How Does the Critical Point Change during the Hydrogenation of

Apr 5, 2002 - The determination of critical points of mixtures is very important for using supercritical fluid as a clean solvent in reaction process...
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J. Phys. Chem. B 2002, 106, 4496-4502

How Does the Critical Point Change during the Hydrogenation of Propene in Supercritical Carbon Dioxide? Jie Ke,† Michael W. George,† Martyn Poliakoff,*,† Buxing Han,‡ and Haike Yan‡ School of Chemistry, UniVersity of Nottingham, UniVersity Park, Nottingham, NG7 2RD, U.K., and Center for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, P. R. China ReceiVed: July 31, 2001; In Final Form: February 21, 2002

The determination of critical points of mixtures is very important for using supercritical fluid as a clean solvent in reaction process. The critical temperatures, Tc, and pressures, Pc, are reported here for mixtures for the hydrogenation of propene in CO2 at various stages of reaction and for different reactant concentrations. These data were measured by direct observation of the critical phase transition. Our results show that the critical pressure for the mixture with an initial mole fraction of 0.40 decreases by ca. 80 bar along the reaction path from 100% reactants to 100% products. The critical temperature increases by only 7 K during this process. The Peng-Robinson equation of state has been used to calculate both critical points and P-T phase diagrams for the multicomponent mixtures using only the interaction parameters regressed from the binary subsystems. The calculated results are used to understand the phase behavior problem for reactions in supercritical fluids.

Introduction Supercritical fluids are becoming increasingly important as environmentally acceptable replacements for more traditional solvents in green chemistry.1-4 There is considerable evidence that, in some cases, the outcome of a reaction can strongly depend on the phase behavior of the reaction mixture; twophase reaction mixtures can give a different product distribution from that of single-phase mixtures.5 This idea is particularly important because it offers an opportunity to control the chemical reaction in a way that is not possible in more conventional solvents. However, the complexity of multicomponent reaction mixtures means that the study of their phase behavior is still in an early stage. In this article, we extend our earlier work6 of measuring the critical points of reaction mixtures. Two groups have already made major contributions to this field. Chrisochoou, Stephan, and their co-workers have studied the phase behavior of a five-component reaction mixture involved in an enzymatic reaction in supercritical carbon dioxide (scCO2).7-9 Brennecke, Stadtherr, and their groups at Notre Dame have studied the phase behavior of epoxidation reactions involving eight-component mixtures for allylic epoxidation in scCO2.10,11 They have also presented an elegant approach to computing the critical points of such mixtures.12 These studies have all focused on measurements of phase equilibrium rather than on the specific measurement of critical points. By contrast, we have approached this problem by measuring the critical points of reaction mixtures and using these data to validate models for the phase equilibrium of reaction mixtures. These models are then used to calculate the appropriate phase boundaries. Recently, we reported extensive data for the hydroformylation of propene in scCO2 to form a mixture of n- and iso* Corresponding author. E-mail: [email protected]. Website: http://www.nottingham.ac.uk/supercritical/. Fax: +44 115 9513058. † University of Nottingham. ‡ Chinese Academy of Sciences.

butyraldehydes. The study used the stoichiometry of the reaction to reduce the mole fraction description of the mixture to only two parameters: χ0, the initial total mole fraction of the reactants (i.e., χC3H6 + χH2 + χCO), and R, the degree of conversion. R equals 0 at the start of the reaction and 1 at the completion. Our main conclusions were as follows: (i) In multicomponent reaction mixtures, the concentration of the individual components will usually be relatively low, which means that the phase behavior of the mixtures is dominated by the interactions between CO2 and the individual components. Therefore, the interaction between the different components can be ignored without significant error. Indeed, we successfully modeled the behavior of the six-component mixture involved in this hydroformylation reaction using only fiVe parameters, which were derived from the phase behavior of the appropriate binary mixtures with CO2. (ii) We introduced a new type of phase envelope to define the boundary inside which a reaction mixture will separate into gas and liquid phases at some point during the reaction. In the case of the hydroformylation reaction, the diagram showed that different strategies would be needed to keep a mixture in a single phase in continuous and batch reactors; a much higher initial pressure is needed in the batch reactor. In this article, we apply the same approach to a rather simpler reaction, the hydrogenation of propene. This reaction has been chosen because it is sufficiently close to the hydroformylation to allow a useful comparison to be made, yet it is sufficiently different to allow substantial differences to be observed in the phase behavior of the two reactions. Our study of hydroformylation was almost entirely based on an acoustic measurement used to locate the critical points; view-cell methods were used only to validate our results. However, as we have previously reported,6 high levels of permanent gases (e.g., H2) prevent acoustic measurements from working effectively. Therefore, the present study has been carried out using a variable-volume view cell (see Experimental Section).

10.1021/jp0129333 CCC: $22.00 © 2002 American Chemical Society Published on Web 04/05/2002

Hydrogenation of Propene in Supercritical CO2

Figure 1. Schematic diagram of the apparatus used for critical point measurements. B, water bath; C, view cell; H, circulator; HA, handle; MS, magnetic stirrer; P, pressure gauge; PL, plunger; S, stir bar; SC, graduated scale; T, thermocouple; V1, V2, valves; W, window.

Experimental Section Apparatus and Experimental Procedure. Critical points were measured by the observation of the appearance and disappearance of the meniscus between liquid and gas. A schematic diagram of the apparatus is shown in Figure 1. The major part of the apparatus is a view cell, modified from a Jerguson sight gauge with two borosilicate glass windows. In addition, the cell was equipped with a moveable plunger so that its volume could be varied between 20 and 50 cm3. The plunger was operated manually by rotating the handle that was attached to one end of the plunger. The actual volume of the cell can be found from the position of the plunger. A linear scale on the front face of the cell was used to indicate the liquid level. The relation between the liquid-phase volume and the liquid level was calibrated with water. A detailed description of the view cell has been given previously by Han and co-workers.13,14 The view cell was fitted with a thermocouple and a pressure transducer (RDP Electronics, Series TJE). The accuracy of the temperature measurements was (0.1 K, and the pressure transducer was calibrated to (0.1% of full scale. The cell was immersed in a water bath, the temperature of which was maintained to within (0.1 K by a heater/circulator (Techne, TU-16D). A magnetic stirrer was used to ensure that the contents of the cell were well-mixed. Measurements were carried out at several conversions but with the molar ratio of C3H6/H2/C3H8 fixed during a particular series of experiments. The key factor of the sample preparation is that, after a known weight of the first component (usually C3H8, which has the lowest vapor pressure at room temperature) has been loaded, specific amounts of the second and the third components (C3H6 and H2) need to be added to the cell. The following procedure was used to prepare samples of these multicomponent mixtures. Before a sample was made, the cell was rinsed several times with a suitable solvent and then evacuated. First, C3H8 was introduced from a high-pressure bomb. The mass difference of the bomb was used to determine the amount of C3H8 that had been added. Care is needed when

J. Phys. Chem. B, Vol. 106, No. 17, 2002 4497 adding the second gas, C3H6, because it readily condenses at room temperature. Second, C3H6 was loaded into a 10-mL bomb (Swagelok, SS-4CS-TW-10). After the bomb had been connected to the system, all valves between the cell and the bomb were opened. The bomb was then heated to ∼400-500 K.15 The weight of gaseous C3H6 remaining in the bomb was 0.14 ( 0.02 g. By knowing the amount of residual C3H6, we can transfer a target amount of C3H6 into the cell by controlling the initial weight of the bomb. Third, H2 was added from a highpressure screw pump (HIP, model 87-6-5). Because the P-V-T behavior for pure H2 is well-known, the amount of H2 can be obtained from the temperature, pressure, and volume of the pump before and after the injection of H2 into the cell. Usually, the pump volume was used as a controllable variable to ensure that a target amount of H2 could be transferred to the cell. Finally, CO2 was expanded into the system from another highpressure bomb. The amount of CO2 expanded into the cell was obtained by difference. It is estimated that the mole fractions are accurate to (0.2% for CO2, (1% for C3H6 and C3H8, and (3% for H2. In principle, the meniscus should appear exactly in the middle of the cell when the phase transition occurs at the critical point. We used the following procedure in this work. The overall density of the mixture was first roughly adjusted to the critical density by changing the volume of the cell. The temperature of the cell was then gradually increased to ca. +5 K above the temperature at which the contents of the cell formed a singlephase fluid. Prior to any experiments, the cell was rocked to improve mixing. The cell was then cooled at a rate of 0.1-0.5 K min-1 until a meniscus appeared. The volumes of the liquid and gas phases were estimated from the scale on the front face. If the liquid-phase volume was equal to that of the gas-phase, the temperature and the pressure at which the meniscus appeared were noted as Tc and Pc. Otherwise, the overall density of the mixture was increased or decreased, and the above procedure was repeated until the critical condition was found. We also observed a strong opalescence in the critical region. Materials. Propane and hydrogen (Air Products, purities of 99.9% and 99.999%, respectively) and propene and carbon dioxide (BOC, purities of 99.8% and 99.99%, respectively) were used as supplied. Results and Discussion Critical Points of the Reaction Mixture. The reaction mixture for the hydrogenation of propene consists of four components: CO2 (solvent), C3H8 (product), C3H6 (reactant), and H2 (reactant). It is relatively difficult to obtain a comprehensive picture of the phase equilibrium for such a complicated system. Our previous article6 pointed out that the stoichiometric expression of the composition greatly simplifies the phasebehavior problem for complex reaction mixtures. Following this strategy, we fixed the molar ratio of C3H6/H2 at 1:1. Then, the mole fraction of the four components can be represented by only two variables, χ0 and R. χ0 is the initial total mole fraction of the reactants at the start of the reaction. R is the conversion, which we define as the fraction of reactants that have been converted to products at a given stage of the reaction. Critical points were measured for mixtures corresponding to five conversions: 0, 0.14, 0.44, 0.70, and 1.0. The initial total mole fractions, χ0, ranged from 0 to 0.48. Not more than two phases were found for any of the mixtures under the experimental conditions that were used. The experimental results are presented in Table 1, and three projections, P-χ0, T-χ0, and P-T of the critical points are shown in Figure 2. In the χ0 range

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TABLE 1: Critical Pointsa of CO2 + H2b+ C3H6b+ C3H8 Mixtures χ0c

Tc/K

Pc/bar

χ0c

R ) 0d

Tc/K

Pc/bar

R ) 0.70 d

0.073 0.12 0.18 0.23 0.24

303.7 303.5 303.2 303.2 303.3 R ) 0.14d

83.2 90.0 101.9 111.2 113.7

0.068 0.19 0.30 0.37 0.44

304.2 305.1 307.8 310.6 313.4 R ) 1.00d,e

74.3 79.2 82.3 86.4 87.1

0.094 0.22 0.23 0.31

303.7 303.6 303.6 305.2

82.6 103.1 103.3 113.7

0.121 0.209 0.335 0.437 0.479

304.7 306.1 310.3 314.7 316.1

70.7 69.0 67.7 66.8 66.5

R ) 0.44d 0.088 0.13 0.29 0.37 0.48

303.8 304.2 306.3 308.8 314.3

78.8 82.3 93.9 103.0 113.0

Errors in Tc and Pc are (0.2 K and (0.3 bar, respectively. b The molar ratio H2/C3H6 is 1:1. c χ0 represents the initial total mole fraction of the reactants when there are no products. d R is the conversion; R ) (moles of reactants reacted)/(initial moles of reactants). e When R ) 1, all reactants have been consumed, and the mixture contains only CO2 + C3H8. a

Figure 2. Critical points of the reaction mixture for the hydrogenation of C3H6. (a) P-χ0 projection, (b) P-T projection, (c) T-χ0 projection. 9, R ) 0; b, R ) 0.14; 2, R ) 0.44; 1, R ) 0.70; [, R ) 1.00; s, curves fitted to experimental data. Open points represent the literature data for the binary system CO2 + C3H8.19,20

studied in this work, mixtures with the same conversion show a continuous critical line. All of these lines start from the same point, the critical point of pure CO2, but the direction of each line is strongly dependent on the conversion (Figure 2b). At R ) 0, there is a ternary mixture CO2 + H2 + C3H6. Tc of these ternary mixtures change slightly as χ0 increases from 0 to 0.24, and all are less than 1 K below Tc of pure CO2. By contrast, Pc is a strong function of χ0, rising with increasing χ0. As R increases, the mixture contains more propane, and the mole fractions of C3H6 and H2 decrease correspondingly. Because

Figure 3. Critical points of the reaction mixture for the hydrogenation of C3H6. (a) T-R projection, (b) P-R projection, (c) P-T projection. 9, χ0 ) 0.1; b, χ0 ) 0.2; 2, χ0 ) 0.3; 1, χ0 ) 0.4; s, curves fitted to experimental data. The data in this Figure are smoothed values taken from Table 1.

H2 is a permanent gas with a very low Tc, the lower the concentration of H2, the higher the critical temperature. Thus, the Tc-χ0 curve is shifted to higher temperature with increasing R (Figure 2c). It can be seen from Figure 2a that Pc is almost a linear function of χ0 for the mixtures with the same R. Pc increases with increasing χ0 when R < 0.70, but it decreases with increasing χ0 for the mixtures with R ) 1.0. It has been reported that only a small amount of H2 can raise Pc dramatically in a CO2 solution;16 our measurements indicate that the concentration of H2 also has a dominant effect on Pc for this four-component system. At R ) 1, the reaction mixture contains only CO2 and C3H8, the solvent and product, respectively. The critical curve for this binary system has been investigated by a variety of experimental techniques.17-20 The data obtained by Roof and Baron19 and by Niesen and Rainwater20 are depicted for comparison in Figure 2 as open symbols. It can be seen from the Figure that our results are in good agreement with those obtained by these authors.21 Figure 3 illustrates the dependence of Tc and Pc on R for different values of χ0. It is clear that for a given χ0 Tc increases with increasing R (Figure 3a) and no maximum or minimum is observed. At χ0 ) 0.40, the highest value of χ0 in Figure 3a, Tc increases by only +7 K (from 306 to 313 K) as R increases from 0 to 1. At a lower χ0 value, the increase in Tc is less than 7 K. However, Pc decreases very substantially, ∼80 bar in the course of the reaction (Figure 3b). A crossover point is observed at R ) 0.89 where Pc for all mixtures is the same, corresponding to that of pure CO2 (74 bar). This result indicates that Pc is independent of χ0 at R ) 0.89 for all mixtures with χ0 up to 0.40. Before discussing the modeling of this system, it is worth comparing the results with those previously obtained6 for the hydroformylation of C3H6. Figure 4 compares the variation of Pc and Tc with R for the two reactions. It can be seen that the results appear somewhat complementary in that the plot for Tc in one reaction resembles the plot for Pc in the other reaction and vice versa. The reason for this result is that the hydrogena-

Hydrogenation of Propene in Supercritical CO2

J. Phys. Chem. B, Vol. 106, No. 17, 2002 4499 TABLE 2: Pure Component Parametersa for the Peng-Robinson Equation of State

a

component

Tc/K

Pc/bar

ω

carbon dioxide hydrogen propene propane

304.1 33.2 364.9 369.8

73.8 13.0 46.0 42.5

0.239b -0.218 0.144 0.145

Taken from ref 24. b See also ref 44.

a model for the calculation of phase behavior.

P)

a RT V - b V(V + b) + b(V - b)

(1)

For pure substances, Tc, Pc, and ω (the acentric factor) are required to calculate the parameters a and b. For mixtures, the van der Waals one-fluid mixing rule is used; a and b are calculated from the pure substance parameters by eqs 2 and 3: Figure 4. Comparison of the critical points for (a) and (b), hydrogenation (see also the caption for Figure 3 in this article) and (c) and (d), hydroformylation, the details of which can be found from the caption of Figure 3 in ref 6.

tion mixture is dominated by the permanent gas, H2. On the other hand, the hydroformylation reaction is dominated by the fact that the product aldehydes are relatively heavy components in the system. The presence of permanent gases has a major positive effect on Pc of the systems but a much smaller negative effect on the value of Tc over the concentration range we studied. Conversely, the presence of a heavy component (C4H8O) produces a relatively small change in Pc when the concentration is low but a large increase in Tc. Thus, in the case of hydrogenation, there is a very substantial decrease in Pc during the reaction as H2 is consumed (Figure 4b). In the hydroformylation reaction, the effects of the permanent gases and heavy components largely cancel out, giving only a modest change in Pc in the course of the reaction (Figure 4d). By contrast, in the case of Tc, the formation of the heavy component in the reaction reinforces the effect of the consumption of H2 + CO, giving a very substantial increase in Tc (Figure 4c). In the hydrogenation reaction, Figure 4a, there is little difference between the weights of the reactant C3H6 and product C3H8 so that the increase in Tc is modest by comparison with that of the hydroformylation. It is striking that in both reactions there is a particular concentration where one of the parameters, Tc for hydroformylation (Figure 4c) or Pc for hydrogenation (Figure 4b), is independent of χ0 over the concentration ranges studied. The presence of this constant point for the hydrogenation reaction exists up to χ0 ) 0.40, but in both reactions, this point will certainly disappear as the value of χ0 approaches 1. In general, this conclusion about hydrogenation should apply to most reactions where H2 is added to a CdC bond. In such reactions, the critical parameters of reactants and products (e.g., cyclohexane and cyclohexane22) are usually very similar. On the other hand, hydrogenation of functional groups, for example, R1R2CdO f R1R2CHOH, will change the fundamental nature of the interaction between the molecules and CO2, thereby altering the phase behavior. Modeling. Critical point measurements can give only a limited number of points on a phase transition boundary. The objective of our modeling work is to construct a series of P-T phase diagrams that can be used to study how the two-phase region changes in P-T space as the reaction proceeds in SCF. As in our previous work on hydroformylation,6 the PengRobinson equation of state (PR EOS),23 eq 1, has been used as

a)

∑i ∑j xixj(1 - kij)(aiaj)0.5

(2)

∑i xibi

(3)

b)

xi is the mole fraction of the ith component; ai and bi are the pure substance parameters defined by Peng and Robinson;23 and kij represents the binary interaction parameter for the (i, j) pair. The physical property information (Tc, Pc, and ω) used for the primary components in the reaction mixture is taken from the literature24 (see Table 2). Three algorithms have been used in this work: (1) a rigorous algorithm developed by Heidemann and co-workers25,26 for the direct calculation of critical points; (2) an efficient procedure described by Michelsen27 for constructing the phase boundary (P versus T at a fixed composition), and (3) conventional methods for bubble pressure, dew pressure, and isothermal flash calculations.28-30 Binary interaction parameters are empirical parameters that can be directly fitted to the experimental critical points of the binary systems when these are available by using an optimization algorithm with the weight factors suggested by Kola´r.31 In other cases, they can be regressed from the binary data by minimizing the average absolute deviation for bubble and dewpoint pressures. The four-component reaction mixture results in six binary interaction parameters (kij). Three out of six of these parameters have already been reported by us in our previous article.6 The binary critical points reported here are used to determine the binary parameters for the system CO2 + C3H8. The average absolute deviations are 0.4% for Tc and 1.5% for Pc. The system C3H6 + C3H8 has been extensively studied in the literature.32-37 On the basis of the data published by Reamer and Sage,32 the interaction parameter can be fitted to 0.0048, which is a quite reasonable low value for the interaction parameter between two species having such similar physical properties. Usually it is difficult to model the phase behavior for mixtures containing H2 because the size of the H2 molecule is so much smaller than that of the other molecules in the mixture. A variety of approaches have been employed to deal with such systems.38-42 We find that for the system C3H8 + H2,43 the VLE data could be fitted using the temperature-dependent parameters kij ) kaij + kbijT where T is the absolute temperature and kaij and kbij are constants. (By introducing the temperature dependence, we increase the number of parameters from six to eight.) Table 3 summarizes all of the binary interaction parameters used in our calculations.

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TABLE 3: Binary Interaction Parameters (kij) for the Peng-Robinson Equation of State component i

component j

kij

CO2 CO2 CO2 H2 H2 C3H6

H2 C 3H 6 C 3H 8 C 3H 6 C 3H 8 C 3H 8

0.154a 0.067 0.108 -0.20748 + 0.001555Tb -0.048484 + 8.8145 × 10-4Tb 0.0048

a This value of kij can be applied only to relatively dilute mixtures of H2 in CO2 (see ref 6). b The binary interaction parameter is temperature-dependent. T is the absolute temperature in K.

Figure 5. Calculated critical points of the hydrogenation reaction mixture. The solid lines (s) indicate mixtures with the same conversion, and the dashed lines (---) link the mixtures of constant χ0. * represents experimental critical points taken from Figure 3.

Calculation of the Critical Surface for the Reaction Mixtures. No information other than that obtained from binary systems is used to calculate the phase diagram for these reaction mixtures. The measured critical points of the mixtures (see Table 1) are used to validate the PR EOS and the interaction parameters listed in Table 3. Figure 5 shows the predicted critical surface of the full quaternary reaction mixtures as a function of R. The dashed lines indicate mixtures with the same χ0. The average absolute deviation between the experimental and predicted values is 0.2% for Tc and 3.3% for Pc. Large deviations are found only for those reaction mixtures with R ) 0, which contain a high concentration of H2. Nevertheless, the PR EOS provides an acceptable prediction for the critical point, even when the mixtures have >10% (mole fraction) of H2. More importantly, changes in the critical point during the reaction process are described correctly. Furthermore, the calculated results show that the PR EOS is capable of predicting the crossover point of Pc with respect to R (see Figure 3b), where Pc for all mixtures is the same as that of pure CO2, 74 bar, at R ) 0.89. P-T Phase Boundary for Reaction Mixtures. We now calculate the boundary between regions of single and binary phases for a particular concentration and show how this boundary moves during the reaction. The mole ratio of C3H6/ H2 is kept at 1:1, and χ0 is fixed at 0.40. We have calculated the P-T phase boundary for five conversions (i.e., 0, 0.14, 0.44, 0.70, and 1) that are presented graphically in Figure 6a. For comparison, the calculated and experimental critical points of the mixtures are shown as solid and open points, respectively. The critical point for mixtures with R < 0.70 is located below the temperature maximum. For the mixture CO2 + C3H8 (i.e.,

Figure 6. Calculated phase boundary for the hydrogenation reaction mixture (the initial total mole fraction is 0.40, and the molar ratio of C3H6/H2 is 1:1). (a) Phase boundary at different conversions: s R, R ) 0; - - -, R ) 0.14; ‚‚‚, R ) 0.44; - ‚ -, R ) 0.70; s P, R ) 1.00. Solid symbols, b, represent the calculated critical points, which lie on the calculated phase boundary under each conversion. Open symbols, O, represent experimental critical points for the corresponding conversion. (b) Envelope of the global two-phase region during the reaction. (c) Density45-47 at the phase boundaries shown in Figure 6a.

R ) 1), the critical point is located at the head of the P-T loop, and it is fairly close to the point of maximum temperature. It should be clear from Figure 6a that the area of the twophase region for the mixture with R ) 0 is much larger than that for the mixture with R ) 1. Moreover, the upper branch of the phase boundary lies in the high-pressure region at the start of the reaction. It then moves toward low pressure as R increases. When all of the reactants have been converted to the product (R ) 1), the maximum pressure for the two-phase region is only ca. 68 bar, which is significantly less than Pc of pure CO2. It can be concluded that the product forms a homogeneous solution with solvent more easily than the reactants do. After the P-T phase diagrams have been obtained at various conversions, the two-phase region can be mapped for the same reaction mixture throughout the reaction (i.e., R ) 0-1). The resulting diagram is shown in Figure 6b by drawing the overall envelope of all of the two-phase regions shown in Figure 6a.

Hydrogenation of Propene in Supercritical CO2

Figure 7. Comparison of the P-T phase boundaries for (a) and (b), hydrogenation, χ0 ) 0.20 (see also the caption for Figure 6 in this article) and (c) and (d), hydroformylation, χ0 ) 0.20, the details of which can be found from the caption of Figure 10 in ref 6.

The gray region of Figure 6b represents the area in P-T space in which a reaction mixture will be two-phase at some stage during the reaction. Point A (314 K, 68 bar) is the temperature maximum for the mixture with χ0 ) 0.40 in the overall phase boundary. The reaction mixture will always be homogeneous irrespective of the pressure when the reaction temperature is higher than 314 K. No pressure maximum or minimum has been found in the critical region. In general, if the mixture starts at a pressure that lies above the bubble-point line, R, in Figure 6a, it will remain in a single phase throughout the reaction, whatever the temperature. G-T Phase Boundary for Reaction Mixtures. As discussed in our previous article,6 the majority of reactions in SCFs are carried out as batch processes in sealed autoclaves where the overall density remains constant throughout the reaction. Therefore, we have calculated the corresponding F-T phase boundary for the mixture with χ0 ) 0.40 (Figure 6c). Unlike the P-T boundaries (Figure 6a), the F-T boundaries for the mixtures with different R values do not intersect in the critical region, and the size of the F-T loops increases with R. In principle, temperature and pressure can be manipulated to keep a reaction mixture in a single phase. Figure 6a-c indicates that increasing the temperature is the more effective strategy for the hydrogenation of propene in both continuous and batch processes. Temperature is more important than other controllable variables (e.g., P or F) because the point of maximum temperature, A in Figure 6b and c, is close not only to room temperature but also to Tc of the mixture. As explained above, the formation of a heavy product in the hydroformylation of C3H6 has a major effect on Tc. This effect can be seen very clearly in Figure 7 where the phase envelopes for the hydrogenation and hydroformylation of propene are compared. Even though changes in Tc predominate in the hydroformylation, it is the pressure that needs to be manipulated, in practice, because such reactions are generally carried out isothermally. Conclusion In this article, we have shown how parameters derived from binary mixtures can be used to reproduce the experimental observation of the phase behavior of quaternary reaction mixtures. We have also shown that the modeling technique developed for the hydroformylation of relatively dilute reaction mixtures can also be used to acceptable accuracy on more concentrated mixtures up to χ0 ) 0.4. Previously, our major assumption was to neglect all binary interactions apart from

J. Phys. Chem. B, Vol. 106, No. 17, 2002 4501 those involving CO2. In this case, however, the total mole fraction is higher, χ0 ) 0.4, and also, the individual mole fractions are proportionally even higher because there are fewer components for hydrogenation than there were for hydroformylation. Therefore, we have included the interaction between all four components explicitly, which means that we have used more parameters to fit the data for the four-component hydrogenation mixture than were needed for the six-component hydroformylation reaction. Our experimental results show that Pc for the reaction mixtures decreases substantially, but the increase in Tc is relatively small in the course of the reaction. The measured critical points, together with the calculated results for the twophase boundary, suggest that it would be more convenient to set the reaction temperature above the maximum temperature in the phase envelope (see Figure 6b) than to increase the pressure sufficiently to ensure homogeneity throughout the reaction. In general, the concentration of H2 has a dominant effect on Pc for the hydrogenation reaction mixtures. The reaction mixture always has the highest Pc at the start of the reaction. Furthermore, the two-phase region of the initial mixture (H2 + substrate) occurs at a higher pressure than do those for the mixtures with larger conversions. However, Tc mainly depends on the properties of the substrate and product. It will not increase very much if the substrate and product are similar. We believe that temperature is a more important factor in keeping the hydrogenation reaction mixture in a single phase, although increasing the pressure can enhance the miscibility of H2 and the substrate. Acknowledgment. We thank Dr. A. Caban˜as, Dr. P. J. King, Dr. C. J. Mellor, Dr. R. M. Oag, Mr. D. Merrifield, and Mr. C. Valder for helpful discussions and Mr. M. Guyler and Mr. K. Stanley for their technical assistance. We also gratefully acknowledge support from the National Natural Science Foundation of China, the Office of Science and Technology of the U.K., and the Ministry of Science and Technology of China. This research was funded by EPSRC, GlaxoSmithKline plc, and the Royal Society. References and Notes (1) Jessop, P. G. Top. Catal. 1998, 5, 95. (2) Baiker, A. Chem. ReV. 1999, 99, 453. (3) Darr, J. A.; Poliakoff, M. Chem. ReV. 1999, 99, 495. (4) Chemical Synthesis Using Supercritical Fluids; Jessop, P. G., Leitner, W., Eds.; Wiley-VCH: Weinheim, 1999. (5) Licence, P.; Gray, W. K.; Poliakoff, M. Unpublished work. (6) Ke, J.; Han, B.; George, M. W.; Yan, H.; Poliakoff, M. J. Am. Chem. Soc. 2001, 123, 3661. (7) Chrisochoou, A.; Schaber, K.; Bolz, U. Fluid Phase Equilib. 1995, 108, 1. (8) Chrisochoou, A. A.; Schaber, K.; Stephan, K. J. Chem. Eng. Data 1997, 42, 551. (9) Chrisochoou, A. A.; Schaber, K.; Stephan, K. J. Chem. Eng. Data 1997, 42, 558. (10) Stradi, B. A.; Kohn, J. P.; Stadtherr, M. A.; Brennecke, J. F. J. Supercrit. Fluids 1998, 12, 109. (11) Stradi, B. A.; Stadtherr, M. A.; Brennecke, J. F. J. Supercrit. Fluids 2001, 20, 1. (12) Stradi, B. A.; Brennecke, J. F.; Kohn, J. P.; Stadtherr, M. A. AIChE J. 2001, 47, 212. (13) Zhang, H.; Liu, Z.; Han, B. J. Supercrit. Fluids 2000, 18, 185. (14) Zhang, H.; Han, B.; Li, H.; Hou, Z. J. Chem. Eng. Data 2001, 46, 130. (15) Safety note: a sealed bomb should not be heated because of possibly exceeding its safety limit. (16) Kordikowski, A.; Robertson, D. G.; Poliakoff, M. Anal. Chem. 1996, 68, 4436. (17) Poettman, F. H.; Katz, D. L. Ind. Eng. Chem. 1945, 37, 847.

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Ke et al. (35) Manley, D. B.; Swift, G. W. J. Chem. Eng. Data 1971, 16, 301. (36) Laurance, D. R.; Swift, G. W. J. Chem. Eng. Data 1974, 19, 61. (37) Harmens, A. J. Chem. Eng. Data 1985, 30, 230. (38) Boston, J. F.; Mathias, P. M. In Phase Equilibria In a ThirdGeneration Process Simulator, Phase Equilibria and Fluid Properties in the Chemical Industry, 2nd International Conference, Berlin, Germany, 1980. (39) Valderrama, J. O.; Reyes, L. R. Fluid Phase Equilib. 1983, 13, 195. (40) Valderrama, J. O.; Molina, E. A. Fluid Phase Equilib. 1986, 31, 209. (41) Huang, H.; Sandler, S. I.; Orbey, H. Fluid Phase Equilib. 1994, 96, 143. (42) Ioannidis, S.; Knox, D. E. Fluid Phase Equilib. 1999, 165, 23. (43) Burriss, W. L.; Hsu, N. T.; Reamer, H. H.; Sage, B. H. Ind. Eng. Chem. 1953, 45, 210. (44) A reviewer has suggested that 0.225 is a more acceptable value for the acentric factor of CO2. We have tested this value with some of our mixtures and found that no significant difference was observed for the calculation of critical points, even without optimizing the binary interaction parameters for the different acentric factor. (45) The calculated density in Figure 6c is based on the liquid density at the bubble point and the vapor density at the dew point. It is likely that the results are only semiquantitative because cubic equations of state are known to give rather poor predictions of density, especially in the critical region.46,47 However, we believe that the calculation describes the changes of the F-T boundary sufficiently well for the purposes of our discussion. (46) Chou, G. F.; Prausnitz, J. M. AIChE J. 1989, 35, 1487. (47) Kutney, M. C.; Dodd, V. S.; Smith, K. A.; Herzog, H. J.; Tester, J. W. Fluid Phase Equilib. 1997, 128, 149.