Experimental determination and modeling of the phase behavior for the selective oxidation of benzyl alcohol in supercritical CO2

Fluid Phase Equilibria 302 (2011) 83–92

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Experimental determination and modeling of the phase behavior for the selective oxidation of benzyl alcohol in supercritical CO2 Ioannis Tsivintzelis a,b , Matthias Josef Beier a , Jan-Dierk Grunwaldt a,c , Alfons Baiker d , Georgios M. Kontogeorgis a,b,∗ a

Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark Center for Energy Resources Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark c Institute for Chemical Technology and Polymer Chemistry, Karlsruhe Institute of Technology (KIT), Engesserstr. 20, D-76131 Karlsruhe, Germany d Institute for Chemical and Bioengineering, Department of Chemistry and Applied Biosciences, ETH Zurich, Hönggerberg, HCI, CH 8093 Zurich, Switzerland b

a r t i c l e

i n f o

Article history: Received 27 May 2010 Received in revised form 30 September 2010 Accepted 1 October 2010 Available online 8 October 2010 Keywords: Oxidation of alcohols Supercritical CO2 Equations of state CPA

a b s t r a c t In this study the phase behavior of mixtures relevant to the selective catalytic oxidation of benzyl alcohol to benzaldehyde by molecular oxygen in supercritical CO2 is investigated. Initially, the solubility of N2 in benzaldehyde as well as the dew points of CO2 –benzyl alcohol–O2 and CO2 –benzaldehyde–water ternary mixtures were experimentally determined. The cubic plus association (CPA) equation of state was used to model the phase behavior of the experimentally investigated systems as well as the phase behavior of relevant mixtures that can exist inside the reactor during the reaction time. In this direction, the CPA binary interaction parameters were estimated from the corresponding binary systems and the phase behavior of two ternary systems, i.e. CO2 –benzyl alcohol–O2 (reacting mixture) and CO2 –benzaldehyde–water (mixture of products) as well as the phase behavior of multicomponent mixtures containing both reactants and products were predicted. CPA was proved to be a versatile model that can predict the complex phase behavior of the aforementioned systems. The results reveal that the ternary mixture of products (CO2 –benzaldehyde–water) and the intermediate multicomponent mixtures containing both products and reactants require lower pressure than the corresponding mixture of the reactants (CO2 –benzyl alcohol–O2 ) in order to be in a single phase. © 2010 Elsevier B.V. All rights reserved.

1. Introduction The selective oxidation of alcohols to aldehydes or ketones in the liquid phase has been intensively investigated in the last years [1,2]. Using heterogeneous noble metal catalysts, toxic and expensive oxidizing agents were replaced by oxygen being environmentally benign [3]. On the other hand, gaseous oxygen introduced an additional phase boundary to the liquid/solid reaction system inducing further mass transport limitations. These limitations could be overcome using pressurized CO2 as an alternative solvent having a high solubility for oxygen compared to standard organic solvents frequently used for these reactions. In addition, dense CO2 features the advantage of being environmentally benign, safer in combination with oxygen and chemically stable with respect to oxidation [4–6]. Indeed, higher reaction rates were observed in alcohol oxidation [6–9]. In order to optimize catalytic processes

∗ Corresponding author at: Center for Energy Resources Engineering (CERE), Technical University of Denmark, Søltofts Plads, DK-2800 Kgs. Lyngby, Denmark. Tel.: +45 45 25 28 59; fax: +45 45 88 22 58. E-mail address: [email protected] (G.M. Kontogeorgis). 0378-3812/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2010.10.001

involving CO2 as a solvent knowledge about the phase behavior is important and depending on the substrate it can be both advantageous to work in the single phase [10] or two phase region [11]. Determining optimal reaction conditions in CO2 is experimentally elaborate and requires special equipment such as a high pressure view cell. Therefore, catalytic reactions in supercritical CO2 reported in the literature are often only optimized to a small extend for a very limited set of reaction parameters. This may result in missing close-to-optimal reaction conditions. In contrast to this trial and error approach modeling the phase behavior offers a great chance of conducting experiments in a more controlled way. Since the process includes associating compounds, such as alcohols or water, at high pressures an advanced equation of state capable of describing systems with highly non-ideal behavior is needed. Between the most popular models of this type are the SAFT (Statistically Associating Fluid Theory) variants [12], advanced lattice theories, such as the NRHB (Non Random Hydrogen Bonding) model [13] and the CPA (Cubic plus Association) model [14]. The SAFT and the CPA equations of state use the same association term, which is based on Wertheim’s first order thermodynamic perturbation theory [15], in order to describe strong specific inter-

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Scheme 1. Palladium catalyzed oxidation of benzyl alcohol by molecular oxygen.

actions such as hydrogen bonding. Some lattice theories, such as the NRHB model, use a different approach, which is also based on statistical thermodynamics [16]. Similarities between these two approaches were shown in the literature [17,18], while all of the aforementioned models have been successfully used in modeling highly non-ideal systems [19–24]. The aim of this study is to investigate the phase behavior of systems relevant to the selective oxidation of benzyl alcohol to benzaldehyde in supercritical CO2 according to Scheme 1. The phase behavior of such reaction mixtures may include the appearance of two phase vapor–liquid or liquid–liquid equilibria or a three phase vapor–liquid–liquid equilibrium. Experimental data, especially for multicomponent mixtures, are rare and the use of an appropriate model, which can capture this complex phase behavior, is of great importance allowing the optimization of the reaction conditions in a rational manner. Consequently, with benzyl alcohol as a model substrate, we investigate the phase behavior of substrate mixtures with relevant compositions containing also CO2 , O2 , H2 O and benzaldehyde. Experimental measurements have been performed in order to guide the modeling of the phase behavior of such complicated mixtures. The phase behavior of the investigated systems was modeled using the CPA (cubic plus association) equation of state, which is a versatile model that can be used to predict thermodynamic properties of pure fluids and mixtures with highly non-ideal behavior, such as mixtures with hydrogen bonding fluids in gas, liquid or supercritical state. During the last years the model has been successfully applied for the modeling of various systems. CPA was shown to successfully predict the phase behavior for systems that contain associating compounds (water, alcohols, glycols, acids, amines) and inert nonassociating compounds (e.g. hydrocarbons) [23,24].

acetone and CO2 and dried in a N2 stream. For experiments the cell was charged with the desired amounts of benzyl alcohol (Aldrich, 99+%, freshly distilled, stored under argon atmosphere), benzaldehyde (Fluka, 99.5%+, redistilled, stored under argon atmosphere) and/or water (Fluka, >2 ␮S/cm) at 288 K. The sealed cell was carefully flushed several times with either O2 or N2 (both PanGas, 5.0) or CO2 (PanGas, 3.0) to remove air and charged with the appropriate amount of O2 or N2 (calculated using data from NIST [27]). CO2 was added by means of a CO2 compressor (NWA, Loerrach, Germany) and quantified with a mass flow transmitter (Rheonik Messgeräte GmbH, Germany) at a constant pressure of 100 bar provided by an interconnected reducing valve. The cell was heated to the desired temperature and a pressure significantly higher than the dew point applied by adjusting the cell volume. Under these conditions the cell was equilibrated for an appropriate amount of time (min. 2 h–overnight). After a first rough investigation of the respective system, dew points were determined by changing the pressure in intervals of 0.5–2 bar, equilibration (15 min–2 h) and visual inspection. Accordingly, a pressure interval between a high and a low pressure limit in between phase separation occurred was noted. Usually, dew points were determined by following the dissolution of droplets. Prior to formation of drops by decreasing the pressure the feed lines were heated by means of a heat gun to assure that the drop formation does not occur in the non-visible part of the cell. Dew points were usually measured three times for each composition and temperature from which a standard deviation was obtained. The uncertainty of the high and low pressure limit around the dew point was then determined by twice the standard deviation plus the uncertainty due to the pressure sensor (±0.5 bar). The dew point was calculated as the center of the thus obtained pressure interval in which phase separation occurred and the maximum error was considered in order to describe the interval boundaries. Further experimental uncertainties are estimated to be ±0.02 mol% for the molar fraction of each component and ±0.5 K for the temperature.

3. Experimental results 2. Experimental 2.1. Description of the apparatus Phase experiments were performed in a high pressure view cell (15–65 mL, SITEC, Switzerland) with variable volume which was custom-designed from a screw-type manual pump similar to the system described by Crampon et al. [25]. Temperature and pressure measurements, respectively, were performed with a J type thermocouple and a Dynisco pressure sensor (MDT422H-1/2-2C-15/46). The cell was equipped with a CO2 and a gas (O2 /N2 ) inlet as well as a rupture disc for preventing overpressures. Stirring was achieved by a magnetic stir bar in connection with a magnetic stirrer (Heidolph MR 2002). Heating of the cell was accomplished by means of an oil-containing heating jacket controlled by thermo-/cryostat (Julabo F25 HD). A sapphire window covering the whole diameter of the cell (26 mm) allowed optical identification of phases. A cold light source applied from the front illuminated the cell. Construction details and the flowchart of the cell can be found in Ref. [26]. In this project phase identification was performed without the previously described CCD camera by direct optical identification giving more accurate results when the light source is used in the viewing direction. 2.2. Experimental procedure Leak checks of the view cell were performed in weekly intervals. Prior to experiments the cell was thoroughly cleaned with

Using the aforementioned procedure, dew points of two binary mixtures, benzaldehyde–N2 and benzyl alcohol–CO2 , and two ternary mixtures, CO2 –benzyl alcohol–O2 and CO2 –benzaldehyde–water, were determined as intervals in between phase separation occurred with a high and a low pressure limit. The systems were usually measured three times as described in Section 2. Results are presented in Table 1.

4. Modeling with cubic plus association (CPA) CPA is a combination of the SRK (Soave–Redlich–Kwong) cubic equation of state with the Wertheim’s first order thermodynamic perturbation theory. For mixtures it can be expressed in terms of pressure P, as [14,23,24]: P =

RT ˛(T ) − Vm − b Vm (Vm + b) −

1 RT 2 Vm



1+

∂ ln g ∂

  xi

i

(1 − XAi )

(1)

Ai

The key element of the association term is XAi , which represents the fraction of A-sites on molecule i that do not form bonds with other active sites, while xi is the mole fraction of component i. XAi is related to the association strength Ai Bj between two sites belonging to two different molecules, e.g. site A on molecule i and site B

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85

Table 1 Pressure limits Phigh and Plow in between phase separation found for the investigated systems. Phigh a (bar)

Temperature (K)

Plow b (bar)

98.00 ± 0.02 mol% benzaldehyde and 2.00 ± 0.02 mol% N2 333.2 ± 0.5 54.6 ± 2.1 353.2 ± 0.5 53.5 ± 2.5 99.60 ± 0.02 mol% benzyl alcohol and 0.40 ± 0.02 mol% CO2 353.2 ± 0.5 137.0 ± 1.5 0.45 ± 0.02 mol% benzyl alcohol, 0.16 ± 0.02 mol% oxygen and 99.39 ± 0.02 mol% CO2 333.2 ± 0.5 123.0 ± 1.9 343.2 ± 0.5 133.0 ± 4.1 353.2 ± 0.5 140.0 ± 2.5 0.60 ± 0.02 mol% benzyl alcohol, 0.30 ± 0.02 mol% oxygen and 99.10 ± 0.02 mol% CO2 333.2 ± 0.5 151.5 ± 1.7 0.91 ± 0.02 mol% benzyl alcohol, 0.43 ± 0.02 mol% oxygen and 98.66 ± 0.02 mol% CO2 333.2 ± 0.5 133.0 ± 3.3 343.2 ± 0.5 150.0 ± 3.3 353.2 ± 0.5 163.0 ± 3.5 0.45 ± 0.02 mol% benzaldehyde, 0.45 ± 0.02 mol% H2 O and 99.10 ± 0.02 mol% CO2 333.2 ± 0.5 105.0 ± 1.7 353.2 ± 0.5 110.0 ± 1.1 0.90 ± 0.02 mol% benzaldehyde, 0.90 ± 0.02 mol% H2 O and 98.20 ± 0.02 mol% CO2 333.2 ± 0.5 112.0 ± 2.5 353.2 ± 0.5 133.0 ± 2.5 a b c

Psep c (bar)

50.5 ± 1.9 49.8 ± 1.7

52.7 ± 4.0 52.1 ± 4.0

136.0 ± 1.5

136.5 ± 2.0

122.0 ± 1.9 132.0 ± 3.9 139.0 ± 3.1

122.5 ± 2.4 132.6 ± 4.5 139.2 ± 3.3

150.5 ± 2.3

150.7 ± 2.5

132.0 ± 3.5 149.0 ± 3.9 162.0 ± 3.5

132.4 ± 3.9 149.2 ± 4.1 162.5 ± 4.0

104.0 ± 1.3 109.0 ± 2.1

104.7 ± 2.0 109.0 ± 2.1

111.0 ± 2.5 131.0 ± 1.5

111.5 ± 3.0 132.5 ± 3.0

Average high pressure limit. Average low pressure limit. Pressure interval for phase separation.

on molecule j, determined from: XAi =

The expressions of the cross-association energy and crossassociation volume parameters with CR-1 are:

1

1+

  x j j

Bj

(2)

XBj Ai Bj

where the association strength Ai Bj in CPA is expressed as: Ai Bj





= g() exp

 εAi Bj  RT



− 1 bij ˇ

Ai Bj

(3)

with the radial distribution function g() = 1/(1 − 1.9), the reduced density  = (1/4)b while bij = (bi + bj )/2. bi is the temperatureindependent co-volume parameter of the component i and  is the molar density. The energy parameter of the EoS is given by a Soave-type temperature dependency:





˛(T ) = ˛0 1 + c1 1 −

 2 Tr

(4)

Tr = T/Tc is the reduced temperature, while Tc is the experimental critical temperature. Finally c1 is a CPA parameter in the energy term (Eq. (4)). In the expression for the association strength Ai Bj , the parameters εAi Bj and ˇAi Bj are called the association energy and the association volume, respectively. These two parameters, which are used for associating components, and the three additional parameters of the SRK term (a0 , b, c1 ) are the five pure compound parameters of the model.When the CPA EoS is used for mixtures, the conventional mixing rules are employed in the physical term (SRK) for the energy and co-volume parameters. The geometric mean rule is used for the energy parameter ˛ij . The interaction parameter kij is, for applications with aliphatic hydrocarbons and other inert (non self-associating) molecules, the only adjustable binary parameter of CPA: ˛=

 i

b=



xi xj ˛ij ,

where ˛ij =



˛i ˛j (1 − kij )

(5)

j

xi bi

(6)

i

For extending the CPA EoS to mixtures of two associating compounds, e.g. alcohols or glycols with water, combining rules for the association energy (εAi Bj ) and the association volume (ˇAi Bj ) are required. The CR-1, described below, has previously been used successfully.

εAi Bj = εcross =

εAi Bi + εAj Bj 2

and

ˇAi Bj = ˇcross =



ˇAi Bi ˇAj Bj (7)

To account for cross-association between one self- and one non self-associating molecule (solvation), Folas et al. used the so-called modified CR-1 rule [33]: εAi Bj = εcross =

εassociating 2

and

ˇAi Bj = ˇcross = fitted

(8)

Then, the association strength will be estimated by Eq. (3) and in this way the in-built temperature dependency of the crossassociation strength is retained for solvating systems. Previous calculations [23,24] have showed that this approach, i.e. using the modified CR-1 rule, yields satisfactory results, e.g. for mixtures of water and glycols with aromatic hydrocarbons over large temperature ranges. 4.1. Pure fluids The CPA equation of state requires the estimation of three pure fluid parameters for the physical interactions (a0 , b, c1 ) and two additional parameters for self-association interactions (εAi Bj , ˇAi Bj ). Usually, these parameters are obtained by fitting vapor pressure and liquid density data. However, for inert components e.g. hydrocarbons, only the three parameters of the SRK term are required, which can be obtained either from vapor pressures (Psat ) and liquid densities (Vliq ) or calculated in the conventional manner (critical data, acentric factor). In this work, the former approach is adopted and parameters for all the examined pure fluids were estimated using saturated liquid density and vapor pressure data from DIPPR correlation [28] or, when it was possible were obtained from the literature. The pure fluid parameters are presented in Table 2. 4.2. Binary mixtures Calculations for binary systems that contain benzyl alcohol, benzaldehyde, CO2 , O2 or water were performed in order to estimate the corresponding binary parameters of the model. In the CO2 –benzyl alcohol system, a temperature dependent binary interaction parameter (kij ) was used, while in all other mixtures a single

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Table 2 CPA parameters for pure fluids. Association schemeb

Tc (K)

Benzyl alcohol (0.4Tc − 0.9Tc ) 3B 720.15 Benzaldehyde (0.4Tc − 0.9Tc )a – 695.0 CO2 (Tm − 0.9Tc )a – 304.21 O2 (0.5Tc − 0.9Tc )a – 154.58 Water [23] 4C 647.13

˛0 (L2 bar mol−2 )

b (L mol−1 )

c1

ε (bar L mol−1 )

ˇ

%AADc in Psat

%AADc in Vliq

29.141

0.0973

0.7533

205.41

0.0024

0.74

0.93

27.836

0.0932

0.8814

–

–

0.89

0.86

3.508

0.0272

0.7602

–

–

0.2

0.8

1.390

0.0216

0.4754

–

–

0.3

1.9

1.228

0.0145

0.6736

166.55

0.0692

0.8

0.5

a

a b

The temperature range of the regression is given in parenthesis, Tc : critical temperature, Tm melting point. 3B and 4C association schemes according to the notation of Huang and Radosz [29].  

c

%AAD =

1 n

  X cal −X exp   i X expi  × 100 where X stands for Psat or Vliq and n is the number of experimental data points. i

i

100

(a)

60

403.15 K 353.15 K

(b)

50

Pressure / bar

Pressure / bar

80

453.15 K 60

40

40 30 20 CPA 333 K CPA 353 K Exp. data 333 K Exp. data 353 K

10 20 0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0 0.000

0.005

0.010

0.015

0.020

0.025

N2 mole fraction

N2 mole fraction

Fig. 1. Experimental data [30,this work] (points) and CPA correlations (lines) for the solubility of (a) N2 in benzyl alcohol (kij = 0.20701) and (b) in benzaldehyde (kij = 0.00535).

temperature independent binary kij was optimized by the experimental data. 4.2.1. Solubility of N2 and O2 in benzyl alcohol and benzaldehyde Experimental data for the solubility of O2 in benzyl alcohol and benzaldehyde are not available, since these mixtures react under certain conditions. Consequently, calculations and experiments were performed for the solubility of N2 instead of O2 . The estimated binary interaction parameters were adopted in order to model the corresponding mixtures with O2 . Results are

300

(a)

(b)

200

Pressure / bar

Pressure / bar

300

presented in Fig. 1, from which it can be concluded that the solubility of N2 is higher in benzaldehyde than in benzyl alcohol. Using the binary interaction parameters from the corresponding systems with N2 , the model was applied to predict the solubility of O2 in benzyl alcohol and benzaldehyde. As it is shown in Fig. 2, the model predicts that the solubility of O2 in benzyl alcohol increases with increasing temperature, while the solubility in benzaldehyde does not significantly change with temperature in the investigated temperature range.

100 333 K 353 K 373 K 393 K

0 0.00

0.02

0.04

0.06

O2 mole fraction

0.08

0.10

200

100 333 K 353 K 373 K 393 K

0 0.00

0.05

0.10

0.15

0.20

O2 mole fraction

Fig. 2. CPA predictions for the solubility of O2 (a) in benzyl alcohol (kij = 0.20701, adopted from benzyl alcohol–N2 ) and (b) in benzaldehyde (kij = 0.00535, adopted from benzaldehyde–N2 ).

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87

450

180 160 140

400

Temperature / K

Pressure / bar

120 100 80

283.15 K

60

350

263.14 K

40

243.14 K 20

223.14 K

300

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.0

1.0

0.2

0.4

0.6

Benzyl alcohol mole fraction

CO2 mole fraction Fig. 3. CO2 –O2 VLE. Experimental data [31] (points) and CPA calculations (lines, kij = 0.08971).

4.2.2. CO2 –O2 vapor–liquid equilibrium Next, the CO2 –oxygen vapor–liquid (VLE) equilibrium was calculated and results are illustrated in Fig. 3. Using a single temperature independent binary interaction parameter the model accurately describes the vapor–liquid equilibrium at low and moderate pressures, but overpredicts the mixtures’ critical point, a behavior that is common in most association equation of state models like CPA, SAFT and similar ones [12–14]. 4.2.3. Benzyl alcohol–Benzaldehyde vapor–liquid equilibrium In order to model the vapor–liquid equilibrium of benzyl alcohol–benzaldehyde no cross association interactions between benzyl alcohol’s proton donors and benzaldehyde’s proton acceptors were assumed. Using such a simple association scheme (i.e. only accounting for self associating interactions between benzyl alcohol molecules) the performance of the model is satisfactory (Fig. 4) and as a result the calculations are simplified. 4.2.4. Benzyl alcohol–water LLE The benzyl alcohol–water binary system exhibits liquid–liquid equilibrium (LLE) up to 421 K. In order to model this system cross

Fig. 5. Benzyl alcohol–water LLE. Experimental data [34] (points) and CPA calculations (lines, kij = 0.00841).

association interactions were accounted for and the corresponding association parameters were estimated using the CR-1 combining rule (Eq. (7)). As can be seen in Fig. 5 the model accurately describes the aqueous phase, while it overestimates the water concentration in the organic phase. A reasonable explanation of this behavior should be the inability of the combining rule to capture the correct association strength between such hydrogen bonding compounds. However, since experimental data for the cross association energy, from spectroscopic or calorimetric studies, are not available the use of the combining rule cannot be avoided. 4.2.5. Benzaldehyde–water LLE Next the model was applied to describe the benzaldehyde– water liquid–liquid equilibrium. Cross association interactions were accounted for and the corresponding association parameters were estimated using the modified-CR-1 combining rule (Eq. (8)). Two association sites were assumed in benzaldehyde’s molecule, which are only able to cross associate with water. Results are presented in Table 3 and illustrated in Fig. 6. It can be seen that the water–benzaldehyde system presents a large immiscibility gap, which renders the modeling of the phase behavior a very challenging task. The model accurately describes the organic phase,

480 0.1

470

water in Benzaldehyde

1.01 bar

mole fraction

Temperature / K

460 450 440

0.01 Benzaldehyde in water

430

0.4 bar

1E-3

420 410 0.0

0.2

0.4

0.6

0.8

1.0

Benzylaldehyde mole fraction Fig. 4. Benzyl alcohol–benzaldehyde VLE. Experimental data [32,33] (points) and CPA calculations (lines, kij = −0.02338).

260

280

300

320

340

360

380

Temperature / K Fig. 6. Benzaldehyde–water LLE. Experimental data [35] (points) and CPA calculations (lines).

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Table 3 CPA binary interaction parameters and deviations from experimental data for benzaldehyde–water system. System Benzaldehyde–water a

x = (100/n)



Temp. range (K)

kij

ˇcross

Benzaldehyde in water xa

Water in benzaldehyde xa

298.2–420.2

−0.06387

0.13074

2.2

1.09

|xexp − xcalc |, where n is the number of experimental points and x the mole fraction.

Table 4 CPA binary interaction parameters and deviations from experimental data for CO2 –water system. System

Temp. range (K)

kij

ˇcross

% AAD in XCO2

% AAD in YCO2

CO2 –water

353.2

0.15476

0.02362

3.8

2.4

%AAD = (100/n)



[|xexp − xcalc |/xexp ], where n is the number of experimental points and x stands for mole fraction.

(a) Liquid phase

(b) Vapor Phase

0.035

0.05

353.2 K

0.030

353.2 K 0.04

Water mole fraction

CO2 mole fraction

0.025

0.020

0.015

0.010

0.03

0.02

0.01 0.005

0.00

0.000 0

100

200

300

400

500

0

600

100

200

Pressure / bar

300

400

500

600

Pressure / bar

Fig. 7. CO2 –water VLE. Experimental data [39–41] (points) and CPA calculations (lines): solubility of CO2 in water (a) and water content in the vapor phase (b).

4.2.6. CO2 –water vapor–liquid equilibrium Recently, relatively strong Lewis acid–base interactions between CO2 and water molecules have been put in evidence [36]. In such interactions, the CO2 carbon atom acts as an electron acceptor, while the H2 O oxygen atom acts as an electron donor. On the other hand, hydrogen bonding interactions between CO2 oxygen atoms and H2 O protons can also be present, but are less stable than the electron donor–acceptor interactions [36]. Consequently, in order to correlate the CO2 –water phase behavior, CO2 was modeled assuming that its molecule has one association site, which is only able to cross associate with water. The corresponding energy for such cross interactions was set equal to a value that is based on experimental calorimetric data (−14,200 J/mol) [37], while the second association parameter of the model (ˇcross ) was optimized by the experimental data. The same approach has been successfully applied in a previous study [38]. Results for the vapor–liquid equilibrium at 353.2 K are presented in Table 4 and are illustrated in Fig. 7.

4.2.8. CO2 –benzyl alcohol The increased solubility of alcohols, such as methanol and ethanol in CO2 compared with their solubility in other gases such as light hydrocarbons or nitrogen suggests the presence of some association, which can be explained by strong specific interactions between CO2 and alcohol molecules [43,44]. In a similar way to that described above for the CO2 –water system, such interactions have been mainly identified as Lewis acid–Lewis base interactions between the CO2 carbon atom and the oxygen atom of the alcohol’s hydroxyl group. Such association is more stable than the possible 300

393.2 K 250

373.2 K 200

Pressure / bar

but overestimates the benzaldehyde content of the aqueous phase, which also implies that the combining rule is not able to capture the correct association strength, as for the benzyl alcohol–water system discussed previously.

353.2 K 150

333.2 K 100

313.2 K 50

4.2.7. CO2 –benzaldehyde vapor–liquid equilibrium For CO2 –benzaldehyde, vapor–liquid equilibrium calculations were performed in a wide temperature range (313.2–393.2 K) and the results are presented in Fig. 8. Using a single temperature independent binary interaction parameter the model describes rather accurately the vapor–liquid equilibrium for this system.

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

CO2 mole fraction Fig. 8. CO2 –benzaldehyde VLE. Experimental data [42] (points) and CPA calculations (lines, kij = 0.04284).

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89

Table 5 CPA binary interaction parameters and deviations from experimental data for CO2 –benzyl alcohol system (experimental data from [30,45]). System

Temp. range (K)

CO2 –benzyl alcohol %AAD = (100/n)



kij −4

−0.063819 + 8.35310

333.1–453.1

× T (K)

ˇcross

% AAD in XCO2

% AAD in YCO2

0.26337

8.21

0.089

[|xexp − xcalc |/xexp ], where n is the number of experimental points and x stands for mole fraction.

a

300

b

1.000

0.996

CO2 mole fraction

Pressure / bar

250 200 150 100

0.992

0.988

0.984

50

Experimental data Walther and Maurer (1993) Experimental data (this work) CPA

0.980

0 0.0

0.2

0.4

0.6

0.8

1.0

0

20

40

60

80

100 120 140 160 180 200

Pressure / bar

CO2 mole fraction

Fig. 9. CO2 –benzyl alcohol vapor–liquid equilibrium at 353.2 K. Experimental data (open symbols: Ref. [45], solid symbols: this work) and CPA calculations (lines): composition of coexisting phases (a) and composition of the vapor phase (b).

hydrogen bonding between the alcohol’s hydroxyl proton and CO2 oxygen atoms, implying that one CO2 molecule is more likely to accept an electron pair than donate one. Consequently, CO2 –benzyl alcohol was modeled assuming cross association interactions between CO2 and alcohol molecules. The corresponding association parameters were estimated using the modified CR-1 combining rule (Eq. (8)). One association site was assumed on the CO2 molecule that is only able to cross associate with benzyl alcohol. Results are presented in Table 5, while characteristic calculations are presented in Fig. 9.

oxidation of benzyl alcohol to benzaldehyde inside supercritical CO2 . Firstly, the ternary CO2 –benzyl alcohol–O2 system was modeled at 353.2 K and various pressures, which are similar conditions to those used by Caravati et al. in experimental studies for the selective oxidation of benzyl alcohol in supercritical CO2 [7,10]. As it is shown in Fig. 10, at such temperature and pressure conditions this system can exhibit vapor–liquid equilibrium, where a CO2 or O2 rich vapor phase is in equilibrium with an alcohol rich liquid phase.By introducing a CO2 –benzyl alcohol–O2 mixture with a certain composition as a feed to a reactor packed with a Pd catalyst, Caravati et al. [10] observed that the transition from the two phase region to the one phase region was accompanied with an increase of the reaction rate. In this direction the dew points of three mixtures with different compositions were predicted using the CPA model and compared with the experimental data obtained in this work. As it is shown in Fig. 11, the model accurately describes the experimental data, which were obtained in this study, for the mixture

4.3. Prediction of the phase behavior in ternary and multicomponent mixtures Having the binary parameters of the model from the corresponding binary systems the CPA equation of state was applied to predict the phase behavior of two ternary and four multicomponent mixtures consisting of compounds involved in the selective

0.00

353.2 K 140 bar

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Vapor phase 0.25

0.25

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2

O

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CO 2

CO 2

O

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353.2 K 200 bar

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Benzyl alcohol

0.75

1.00

1.00 0.00

0.25

0.50

0.75

0.00 1.00

Benzyl alcohol

Fig. 10. CPA predictions for the CO2 –benzyl alcohol–O2 vapor–liquid equilibrium at 353.2 K and two different pressures.

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250

150

Benzyl alcohol: 0.91 % mol O2 : 0.43 % mol

O2 : 0.30 % mol

CO2:98.66 % mol

CO2:99.10 % mol

200

145

150

Single phase

100

O2 : 0.16 % mol CO2:99.39 % mol

50

Pressure / bar

Pressure / bar

Benzyl alcohol: 0.60 % mol

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Benzyl alcohol: 0.45 % mol

VLE 0

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Temperature / K

with low alcohol content, while the deviation from the experimental data increases somewhat by increasing alcohol concentration in the same way as in the binary CO2 –benzyl alcohol system (Fig. 9b). Often, the reaction takes place in excess of oxygen. In order to investigate the effect of oxygen concentration on the pressure, where the transition from two phases to a single phase takes place, the model was applied to calculate the dew point pressure at 353.2 K for a mixture with constant benzyl alcohol content (0.45 mol%). As shown in Fig. 12 the addition of more oxygen up to ten times the stoichiometric ratio only slightly increases the dew point pressure for this mixture. Benzaldehyde and water are produced from the oxidation of benzyl alcohol using molecular oxygen. Consequently, in a second step, the phase behavior of the CO2 –benzaldehyde–water ternary system was modeled. As is shown in Fig. 13, the phase behavior of this system is significantly more complicated than the corresponding mixture of reactants (CO2 –benzyl alcohol–O2 ). Depending on the composition, at 353.2 K and pressures lower than the critical point of the binary CO2 –benzaldehyde system, this system exhibits liquid–liquid (LLE), vapor–liquid (VLE) and 0.0

vapor–liquid–liquid (VLLE) equilibria. At pressures higher than the critical point of the CO2 –benzaldehyde binary system it exhibits liquid (or fluid like, at compositions rich in CO2 )–liquid equilibria. The dew points of two mixtures with different compositions were also predicted using the CPA model (Fig. 14). The compositions of these mixtures (mixtures of products) correspond to similar compositions as the mixtures presented in Fig. 11 (mixtures of reactants) assuming that all benzyl alcohol was oxidized to benzaldehyde. As shown in Fig. 14, the mixture of products requires lower pressures in order to be in a single phase compared to the mixture of the corresponding reactants (Fig. 11). The CPA model satisfactorily describes the experimental data obtained in this study. Finally, pressures at which the multicomponent system consisting of both reactants and products (CO2 , O2 , benzyl alcohol, water and benzaldehyde) is in a single phase were predicted at 353.2 K. The results are illustrated in Fig. 15. As it was expected the system requires higher pressures in order to be in a single phase as the absolute concentration of reactants and products increases. However, a comparison of Figs. 11, 14 and 15 reveals that, at the investigated conditions and for a certain composition of a batch

353.2 K 200 bar

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Be nz ald eh yd e

eh Be nz ald

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Fig. 12. CPA predictions for the dew point pressure at 353.2 K as function of O2 concentration for a mixture containing also CO2 and 0.45 mol% benzyl alcohol.

yd e

VLE

1.6

% mol O2

Fig. 11. Experimental data (points) and CPA predictions (lines) for the dew and bubble point curves of three reaction mixtures: CO2 : 98.66, O2 : 0.43, benzyl alcohol: 0.91 mol% (open circles, dash line); CO2 : 99.10, O2 : 0.30, benzyl alcohol: 0.60 mol% (open triangles, dot line) and CO2 : 99.39, O2 : 0.16, benzyl alcohol: 0.45 mol% (solid circles, solid line).

353.2 K 140 bar

1.2

0.2

1.0 0.0

0.0 0.2

0.4

0.6

0.8

Water

Fig. 13. CPA predictions for the CO2 –benzaldehyde–H2 O phase equilibria at 353.2 K and two different pressures.

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200 180

Benzaldehyde: 0.90 % mol H2O: 0.90 % mol

160

CO2:98.20 % mol

Single phase

Pressure / bar

140 120 100 80 60

Benzaldehyde : 0.45 % mol H2O: 0.45 % mol CO2: 99.10 % mol

40 20 0 330

VLE

340

350

360

370

380

390

400

410

Temperature / K Fig. 14. Experimental data (points) CPA predictions (lines) for the dew and bubble point curve of two benzaldehyde mixtures: CO2 : 98.20, H2 O: 0.90, benzaldehyde: 0.90 mol% (dash line) and CO2 : 98.10, H2 O: 0.45, benzaldehyde: 0.45 mol% (solid line).

single phase region

220 200

Pressure / bar

180 160 140 120 100

two phase region

91

and benzaldehyde–H2 O–CO2 ternary mixtures. Thereby, valuable and easily obtainable data are delivered for the optimization of a catalytic alcohol oxidation such as the aerobic benzyl alcohol oxidation shown here. The CPA equation of state was used to model the phase behavior of the investigated systems and to predict the phase behavior of multicomponent mixtures that can exist inside the reactor during the reaction time. Initially, the binary interaction parameters of the model were estimated using experimental data from this study or data obtained from the literature for all the corresponding binary systems. Having the required binary parameters, the model was applied to predict the phase behavior of two ternary systems consisting of reactants (CO2 –benzyl alcohol–O2 ) and products (CO2 –benzaldehyde–water), respectively. According to the model predictions, at the investigated pressure and temperature (353.2 K and 100–200 bar, which are similar to the experimental conditions for the oxidation of benzyl alcohol) the mixture of reactants can either exhibit vapor–liquid equilibrium or can be in a single phase depending on the composition and consequently conversion. On the other hand, the mixture of products either can be in a single phase or can exhibit a more complicated phase behavior consisting of liquid–liquid, vapor–liquid or vapor–liquid–liquid equilibria depending on pressure and composition at a given temperature. Finally, the dew or bubble points were estimated for the ternary mixtures of reactants and products as well as for multicomponent mixtures of both reactants and products that can occur inside the reactor during the reaction time. All mixture compositions were similar to those used in the experimental studies. The results reveal that the ternary mixture of products that can possibly exist at the end of the reaction and the intermediate multicomponent mixtures containing both products and reactants require less pressure than the mixture of the reactants in order to be in a single phase. This implies that the phase behavior of the CO2 –benzyl alcohol–O2 system determines the optimum pressure and temperature conditions as well as the optimum compositions inside the reactor. Future catalytic studies will be performed to verify this point and optimize the catalytic oxidation of benzyl alcohol in supercritical CO2 in a continuous fixed bed reactor.

80 330

340

350

360

370

380

390

400

410

420

List of symbols

Tenperature / K Fig. 15. CPA predictions for the dew point curve at 353.2 K of four reaction mixtures: CO2 : 97.39, O2 : 0.33, benzyl alcohol: 0.76, water: 0.76, benzaldehyde: 0.76 mol% (dash dot line); CO2 : 98.08, O2 : 0.27, benzyl alcohol: 0.55, water: 0.55, benzaldehyde: 0.55 mol% (dot line); CO2 : 98.46, O2 : 0.22, benzyl alcohol: 0.44, water: 0.44, benzaldehyde: 0.44 mol% (dash line); CO2 : 99.23, O2 : 0.11, benzyl alcohol: 0.22, water: 0.22, benzaldehyde: 0.22 mol% (solid line).

reactor’s loading, the pressure required for a single phase decreases with mixtures corresponding to higher conversions. In other words, both the mixture of products in the end of the reaction and the intermediate mixtures containing products and reactants require lower pressure than the initial mixture of the reactants in order to be in a single phase. Hence, the pressure required for the substrate mixture to be in a single phase is a good indication of the optimal pressure for the catalytic benzyl alcohol oxidation. 5. Discussion and conclusions Using the CPA equation of state the phase behavior of relevant ternary systems for the aerobic oxidation of benzyl alcohol has been predicted. Experimental phase behavior investigations validated the theoretical data and showed that this approach is capable of reliably modeling the phase behavior of benzyl alcohol–O2 –CO2

b c1 g, g() kij n P Psat R T Tc Tr Vliq x XAi

CPA fluid specific parameter CPA fluid specific parameter Radial distribution function Binary interaction parameter Number of experimental points Pressure Vapor pressure Gas constant Temperature Critical temperature Reduced temperature Liquid volume Mole fraction Fraction of free sites of type A belonging to molecule i

Greek letters ˛0 Fluid specific parameter ˇAi Bj Association volume for the hydrogen bond between sites A and B belonging in molecules i and j, respectively Cross association volume ˇcross Ai Bj Association strength between two sites A and B belonging to molecules i and j, respectively

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Association energy for the hydrogen bond between sites A and B belonging to molecules i and j, respectively Cross association energy Reduced density Density

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