Article pubs.acs.org/jced
Phase Equilibrium Behavior for Methoxymethane + Pentaerythritol Tetraheptanoate and Methoxymethane + Pentaerythritol Tetranonanoate Systems Yanjun Sun,†,§ Xiaopo Wang,*,‡ Hanxiao Lang,‡ Liwen Jin,† and Zhigang Liu‡ †
Department of Building Environment and Energy Engineering and ‡Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an 710049, China § Key Laboratory of Cryogenics, TIPC CAS, China ABSTRACT: Methoxymethane (called dimethyl ether, DME) is recognized as a promising alternative refrigerant. Knowledge of the phase equilibrium behavior of DMElubricant is essential for selecting a suitable oil. A long-term systematic research program on the phase equilibrium for systems of DME and oils was carried out in our laboratory, making the effort to determine its dependence on the molecular structure of oils, temperature, and pressure. In this article, phase equilibrium data of the DME + pentaerythritol tetraheptanoate system and the DME + pentaerythritol tetranonanoate system were reported from (293.15 to 353.15) K using the isochoric saturation method. Experimental data of phase equilibrium were modeled by the Peng−Robinson (PR) equation of state using the HVOS mixing rule and the NRTL excess-free-energy model. Moreover, the influence of the molecular weight of pentaerythritol esters on the phase equilibrium behavior of DME/ester mixtures was analyzed.
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INTRODUCTION Because of the negative environmental impact of chlorofluorocarbons and hydrofluorocarbons, researchers have concentrated on potential green refrigerants with low ODP and GWP in the refrigeration industry. Among the possible alternative refrigerants, methoxymethane (DME) is considered to be one of the most promising working fluids owing to its zero-ODP, GWP of 0.1 (100 years), low cost, and excellent thermodynamic properties, with ASHRAE refrigerant designation RE170.1−3 In the compressed refrigeration cycles, the thermodynamic behavior of refrigerant and lubricant oil mixtures is necessary in the selection of optimal lubricant oil.4−6 However, the phase equilibrium of the DME + lubricant system is still very limited in the literature. In addition, POE oil, a commercial synthetic oil widely used in refrigeration systems, is mainly composed of linear, cyclic, and branched-chained pentaerythritol esters.7 To explore the effect of differences on the molecular structure of homologous series for POE precursors, experimental measurements of the phase equilibrium for binary systems consisting of DME and six various linear-chained pentaerythritol esters (PECs) were carried out in our laboratory. These six linearchained pentaerythritol esters are PEC4 (pentaerythritol tetrabutyrate, C21H36O8), PEC5 (pentaerythritol tetrapentanoate, C25H44O8), PEC6 (pentaerythritol tetrahexanoate, C 2 9 H 5 2 O 8 ), PEC7 (pentaerythritol tetraheptanoate, C33H60O8), PEC8 (pentaerythritol tetraoctanoate, C37H68O8), and PEC9 (pentaerythritol tetranonanoate, C41H76O8). The chemical structures of the six PECs are shown in Figure 1. The © XXXX American Chemical Society
previous results of DME + PEC4, DME + PEC5, DME + PEC6, and DME + PEC8 systems have been published already.8,9 In this work, phase equilibrium data for DME + PEC7 and DME + PEC9 are presented. In addition, an analysis of the effect of the molecular structure of PECs on the phase equilibrium behavior for these systems was conducted.
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EXPERIMENTAL METHODOLOGY Materials. Table 1 lists the sample information. Before the experiment, methoxymethane was degassed three to five times using a high-vacuum system and liquid nitrogen. The mass purity of methoxymethane was higher than 99.95%, which was analyzed by means of a gas chromatograph in our laboratory. PEC7 and PEC9 were obtained from CHEMIPAN R&D Laboratories (Poland) and used as received. The declared mass purity was better than 98%. Experimental Technique. The phase equilibrium measurement was performed by a specifically self-designed apparatus on the basis of the isochoric saturation method, and the detailed procedure can be found in our previous papers.8−11 Only brief descriptions of the apparatus are given here. As shown in Figure 2, the gas system cell and equilibrium cell are located in a Fluke 7008 thermostatic oil bath. Calibrated volumes of the above two Received: May 20, 2016 Accepted: August 9, 2016
A
DOI: 10.1021/acs.jced.6b00412 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 1. Chemical structure of the pure pentaerythritol tetraalkyl esters.
eliminated, DME was transferred to the gas system cell from a gas storage bottle, and the pressure data of the gas system cell was recorded. Then, DME entered the equilibrium cell when a valve (V4) was opened. Subsequently, a self-made magnetic stirrer started to speed up the dissolution, and the stirrer was closed once the pressure approached a constant value. Vapor−liquid equilibrium was achieved after about 1 h; i.e., the fluctuation of pressure was less than 0.5 kPa. The next experimental procedure was then to change the bath temperature to get a new equilibrium point. Calculation of Phase Equilibrium. The mole fraction x1 of dissolved DME in PEC7 or PEC9 can be obtained using x1 = n1/ (n1 + n2), where n2 is the number of moles of PEC7 or PEC9. Because the vapor pressure of PEC7 or PEC9 is very low,12 only gaseous DME was in the vapor phase. Therefore, n1, the number of moles of DME dissolved in PEC7 or PEC9, can be calculated by9
Table 1. Samples Used in the Measurements chemical name
CAS number
DMEa
115-10-6
PEC7c
25811-35 -2 14450-05 -6
PEC9d
source Shandong Jiutai Chemical Co. Ltd. (China) Chemipan (Poland) Chemipan (Poland)
mass fraction purity
purification method
analysis method GCb
0.98
freeze− pump− thaw none
0.98
none
none
0.9995
none
a
DME is methoxymethane. bGas chromatography. cPEC7 is [3heptanoyloxy-2,2-bis(heptanoyloxymethyl)propyl] heptanoate. dPEC9 is [3-nonanoyloxy-2,2-bis(nonanoyloxymethyl)propyl] propylnonanoate.
cells are 31.33 and 73.26 cm3, respectively. The temperature was measured with a Fluke 5608 thermometer. The combined standard uncertainty of the measured temperature was within 0.03 K at the 95% confidence level. The pressure of the experimental system was measured with a Rosemount 3051S transducer, and the combined standard uncertainty of pressure at the 95% confidence level was estimated to better than 2.0 kPa. Before measurement, the equilibrium cell was injected with a known amount of PEC7 or PEC9, the weight of which was measured with a Mettler Toledo ME204 balance with an uncertainty of 0.002 g. After the air inside the system was
Vsys
n1 =
υgas(Tini , pini )
−
Vsys υgas(Tequilib , pequilib )
1−
+
V2,cell − Vcell υgas(Tequilib , pequilib )
υabs,gas υgas(Tequilib , pequilib )
(1)
where ini and equilib mean initial and equilibrium conditions, respectively. Vcell and Vsys are the volumes of the equilibrium and gas system cells. The volume of PEC7 or PEC9, V2,cell, can be calculated by its density and mass. Density data for PEC7 or
Figure 2. Schematic diagram of the solubility measurement system. B
DOI: 10.1021/acs.jced.6b00412 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 2. Vapor−Liquid Phase Equilibrium of DME and Pentaerythritol Tetraheptanoate (PEC7)a x1
p/MPa
x1
T = 293.15 K 0.2926 0.5090 0.6647 0.7624 0.8222 0.8633 0.9034 0.9345
0.074 0.153 0.239 0.311 0.363 0.401 0.439 0.467
0.2673 0.4842 0.6387 0.7425 0.8077 0.8531 0.8976 0.9316
0.124 0.276 0.460 0.645 0.807 0.952 1.124 1.264
0.1765 0.3558 0.5130 0.6305 0.7136 0.7778 0.8480 0.9057
T = 333.15 K 0.1969 0.3852 0.5457 0.6618 0.7418 0.8021 0.8655 0.9155 a
p/MPa
x1
p/MPa
T = 303.15 K
x1
T = 313.15 K 0.087 0.182 0.295 0.391 0.464 0.520 0.576 0.618
0.2427 0.4482 0.6096 0.7188 0.7895 0.8399 0.8898 0.9278
0.135 0.304 0.511 0.724 0.919 1.102 1.333 1.539
0.1575 0.3278 0.4810 0.5988 0.6839 0.7511 0.8268 0.8925
T = 343.15 K
p/MPa T = 323.15 K
0.099 0.216 0.351 0.476 0.575 0.654 0.738 0.801
0.2192 0.4162 0.5782 0.6915 0.7674 0.8228 0.8793 0.9226
0.112 0.247 0.407 0.561 0.691 0.801 0.923 1.016
T = 348.15 K 0.147 0.330 0.559 0.799 1.025 1.244 1.539 1.831
The combined expanded uncertainties Uc are Uc(T) = 0.03 K, Uc(p) = 2.0 kPa, and Ur(x1) = 0.03 with a 0.95 level of confidence (k = 2).
Table 3. Vapor−Liquid Phase Equilibrium of DME and Pentaerythritol Tetranonanoate (PEC9)a x1
p/MPa
x1
0.078 0.159 0.225 0.317 0.374 0.416 0.454 0.474
0.3133 0.5321 0.6521 0.7774 0.8433 0.8880 0.9288 0.9515
0.127 0.279 0.414 0.639 0.825 0.998 1.190 1.298
0.2084 0.4004 0.5209 0.6661 0.7537 0.8214 0.8918 0.9329
T = 293.15 K 0.3426 0.5638 0.6800 0.7970 0.8566 0.8965 0.9329 0.9535
a
x1
0.092 0.191 0.274 0.396 0.479 0.541 0.599 0.629
0.2856 0.4990 0.6211 0.7538 0.8263 0.8768 0.9233 0.9488
0.138 0.305 0.446 0.702 0.936 1.154 1.422 1.588
0.1863 0.3701 0.4881 0.6344 0.7251 0.7967 0.8745 0.9228
T = 303.15 K
T = 333.15 K 0.2323 0.4325 0.5545 0.6972 0.7809 0.8435 0.9055 0.9400
p/MPa
p/MPa
x1
0.105 0.221 0.323 0.478 0.592 0.684 0.771 0.816
0.2578 0.4658 0.5880 0.7268 0.8053 0.8620 0.9158 0.9451
T = 313.15 K
T = 343.15 K
p/MPa T = 323.15 K 0.117 0.250 0.370 0.560 0.710 0.838 0.970 1.039
T = 348.15 K 0.149 0.330 0.486 0.772 1.038 1.300 1.652 1.897
The combined expanded uncertainties Uc are Uc(T) = 0.03 K, Uc(p) = 2.0 kPa, and Ur(x1) = 0.03 with a 0.95 level of confidence (k = 2).
PEC9 are obtained from Fandino et al.13 υgas represents the molar volume of gaseous DME and is obtained from the Refprop 9.1 database.14 Because the critical temperature of DME is higher than the experimental temperature in this work, the molar volume of dissolved DME in PEC7 or PEC9 (υabs,gas in eq 1) is assumed to be a liquid-specific volume under equilibrium conditions. Considering all measurement factors, the relative standard uncertainty of solubility was estimated to better than 0.03 at a level of confidence of 95%.
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liquid phase decreases as the temperature increases, whereas it increases when the pressure rises. Experimental data were modeled by the Peng−Robinson (PR) equation of state15 and the HVOS16 mixing rule combined with the NRTL excess-free-energy model.17 PR EOS is given by p=
RT a − 2 v−b v + 2vb − b2
(2a)
a=
0.45724(1 + k(1 − (T /Tc)1/2 ))(RTc)2 pc
(2b)
0.0778RTc pc
(2c)
RESULTS AND DISCUSSION
Phase equilibrium measurements of the DME + PEC7 system and DME + PEC9 system have been performed between (293.15 and 353.15) K. Tables 2 and 3 list the experimental data. Phase equilibrium diagrams of the two binary systems are plotted in Figures 3 and 4. As expected, the mole fraction of DME in the
b=
k = 0.37464 + 1.54226ω − 0.26992ω 2 C
(2d)
DOI: 10.1021/acs.jced.6b00412 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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⎡⎛ ⎛ ⎛b⎞ a a ⎞ 1⎛ a = b⎢⎜x1 1 + x 2 2 ⎟ + ⎜⎜g E + RT ⎜⎜x1 ln⎜ ⎟ ⎢⎣⎝ b1 b2 ⎠ C ⎝ ⎝ b1 ⎠ ⎝ ⎛ b ⎞⎞⎞⎤ + x 2 ln⎜ ⎟⎟⎟⎟⎟⎥ ⎝ b2 ⎠⎠⎠⎥⎦
(3a)
b = x1b1 + x 2b2
(3b)
With regard to PR EOS, parameter C is expressed as C=
⎛2 + ln⎜ 2 2 ⎝2 − 1
2⎞ ⎟ 2⎠
(3c)
E
In eq 3a, g (the excess Gibbs energy) is calculated by the NRTL model ⎛ τ21 exp( −ατ21) g E = RTx1x 2⎜ ⎝ x1 + x 2 exp( −ατ21) Figure 3. Phase equilibrium of DME and PEC7 at ●, 293.15 K; ▲, 303.15 K; ▼, 313.15 K; □, 323.15 K; ○, 333.15 K; Δ, 343.15 K; and ▽, 353,15 K. − , PR-HVOS-NRTL model.
τ12 exp( −ατ12) ⎞ ⎟ x 2 + x1 exp( −ατ12) ⎠
+
(4)
Subscripts 1 and 2 represent DME and PECs, respectively. x is the liquid mole fraction. α, τ12, and τ21 are tuned parameters. τ12 and τ21 could take the following forms τ12 = τ12,0 + τ12,1(T − 273.15)
(5)
τ21 = τ21,0 + τ21,1(T − 273.15)
(6)
where τ12,0, τ12,1, τ21,0, and τ21,1 are the coefficients. All values (τ12,0, τ12,1, τ21,0, τ21,1, and α) are evaluated by N
obj =
∑ i=1
pexp i
where T and p are temperature (K) and pressure (kPa), respectively. v is the molar volume (L·mol−1). The value of R is 8.3145 J·K−1·mol−1. pc, Tc, and ω are the critical pressure, critical temperature, and acentric factor, respectively. Table 4 lists the values of these three parameters of DME, PEC7, and PEC9. The HVOS mixing rules can be expressed as Table 4. Pure Compound Parameters Used in Data Correlation molar mass (g/mol)
Tc/K
pc/kPa
acentric factor
DME PEC7 PEC9
46.068a 584.840b 697.050b
400.38a 887.64b 978.29b
5336.8a 940.0b 825.0b
0.196a 1.589b 1.514b
a
The values from the Refprop 9.1 database14 Razzouk et al.12
b
piexp
(7)
pcal i
where and are the measured and calculated pressures, respectively. N refers to the number of measured data points. The optimized values of α, τ12,0, τ12,1, τ21,0, and τ21,1 are reported in Table 5. Relative pressure deviations between experimental and calculated values are presented in Figures 5 and 6. Absolute average relative deviations in pressure were 0.89 and 1.49% for DME + PEC7 and DME + PEC9, respectively. Maximum deviations were 2.46% for DME + PEC7 and 3.89% for DME + PEC9. The phase equilibrium behavior between DME and PECs is discussed on the basis of the available data obtained from our laboratory. In Figure 7, phase equilibrium data for six binary systems (DME with PEC4 ≈ PEC9) were compared at the same temperatures. The phase equilibrium behavior of these six systems has a similar trend, and the liquid mole fractions of DME increase from PEC4 to PEC9; that is, the longer the linear chain of the carboxylic acid (or the higher the molecular mass), the higher the liquid mole fractions of DME. However, at a liquid mole fraction of DME that is approximately higher than 0.93, the phase equilibrium behavior shows a slight dependence on the size of the PECs, which means that the solubility values of PECs are almost identical in this region.
Figure 4. Phase equilibrium of DME and PEC9 at ●, 293.15 K; ▲, 303.15 K; ▼, 313.15 K; □, 323.15 K; ○, 333.15 K; Δ, 343.15 K; and ▽, 353,15 K. − , PR-HVOS-NRTL model.
compound
|piexp − pical |
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CONCLUSIONS The phase equilibrium of the DME + PEC7 system and the DME + PEC9 system were deduced in the temperature range from (293.15 to 353.15) K. The measured phase equilibrium data were modeled by PR EOS combined with the HVOS mixing rule and
The values from D
DOI: 10.1021/acs.jced.6b00412 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 5. Values of the Binary Interaction Parameters of the Model Derived by Fitting the Experimental Data
a
system
α
τ12,0
τ12,1
τ21,0
τ21,1
DME + PEC7 DME + PEC9
0.45 0.45
2.39545(0.02778)a 2.61818(0.02003)
−0.00104(5.7916 × 10−4) −0.00509(4.4142 × 10−4)
−2.88172(0.00555) −3.10120(0.00389)
−0.00050(1.1568 × 10−4) −0.01070(8.2692 × 10−5)
The standard errors of the fitting coefficients are shown in parentheses.
Figure 7. Phase equilibrium of DME with PEC4[9] (■), PEC5[9] (●), PEC6[8] (▲), PEC7(▼), PEC8[8] (⧫), and PEC9(★) at 293.15, 313.15, 333.15, and 353.15 K. PR-HVOS-NRTL model (−).
Figure 5. Deviation of experimental data from the calculated values with the PR-HVOS-NRTL model for DME + PEC7 at ●, 293.15 K; ▲, 303.15 K; ▼, 313.15 K; □, 323.15 K; ○, 333.15 K; Δ, 343.15 K; and ▽, 353,15 K.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel: 86-29-82668210. Funding
We are very grateful to the NSFC (no. 51476129) and the Key Laboratory of Cryogenics, TIPC CAS for financial support. Notes
The authors declare no competing financial interest.
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REFERENCES
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Figure 6. Deviation of experimental data from the calculated values with the PR-HVOS-NRTL model for DME + PEC9 at ●, 293.15 K; ▲, 303.15 K; ▼, 313.15 K; □, 323.15 K; ○, 333.15 K; Δ, 343.15 K; and ▽, 353.15 K.
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F
DOI: 10.1021/acs.jced.6b00412 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
