LiquidâLiquid Equilibria of Systems with Linear Aldehydes

Article pubs.acs.org/IECR

Liquid−Liquid Equilibria of Systems with Linear Aldehydes. Experimental Data and Modeling with PCP-SAFT Elisabeth Schaf̈ er and Gabriele Sadowski* Laboratory of Thermodynamics, TU Dortmund, Emil-Figge-Straße 70, D-44227 Dortmund, Germany S Supporting Information *

ABSTRACT: Liquid−liquid equilibrium (LLE) data were measured for the binary system propylene carbonate/decane (288.15 to 403.15 K) as well as for the ternary systems propylene carbonate/decane + linear aldehyde (C4, C8, C10, C12, C13) and DMF/decane + linear aldehyde (C4, C8, C10, C13) at 298.15 K using the analytic method. The reliability of the ternary LLE data is ascertained by employing Othmer−Tobias plots. Concerning the aldehyde distribution coefficients in the ternary systems, a distinctive dependency on the chain length of the aldehyde was observed. The LLE data were modeled with the Perturbed Chain Polar Statistical Associating Fluid Theory (PCP-SAFT) equation of state using a heterosegmented approach for describing the aldehyde molecules.

1. INTRODUCTION Aldehydes are of great industrial importance, for example, as intermediates of detergents or as fragrances. They are typically produced via hydroformylation of olefins by homogeneous organometallic catalysis.1 Major industrial feedstocks include olefins of up to about 20 carbon atoms.2 Besides effective separation of the product, efficient catalyst recycling is essential for an economic industrial process, due to the high costs of the catalyst. Short-chain olefins such as propene are hydroformylated economically via the Ruhrchemie/Rhône-Poulenc Process (RCH-RP).3 In the RCH-RP, an aqueous/organic liquid−liquid two-phase system is employed. However, the water solubility of olefins higher than C4 is marginal. Long-chain olefins can therefore not be hydroformylated economically by the classical RCH-RP.1 For these cases, the application of thermomorphic multicomponent solvent (TMS) systems is a promising approach that allows for both optimal reaction and catalyst recycling conditions.3 The TMS principle is based on temperature-controlled switches between homogeneity and heterogeneity of the reaction medium. At high temperatures when the reaction takes place, the reaction medium exhibits only one liquid phase providing minimal mass transport resistance. At low temperatures, on the contrary, the reaction medium is comprised of two liquid phases, so that the catalyst can be separated from the product via phase separation. TMS systems typically consist of at least one polar and one apolar solvent. DMF (dimethylformamide) and PC (propylene carbonate) are typically employed as polar components, while alkanes such as decane are preferred as apolar solvents.3 The applicability of the TMS system concept to the hydroformylation of alkenes of different chain-lengths has yet to be investigated. Thereby, knowledge of the influence of the product, that is, the aldehyde, and the alkene as educt on the phase behavior of the TMS system are essential to successfully apply the TMS system concept. Necessary information includes the values of the distribution coefficients of the aldehyde at separation temperature. Liquid−liquid equilibrium data provide the © 2012 American Chemical Society

base for this information. Literature data on binary PC/alkane LLE (liquid−liquid equilibrium) data is rare. Some data points have been measured by Fahim and Merchant4 and Salem5 for the systems PC/octane4 and PC/heptane.5 However, to the best of our knowledge, LLE data for the system PC/decane have not been published yet. LLE data on aldehyde systems are scarce as well. In the literature, binary LLE data on aqueous ethanal, propanal, or butanal systems can be found as well as LLE data on several ternary systems containing butanal are reported.6,7 Behr et al. studied the effect of n-nonanal on the phase behavior of the TMS system PC/dodecane/p-xylene and observed that the aldehyde acts as solubilizer.8 That is, addition of the aldehyde has a diminishing effect on the miscibility gap of the TMS system. In our previous work,9 the solubilizing effect of the aldehyde was confirmed for dodecanal added to the TMS system DMF/ decane. To investigate the applicability of the TMS system concept to the hydroformylation of alkenes of different chain lengths, LLE data of the corresponding aldehyde systems are required. This paper provides binary LLE data for the system PC/ decane from 288.15 to 403.15 K. Additionally, ternary LLE data for the systems DMF/decane + linear aldehyde and PC/decane + linear aldehyde at 298.15 K are presented. The aldehydes in this investigation were butanal (C4), octanal (C8), decanal (C10), dodecanal (C12), and tridecanal (C13). The LLE data were measured by the analytic method at ambient pressure. The reliability of the ternary LLE data is ascertained by employing Othmer−Tobias plots. Furthermore, the distribution coefficients of the aldehydes between the polar phase (rich in DMF or PC, respectively) and the apolar decane-rich phase were determined to investigate their dependency on the chain length of the aldehydes. Received: Revised: Accepted: Published: 14525

June 14, 2012 October 11, 2012 October 12, 2012 October 12, 2012 dx.doi.org/10.1021/ie301566d | Ind. Eng. Chem. Res. 2012, 51, 14525−14534

Industrial & Engineering Chemistry Research

Article

fractions presented in this work are the arithmetic averages of the three values of each phase analysis.

The LLE data were modeled employing the PCP-SAFT equation of state using a heterosegmented approach for the description of the aldehyde molecules.9 The main idea of this approach is that the aldehyde molecules are thought to consist of two characteristic domains, which is, on one hand, an apolar tail group and, on the other hand, a polar headgroup. By employing the heterosegmented approach to model the aldehyde molecules, the different interaction behavior of the tail and the headgroup of the aldehyde with other polar and apolar molecules is accounted.

3. THEORYPCP-SAFT MODEL The Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT)10,11 model is a state-of-the-art equation of state highly appropriate for engineering applications. It is designed for modeling mixtures of all types of substances that are gases, solvents, and polymers. It has been tested against experimental data for numerous systems, and it has been found to be suitable to calculate phase equilibria and thermophysical properties of pure components and mixtures. The PC-SAFT equation of state is based on a thermodynamic perturbation theory that uses a system of freely jointed hard spheres as reference, referred to as hard-chain system. Various types of interactions such as dispersive, associating, and polar interactions can be accounted for as perturbations. According to the perturbation theory, the residual Helmholtz energy ares is calculated by summing the different contributions. In eq 1, ahc stands for the contribution of the hard-chain reference system, whereas adisp refers to dispersive, aassoc to associative, and adipole to dipolar interactions.

2. EXPERIMENTAL SECTION 2.1. Materials. Table 1 lists all chemicals used for the experiments in this work, together with information about suppliers Table 1. Chemicals Used for Experiments in This Work

a

substance

supplier

purity [%]a

propylene carbonate (PC) dimethylformamide (DMF) decane tridecanal dodecanal decanal octanal butanal

Sigma Aldrich Sigma Aldrich Sigma Aldirch Alfa (Aesar) Merck Sigma Aldrich Sigma Aldrich Sigma Aldrich

99 99 99 96 98 98 99.5 99.5

a res = a hc + adisp + aassoc + adipole

(1)

Accounting for dipolar interactions by the expression proposed by Gross and Vrabec12 leads to the PCP-SAFT equation of state. The model by Gross and Vrabec is a segmentlevel approach based on third-order perturbation theory using the Padé approximation. In contrast to the expressions (e.g., developed by Jog and Chapman13,14 and Saager and Fischer),15 no additional fitted model parameter is required if the experimental value of the dipole moment is used. The PCP-SAFT equation of state is applicable to nonpolar, polar, and associating pure components, as well as to their mixtures. Besides the original, homosegmented PCP-SAFT concept, where every component is thought to consist of only one type of sphere, Gross et al.16 derived the Copolymer PC-SAFT concept based on the idea of introducing heterosegmented components. They may consist of two or more different types of spheres. In this work, the PCP-SAFT equation of state and the heterosegmented PC-SAFT concept were combined to model the aldehydes. The combination required adapting the dipolar expression by Gross and Vrabec.12 That is, an additional summation over all segment types has to be accounted for if a molecule is treated as being heterosegmented. The expression for the dipolar contribution by Gross and Vrabec12 plus inclusion of the summation over all segment types has already been reported in our previous paper.9 Generally, employing the PC(P)-SAFT equations of state involves fitting pure-component parameters for each component. The number of pure-component parameters depends on the types of perturbation contributions that have to be considered and whether the component is treated as being homo- or heterosegmented. For apolar, homosegmented components, there exist three pure-component parameters, namely the segment number m, the segment diameter σ, and the dispersionenergy parameter ε/k. If the component is treated as being heterosegmented, there exists one segment number that accounts for the total number of segments of the molecule. Additionally, one segment diameter and one dispersion-energy parameter for each type of segment as well as the corresponding segment fractions ziα and bonding fractions Biαiβ have to be defined.16

GC.

and purities. All chemicals were used without further purification and stored over molecular sieves for drying purposes. Purity of the chemicals was confirmed by gas chromatography (GC) analysis. Oxidation and dimerization are major problems when dealing with higher aldehydes. Therefore, the aldehyde is stabilized with α-tocopherol, for example. Concerning tridecanal, impurities are mainly aldehydes > C13. The effect of the stabilizer and the impurities on the experimental data could not be quantified as tridecanal with a purity greater than 96% (GC) was not available on the market and further purification was difficult due to the instability of the aldehyde. 2.2. Apparatus and Measurement Procedure. The apparatus for measuring the LLE data consisted of a doublejacketed, thermostatted glass equilibrium cell. The equilibrium cell was additionally placed into a separately thermostatted bath. Silicon oil (Baysilone KT20) was used as the heating, and respectively cooling, medium. The inner volume of the equilibrium cell was 20 mL. A magnetic stirrer provided extensive mixing within the equilibrium cell. Mixture components were weighted with a precision of ±0.001 g. The composition of samples taken from the equilibrium cell was analyzed via gas chromatography (Agilent GC 7890, Agilent Technologies Deutschland GmbH, Germany) equipped with a capillary column (HP-5 5% Phenyl Methyl Siloxan) and a flame ionization detector (FID). The LLE data were measured by the analytic method. The procedure had three steps. First, the heterogeneous sample filled into the equilibrium cell was stirred at constant temperature for about an hour. The temperature of the mixture in the equilibrium cell was kept constant within ±0.03 K. Second, stirring was stopped, and the two phases were kept at constant temperature until the two phases were transparent and a sharp phase boundary appeared. In the third step, samples of the two phases were taken using injection syringes for chemical analysis and analyzed via GC. Each phase composition was analyzed at least three times whereby reproducibility was 99.9%. The mole 14526

dx.doi.org/10.1021/ie301566d | Ind. Eng. Chem. Res. 2012, 51, 14525−14534


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LLE data for the system PC/decane were measured between 288.15 and 403.15 K. The data are listed in Table 2. Figure 1 presents the experimentally determined miscibility curve. xi is the mole fraction of component i.

For modeling polar components, a value for the dipole moment μ is needed as well. The value of the dipole moment employed for modeling phase equilibria often corresponds to the literature value for the gas phase, and respectively the vacuum dipole moment.12 The dipolar model by Gross and Vrabec12 was tested against experimental data for numerous polar components and their mixtures. In most cases, considerable improvement of the representation of experimental data was achieved using the vacuum value of the dipole moment.12 However, the gas phase or vacuum value of the dipole moment neglects intermolecular dipole interactions that occur in the liquid state. That is, the gas phase or vacuum value of the dipole moment does not necessarily represent the dipolar characteristic of the substance in the liquid state correctly. Therefore, Gross and Kleiner17 developed an extended version of the original model by Gross and Vrabec12 including the induction of a dipole moment through polarizability (PCIP-SAFT).17 Yet, introducing polarizability was found to have a rather small effect on the modeling results, and the complexity of the calculations inevitably increases.17 Another point concerns the orientation of the dipole moment. The expression by Gross and Vrabec12 incorporates an axial alignment of the dipole moment. It does not account for dipole moments perpendicular to the molecular axis that might cause the dipolar contribution to be too low if the literature value of the dipole moment is employed. Korden et al.18 investigated orientational effects of the dipole moment on thermodynamic properties. The results reveal that a fixed dipole angle is probably not sufficient to describe real fluids properly. It is suggested to use adjusted effective dipole moments to consider different angles of the dipole moment. As an alternative approach, the parametrization of the model by Gross and Vrabec12 was extended to take into account different deflection angles of the dipole moment. Results provided by using this modified model are in good agreement with molecular simulation data. If the approach is applied to real substances, however, calculated data fit best for the case where the dipole moment is axial aligned.18 As a consequence of the above-mentioned issues, the dipole moment can also be treated as a fitted parameter. Concerning modeling thermodynamic properties of acetonitrile, for instance, Kleiner and Gross17 found that an adjusted dipole moment instead of the vacuum value improved the modeling results for pure component data as well as mixture phase equilibria significantly. Consequently, in this work, the version of the dipolar model by Gross and Vrabec12 without the extension for a deflection angle was applied and the dipole moment was treated as a fitted parameter. Modeling mixtures of two or more components requires one additional binary interaction parameter kij for each binary combination of the components to correct the combining rule for the dispersion energy of the mixture, which is given in eq 2. εij = (1 − kij) εiεj

Table 2. Experimental LLE Data for the Binary System PC/Decane Measured within This Work decane-rich phase

PC-rich phase

T (K)

xdecane (mol/mol)

xdecane (mol/mol)

288.15 298.15 298.15 318.15 318.15 338.15 338.15 343.15 358.15 363.15 378.15 398.15 403.15

0.996 0.994 0.994 0.993 0.993 0.992 0.992 0.992 0.992 0.990 0.986 0.973 0.967

0.006 0.008 0.009 0.014 0.015 0.019 0.022 0.022 0.025 0.027 0.034 0.045 0.047

Figure 1. Liquid−liquid equilibrium of the system PC/decane. Symbols are experimental data measured within this work.

The LLE data presented in Figure 1 for the binary system PC/decane illustrate that the system has a very large miscibility gap. Miscibility between the two components is marginal between 290 and 410 K. At 298 K, for instance, the miscibility gap extends from 0.02 < xdecane < 0.98. The effect is primarily caused by the large difference in polarity of the two components. The literature value of the dipole moment in the gas phase of PC is 4.95 D,3 whereas decane is an apolar solvent. By comparison, DMF has a dipole moment of 3.82 D,3 and the LLE of the system DMF/decane exhibits an upper critical solution temperature (UCST) at 357.76 K.23 That is, miscibility of DMF and decane is considerably more extensive in contrast to that of PC and decane. The ternary LLE data for the systems PC/decane + linear aldehyde (C4, C8, C10, C12, C13) and DMF/decane + linear aldehyde (C4, C8, C10, C13) were measured at 298.15 K. Tables 3 and 4 contain the experimental data. In Figures 2 and 3, the miscibility curves of the aforementioned systems are shown.

(2)

The pure-component parameters are typically fitted to purecomponent liquid volume and vapor pressure data. This is also true for the parameter-fitting done in this work. The binary interaction parameters were fitted to LLE data. For more details of the PC-SAFT concept, see refs 10−22

4. RESULTS AND DISCUSSION 4.1. Experimental LLE Data. In the following, experimentally determined LLE data are presented. Modeling results using the PCP-SAFT equation are discussed in the subsequent section. 14527



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Table 3. Experimental LLE Data for the Ternary System PC/Decane + Linear Aldehyde Measured within This Work at 298.15 K decane-rich phase xdecane (mol/mol) PC/decane/butanal 0.968 0.915 0.867 0.849 0.820 0.776 0.770 0.707 0.674 0.662 0.607 0.578 0.441 0.315 PC/decane/octanal 0.916 0.914 0.844 0.765 0.679 0.631 0.546 0.503 0.469 0.392 0.365 0.267 PC/decane/decanal 0.953 0.891 0.788 0.782 0.724

decane-rich phase

PC-rich phase

xPC (mol/mol)

xdecane (mol/mol)

xPC (mol/mol)

0.006 0.007 0.007 0.007 0.006 0.011 0.011 0.017 0.021 0.021 0.035 0.039 0.091 0.161

0.012 0.014 0.022 0.016 0.019 0.030 0.028 0.036 0.044 0.046 0.062 0.068 0.139 0.224

0.933 0.828 0.764 0.753 0.683 0.613 0.608 0.546 0.508 0.490 0.440 0.416 0.320 0.228

0.007 0.007 0.006 0.016 0.018 0.030 0.050 0.057 0.075 0.116 0.122 0.209

0.014 0.014 0.013 0.013 0.015 0.024 0.029 0.025 0.031 0.043 0.051 0.067

0.953 0.953 0.924 0.900 0.872 0.836 0.795 0.788 0.763 0.709 0.687 0.592

0.007 0.007 0.016 0.016 0.027

0.008 0.010 0.013 0.012 0.019

0.982 0.969 0.947 0.947 0.930

xdecane (mol/mol)

xPC (mol/mol)

PC/decane/decanal 0.690 0.635 0.589 0.549 0.510 0.458 0.429 PC/decane/dodecanal 0.920 0.917 0.834 0.747 0.746 0.721 0.675 0.557 0.556 0.516 0.383 0.356 PC/decane/tridecanal 0.947 0.898 0.861 0.775 0.657 0.612 0.524 0.517 0.508 0.413 0.334 0.305

PC-rich phase xdecane (mol/mol)

xPC (mol/mol)

0.033 0.050 0.060 0.077 0.091 0.122 0.137

0.019 0.018 0.021 0.019 0.022 0.026 0.025

0.922 0.917 0.907 0.900 0.889 0.874 0.868

0.004 0.007 0.010 0.021 0.021 0.031 0.043 0.082 0.080 0.091 0.157 0.171

0.009 0.009 0.010 0.009 0.009 0.007 0.008 0.008 0.009 0.008 0.008 0.008

0.985 0.985 0.980 0.976 0.976 0.974 0.970 0.963 0.963 0.961 0.951 0.948

0.007 0.007 0.007 0.018 0.036 0.041 0.067 0.070 0.065 0.104 0.144 0.164

0.008 0.009 0.010 0.008 0.012 0.006 0.010 0.004 0.008 0.007 0.008 0.009

0.985 0.983 0.982 0.980 0.969 0.975 0.968 0.973 0.967 0.964 0.962 0.960

lines in ternary systems and to verify the consistency of experimental LLE data for ternary systems. They developed a plotting method for ternary tie line data that reveals a straight-line relation between the tie lines of ternary systems.24 The underlying mathematical correlation of these tie line plots for ternary systems suggested by Othmer and Tobias24 is the following linear equation

For reasons of completeness, LLE data for the system DMF/ decane/dodecanal at 298.15 K, which was published earlier by the authors,9 are presented as well in Figure 3. Comparison of the miscibility curves in Figures 2 and 3 reveals that the miscibility gaps of the PC systems are generally much larger compared to those of the DMF systems, which is due to the strong difference in the value of dipole moments of the polar components. Concerning the general size of the miscibility gaps in the PC systems, Figure 2 shows that there is no clear dependency between the size of the miscibility gap and the number of C atoms of the aldehydes. The size of the miscibility gaps is very similar for all aldehyde systems. The DMF systems shown in Figure 3 reveal a certain trend concerning the general size of the miscibility gaps. The miscibility gap of the butanal system is considerably larger than that of the other systems. The octanal miscibility gap is the second largest while the differences between the miscibility gaps of the C10 to C13 aldehyde systems are marginal. The reliability of the experimentally determined LLE data of the ternary systems is ascertained by employing Othmer−Tobias plots. Othmer and Tobias24 studied the relation between tie lines in ternary systems in order to improve the interpolation of tie

⎛ 1 − x Ph2 ⎞ Ph1 ⎞ ⎛ polar solvent ⎟ = a + b ln⎜⎜ 1 − xdecane ⎟⎟ ln⎜⎜ ⎟ Ph2 Ph1 ⎝ xdecane ⎠ ⎝ xpolar solvent ⎠

(3)

with xPh1 decane being in this work the mole fraction of decane in the decane-rich phase (Ph1) and xPh2 polar solvent being the mole fraction of the polar solvent (i.e., PC- or DMF) in the polar phase (Ph2), which is in equilibrium with the first one. a and b are correlation parameters. The Othmer−Tobias plots for the ternary LLE data measured within this work are presented in Figures 4 and 5 (see the Supporting Information for correlation coefficients and coefficients of determination for Othmer−Tobias plots). The LLE data for all systems show a remarkable consistency with respect to the Othmer−Tobias plots in Figures 4 and 5, as they are clearly linearly correlated. The comparatively larger discrepancies occurring for the system PC/decane/tridecanal are 14528



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Table 4. Experimental LLE Data for the Ternary System DMF/Decane + Linear Aldehyde Measured within This Work at 298.15 K decane-rich phase xdecane (mol/mol)

xDMF (mol/mol)

DMF/decane/butanal 0.865 0.837 0.812 0.772 0.637 0.414 0.372 DMF/decane/octanal 0.846 0.838 0.785 0.683 0.539 0.496 0.460 DMF/decane/decanal 0.888 0.786 0.732 0.602 0.528 0.405 DMF/decane/tridecanal 0.884 0.841 0.831 0.821 0.748 0.709 0.637 0.635 0.578 0.381 0.378 0.362 DMF/decanea 0.929 0.927 0.927 a

DMF-rich phase xdecane (mol/mol)

xDMF (mol/mol)

0.085 0.093 0.099 0.112 0.184 0.317 0.347

0.043 0.046 0.051 0.061 0.096 0.202 0.226

0.858 0.839 0.807 0.761 0.659 0.497 0.473

0.099 0.102 0.118 0.177 0.276 0.307 0.345

0.048 0.050 0.059 0.086 0.140 0.156 0.174

0.911 0.908 0.875 0.810 0.711 0.687 0.663

0.085 0.137 0.169 0.260 0.321 0.441

0.043 0.057 0.069 0.102 0.130 0.191

0.941 0.902 0.873 0.810 0.768 0.683

0.085 0.113 0.113 0.118 0.167 0.184 0.238 0.237 0.286 0.468 0.466 0.485

0.036 0.037 0.038 0.043 0.046 0.053 0.059 0.056 0.080 0.123 0.120 0.131

0.956 0.951 0.948 0.939 0.930 0.913 0.896 0.905 0.869 0.793 0.795 0.777

0.071 0.073 0.073

0.029 0.030 0.030

0.971 0.970 0.970

Figure 2. Liquid−liquid equilibrium data of the systems PC/decane + aldehyde at 298.15 K. Symbols are experimental data measured within this work. ▲: C4-. ○: C8-. ◊: C10-. ■: C12-. Δ: C13-aldehyde.

Figure 3. Liquid−liquid equilibrium data of the systems DMF/decane + aldehyde at 298.15 K. Symbols are experimental data measured within this work. ▲: C4-. ○: C8-. ◊: C10-. ■: C12-. Δ: C13-aldehyde.

Published earlier,9 measured with analytic method.

probably caused by only marginal differences in the composition and very high PC mole fractions of the PC-rich phases along the miscibility curve. Thus, even small experimental inaccuracies have a strong impact on the location of points in the Othmer− Tobias plot. The distribution coefficients of the aldehydes between the polar DMF-, respectively PC-rich phase and the apolar decanerich phase are calculated by K=

Ph1 xaldehyde Ph2 xaldehyde

Figure 4. Othmer−Tobias plots for the ternary systems PC/decane + aldehyde at 298.15 K. Symbols are experimental data. ▲: C4-. ○: C8-. ◊: C10-. ■: C12-. Δ: C13-aldehyde. Lines are linear regression curves according to eq 3.

(4)

xPh1 aldyhide

with being the mole fraction of the aldehyde in the decane-rich phase (Ph1) and xPh2 aldyhide being the mole fraction of the aldehyde in the related polar (PC- or DMF-rich) phase

(Ph2). In Figures 6 and 7, the distribution coefficients of the aldehydes of the PC and DMF systems are plotted against xPh1 decane, 14529



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Figure 5. Othmer−Tobias plots for the ternary systems DMF/decane + aldehyde at 298.15 K. Symbols are experimental data. ▲: C4-. ○: C8-. ◊: C10-. ■: C12-. Δ: C13-aldehyde. Lines are linear regression curves according to eq 3.

Figure 7. Distribution coefficients K of the aldehydes between the DMF-rich and the decane-rich phase of the DMF/decane systems at 298.15 K. xPh1 decane is the mole fraction of decane in the decane-rich phase (Ph1). Symbols are experimental data. ▲: C4-. ○: C8-. ◊: C10-. ■: C12-. Δ: C13-aldehyde.

probably due to PC being the more polar component compared to DMF. 4.2. Modeling of the LLE Data. The LLE data of the beforementioned binary and ternary solvent systems were calculated using the PCP-SAFT equation of state. Thereby, the PCP-SAFT equation was combined with the heterosegmented PC-SAFT concept to model the linear aldehydes. Decane is an apolar component, which means that only the hardchain term and dispersive interactions have to be considered to describe the decane molecule within the PCP-SAFT concept. PC, DMF, and the aldehydes were considered as polar components in this work. The dipole moments of DMF and of the aldehydes were treated as fitting parameters. In case of PC, the literature value of the gas phase dipole moment was used for modeling the PC systems. Decane, PC, and DMF were described as being homosegmented, which is the usual approach for solvents. In our previous work, we demonstrated that LLE modeling results for the aldehyde system DMF/decane/dodecanal were considerably improved when employing a heterosegmented approach to describe the aldehyde molecule instead of the common homosegmented approach.9 The reason for the improvement is probably due to the characteristic structure of the aldehyde, which is taken into account by the heterosegemented approach but not by the homosegmented approach. Concerning the heterosegmented approach, the aldehyde molecule is thought to consist of two domains: an apolar tail and a polar headgroup containing the carbonyl group, which show different interaction behavior with other polar and apolar molecules. That means, different types of possible interactions are accounted for depending on which domain of the aldehyde molecules interacts with another molecule. In this work, the LLE data of all aldehyde systems investigated were modeled using the heterosegmented approach to describe the aldehyde molecules as the homosegmented approach provided poorer results.9 The apolar tail group of the aldehydes was modeled using the pure-component parameters of the alkanes, whereby the number of C atoms of these alkanes was always the number of C atoms of the considered aldehyde minus two. That is, for dodecanal, for instance, the pure-component parameters of the tail group corresponded to the parameters of decane. The values of the parameters for the headgroup were fitted

Figure 6. Distribution coefficients K of the aldehydes between the PCrich and the decane-rich phase of the PC/decane systems at 298.15 K. xPh1 decane is the mole fraction of decane in the decane-rich phase (Ph1). Symbols are experimental data. ▲: C4-. ○: C8-. ◊: C10-. ■: C12-. Δ: C13-aldehyde.

which is the mole fraction of decane in the respective decane-rich phases (Ph1). As can be seen from Figures 6 and 7, the chain length of the aldehyde obviously has a strong influence on the distribution coefficients of the aldehydes. For the aldehyde systems investigated, there exists a clear correlation: the longer the chain length of the aldehyde, the larger the average distribution coefficients of the aldehyde. For butanal, the distribution coefficients are even smaller than 1 in the DMF as well as in the PC system, while the distribution coefficients of the other aldehydes are larger than 1. The largest distribution coefficients occur for tridecanal, which are above 15 in the PC system. That is, the sign of the slope of the tie lines changes between the butanal and the octanal system. The chain length dependency of the distribution coefficients is additionally more distinctive for the PC systems, which is 14530



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Table 5. PCP-SAFT Pure-Component Parameters of Substances Employed in This Work as Well as Max RD and ARD Values for Vapor Pressures and Liquid Volumes vapor pressure refa

substance

decane published10 DMF published9 PC this work25−29 butanalh -tail published10 -head published9 h octanal -tail published10 -head published9 h decanal -tail published10 -head published9 h dodecanal -tail published10 -head published9 tridecanalh -tail published10 -head published9

μib (D)

μic (D)

max RD (%)f

ARD (%)g

243.87 312.99 312.92

3.823 4.953

4.12 4.95

19.18 14.59

3.5206 3.0601

191.42 220.56

2.7230

2.88

3.0576 1.5599

3.7983 3.0601

236.77 220.56

2.32d

2.88

3.8176 1.5599

3.8373 3.0601

242.78 220.56

2.5831

2.88

4.6627 1.5599

3.8384 3.0601

243.87 220.56

2.5831

2.88

4.9082 1.5599

3.8893 3.0601

248.82 220.56

2.5831

2.88

Mi (g/mol)

mi

σi (Å)

εi/k (K)

142.285 73.095 102.09

4.6627 2.3660 3.3106

3.8384 3.6359 3.3575

72.11

1.6069 1.5599

128.21

156.265

184.32

198.345

liquid volume T range (K)

max RD (%)f

ARD (%)g

7.09 2.29

243−617 290−490 288−515

10.82 6.64

4.39 1.07

26.35

20.93

320−500

11.46

5.58

26.41

15.93

390−600

8.36

1.86

23.52

13.68

390−630

5.05

1.10

24.01

11.48

390−630

1.97

1.20

22.67

14.72

390−630

3.29

2.03

a

If parameters were published previously, then references refer to the source of these parameters. Otherwise the references refer to the source of data employed to fit the parameters. bLiterature value of dipole moment in the gas phase. c(Fitted) value of dipole moment employed to model LLE data in this work. dDipole moment value in heptane 31 f

max RD = 100 × max

ycalc, i − yexp , i yexp , i

g

ARD = 100

1 nexp

nexp

∑ i=1

ycalc, i − yexp , i yexp , i

h

Segment fractions ziα were calculated by miα ziα = ∑α miα

with α being either the segment type of the head or the tail group of the aldehyde.16 Bonding fractions Biαiβ were calculated by Biαiβ =

1 ∑α miα − 1

Biαiα =

miα − 1 ∑α miα − 1

with α being either the segment type of the head or the tail group of the aldehyde.16

simultaneously to experimental vapor pressure and liquid volume data of butanal, octanal, decanal, dodecanal, and tridecanal. That means that one set of head parameters was determined for all these aldehydes. Table 5 lists the values of the pure-component parameters, the maximum relative deviation (max RD) as well as the average relative deviation (ARD) between experimental and calculated vapor pressures and liquid volumes for all components employed in this work. Additionally, the literature values of the dipole moments in the gas phase of polar components are given. Comparison of the literature values and fitted dipole moments for DMF and the aldehydes shows that the fitted dipole moments are always slightly larger than the gas phase values. This can be explained by the fact that the gas phase values neglect dipolar intermolecular

interactions and by the characteristics of the dipolar expression by Gross and Vrabec,12 which was mentioned in section 3. Table 6 lists the kij values for binary combinations of components employed in this work, which were assumed to be Table 6. Constant kij Values for Binary Combinations of Components Employed in This Work

14531

binary combination of componets

kij

PC/decane PC/aldehyde tail PC/aldehyde headgroup decane/aldehyde headgroup DMF/aldehyde headgroup

0.026 0.026 −0.049 0.01 0.000



Article

independent from temperature and, in case of combinations with an aldehyde tail group, independent from the number of C atoms of the aldehyde tail group. The kij values of decane/aldehyde tail group combinations were found to follow a linear trend, given in eq 5, which depends on the number of C atoms of the aldehyde tail group. kij = 0.009375C − 0.09375

(5)

Concerning DMF/alkane combinations (i.e., DMF/decane, DMF/aldehyde tail group), it was observed that there also exists a relation between the kij values. The kij values were calculated using the expression given in eq 6, whereby C is the number of C atoms of the alkane and T is the temperature in K. The expression was determined by fitting kij values to binary LLE data of different DMF/alkane systems including LLE data of DMF/ hexane,32,33 DMF/heptane,32,33 DMF/octane,32,33 DMF/nonane,33 and DMF/decane.9,24,34 kij = − 0.000315

T + 0.001359C + 0.102308 K

Figure 9. Liquid−liquid equilibrium of the system PC/decane/butanal at 298.15 K. Symbols are experimental data measured within this work. Solid line is modeling with PCP-SAFT using the parameters in Table 5.

(6)

Modeled LLE data for the PC/decane system are shown in comparison with experimental data of this work in Figure 8.

Figure 10. Liquid−liquid equilibrium of the system PC/decane/ dodecanal at 298.15 K. Symbols are experimental data measured within this work. Solid line is modeling with PCP-SAFT using the parameters in Table 5. Figure 8. Liquid−liquid equilibrium of the system PC/decane. Symbols are experimental data measured within this work. Solid line is modeling with PCP-SAFT using the parameters given in Table 5.

Figure 8 illustrates that modeled and experimentally determined LLE data for the system PC/decane coincide well taking into account the scaling of the axis of the mole fraction. Discrepancies between measured and modeled data increase with increasing temperature. In Figures 9 and 10, exemplary modeling results for the systems PC/decane + aldehyde are given in comparison with the corresponding experimental data. The LLE data of the system PC/decane + butanal (C4) are shown in Figure 9, and in Figure 10, the LLE data for PC/decane + dodecanal (C12) are presented. Regarding the DMF/decane + aldehyde systems, experimental and modeled data are shown in Figures 11 and 12 for the butanal (C4) and for the tridecanal (C13) mixtures. As can be seen from Figures 9−12, the modeled LLE data reproduce the corresponding experimentally determined LLE data satisfactorily for the DMF as well as for the PC systems. A clear trend concerning the relationship between coincidence of modeled and experimental data and the chain length of the

Figure 11. Liquid−liquid equilibrium of the system DMF/decane/ butanal at 298.15 K. Symbols are experimental data measured within this work Solid line is modeling with PCP-SAFT using the parameters in Table 5.

aldehyde can not be discovered. The concept of the heterosegmented modeling approach to describe the aldehyde 14532



Article

heterosegmented modeling approach applied to the aldehyde molecules works for all chain lengths of linear aldehydes investigated. It can be concluded that the modeling concept, which describes the aldehyde as consisting of an apolar tail and a polar headgroup, provides suitable LLE modeling results.

■

ASSOCIATED CONTENT

S Supporting Information *

Correlation coefficients (a,b) and coefficients of determination (R2) for the Othmer−Tobias plots (Table S1). This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Fax: +49 231 755 2572. E-mail: [email protected]. Figure 12. Liquid−liquid equilibrium of the system DMF/decane/ tridecanal at 298.15 K. Symbols are experimental data measured within this work Solid line is modeling with PCP-SAFT using the parameters in Table 5.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank the Deutsche Forschungsgemeinschaft (DFG) for financial support within the Sonderforschungsbereich/Transregio 63 Integrated Chemical Processes in Liquid Multiphase Systems.

molecules works for all chain lengths of linear aldehydes investigated.

■

5. CONCLUSION In this work, binary LLE data for the system PC/decane (288.15 to 403.15 K) and ternary LLE data for the systems DMF/decane + linear aldehyde and PC/decane + linear aldehyde at 298.15 K were measured. The linear aldehydes employed in this work were butanal (C4), octanal (C8), decanal (C10), dodecanal (C12), and tridecanal (C13). Application of the Othmer−Tobias correlation to the ternary LLE data confirmed the data to be reliable. The LLE data of the ternary systems were used to calculate the distribution coefficients of the aldehydes between the polar DMF-, respectively PC-rich phase and the apolar decane-rich phase. A clear correlation between the chain length of the aldehyde and the quantity of the distribution coefficients was observed: the longer the chain length of the aldehyde, the larger the average distribution coefficients of the aldehyde in relation to the decane-rich phase. Concerning the TMS system concept, large distribution coefficients of the aldehyde with respect to the apolar phase are essential for an efficient catalyst/product separation after the hydroformylation reaction, since the catalyst is mainly soluble in the polar phase. That means, the TMS system concept is especially appropriate for the production of long-chain aldehydes via hydroformylation. In general, the presented data demonstrate that the influence of the product and the educt, respectively, on the phase behavior of the TMS system must not be neglected if an appropriate TMS systems has to be selected. In our previous work, it was demonstrated by hydroformylation experiments using DMF/decane as TMS system that low catalyst loss can be achieved. At a DMF/decane ratio of 50:50 (g/g), catalyst leaching was 7 ppm.9 The large distribution coefficients of long-chain aldehydes determined in this work for the solvent systems DMF/decane and PC/decane confirm that these systems are probably appropiate solvent systems for the hydroformylation of long-chain alkenes. The above-mentioned LLE data were modeled employing the PCP-SAFT equation of state using a heterosegmented approach to describe the aldehyde molecules. The modeled LLE data reproduce the corresponding experimentally determined LLE data successfully for all DMF and PC systems. That means, the

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