3118
Ind. Eng. Chem. Res. 1994,33, 3118-3124
Oxidation of Cyclohexane in Supercritical Carbon Dioxide Medium P. Srinivas and M. Mukhopadhyay' Department of Chemical Engineering, Indian Institute of Technology, Powai, Bombay 400 076, India
Cyclohexane oxidation has been studied in supercritical carbon dioxide medium for homogenizing the initial reaction mixture to produce cyclohexanone and cyclohexanol as the chief reaction products. The kinetic experiments have been performed a t three temperatures 410, 423, and 433 K and two pressures 170 and 205 bar. The results have been interpreted in the light of transition state theory and cage effects. Conversions obtained are low compared to the liquid phase oxidation because of dilute concentrations of the reactants. Cyclohexanone is more selectively formed and favored by both pressure and temperature. A 20% increase in pressure results in (i) reduction of the induction period by 50%, (ii) a change in activation energy from 13.0 k c d m o l a t 170 bar to 22.6 kcal/mol at 205 bar, (iii)a n increase in the preexponential factor by 5 orders of magnitude, and (iv) an increase in the first-order rate constant a t 433 K by about 70%. The variation in the observed activation volume from 36 cm3/mol at 410 K and 170 bar t o -775 cm3/mol at 433 K and 205 bar suggests that the reaction in supercritical C02 medium can be greatly manipulated.
Introduction In recent years supercritical fluids (SCF) have gained considerable importance as media for separation and chemical reactions owing to their flexible physicochemical properties which can be varied over a wide range with a small change in temperature or pressure. With an SCF medium some of the diffusion-controlled heterogeneous reactions can be carried out homogeneously by dissolving both the reactant and catalyst in a single fluid phase. Further it is possible to device a suitable reaction-separation scheme to improve the selectivity to the desired product. Chemical reactions are well known to be influenced by solvent effects. The advantage of an SCF solvent is that all the solvent properties are extremely pressure sensitive in the vicinity of the mixture critical point. Thus it is important to understand how they can influence the reaction rate, conversion, and reaction pathways. Subramaniam and McHugh (1986) suggest that the increased rates in SCF phase may be due to efficient production of free radicals at lower viscosities and their enhanced rate of diffusion than in the liquid phase. Oxygen is reported to be a better free radical initiator in the SC phase (McHugh and Krukonis, 1994). Several catalytic (Tiltscher and Schelchshorn, 1984; Dooley, 1987; Tiltscher and Hofmann, 1987; Collins et al., 1988; Yokota and Fujimoto, 19911, noncatalytic (Abraham and Klein, 1985; Kim and Johnston, 1987; Johnston and Haynes, 1987; Dombro et al., 1988; Townsend and Abraham, 1988; Occhiogrosso and McHugh, 1987; Suppes et al., 1989; Houser et al., 1989; Huppert et al., 1989; Suppes and McHugh, 1989; Wu et al., 1989), and enzymatic (Randolph et al., 1985, 1988a,b; Nakamura, 1990; Miller et al., 1991; Ginosar and Subramaniam, 1992) reactions were studied employing SCF solvents to explore the possible ways chemical reactions can be affected. Complete oxidation of organics in supercritical water (Webley et al., 1991; Webley and Tester, 1991) is of prime interest t o environmentalists today. One possible application where all of these advantages could be utilized, is in the oxidation of hydrocarbons. In the conventional process, these free radical reactions are carried out in the liquid phase with either air or oxygen as the coreactant. The reactions are in general autocatalytic in nature and a catalyst only helps
in reducing the induction period. One among this class of reactions, namely, oxidation of cumene is reported in the literature (Occhiogrosso and McHugh, 1987; Suppes et al., 1989) which was studied in a homogeneous phase at the mixture critical conditions in SC C 0 2 , xenon, and krypton media. They found that the pressure or proximity to the mixture critical region had little effect on the overall rate of oxidation of cumene at 383 K in the three SC solvents. However, they did not study the effect of temperature on the reaction in the supercritical region. The reaction products can be made to condense by manipulating the phase behavior circumventing unnecessary side reactions. The reaction rates and conversions can thus be manipulated by adjusting the operating conditions of temperature, pressure, and feed composition near the mixture critical point. In the present work attention is focused on the effects of temperature, pressure, and solvent effects on cyclohexane oxidation to form cyclohexanone and cyclohexanol in SC COz medium. The paper presents the experimental data of the reaction kinetics and analyzes the behavioral trends of the reaction rates and conversion in the light of transition state theory and cage effects.
Reaction Mechanism In general, oxidation of cyclohexane is carried out in the liquid phase at 393-413 K and pressures greater than 20 bar with air or oxygen as coreactant under different oxidation conditions, such as uncatalyzed, catalyzed by transition metals, or promoted by initiators (Berezin et al., 1966). For the vapor phase oxidation, high temperatures of 593-613 K are normally required. This leads to degradative oxidation, and the yields of desired individual products are low (Berezin et al., 1966). The reaction in a SCF solvent is expected to follow the same free radical mechanism-based elementary steps of initiation, propagation and termination as in the case of liquid phase oxidation. These hypothesized steps are given in Table 1. When a sufficient amount of chain branching intermediates have accumulated, degenerate branching becomes the main source of free radicals, as this forms free radicals more efficiently than the parent hydrocar-
0888-588519412633-31I8$04.5OlO 0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 3119 Table 1. Reaction Mechanism of Cyclohexane Oxidation in SC C02 Medium initiation:
OdOf+H.
propagation:
0 O""* * 0' +
+
()"OH
(R3)
degenerate chain branching:
bon. After an initial induction period, during which the oxygen uptake is usually low, there is a steady increase in rate as the chain branching takes over followed by an increase in the radical concentration. The chain branching step is believed to be responsible for the formation of the desired products, such as cyclohexanone and cyclohexanol.
Activation Volume According to the transition state theory, the activation volume is equal to the difference in partial molar volumes between the transition state and the reactants (Combes et al., 1992). For a bimolecular reaction A B [transition state]* C, where the rate r = kJA1 [Bl, the effect of pressure on the rate constant, k,, is given by the relation
+
-
a In k, (
d
T
compound cyclohexyl hydroperoxide
Tb,K
T,,K
P,,bar
w
463
694
50.4
0.4612
Table 3. Regressed Binary Interaction Constants in P-R EOS binarypair T,K k~ nu %AARD,aP C0z-C6H1zb 423 0.099 Nz-CsHiz' 423 0.076 C02-CtjHiiOHd 423 0.2018 -0.0900 6.71 Nz-C6H110Hd 423 0.3548 12.55 C&z-CsH1iOHd 423 0.0200 -0.0090 4.71 a %AARD, P = C CIPeq - PdI/P,,)/NDP x 100. Interpolated from the regressed data of Shibata and Sandler (1989)at 366.5K and 410.9K and of Krichevskii and Sorina (1960)at 473 K Same as that at 410.9 K from the data of Shibata and Sandler (1989). Srinivas and Mukhopadhyay (1994).
termination:
-
Table 2. Esthated Critical Properties of Cyclohexyl Hydroperoxide
AV +=-
RT - KT
(1)
where, KT is the isothermal compressibility and A P is the activation volume given as
where M represents the activated complex. Thus in a highly compressible SCF solvent, in which the partial molar volumes have large negative values, the pressure effect on the reaction rate constant may be significant if the activation volumes are very large. For dilute systems, the activation volume is dictated by the differences in the van der Waals attractive and repulsive forces of the reactants and transition state with the solvent and the isothermal compressibility of the solvent. Large compressibility factors may magnify or nullify the pressure effects, depending on whether the activation volume is large, either positive or negative. This pressure effect is very much different in liquid solvents in which partial molar volumes are only a few cubic centimeters per mole. Hence activation volumes
can be used t o ascertain the size change that occurs in going from the reactants to the transition state. As a result the pressure effect on rate constant may discern information on the reaction mechanism. To evaluate the possible pressure effects, the partial molar volume ( P W ) and isothermal compressibility data have been calculated in the present study, using the P-R EOS (Peng and Robinson, 1976) and quadratic mixing rules with two binary interaction constants, Ku and nu in the attractive energy term ag and size parameter bG respectively for each of the binary pair. The properties of the transition state have been assumed to be those of cyclohexyl hydroperoxide, and the critical properties, accordingly estimated (Reid et al., 19871, are given in Table 2. Critical properties of all other compounds are taken from literature (Reid et al., 1987). The binary interaction constants necessary for this purpose have been regressed using the binary experimental data of carbon dioxide-cyclohexane available in the literature (Shibata and Sandler, 1989; Krichevski and Sorina, 1960). The regressed binary interaction constants are given in Table 3. The binary interaction constants with cyclohexylhydroperoxide are assumed to be same as those with cyclohexanol. In a separate study (Srinivas and Mukhopadhyay, 19941, binary SCF liquid equilibria of COZ and N2 with cyclohexanol and cyclohexanone have been measured and the regressed binary interaction constants for the systems with cyclohexanol are given in Table 3. The activation volumes thus calculated would have some error due to the fact that oxygenated compounds are poorly represented by P-R EOS besides the uncertainties in their properties estimation. Simulating the initial homogeneous reaction mixture, the P W s have been calculated in a mixture of cyclohexane (10 mol %), oxygen (10 mol %), and CO2 (80 mol %) with cyclohexyl hydroperoxide infinitely dilute in it at 423 K and two pressures 170 and 205 bar. The activation volume thus calculated is -300 cm3/mol at 170 bar and -244 cm3/mol at 205 bar. From this analysis, the activation volumes being negative, it is anticipated to observe a positive pressure effect on the reaction rate.
Phase Behavior The condition of homogeneity of the initial reaction mixture at the desired temperature and pressure, is decided by the phase boundary exhibited by the interaction of various components involved. The actual reaction mixture consists of three components initially and
3120 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 Teiiiperature Controller/Iiidicator
Pressure Indicator
P-7iI Pressilre Transducer
A
vs
In1 I Thermocouple Magnetic Bar
Pressure Generator
j j J if; Glass Window ni
Light Source Mirror
Figure 2. Schematic diagram of the experimental setup.
/ 100*/,
V
V
V
V
20
40
60
80
co2
100% N2
Figure 1. Phase behavior for the ternary system of C02-C&2Nz a t 410 K predicted using P-R EOS based on reported binary data of Shibata and Sandler (1989). Open circles (0)indicate experimental reaction conditions.
at least six during the course of reaction when the products are formed. The binary system C02-CsH12 follows a simple type I phase behavior (Streett, 19831, exhibiting a maximum pressure of 148 bar at 423 K on the critical locus curve which corresponds t o a mixture composition of 72 mol % CO2 and 28 mol % C6Hl2 (Krichevskiiand Sorina, 1960). The operating conditions for the present study have been chosen above this pressure, namely, 170 and 205 bar at temperatures 410, 423, and 433 K. Phase behavior of the ternary system C02-CsH12N2 (nitrogen being chosen here as a homomorph t o avoid reaction during the phase equilibria studies) has been investigated which gives a more realistic picture of the initial condition of the reacting system. Figure 1shows the triangular diagram of this system at a constant temperature of 410 K at two pressures. The reaction conditions are shown by open circles in the figure. The phase diagram at other reaction temperatures 423 and 433 K would not be very much different from the one at 410 K and hence the reactions at these temperatures have been performed with the same feed composition. The initial reaction mixture has been taken as CsHlz (10 mol %I, 0 2 (10 mol %), and CO2 (80 mol %). It is thus assumed that the reaction mixture is sufficiently dilute so that the reaction takes place only in the SCF phase and that the products condensed do not induce transfer of the reactants t o the liquid phase.
Experimental Section Apparatus. The schematic diagram of the experimental setup is shown in Figure 2. The microreactor is made up of 316 L (low carbon) stainless steel of 0.d. 63 mm and i.d. 16 mm. The volume can be varied from
18 to 5 cm3 with the help of a movable piston which also acts as a pressure seal between the pressurizing fluid (mercury) and the reactants. A borosilicate glass window is secured at one end of the reactor to visually inspect the contents of the reactor and to ensure that a single homogeneous phase exists at the reaction conditions. The cell contents are mixed by a teflon-coated magnetic stirring bar (10 mm length and 9 mm 0.d.) placed in the reactor and moved by a magnet located below. A heating tape is wound round the reactor and insulated by an asbestos rope to reduce heat losses. The temperature is measured by a 1.5 mm diameter Fe-K thermocouple placed 5 mm deep onto the body of the reactor and controlled within kl.0 K by a temperature controllerhndicator (Arun Electronics, Bombay). The pressure is maintained constant by adjusting the piston position by the communicating fluid from a syringe pump (D. B. Robinson Associates, Canada). The system pressure is measured in the mercury line by a pressure transducer (Sensotec Inc., USA, accuracy 4~0.1%)and read on a digital indicator (Sensotec Inc., USA, accuracy 11.0%). The vapor pressure of mercury at the temperatures of interest is low compared to the operating pressures and hence neglected. The contents of the vessel are illuminated by a light source and are viewed from a mirror located at an angle in front of the reactor. Procedure. The reactor is thoroughly cleaned and evacuated before the start of every run. The Viton “0”rings and the teflon rings are changed after every run of the kinetic experiments to ensure similar conditions for every set of data. A known amount of cyclohexane is accurately transferred into the reactor with the help of a small burette of 2.0 cm3capacity, which is weighed before and after the transfer. Known amounts of oxygen and carbon dioxide by weight are next fed from sample cylinders made of 316 SS (Whitey, USA) and the reactor is sealed off. The stirrer and heater are then switched on. When the temperature attained is about 10 degrees less than the desired temperature, the pressure is adjusted to about 10-20 bar less than the desired pressure. The final pressure adjustment is made after the temperature reaches the desired value. This entire procedure of attaining the reaction conditions takes about an hour and the time of reaction is considered from this instant onward. A separate reaction mixture having same composition and number of moles is
Ind. Eng. Chem. Res., Vol. 33, No. 12,1994 3121 0
015
-008
(a1
Y
E 0 E
3
; 0.010
0 V
%
u
V
L .c
0*005
d
0
E 0~000
t i m e , hrs.
time, hrs
1
0.030)
0.006
-
E 0 E
0 E
m x
9,
E
0
0.00L
V
%
u V
2
-
.r
0
-
E
E
0.002
0
0 eo00
IO
t i m e , hrs.
20
30
t i m e ,hrs
Figure 3. Effect of temperature on cyclohexanone formation at (a) 170 and (b) 205 bar pressure: (0)410 K, (0)423;(A)433.
Figure 4. Effect of temperature on cyclohexanol formation at (a) 170 and (b) 205 bar pressure: (0)410 K (0) 423;(A)433.
charged for each experimental data point of a single kinetic run. Analysis. After the lapse of set reaction time, the contents of the vessel are slowly transferred into a cold trap containing 5-10 cm3of chilled ethyl acetate. After the transfer, the reactor is cleaned with approximately 10 cm3of ethyl acetate and the washings were collected in the same collector. A small portion of this sample is weighed and taken into a sample bottle to which a definite quantity of triphenylphosphine is added to convert all the cyclohexyl hydroperoxide formed to cyclohexanol (Suresh et al., 1988). This sample is then analyzed on a 10% Supelcowax fused silica glass capillary column on a gas chromatograph (Shimadzu,GCRlA, Japan) using a flame ionization detector, t o quantify cyclohexanone and cyclohexanol (along with the converted cyclohexyl hydroperoxide). The amount of water formed is calculated from the composition of other products analyzed.
catalytic. At 410 K the conversions are very low for a period up to about 12 h after which it rises sharply. The period of low conversion or so-called induction period is not observed as the temperature is increased. Similar behavior is observed at higher pressure of 205 bar. The maximum in cyclohexanone concentration 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 in cyclohexanol concentration (which also includes cyclohexyl hydroperoxide) is less at 433 K than at 423 K as shown in Figure 4. This may be attributed to the formation of CsH1102* radical in larger proportion than CsH110* radical which subsequently give the products cyclohexanone and cyclohexanol respectively (see Table 1). In other words, the reaction R2 followed by R6 is presumably preferred to reaction R3 (see reaction mechanism steps given in Table 1). The induction period which is about 12 h at 410 K and 170 bar is reduced by 50% when the pressure is raised to 205 bar. The maximum concentration of cyclohexanone increases with pressure at each of the three temperatures. On the other hand, the maximum concentration of cyclohexanol increases at a much slower rate with pressure. This may be attributed to the suppression of reaction R3 at higher pressures,
Results and Discussion Product Profile. The experimental kinetic data of cyclohexanone formation in mole fraction units, on COZ and 0 2 free basis, are shown in Figure 3, for 170 and 205 bar pressure at various temperatures. The “S” shape curves testify the fact that the reaction is auto-
3122 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 Table 4. Physical Parameters of Cyclohexane Oxidation in SC COa Medium 410 K 423 K 433 K 170 205 170 205 170 205 property bar bar bar bar bar bar density x lo3, mol/cm3 7.11 8.50 6.46 7.92 6.09 7.35 6.43 4.69 6.41 4.81 6.39 4.86 isothermal x lo3 compressibility, bar-' rate x 103 1.95 1.50 2.30 2.28 3.61 6.13 constant, h-l activation 36 96 -217 -161 -775 -720 volume, cm3/mol (from eq 1)
300
* 0
c
200
0
a
z \
a
z
Y
C
,
d
100
0
IO
1s
time (hrs) Figure 5. Conversion kinetics plot of cyclohexane oxidation: (0) 410 K, 170 bar; (0) 410,205; ( 0 )423, 170; (A) 423,205; (0) 433, 170; (W) 433,205.
which would have otherwise resulted in a similar increase for both the products. Another important observation made was the appearance of a visual aberration or haziness on the glass window of the reactor which coincides with the end of induction period. The phase behavior of the reacting system consisting of six components is very complex. By utilizing the high pressure VLE data of the constituent binaries, the phase equilibrium calculations for the 6-component system were carried out and reported elsewhere (Srinivas and Mukhopadhyay, 1994). The product distribution in the two phases indicates the possibility of condensation of water. However, more elaborate experimenta are needed to establish individual effects of the reaction, separation, and distribution on the reaction rates and conversion with varying concentrations. Reaction Rates. In the low conversion ranges it can be reasonably assumed that the majority of the conversion of cyclohexane takes place by the propagation steps R5 or R6 as the products formed are mainly cyclohexanol and cyclohexanone. Accordingly, the rate of oxidation becomes independent of oxygen concentration at sufficiently high oxygen concentrations. Therefore, the rate of reaction in the presence of sufficiently high concentrations of free radicals, is assumed to follow pseudo-first-order kinetics and is given by
pressure of 205 bar. Conversion in this slow reaction regime is less than 0.1% as can be seen from the figure. Hence this value has been taken as a conservative (maximum) conversion in the slow reaction regime or the induction period as also during the heating period. Data above this conversion only have been considered for the analysis. The simplified model proposed for the low conversion range is depicted by the straight line plots obtained in Figure 5. The error bars indicated in the figure are due to the uncertainties in the product analysis, and the actual errors may be larger than shown due to various experimental uncertainties. For example, each data point corresponds to a separate feed reaction mixture whose composition is difficult to exactly reproduce for each experiment at the same temperature, pressure, and feed composition. The values of the reaction rate constants at six conditions are given in Table 4. Unlike liquid phase oxidation, there is a significant 1.7 times increase in the rate constant for a 20% rise in pressure from 170 bar t o 205 bar at 433 K. This effect is not so significant at other temperatures studied in this work. This observation is in conformity with the occurrence of positive pressure derivative in eq 1. A similar behavior of a 3-fold increase in the rate constant for a Menschutkin reaction for a 3-fold increase in pressure a t far beyond critical point of the mixture is found in the literature (Dooley et al., 1987). Temperature and Pressure Effects on Reaction Rate Constants. The behavior of the logarithmic rate constant with reciprocal temperature is shown in Figure 6, parts a and b, for 170 and 205 bar, respectively, in the form of straight lines which indicate Arrhenius type of behavior. Thus, the temperature dependence of the rate constants can be expressed as
k, = 1.25 x
lo4 exp(-13.0/RT)
at 170 bar ( 5 )
k, = 1.45 x
lo9 exp(-22.6/RT)
at 205 bar (6)
and
where [A] is the concentration of cyclohexane in mol/ cm3, k, is the pseudo-first-order rate constant in h-l, N A is the number of moles of cyclohexane reactant at any given time, and Vis the total volume of the reactor. With moles of reactant changing from NAOa t the start of reaction to N Aat any given time t , the above equation after integration reduces to 1VA
- In -= k,t
(4)
NAO
Figure 5 describes the behavior of conversion data with time for the homogeneous kinetic experiments a t the three temperatures studied. At 410 K, the induction period is quite substantial though reduced at higher
with an activation energy of 13.0 kcaYmo1 at 170 bar and 22.6 kcal/mol at 205 bar. These values compare well with the reported value of 13 kcal/mol (Berezin et al., 1966) for the reaction between CsH1102* radicals and C6H12 molecule t o give cyclohexyl hydroperoxide and cyclohexyl radical. The increase in activation energy with increase in pressure is attributed to the cage effects wherein the free radicals and cyclohexane are surrounded by the solvent molecules. The solvent clustering being more at lower pressures, the cage effect is more pronounced a t lower pressures in the vicinity of the mixture critical point (Gehrke et al., 1990). In other words, solvent aggregation can move the energy levels of the reactants and/or activated complex, lowering the activation energy for the reaction. The change
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 3123 - 3 .2
- 5.6 "
-
- 6 . 0
x
C
-6.4
-6 *8 - 7 . 2 2
'5
1
I
2.30
2.35
I / T
I 2.40
2
5
x l o 3 (H")
b/
I
\
\
-'.O
t
- 7 . 25. 2 5
2.35
2.30
I
/
T
2.40
2.45
~l o 3 ( K - ' )
Figure 6. Arrhenius plot of In k, versus 1/T at (a) 170 and (b) 205 bar.
in the value of preexponential factor from 1.25 x lo4 at 170 bar t o 1.45 x lo9 at 205 bar indicates that the concentration of peroxide radical increases which means that formation of peroxy radicals is favored by pressure. Activation Volumes. In SCF medium, the pressure effect on rate constant reflects the relative strengths of intermolecular interactions between the reactants and the transition state with the SCF solvent. The characteristics of the transition state are not known and hence the difficulty in prediction of the thermodynamic pressure effect on the reaction. Also, the EOS do not accurately predict the PMV's near the highly compressible critical region that make up the activation volume. Nevertheless, an attempt has however been made, as described in the earlier section, to quantitatively describe the pressure effect on the rate by assuming the properties of the transition state to be those of intermediate, cyclohexyl hydroperoxide. The result though grossly approximate, has shown that the activation volumes could be negative which implies that pressure would have a positive effect on the rate constant. Although elaborate experiments could not be performed in the present study due to the limitations of
the reactor, the observed rate constants can give an assessment of the magnitudes of the activation volumes. As an approximation, the slope of In k, versus pressure (eq 1)is taken to be constant within the pressure range 170-205 bar. The activation volumes thus calculated have been tabulated in Table 4. As can be seen, the activation volume ranges from 36 t o -775 cm3/mol as the temperature is increased from 410 to 433 K a t 170 bar. Activation volumes could also be helpful in elucidating the reaction mechanism (Caralp et al., 1993).The positive value a t 410 K implies an activated complex of increased congestion disfavored by pressure. This effect is seen by the rate constant decreasing at 410 K from 1.95 x h-l a t 170 bar t o 1.50 x h-l a t 205 bar. The negative values signify dissociative mechanism which is favored by pressure which is substantiated by an increase in rate constant at 443 K from 3.61 x h-l a t 170 bar to 6.13 x h-I a t 205 bar. The large negative activation volumes observed in the SCF's are often compensated by the large compressibilities in the critical region. Thus the pressure effect is not very pronounced though the activation volumes are negative. Another reason for the activation volumes being so high at the lower temperatures could be because the feed mixture is in the SCF-rich phase and not in the mixture critical region at 410 K. In liquid phase oxidation, the activation volumes are usually of the order of h25 cm3/mol (le Noble et al., 1978).
Conclusions The oxidation of cyclohexane in supercritical fluid carbon dioxide is observed to be an autocatalytic reaction. Enhanced conversions and rates have been observed with increasing temperature and pressure in the mixture critical region. With a 20% increase in pressure the induction period is reduced by 50%. Cyclohexanone formation is more selective than cyclohexanol. Cyclohexanone formation increases with an increase in pressure. The increased rates of formation of products a t higher times may be attributed to the simultaneous reaction in the supercritical phase with condensation of the products such as water. The pseudo-first-order rate constant of cyclohexane molecule with the hydroperoxide radicals follows an Arrhenius type of dependency on temperature. The activation energy in the present study is found to be 13.0 kcal/mol at 170 bar and 22.6 kcdmol at 205 bar. The increase in activation energy with pressure is due to reduction in cage effects a t higher pressures close to the mixture critical region. Very low preexponential factors imply that the concentration of hydroperoxide radicals is low. The free radicals concentration increases with an increase in pressure which is substantiated by an increase in the preexponential factor by 5 orders of magnitude. The pressure effect on the reaction rate constant is quite pronounced. At 433 K, for an initial feed consisting cyclohexane and oxygen in the molar ratio of about 1:1, an increase of 20% in pressure from 170 bar, increases the rate constant by 1.7 times. The activation volume ranges from -775 t o f 3 6 cm3/molwhich elucidates the reaction mechanism changing with pressure and temperature near the critical region. The reaction rate and conversion can be manipulated by varying the reaction temperature, pressure, and feed composition. Pressure can be used as an additional processing parameter for controlling the reaction using supercritical fluid solvent. Nomenclature [A] = concentration of species A, mol ~ m - ~ [B] = concentration of species B, mol ~ r n - ~
3124 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994
k, = reaction rate constant, h-l N A = moles of reactant A P = pressure, bar
P, = critical pressure, b a r r = rate of reaction, mol cm-3 h-l R = gas constant, cm3 mol-' K-l t = reaction time, h-' T = temperature, K Tb = normal boiling temperature, K T , = critical temperature, K V = total volume of the reactor, cm3 A F = activation volume, cm3 mol-' Vi = partial molar volume of species z, cm3 mol-' Greek Symbols KT
= isothermal compressibility, bar-l
w =
acentric factor
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* Abstract published in Advance ACS Abstracts, October 15, 1994.
