ARTICLE pubs.acs.org/IECR
Measurement of Thermophysical Pure Component Properties for a Few Siloxanes Used as Working Fluids for Organic Rankine Cycles Rima Abbas,†,‡ Andre Schedemann,† Christian Ihmels,§ Sabine Enders,‡ and J€urgen Gmehling*,† †
Lehrstuhl f€ur Technische Chemie, Carl von Ossietzky Universit€at Oldenburg, 26111 Oldenburg, Germany Fachgebiet Thermodynamik und Thermische Verfahrenstechnik, Institut f€ur Prozess- und Verfahrenstechnik, Technische Universit€at Berlin, 10623 Berlin, Germany § Laboratory for Thermophysical Properties (LTP GmbH), Marie-Curie-Str. 10, 26129 Oldenburg, Germany ‡
ABSTRACT: In this work, heat capacities for three linear siloxanes (hexamethyl disiloxane (MM), octamethyltrisiloxane (MDM), and decamethyltetrasiloxane (MD2M)) in the temperature range of 205.15395.15 K and for two cyclic siloxanes (octamethylcyclotetrasiloxane (D4) and decamethylcyclopentasiloxane (D5)) in the temperature range of 288.15443.15 K have been measured with the help of a TianCalvert calorimeter. Furthermore, vapor pressures for the five mentioned compounds in the temperature range of 250620 K and pressures from 2 mbar to 1 bar have been determined with the help of a Scott ebulliometer. The prediction of the heat capacities using the group contribution equation of state VTPR were improved by fitting the Twu parameters simultaneously to the new vapor pressure and heat capacity data. In addition, melting temperatures and heat of fusions for these five siloxanes have been measured using a differential scanning calorimeter (DSC). Furthermore, density measurements for the three linear siloxanes (MM, MDM, and MD2M) between 278 and 437 K and pressures up to 130 MPa were carried out using a vibrating tube densimeter. The densities were correlated with the TRIDEN model.
1. INTRODUCTION Organic Rankine cycle (ORC) processes are gaining increasing interest15 for the utilization of renewable energy such as geothermal heat, solar energy, biomass, and waste heat for the generation of electricity. The selection of the working fluid for ORC processes is a major challenge. While fluorinated alkanes, ethers, alkanes, and fluorinated ethers are used as working fluids for ORC at low temperatures (up to 100 °C),4,5 for higher temperature ORC (200400 °C) processes, the use of pure siloxanes and their mixtures is considered.68 Therefore, it is the aim of this work (i) to provide comprehensive and reliable (P,F,T) data, vapor pressures, and heat capacities for selected pure siloxanes, and, on the other hand, (ii) to improve the predictions of these properties using the VTPR-EOS (volume-translated PengRobinson equation of state) by fitting the Twu R-parameters simultaneously to vapor pressure and heat-capacity data. The VTPR-EOS is given by the following equation:9,10 P¼
RT aðTÞ v þ c b ðv þ cÞðv þ c þ bÞ þ bðv þ c bÞ ð1Þ
Here, a(T) is the temperature-dependent attractive parameter, b the co-volume, c the translation parameter, R the ideal gas constant, T the absolute temperature, v the molar volume, and P the pressure. The pure compound parameter aii and bii can be calculated using the critical temperature (Tc,i) and the critical pressure (Pc,i): ! R 2 Tc,i 2 ð2Þ aii ðTÞ ¼ 0:45724 Ri ðTÞ Pc,i r 2011 American Chemical Society
RTc,i Pc,i The R-function proposed by Twu et al.11 is used: h i N ðM 1Þ N i Mi Ri ðTÞ ¼ Tr,ii i exp Li 1 Tr,i
bii ¼ 0:0778
ð3Þ
ð4Þ
where Tr, i is the reduced temperature for compound i, and Ni, Mi, and Li are the TwuBluckCunninghamCoon R-function parameters. In this work, the Twu R-function parameters were fitted simultaneously to the experimentally obtained vapor pressure and heat-capacity data. If experimental liquid densities are available at a reduced temperature of Tr,i = 0.7, the translation parameter can be determined by the following equation: ci ¼ vcalc,i vexp,i
ðTr,i ¼ 0:7Þ
ð5Þ
If liquid density data are not available, ci can be estimated from the critical data and the compressibility factor at the critical point of compound i (zc,i), using the following correlation:12,13 ! RTc,i ci ¼ 0:252 ð6Þ 1:5448zc,i 0:4024 Pc,i Ahlers and Gmehling1315 have developed a universal groupcontribution equation of state (VTPR-GCEOS) to improve the prediction for mixtures, where the residual part of the modified UNIFAC model1620 was employed. Received: February 4, 2011 Accepted: June 30, 2011 Revised: June 19, 2011 Published: June 30, 2011 9748
dx.doi.org/10.1021/ie200256f | Ind. Eng. Chem. Res. 2011, 50, 9748–9757
Industrial & Engineering Chemistry Research
ARTICLE
Table 1. Experimental Vapor Pressures for MM temperature, T [K]
pressure, P [kPa]
284.04
2.5
286.71
2.93
291.1
3.85
294.93
temperature, T [K]
pressure, P [kPa]
temperature, T [K]
pressure, P [kPa]
306.42
8.25
341.97
35.52
311.01
10.18
349.68
46.61
319.94
15.12
356.98
59.43
4.85
327.41
20.58
364.59
75.17
298.68
5.69
332.46
25.01
370.68
302.87
6.99
337.55
30.31
374.41
100.8
pressure, P [kPa]
temperature, T [K]
pressure, P [kPa]
90.26
Table 2. Experimental Vapor Pressures for MDM temperature, T [K]
pressure, P [kPa]
temperature, T [K]
292.13
0.33
336.13
4.08
394.64
39.74
301.11
0.63
341
5.12
402.15
50.21
307.63
0.88
349.74
7.62
408.17
60.05
311.89
1.13
356.48
10.13
413.79
70.36
318.43 323.21
1.63 2.11
366.42 374.41
15.02 20.19
418.71 422.71
80.59 90.25
327.39
2.63
380.79
25.2
425.72
97.86
330.74
3.13
385.97
30.03
Table 3. Experimental Vapor Pressures for MD2M temperature, T [K]
pressure, P [kPa]
temperature, T [K]
pressure, P [kPa]
temperature, T [K]
pressure, P [kPa]
320.23
0.27
371.2
4.07
433.99
39.92
325.63
0.37
376.37
5.11
442.1
50.17
334.93
0.63
385.94
7.63
448.61
59.91
341.07
0.86
393.25
10.15
454.65
70.34
352.3
1.61
403.94
15.11
459.46
79.61
356.76
2.02
412.19
20.11
464.39
90.16
361.16 365.21
2.54 3.08
419.11 424.83
25.18 30.18
467.35
96.87
Table 4. Experimental Vapor Pressures for D4 temperature, T [K]
pressure, P [kPa]
temperature, T [K]
pressure, P [kPa]
temperature, T [K]
pressure, P [kPa]
312.97 321.76
0.35 0.62
361.65 370.53
4.99 7.61
413.49 417.59
36.27 41.02
331.26
1.08
377.32
10.01
424.59
50.7
344.06
2.12
386.89
14.51
438
73.85
352.18
3.17
395.06
19.15
444.71
88.84
356.7
3.96
407.58
30.82
450.42
102.16
2. EXPERIMENTAL SECTION 2.1. Chemicals. All studied siloxanes were received from Wacker Chemie AG (Germany). The chemicals used in this work were distilled and dried over a molecular sieve. The water content measured by Karl Fischer titration was always less than
