degenerate chain-branching step (R3), whereas C6H11O* is formed by only (R3). The increase in the value of preexponential factors with increase in pressure indicates a favorable influence of pressure on retaining the free radicals.
Conclusions The product formation is favored in the SCF region compared to the SC CO2-rich vapor phase. However, the reaction is faster in the CO2-dissolved cyclohexane liquid phase. The pseudo-first-order rate constant for the reaction between the cyclohexane molecule and the free radicals follows an Arrhenius-type dependency on temperature. The activation energy is observed to be a function of pressure. The increase in activaion energy with pressure is due to the reduction in cage effects at higher pressures close to the mixture critical region. Very low preexponential factors imply that the concentration of radicals is low, which increase with pressure as substantiated by an increase in the preexponential factor by about 5 orders of magnitude. The density effect on the reaction rate constant is quite pronounced at 433 K. For an initial feed consisting of cyclohexane and oxygen in a molar ratio of about 1, an increase of 20% in pressure from 170 bar increases the overall rate constant by 1.7 times. Such an effect is also observed with a feed of cyclohexane and oxygen in a molar ratio of about 5. This indicates the positive effect of working in the mixture critical region at conditions close to the plait point, where the densities are close to that of
2074 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
liquids. The overall rate constant increases with the density of the medium. It is shown in the present study that the reaction rate and conversion can be manipulated by varying the reaction temperature, pressure, and feed composition. The proximity to the plait point or the initial phase of the feed may be used as an additional process variable for performing the reaction in the supercritical solvent medium. Literature Cited Berezin, I. V.; Denisov, E. T.; Emanuel, N. M. The oxidation of Cyclohexane; Pergamon: New York, 1966. Caralp, M. H. M.; Clifford, A. A.; Coleby, S. E. Other uses for nearcritical solvents: chemical reaction and recrystallization in nearcritical solvents. In Extraction of Natural Products using NearCritical Solvents; King, M. B., Bott, T. R., Eds.; Blackie Academic: New York, 1993; Chapter 3. Dooley, K. M.; Brodt, S. R.; Knopf, F. C. Comments on “Reactions in Supercritical FluidssA Review”. Ind. Eng. Chem. Res. 1987, 26, 1267. Peng, D. Y.; Robinson, D. B. New two constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. Pure Component constants. In Properties of gases and liquids; McGraw-Hill: New York, 1987; Chapter 2.
Shibata, S. K.; Sandler, S. I. High pressure vapor-liquid equilibria of mixtures of Nitrogen Carbon Dioxide, and Cyclohexane. J. Chem. Eng. Data 1989, 34, 419. Srinivas, P. Oxidation of Cyclohexane in Supercritical Carbon Dioxide Medium, Ph.D. Thesis, Indian Institute of Technology, Bombary, India, 1994. Srinivas, P.; Mukhopadhyay, M. Oxidation of Cyclohexane in Supercritical Carbon Dioxide Medium. Ind. Eng. Chem. Res. 1994a, 33, 3118-3124. Srinivas, P.; Mukhopadhyay, M. Supercritical fluid-liquid equilibria of binary and ternary mixtures of cyclohexanone and cyclohexanol with CO2 and N2. Paper presented at the 1994 AIChE National Spring Meeting, Atlanta, GA, 1994b; Paper 95f. Srinivas, P.; Mukhopadhyay, M. Ind. Eng. Chem. Res. 1997, in press.
Received for review August 23, 1996 Revised manuscript received February 12, 1997 Accepted February 18, 1997X IE960530X
X Abstract published in Advance ACS Abstracts, April 15, 1997.
