An Equation of State Based on PC-SAFT for Physical Solvents

Article pubs.acs.org/IECR

An Equation of State Based on PC-SAFT for Physical Solvents Composed of Polyethylene Glycol Dimethylethers Nawin R. Nannan,† Carlo M. De Servi,‡ Teus van der Stelt,¶ Piero Colonna,§ and André Bardow*,∥ †

Mechanical Engineering Discipline, Anton de Kom University of Suriname (AdeKUS), Leysweg 86, PO Box 9212, Paramaribo, Suriname ‡ Energy Department, Politecnico di Milano, Via Lambruschini 4, 20156, Milano, Italy ¶ Process and Energy Department, Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands § Power and Propulsion, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands ∥ Lehrstuhl für Technische Thermodynamik, RWTH Aachen University, Schinkelstraße 8, 52062 Aachen, Germany ABSTRACT: A technical equation of state (EoS), according to the perturbed chain statistical associating fluid theory (PCSAFT), is developed for solvent blends composed of polyethylene glycol dimethylethers (PEGDMEs/glymes), that is, CH3O[CH2CH2O]nCH3 with n = 3, ..., 9. These solvent blends are employed in industry under the commercial names Selexol or Genosorb, primarily for the physical absorption of H2S and CO2 from acid gases. The molecular parameters for the EoSs of the pure fluids comprising the solvent, notably for the n = 3 and 4 members of the homologous series, are obtained by fitting the PCSAFT EoS to published vapor pressure and liquid density data. Because of the limited availability of experimental data for the glymes with n ≥ 5, PC-SAFT is used as a predictive tool to determine the molecular parameters for the n = 5, ..., 9 members of the homologous series. To exploit the extrapolative capabilities of PC-SAFT, the n = 1 and 2 members of the homologous series are included in this study. The mixture of glymes is modeled using the van der Waals one-fluid mixing rules with the Lorentz− Berthelot combining rules, whereby the binary interaction parameters kij among the members of the homologous series are all set to zero. The performance of the mixture EoS is assessed by a comparison of predicted properties with experimental data. The thermodynamic model is also briefly applied to describe the vapor−liquid equilibrium behavior of glymes and their blends with CO2. The comparison with available experimental data shows that the resulting model provides a description of the thermodynamic behavior of this system suitable for engineering purposes.

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EoS,4 complemented by thermodynamically consistent mixing rules (e.g., those of Wong and Sandler5). Because of its success in predicting VLE of complex fluids, the statistical associating fluid theory (SAFT) and its variants, for example, perturbed chain (PC-SAFT) or soft-SAFT, have gained increased interest in recent years.6 EoSs based on molecular models, like SAFT and its variants, with PC-SAFT7 as the most-used variant, provide several advantages and features. SAFT-based EoSs are suitable for property estimation of complex fluids like macromolecules, copolymer systems,8−10 and fluid mixtures in general, in case standard methods fail or are inaccurate even for engineering applications;11,12 examples of these include mixtures containing strongly polar compounds and an ionic liquid + CO2.13−16 SAFT-based thermodynamic models also provide for the explicit accounting of molecular interactions such as, for example, polar interactions or (self) association.17,18 Moreover, because of the strong physical background, SAFT-based EoSs are robust, consistent, and extrapolative.7,11 This type of thermodynamic model thus allows for the performing of systematic studies on the influence of chain length and molecular structure on VLE behavior.8,11

INTRODUCTION

Blends of polyethylene glycol dimethylethers (PEGDMEs/ glymes), that is, CH3O[CH2CH2O]nCH3, are known as commercial solvents under the names Selexol (typically n varies from 3, ..., 9) and Genosorb (typically n varies from 3, ..., 12). The main field of application of these solvents is in gas purification, especially in the selective removal, by physical absorption, of H2S (and other sulfur-containing compounds) from sour natural gas or synthesis gas. The solvent is also appropriate for the bulk removal of CO2, and for years the Selexol process has been the dominant acid−gas removal technology in gasification, especially of coal.1,2 The Selexol process is also usually considered to be the state-of-the-art reference technology for precombustion CO2 capture in energy conversion applications.3 The design of a CO2 capture plant requires sufficiently accurate knowledge of the thermodynamic properties of the fluids involved. It is therefore important to develop a tool that allows for the consistent and robust prediction of vapor−liquid equilibria (VLE). Henry’s law or ad hoc activity coefficient models are often selected for the design and analysis of industrial processes involving gas purification. Alternatively, cubic equations of state (EoSs) with simple mixing rules are employed. For example, a common choice in process simulations for the chemical industry is the Peng−Robinson © 2013 American Chemical Society

Received: Revised: Accepted: Published: 18401

May 8, 2013 November 22, 2013 November 26, 2013 November 26, 2013 dx.doi.org/10.1021/ie401456q | Ind. Eng. Chem. Res. 2013, 52, 18401−18412

Industrial & Engineering Chemistry Research

Article

Table 1. Summary of Available and Selected Experimental Thermodynamic Data for Mono-, Di-, Tri-, and Tetraethylene Glycol Dimethylethera property of liquid

a

T range [K]

number of points

density speed of sound isobaric heat capacity vapor pressure

357 77 29 45


211 82 18 17


303 85 31 16


378 77 15 17

monoEGDME 198−534 293−353 288−515 305−533 diEGDME 283−423 293−353 209−350 286−433 triEGDME 278−373 288−353 229−421 376−490 tetraEGDME 278−423 293−353 312−421 373−533

P range [kPa]

source

100−100 000 100−100 000 100−1000

30−42 41 31,42,43 31,44−46

100−100 000 100−100 000 unspecified

30,38,41,42,47−50 41,48,49 51 29

100−100 000 100−100 000 100−1000

42,52−59 55,58,59 42,51,54−56,60 61,62

100−100 000 100−100 000 1000

42,53,56,59,63,64 59 42,56 65

Derived properties such as the coefficient of volume expansion and the isothermal compressibility are not included.

it is for the members of the homologous series employed in solvent applications for acid gases. This paper is structured as follows. At first, a brief description of the EoS is presented. Next, a survey of published data is provided for each relevant member of the homologous series, namely, for the n = 3, ..., 9 members. The survey showed that relevant thermodynamic data are unavailable for the n = 5, ..., 9 members of the homologous series. The PC-SAFT EoS can be used as a tool for extrapolation; thus, data for the lighter members of the homologous series can be used to estimate the needed parameters for the heavier members. It was therefore deemed necessary to include the n = 1 and 2 members in the development of the solvent EoS, even if those members are not constituents of the solvent blends used in practice. Consistent experimental data are used to fit the pure-component parameters of the EoS. Once the pure-component parameters are known, the binary interaction parameter kij for each glyme pair should be determined. Here, however, mutual mixture data for the homologous series of glymes are unavailable, and therefore all mutual kij values are set to zero (0). The quality of the established EoS is then assessed for mixtures of glymes and for selected glyme + CO2 binary systems using published data on Henry’s law constants. Finally, conclusions are presented.

Another advantage is that the number of pure-component parameters in the EoS is rather small, for example, from three to five, contrary to, for example, multiparameter EoSs with parameters on the order of 10 such as Wagner-type EoSs.19 The pure-component parameters in multiparameter EoSs usually lack physical meaning, and the multiparameter EoSs can exhibit numerical artifacts such as discontinuities or thermodynamic inconsistency. PC-SAFT is therefore a useful tool for integrated solvent and process design.20 However, a known limitation of SAFT-type models, as for any mean-field theory, is the poor description of the region near the critical point. Renormalization-group corrections have only recently been developed to improve the behavior of SAFT-type models in the critical region.21,22 The objective of this work is the modeling of equilibrium properties of blends of glymes at moderate pressure and low temperature. The PC-SAFT EoS is selected because of its documented positive features. Moreover, blends of glymes are typically employed for acid gas removal, for example, precombustion CO2 capture from product gas, in which compounds such as CH4, CO, CO2, H2O, H2S, and N2 are encountered. For these compounds, the pure-component parameters for the PC-SAFT EoS have already been published.7,12 For the sake of completeness, we refer to two Selexol models developed by a process manufacturing software company.23,24 One model uses a copolymer approach to model the solvent,24 whereas in an earlier model,23 the Selexol solvent is modeled with PC-SAFT using a pseudopure fluid approach (refer to help files available/delivered with the software).23,24 The EoS developed in this work is not assessed with respect to these older models; nonetheless, the input data provided in the following can easily be added to databases accompanying process simulation programs. In the scientific literature, a pseudopure fluid model for PEGDME with a molar mass of 2000 g/mol (PEGDME2000) has been developed using PCSAFT.25 The molar mass of PEGDME2000 is much larger than

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PC-SAFT: AN OVERVIEW The molecular model underlying PC-SAFT assumes that a molecule is a chain of spherical segments exhibiting various interactions. The EoS is formulated in terms of the reduced Helmholtz free energy a̅ ≡ A/(NkBT), where A denotes the Helmholtz free energy in joules, N is the total number of molecules, kB is Boltzmann’s constant, and T is the temperature in Kelvin. Typically, the reduced-Helmholtz free-energy function is split into the ideal gas term aIG ̅ , which according to theory depends only upon the ideal gas (isobaric) heat capacity, and the residual contribution aRES ̅ , which takes into account the departure of real-gas properties from those computed according to the ideal gas assumption 18402

dx.doi.org/10.1021/ie401456q | Ind. Eng. Chem. Res. 2013, 52, 18401−18412


Article

(1) a ̅ = a ̅ IG + a ̅ RES In PC-SAFT, the residual term sums the following additional contributions: the hard-sphere (HS) term accounting for hardsphere repulsive interactions, a contribution due to mean-field dispersive attraction (DISP), a chain term (CHAIN) due to the formation of covalent chain-forming bonds, and a term for associating interaction (ASSOC), for example, H-bonding. In summary,

Table 2. Main Thermophysical Property Data for Monoethylene Glycol Dimethylether property

critical pressure, PC

a ̅ = a ̅ IG + a ̅ RES + = a ̅ IG + [a ̅ HS + a ̅ DISP + a ̅ CHAIN + a ̅ ASSOC] (2) Analytical expressions for each of the terms in eq 2 can be found in various works of Gross et al.17,18,26 If associating interaction is absent, only three pure-component parameters need to be determined by fitting eq 2 to experimental data. The three parameters are the segment number m, the segment diameter σ, and the segment energy parameter ε/kB. Since the glymes are not self-associating, the association terms are not used for the pure components, and therefore aASSOC = 0. ̅ Mixtures are modeled with the van der Waals one-fluid mixing rules, and the parameters for an unlike pair of segments are obtained with the Lorentz−Berthelot combining rules, namely, σi + σj σij = (3) 2

critical specific volume, vC normal boiling point, TB molar mass, M dipole moment, μ

unit

source

K

31 44 46 31 44 46 31 46 29 27 27 30

kPa

cm3/mol K kg/kmol D

CIG P [kJ/kmol K]

(4)

T [K]

n=1

n=2

n=3

n=4

300 400 500 600 800 1000

122 154 179 201 239 265

189 226 261 293 347 384

250 299 344 387 458 506

311 371 428 481 569 628

a Data for monoglyme are obtained from a database27 with an estimated uncertainty of less than 25%. The other data are estimated using Joback’s method as documented in Poling et al.66 Note that the upper temperature limit is arbitrarily chosen, as these complex organic molecules are not thermochemically stable at 1000 K.

where kij is the constant binary interaction parameter for a pair ij. Note that sometimes it may be necessary to introduce a temperature-dependent kij as, for instance, in the CO2 + H2O system.12

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The parameters A, B, C, and D of eq 5 are listed in Table 4. This table also contains the pure-component parameters m, σ, and ε/kB determined by fitting the PC-SAFT model to selected density and vapor pressure data listed in Table 1.

EQUATIONS OF STATE FOR THE PURE COMPONENTS (GLYMES, CH3O[CH2CH2O]NCH3 WITH N = 1, ..., 9) Equation of State for Monoethylene Glycol Dimethylether. The results of a data survey performed for monoethylene glycol dimethylether (monoEGDME, H3 COCH 2CH2 OCH 3, monoglyme, 1,2-dimethoxyethane, CAS Registry Number 110−71−4) are presented in Tables 1 and 2. An assessment of the quality of the data is based on several well-known fluid databases27−29 and on the judgment of the authors. As mentioned in the previous section, the ideal gas heat capacity CPIG is necessary for computing the ideal gas contribution aIG ̅ to the Helmholtz free energy. Since ideal gas heat capacity data are unavailable for monoEGDME, it was necessary to estimate the required numbers. For this purpose, an evaluated database27 was consulted, and the data reported therein are listed in Table 3. These CIG P data have been assessed by comparison with those available in the online database29 that contains the computational chemistry comparison and benchmark database (CCCBDB) and with the results obtained by application of Joback’s method.66 The numbers obtained from the database27 and by applying Joback’s method are within the estimated uncertainty of the data reported in Table 3. The predicted ideal gas isobaric heat capacities are fitted to a suitable polynomial correlation of the form CPIG = A + BT + CT 2 + DT 3

537 ± 2 539.2 ± 0.5 536 ± 2 3960 ± 250 3860 ± 20 3870 ± 28 308 ± 13 271 ± 5 358 ± 1 90.1210 1.71 1.62

Table 3. Estimated Ideal Gas Isobaric Heat Capacities of Mono-, Di-, Tri-, and Tetraethylene Glycol Dimethylether Spanning the Range of 300−1000 Ka

and εij = (1 − kij) εiεj

value

critical temperature, TC

Table 4. Parameters for the PC-SAFT EoS of Monoethylene Glycol Dimethylether and the Average Absolute Relative Deviations of the Model with Respect to the Experimental Dataa parameter M m σ ε/kB A B × 103 C × 106 D × 109

value

unit

90.1210 kg/kmol 3.589 940 3.346 036 Å 233.1489 K 4.042 08 kJ/(kmol 471.497 kJ/(kmol −274.541 kJ/(kmol 64.1523 kJ/(kmol Average Absolute Relative Deviations (AARDs)

densities vapor pressures heat capacities

0.33 0.99 4.5

K) K2) K3) K4) % % %

a The temperature range of validity for the parameters is set to 300− 1000 K, on the basis of the applicability range of the adopted correlations. For (thermal) property computations, the lower temperature limit may be relaxed and set to the triple-point temperature of 215 K without loss of accuracy and quality.

(5) 18403



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Note that the influence of dipolar forces can be neglected with respect to typical van der Waals forces if μ* ≡ 4300 μ2/ (TCvC) < 0.03, where the dipole moment μ is expressed in debye, the critical temperature TC is expressed in Kelvin, and the critical specific volume vC is expressed in cm3/mol (see page 2.35 of Poling et al.66). Polar forces are relevant in the case of monoEGDME because μ* is somewhat greater than 0.03. Yet, a subsequent evaluation of the performance of the EoS with respect to experimental data shows that PC-SAFT suffices with regard to typical engineering accuracy, without the explicit accounting of polar forces via inclusion of the dipole moment. Moreover, observe that as the chain length increases, μ* gets closer to 0.03, implying that, for the larger glymes, polar effects are less important. The EoS for monoEGDME describes liquid density data with an average absolute relative deviation (AARD) of 0.33% (four data points of Steele et al.31 are excluded in this evaluation, since the original data contain large errors), vapor pressure data with an AARD of 0.99% (the critical-point data of Quadri and Kudchadker44 are excluded in this evaluation), and liquid isobaric heat capacities with an AARD of 4.5% (this value includes a saturated liquid data point measured at T/TC ≈ 0.959, where the absolute deviation with respect to the computed value is 18%). In Figure 1, the densities computed

Figure 2. Primary ordinate: experimental and computed values of selected experimental saturated liquid density ρL for monoEGDME. Secondary ordinate: deviation of these values for ρL with respect to computed data using the established PC-SAFT model (parameters in Table 4). The continuous line represents saturated liquid densities computed using the established EoS. DEV [%] = 100(ρLexp − ρLcalc)/ ρLexp, where “exp” is the abbreviation for experimental, and “calc” is that for calculated.

available are very well-described. Figures 3 and 4 show experimental data of vapor pressures and ideal gas isobaric

Figure 1. Primary ordinate: experimental and computed densities for monoEGDME along isotherms spanning the range 243, 253, ..., 373 K. Secondary ordinate: deviation of experimental liquid density data sets along the mentioned isotherms with respect to computed data using the established PC-SAFT model (parameters in Table 4). Continuous lines represent densities, computed using the established EoS, along isotherms. The higher the temperature, the lower the line (thus, along an isobar, a temperature increase yields a lower density). The various colors represent the individual isotherms. DEV [%] = 100(ρexp − ρcalc)/ρexp, where “exp” is the abbreviation for experimental, and “calc” is that for calculated.

Figure 3. Primary ordinate: experimental and computed vapor pressures of monoEGDME as a function of temperature for selected data sets. Secondary ordinate: deviations of the experimental data with respect to the computed values using the established PC-SAFT model (parameters in Table 4). The continuous line represents the vapor pressure curve computed using the established EoS. DEV [%] = sat sat 100(ρsat exp − ρcalc)/ρexp, where “exp” is the abbreviation for experimental, and “calc” is that for calculated.

by the PC-SAFT model for monoEGDME are seen to correspond well to the experimental data, with a tendency to overpredict the experimental values. While the influence of temperature is well-captured, deviations between the model and experiments increase systematically with higher pressures. For the saturated liquid densities shown in Figure 2, the model overpredicts the experimental data of Carvajal et al.,39 in particular at lower temperature, while the other two data sets

heat capacities, respectively, together with the values calculated by the PC-SAFT model. These figures can be used to assess the performance of the PC-SAFT model for monoEGDME in further detail. The typical loss of performance for mean-field EoSs in the critical region is also observed for the established 18404



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Table 5. Estimated Normal-Boiling-Point and Critical-Point Data for Di-, Tri-, and Tetraethylene Glycol Dimethylether Obtained with the Marrero−Pardillo Method67 fluid name

TB [K]

TC [K]

PC [kPa]

vC [cm3/mol]

diEGDME triEGDME tetraEGDME

435.7 489.2 549.0

613.1 657.6 713.5

2922 2318 1884

408 534 660

provided in Table 6. The EoSs for the n = 2, 3, and 4 members of the homologous series describes liquid density data with an AARD between 0.47% and 0.51%, vapor pressure data with an AARD between 2.4% and 4.2%, and liquid isobaric heat capacities with an AARD between 2.2% and 4.1%. The description is thus of very similar quality as for monoEGDME. Equations of State for Glymes with n = 5, ..., 9. Once the pure-component parameters of the n = 1, ..., 4 members of the homologous series are known, PC-SAFT can be used as a tool to predict the pure-component parameters of the EoSs for the heavier members of the homologous series, which constitute the solvents used in practice. In this respect, it is first of all investigated if the three parameters m, σ, and ε/kB exhibit a certain trend. Following Gross and Sadowski7 and Pedrosa et al.,11 the scaled pure-component parameters m, mσ3, and mε/kB of the n = 1, ..., 4 members are correlated with the corresponding molar masses M. The result is displayed in Figure 5. As expected, since the compounds belong to the same fluid family, the molar masses are large, and the molecular structure is basically a long chain, scaled pure-component parameters of the glymes can be correlated with linear functions of the molar mass M according to

Figure 4. Primary ordinate: experimental and computed CP values of monoEGDME as a function of temperature for selected data sets. Secondary ordinate: deviations of the experimental data with respect to the computed values. The continuous line represents computed CP values at a pressure of 10 bar according to data from Conesa et al.,42 the dash-dot-dot line illustrates computed CP data at 1 atm according to data from Francesconi et al.,43 and the dashed line represents computed saturated liquid CP data according to data from Steele et al.31 Computations are done using the parameters listed in Table 4. DEV [%] = 100(CP,exp − CP,calc)/CP,exp, where “exp” is the abbreviation for experimental, and “calc” is that for calculated.

EoS for monoEGDME. The EoS predicts a critical pressure of 4573 kPa and a critical temperature of 546.5 K. These predicted data are off by about 700 kPa and 9 K with respect to the experimental data listed in Table 2. Equations of State for Glymes with n = 2, 3, and 4. The PC-SAFT EoSs for the n = 2, 3, and 4 members of the homologous series are formulated analogously to that of monoEGDME. A summary of available experimental data is provided in Table 1. Although the determination of the critical properties is not required to obtain the pure-component fluid parameters of the PC-SAFT model, the value of critical properties is relevant in general. Experimental critical-point data were not found in the open literature, with the exception of those for monoEGDME. The estimation of the critical properties of the other constituents of the solvent is briefly described here for the sake of completeness. The values of critical temperature are obtained with the Marrero−Pardillo method,67 as suggested in ref 66, using either the estimated or experimental values of the normal boiling point from an evaluated database.27 The critical pressure PC and the critical specific volume vC are also obtained with the Marrero−Pardillo method. If a single estimation method is used, data inconsistency among homologues within a fluid family is less of an issue. Numerical values for estimated normal-boiling-point and critical-point data are listed in Table 5. Experimental ideal gas (isobaric) heat capacity data are not available, and therefore values had to be estimated. Following the adoption of Joback’s method for monoEGDME, this method was used also for the other compounds. The estimated data are listed in Table 3 for diEGDME, triEGDME, and tetraEGDME. The pure-component parameters for the PCSAFT EoS of diEGDME, triEGDME, and tetraEGDME are

m = 0.0243M + 1.4177

(6)

mσ 3/100 = 0.0130M + 0.1738

(7)

mε /kB = 6.5902M + 248.25

(8)

These equations are then employed to predict the purecomponent parameters for the glymes with n = 5, ..., 9.These equations can also be used to compare the parameter values found by Kiesow et al.25 for a glyme with a molar mass of 2000 g/mol. For this component, these authors obtained purecomponent parameters m = 40.7, σ = 4.0261, and ε/kB = 250.00, while the equations developed in this work would predict values of m = 50.0, σ = 3.74, and ε/kB = 268.5. This good correspondence despite the very large extrapolation provides reassurance that the developed equations are accurate. Joback’s method for the estimation of the ideal gas isobaric heat capacity is used also for these substances for consistency. Table 7 reports the resulting pure-component parameters. The critical properties are not estimated for the larger glymes, since the molecules of these compounds are not thermochemically stable in the range of expected critical temperatures. For example, the TC of tetraEGDME, 713.5 K, is already in the range of the thermal decomposition temperature of the most stable organic compounds in contact with stainless steel, which is around 673.15 K.68,69 Glyme-Based Commercial Solvents. The glyme-based commercial solvents are usually blends. In this section, the work is extended to model mixtures by considering binary interaction parameters among the constituents. Because of the unavailability of experimental VLE thermodynamic data for mixtures of the homologous members, all binary interaction 18405



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Table 6. Input Data for the EoSs of Di-, Tri-, and Tetraethylene Glycol Dimethylether and the Average Absolute Relative Deviations of the Model with Respect to the Experimental Dataa value n=2

parameter M m σ ε/kB A B × 103 C × 106 D × 109

134.1736 4.718 02 3.431 13 240.540 73.9340 384.240 30.4000 −104.20

densities vapor pressures heat capacities a

0.51 3.9 2.2

n= 3

n=4

178.266 5.737 24 3.512 60 247.930 97.6208 511.014 32.6438 −135.223 Average Absolute Relative Deviations (AARDs) 0.49 4.2 4.1

unit

222.279 6.823 18 3.553 23 250.720 121.301 637.827 34.8200 −166.210

kg/kmol Å K kJ/(kmol kJ/(kmol kJ/(kmol kJ/(kmol

0.47 2.4 4.1

K) K2) K3) K4)

% % %

The temperature range of validity for these parameters is set to 300−1000 K.

Table 8. The Approximate Composition of the Selexol Solvent1 Taken from Ameen and Seymoura fluid name

mole fraction from ref 42 (PEGDME250)

mole fraction from ref 1 (Selexol)

triEGDME tetraEGDME pentaEGDME hexaEGDME heptaEGDME octaEGDME nonaEGDME molar mass [kg/kmol]

0.024 0.128 0.266 0.318 0.208 0.050 0.005 298

0.092 0.283 0.267 0.185 0.108 0.047 0.018 273

a

Figure 5. Correlation of the pure-component parameters m, σ, and ε/ kB with respect to the molar mass of the n = 1, ..., 4 members of the homologous series of the glymes. The squares (□) refer to m, the triangles (△) refer to mε/kB, and the circles (○) refer to mσ3/100. The correlations are used to predict the pure-component parameters for the n = 5, ..., 9 members of the homologous series of the glymes.

The composition is similar to that of GENOSORB1753, for which some experimental thermodynamic data are available (supplied by the manufacturer70). Note that a well-known fluid database28 does not make a distinction between GENOSORB1753 and the Selexol solvent. The composition of PEGDME250 is also listed.42 PEGDME250 is considered solely because some experimental data, albeit scarce, are available, and therefore a performance assessment can be made with regard to the developed thermodynamic model of the mixture.

parameters within the glyme series are set to a value of zero (0). This assumption holds well when PC-SAFT is used to model mixtures of a homologous series.7 The approximate composition of the Selexol solvent is taken from Ameen and Seymour1 and is listed in Table 8. Computations with the new EoS for the Selexol mixture of glymes yield liquid-density predictions with an AARD of 1.0%,

based on 18 data points; see Figure 6, showing only the data from Li et al.71 The experimental data are for GENOSORB1753, which, according to literature, should have about the same composition as the Selexol solvent. Liquid heat capacities are predicted to have an AARD of 3.9%, on the basis of nine data points at pressures of 100 kPa and temperatures spanning the range of 283−397 K. The predictions of mixture

Table 7. Input Data for the EoSs of Penta-, Hexa-, Hepta-, Octa-, and Nonaethylene Glycol Dimethylethera value parameter

n=5

n=6

n=7

n=8

n=9

M m σ ε/kB A B × 103 C × 106 D × 109

266.3312 7.8895 3.5853 253.93 144.98 764.64 37.000 −197.20

310.0 8.9507 3.6080 255.98 168.66 891.44 39.200 −228.20

354.0 10.020 3.6257 257.60 192.344 1018.2 41.400 −259.20

398.0 11.089 3.6399 258.92 216.03 1145.0 43.600 −290.20

442.0 12.158 3.6516 260.00 239.71 1271.8 45.800 −321.20

unit kg/kmol Å K kJ/(kmol kJ/(kmol kJ/(kmol kJ/(kmol

K) K2) K3) K4)

a

The temperature range of validity for these parameters is set to 300−1000 K, on the basis of the applicability range of the adopted correlations. The parameters A, B, C, and D for the ideal gas isobaric heat capacity correlation were determined with Joback’s method, as documented by Poling et al.66 18406



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Conesa et al.,42 is shown. The reason for doing so is simply to display the difference between the two solvent blends in terms of the vapor pressure predictions. Moreover, since the composition of PEGDME250 is documented (see Table 8), the few experimental data regarding PEGDME250 can also be utilized to assess the quality of the thermodynamic model developed in this work. With mutual kij values set to zero (0), the EoS for PEGDME250 predicts liquid densities with an AARD of 0.42%, based on 23 data points (see Figure 8), and liquid heat capacities with an AARD of 4.4%,

Figure 6. Experimental liquid density data for GENOSORB1753 taken from Li et al.71 and the corresponding computed density data. The line represents computed data, the open symbols (□) represent the experimental data, and the filled symbols (■) represent the deviations on the second ordinate.

densities and heat capacities thus retain the quality of the fitted EoS for the individual pure components. Vapor pressure data for GENOSORB1753 were obtained from the manufacturer.70 The EoS for the solvent predicts the GENOSORB1753 vapor pressure data with an average absolute deviation (AAD) of 10 kPa. However, the vapor pressure data span a temperature range of 383−469 K and a pressure range of 0.97−63 kPa; thus, at such low vapor pressures, the accurate composition of GENOSORB1753 is required for reliable and accurate predictions. From this perspective, Figure 7a illustrates the experimental data in the P−T diagram of Selexol on a logarithmic pressure scale to better visualize the points. Here, absolute differences between experimental and predicted data are presented instead of relative deviations; because the vapor pressure values are low, computing a relative deviation would result in large values (thereby giving a distorted view of the quality of predictions). The computed P−T diagram of the Selexol solvent is shown in Figure 7b. Therein also the P−T diagram of PEGDME250, using the composition according to

Figure 8. Deviations of experimental liquid density data for PEGDME250 taken from Conesa et al.42 with respect to computed density data. The line represents computed data, the open symbols (□) represent the experimental data, and the filled symbols (■) represent the deviations (scale on the secondary ordinate).

based on 12 data points at pressures and temperatures spanning the ranges of 100−1000 kPa and 293−423 K (see Figure 8). A closer inspection of the data presented in Figure 8 shows that density predictions of PC-SAFT are consistently higher than the experimental values. According to Figure 9, PC-SAFT predictions for the liquidphase isobaric heat capacity are consistently lower than experimental values. Still, the prediction of mixture properties

Figure 7. The P−T diagram of Selexol-type solvents. (a) Experimental vapor pressure data obtained from the manufacturer70 (open squares □) are included as well as the deviations between predicted vapor pressures (using the composition according to Ameen and Seymour1) and experimental values (filled squares ■, values on the secondary ordinate). The pressure scale is adapted to better visualize the data. (b) P−T diagram of two mixtures composed of glymes. The continuous line refers to the composition (PEGDME250) according to Conesa et al.,42 whereas the dash-dot-dot line is calculated using the approximate composition (Selexol) given by Ameen and Seymour1. The computed critical points are indicated using circles (○). 18407



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also be estimated.72,73 In this section, the focus is briefly on the binary mixtures of CO2, H2S, CH4, and water with these solvents. For the other gas/vapor components, no binary data with glymes were found. As a preliminary model performance test, Table 9 lists experimental data for Henry’s law constants of selected glymes + CO2 mixtures and values determined with the EoS. If fi ̂ represents the fugacity of component i in solution, then the Henry’s law constant is determined using HCO2 ≡ lim

xCO2 → 0

̂ fCO

2

xCO2

⎛ df ̂ ⎞ CO2 ⎟ =⎜ ⎜ dxCO ⎟ 2⎠ ⎝ x

CO2 = 0

(9)

̂ /dxCO )x = 0 for PC-SAFT can be An expression for (dfCO 2 2 CO2 developed. All involved binary interaction parameters for the glyme + CO2 mixtures are picked to get the lowest AARD of the experimental data with respect to the computed data. The Henry’s law constants of the solvent blends PEGDME250 and Selexol can be described with an AARD of 11% and 6.3%, respectively, over the temperature range from 25 to 60 °C, using constant binary interaction parameters. Note that, if thermodynamic properties of CO2 are modeled using the perturbed chain polar (PCP)-SAFT (see Gross17 for the EoS parameters), the Henry’s law constants predicted using optimized binary interaction parameters exhibit slightly greater deviations with respect to experimental data for all substances considered in Table 9b, except for the monoglyme. This result is unexpected since the thermodynamic model for CO2 is not only more accurate when quadrupolar effects are considered but also physically sound. In analogy with the procedure used to determine kij for the glymes + CO2 binary systems of Table 9, kij for the system tetraEGDME + H2S can also be optimzed. Taking the EoS parameters for H2S from ref 12 and Henry’s law constants from ref 77, kij for the system of tetraEGDME + H2S becomes

Figure 9. Deviation of experimental liquid isobaric heat capacity data for PEGDME250 taken from Conesa et al.42 with respect to computed heat capacity data. The line represents computed data, the open symbols (□) represent the experimental data, and the filled symbols (■) represent the deviations (scale on the secondary ordinate).

is again of the same quality as the fitted EoS of the pure components. Vapor pressure data for PEGDME250 have not been found in the literature.

■

MIXTURES OF THE SELEXOL SOLVENT WITH GASES TYPICALLY ENCOUNTERED IN GAS-CLEANING APPLICATIONS Glyme-based blends are typically used in gas-cleaning applications in which the solvent is mostly in contact with the following gases/vapors: Ar, CH4, CO, CO2, H2, H2O, H2S, and N2. To model such gas-cleaning processes, the properties of mixtures of these gases together with the solvent must be computed with sufficient accuracy. For this purpose, the PCSAFT EoS is a suitable tool, provided that binary interaction parameters are available. In addition, transport properties can Table 9. Henry’s Law Constant H for CO2 in Selected Glymesa fluid T [°C]

n=1 exp.

n=2 EoS

exp.

n=3 EoS

exp.

n=4 EoS

exp.

PEGDME250 EoS

25 30 40 50 60 optimal kij AARD [%]

55

48

(a) CO2 Modeled Using the Parameters Given by Gross and Sadowski 48 64 44 50 30/31.6 34

59

59

82

76

119

25 30 40 50 60 optimal kij AARD [%]

55 59

71

−0.068 5.1

60

61

43 47.4 65

42 47.5 53

EoS

exp.

EoS

32

36

43

44

35.2 39.5 46.7 56.2 65.5

38.4 41.0 46.5 52.2 58.1

7

66

49

97 89 76 0.075 0.065 0.040 20 10 8.4 (b) CO2 Modeled Using the Parameters Given by Gross17 48 70 44 51 30/31.6 35

32

36

59

82

43

43

74

119

0.037 6.9

71

77

−0.022 21

82

60

98

89

60 73 −0.045 11

43 47.4 65

42 47.7 53 −0.072 9.4

Selexol

exp.

55 0.060 11

66

0.065 6.3

53 −0.055 11

35.2 39.5 46.7 56.2 65.5

38.7 41.0 45.9 50.9 56.0 −0.048 7.9

a

The unit of H is bar. Note that the kij values are optimized to get the lowest AARD with respect to experimental data, given the temperature range. Data are from Henni et al., Xu et al., and Sweeney.74−76 Note that, for the kij for the mixtures of PEGDME250 + CO2 and Selexol + CO2, the solvent is modeled using the composition listed in Table 8, whereby the kij values for the pairs triEGDME + CO2 and tetraEGDME + CO2 are set to the optimal value, and the kij values for the other glyme + CO2 pairs are all assumed to be the same. The latter value is fitted and reported. “exp.” is the abbreviation for experimental. 18408



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−0.075 for temperatures spanning the range of 25−100 °C (data about other glyme + H2S systems were not found in the literature). Similarly, for CH4, using the EoS parameters from ref 7 and Henry’s law constants published by Henni et al.,78 kij = 0.031 and kij = 0.028 for the systems of triEGDME + CH4 and tetraEGDME + CH4, respectively, in the temperature range between 25 and 60 °C. Data about other glyme + CH4 systems were not found in the literature. With regard to the modeling of glyme + water mixtures a caveat must be added. These kinds of mixtures are more difficult to treat: even if glymes are nonself-associating compounds, as a mixture effect they may show cross-association interactions with a self-associating substance (e.g., H2O, H2S). Whereas cross-association interactions seem negligible in mixtures of glymes and H2S, the formation of oxygen− hydrogen bonds among glymes and water is suggested by different authors,79−81 on the basis of the observations that (a) the excess molar volumes of these kinds of mixtures at all temperatures and compositions are negative, and that (b) viscosity increases sharply and deviates considerably from a linear dependence on mole fractions. Although the interpretation of these mixture properties can be questionable (e.g., negative deviations from ideality of the molar volume can be due to changes in the water structure80), spectroscopy measurements carried out by Trouw et al.82 seem to certify the extensive presence of hydrogen bonds between the water and the ether oxygens of the glymes. This type of interaction is defined as “induced association” since the cross association of glymes is only induced by the presence of water. Kleiner and Sadowski83 proposed a simple approach to account for induced association, only based on the combining rules of Wolbach and Sandler (eqs 10 and 11) and the knowledge of pure-component parameters. The combining rules of Wolbach and Sandler read ε AiBj =

1 AiBi (ε + ε AjBj) 2

Tx data points are available in the temperature range of 309− 380 K.) With cross-association interactions modeled following Kleiner and Sadowski,83 kij for the tetraEGDME + H2O is −0.127. Using these scarce data, it is not possible to decide about the relevance of induced association. For theoretical soundness, we recommend considering the effect.

■

SUMMARY This paper documents the development of an EoS for Selexoltype solvents composed of glyme blends. The thermodynamic model developed in this work is intended to account for the true thermodynamic behavior of Selexol-type solvents, since it indeed models the solvent as a mixture rather than as a pseudopure fluid or a copolymer. Because of the scarcity of pure-fluid and mixture data on polyEGDMEs, it was decided a priori to use a functional relationship for the EoS that is both simple and allows for the consistent and robust prediction of thermodynamic properties. Another advantage is that it provides enough flexibility to improve the thermodynamic description of the fluid when more experimental data become available. The selected EoS is based upon the PC-SAFT. The EoS for pure components requires only three pure-component parameters. The modeling of a mixture of components with the PC-SAFT EoS requires only binary interaction parameters. Here, because of the unavailability of mixture data among the glymes, all involved binary interaction parameters are set to a value of zero (0). Nonetheless, computations with the new EoS for the Selexol solvent yield liquid-density predictions with an AARD of 1.0% (based on 18 data points) and predict liquid heat capacities with an AARD of 3.9% (based on nine data points), at a pressure of 100 kPa and temperatures spanning the range of 283−397 K. Available vapor pressure data span a temperature range of 383−469 K and a pressure range of 0.97−63 kPa, and computations with the EoS yield a consistent overprediction of vapor pressure data. The highest overprediction is 21 kPa at 469 K/63 kPa. The lowest overprediction is 1.9 kPa, and it occurs at 383 K/0.97 kPa. However, the vapor pressure values are quite low, and at such low vapor pressures, the accurate composition of the solvent must be known, for reliable predictions to be made. To assess the performance of the EoS of a mixture composed of the n = 3, ..., 9 members of the homologous series of glymes, the solvent PEGDME250 was also considered, since its composition has been published in the open literature. With mutual kij values set to zero, the EoS for PEGDME250 predicts liquid densities with an AARD of 0.42% (based on 23 data points) and liquid heat capacities with an AARD of 4.4% (based on 12 data points), at pressures and temperatures spanning the ranges of 100−1000 kPa and of 293−423 K. Vapor pressure data were not found in the literature. In addition, using Henry’s law constants, kij values are provided for mixtures of glymes and componentsspecifically, carbon dioxide, hydrogen sulfide, methane, and water typically encountered in gas-cleaning applications. The developed thermodynamic model should provide a valuable engineering tool and starting point for process design and optimization.

(10)

and κ

AiBj

=

κ

⎛ ⎞3 σiiσjj ⎜ 1/2(σ + σ ) ⎟⎟ ⎝ ii jj ⎠

AiBi AjBj ⎜

κ

(11)

By setting to zero the εAiBi for glymes, the non-selfassociating nature of these compounds is preserved in the thermodynamic model, while the association volume parameter κAiBi is set to equal the value of the associating component. It is not necessary to fit to experiments the κAiBi of the non-selfassociating substance, because, according Kleiner and Sadowski,83 the phase behavior predicted by the model is less sensitive to this parameter. The experimental thermodynamic property data available in literature for mixtures of glymes and water are limited to the density measurements of refs 79−81. The analysis of these published data does not allow the demonstration of the importance of considering induced association, because the improvements in the description of mixture densities are only marginal, far less than the inaccuracies due to the error in the estimation of pure water density. Better results might be possible using improved models for pure water.84 As expected, the benefits of the extended thermodynamic model are larger for VLE. However, these data are scarce, apart from confidential data purchased from a well-known fluid database.28 (For tetraEGDME + water, for example, eight P−

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 18409



Article

Notes

(18) Gross, J.; Vrabec, J. An Equation-of-State Contribution for Polar Components: Dipolar Molecules. AIChE J. 2006, 52, 1194−1204. (19) Lemmon, E. W.; McLinden, M. O.; Huber, M. L. REFPROP Reference Fluid Thermodynamic and Transport Properties Database. Version 9.1.; National Institute of Standards and Technology: Gaithersburg, MD, 2002. (20) Bardow, A.; Steur, K.; Gross, J. Continuous-Molecular Targeting for Integrated Solvent and Process Design. Ind. Eng. Chem. Res. 2010, 49, 2834−2840. (21) Bymaster, A.; Emborsky, C.; Dominik, A.; Chapman, W. G. Renormalization-Group Corrections to a Perturbed-Chain Statistical Associating Fluid Theory for Pure Fluids near to and Far from the Critical Region. Ind. Eng. Chem. Res. 2008, 47, 6264−6274. (22) Tang, X.; Gross, J. Renormalization-Group Corrections to the Perturbed-Chain Statistical Associating Fluid Theory for Binary Mixtures. Ind. Eng. Chem. Res. 2010, 49, 9436−9444. (23) Aspen Plus Model of the CO2 Capture Process by DEPG; Aspen Technology, Inc.: Burlington, MA, 2008. (24) Li, Z.; Chen, C.-C. Development of a DEPG-Based CO2 Capture Process Model. Poster 2−17, The 12th International Conference on Properties and Phase Equilibria for Product and Process Design (PPEPPD), Suzhou, China, May 16−21, 2010. (25) Kiesow, K.; Ruether, F.; Sadowski, G. Solubility, Crystallization and Oiling-out Behavior of PEGDME: 1. Pure-Solvent Systems. Fluid Phase Equilib. 2010, 298, 253−261. (26) Vrabec, J.; Gross, J. VaporLiquid Equilibria Simulation and an Equation of State Contribution for Dipole-Quadrupole Interactions. J. Phys. Chem. B 2008, 112, 51−60. (27) Rowley, R. L.; Wilding, W. V.; Oscarson, J. L.; Yang, Y.; Zunderland, N. A.; Daubert, T. P.; Danner, R. P. DIPPR Data Compilation of Pure Chemical Properties; Taylor and Francis Publishing Company: New York, NY, 2004. (28) Dechema Department Information Systems and Databases; http:// i-systems.dechema.de/. (29) NIST Chemistry WebBook; NIST: Gaithersburg, MD, http:// webbook.nist.gov/. (30) Lago, A.; Rivas, M. A.; Legido, J.; Iglesias, T. P. Study of Static Permittivity and Density of the Systems (n-Nonane + Monoglyme Or Diglyme) At Various Temperatures. J. Chem. Thermodyn. 2009, 42, 257−264. (31) Steele, W. V.; Chirico, R. D.; Knipmeyer, S. E.; Nguyen, A.; Smith, N. K. Thermodynamic Properties and Ideal Gas Enthalpies of Formation for Butyl Vinyl Ether, 1,2-Dimethoxyethane, Methyl Glycolate, Bicyclo[2.2.1]hept-2-ene, 5-Vinylbicyclo[2.2.1]hept-2-ene, trans-Azobenzene, Butyl Acrylate, di-tert-Butyl Ether, and Hexane-1,6diol. J. Chem. Eng. Data 1996, 41, 1285−1302. (32) Pal, A.; Sharma, S. Excess Molar Volumes and Viscosities of 1Propanol + Ethylene Glycol, + Ethylene Glycol Monomethyl, + Ethylene Glycol Dimethyl, + Diethylene Glycol Dimethyl, + Triethylene Glycol Dimethyl, + Diethylene Glycol Diethyl, And + Diethylene Glycol Dibutyl Ethers at 298.15 K. J. Chem. Eng. Data 1998, 43, 532−536. (33) Zheng, P.; Meng, X.; Wu, J.; Liu, Z. Density and Viscosity Measurements of Dimethoxymethane and 1,2-Dimethoxyethane from 243 to 373 K up to 20 MPa. Int. J. Thermophys. 2008, 29, 1244−1256. (34) Roy, M. N.; Sarkar, B. K.; Chanda, R. J. Viscosity, Density, And Speed of Sound for the Binary Mixtures of Formamide with 2Methoxyethanol, Acetophenone, Acetonitrile, 1,2-Dimethoxyethane, And Dimethylsulfoxide at Different Temperatures. J. Chem. Eng. Data 2007, 52, 1630−1637. (35) Manfredini, M.; Marchetti, A.; Sighinolfi, S.; Tassi, L.; Ulrici, A.; Vagnali, M. Densities and Excess Molar Volumes of Binary Mixtures Containing 1,2-Dichloroethane + 2-Methoxyethanol or 1,2- Dimethoxyethane at Different Temperatures. J. Mol. Liq. 2002, 100, 163− 181. (36) Cocchi, A.; Manfredini, M.; Marchetti, A.; Sighinolfi, A.; Tassi, L.; Ulrici, A.; Vignali, M. The Ethane-1,2-Diol + 2-Methoxyethanol + 1,2-Dimethoxyethane Ternary Solvent System: Density and Volume

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work is part of the CO2 Catch-up R&D program to demonstrate and optimize precombustion CO2 capture technology for the energy sector, conducted by Nuon (Vattenfall Business Group Benelux) together with partners. The authors wish to thank Kay Damen for helpful discussions and support of this work and Prof. Joachim Gross for making the code of PC-SAFT available and helpful suggestions on modeling using PC-SAFT.

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REFERENCES

(1) Ameen, J.; Seymour, A. Solvent Composition Useful in Acid Gas Removal from Gas Mixtures. United States Patent Office (No. 3,737,392), 1973. (2) Rubin, E. S.; Berkenpas, M. B.; Frey, H. C.; Chen, C.; McCoy, S.; Zeremsky, C. J. Development and Application of Optimal Design Capability for Coal Gasification Systems; Final Report to the U.S. Department of Energy under Contract No. DE-AC21-92MC29094; Carnegie Mellon University: Pittsburgh, PA, 2007. (3) Krishnan, G.; Steele, D.; O’Brian, K.; Callahan, R.; Berchtold, K.; Figueroa, J. Simulation of a Process to Capture CO2 from IGCC Syngas using a High-Temperature PBI Membrane. Energy Procedia 2009, 1, 4079−4088. (4) Peng, D.-Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (5) Wong, H.; Shan, D.; Sandler, S. I. Theoretically Correct Mixing Rule for Cubic Equations of State. AIChE J. 1992, 38, 671−680. (6) Vega, L. F.; Jackson, G. 20 Years of the SAFT Equation of State: Recent Advances and Challenges. Fluid Phase Equilib. 2011, 306, 1−3. (7) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40, 1244−1260. (8) Kozgowska, M. K.; Jurgens, B. F.; Schacht, C. S.; Gross, J.; De Loos, T. W. Phase Behavior of Hyperbranched Polymer Systems: Experiments and Application of the Perturbed-Chain Polar SAFT Equation of State. J. Phys. Chem. B 2009, 113, 1022−1029. (9) Tumakaka, F.; Gross, J.; Sadowski, G. Thermodynamic Modeling of Complex Systems Using PC-SAFT. Fluid Phase Equilib. 2005, 228− 229, 89−98. (10) Gross, J.; Spuhl, O.; Tumakaka, F.; Sadowski, G. Modeling Copolymer Systems Using the Perturbed-Chain SAFT Equation of State. Ind. Eng. Chem. Res. 2003, 42, 1266−1274. (11) Pedrosa, N.; Pàmies, J. C.; Coutinho, J. A. P.; Marrucho, I. M.; Vega, L. F. Phase Equilibria of Ethylene Glycol Oligomers and Their Mixtures. Ind. Eng. Chem. Res. 2005, 44, 7027−7037. (12) Tang, X.; Gross, J. Modeling the Phase Equilibria of Hydrogen Sulfide and Carbon Dioxide in Mixture with Hydrocarbons and Water Using the PCP-SAFT Equation of State. Fluid Phase Equilib. 2010, 293, 11−21. (13) Kroon, M. C.; Karakatsani, E. K.; Economou, I. G.; Witkamp, G.-J.; Peters, C. J. Modeling of the Carbon Dioxide Solubility in Imidazolium-Based Ionic Liquids with the tPC-PSAFT Equation of State. J. Phys. Chem. B 2006, 110, 9262−9269. (14) Karakatsani, E. K.; Economou, I. G.; Kroon, M. C.; Peters, C. J.; Witkamp, G.-J. tPC-PSAFT Modeling of Gas Solubility in Imidazolium-Based Ionic Liquids. J. Phys. Chem. C 2007, 111, 15487−15492. (15) Ji, X.; Adidharma, H. Thermodynamic Modeling of CO2 Solubility in Ionic Liquid with Heterosegmented Statistical Associating Fluid Theory. Fluid Phase Equilib. 2010, 293, 141−150. (16) Ji, X.; Held, C.; Sadowski, G. Modeling Imidazolium-Based Ionic Liquids with ePC-SAFT. Fluid Phase Equilib. 2012, 335, 64−73. (17) Gross, J. An Equation-of-State Contribution for Polar Components: Quadrupolar Molecules. AIChE J. 2005, 51, 2556−2568. 18410



Article

Properties at Different Temperatures. Phys. Chem. Liq. 2001, 39, 481− 498. (37) Ferrari, G.; Foca, G.; Manfredini, M.; Manzini, D.; Marchetti, A.; Tassi, L.; Ulrici, A. Density and Volume Properties of the 2Chloroethanol + 2-Methoxyethanol + 1,2-Dimethoxyethane Ternary Solvent System at Different Temperatures. J. Solution Chem. 2003, 32, 93−116. (38) Comuñas, M. J. P.; Baylaucq, A.; Boned, C.; Fernández, J. Volumetric Properties of Monoethylene Glycol Dimethyl Ether and Diethylene Glycol Dimethyl Ether up to 60 MPa. J. Chem. Eng. Data 2003, 48, 1044−1049. (39) Carvajal, C.; Tölle, K. J.; Smid, J.; Szwarc, M. Studies of Solvation Phenomena of Ions and Ion Pairs in Dimethoxyethane and Tetrahydrofuran. J. Am. Chem. Soc. 1965, 87, 5548−5553. (40) Ulrici, A.; Cocchi, M.; Foca, G.; Manfredini, M.; Manzini, D.; Sighinolfi, S.; Tassi, L. Study of the Dependence on Temperature and Composition of the Volumic Properties of Ethane-1,2-Diol + 2Methoxyethanol + 1,2-Dimethoxyethane + Water Solvent System and Graphical Representation in the Quaternary Domain. J. Solution Chem. 2006, 35, 139−159. (41) López, E. R.; Daridon, J. L.; Plantier, J. L.; Boned, C.; Fernández, J. Temperature and Pressure Dependences of Thermophysical Properties of Some Ethylene Glycol Dimethyl Ethers from Ultrasonic Measurements. Int. J. Thermophys. 2006, 27, 1354−1372. (42) Conesa, A.; Shen, S.; Coronas, A. Liquid Densities, Kinematic Viscosities, and Heat Capacities of Some Ethylene Glycol Dimethyl Ethers at Temperatures from 283.15 to 423.15 K. Int. J. Thermophys. 1998, 19, 1343−1358. (43) Francesconi, R.; Comelli, F.; Bigi, A.; Rubini, K. Thermophysical Properties of Dimethyl Sulfoxide + Cyclic and Linear Ethers at 308.15 K. Application of an Extended Cell Model. Thermochim. Acta 2006, 447, 154−160. (44) Quadri, S. K.; Kudchadker, A. P. Measurement of the Critical Temperatures and Critical Pressures of Some Thermally Stable or Mildly Unstable Esters, Ketones, And Ethers. J. Chem. Thermodyn. 1991, 23, 129−134. (45) Treszczanowicz, T. VaporLiquid Equilibria of Non-Electrolytes 0.4. VaporLiquid Equilibria of Binary Systems Formed by 1,2Dimethodyethane with Normal-Propyl Ether and Isopropyl Ether. Bull. Acad. Pol. Sci., Ser. Sci. Chim. 1979, 27, 697−703. (46) Kobe, K. A.; Ravicz, A. E.; Vohra, S. P. Critical Properties and Vapor Pressures of Some Ethers and Heterocyclic Compounds. J. Chem. Eng. Data 1956, 1, 50−56. (47) Ku, H.-C.; Tu, C.-H. Densities and Viscosities of Seven Glycol Ethers from 288.15 to 343.15 K. J. Chem. Eng. Data 45, 2. (48) Aminabhavi, T. M.; Phayde, H. T. S.; Aralaguppi, M. I.; Khinnavar, R. S. Densities, Viscosities, and Speeds of Sound for Diethylene Glycol Dimethyl Ether + Methyl Acetate. J. Chem. Eng. Data 1993, 38, 540−541. (49) Aminabhavi, T. M.; Phayde, H. T. S.; Khinnavar, R. S.; Bindu, G. Densities, Refractive Indices, Speeds of Sound, and Viscosities of Diethylene Glycol Dimethyl Ether + Butyl Acetate at 298.15, 303.15, 308.15, 313.15, and 318.15 K. J. Chem. Eng. Data 1993, 38, 542−545. (50) Aminabhavi, T. M.; Phayde, H. T. S.; Khinnavar, R. S.; Gopalakrishna, B.; Hansen, K. C. Densities, Refractive Indices, Speeds of Sound, And Shear Viscosities of Diethylene Glycol Dimethyl Ether with Ethyl Acetate, Methyl Benzoate, Ethyl Benzoate, and Diethyl Succinate in the Temperature Range from 298.15 to 318.15 K. J. Chem. Eng. Data 1994, 39, 251−260. (51) Beaumont, R. H.; Clegg, B.; Gee, G.; Herbert, J. B. M.; Marks, D. J.; Roberts, R. C.; Sims, D. Heat Capacities of Propylene Oxide and of Some Polymers of Ethylene and Propylene Oxides. Polymer 1966, 7, 401−417. (52) Comuñas, M. J. P.; Fernández, J.; Baylaucq, A.; Canet, X.; Boned, C. PρTx Measurements for HFC-134a + Triethylene Glycol Dimethylether System. Fluid Phase Equilib. 2002, 199, 185−195. (53) Comuñas, M. J. P.; López, E. R.; Pires, P.; García, J.; Fernández, J. PρT Measurements of Polyethylene Glycol Dimethylethers between

278.15 and 328.15 K at Pressures to 12 MPa. Int. J. Thermophys. 2000, 21, 831−851. (54) Trejo, L. M.; Costas, M.; Patterson, D. Effect of Molecular Size on the W-Shaped Excess Heat Capacities: Oxaalkane-Alkane Systems. J. Chem. Soc., Faraday Trans. 1991, 87, 3001−3008. (55) Benson, G. C.; Kumaran, M. K.; Treszczanowicz, T.; D’arcy, P. J.; Halpin, C. J. Thermodynamic Properties for 2,5,8,11-Tetraoxadodecane + n-Dodecane Mixtures at 298.15 K. Thermochim. Acta 1985, 95, 59−66. (56) Tovar, C. A.; Carballo, E.; Cerdeiriña, C. A.; Legido, J. L.; Romaní, L. Effect of Temperature on W-Shaped Excess Molar Heat Capacities and Volumetric Properties: Oxaalkane-Nonane Systems. Int. J. Thermophys. 1997, 18, 761−777. (57) Pal, A.; Kumar, A. Volumetric Properties of (n-Alkanol + Polyether) Systems at 298.15 K. Fluid Phase Equilib. 1999, 161, 153− 168. (58) Pereira, S. M.; Rivas, M. A.; Real, J. N.; Legido, J. L.; Iglesias, T. P. Densities, Speeds Of Sound, And Refractive Indices Of The Mixture Nonane + Triethylene Glycol Dimethyl Ether At 288.15 K, 293.15 K, 298.15 K, and 308.15 K. J. Chem. Eng. Data 2002, 47, 919−922. (59) Lopez, E. R.; Daridon, J. L.; Baylaucq, A.; Fernández, J. Thermophysical Properties of Two Poly(alkylene glycol) Derivative Lubricants from High Pressure Acoustic Measurements. J. Chem. Eng. Data 2003, 48, 1208−1213. (60) Tovar, C. A.; Carballo, E.; Cerdeiriña, C. A.; Romaní, L. Excess Molar Volumes and Excess Molar Heat Capacities of (2,5,8,11Tetraoxadodecane + C4H8O2 Ester Isomers) at Several Temperatures. J. Chem. Thermodyn. 1997, 29, 1353−1361. (61) Detherm confidential data (company research reports, 1982/ 1986). 1982/1986; PRP-21087i.1986 [369578] and PRP-22018i.1982 [374213]. (62) Treszczanowicz, T.; Lu, B. C.-Y. Isothermal VapourLiquid Equilibria for 11 Examples of (an Ether + a Hydrocarbon). J. Chem. Thermodyn. 1986, 18, 213−220. (63) Comuñas, M. J. P.; Baylaucq, A.; Boned, C.; Canet, X.; Fernández, J. High-Pressure Volumetric Behavior of x 1,1,1,2Tetrafluoroethane + (1  x) 2,5,8,11,14-Pentaoxapentadecane (TEGDME) Mixtures. J. Chem. Eng. Data 2002, 47, 233−238. (64) Acevedo, I. L.; Lugo, L.; Comuñas, M. J. P.; Arancibia, E. L.; Fernández, J. Volumetric Properties of Binary Tetraethylene Glycol Dimethyl Ether + Heptane Mixtures between (278.15 and 353.15) K and up to 25 MPa. J. Chem. Eng. Data 2003, 48, 1271−1278. (65) Chaudhari, S. K.; Patil, K. R.; Allepús, J.; Coronas, A. Measurement of the Vapor Pressure of 2,2,2-Trifluoroethanol and Tetraethylene Glycol Dimethyl Ether by Static Method. Fluid Phase Equilib. 1995, 108, 159−165. (66) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. On the Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 2001. (67) Marrero-Morejón, J.; Pardillo-Fontdevila, E. Estimation of Pure Compound Properties Using Group-Interaction Contributions. AIChE J. 1999, 45, 615−621. (68) Cole, R. L.; Demirgian, J. C.; Allen, J. W. Predicting Toluene Degradation in Organic Rankine Cycle Engines. Proceedings of the 20th Intersociety Energy Conversion Engineering Conference (IECEC), paper 879075, Philadelphia, 1987. (69) Calderazzi, L.; di Paliano, P. C. Thermal Stability of R-134a, R141b, R-13I1, R-7146, R-125 Associated with Stainless Steel as a Containing Material. Int. J. Refrig. 1997, 20, 381−389. (70) Genosorb Technical Data Sheet; Clariant Produkte GmbH, Functional Chemicals Division: Germany, 2008. (71) Li, J.; Mundhwa, M.; Henni, A. Volumetric Properties, Viscosities, Refractive Indices, And Surface Tensions for Aqueous Genosorb 1753 Solutions. J. Chem. Eng. Data 2007, 52, 955−958. (72) Novak, L. Fluid Viscosity-Residual Entropy Correlation. Int. J. Chem. React. Eng. 2011, 9, 1542−6580. (73) Novak, L. Self-Diffusion Coefficient and Viscosity in Fluids. Int. J. Chem. React. Eng. 2011, 9, 1542−6580. 18411



Article

(74) Henni, A.; Tontiwachwuthikul, P.; Chakma, A. Solubilities of Carbon Dioxide in Polyethylene Glycol Ethers. Can. J. Chem. Eng. 2005, 82, 358−361. (75) Xu, Y.; Schutte, R. P.; Hepler, L. G. Solubilities of Carbon Dioxide, Hydrogen Sulfide and Sulfur Dioxide in Physical Solvents. Can. J. Chem. Eng. 1992, 70, 569−573. (76) Sweeney, C. W. Solubilities and Partial Molar Enthalpies of Solution for Polar GasLiquid Systems Determined by Gas Chromatography. Chromatographia 1984, 18, 663−667. (77) Härtel, G. Low-Volatility Polar Organic Solvents for Sulphur Dioxide, Hydrogen Sulfide, and Carbonyl Sulfide. J. Chem. Eng. Data 1985, 30, 57−61. (78) Henni, A.; Tontiwachwuthikul, P.; Chakma, A. Solubility Study of Methane and Ethane in Promising Physical Solvents for Natural Gas Sweetening Operations. J. Chem. Eng. Data 2006, 51, 64−67. (79) Pal, A.; Singh, Y. P. Viscosity in Water + Ethylene Glycol Dimethyl, + Diethylene Glycol Dimethyl, + Triethylene Glycol Dimethyl, And + Tetraethylene Glycol Dimethyl Ethers at 298.15 K. J. Chem. Eng. Data 1996, 41, 1008−1011. (80) Henni, A.; Tontiwachwuthikul, P.; Chakma, A. Densities, Viscosities, and Derived Functions of Binary Mixtures: (Tetraethylene Glycol Dimethyl Ether + Water) from 298.15 to 343.15 K . J. Chem. Eng. Data 2004, 49, 1778−1781. (81) Henni, A.; Naami, A.; Tontiwachwuthikul, P. Densities, Viscosities, and Derived Functions of Binary Mixtures: (Triethylene Glycol Dimethyl Ether + Water) and (N-Acetylmorpholine + Water) from 298.15 to 343.15 K. J. Chem. Eng. Data 2005, 50, 1038−1042. (82) Trouw, F. R.; Borodin, O.; Cook, J. C.; Copley, J. R. D.; Smith, G. D. Quasielastic Neutron-Scattering Study of the Local Dynamics of Poly(ethylene glycol) Dimethyl Ether in Aqueous Solution. J. Phys. Chem. B 2003, 107, 10446−10452. (83) Kleiner, M.; Sadowski, G. Modeling of Polar Systems Using PCP-SAFT: An Approach to Account for Induced-Association Interactions. J. Phys. Chem. C 2007, 111, 15544−15553. (84) Held, C.; Cameretti, L. F.; Sadowski, G. Modeling Aqueous Electrolyte Solutions: Part 1. Fully Dissociated Electrolytes. Fluid Phase Equilib. 2008, 270, 87−96.

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An Equation of State Based on PC-SAFT for Physical Solvents

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