Solubility of Dimethyl Ether in Pentaerythritol Tetrahexanoate (PEC6

Oct 3, 2014 - ABSTRACT: The solubilities of dimethyl ether (DME) in pentaerythritol tetrahexanoate. (PEC6) and in pentaerythritol tetraoctanoate (PEC8...
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Solubility of Dimethyl Ether in Pentaerythritol Tetrahexanoate (PEC6) and in Pentaerythritol Tetraoctanoate (PEC8) Between (283.15 and 353.15) K Yanjun Sun, Xiaopo Wang,* Na Gong, and Zhigang Liu Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an 710049, China ABSTRACT: The solubilities of dimethyl ether (DME) in pentaerythritol tetrahexanoate (PEC6) and in pentaerythritol tetraoctanoate (PEC8) have been measured from (283.15 to 353.15) K based on the isochoric method. The expanded uncertainty (k = 2) of the measured solubility data was estimated to be less than 3.0 %. The experimental solubility data were correlated based on the Peng−Robinson equation of state with Huron−Vidal mixing rules and the NRTL equation for the excess Gibbs energy at infinite pressure. The absolute average deviation between experimental data and calculated values was 1.1 % and 1.0 % for DME + PEC6 system and DME + PEC8 system, respectively. The maximum absolute deviation was 2.93 % for the DME + PEC6 system and 2.90 % for DME + PEC8 system.

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INTRODUCTION According to the Montreal Protocol and its amendments, chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) are among the most restricted and prohibited compounds. This has led to a strong research effort to find environmentally benign substitutes for the traditional chlorinated refrigerants. Recent investigation showed that dimethyl ether (RE170, DME) has acceptable efficiency in the refrigerating system.1 In addition, it has excellent environmental properties,2 such as zero ozone depletion potential and zero global warming potential. Therefore, DME was suggested as a natural promising HCFCs alternative.3 Many kinds of refrigerant blends including DME, such as RE170/R134a, RE170/R236fa, etc., were proposed by researchers.4,5 Krauss et al.6 found that the mixture of 60 % in mass of ammonia and 40 % in mass of dimethyl ether forms an interesting azeotrope (R723) as a new refrigerant blend. Park et al.7,8 also studied that R1270/R290/RE170 and R1270/RE170 can be used to substitute R22 in residential air-conditioners, and these alternative blends provide better thermodynamic performance than R22. In the refrigeration system, the circulating refrigerant comes into contact with the lubricant used in the compressor and some of the refrigerant may dissolve into the oil. The solubility of the refrigerant in the lubricant affects the lubrication properties of actual oil in the compressor. In addition, the refrigerantlubricant phase separation during the refrigeration cycle can result in serious problems such as reducing heat transfer and overall performance. Hence, the knowledge of the solubility and miscibility limits between refrigerant and lubricant is very important for refrigeration plants. However, there are no reports about the behavior between DME and the commonly used lubricants in the literature. © 2014 American Chemical Society

The structure and composition of the commercial synthetic oils, such as polyalkylene glycols (PAG) and pentaerythritol tetraalkyl esters (POE), is usually not defined. It may include several pure components and additives. Hence, it is difficult to develop proper thermodynamic models able to work both in a correlative and predictive way.9 Therefore, to study the solubility of refrigerant in the precursors of commercial lubricants with the known structure has attracted more attention. In this work, the solubility of DME in two pure linear chained precursors of POE lubricants, pentaerythritol tetrahexanoate (PEC6) and pentaerythritol tetraoctanoate (PEC8), was measured for temperatures ranging from (283.15 to 353.15) K, and the experimental data were correlated by means of the Peng−Robinson equation of state with the Huron−Vidal mixing rules in which the excess Gibbs energy at infinite pressure was represented by the NRTL equation.

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EXPERIMENTAL SECTION Materials. Dimethyl ether (DME) was provided by Shandong Jiutai Chemical Co. Ltd., China, and the mass purity was higher than 99.95 % by analysis with a gas chromatograph (Agilent Technologies 6890N). Pentaerythritol tetrahexanoate (PEC6) and pentaerythritol tetraoctanoate (PEC8) are the pure linear chained pentaerythritol alkyl esters obtained by combining an alcohol (pentaerythritol) with four equal alkyl linear chains, derived from carboxylic acids with different number of carbons and which were synthesized by Chemipan (Poland) on a laboratory scale with a declared mass purity

Received: July 16, 2014 Accepted: September 23, 2014 Published: October 3, 2014 3791

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Figure 1. Chemical structure of PEC6 and PEC8.

higher than 98.0 %. All of these reagents were used directly without further purification. Figure 1 shows the chemical structure of the linear chained pentaerythritol alkyl esters (PEC6 and PEC8). Table 1 shows the sample descriptions used in the Table 1. Samples Used in the Measurements chemical name DMEa PEC6c PEC8d CO2e

source Shandong Jiutai Chemical Co. Ltd. (China) Chemipan (Poland) Chemipan (Poland) Praxair Inc. (China)

mass fraction purity

purification method

analysis method

0.9995

none

GCb

0.98 0.98 0.99999

none none none

none none GCb

Figure 3. Comparison of solubility of CO2 in PEC6 at temperatures 303.15 K between this work (●) and Bobbo et al. (◊).19

0.95 (k = 2). For the pressure measurement, a ROSEMOUNT 3051S pressure transducer with a full scale of 5.5 MPa which was also connected to the KEITHLEY 2700 was employed. The accuracy of the pressure transducer is 0.025 % for full scale. The combined expanded uncertainty (k = 2) in the pressure measurement was 2.0 kPa. A specifically built magnetic stirrer with a remote control by the motor placed below the equilibrium cell was used to force the vapor phase through the liquid one to accelerate the achievement of equilibrium. Measurement Procedure. For the solubility measurement, a specified amount of lubricant oil (about 5g) was directly charged in the equilibrium cell by means of a syringe, after cleaning it with acetone. The weight of the syringe was measured before and after the charge by means of an analytical balance (Mettler Toledo ME204, 220 g full scale) with an uncertainty of 0.002 g. After this operation, the equilibrium cell was connected to the gas system cell, placed inside the bath, and kept under vacuum about 12 h. Then the gas was fed into the gas system cell, and the initial pressure was recorded. After that, the interconnecting valve (V4) was opened, and the gas was admitted into the equilibrium cell. Then the stirrer was turned on, and the absorption of gas in the stirred solvent is started. When the pressure remained constant, the magnetic stirrer was stopped, and the system reached equilibrium, then the equilibrium pressure was recorded again. The next step was to change the temperature of the system, and when the pressure remained constant, a new equilibrium point had been reached. After all the desired temperatures were performed, the interconnecting valve was closed, a new amount of gas was added to the gas system cell, and the procedure described above was repeated for the other pressure. Calculation of the Gas Solubility. The mole fraction x1 of absorbed DME (1) in the solvent PECs (2) is calculated by x1 = n1/(n1 + n2), where n2 is the number of moles of the solvent. It can be calculated from the mass charged in the equilibrium cell. The number of moles of gas n1 absorbed in the solvent is calculated from

a DME = methoxymethane. bGas chromatography. cPEC6 = [3octanoyloxy-2,2-bis(octanoyloxymethyl)propyl] octanoate. dPEC8 = 3-(hexanoyloxy)-2,2-bis[(hexanoyloxy)methyl]propyl hexanoate. e CO2 = Carbon dioxide

present work. Carbon dioxide (CO2) which was used to calibrate the volume of the experimental system was also listed in Table1. Apparatus Description. In this work, the gas solubility was measured by means of an isochoric technique. The experimental method in this work is similar as that used by Wahlstrom and Vamling10−12 and Fernandez et al.13−15 Figure 2 shows the schematic diagram of solubility measurement system. The experimental equipment consists of two

Figure 2. Schematic diagram of the solubility measurement system.

different volume stainless steel cells named as equilibrium cell and gas system cell, which were immersed in FLUKE 7008 thermostat bath with the stability and uniformity of better than 0.01 K. A calibrated Pt-100 Ω resistance thermometer (FLUKE 5608) connected to the KEITHLEY 2700 was used to measure temperature. The combined expanded uncertainty of temperature measurement was 0.03 K with a level of confidence of

n1 = n10 − n11 3792

(1)

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Table 2. Solubility of DME in Pentaerythritol Tetrahexanoate (PEC6)a x1

p/MPa

x1

T = 283.15 K 0.3494 0.5543 0.6785 0.7583 0.8074 0.8535 0.8979 0.9275

0.0707 0.1390 0.1962 0.2438 0.2748 0.3091 0.3387 0.3537

0.3264 0.5301 0.6583 0.7405 0.7956 0.8454 0.8933 0.9250

0.1356 0.2824 0.4216 0.5577 0.6581 0.7866 0.9255 1.0154

0.2353 0.4158 0.5507 0.6476 0.7163 0.7842 0.8554 0.9043

T = 323.15 K 0.2571 0.4450 0.5809 0.6756 0.7414 0.8046 0.8689 0.9119

p/MPa

x1

T = 293.15 K

p/MPa

x1

T = 303.15 K 0.0868 0.1733 0.2489 0.3212 0.3568 0.4053 0.4502 0.4790

0.3024 0.5032 0.6345 0.7238 0.7807 0.8349 0.8873 0.9218

0.1513 0.3174 0.4798 0.6414 0.7684 0.9317 1.1238 1.2559

0.2148 0.3872 0.5202 0.6183 0.6888 0.7608 0.8383 0.8941

T = 333.15 K

p/MPa T = 313.15 K

0.1036 0.2095 0.3061 0.3906 0.4508 0.5186 0.5853 0.6270

0.2801 0.4744 0.6098 0.7013 0.7621 0.8214 0.8794 0.9176

0.1664 0.3510 0.5354 0.7221 0.8758 1.0766 1.3316 1.5223

0.1962 0.3586 0.4906 0.5886 0.6604 0.7353 0.8182 0.8807

T = 343.15 K

0.1194 0.2462 0.3620 0.4731 0.5542 0.6470 0.7443 0.8056 T = 353.15 K 0.1807 0.3840 0.5880 0.7989 0.9777 1.2158 1.5376 1.8067

a The combined expanded uncertainty (k = 2) in temperature is u(T) = 0.03 K. The combined expanded uncertainty (k =2) in pressure is u(p) = 2.0 kPa. The expanded uncertainty in mole fraction ur(x1) = 3.0 %

⎡ Vsys Vsys − n1 = ⎢ ⎢⎣ υgas(Tini , p ) υgas(Tequilib , pequilib ) ini

where n01, the initial number of moles of gas in the system, is given by n10 =

Vsys υgas(Tini , pini )

+

(2)

and n11, the number of moles of gas remaining in the system when it reaches equilibrium, is

(4)

According to the experimental conditions, the measured temperature T is lower than the saturation temperature of DME at each measured temperature, the molar volume υabs,gas of the absorbed DME in the PECs is calculated as the liquid specific volume at the bubble point at temperature T. This procedure has been used by Wahlstrom and Vamling,10−12 Fernandez et al.,13−15 and Hong et al.21 The volumes Vsys and Vcell were determined by calibration with the following procedure. The cell was filled with a known amount of carbon dioxide which was supplied by Praxair Inc. with declared mass purity of 99.999 %. The density of carbon dioxide can be calculated by Refprop 9.117 at a certain temperature and pressure. The volume can be obtained based on the charged mass and the calculated density. The procedure was repeated several times at different amounts of carbon dioxide, obtaining a repeatability of the results within 0.05 cm3. The expanded uncertainty (k = 2) of the solubility data was estimated to be less than 3.0 %.

⎛ V −V Vsys cell 2,cell + ⎜⎜ n11 = υgas(Tequilib , pequilib ) ⎝ υgas(Tequilib , pequilib ) −

⎞ ⎟ υgas(Tequilib , pequilib ) ⎟⎠

⎤ ⎡ ⎤ υabs,gas ⎥ / ⎢1 − ⎥ υgas(Tequilib , pequilib ) ⎥⎦ ⎢⎣ υgas(Tequilib , pequilib ) ⎥⎦ V2,cell − Vcell

Vabs,gas

(3)

where Tini and pini are the conditions of gas system at the beginning of the measurement and Tequilib and pequilib are the equilibrium temperature and pressure. Vsys and Vcell are the volume of the gas system and the volume of the equilibrium cell, respectively. V2,cell is the volume of the pure PECs, which was calculated from the charged mass and its density. The densities of PECs were obtained from Fedele et al.,16 and the expanded uncertainty with a level of confidence of 0.95 (k = 2) is 0.03 %. The mole volume υgas of DME in the vapor phase is calculated with Refprop 9.1.17 The vapor pressures for pentaerythritol esters (PEC5, PEBE8) were measured to be between (5.6·10−5 and 0.94) Pa and between (334 and 476) K.18 In addition, Bobbo et al.19 and Fedele et al.20 also pointed out that the volatility of PEC6 and PEC8 can be considered practically negligible in the temperature range of (283 to 343) K. Therefore, the vapor phase in the cell is consisting only of pure gaseous dimethyl ether in this work. The volume of gas absorbed in the solvent, Vabs, gas, can be expressed by Vabs, gas = n1υabs,gas, the number of moles of n1, absorbed in the solvent is

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RESULTS AND DISCUSSION In order to validate the performance of the apparatus, the solubility of CO2 in pentaerythritol tetrahexanoate (PEC6) was measured at 303.15 K. Figure 3 shows that good agreement between our experimental results and those from Bobbo et al.19 The absolute average deviation (AAD) between our experimental data and values of Bobbo is 0.95 %, and the maximum deviation is 2.0 %. Before measuring the solubility of DME in PEC6 and PEC8, the miscibility measurement was carried out. The results show that there was no stratification and no sediment generation, and the color of oil had no change at temperature between 3793

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Table 3. Solubility of DME in Pentaerythritol Tetraoctanoate (PEC8)a x1

p/MPa

x1

T = 283.15 K 0.4110 0.6033 0.7180 0.7886 0.8323 0.8742 0.9124 0.9376

0.0822 0.1520 0.2123 0.2626 0.2959 0.3303 0.3527 0.3630

0.3853 0.5787 0.6985 0.7739 0.8211 0.8667 0.9082 0.9352

0.1501 0.2914 0.4332 0.5706 0.6659 0.8070 0.9512 1.0380

0.2861 0.4619 0.5947 0.6825 0.7471 0.8093 0.8716 0.9152

T = 323.15 K 0.3111 0.4921 0.6245 0.7094 0.7711 0.8284 0.8846 0.9226

p/MPa

x1

T = 293.15 K

p/MPa

x1

T = 303.15 K 0.0998 0.1870 0.2650 0.3312 0.3769 0.4283 0.4652 0.4953

0.3590 0.5514 0.6753 0.7556 0.8070 0.8569 0.9027 0.9322

0.1668 0.3244 0.4904 0.6512 0.7730 0.9478 1.1447 1.2755

0.2625 0.4327 0.5645 0.6543 0.7208 0.7875 0.8552 0.9051

T = 333.15 K

p/MPa T = 313.15 K

0.1175 0.2234 0.3219 0.4077 0.4692 0.5436 0.6059 0.6413

0.3371 0.5222 0.6528 0.7340 0.7895 0.8442 0.8954 0.9281

0.1868 0.3638 0.5450 0.7286 0.8766 1.0869 1.3452 1.5364

0.2405 0.4046 0.5346 0.6257 0.6936 0.7636 0.8361 0.8920

T = 343.15 K

0.1328 0.2544 0.3744 0.4885 0.5697 0.6703 0.7604 0.8284 T = 353.15 K 0.2062 0.3951 0.5967 0.8019 0.9744 1.2203 1.5413 1.8071

a The combined expanded uncertainty (k = 2) in temperature is u(T) = 0.03 K. The combined expanded uncertainty (k =2) in pressure is u(p) = 2.0 kPa. The expanded uncertainty in mole fraction ur(x1) = 3.0 %

Figure 4. Solubility in mole fraction of DME in PEC6 at: ●, 283.15 K; ⧫, 293.15 K; Δ, 303.15 K; ▼, 313.15 K; ★, 323.15 K; ○, 333.15 K; □, 343.15 K; ▲, 353,15 K; ―, PR-HV-NRTL EoS model.

Figure 5. Solubility in mole fraction of DME in PEC8 at: ●, 283.15 K; ⧫, 293.15 K; Δ, 303.15 K; ▼, 313.15 K; ★, 323.15 K; ○, 333.15 K; □, 343.15 K; ▲, 353,15 K; ―, PR-HV-NRTL EoS model.

(283.15 and 353.15) K and pressures between (0.07 and 1.9) MPa for each system. All suggested that DME was completely miscible with these two oils in the range of temperatures and pressures studied. Experimental Data. The isothermal solubility of DME in PEC6 and PEC8 have been measured for temperatures ranging from (283.15 to 353.15) K. The experimental data are listed in Tables 2 and 3. The solubility isotherms for the two DME + PECs systems in terms of mole fraction of DME in liquid phase are presented in Figures 4 and 5. For the two systems, the gas solubility decreases when the temperature increases, and the solubility increases with the pressure increasing at a constant temperature. In Figure 6, the experimental solubility data for the two systems at 283.15, 303.15, 323.15, and 343.15 K were compared.

It was shown that the solubility of DME in the two PECs is quite similar. The solubility of DME in PEC8 is higher than the solubility of DME in PEC6 at lower mole fractions, and the solubility of DME in PEC8 is slightly lower than the solubility of DME in PEC6 at higher mole fraction. Data Correlation. The solubility data were correlated using the Peng−Robinson (PR)22 Equation of State (EoS) with Huron-Vidal mixing rules (HV)23 and NRTL equation24 for the excess Gibbs energy (gE) at infinite pressure. The critical parameters and the acentric factor, ω are shown in Table 4. The expression of the HV mixing rules is ⎡ ⎛a ⎞ gE ⎤ a = b⎢∑ xi⎜ i ⎟ − ∞ ⎥ ⎢⎣ i ⎝ bi ⎠ C ⎥⎦ 3794

(5a)

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Figure 6. Solubility in mole fraction of DME in PEC6 (●) and in PEC8 (◊), at 283.15, 303.15, 323.15, and 343.15 K; PR-HV-NRTL EoS model (―).

Figure 7. Deviation of experimental data from the calculated values with PR-HV-NRTL EoS model for DME + PEC6. ●, 283.15 K; ⧫, 293.15 K; Δ, 303.15 K; ▼, 313.15 K; ★, 323.15 K; ○, 333.15 K; □, 343.15 K; ▲, 353,15 K.

Table 4. Pure Compound Parameters Used in the Data Correlation compound

molar mass (g/mol)

Tc/K

pc/kPa

acentric factor

DME PEC6 PEC8

46.068a 528.73b 640.94b

400.3a 931.2b 972.5b

5340.5a 848.7b 681.1b

0.197a 1.546c 1.527c

where xi and yi are the mole fractions of component i in liquid and vapor phases, respectively. ϕLi and ϕVi fugacity coefficient of component i in liquid and vapor phases, respectively. p is the equilibrium pressure. In eq 5a, gE∞ is represented by the NRTL equation gE = RT

a

The values from the Refprop 9.1 database.17 bThe values from Pernechele et al.25 cPredicted by means of Nath and Yadava method.26

Table 5. Values of the Binary Interaction Parameters of the Model Derived by Fitting the Experimental Data τ12,0 τ12,1 τ12,2 τ21,0 τ21,1 τ21,2 α AAD %b MAD %c no. of points

DME + PEC6

DME + PEC8

1.3489 (0.17427)a 0.0316 (0.00889) −0.0002 (9.63726·10−5) −3.3058 (0.03566) 0.0097 (0.00182) −0.00006 (1.97188·10−5) 0.4 1.1 2.93 64

0.3347 (0.03751) 0.0492 (0.00191) −0.0003 (2.07447·10−5) −2.878 (0.02077) −0.0067 (0.00106) 0.00005 (1.14859·10−5) 0.4 1.0 2.90 64

∑ xi i

τji = Δgji /(RT )

(9)

Gji = exp( −ατji)

(10)

(11) 2

τ21 = τ21,0 + τ21,1(T − 273.15) + τ21,2(T − 273.15)

(12)

where τ12,0, τ12,1, τ12,2, τ21,0, τ21,1, and τ21,2 are the parameters. The values of the parameters are obtained by fitting the experimental data, the objective function is N

obj =

⎛2 + ln⎜ 2 2 ⎝2 − 1

2⎞ ⎟ 2⎠

(6)

The condition of thermodynamic equilibrium is given by fiV = yi ϕi V p = xiϕi Lp = fiL

|piexp − pical | piexp

(13)

The optimized values of τ12,0, τ12,1, τ12,2, τ21,0, τ21,1, and τ21,2 and α are tabulated in Table 5. The results calculated by the model are shown in Figures 4 and 5, and the deviations in pressure are presented in Figures 7 and 8. The absolute average deviation between experimental data and calculated values was 1.1 % and 1.0 % for the DME + PEC6 system and the DME + PEC8 system, respectively. The maximum relative deviation was 2.93 % for the DME + PEC6 system and was 2.90 % for DME + PEC8 system.

For the PR EoS, the parameter C can be expressed as C=

∑ i=1

(5b)

i

(8)

τ12 = τ12,0 + τ12,1(T − 273.15) + τ12,2(T − 273.15)2

The standard errors of the fitting coefficients are shown in the parentheses. bAAD % = (∑iN= 1|x1,exp − x1,cal|/x1,exp·100)/N cMAD % = max(|x1,exp − x1,cal|/x1,exp·100)N

∑ xibi

∑l Glixl

where α and τij are the parameters of NRTL equation. The value of α was set 0.4 for the two systems in this work. τij are considered as the function dependent on the temperature and can be expressed as

a

b=

∑j τjiGjixj

(7) 3795

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Figure 8. Deviation of experimental data from the calculated values with PR-HV-NRTL EoS model for DME + PEC8. ●, 283.15 K; ⧫, 293.15 K; Δ, 303.15 K; ▼, 313.15 K; ★, 323.15 K; ○, 333.15 K; □, 343.15 K; ▲, 353,15 K.

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CONCLUSIONS In this work, the isothermal solubilities of DME in pentaerythritol tetrahexanoate (PEC6) and pentaerythritol tetraoctanoate (PEC8) were measured from (283.15 to 353.15) K. The solubility data were correlated with a model based on the Peng−Robinson equation of state and Huron−Vidal mixing rules with NRTL equation for the gE at infinite pressures. Moreover, the experimental solubility data for the two systems were compared over the same temperature range, and the results show that DME is highly soluble in these two oils. It seems evident that the solubility of DME in PEC8 is higher than the solubility of DME in PEC6 at lower mole fraction, but at higher mole fraction, the solubility of DME in PEC8 is slightly lower than the solubility of DME in PEC6.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +86 29 82668210. Fax: +86 29 82668789. E-mail: [email protected]. Funding

This research was supported by the National Natural Science Foundation of China (Grant 51376149) and the Fundamental Research Funds for the Central Universities. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are very grateful to Dr. Laura Fedele and Mr. Mauro Scattolini of National Research Council, Italy, for their kindly help concerning this work.

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