Thermodynamic Properties of Amines Under High Temperature and

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Thermodynamics, Transport, and Fluid Mechanics

Thermodynamic Properties of Amines Under High Temperature and Pressure: Experimental Results, Correlating with a new modified Tait-like equation and PC-SAFT Rokhsareh Mohammadkhani, Ameneh Paknejad, and Hosseinali Zarei Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b04732 • Publication Date (Web): 16 Nov 2018 Downloaded from http://pubs.acs.org on November 17, 2018

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Industrial & Engineering Chemistry Research

Thermodynamic Properties of Amines Under High Temperature and Pressure: Experimental Results, Correlating with a new modified Tait-like equation and PC-SAFT Rokhsareh Mohammadkhani, Ameneh Paknejad and Hosseinali Zarei* Department of Physical Chemistry, Faculty of Chemistry, Bu-Ali Sina University, Hamedan, Iran

ABSTRACT

New experimental densities for diethylamine (DEA), dibutylamine (DBA), and tributylamine (TBA) at 11 isotherms in the range of 293.15–473.15 K and 18 isobars up to 37.5 MPa are reported. PrT measurements (176 experimental data points) have been performed using a highpressure vibrating-tube densimeter. These data were correlated with a new modified Tait-like equation considering standard deviations of less than 2  104 g  cm 3 , then isothermal compressibility  T  and thermal expansion coefficient  P  were calculated. This study is supported by the results of modeling using the perturbed-chain statistical associating fluid theory

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(PC-SAFT). The parameters of PC-SAFT equation of state (EoS), for pure solvents, were rigorously determined by fitting the equation to the liquid PrT experimental data. In this study, the correlations, which are based on minimizing the total objective functions—density, pressure, and temperature—simultaneously, were developed to estimate the PC-SAFT parameters. The model reasonably predicted the behaviour of PrT and the first- and second-derivatives properties such as isothermal compressibility  T  , thermal expansion coefficient  P  , isobaric heat capacities C P  , and speed of sound (u). The results undoubtedly suggest that the model performance is enhanced for either cases of the new modified Tamman–Tait equation and the PC-SAFT EoS, based on employing the proposed parameters.

1. Introduction An accurate and predictive thermodynamic model is required for the calculations of thermodynamic derivative properties needed in several process engineering.1-3 Apart from their technological importance, obtaining these properties accurately is an interesting issue from a scientific standpoint.4 Although thermodynamic models are employed to predict some derivative properties as well as extrapolate the experimental data, a large number of high quality and accurate PrT experimental data is vital for parameter fitting, validation and development of the model. Such data are essential for engineering design in industrial practice.5, 6 Alkylamines are a very interesting class of compounds because of their strong electron donating capability.7 Amines are used to make azo-dyes, various drugs, and medicines.8 The most important use of diethylamine is principally as a production of vulcanization accelerators.9 Trialkylamines are industrially important liquids; used as intermediates in the production of


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polymers such as phenolic resins, lubricating additives, corrosion inhibitors, pharmaceuticals, textile dyes, paints, agrochemicals and polyurethane foams.10 To the best of our knowledge there is no experimental data in the literature. The only available experimental density data are at the ambient conditions and different temperatures.7, 8, 11-14 To derive the thermodynamic properties from PrT data, an equation of state is required that is able to thoroughly correlate density values over the full range of temperatures and pressures. Traditionally, empirical equations15 such as the Tamman–Tait equation16, which basically has been developed for isothermal compressed liquid, are employed. So, it seems that this equation needs some modifications depending on the class of liquids. Accordingly, several authors have attempted to modify it.6, 17-21 Here, we developed a new modification of this equation. Primary and secondary amines are so-called associating compounds which are capable of forming hydrogen bonds.22 The modeling of such associating compounds requires a physicalbased model which is capable of accounting the association term. The cubic equation of state (EoS) does not consider the associations explicitly and performs weakly in dealing with compounds containing associating.23, 24 One of the most important applied association equation of state based on the perturbation theory is SAFT (Statistical Associating Fluid Theory). Over the last few years, the popularity of the SAFT EoS has grown quickly and many modifications to the original SAFT have been put forth such as soft-SAFT, PC-SAFT, LJ-SAFT, and SAFT-VR. In this study, the perturbed-chain SAFT (PC-SAFT) equation of state25 was employed to correlate the experimental data. This work presents a part of our ongoing research related to the determination of densities and derivative thermodynamic properties at HTHP for pure compounds and binary mixtures of different class of substances.26-28 In current study, the PρT data of diethyamine (DEA),


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dibutylamine (DBA), and tributylamine (TBA) at temperature range of (293.15 to 473.15) K and pressures up to 37.5 MPa were measured. These data were correlated with a new modified Tait equation and thermodynamic properties such as isothermal compressibility  T  and thermal expansion coefficient  P  were calculated. The study is completed with modeling in terms of the PC-SAFT equation of state on the basis of parameters obtained by correlating PrT data. The validity of the parameters was tested by the evaluation of densities and derived properties such as isothermal compressibility, thermal expansion coefficient, isobaric heat capacities C P  , and speed of sound (u). All predicted results, using the PC-SAFT, were compared with the new modified Tait equation and experimental literature data and was found to give good results. 2. Experimental Section 2.1 Materials Dibutylamine was supplied form Sigma-Aldrich with 0.99 mass fraction purity, and diethylamine and tributylamine were the products of Merck with purities greater than 0.99%. All chemicals were used as received and stored in dark bottles at the temperature between 15 to 25 ±C. The purity of the samples was confirmed by gas chromatography. Also, in order to check the purity of the substances, a rigorous comparison between the literature and experimental data of the density, speed of sound, refractive index, isobaric thermal expansion coefficient, and isothermal compressibility are given in Table S1 of the Supporting Information. They were in good agreement with those reported in the literature data.7-12, 22, 29-45 2.2 Apparatus and Procedure The Anton Paar DSA 5000 was applied to measure the densities and speeds of sound of the amines at atmospheric pressure. The density determination is based on measuring the period of


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oscillating a vibrating U-shaped tube filled with the fluid sample. Given that density and sound velocity are extremely sensitive to temperature, the temperatures were adjusted to  1102 K by a built-in solid-state thermostat. The uncertainties in the density and the speed of sound at atmospheric pressure were 2  10 3 kg  m -3 and 3  10 1 m  s -1 , respectively. The refractive indices were measured using a thermostated Abbemate-500 refractometer. The uncertainty in refractive index was in the order of 5 10 5 units. The high-pressure density measurements were carried out with an Anton Paar DMA HP vibrating tube densimeter. The pressure is generated with a manually operated hand pump and is measured with a pressure transducer (Gems, 3100, England, accuracy of 0.25% FS) and digital manometer (KELLER, LEO 2, Swiss, accuracy of DBA ¥ TBA. Qualitative agreement is obtained for all the cases. The absolute average percentage deviation (AAD%) between the PCSAFT predictions and the new modified Tamman–Tait calculations has been reported in Table 4. Mean AAD% for all fluids are 3.5 and 6.1 for the thermal expansion coefficient and the isothermal compressibility, respectively. It can be concluded that the isothermal tangent compressibility is extremely sensitive to the equation form of density. The deviations of the isothermal compressibility were already observed in the prediction of pure fluids.4, 15 To further test the PC-SAFT EoS we turned our attention to the prediction of isobaric heat capacity. Part e of Figures 2–4 depicts the prediction of isobaric heat capacity at different temperature as a function of pressure. Unfortunately, there is no experimental data of isobaric heat capacity at elevated pressure, we only compared this property with the literature data at atmospheric pressure.8,

12, 39, 41, 43, 44

As can be seen, an overestimation is observed for all

compounds. Considering that these data have been taken from different literature, their precision and uncertainty are different. Table 4 reports the AAD% in isobaric heat capacity. Mean AAD% for all fluids is 8.5. This is a result to be expected because this property is second order derivative from the residual Helmholtz free energy of the system and is very sensitive to errors. The correct prediction of the isothermal compressibility value is the key for an accurate prediction of the isobaric heat capacity.


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Another severe test for an EoS is the estimation of speed of sound. In fact, it is a stringent test to any EoS since its formulation involves the combination of several second-order derivative properties. Part f of Figures 2–4 represents the PC-SAFT estimation of the speed of sound in comparing with the experimental data at atmospheric pressure. Again, the values of AAD% in speed of sound have been listed in Table 4. Mean AAD% for all fluids is 2.1. Better performance of the speed of sound compared to the other derivative properties can be argued that the ratio of

CP and Cv in the equation of speed of sound (eq 17) produces some cancellation of errors in the calculations. Note that these calculations are predictions without any extended fitting, it means that these derivative properties were not included in the fitting procedure. Consequently, the overall agreement is good in all cases. These plots clearly illustrate the ability of the PC-SAFT with these provided parameters to predict the derivative properties. 4. Conclusion Experimental PrT data of three amines (DEA, DBA, and TBA) are reported at temperatures T = (293.15–473.15) K and pressures up to 37.5MPa. To correlate liquid density data over the entire range of temperature and pressure, we have developed a new expansion in the framework of Tamman–Tait equation in which the parameter values have been provided. The values of absolute average deviation of density obtained were 0.03%, 0.01%, and 0.01% for DEA, DBA, and TBA, respectively. This new modification was employed to calculate the isothermal compressibility and thermal expansion coefficient at different temperatures and pressures. The obtained values are in good agreement with those reported in the literature. The perturbed chain statistical associating fluid theory (PC-SAFT) was applied to model the PrT data. By minimizing the total objective functions—density, pressure and temperature—simultaneously, a new set of PC-SAFT parameters for amines obtained that, in return, gave the AAD of density 0.24%,


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0.12%, and 0.16% for DEA, DBA, and TBA, respectively. To check the reliability of the obtained PC-SAFT parameters, derivative properties such as isothermal compressibility κ T  , thermal expansion coefficient  P  , isobaric heat capacities C P  , and speed of sound (u) were predicted and compared with those obtained by the new modified Tamman–Tait equation and the literature data. The results show that the PC-SAFT equation of state along with the proposed correlations, present good values for modeling of these amines.

ASSOCIATED CONTENT Supporting Information Table S1 reports the physical properties of density (r), speed of sound (u), refractive index (nD), isobaric thermal expansion coefficient  P  and isothermal compressibility

κ T 

of

diethylamine, dibutylamine, and tributylamine at different temperatures. Tables S2−S4 list the experimental density data, isothermal compressibility κ T  and thermal expansion coefficient

 P 

(calculated by the new modified Tamman–Tait equation) and, isobaric heat capacities

C P 

(predicted by PC-SAFT EoS) at the whole range of temperature and pressure. Figure S1

depicts the results of correlation of density via two Tait-like equations, namely, the traditional and the new modified Tamman–Tait equation. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author


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E–mail address: [email protected] *; Telephone: +98 8138282807; Mailing Address: Shahid Fahmide Street, Hamedan 65178, Iran ACKNOWLEDGMENT The authors would like to thank the Bu-Ali Sina University for providing the necessary facilities to carry out this research work.


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(50) Retsina, T.; Richardson, S.; Wakeham, W., The theory of a vibrating-rod densimeter. Appl. Sci. Res. 1986, 43, (2), 127-158. (51) Crespo, E. A.; Costa, J. M. L.; Hanafiah, Z. B. M. A.; Kurnia, K. A.; Oliveira, M. B.; Llovell, F.; Vega, L. F.; Carvalho, P. J.; Coutinho, J. A. P., New measurements and modeling of high pressure thermodynamic properties of glycols. Fluid Phase Equilib. 2017, 436, 113-123. (52) Regueira, T.; Lugo, L.; Fernández, J., High pressure volumetric properties of 1-ethyl-3methylimidazolium ethylsulfate and 1-(2-methoxyethyl)-1-methyl-pyrrolidinium bis (trifluoromethylsulfonyl) imide. J. Chem. Thermodyn. 2012, 48, 213-220. (53) Barker, J. A.; Henderson, D., Perturbation theory and equation of state for fluids: the square-well potential. J. Chem. Phys. 1967, 47, (8), 2856-2861. (54) Barker, J. A.; Henderson, D., Perturbation theory and equation of state for fluids. II. A successful theory of liquids. J. Chem. Phys. 1967, 47, (11), 4714-4721. (55) 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, (6), 1266-1274. (56) Kontogeorgis, G. M.; Folas, G. K., Thermodynamic models for industrial applications: from classical and advanced mixing rules to association theories. John Wiley & Sons: 2009. (57) Rozmus, J.; de Hemptinne, J.-C.; Mougin, P., Application of GC-PPC-SAFT EoS to amine mixtures with a predictive approach. Fluid Phase Equilib. 2011, 303, (1), 15-30. (58) Avlund, A. S. Extension of association models to complex chemicals. Technical University of Denmark (DTU), 2011. (59) Burgess, W. A.; Tapriyal, D.; Morreale, B. D.; Soong, Y.; Baled, H. O.; Enick, R. M.; Wu, Y.; Bamgbade, B. A.; McHugh, M. A., Volume-translated cubic EoS and PC-SAFT density models and a free volume-based viscosity model for hydrocarbons at extreme temperature and pressure conditions. Fluid Phase Equilib. 2013, 359, 38-44. (60) Burgess, W. A.; Tapriyal, D.; Morreale, B. D.; Wu, Y.; McHugh, M. A.; Baled, H.; Enick, R. M., Prediction of fluid density at extreme conditions using the perturbed-chain SAFT equation correlated to high temperature, high pressure density data. Fluid Phase Equilib. 2012, 319, 5566. (61) Llovell, F.; Peters, C.; Vega, L., Second-order thermodynamic derivative properties of selected mixtures by the soft-SAFT equation of state. Fluid Phase Equilib. 2006, 248, (2), 115122. (62) Maghari, A.; Sadeghi, M. S., Prediction of sound velocity and heat capacities of n-alkanes from the modified SAFT-BACK equation of state. Fluid Phase Equilib. 2007, 252, (1-2), 152161. (63) Dias, A.; Llovell, F.; Coutinho, J.; Marrucho, I.; Vega, L., Thermodynamic characterization of pure perfluoroalkanes, including interfacial and second order derivative properties, using the crossover soft-SAFT EoS. Fluid Phase Equilib. 2009, 286, (2), 134-143. (64) Lafitte, T.; Bessieres, D.; Piñeiro, M. M.; Daridon, J.-L., Simultaneous estimation of phase behavior and second-derivative properties using the statistical associating fluid theory with variable range approach. J. Chem. Phys. 2006, 124, (2), 024509. (65) Costas, M.; Patterson, D., Heat capacities of water + organic-solvent mixtures. J. Chem. Soc., Faraday Trans. 1985, 81, (10), 2381-2398.


22

Page 23 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Comparison between the values of standard deviation, s, AAD, MD, and Bias of three amines for eqs 5 and 7. Diethylamine

Dibutylamine

Tributylamine

deviations

eq 5a

eq 7b

eq 5

eq 7

eq 5

eq 7

 / kg  m -3 

4.47

0.42

0.30

0.31

0.29

0.30

%AAD

0.47

0.03

0.01

0.01

0.01

0.01

%MD

5.06

0.37

0.17

0.17

0.15

0.15

%Bias

-9.64μ10-3

1.73μ10-3

-1.62μ10-3

-4.30μ10-3

2.81μ10-3

1.68μ10-3

a

the traditional form of Tamman–Tait equation

b

the new modified form of Tamman–Tait equation


23


Page 24 of 33

Table 2. The coefficients of Tamman–Tait equation used in eq 7. parameter



a0, 0 kg  m 3



Diethylamine

Dibutylamine

Tributylamine

1952.15

1110.06

1062.14





0.7710

4.07931

0.7281





7.7367ä10-3

-4.3487ä10-4

9.2753ä10-4

-9.6623

-1.8167

-1.3309

a0,1 kg  m 3  MPa -1

a0, 2 kg  m 3  MPa -2



a1,0 kg  m 3  K -1







4.9240ä10-2

-8.4610ä10-3

1.1441ä10-3





-8.4314ä10-5

-4.8737ä10-6

-1.0144ä10-5

2.6400ä10-2

3.0718ä10-3

1.7553ä10-3

a1,1 kg  m 3  MPa -1  K -1

a1, 2 kg  m 3  MPa -2  K -1



a2,0 kg  m 3  K -2







-1.5793ä10-4

2.4609ä10-6

-8.8154ä10-6





2.5777ä10-7

2.5845ä10-8

3.1306ä10-8

-2.7132ä10-5

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-1.8053ä10-6

1.5778ä10-7

7.7562ä10-9

1.1881ä10-8

-2.5017ä10-10

-3.1294ä10-11

-3.1497ä10-11

b0 MPa

1672.99

643.893

547.652

b1 MPa  K -1 

-0.9679

2.6824

2.6460

C

-10.8986

-3.6452

-0.9097

a2,1 kg  m 3  MPa -1  K -2 a2, 2 kg  m 3  MPa-2  K -2



a3,0 kg  m 3  K -3





a3,1 kg  m 3  MPa-1  K -3





a3, 2 kg  m 3  MPa -2  K -3




24

Page 25 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. Obtained values for the PC-SAFT parameters used for prediction of density and other derivative properties.

MW

m

kg m  3

s

ε/k

 AB

(Å)

(K)

(K)

 AB

AADP

AADr

AADT

AADtotal

%

%

%

%

0.24

0.36

12.78

DEA

73.1369

3.424 3.3851 219.77 1094.01 0.011 12.18

DBA

129.2432 5.095 3.5742 234.78 1621.49 0.014 8.49

0.12

0.28

8.89

TBA

185.3495 8.272 3.3941 223.48 -

0.16

0.42

10.09

-

9.50


25


Page 26 of 33

Table 4. Absolute average percentage deviation (AAD%) of the thermal expansion coefficient

 P  ,

the isothermal compressibility  T  , the isobaric heat capacity C P  , and the speed of

sound (u). AAD%

p

T

Cp

u

Diethylamine

3.86

5.24

6.25

1.02

Dibutylamine

2.46

6.44

8.99

3.35

Tributylamine

4.31

6.61

10.42

1.84


26

Page 27 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure Captions Figure 1: Schematic diagram of the high-pressure apparatus. Figure 2: Plot of experimental density and thermodynamic derivative properties of diethylamine against pressure; (a) density data, (b) relative deviations, (c) isobaric thermal expansion  P  , (d) isothermal compressibility  T  , (e) isobaric heat capacity C P  , and (f) speed of sound (u) at temperatures; 293.15 (▼), 298.15 (○), 313.15 (■), 333.15 (ó), 353.15 (●), 373.15 (□), 393.15 (î), 413.15 (ä), 433.15 (), 453.15 (▲), and 473.15 (ï), the new modified Tamman–Tait correlations were presented with dashed lines (---), PC-SAFT correlations were presented with solid lines (uuuuu), and literature data12, 41, 65 at temperatures 293.15 (0), 298.15 (ñ), 313.15 (@). Figure 3: Plot of experimental density and thermodynamic derivative properties of dibutylamine against pressure; (a) density data, (b) relative deviations, (c) isobaric thermal expansion  P  , (d) isothermal compressibility  T  , (e) isobaric heat capacity C P  , and (f) speed of sound (u) at temperatures; 293.15 (▼), 298.15 (○), 313.15 (■), 333.15 (ó), 353.15 (●), 373.15 (□), 393.15 (î), 413.15 (ä), 433.15 (), 453.15 (▲), and 473.15 (ï), the new modified Tamman–Tait correlations were presented with dashed lines (---), PC-SAFT correlations were presented with solid lines (uuuuu), and literature data8, 41 at temperatures 293.15 (0), 298.15 (ñ), 313.15 (@). Figure 4: Plot of experimental density and thermodynamic derivative properties of tributylamine against pressure; (a) density data, (b) relative deviations, (c) isobaric thermal expansion  P  , (d) isothermal compressibility  T  , (e) isobaric heat capacity C P  , and (f) speed of sound (u) at temperatures; 293.15 (▼), 298.15 (○), 313.15 (■), 333.15 (ó), 353.15 (●), 373.15 (□), 393.15 (î), 413.15 (ä), 433.15 (), 453.15 (▲), and 473.15 (ï), the new modified Tamman–Tait correlations


27


Page 28 of 33

were presented with dashed lines (---), PC-SAFT correlations were presented with solid lines (uuuuu), and literature data8, 22, 34, 39, 41 at temperatures 293.15 (0), 298.15 (ñ), 313.15 (@), 333.15 (≈).


28

Page 29 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


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Page 30 of 33

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 33

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32

Page 33 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


For Tablee of Contentss Only


33

Thermodynamic Properties of Amines Under High Temperature and

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