Phase Behavior of Binary Mixtures Containing ... - ACS Publications

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Phase Behavior of Binary Mixtures Containing Succinic Acid or Its Esters Emrah Altuntepe, Annika Reinhardt, Joscha Brinkmann, Tom Briesemann, Gabriele Sadowski, and Christoph Held* Laboratory of Thermodynamics, Department of Biochemical and Chemical Engineering, Technische Universität Dortmund, Emil-Figge-Strasse 70, 44227 Dortmund, Germany S Supporting Information *

ABSTRACT: This work provides experimental data and thermodynamic modeling on phase equilibria of binary mixtures that are relevant for esterification reactions. The components under investigation include water, succinic acid (SA), ethanol (EtOH), 1-butanol (1-BuOH), and the diesters of SA, namely, diethyl succinate (DES) and dibutyl succinate (DBS), respectively, as well as the organic solvents acetonitrile (ACN) and tetrahydrofuran (THF). Liquid−liquid equilibria (LLE) of water/DBS were measured at ambient pressure for temperatures between 313 and 353 K. Isobaric vapor−liquid equilibria (VLE) were measured for the binary systems ACN/DES, ACN/DBS, 1-BuOH/DBS, and THF/DBS at pressures of 10 or 20 or 30 kPa. Temperature ranges for the isobaric VLE varied between 300 and 500 K. The measured data and phase equilibria reported in literature were accurately modeled using perturbed-chain statistical associating fluid theory (PC-SAFT). For this purpose, pure-component PC-SAFT parameters, which were not already reported in the literature, were adjusted to experimental literature purecomponent data. Applying binary interaction parameters allowed precise phase-equilibrium modeling results of the binary systems under investigation. Two different association schemes for water were used (“2B” and “4C”). Both schemes appeared to be suitable to describe phase equilibria of aqueous mixtures; however, a binary parameter for the Wolbach−Sandler mixing rule was required for aqueous mixtures modeled with the 4C scheme. For LLE modeling the 2B scheme was found to give better modeling results. In general, the 4C association scheme for water yields better results for mixtures with two self-associating components while the 2B association scheme for water should be preferred if mixtures are considered with water and a non-selfassociating component. Further, the modeling concept of “induced association” has been investigated and discussed. Especially for mixtures with esters, which are of main importance for esterification mixtures, the induced-association approach turned out to be a more accurate modeling strategy compared to the nonassociative approach.

1. INTRODUCTION Carboxylic acids play an important role in chemical industry, pharmacy, food industry, and biotechnology. Within this class of compounds, succinic acid (SA) is among the most attractive chemicals as it is used as the starting point for many chemical derivatives. SA can be synthesized by fermentation replacing the chemical petroleum based synthesis route, which uses maleic anhydride.1−4 However, carboxylic acid streams obtained from fermentation processes contain huge diversity of impurities, and state-ofthe-art purification methods are very cost-intensive. Recovering carboxylic acids from fermentation broths is still an important research field as this step contributes up to 50−80% of the final costs of chemical processes.5−7 Reactive separation technologies such as reactive distillation or reactive extraction are attractive alternatives to the physical separation technologies for the recovery of SA from aqueous medium. In this context the esterification of SA is a practicable route, because the esters have promising potential for further synthesis and recovery.8−12 Esterification combines recovering SA and producing interest© XXXX American Chemical Society

ing derivatives in one step. Dimethyl esters and diethyl esters of dicarboxylic acids are valuable reactants for deriving further compounds.12 Diethyl succinate (DES) is reported to be an excellent solvent and to be a building block unit for the synthesis route to polybutylene succinate (PBS) polymers.13,14 The monoesters of dicarboxylic and monocarboxylic acids are also interesting compounds. Monoethyl succinate (MES) is reported to be used in diabetes treatment15,16 and can be used as the starting point for asymmetric synthesis of succinic ester and other derivatives.17 For concrete development of any separation process in which such esters are involved, basic thermodynamic data are needed for process design. There is still a lack of information on phase equilibria such as vapor−liquid, liquid−liquid, and solid−liquid equilibria (VLE, LLE, and SLE). LLE data exist for mixtures with esters/water/organic solvents, including different shortReceived: January 3, 2017 Accepted: June 9, 2017

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DOI: 10.1021/acs.jced.7b00005 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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kB is the Boltzmann constant. These three parameters are sufficient to characterize nonassociating pure components. If a component is regarded as being able to form association interactions, two further parameters are needed. These are the

chained esters of SA (methyl-, ethyl-, and isobutyl esters) and different organic solvents such as propionic acid, acetic acid, ethanol, or methanol.14,18−20 Phase-equilibrium data of mixtures of these esters with alcohol and/or with water are partly reported in the literature.13,21,22 In addition SLE data of SA/water and SA/alcohol mixtures are available in the literature.23−25 Besides the experimental data as such, further process intensification, optimization, and design require accurate thermodynamic modeling. The kinds of systems as investigated in this work (acid/water, acid/organic solvent, ester/water, and ester/organic solvent) are complex binary mixtures that are thermodynamically highly nonideal. A thermodynamic model appropriate to describe these mixtures must account for the strong associative interactions between like and/or unlike mixture constituents. Such a model should be further appropriate to the calculation of multicomponent systems including carboxylic acids and their esters, water, and organic solvents. Some efforts to model phase equilibria (VLE and LLE) of binary mixtures (and in some cases ternary) have been made in earlier works. These published efforts use different methods, e.g., excess Gibbs energy models (gE models) such as UNIFAC or UNIQUAC or NRTL.13,18,19,21 It has to be noted that these methods remain challenging for the application to multicomponent mixtures.26,27 Thus, using classical gE models such as UNIQUAC or NRTL to higher systems usually requires experimental data in these higher systems. PCSAFT28,29 has been shown to be predictive for the calculation of VLE and LLE in multicomponent mixtures, including those with carboxylic acids and even reactions with carboxylic acids.7,30,31 In most cases, phase equilibria of binary mixtures for the estimation of binary interaction parameters are required for PC-SAFT modeling multicomponent systems. This work aims at closing the gap of experimental phaseequilibrium data of binary mixtures and the corresponding modeling with PC-SAFT in order to apply these in the future to multicomponent esterification reaction mixtures. The systems under consideration contain SA and its ethyl and butyl esters, water, alcohols, and some organic solvents.

association parameters

and κ A i B i . For association

interactions, it is essential to define a specific number of associating sites Nassoc for each component. Thus, three or five i pure-component parameters have to be estimated for each component, which is usually realized by regression to experimental vapor pressures and densities of the pure components. To describe mixtures, combining rules are necessary for the PC-SAFT parameters. Lorentz−Berthelot combining rules are applied for the modeling of mixtures of components i and j for estimating the segment diameter σij and the dispersion energy uij σij =

1 (σi + σj) 2

uij =

(2)

uiuj (1 − kij)

(3)

Here kij is a binary interaction parameter between two components i and j and is introduced to correct the crossdispersion energy. In some cases, it is necessary to regard kij as temperature-dependent. Then kij is approximated with a linear function kij = kij , TT + kij , m

(4)

where T is the absolute temperature in Kelvin. Similar to the segment diameter and the dispersion energy, mixing rules have to be applied to the association parameters while modeling mixtures. In this work Wolbach−Sandler rules were used34 that may contain the binary interaction parameter kws ij ε A iBj =

2. PC-SAFT MODELING In this work, experimental data of pure components and binary systems were modeled using PC-SAFT equation of state (EOS). PC-SAFT is based on the statistical associating fluid theory (SAFT),32,33 which is a perturbation theory. Within classical PC-SAFT molecules are characterized as chains of equally sized hard spheres (the classical “homonuclear” approach). The so-called hard-chain system (hc) represents the reference system for PC-SAFT that is perturbed by additive energy contributions to residual Helmholtz energy (ares) in the form attractive Helmholtz energy contributions caused by dispersive van der Waals attraction (adisp) and association (hydrogen bonds; aassoc)28,29 a res = a hc + adisp + aassoc

ε A iBi kB

κ

A iBj

1 A iBi (ε + ε A jBj)(1 − kijws) 2

⎛

=

κ

(5)

⎞3 ⎟ ⎜ 1 (σ + σ ) ⎟ j ⎠ ⎝2 i

A iBi A jBj ⎜

κ

σσ i j

(6)

res

Once a is calculated, the fugacity coefficient of a component can be expressed through the equation ln(φi) = (Z − 1) − ln(Z) + a res +

∂a res − ∂xi

⎛ ∂a res ⎞ ⎟⎟ ⎝ ∂xj ⎠

∑ ⎜⎜ j

(7)

where Z is the compressibility factor which can be obtained through ⎛ ∂a res ⎞ ⎟⎟ Z(ρN ) = 1 + ρN ⎜⎜ ⎝ ∂ρN ⎠T , x

(1)

For specific applications, further perturbation terms can be conceivable, which are not considered in this work. The concrete equations behind eq 1 are described in the mentioned publications of Gross and Sadowski.28,29 Each component i must be parametrized for PC-SAFT calculations. It is described as a chain of mi segments, all having the same segment diameter σi. The dispersion interactions are characterized through a dispersion-energy parameter ui , where

(8)

ρN is the number density of the system. If the fugacity coefficient is available, the last step to obtain activity coefficients is ⎯⇀

γi =

kB

B

φi(T , p , x ) φ0i(T , p , xi = 1)

(9) DOI: 10.1021/acs.jced.7b00005 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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φi indicates the fugacity coefficient at a certain temperature and pressure. The vector of mole fractions indicates the actual composition of the solution. The subscript 0i denotes the reference state “pure component”. In cases where experimental data exist, the calculation was evaluated based on the absolute relative deviation (ARD) ARD = 100

NP y cal 1 ∑ 1 − kexp yk NP k = 1

vapor condenser were tempered using a Lauda thermostat ECO RE 420 (LAUDA Dr. R. Wobser GmbH & Co. KG, LaudaKönigshofen, Germany). The temperature in the equilibrium chamber was measured using a PT100 thermocouple. The system pressure in the apparatus was adjusted by the vacuum pump PC 3004 Vario (Vacuubrand, Wertheim, Germany). Binary mixtures were measured by isobaric heating of the pure low-boiling component until boiling. Further, a small amount of the high-boiling component was added. The mixture was equilibrated at constant pressure for about 30 min until the measured temperature was constant. Samples of the liquid phase and of the vapor phase were taken. This approach was repeated until at least five samples have been obtained. These were then analyzed via gas chromatography (GC; see section 3.4). All samples were measured 3-fold, and the results were averaged. 3.3. Liquid−Liquid Equilibrium Measurements. LLE measurements of binary mixtures were performed in jacketed 10 mL glass vessels. The amount of each component (4 g each) was prepared gravimetrically. The temperature was set to the desired value with an ECO RE 304 thermostat from Lauda (Lauda-Königshafen, Germany). The vessels were placed on magnetic stirrers, and phases were mixed for several hours at 800 rpm. After mixing, the stirrers were switched off and the two liquid phases remained at the temperature for equilibration and settling for 1 day. After 24 h phase separation was assured, and samples from both phases were taken and analyzed in triplicate with Karl Fischer titration and GC (see the following section). 3.4. Analytics. The amount of water in aqueous mixtures was measured using Karl Fischer titration with the titrator 915 KF Ti-Touch (Metrohm, Herisau, Switzerland). Each sample was measured in triplicate, and the results were averaged. Determination of component concentrations of organic solvents in the different phases of different mixtures was performed by gas chromatography. All measurements were performed as triplets. The used GC system Agilent Technology 7890A was equipped with an Agilent INNOWax column (30 m, 0.32 mm, and 0.5 mm) and a flame ionization detector. GC measurements were calibrated separately for each binary mixture, and quantification of the components’ concentrations was performed in triplicate.

(10)

cal

where y stands for the modeled quantity with PC-SAFT and yexp the respective experimental value. NP denotes the number of available experimental data points.

3. MATERIALS AND METHODS 3.1. Chemicals. The chemicals used in this study are summarized in Table 1. All chemicals were used in this work without further purification, and the purities are given in Table 1. Deionized water from the Millipore system (Merck KGaA) was used. Table 1. Substances Used in This Work, Including the Respective Chemical Abstracts Service (CAS) Registry Number, Molecular Weight, Supplier, and the Mass-Fraction Purity As Provided by the Supplier (S = Sigma-Aldrich Chemie GmbH, M = Merck KGaA, T = TCI Deutschland GmbH, and V = VWR International GmbH). substance

CAS reg. no.

Mw (g/mol)

supplier

purity

diethyl succinate 1-butanol dibutyl succinate acetonitrile tetrahydrofuran hydranal methanol dry Apura Combi titrant 5

123-25-1 71-36-3 141-03-7 75-05-8 109-99-9 67-56-1

174.19 74.12 230.3 41.05 72.11 32.04

S V T V M S M

0.99 0.998 0.99 0.999 0.999 0.9999

3.2. Vapor−Liquid Equilibrium Measurements. VLE measurements of binary mixtures were performed in an equilibrium apparatus (NORMAG GmbH, Ilmenau, Germany) at pressures between 10 and 30 kPa. The apparatus consisted of three units, an electric heater at the bottom, an equilibrium chamber with an oil-filled heating jacket, and a vapor condenser. The heating jacket and the cooling water in the

Table 2. PC-SAFT Pure-Component Parameters Used in This Work ref substance

M (g/mol)

mseg i

σi (Å)

ui/kB (K)

κAiBi

εAiBi/kB (K)

assoc scheme

params

H2O (2B) H2O (4C) EtOH 1-BuOH ACN THF DMSO SA MES DES DBS

18.015 18.015 46.070 74.120 41.052 72.110 78.130 118.090 146.140 174.190 230.300

1.2047 2.5472 2.3827 2.7515 2.329 2.4250 2.9223 6.3053 4.8520 6.2233 6.4549

a 2.1054 3.1771 3.6139 3.1898 3.4966 3.2778 2.6934 3.2981 3.3197 3.7070

353.9449 138.6300 198.2365 259.5909 311.31 280.4100 355.6900 327.5047 223.0259 238.2100 259.4918

0.0451 0.2912 0.0324 0.0067 b b b 0.0023 0.0007 b b

2425.6714 1718.2000 2653.3837 2544.5600 0 0 0 2366.8895 5628.7243 0 0

1:1 2:2 1:1 1:1 1:0b 1:0b 1:0b 1:1 1:1 2:0b 2:0b

37 38 29 29 39 31 39 this work this work 41 this work

data

35, 40 21 36, 42, 43

a σi = 2.7927 + 10.11 exp(−0.01775T) − 1.417 · exp(0.01146T). bInduced association: in binary mixtures with a self-associative component, the association volume was set equal to the association volume of the associating component (for detailed description see ref 44).

C



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4. RESULTS AND DISCUSSION 4.1. Pure-Component Parameter Estimation. Purecomponent PC-SAFT parameters of several components of interest in this work are already available in the literature. These parameters are summarized in Table 2. For those components for which PC-SAFT parameters were not known from literature works, the pure-component parameters were adjusted in this work to experimental density data and vapor-pressure data from the literature using an objective function OF1 per eq 11: NP p LV 0i

OF1 =

∑ k=1

⎛ p LV,cal ⎞ 1 − ⎜⎜ oiLV,exp ⎟⎟ + ⎝ p0i ⎠k

NPρ

0i

∑ m=1

⎛ ρcal ⎞ 1 − ⎜⎜ oiexp ⎟⎟ ⎝ ρ0i ⎠m (11)

Figure 1. Overview of the binary phase equilibria that are needed for kij fitting in a typical esterification reaction mixture. Six binary interaction parameters are required for a neat reaction mixture (alcohol is solvent), and four additional kij must be determined for an esterification in an inert solvent.

SA and MES were treated as self-associating components, and five pure-component parameters were adjusted using eq 11. In contrast, the diesters are not allowed to interact via selfassociation. However, in mixtures of a diester/self-associating component, the diesters were assumed to build hydrogen bonds with unlike molecules but not with themselves (induced associating). Induced association was also considered in mixtures of THF, ACN, or DMSO with a self-associating mixture partner. The so-determined PC-SAFT parameters were validated by comparing experimental densities and vapor pressures of the pure components with the PC-SAFT modeling results, and expressed as the ARD values. For the three components SA, MES, and DBS (Table 2) the PC-SAFT parameters were fitted in this work. ARDs of 4.90%, 0.70%, and 0.14% were obtained for densities of SA, MES, and DBS, respectively. Experimental density data at different temperatures of SA were collected from ref 35, for MES from the safety data sheet of Alfa Aesar, and for DBS from ref 36 also at different temperatures. For SA, experimental sublimation pressures reported in the literature were used for parametrization. The comparison of experimental sublimation pressures and PC-SAFT calculated sublimation pressures of SA is shown in Supporting Information Figure S1. Because the experimental sublimation pressures of SA are very small, it is reasonable to obtain ARD values between experimental and PC-SAFT modeled sublimation pressures in the observed order of magnitude (ARD = 8.41% for SA). The PC-SAFT modeled vapor pressures of MES and DBS agree very well with experimental data. The comparison of these is shown in Figure S2. The resulting ARDs are 3.58% and 1.88%, respectively. 4.2. Binary Mixtures. Modeling phase equilibria of multicomponent mixtures requires a precise modeling of binary systems in a first step. Phase equilibria of binary mixtures were used to adjust the binary interaction parameters kij or kws ij . Considering a typical neat esterification reaction mixture, four reacting agents (acid, alcohol, ester, and water) are present, and six kij parameters have to be defined. This number exponentially increases if an inert compound (e.g., a cosolvent) is added to this neat reaction mixture. For esterification reactions, usually at least four to five reacting agents are participating and in many cases also one additional cosolvent is present. In such a mixture, 10 kij parameters must be known, as is illustrated in Figure 1. In the following, experimental results of phase equilibria of binary systems and the corresponding thermodynamic modeling are presented. The binary mixtures composed of the components illustrated in Figure 1 may form either solid− liquid equilibrium (SLE), liquid−liquid equilibrium (LLE), or

vapor−liquid equilibrium (VLE). The following results are divided into the respective types of phase equilibrium the components actually form. 4.2.1. SLE. SA is a solid at ambient conditions. Thus, SLE data with mixtures of SA were used in order to adjust kij parameters between SA and any other component. For this purpose, solubility data of SA in the alcohols under investigation, in water, and in organic solvents were necessary; these data were taken from the literature.23,24,45,46 The kij parameter between SA and THF was set to zero, as literature data of the solubility of SA in THF were not available. In order to estimate kij parameters to SA solubility xLSA, the following objective function OF2 was minimized: NP x L

SA

∑

OF2 =

k=1

where

xcal SA

⎛ x L,cal ⎞ ⎟ 1 − ⎜⎜ SA L,exp ⎟ ⎝ xSA ⎠k

(12)

was calculated by the following equation:

L,calc = xSA

⎡ SL ⎛ ⎞ 1 ⎢ − ΔhSA ⎜1 − T ⎟ exp L SL ⎢⎣ RT ⎝ γSA TSA ⎠ −

SL ⎛ T SL ⎞⎞⎤ ΔcpSL,SA ⎛ TSA ⎜⎜ − 1 − ln⎜ SA ⎟⎟⎟⎥ R ⎝ T ⎝ T ⎠⎠⎥⎦

(13)

In eq 13, TSL SA is the melting temperature of SA and is 461.15 K, ΔhSL SA is the melting enthalpy and is 38.91 kJ/mol, and ΔcSL p,SA is the difference of the liquid and solid heat capacities of SA and is 69.79 J/(mol·K). The values are obtained from Riipinen et al.47 γLSA required in eq 13 was obtained by PC-SAFT. Applying OF2 as described in eq 12 yielded kij values that are summarized in Table 3. Note that the kij in Table 3 are only valid for calculations with the previously summarized purecomponent parameters in Table 2. The ARDs (eq 10) between modeled and experimental solubilities of the binary mixtures are also shown in Table 3. The results of the SLE calculations and the comparison to experimental data are illustrated in Figure 2 for SA solubility in alcohols, water, and ACN. Figure 2 indicates very accurate calculations of the SA solubilities in water, EtOH, 1-BuOH, and ACN. The data show D



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own laboratory. For the estimation of kij parameters in LLE systems, the objective function OF3 was defined for minimization:

Table 3. Binary Interaction Parameters (kij) for SLE Systems Considered in This Worka substance i

substance j

kij

ARD (%)

ref

SA

water (2B)

kij = −0.0002T + 0.0126

4.61

24 and 46

SA SA SA SA

water (4C) EtOH 1-BuOH ACN

kij kij kij kij

= = = =

−0.00055T + 0.1068 0.000047T − 0.1774 −0.105 0.000643T − 0.2208

10.87 4.90 6.68 3.81

NPxi

OF3 =

∑ k=1

24 23 45

⎛ x cal,L1 ⎞ ⎛ x cal,L2 ⎞ 1 − ⎜⎜ iexp,L1 ⎟⎟ − ⎜⎜ iexp,L2 ⎟⎟ ⎝ xi ⎠k ⎝ xi ⎠k

(14)

Mole fractions of component i for both liquid phases L1 and L2 were calculated by the γ−γ concept xiL1γi L1 = xiL2γi L2

a

Average relavie deviations (ARDs) of calculated and experimental solubilities are given. Reference of experimental data. Note that these binary interaction parameters are valid with the previously described pure-component parameters in Table 2.

(15)

where the activity coefficients of component i in the two liquid phases and one of the mole fractions are calculated with PCSAFT by presetting one mole fraction at constant temperature and pressure. The LLE consisting of water and 1-BuOH is not described in detail here. Experimental data and PC-SAFT modeling results are available in the literature.50 The binary LLE between water and DES is reported in the literature. These data were used for PC-SAFT modeling. The experimental data and the modeling results are shown in Figure 3.

Figure 2. Solubility of SA (xSA) in ACN (stars),45 water (circles),46 1BuOH (triangles),23 and EtOH (squares)24 at atmospheric pressure vs temperature. Lines correspond to the PC-SAFT modeling with parameters shown in Tables 2 and 3. Dashed line indicates the modeling of SA solubility in water using the 4C association scheme for water.

that the solubility of SA is highest in EtOH while solubility in water and 1-BuOH are comparable. The comparison of solubilities in EtOH and water is also nicely compared in the work of Jiang et al.48 Here the work of Mahali et al. is worth mentioning, where the interactions between SA and water or EtOH are examined in a detailed manner.49 In ACN, the solubility of SA is very low. The temperature of the solubility values of SA in ACN is restricted to the relatively low boiling point of ACN at 1 bar. The given solubility in water is the intrinsic solubility of SA, meaning the equilibrium solubility of the neutral acid. Considering the pKa values of SA and the concentrations of SA in water at phase equilibrium, the acid is almost exclusively present in its nondissociated form, meaning that the fitted kij parameter is the interaction parameter between neutral SA and water. Although Figure 2 illustrates an apparently good agreement between modeling results and experimental data, the ARDs listed in Table 3 are still high. This is due to the small mole fractions at low temperatures, where small deviations result in higher ARD values. In this context, it seems that using the 2B water model yields a lower error than using the 4C water model. In general, the results are satisfying. 4.2.2. LLE. Considering the components in Figure 1, LLE will be formed between higher alcohols (in this work, 1-BuOH) and water as well as between water and the SA diesters (in this work, ethyl ester and butyl ester of SA). The monoester MES builds a VLE with water.21 To our best knowledge, no data for MBS are available in the literature and there is no supplier known that would allow us to perform measurements in our

Figure 3. LLE of binary water/DES mixture at different temperatures and atmospheric pressure. Squares indicate experimental data.22 Solid line represents PC-SAFT modeling with 2B association scheme for water, and dashed and dotted lines represent PC-SAFT modeling with 4C association scheme for water without and with using the binary kws ij parameter (see eq 5). PC-SAFT calculations were performed with parameters summarized in Tables 2 and 4.

The experimental data show that the water solubility in the ester-rich phase is much higher than the ester solubility in the aqueous phase. This type of asymmetrical LLE is usually difficult to describe accurately with thermodynamic models. Using PC-SAFT and the 2B association scheme for water, applying a temperature-dependent kij allows representing the LLE accurately. This was not possible with the 4C association scheme for water. The ester-rich phase could only be modeled satisfyingly by correcting the association energy of the mixture. Regarding the major difference in the two water association models, it is obvious that the self-association of water is much stronger represented with the 4C association scheme. This might be the reason for the fact that PC-SAFT underestimates the water content in the ester-rich phase. Thus, increasing the association energy between ester and water might overcome this issue, which was attributed to by accounting for the binary interaction parameter kws ij between water and DES. This is important information as recently modeling aqueous mixtures using the 4C scheme for water has been recommended. E



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strongly underestimate the attraction between DES/water and DBS/water. Table 4 suggests that strong cross-association forces between diester and water cause these attractions. Table 4 further reveals that this effect decreases by increasing the chain length of the diester. 4.2.3. VLE. Most of the components illustrated in Figure 1 are liquids at ambient conditions, and many binary mixtures composed of them are completely miscible. For these mixtures, VLE data might be used to parametrize models such as PCSAFT. Regarding binary pairs of the component classes water, alcohols, and organic solvents, many of these VLE data are reported in the literature. For some mixtures including DES, experimental VLE data are also available. Nevertheless, some combinations of DES with solvent and almost all data of systems including DBS had to be measured prior to PC-SAFT modeling in this work. Here, some of these measurements and calculations will be presented. The binary mixtures that will be discussed in the following contain either DBS or ACN as a mixture constituent; VLE data in these systems are very scarce compared to other pairs formed from the components of Figure 1. All other mixtures not presented in the main text are summarized in the Supporting Information of this work. The relevant objective function OF4 for kij fitting with VLE systems is described in eq 16.

In Figure 3 it is shown that only applying a very low negative kws ij = − 0.5 allows accurately describing the DES-rich phase. Referring to eq 5, this means that water and DES must strongly interact by cross-association interactions. The same behavior is observed for the system DBS/water (see Figure 4). The experimental data were measured in this

Figure 4. LLE of binary water/DBS mixture at different temperatures and atmospheric pressure. Squares indicate experimental data listed in Table S3. Solid line represents PC-SAFT calculations with 2B association scheme for water, and dashed and dotted lines represent PC-SAFT modeling with 4C association scheme for water without and with using the binary kws ij parameter (see eq 5). PC-SAFT calculations performed with parameters summarized in Tables 2 and 4. Standard uncertainty of temperature: u(T) = (0.15 + 0.002(T − 273.15)) K.

NP

OF4 =

∑ k=1

⎛ T LV,cal ⎞ 1 − ⎜ LV,exp ⎟ ⎝T ⎠k

(16)

LV,cal

where T is the modeled boiling point. The mole fraction of a component i in the liquid phase xLi is preset for a specific temperature and pressure, and the mole fraction of a component i in the vapor phase, xVi , was calculated using the φ−φ concept

work (Table S3 in the Supporting Information). The experimentally observed miscibility gap is larger compared to the mixture DES/water, since the butyl ester DBS is more hydrophobic than DES and the water solubility in the butyl ester-rich phase is smaller than in the ethyl ester-rich phase of the binary diester/water mixtures. The observations regarding the PC-SAFT modeling results are similar for the DBS/water and the DES/water systems. For both systems, using the 2B association scheme for water yields the best modeling results. Using the 4C association scheme for water requires a very low negative kws ij value in order to accurately describe the LLE. The described parameters and the calculated ARD for the LLE of these systems are summarized in Table 4. Since the alkyl chains of 1-BuOH are longer and thus the ester is more hydrophobic, the cross-association between water and DBS is weaker than between water and DES. It can be observed from Table 4 that the kws ij (4C association scheme for water) and the kij (at constant temperature for the 2B association scheme for water) are both negative, and more negative values are found for the pair DES/water than for DBS/ water. Thus, for DES/water, the mixing rules in eqs 3 and 5

φi V xiV = φi LxiL

(17)

This means for an isobaric VLE that temperature and xVi are calculated by giving the system pressure and a value for xLi .

Binary Systems Relevant for Ethanolic Esterification Mixtures. Considering esterification of SA in EtOH, VLE data for relevant binary mixtures were measured by Orjuela et al.13,21 These mixtures comprise the binary mixtures water/ MES, EtOH/MES, and EtOH/DES, and water/EtOH is available in the literature.51 These experimental data were used to adjust the binary kij parameters in order to obtain accurate modeling results with PC-SAFT. The respective results are summarized in the Supporting Information. Considering the aqueous mixtures, it can be concluded from Figures S3 and S4 that these can be modeled very accurately with PC-SAFT. The 4C association scheme for water is very accurate for modeling the VLE water/EtOH (Figure S3), while the 2B

a Table 4. Binary Interaction Parameters (kij and kws ij ) for DES/Water and DBS/Water

substance i DES

DBS

kij or kws ij

substance j water water water water water water

(2B) (4C) (4C) with additional kws ij (2B) (4C) (4C) with additional kws ij

kij kij kij kij kij kij

= = = = = =

0.00025974T − 0.14351 0.05 0.05 and kws ij = −0.5 0.000625T − 0.23072 0.05 0.05 and kws ij = −0.25

ARD (%) 2.52 45.84 2.41 4.66 37.09 11.33

ref 22

this work

a

ARDs of calculated and experimental mole fractions at liquid−liquid equilibrium are given with reference to the source of the experimental data. Note that these binary interaction parameters are valid with the previously described pure-component parameters in Table 2. F



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uncertainty in the ester-rich phase, as it can be seen in Figure 5. This explains the higher deviation between measurements and PC-SAFT at temperatures higher than 380 K. Further VLE of binary mixtures relevant for butanolic esterification mixtures are presented in the Supporting Information (Figures S7−S12). Interestingly, for binary mixtures containing water, the 4C association scheme yields better results for mixtures with two self-associating components (e.g., water/1-BuOH, Figure S7). In contrast, the 2B association scheme for water should be preferred if mixtures are considered with water and a non-self-associating component (THF/water and DMSO/water, Figure S11 and Figure S12). Binary Systems Relevant for Solvent Influence on Esterification Mixtures. Considering esterification of SA in the alcohols EtOH and 1-BuOH, the experimental data for all binary systems are available at this point. Often, these reactions are carried out in inert organic solvents to increase yield or kinetics. In this section, ACN is considered here exemplarily as an inert organic solvent, and the results using THF as organic solvent are reported in the Supporting Information. Experimental VLE data for the binary mixture ACN/1-BuOH and ACN/water are reported in the literature.52 These data were used in this work to adjust kij values for PC-SAFT modeling. For the binary mixture ACN/1-BuOH the VLE could be predicted accurately; i.e., the kij was set to zero, yielding an ARD of 0.61% only. The binary mixture ACN/water shows a temperature-minimum azeotrope. The kij parameter between water and ACN was fitted to best describe the ARD with specific attention to model the azeotropic composition as accurately as possible. Applying a kij of −0.036 for the 2B water/ACN resulted in an ARD of 0.83%, and a kij of −0.03 for the 4C water/ACN yielded an ARD of 1.23%. The modeling results for the two binary mixtures ACN/1-BuOH and ACN/ water are illustrated in Figure 6. Modeling results with both association schemes (2B and 4C) for water are shown. It can be observed from these results that both association schemes for water yielded similar results. This means that in the binary mixture water/ACN the association interaction (that is differently regarded in the two models 2B and 4C) is not that decisive compared to the mixtures water/diester as shown in Figures 3 and 4. Nevertheless, the azeotropic temperature is described better with the 2B association scheme for water. VLE data of organic solvents with esters are scarcely found in the literature, but according to Figure 1 the mixtures consisting of diester with ACN (solvent) are of interest in esterification mixtures. In the following, experimental results and PC-SAFT modeling of the system ACN/DES will be presented. This isobaric VLE of this mixture was measured at 10 kPa, and the temperatures were between 295 and 372 K in this work. The results are summarized in Table 6. Applying OF4 (eq 16) yields ARD values of only 0.98%, which is a promising result considering the fact that only a very small kij (+0.01) between ACN and DES was applied for this result. For the measurements at temperatures higher than 350 K, it was difficult to take vapor samples. Additionally, samples with low ACN content resulted in higher experimental deviations. Due to these issues, reliable experimental data could be obtained only in the temperature range between 295 and 346 K. In Figure 7 experimental and calculation results are compared graphically. A very good agreement can be observed

association scheme yields slightly lower ARD values for the VLE of the system water/MES (Figure S4). The systems MES/ EtOH and DES/EtOH are comparatively ideal mixtures, which can be modeled with PC-SAFT as expected for the system MES/EtOH (Figure S5). Surprisingly, PC-SAFT seems to predict a pronounced nonideal behavior of the mixture DES/ EtOH (Figure S6). Binary Systems Relevant for 1-Butanolic Esterification Mixtures. Considering esterification of SA in 1-BuOH, phaseequilibrium data are partly missing in the literature. Monobutyl succinate is not available commercially, and the most important system that forms a VLE in the 1-butanolic system is 1-BuOH/ DBS. The kij parameter between 1-BuOH/DBS was fitted to binary VLE data measured in this work. The experimental results are listed in Table 5. Table 5. Isobaric VLE of 1-BuOH with DBS at 20 kPa Measured in This Worka T (K)

xLBuOH

xVBuOH

352.85 358.65 357.65 360.65 368.65 380.05 396.15 405.75 428.95

0.9273 0.8086 0.6812 0.5591 0.3935 0.2378 0.1619 0.1564 0.0997

0.9989 0.9961 0.9963 0.9961 0.9940 0.9899 0.9814 0.9465 0.8667

Standard uncertainties are u(T) = (0.15 + 0.002(T − 273.15)) K and u(x) = 0.041. Superscripts: L, liquid phase; V, vapor phase. a

The isobaric VLE was measured at a constant pressure of 20 kPa in a temperature range of between 350 and 430 K. These data were used for the fitting of kij between these two components, which was found to be a negative value of kij = −0.015, yielding an ARD of 1.88%. The results are compared in Figure 5 graphically showing again very good agreement

Figure 5. VLE of 1-BuOH with DBS at 20 kPa measured in this work (squares). The lines were modeled with PC-SAFT with parameters shown in Tables 2 and 8.

between experimental data and modeling results. Samples were not collectable for higher temperatures in the vapor phase. This was due to the high boiling temperature of DBS, which made the accumulation of enough vapor samples hard, although the applied system pressure was low. The low mole fraction of 1BuOH at temperatures above 380 K causes high experimental G



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Figure 6. Vapor−liquid equilibria of the binary mixtures ACN/1-BuOH (a)52 and ACN/water (b).53 Lines are calculations with PC-SAFT with parameters shown in Tables 2 and 8. Solid line indicates calculations with the 2B association scheme for water and dashed line indicates calculations with the 4C association scheme for water in panel b.

Table 6. Isobaric Vapor−Liquid Equilibrium of ACN/DES at 10 kPa Measured in This Worka

Table 7. Isobaric VLE of ACN with DBS at 10 kPa Measured in This Worka

T (K)

xLACN

xVACN

T (K)

xLACN

xVACN

295.25 299.25 304.52 308.05 311.75 314.31 320.05 334.85 346.65

1 0.7919 0.7694 0.5448 0.4554 0.4726 0.2849 0.1506 0.1346

1 0.9993 0.9996 0.9974 0.9956 0.9987 0.9912 0.9759 0.9494

295.4 297.49 313.96 325.95 334.93 338.09 341.79 349.48 363.08 383.01

1 0.8746 0.4267 0.2803 0.2090 0.1893 0.1688 0.1342 0.0916 0.0547

1 0.9999 0.9999 0.9999 0.9995 0.9998



between experimental and PC-SAFT modeled VLE between 295 and 346 K. was at least possible to collect some more liquid samples at higher temperatures (340 K) was difficult, and experimental uncertainty in this region is higher than for the lower temperature (

Phase Behavior of Binary Mixtures Containing ... - ACS Publications

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