Phase Equilibria for the Hydroesterification of 10-Undecenoic Acid

Article pubs.acs.org/jced

Phase Equilibria for the Hydroesterification of 10-Undecenoic Acid Methyl Ester Max Lemberg and Gabriele Sadowski* Department of Biochemical and Chemical Engineering, Laboratory of Thermodynamics, TU Dortmund University, Emil-Figge-Straße 70, D-44227 Dortmund, Germany ABSTRACT: This paper investigates phase equilibria of interest for the hydroesterification of 10-undecenoic acid methyl ester with methanol and carbon monoxide to dodecanedioic acid dimethyl ester in a solvent system composed of methanol and ndodecane. Carbon monoxide solubilities were measured in 10-undecenoic acid methyl ester, dodecanedioic acid dimethyl ester, and a mixture of methanol/dodecanedioic acid dimethyl ester at 363 and 393 K and at pressures up to 15 MPa. Vapor−liquid equilibrium measurements in the systems methanol/10-undecenoic acid methyl ester, methanol/dodecanedioic acid dimethyl ester, n-dodecane/10-undecenoic acid methyl ester, n-dodecane/dodecanedioic acid dimethyl ester, and 10-undecenoic acid methyl ester/dodecanedioic acid dimethyl ester were performed at temperatures between 342 and 437 K and at pressures of 2 or 80 kPa. The measured data were accurately modeled using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT).

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version as well as high selectivity.11 For the HE of 10-UME, Gaide et al. proposed a methanol/n-dodecane TMS and two palladium-complex catalysts with methanesulfonic acid (MSA) as cocatalyst.12,13 Two mechanistic pathways are assumed to be possible for the HE, whereby for the HE of alkenes the hydride pathway is preferred in recent publications.14−16 For the HE of plant oils, Roesle et al.17 reported a catalytically active palladium-hydride species. As described by Gaide et al.,12,13 MSA stabilizes and supports the formation of palladium−hydride complexes. Therefore, the hydride pathway is very likely for the HE investigated in this work. For reactions following the hydride pathway, a nonlinear relation between the reaction rate and the CO-pressure was observed, indicating that CO not only acts as a reactant but also adds to catalytic intermediates and thereby competes with the subtrates.14,18 Also, a maximum reaction rate at a certain CO pressure and a dependence of the selectivity for the linear product on the CO pressure was observed. As these effects are not directly connected to the CO pressure as such, rather to the concentration of CO in the liquid phase, reliable gas-solubility data are necessary for the analysis and description of these effects. For the TMS components methanol and n-dodecane, CO solubility data are available in literature. CO solubility data in methanol were reported from various sources19−24 with different reliabilities.19 The most consistent data that also cover a broad temperature range and high pressure were published by Brunner et al.19 CO solubility data in n-dodecane are available from Gasem et al.25 and Makranzy et al.,26 whereby only Gasem et al. report high-pressure data in a

INTRODUCTION The limitation of fossil resources and their worldwide increasing consumption demand new pathways for the production of energy and chemicals. Today, the vast majority of organic chemicals is produced out of fossil resources. The processing of renewable feedstocks is thereby the only sustainable alternative and offers a great potential, as at the moment they only contribute about 10% to the raw materials for chemical industry in Germany and the US.1,2 One promising transformation of renewables poses the hydroesterification (HE) of oleo compounds, as they already provide necessary CC-double bonds.3 This work refers to the HE of 10-undecenoic acid methyl ester (10-UME), a linear ricin oil-based fatty acid ester,4 with methanol and carbon monoxide (CO) to dodecanedioic acid dimethyl ester (DDDME) according to Figure 1. DDDME, as a α,ω-diester, can subsequently be used as a monomer unit for the formation of polyesters and polyamides.5,6 As the HE is homogeneously catalyzed by transition-metal complexes, a complete recovery and reuse of the catalyst is necessary for industrial applications from the economical as well as ecological point of view.7 One strategy that allows an effective recycling of homogeneous catalysts is the application of temperature-dependent multicomponent solvent (TMS) systems.7−9 TMS systems usually consist of a polar and a nonpolar solvent that show a temperature-dependent miscibility gap. This allows to perform the reaction at higher temperatures in the homogeneous system without masstransfer limitations. For separation, the mixture is cooled down and forms a product-rich and a catalyst-rich phase. In this way, catalyst recycling and product removal are achieved in one step.10 It has been shown that TMS systems are applicable to various C−C-bond-forming reactions and allow high con© 2016 American Chemical Society

Received: May 2, 2016 Accepted: August 3, 2016 Published: August 12, 2016 3317

DOI: 10.1021/acs.jced.6b00360 J. Chem. Eng. Data 2016, 61, 3317−3325

Journal of Chemical & Engineering Data

Article

Figure 1. HE reaction of 10-UME to DDDME.

relevant temperature range. For the reacting agents 10-UME and DDDME, CO solubility data are not available to best of our knowledge. Within this work, the CO solubility in 10-UME and DDDME was measured at temperatures between 363 and 393 K up to pressures of 13.5 MPa. As the CO solubility is influenced by all components in the reaction mixture, the CO solubility in pure components is no sufficient basis for reaction optimization and process development. On the other hand, tremendous effort would be necessary to scan the quaternary reaction mixture (methanol, n-dodecane, 10-UME, DDDME) at all relevant compositions via CO solubility measurements. Therefore, a thermodynamic model was applied in this work to reduce the experimental effort. As gE-models can describe gas solubilities only at rather low pressures,27−29 their application to the HE of oleocompounds, which is performed at pressures above 2 MPa,12,17,30 is unsuitable. In contrast to this, equations of state allow the description of gas solubilities up to high pressures.31,32 In this work, the Perturbed-Chain Statistical Associating Fluid Theory33 (PC-SAFT) was used for the modeling. As it was shown earlier, PC-SAFT has excellent correlative and also predictive capabilities for the phase behavior of binary systems containing various gases and liquids over a broad temperature and pressure range.34−37 Furthermore, PC-SAFT explicitly accounts for associative interactions like hydrogen bonds (as e.g. for methanol).37−40 Also, it is applicable for the description of multicomponent systems containing gases up to high pressures.41−43 Recently, PC-SAFT was also applied to systems relevant for the hydroformylation of 1-dodecene and proved to allow very good predictions of gas solubilities in multicomponent systems based on the knowledge of binary systems only.44−46 In this work the same procedure as for the hydroformylation reaction was applied here to the hydroesterification system. Along with CO solubilities, binary vapor−liquid equilibria (VLEs) are presented for the liquid components (methanol, ndodecane, 10-UME, DDDME) and modeled with PC-SAFT.

In this work the polar contribution was set to zero, as the dipole moments of the components in this work are negligible except for methanol. Methanol was instead treated as associating compound. For the modeling of pure components with PC-SAFT, in general three parameters are needed. These are the segment number miseg, the segment diameter σi and the dispersionenergy parameter ui/kB. In case of associating components, two additional parameters, namely, the association volume κAiBi and the association energy parameter εAiBi/kB, are required. The pure-component parameters were identified by fitting them to vapor pressures and liquid densities of the respective components. Mixtures of components are described by applying Berthelot−Lorenz mixing rules: σi + σj σij = (2) 2 uij = (1 − kij) uiuj

Herein, kij is a binary parameter that corrects the dispersion energy between unlike components and is usually fitted to binary phase-equilibrium data. The kij parameter can be treated as temperature-dependent according to

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kij = aT + b

(4)

MATERIALS All chemicals used in this work are summarized in Table 1. They were used as purchased without further purification. The Table 1. Chemicals Used for Experiments within This Work

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THEORY In this work, PC-SAFT33 was applied for the modeling of the experimental data. The PC-SAFT model is a modification of the earlier-published SAFT model47 and also considers a molecule as a chain composed of freely jointed spherical segments. The interaction between two chains is described by applying the perturbation theory of Barker and Henderson48 to a hard-chain reference system (hc). The reference system thereby accounts for the repulsive interactions between the chains. The attractive part of the interaction is, as characteristically for perturbation theories, described by different attractive perturbations of the reference system such as dispersion (disp), association (assoc) and polar interations (dipole). In this way, the residual (res) Helmholtz energy of a system ares is calculated as the sum of separate contributions: a res = a hc + adisp + aassoc + adipole

(3)

chemical

supplier

purity/%

CO methanol n-dodecane 10-UME DDDME

Messer Industriegase GmbH Merck KGaA Alfa Aesar GmbH & Co KG TCI Europe N.V. TCI Europe N.V.

>98 99.9 >99 97.2 >98

purity of CO is given in volume percent. All other purities are defined as share of area in the gas chromatogram as determined by the manufactures.

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METHODS Liquid-Density Measurements. For the pure components 10-UME and DDDME, liquid densities were measured at ambient pressure (101.3 kPa) and 40 MPa using the vibrationtube densimeters DMA 602 and DMA 512 (Anton Paar KG, Graz, Austria), respectively. These were used in combination with the data interpretation unit DMA 60. For the DMA 602, air and water were used for calibration. The ambient pressure was measured with a GE DPI 740 precision pressure indicator. The DMA 512 was calibrated using n-hexane and water. The pressure was measured with a WIKA bourdon-tube gauge (0− 60 MPa, accuracy class 1.0). The temperature in both apparatuses was measured using a Pt 100 resistance

(1) 3318



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thermometer with an uncertainty of ±(0.30 + 0.005(T − 273.15)) K. The relative uncertainty of the measured densities was estimated based on the purity of the substances according to Chirico et al.49 to ur(ρ10‑UME) = 0.0028 and ur(ρDDDME) = 0.002. VLE Measurements. VLE measurements of the binary mixtures were performed in a dynamic equilibrium apparatus as introduced by Rogalski and Malanowski50 at pressures of 2 or 80 kPa depending on the system. The apparatus (NORMAG GmbH, Ilmenau, Germany) consist of an electric heating at the bottom, an equilibrium chamber with an oil-filled heating jacket, and a condenser for the vapor phase. The oil and the cooling water were temperated using Lauda ECO RE 420 thermostats (LAUDA Dr. R. Wobser GmbH & Co. KG, LaudaKönigshofen, Germany). The temperature in the equilibrium chamber was measured using a Pt100 resistance thermometer with an uncertainty of ±(0.15 + 0.002(T − 273.15)) K. The pressure in the apparatus was adjusted by a vacuum pump (PC 3004 Vario, Vacuubrand, Wertheim, Germany) with an uncertainty according to the manufacturer of u(p) = 0.1 kPa. The experimental procedure was the same as described in a previous work10 of our group. For the systems n-dodecane/10UME and n-dodecane/DDDME, the analysis of the two phases was carried out by measuring the refractive index (AbbeRefractometer model A, Carl Zeiss AG, Oberkochen, Germany). The systems methanol/10-UME and 10-UME/ DDDME were analyzed via gas chromatography (7890A GC, Agilent Technologies, Santa Clara, USA). All samples were measured 3-fold, and average values are reported. CO Solubility Measurements. CO solubility measurements were performed in a high-pressure view cell with variable volume (New Way of Analytics GmbH, Lörrach, Germany). The volume in the cell can be adjusted hydraulically from 30 to 60 mL by a movable piston. A sapphire window at the front of the cell allows the observation of the phase behavior during the experiments at high pressure. The cell is equipped with an electric stirrer for quick equilibration and an electric heating jacket. The temperature and pressure were measured directly in the cell via a Pt100 resistance thermometer (uncertainty 0.1 K) and a WIKA S11 pressure transmitter (pmax = 40 MPa), respectively. The measurement was performed according to the synthetic method, which means that the composition in the cell was known and the phase transition pressure was measured. For that purpose a syringe pump (260D, Teledyne Isco, Lincoln, USA) was used to dose the compressed CO into the cell. The experimental procedure was the same as already described in a previous work44 of our group. There it was also shown that gas solubility data obtained with this method is in good agreement (deviation less than 2%) with experimental data from the literature.

(Table 2). Vapor pressures were available from literature51 over a temperature range from 400 to 500 K and from 440 to 560 K, respectively. Table 2. Liquid Densities of 10-UME and DDDME at 101.3 kPa and 40 MPa Measured in This Worka T/K

ρ10‑UME/(kg/m3) at 101.3 kPa

ρ10‑UME/(kg/m3) at 40 MPa

280.15 293.15 303.15 313.15 323.15 333.15 343.15 352.15

897.46 886.83 878.63 870.71 862.33 854.49 845.80 838.42

914.37 906.75 895.63 888.48 881.75 874.61

ρDDDME/(kg/m3) at 101.3 kPa

959.4 951.0 943.1 934.4 927.0

Uncertainties are u(T) = (0.30 + 0.005(T − 273.15)) K, u(p = 101.3 kPa) = 0.1 kPa, u(p = 40 MPa) = 0.6 MPa, ur(ρ10‑UME) = 0.0028, and ur(ρDDDME) = 0.002. a

For the liquid density of 10-UME at ambient pressure 101.3 kPa, also literature data is available.52 In Figure 2, these data are compared to the data measured within this work.

Figure 2. Liquid densitiy of 10-UME at 101.3 kPa. Symbols are experimental data measured within this work (circles) and from the literature52 (squares).

As it can be seen, the data sets are in very good agreement. With increasing temperature the deviation increases to about 2 kg/m3 at 360 K, which lies within the uncertainty range of the data measured within this work. The densities of the data sets at lower temperatures are nearly identical. The literature data was measured using a pycnometer which was calibrated with water.53 The authors did not mention whether the thermal expansion of the glass vessel at higher temperatures was taken into account. The thermal expansion leads to an increase of the pycnometer-volume which could explain why the literature density at higher temperatures is higher than the density measured within this work. The liquid density of 10-UME given in Table 2 and vapor pressure of 10-UME from the literature51 could be described with PC-SAFT by fitting three pure-component parameters with an average relative deviation (ARD) of 0.78% and 1.93%, respectively. ARDs of 0.08% and 1.94% resulted for liquid densities and vapor pressures of DDDME, respectively. The pure-component PC-SAFT parameters of all components considered in this work are presented in Table 3. Binary Parameters. To allow a description of the whole multicomponent system considered within this work with PCSAFT, ten binary kij parameters have to be known for the pairs

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RESULTS AND DISCUSSION PC-SAFT Parameters. Pure-Component Parameters. The pure-component parameters for three out of five components that are considered in this work (CO, methanol, n-dodecane) were already available from literature. All components except methanol were treated as apolar and nonassociating components, as their dipole moment is negligible and they do not form hydrogen bonds. Methanol was modeled as an associating component. Parameters for 10-UME and DDDME were fitted within this work to liquid densities and vapor pressures of these components. Liquid densities were measured in this work 3319



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Table 3. Pure-Component Parameters Applied in This Work substance

miseg

σi/Å

ui/kB/K

CO methanol n-dodecane 10-UME DDDME

1.3097 1.5255 5.3060 6.9385 8.8381

3.2507 3.2300 3.8959 3.5338 3.4575

92.15 188.90 249.21 237.68 237.25

κAiBi

εAiBi/kB/K

0.035176

ref 33 38 33 this work this work

2899.5

of the five components. Figure 3 gives an overview of the kind of phase equilibrium data that was used to fit the kij parameters.

Figure 4. Boiling pressure of a methanol/n-dodecane mixture (xmethanol = 0.849) over temperature. The circles are experimental data.54 The line was modeled with PC-SAFT. Figure 3. Overview of the kinds of phase equilibrium data that were used to fit the binary kij parameters. kij’s that were fitted to CO solubility data are represented by gray arrows. White arrows indicate the kij’s that were fitted to VLE data. Dashed edging marks that the phase equilibrium data was available from literature.

As the experimental data covers a broad temperature range from 420 to 540 K, a temperature-dependent kij was used for the modeling (Table 4). This allowed a highly accurate description over the whole temperature range with an ARD of only 0.93%. VLE data for the system methanol/10-UME was measured at 80 kPa over a temperature range from 342 to 373 K (Table 5). The experimental data together with the modeling results are shown in Figure 5.

In general, kij’s between CO and one of the other components were fitted to binary CO solubility data, and kij’s between two of the other components were fitted to binary VLE data. An exception was made in the case of the system methanol/DDDME, as the VLE of these components is not sensitive to the kij parameter. The kij was instead fitted to ternary CO solubility data. For the binary systems CO/ methanol, CO/n-dodecane, and methanol/n-dodecane, phaseequilibrium data were available in the literature19,25,54 and was not measured again in this work. The kij between CO and ndodecane was already published by Ghosh et al.34 The remaining nine kij’s were fitted in this work. All obtained kij’s are summarized in Table 4. Experimental and Modeling Results. VLEs. The equilibrium pressure for the system methanol/n-dodecane, as a function of temperature for different methanol mole fractions in the liquid phase (xmethanol), was reported by Loos et al.54 The data for xmethanol = 0.849 was found to be most sensitive for kij and was therefore used for the fitting. The modeling results as well as the experimental data are shown in Figure 4.

Table 5. VLE of Methanol with 10-UME at 80 kPa Measured in This Worka T/K

xliquid methanol

373.35 365.05 356.55 356.35 353.45 349.75 348.05 345.45 344.25 341.85

0.134 0.136 0.177 0.176 0.176 0.264 0.272 0.280 0.280 0.345

Uncertainties are u(p) = 0.1 kPa, u(T) = (0.15 + 0.002(T − 273.15)) K and u(xliquid methanol) = 0.023. a

Table 4. Binary Parameters Applied in This Work substance i

substance j

kij

AAD

ARD/%

CO CO CO CO methanol methanol methanol n-dodecane n-dodecane 10-UME

methanol n-dodecane 10-UME DDDME n-dodecane 10-UME DDDME 10-UME DDDME DDDME

0.042 0.12534 0.059 0.067 3.6960 × 10−4 T/K − 0.0952 −2.4444 × 10−3 T/K + 0.80333 −0.047 0.0168 0.0162 0.0097

59 kPa

1.02

84 kPa 121 kPa 47 kPa 2.92 K 195 kPa 0.86 K 2.77 K 1.75 K

1.29 2.89 0.93 0.81 2.37 0.22 0.70 0.42

3320

ref. for phase equilibrium data 19 25 this this 54 this this this this this

work work work work work work work



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Figure 6. VLE of n-dodecane with 10-UME at 2 kPa. The circles are experimental data as reported in Table 6. The lines were modeled with PC-SAFT.

Figure 5. VLE of methanol with 10-UME at 80 kPa. The circles are experimental boiling points as reported in Table 5. The line was modeled with PC-SAFT.

Table 7. VLE of n-Dodecane with DDDME at 2 kPa Measured in This Worka

The system shows a highly nonideal boiling-point curve as the pure-component boiling-points of methanol and 10-UME differ enormously (about 140 K at 80 kPa). Starting at pure methanol, the boiling-point curve increases only by approximately 10 K until a methanol mole fraction of 0.3. From this point on to pure 10-UME the boiling-point curve increases by approximately 130 K. To allow an accurate description of the boiling temperatures, a temperature-dependent kij was applied (Table 4) allowing for a description with an ARD of only 0.81%. The VLE of the system n-dodecane/10-UME was measured at 2 kPa between 372 and 393 K. Experimental data are reported in Table 6. Table 6. VLE of n-Dodecane with 10-UME at 2 kPa Measured in This Worka T/K

xliquid n‑dodecane

xvapor n‑dodecane

392.85 392.65 390.95 387.45 387.35 384.45 384.15 380.75 379.65 376.55 376.35 374.45 374.35 373.75 372.25

0.144 0.165 0.197 0.277 0.265 0.352 0.339 0.474 0.560 0.729 0.713 0.925 0.875 1.000 1.000

0.446 0.446 0.531 0.635 0.635 0.729 0.761 0.809 0.842 0.942 0.925 0.976 0.976 1.000 1.000

T/K

xliquid n‑dodecane

xvapor n‑dodecane

426.05 421.25 415.75 412.55 408.95 401.65 396.75 395.65 389.45 386.95 383.85 379.25 378.35 377.35 376.15 373.15 372.25

0.088 0.091 0.109 0.131 0.131 0.168 0.210 0.221 0.361 0.377 0.468 0.666 0.694 0.763 0.809 1.000 1.000

0.809 0.851 0.903 0.910 0.932 0.965 0.961 0.965 0.976 0.987 0.976 0.987 0.990 0.987 0.987 1.000 1.000

Uncertainties are u(p) = 0.1 kPa, u(T) = (0.15 + 0.002(T − 273.15)) vapor K, u(xliquid n‑dodecane) = 0.015, and u(xn‑dodecane) = 0.005. a

a Uncertainties are u(p) = 0.1 kPa, u(T) = (0.15 + 0.002(T − 273.15)) vapor K, u(xliquid n‑dodecane) = 0.031, and u(xn‑dodecane) = 0.012.

Figure 7. VLE of n-dodecane with DDDME at 2 kPa. The circles are experimental data as reported in Table 7. The lines were modeled with PC-SAFT.

As shown in Figure 6, the two-phase region shows to be comparably small, as the pure-component boiling points only differ by about 30 K. The modeling with a very small and temperature-independent kij (Table 4) allows a very accurate description of the experimental data with an ARD of 0.22%. The dew-point curve is overestimated only slightly for higher 10-UME concentrations. For the system n-dodecane/DDDME, VLE data were measured at 2 kPa from 372 to 426 K (Table 7). The experimental and modeling results are shown in Figure 7.

Again, the application of a very small and temperatureindependent kij (Table 4) allows a highly accurate description with an ARD of 0.70%. The 10-UME/DDDME VLE was measured at 2 kPa between 402 and 437 K. The experimental data are reported in Table 8. As shown in Figure 8, the modeling is in very good agreement with the experimental data. Using a temperatureindependent kij (Table 4) an ARD of 0.42% could be achieved. Only at higher 10-UME concentrations, the experimental 3321



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Within the considered concentration range, the CO solubility shows a linear increase with pressure. Furthermore, the CO solubility increases with temperature. This temperature dependency is contrary to the common sense that gas solubility decreases with increasing temperature. However, it was observed also for other gases as already discussed in a previous work of our group.44 Although the temperature dependence for the gas solubility of CO does not follow common sense, PCSAFT is able to predict this effect qualitatively correct even using kij equal to zero because of its physical background. For a quantitative modeling of the gas solubility data of CO/ methanol, a temperature-independent kij was applied (Table 4) and allowed an accurate description of the two isotherms with an ARD of 1.02%. The CO solubility in 10-UME was measured in this work at 363 and 393 K at pressures up to 11.8 MPa (Table 9).

Table 8. VLE of 10-UME with DDDME at 2 kPa Measured in This Worka T/K

xliquid 10‑UME

xvapor 10‑UME

436.95 434.05 428.85 428.25 424.95 424.55 419.05 418.75 414.95 414.35 409.45 405.45 402.65 401.95

0.114 0.154 0.220 0.190 0.303 0.257 0.383 0.413 0.518 0.541 0.701 0.858 1.000 1.000

0.704 0.717 0.790 0.779 0.851 0.831 0.883 0.906 0.937 0.942 0.965 0.984 1.000 1.000

Table 9. CO Solubility in 10-UME at Different Temperatures Measured in This Worka

Uncertainties are u(p) = 0.1 kPa, u(T) = (0.15 + 0.002(T − 273.15)) vapor K, u(xliquid 10‑UME) = 0.016, and u(x10‑UME) = 0.011. a

T/K

u(T)/K

p/MPa

xliquid CO

362.71 362.71 362.71 362.71 362.71 362.71 393.04 393.04

0.12 0.12 0.12 0.12 0.12 0.12 0.18 0.18

2.978 3.010 7.372 7.424 11.812 11.913 6.947 11.089

0.0434 0.0422 0.0994 0.0990 0.1500 0.1501 0.0990 0.1501

a Uncertainties u(T) are reported. The other uncertainties are u(p) = 33 kPa and ur(xliquid CO ) = 0.026.

Figure 8. VLE of 10-UME with DDDME at 2 kPa. The circles are experimental data as reported in Table 8. The lines were modeled with PC-SAFT.

A shown in Figure 10, the CO solubility increases with pressure. Again, the CO solubility also increases with

boiling points are found slightly below the modeled curve. A reason for this could be the insufficient purity of the used 10UME (97.2%). CO Solubilities. For the system CO/n-dodecane, a kij was already reported by Ghosh et al.34 (Table 4). This system was not considered within this work again. The CO solubility data in methanol were available from Brunner et al.19 over broad pressure and temperature ranges. For the kij-fitting, the isotherms at 323 and 373 K were used at pressures up to 11.3 MPa. The modeling results as well as the experimental data are shown in Figure 9.

Figure 10. CO solubility in 10-UME. The symbols are experimental data at 362.71 K (circles) and 393.04 K (squares) as reported in Table 9. The lines were modeled with PC-SAFT.

temperature. In comparison to methanol, the solubility in 10UME, expressed in mole fraction xCO, is three to four times higher. The main reason for this is the big difference in molar mass between methanol and 10-UME. 10-UME molecules are way bigger than methanol molecules and can therefore be surrounded by more CO molecules. But expressed in weight fraction wCO, the CO solubility in methanol is approximately 50% higher than in 10-UME. This means that per kilograms of solvent, CO is actually better soluble in methanol than in 10UME. The experimental data could be described using a small and temperature-independent kij (Table 4) with an ARD of 1.29%.

Figure 9. CO solubility in methanol. The symbols are experimental data19 at 323.15 K (circles) and 373.15 K (squares). The lines were modeled with PC-SAFT. 3322



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modeling of the ternary system CO/methanol/DDDME only the kij between methanol and DDDME was fitted as the other two were already determined. As shown in Figure 11, a good agreement between modeling and experimental results could be achieved in this way with an ARD of 2.37%.

For the system CO/DDDME, gas solubility data were measured at 363 and 393 K up to 13.5 MPa (Table 10). The Table 10. CO Solubility in DDDME at Different Temperatures Measured in This Worka T/K

u(T)/K

p/MPa

xliquid CO

362.63 362.63 362.63 362.63 362.63 362.63 392.87 392.87 392.87

0.10 0.10 0.10 0.10 0.10 0.10 0.28 0.28 0.28

3.500 3.523 8.456 8.524 13.243 13.491 3.121 7.747 12.213

0.0431 0.0431 0.1015 0.1018 0.1512 0.1499 0.0418 0.1009 0.1501

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CONCLUSION Within this work, phase equilibria for the HE reaction of 10UME with methanol and CO in a TMS were investigated. New VLE data were measured for the systems methanol/10-UME, n-dodecane/10-UME, n-dodecane/DDDME, and 10-UME/ DDDME at different temperatures between 342 and 437 K. Also, CO solubilites in 10-UME, DDDME, and in a mixture of methanol/DDDME at 363 and 393 K were measured for the first time. Completed by literature data for the VLE methanol/ n-dodecane, CO solubility in methanol, and in n-dodecane, an experimental database for a full thermodynamic description of the reaction system was established. For the modeling of the mentioned subsystems, PC-SAFT was applied. New pure-component parameters for 10-UME and DDDME were identified by fitting them to liquid densities measured within this work and vapor pressures taken from the literature. Out of ten binary kij parameters, nine were unknown and were determined within this work by fitting them to the VLE and CO solubility data. For the VLEs it was observed, that the two-phase regions get broader, if the difference between the pure component boiling points increases. For components with a very different volatility like methanol/10-UME the vapor phase consists of nearly pure low-boiling component over a big part of the concentration range in the liquid phase. All investigated CO solubilities increased with temperature. The CO solubility in mole fraction was found to be very similar for the systems CO/10-UME and CO/DDDME as these components are both long chain molecules. In contrast to this, the CO solubility in mole fraction in methanol is three to four times lower. The main reason for this is that methanol is a quite smaller molecule and can therefore be surrounded by less CO molecules than 10-UME and DDDME. Expressed in weight fraction, the solubility in methanol is approximately 50% higher than in 10-UME and DDDME. Most phase equilibria could be described with PC-SAFT highly accurate by applying temperature-independent kij parameters. Only for the VLEs methanol/n-dodecane and methanol/DDDME linear temperature-dependent kij parameters were used. The temperature dependence for the CO solubilities could be described accurately with PC-SAFT using temperature-independent kij parameters. For further investigations on the reaction, CO solubilities can be predicted in multicomponent mixtures of the considered components as all PC-SAFT parameters are known. This reduces experimental effort significantly. Furthermore, PCSAFT can be applied in subsequent works to model and predict the chemical equilibrium of the reaction.

a

Uncertainties u(T) are reported. The other uncertainties are u(p) = 35 kPa and ur(xliquid CO ) = 0.026.

Table 11. CO Solubility in a Mixture of Methanol and DDDME (xmethanol = 0.857 in the Gas-Free System) Measured in This Worka T/K

u(T)/K

p/MPa

xliquid CO

362.68 362.68 362.68 362.68

0.17 0.17 0.17 0.17

7.282 7.343 14.769 14.885

0.0350 0.0350 0.0707 0.0708

a Uncertainties u(T) are reported. The other uncertainties are u(xmethanol) = 0.001, u(p) = 28 kPa, and ur(xliquid CO ) = 0.026.

CO solubility in a methanol/DDDME mixture was measured at 363 K up to a pressure of 14.9 MPa. The experimental data of the two systems together with the modeling results are shown in Figure 11.

Figure 11. CO solubilities in a mixture of methanol/DDDME (xmethanol = 0.857 in the gas-free system) and in pure DDDME. Symbols are experimental data with the mixture at 362.68 K (triangles), with pure DDDME at 362.62 K (circles) and 392.87 K (squares) as reported in Tables 10 and 11. The lines were modeled with PC-SAFT.

It can be seen that the CO solubility in the mixture of methanol/DDDME is approximately half as high as in pure DDDME. This was expected as the CO solubility in methanol is low (Figure 9). The CO solubility in DDDME is only slightly lower as in 10-UME as these components are very similar in their molecular structure (Figure 1). For pure DDDME, the CO solubility again increases with temperature, as observed for all systems in this work. The system CO/DDDME could be described with an ARD of 2.89% using a temperature-independent kij (Table 4). For

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

Financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) is gratefully acknowledged (TRR 63). 3323



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Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is part of the Collaborative Research Center/ Transregio 63 “Integrated Chemical Processes in Liquid Multiphase Systems” (subproject A4).

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ABBREVIATIONS AND VARIABLES a Helmholtz energy AAD average absolute deviation ARD average relative deviation assoc association CO carbon monoxide DDDME dodecanedioic acid dimethyl ester disp dispersion εAiBi/kB association energy parameter GC gas chromatography hc hard-chain κAiBi association volume binary interaction parameter kij miseg segment number MSA methanesulfonic acid p pressure PC-SAFT Perturbed Chain Statistical Associating Fluid Theory ρ density σi segment diameter T temperature TMS Temperature-dependent Multicomponent Solvent u uncertainty ur relative uncertainty ui/kB dispersion-energy parameter 10-UME 10-undecenoic acid methyl ester VLE vapor−liquid equilibrium x mole fraction

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Phase Equilibria for the Hydroesterification of 10-Undecenoic Acid

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