ARTICLE pubs.acs.org/IECR
Measurement of Transport Properties for Selected Siloxanes and Their Mixtures Used as Working Fluids for Organic Rankine Cycles Rima Abbas,†,‡ E. 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-Strasse 10, 26129 Oldenburg, Germany ‡
ABSTRACT: Thermal conductivities have been measured for three linear siloxanes [hexamethyl disiloxane (MM), octamethyltrisiloxane (MDM), decamethyltetrasiloxane (MD2M)], two cyclic siloxanes [octamethylcyclotetrasiloxane (D4), decamethylcyclopentasiloxane (D5)], and a mixture of 50 mass % MDM þ 50 mass % MD2M in the temperature range from 290 to 520 K and the pressure range from 500 to 10000 kPa using the transient hot wire method and correlated with a temperaturepressurethermal conductivity relationship. Moreover, the thermal conductivities at atmospheric pressure were measured for MM, D4, D5, and MD2M. The data were compared with the available data from the literature for four compounds. Additionally, the viscosities of the five siloxanes were measured in the temperature range from 238 to 378 K at atmospheric pressure using a rotational Stabinger viscometer.
1. INTRODUCTION To generate electricity from renewable energy, organic Rankine cycle (ORC) processes can be used. The temperature level of the heat source has a major influence on the selection of the working fluid for ORC processes. For heat sources up to 373.15 K, fluorinated alkanes, ethers, alkanes, and fluorinated ethers are often used as working fluids for ORC processes.1,2 Pure siloxanes and their mixtures are considered as working fluids for higher-temperature ORC processes (473.15673.15 K).35 Viscosity and thermal conductivity data are required in heat-transfer calculations for the optimization and design of these thermodynamic cycles. A few thermal conductivity data as functions of temperature have been reported in various works for MM,6 D4,7 and D5.7 Additionally, the dynamic viscosities as functions of temperature for some siloxanes were measured by Palczewska et al.,7 Hurd,8 and Sperkach et al.9 The aim of this work was to provide comprehensive and accurate viscosity data as a function of temperature and thermal conductivity data as a function of pressure and temperature for selected siloxanes. 2. EXPERIMENTAL SECTION 2.1. Chemicals. All studied siloxanes were received from Wacker Chemie AG (M€unchen, Germany). The chemicals used in this work were distilled and dried over molecular sieve. The water content was always less than 100 ppm. The purities of these chemicals were better than 99.8% by gas chromatography (GC). The resulting purities as determined by GC and the water contents obtained by Karl Fischer titration for the studied compounds are listed in Table 1. 2.2. Measurement of Thermal Conductivity. The experimental thermal conductivity data for the five selected pure siloxanes and for the 50 mass % MDM þ 50 mass % MD2M mixture were r 2011 American Chemical Society
Table 1. Purities and Water Contents of the Studied Siloxanes compound
purity (%, GC)
water content (mass ppm)
MM
99.9
20
MDM
99.89
15
MD2M
99.86
30
D4 D5
99.9 99.87
40 50
measured using the transient hot wire method (model Lambda, Flucon, Clausthal-Zellerfeld, Germany). For the measurements, which were carried out in the temperature range from 290 to 520 K and the pressure range from 100 to 10000 kPa, a high-pressure cell (Hastelloy C 274) was used, whereas a glass cell was used for the measurements at atmospheric pressure. The hot wire is the heat source and the sensor at the same time. An electric current flows through the wire and heats it. The variation of the temperature (Ohmic resistance) of the wire depends on the thermal conductivity of the surrounding fluid. Using a Wheatstone bridge, the resistance change can be measured. The platinum heating wire used shows an optimum with respect to steadiness; corrosion resistance; chemical resistance; large specific electrical resistance; and, at the same time, temperature stability. Nieto de Castro et al.10 presented a complete analysis regarding the application of the transient hot wire technique for the measurement of thermal conductivities. The accuracy of the Received: February 5, 2011 Accepted: May 26, 2011 Revised: May 19, 2011 Published: May 26, 2011 8756
dx.doi.org/10.1021/ie2002632 | Ind. Eng. Chem. Res. 2011, 50, 8756–8763
Industrial & Engineering Chemistry Research
ARTICLE
Table 2. Experimental Thermal Conductivities of MM T (K)
P
λ [mW/
(kPa) (m K)]
T (K)
P
λ [mW/
(kPa) (m K)]
T (K)
P
Table 3. Experimental Thermal Conductivities of MDM
λ [mW/
T
(kPa) (m K)]
(K)
P
λ [mW/
(kPa) (m K)]
λ [mW/
T (K)
P (kPa) (m K)]
T (K)
P
λ [mW/
(kPa) (m K)]
295.50
520 106.19 362.85 7994
92.93
440.07 4015
73.11
304.73
500
103.5
362.69
4000
90.6
431.36 7980
83.7
295.48
1996 107.50 362.84 9998
94.29
440.09 5986
75.37
304.76 2000
105.4
362.71
5990
92.1
431.37 9980
86.5
295.44
3967 108.63 372.11
594
84.90
440.09 7997
77.25
304.76 4000
107.1
362.71
7990
94.6
441.04
670
72.3
295.38
5997 109.82 372.22 1994
86.36
440.09 9990
79.29
304.75 6000
108.6
362.71
9980
96.2
441.1
2000
74.5
295.32
7994 111.04 372.27 4015
88.32
449.73 1146
67.41
304.8
8000
110.0
372.4
540
85.1
441.11 4000
77.2
295.24 10000 112.00 372.26 5986
89.28
449.81 1997
68.65
304.82 10000
109.6
372.49
2010
86.3
441.11 5990
79.3
301.44 301.65
554 103.95 372.27 7998 2015 105.36 372.28 9992
91.27 92.68
449.92 4017 449.95 5987
71.22 73.24
314.32 480 314.29 1990
99.7 102.3
372.53 372.58
4000 6000
89.2 90.0
441.15 7990 441.2 9990
82.2 84.7
301.77
3988 106.37 381.93
626
82.61
449.96 7998
75.53
314.28 4000
103.1
372.6
7990
92.4
451.47
720
71.2
301.82
5962 107.96 381.99 1995
83.86
449.95 9991
77.25
314.27 5990
104.3
372.59
9990
94.5
451.54 2000
72.9
301.86
7996 108.36 382.02 4015
85.63
459.53 1279
65.19
314.27 8000
105.9
382.43
550
82.5
451.55 4000
76.0
301.90
9994 109.78 382.02 5986
87.35
459.63 2005
66.75
314.28 10000
108.4
382.44
2010
83.6
451.55 5990
79.6
310.89
512 101.08 382.04 7998
88.78
459.67 3997
69.21
323.91
480
96.3
382.42
4000
86.1
451.54 7990
81.9
311.03
2031 102.54 382.05 9992
90.06
459.71 5987
71.60
323.97 2000
98.5
382.46
6000
88.5
451.54 9980
84.4
311.08 311.13
4002 103.38 391.69 665 5975 104.95 391.84 1995
80.07 81.32
459.71 7999 459.75 9991
73.26 75.15
324.02 4000 324.04 5990
100.5 101.4
382.53 382.57
7990 9980
89.9 92.2
461.17 740 461.37 2000
70.2 72.2
311.15
7999 106.96 391.87 4015
83.53
469.39 1438
63.40
324.04 7990
104.2
392.44
540
79.9
461.45 3980
76.0
311.15
9994 107.11 391.88 5986
85.13
469.52 1998
64.16
324.03 10000
105.5
392.52
1990
82.1
461.48 6000
79.1
319.87
519
98.61 391.88 7999
86.58
469.42 3998
67.50
333.78
490
94.9
392.53
3980
84.4
461.49 7990
81.4
320.07
2036
99.78 391.91 9992
88.27
469.41 5987
69.65
333.87 2000
95.6
392.53
5980
86.9
461.52 9990
84.2
320.18
4007 100.48 401.46
715
78.06
469.28 7999
71.44
333.89 3990
97.8
392.52
8000
88.5
472.63
780
69.8
320.23
5980 102.42 401.54 1996
79.57
469.16 9990
73.56
333.91 6000
100.0
392.52
9990
91.0
472.49 1980
71.9
320.27 320.25
7953 104.10 401.61 4016 9997 105.72 401.64 5987
81.15 83.55
480.61 1600 480.70 1995
60.92 61.51
333.93 8000 333.96 9990
101.7 102.7
402.28 402.38
550 1980
78.2 80.0
472.22 3980 471.87 5990
74.7 78.1
329.13
521
96.11 401.67 7999
85.80
480.75 3982
64.83
343.66
490
91.8
402.46
4000
82.8
471.54 7990
80.4
329.30
2039
96.57 401.72 9992
86.75
480.81 5993
67.18
343.74 1970
93.5
402.47
5990
85.1
471.46 10000
83.4
329.41
4009
98.76 411.52
773
75.71
480.78 7994
68.88
343.78 4000
94.3
402.47
8000
87.5
480.73
850
70.0
329.49
5981
99.91 411.10 1995
77.82
480.98 9986
70.48
343.79 5990
97.9
402.46
9990
89.1
480.85 1990
70.7
329.50
7955 100.59 410.96 4014
80.26
490.86 1808
58.33
343.76 8000
98.0
411.68
570
77.1
480.9
3980
74.0
329.52
9998 102.37 410.97 5985
81.26
491.15 1991
58.75
343.74 9990
100.6
411.86
1980
79.1
480.97 5980
77.0
338.64 338.68
532 2040
92.88 411.09 7996 94.05 411.15 9998
83.49 85.50
490.98 3996 490.95 5998
61.80 64.73
353.43 490 353.43 1990
87.7 90.8
411.83 411.85
3970 6000
81.2 83.6
480.98 8000 480.99 10000
80.4 83.0
339.13
4029
95.83 420.90
839
74.58
491.10 8000
65.89
353.41 4000
92.6
411.9
7990
85.6
490.61
890
69.7
339.81
6000
97.42 420.90 1997
75.93
491.20 9994
68.54
353.4
6000
95.3
411.94 10000
87.7
490.71 1980
70.5
340.13
7957
98.26 420.92 4006
77.70
500.90 2025
56.11
353.45 7990
96.2
421.42
600
75.8
490.89 3990
74.1
340.14
9996
99.80 420.93 5996
79.24
500.85 3990
59.39
353.51 9990
97.7
421.68
1990
77.9
490.88 5990
76.7
352.77
547
90.52 420.94 7998
81.42
500.85 5993
61.69
352.68
510
88.4
421.78
3980
80.4
490.89 7990
80.0
352.86
1997
91.57 420.92 9990
82.78
500.93 7982
63.36
352.8
1990
90.1
421.81
5980
83.0
490.9
9990
82.8
352.94 352.99
4007 5997
92.19 430.60 931 94.36 430.65 1991
71.82 73.47
500.98 9994 507.37 2352
66.06 54.39
352.84 3980 352.91 5980
92.8 93.9
421.8 7970 421.79 10000
85.1 87.5
500.42 1000 500.49 2010
68.2 70.5
353.04
7992
96.20 430.66 4011
75.42
507.44 3992
57.39
352.94 7980
96.3
431.29
640
74.0
500.5
3990
73.1
353.04
9995
97.09 430.64 5981
77.72
507.51 6000
60.07
352.94 9970
98.0
431.33
2000
76.6
500.51 5980
76.2
362.56
570
87.26 430.60 7994
79.82
507.54 7985
62.10
362.61
530
86.4
431.36
3990
78.2
500.53 7980
79.0
362.69
2000
88.69 430.62 9996
80.65
507.56 9998
64.03
362.68 2000
89.3
431.36
5990
81.9
500.54 10000
82.2
362.76
4010
90.60 439.97 1030
69.59
440.07 4015
73.11
362.82
5982
92.33 440.01 1996
71.12
measured thermal conductivities using this technique is about (1%. In the used equipment, the pressure was measured with a calibrated pressure transducer (model PDCR 4010, GE Sensing, Taunton, Somerset, U.K.) with an accuracy of (5 kPa. The temperature was determined with an integrated calibrated Pt(100) probe (accuracy (0.1 K). The overall uncertainty in the
thermal conductivity measurements is about (1% [about ((0.71 mW/(m K)]. The obtained experimental thermal conductivity data at atmospheric pressure and the measured data as a function of temperature and pressure for the five studied pure siloxanes and for the 50 mass % MDM þ 50 mass % MD2M mixture are listed in Tables 211. 2.3. Measurement of Dynamic Viscosity. Dynamic viscosities are among the basic pure-component transport properties 8757
dx.doi.org/10.1021/ie2002632 |Ind. Eng. Chem. Res. 2011, 50, 8756–8763
Industrial & Engineering Chemistry Research
ARTICLE
Table 4. Experimental Thermal Conductivities of MD2M T (K)
P
λ [mW/
(kPa) (m K)]
λ [mW/
T
(K) P (kPa) (m K)]
T (K)
P
Table 5. Experimental Thermal Conductivities of D4
λ [mW/
T
(kPa) (m K)]
(K)
P
λ [mW/
(kPa) (m K)]
λ [mW/
T (K)
P (kPa) (m K)]
T (K)
P
λ [mW/
(kPa) (m K)]
304.03
490 107.5 371.88
500
90.4
439.63
550
77.9
295.56
510
114.7
362.85
8000
103.5
442.98 3990
304.1
2000 109.9 371.99
2000
92.2
439.8
2010
80.2
295.58 1990
115.8
362.92
9990
104.7
442.98 5990
86.2
304.12 3990 111.4 372.06
4000
93.6
439.91
4000
81.9
295.57 3990
116.6
372.11
510
96.2
442.95 7990
88.0
304.13 6030 113.6 372.13
5990
94.9
440.04
5990
85.2
295.61 5990
117.4
372.22
2000
97.1
442.96 9990
89.6
304.22 7990 113.7 372.13
8000
98.0
440.11
8000
87.5
295.59 7990
118.1
372.26
4000
98.6
453.2
304.34 10000 116.3 372.16
9990
98.8
440.12
9990
90.7
295.57 10000
119.6
372.27
6000
312.93 500 105.4 381.77 313.12 2000 106.1 381.8
500 1990
87.5 89.4
449.51 449.52
560 1990
77.3 79.0
302.88 510 303.09 1990
113.6 114.1
372.32 372.36
313.22 3990 108.5 381.86
4000
91.5
449.53
4000
81.9
303.33 4000
114.6
313.28 6030 109.9 381.86
5990
93.4
449.51
5990
83.8
303.44 6000
115.0
313.3
8000
95.9
449.53
8000
86.9
303.51 8000
9990
97.4
449.57
9990
89.8
8020 110.6 381.8
313.3 10020 112.8 381.77 322.5
620
78.8
100.1
453.29 1990
80.5
8000 9990
101.9 103.0
453.33 3990 453.35 5990
82.2 83.8
382.46
500
94.2
453.35 8000
85.5
382.69
2000
94.7
453.32 9990
87.5
115.9
382.82
4000
97.1
462.92
660
77.2
303.52 9990
117.2
382.88
5990
97.8
462.97 1980
79.2
500
85.9
459.11
590
75.4
313.07
500
110.3
382.92
8000
99.4
462.97 4000
80.6
322.69 2000 104.4 391.56
2000
88.2
459.19
2000
77.5
313.19 1990
111.4
382.92
9990
100.8
462.97 6000
81.5
322.87 3990 106.5 391.65 322.99 6000 107.5 391.78
4000 5990
90.6 92.0
459.18 459.19
4000 5990
80.1 82.7
313.3 4000 313.33 5990
111.5 113.2
393.53 393.64
530 2000
91.7 92.8
462.96 8000 462.95 9990
83.8 85.3
323.08 8000 109.6 391.76
8000
93.4
459.22
8000
85.4
313.35 8000
114.3
393.74
4000
94.6
472.57
680
75.0
323.13 9990 110.4 391.79 10000
96.4
459.21
9990
87.8
313.38 10000
115.1
393.75
5990
96.2
472.62 1990
76.4 77.9
332.78
500 103.1 391.5
83.9
98.4 401.21
510
83.3
468.77
610
73.7
322.83
500
108.0
393.76
8000
97.1
472.61 4000
2000 101.4 401.36
2000
86.6
468.99
2020
76.9
323.06 2000
108.2
393.81
9990
98.2
472.6
5990
79.7
332.99 4000 103.1 401.35
3990
88.5
468.99
3990
79.3
323.18 3990
109.5
403.57
550
89.3
472.6
7990
81.2
333.06 6000 103.9 401.41
6000
90.1
469.017 6000
82.3
323.31 5990
111.2
403.62
1990
90.5
472.58 10000
83.0
333.08 8000 106.5 401.4 8000 333.1 9990 108.8 401.41 10000
93.3 95.8
469.04 469.04
7990 9990
85.4 87.4
323.42 8000 323.45 10000
112.2 113.3
403.66 403.7
4000 6000
91.9 94.0
482.42 730 482.38 2010
73.7 74.0 76.1
332.9
342.71
500
500
96.4 410.96
520
82.7
478.62
630
72.9
332.95
500
106.0
403.75
7990
95.4
482.52 3980
342.76 2000
98.2 411.04
2000
84.2
478.65
1990
75.0
333.12 2010
106.3
403.77 10000
96.9
482.47 5980
78.4
342.81 3990
99.9 411.11
3990
86.4
478.74
3980
78.3
333.21 4000
107.6
413.39
530
87.3
482.49 8000
80.1
342.85 6000 102.5 411.16
6000
89.1
478.74
6000
81.5
333.31 6000
109.3
413.54
1990
88.2
482.52 10000
81.0
342.89 7990 103.1 411.19
7990
91.3
478.75
8000
84.0
333.4
8000
109.9
413.63
3990
90.1
492.82
790
71.0
342.88 10000 104.6 411.21 10000
93.8
478.67 10000
86.5
333.45 9990
111.6
413.74
5990
91.9
492.94 2010
72.2
352.47 490 352.57 1990
94.9 420.69 96.4 420.75
520 2000
81.2 82.5
488.21 488.2
680 1990
72.9 75.0
342.88 500 343.13 2010
102.9 104.2
413.74 7990 413.72 10000
93.1 95.1
493.13 4010 493.09 5990
74.4 75.9
352.65 4000
97.3 420.65
3990
84.9
488.25
3990
77.4
343.34 4000
105.8
423.33
570
84.9
493.04 8000
77.8
352.77 6000
99.8 420.63
6000
88.1
488.35
5990
80.7
343.42 6000
106.5
423.41
1980
86.7
493.12 9990
79.2
352.79 8000 101.0 420.72
8000
89.2
488.35
7980
83.6
343.55 8010
108.4
423.44
3990
88.1
502.92
840
69.3
352.81 10000 102.8 420.82
9990
92.7
488.34 10000
86.5
343.68 10000
108.7
423.51
5990
89.6
502.98 1990
70.6 72.8
362.03
500
92.4 430.43
540
79.5
498.29
720
71.5
353.45
500
101.0
423.55
7990
91.1
502.86 4000
362.15 2000
94.6 430.47
2000
81.7
498.26
1990
73.6
353.64 2000
101.6
423.56
9990
92.8
502.92 6000
74.1
362.2 4000 362.31 5990
96.0 430.51 98.3 430.55
3990 5990
83.3 86.1
498.29 498.33
3990 5990
76.7 80.2
353.78 4000 353.86 5990
103.9 104.4
433.28 433.2
580 1990
83.2 84.6
502.95 8000 502.95 10000
76.1 77.8
362.32 8000 100.1 430.55
8000
88.2
498.32
7980
83.1
353.89 7990
105.4
433.3
3990
86.7
512.41
900
67.1
362.42 9990 101.7 430.51
9990
91.2
498.31 10010
85.6
353.87 10000
106.7
433.22
5990
88.0
512.5
1990
68.2
362.52
used for many engineering processes, for calculations, and for optimization of ORC processes. In this work, dynamic viscosities for various siloxanes were measured using a rotational Stabinger viscometer (model SVM 3000, Anton Paar GmbH, Graz, Austria). The sample and a coaxial rotor are located in a rotational cylinder. The movements of the rotational cylinder set the sample in motion, which creates a parallel rotation of the coaxial rotor. A magnet is located on the rotor. This magnet produces a circulated magnetic field and induces a turbulent flow in a block made of copper. The Hall sensor measures the frequency of the rotating magnetic field and the speed of the rotor. The measured
500
98.4
433.12
7990
89.5
512.53 3990
70.8
362.67 2000
99.8
433.11 10000
91.4
512.63 5990
72.3
362.75 4000
101.4
442.67
600
80.6
512.4
8000
74.5
362.82 5990
102.5
442.8
2000
82.5
512.31 10000
75.9
viscosity of the sample depends on the measured speed of the rotor. The temperature is measured with a Pt(100) probe with an accuracy of about 0.05 K. The overall accuracy of the performed viscosity measurements is estimated to be (1%. The measurements were performed at atmospheric pressure and in the temperature range of 238378 K. A more detailed description of this device 8758
dx.doi.org/10.1021/ie2002632 |Ind. Eng. Chem. Res. 2011, 50, 8756–8763
Industrial & Engineering Chemistry Research
ARTICLE
Table 6. Experimental Thermal Conductivities of D5 T (K) 294.92
P
λ [mW/
(kPa) (m K)] 510
116.2
λ [mW/
T (K) 363.91
P (kPa) (m K)] 7990
105.4
T (K) 443.7
P
λ [mW/
Table 7. Experimental Thermal Conductivities of MM at Atmospheric Pressure T (K)
λ [mW/(m K)]
T (K)
λ [mW/(m K)]
86.0
292.20
108.4
333.31
94.9
104.8 100.9
343.81 353.75
92.2 89.6
97.8
363.25
87.2
(kPa) (m K)] 4000
9990
106.5
443.52 6000
87.4
373.74
510
98.0
443.42 7990
89.1
301.53 312.07
373.92
1990
98.9
443.43 9990
90.6
322.87
119.8
374.01
3990
100.4
453.17
540
80.0
121.6
374.06
6000
102.3
453.19 2000
81.3
303.45 510 303.62 2000
114.7 115.5
374.13 374.17
8000 9990
103.5 104.8
453.25 4000 453.32 6000
83.4 84.9
303.77 4000
115.7
383.81
520
95.9
453.25 7990
87.1
T (K)
λ [mW/(m K)]
T (K)
λ [mW/(m K)]
303.87 5990
116.2
383.91
2000
96.8
453.15 10000
88.6
296.66
114.6
343.32
103.0
303.93 7990
117.2
383.97
4000
98.1
463.09
550
77.4
301.58
113.0
353.75
100.5
303.92 10000
119.6
384
6000
100.0
463.25 1990
79.1
313.67
520
111.4
384.04
7990
101.0
463.28 3990
81.0
311.89 322.43
110.5 107.6
363.92 374.07
98.1 95.8
313.86 2000
111.8
384.19 10000
102.0
463.29 5990
83.2
332.90
105.3
313.98 3990 314.04 5990
112.4 114.6
393.92 394.06
500 1990
93.3 94.5
463.26 8000 463.27 9990
84.9 87.1
314.09 8000
116.1
394.13
3990
96.2
473.05
570
75.0
314.12 9990
117.4
394.15
6000
96.8
473.07 2000
76.7
323.8
294.92 2000
118.0
363.93
294.92 4000
118.7
294.92 6000
118.7
294.89 7990 294.88 9990
500
108.7
394.2
8000
98.6
473.02 3990
79.2
323.92 2000
110.2
394.2
9990
100.1
472.96 5990
80.9
324.02 4000
111.2
403.82
500
91.4
472.92 8000
82.3
324.11 6000
113.0
403.92
2000
91.9
472.89 9990
84.3
324.13 7990 324.16 10000
113.6 114.5
404.02 404.12
3990 5990
94.6 95.9
482.74 590 482.77 2010
72.5 74.5
334
490
106.7
404.13
8000
96.6
482.79 3990
76.4
334.14 2000
107.5
404.08
9990
99.0
482.8
5990
78.5
334.23 3990
109.0
414.02
510
90.1
482.81 8000
80.8
334.27 6000
109.6
414.02
2000
90.9
482.82 10000
82.5
334.29 8000
110.7
414.01
3990
92.5
492.25
630
70.1
334.31 9990
111.8
413.96
5990
94.2
492.28 2010
72.2
344.01 500 344.19 2010
103.9 105.9
413.96 413.99
7990 9990
95.2 96.5
492.36 3990 492.38 5990
Table 8. Experimental Thermal Conductivities of D4 at Atmospheric Pressure
Table 9. Experimental Thermal Conductivities of D5 at Atmospheric Pressure T (K)
λ [mW/(m K)]
T (K)
λ [mW/(m K)]
294.04
115.3
364.44
99.2
314.49
111.1
375.31
97.4
325.39 333.30
108.7 106.5
385.76 395.82
94.7 92.7
354.29
101.6
405.81
90.6
Table 10. Experimental Thermal Conductivities of MD2M at Atmospheric Pressure T (K)
λ [mW/(m K)]
T (K)
λ [mW/(m K)]
74.3 76.0
295.98
110.2
344.01
96.9
302.23
107.8
354.37
94.5
104.5 101.9
364.49 374.77
92.8 89.6
100.6
344.24 3990
106.8
423.82
510
87.0
492.41 8000
77.9
344.29 6000
108.3
423.88
1990
88.4
492.39 10000
80.3
312.76 323.28
344.31 8000
108.8
423.9
3990
90.2
501.83
670
66.9
333.76
344.33 9990
110.3
423.9
5990
91.6
501.85 1990
69.2
354.2
500
103.0
423.91
7990
93.3
501.77 4000
71.7
354.25 2000
104.1
423.87
9990
95.2
501.69 6000
74.2
354.24 3990 354.23 5990
105.0 106.2
433.2 433.45
540 2010
84.9 86.0
501.65 7990 501.63 10000
75.5 78.3
354.17 7990
106.9
433.57
3990
88.2
512.42
700
64.5
354.14 10000
109.1
433.54
5990
89.2
512.6
1990
66.3
363.78
520
100.3
433.72
8000
91.4
512.67 4000
68.6
363.82 2000
101.7
433.79 10000
92.7
512.64 6000
71.2
363.89 4000
102.8
443.46
530
82.1
512.63 7990
73.2
363.89 6000
104.6
443.7
2000
84.2
512.81 10000
75.1
can be found in ref 11. The obtained experimental dynamic viscosities for the five siloxanes are listed in Tables 1216.
3. RESULTS AND DISCUSSION The measured thermal conductivities can be correlated as a function of temperature and pressure using the following
polynomial relationship λ ¼ A þ BT þ CP þ DTP þ ET 2
ð1Þ
where λ is the thermal conductivity [mW/(m K)], T is the temperature (K), P is the pressure (kPa), and AE are parameters fitted to the experimental thermal conductivities as functions of temperature and pressure. These parameters are listed in Table 17 for the five siloxanes and the 50 mass % MDM þ 50 mass % MD2M mixture. The temperature and pressure dependencies of the thermal conductivities of MM are shown together with the correlated data (eq 1) in Figure 1. It can be seen from this figure that the correlated data are in good agreement with the experimental data. The correlated thermal conductivities can be extrapolated to other pressures (e.g., atmospheric pressure). In Figure 2, published thermal conductivities at atmospheric pressure6 are shown together with the extrapolated data for MM. As can be seen, good agreement is achieved between the measured data and 8759
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Table 11. Experimental Thermal Conductivities of 50 mass % MDM þ 50 mass % MD2M T (K) 303.34
P
λ [mW/
(kPa) (m K)]
T (K)
P
λ [mW/
T
(kPa) (m K)]
(K)
Table 13. Experimental Dynamic Viscosities of MDM
λ [mW/
P
(kPa) (m K)]
T (K)
η (mPa s)
T (K)
η (mPa s)
258.15
1.413
303.15
0.799
263.15
1.336
313.15
0.707
510
105.6
373.21
520
87.2
441.05
510
76.9
268.15
1.255
323.15
0.628
303.48 1980
106.5
373.32
1990
88.7
441.12 1990
78.9
273.15
1.173
333.15
0.562
303.56 3980
108.0
373.38
3990
90.9
441.17 3990
80.7
278.15
1.104
343.15
0.503
303.61 5980
109.6
373.43
5980
92.4
441.2
5980
85.0
283.15
1.031
353.15
0.45
303.65 7970
110.7
373.46
7980
94.6
441.23 7980
87.0
288.15
0.968
363.15
0.403
303.71 10000
112.4
373.45
9970
96.4
441.27 10000
88.5
293.15
0.909
373.15
0.365
313.5
510
102.9
382.92
520
84.2
450.59
520
74.6
313.61 1990
104.4
383.02
2000
86.0
450.66 1990
78.4
313.72 3990
106.2
383.07
3990
88.5
450.72 3990
80.7
313.79 5980
106.9
383.1
5990
90.6
450.86 5980
83.0
T (K)
η (mPa s)
T (K)
η (mPa s)
313.85 7980
109.4
383.13
7980
92.5
450.87 7980
85.7
313.87 10000
110.6
383.17
9980
94.0
450.86 9970
88.3
238.15 243.15
3.584 3.314
288.15 293.15
1.525 1.422
323.41
Table 14. Experimental Dynamic Viscosities of MD2M
520
99.5
392.48
520
82.3
460.09
520
74.5
248.15
3.05
303.15
1.234
323.61 2000
100.7
392.61
2000
85.4
460.08 2000
76.7
253.15
2.778
313.15
1.079
323.72 3990
101.7
392.66
3990
87.6
460.06 3990
79.1
258.15
2.535
323.15
0.95
323.77 5980
103.1
392.66
5990
89.0
460.12 5980
82.0
263.15
2.32
333.15
0.842
323.81 7980
106.3
392.8
7980
91.8
460.18 7980
84.9
268.15
2.117
343.15
0.751
323.86 9970
107.6
392.79
9980
94.3
460.23 9970
87.5
273.15
1.95
353.15
0.672
278.15 283.15
1.793 1.655
363.15 373.15
0.602 0.54
333.52
520
96.7
402.37
520
80.9
469.34
510
74.6
333.6
2000
96.9
402.49
2000
83.9
469.38 2000
76.4
333.77 3990
99.1
402.58
3990
86.4
469.39 3990
78.9
333.86 5980
100.6
402.61
5990
88.2
469.38 5990
82.0
333.91 7980
103.0
402.65
7980
89.2
469.4
7980
84.9
333.93 9970
105.5
402.69
9970
91.5
469.43 9980
87.0
510
93.5
412.23
510
79.4
478.94
510
73.2
343.34 1990
95.1
412.31
1990
81.9
479.07 2000
75.5
343.45 3990
97.0
412.35
3980
84.8
479.15 4000
343.54 5980
100.1
412.37
5980
86.7
343.62 7980
100.6
412.39
8000
89.1
343.69 10000
102.3
412.43
9990
510
92.1
421.88
353.54 1990
93.7
353.48 3980
94.9
353.46 5980
Table 15. Experimental Dynamic Viscosities of D4 T (K)
η (mPa s)
T (K)
η (mPa s)
78.7
293.15 298.15
2.468 2.227
333.15 343.15
1.222 1.055
479.14 5980
80.8
303.15
2.022
353.15
0.917
479.19 8000
82.8
308.15
1.844
363.15
0.801
90.6
479.24 9990
86.4
313.15
1.687
373.15
0.705
500
78.5
488.76
480
72.5
323.15
1.428
421.91
1980
79.8
488.85 1980
75.2
421.94
3980
83.1
489.01 3990
77.2
95.7
421.93
5970
85.1
489.01 5980
79.6
353.53 8000
99.1
421.91
8000
87.9
489.03 7990
82.7
353.66 9990
99.3
421.91 10000
89.8
489.02 9990
85.1
363.56
510
88.5
431.41
510
77.0
498.25
490
72.2
363.6
1990
91.1
431.46
1980
80.2
498.26 1990
74.7
363.62 3990
92.4
431.52
3980
81.9
498.23 3980
77.2
363.66 5980
94.1
431.54
5970
84.2
498.21 5980
80.1
363.68 7980
96.4
431.55
8000
87.0
497.96 7990
83.4
363.69 10000
98.4
431.56
9990
88.9
497.9
86.1
343.22
353.51
10000
Table 16. Experimental Dynamic Viscosities of D5 T (K)
η (mPa s)
T (K)
η (mPa s)
243.15
19.058
303.15
3.478
248.15
15.609
313.15
2.851
253.15
12.967
323.15
2.371
263.15
9.274
333.15
1.996
273.15
7.139
343.15
1.696
278.15
6.236
353.15
1.454
283.15
5.484
363.15
1.254
288.15 293.15
4.852 4.318
373.15
1.103
Table 12. Experimental Dynamic Viscosities of MM T (K)
η (mPa s)
T (K)
η (mPa s)
273.15
0.611
303.15
0.461
278.15 283.15
0.589 0.566
313.15 323.15
0.414 0.371
293.15
0.514
the available data from the literature.6 It can also be seen that the extrapolated data are in good agreement with the experimental data up to 340 K. Because of convection effects (disturbing the thermal conductivity measurements) caused by partial vaporization of MM at atmospheric pressure and at higher temperatures, larger deviations are obtained at higher temperatures. 8760
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Table 17. Correlation Parameters Fitted to Experimental Thermal Conductivities in This Work parameter compound
A [mW/(m K)]
B [mW/(m K2)]
C [mW/(m K kPa)]
D [mW/(m kPa K2)]
E [mW/(m K3)]
MM
196.053
0.346 86
0.000 210 2
0.000 002 9
0.000 13
MDM
272.32
0.783 28
0.000 447
0.000 004
0.000 746
MD2M
258.11
0.679 65
0.000 498
0.000 004 1
0.000 61
D4
195.86
0.307 60
0.000 187 6
0.000 002 3
0.000 12
D5
171.743
0.166 68
0.000 434
0.000 003
50% MDM þ 50% MD2M
255.235
0.699
0.000 101
0.000 003 1
Figure 1. Experimental (blue circles, high-pressure cell) and correlated (green diamonds, eq 1) thermal conductivities for MM.
Figure 2. Experimental (blue diamonds, this work; red triangles, ref 6) thermal conductivities at atmospheric pressure and (solid red line) extrapolated data (eq 1) for MM.
The measured thermal conductivities as a function of pressure and temperature for D4 are similar to the results for D5 (see Tables 4 and 5). In Figure 3, a comparison of the experimental thermal conductivities at atmospheric pressure obtained in this work are shown together with the published data7 and the extrapolated data as functions of the pressure and temperature for D4 and D5. Although the measured data and the literature data7 for D4 are in good agreement, it can be seen that the maximum deviations are about 10% for D5. The extrapolated data reproduce the obtained data in this work for both compounds (D4 and D5).
0.000 08 0.000 665
Figure 3. Experimental (blue triangles, D4, this work; orange circles, D5, this work; red diamonds, D4, ref 7; maroon squares, D5, ref 7) thermal conductivities at atmospheric pressure and (black lines) extrapolated data (eq 1).
Figure 4. Experimental (blue circles, high-pressure cell) and correlated (green diamonds, eq 1) thermal conductivities for 50 mass % MDM þ 50 mass % MD2M.
Figure 4 shows the measured and correlated thermal conductivities as a function of pressure and temperature for the 50 mass % MDM þ 50 mass % MD2M mixture. The results show that the measured data for the mixture are between the measured data for its pure compounds (see Tables 2, 3, and 9). The linear pressure dependencies of the correlated thermal conductivities at temperature T = 298.15 K for the studied linear siloxanes (MM, MDM, MD2M, and 50 mass % MDM þ 50 mass % MD2M) are shown in Figure 5. 8761
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Figure 5. High-pressure data obtained by eq 1 for (purple 's) MM, (red triangles) MDM, (blue diamonds) MD2M, and (green circles) 50 mass % MDM þ 50 mass % MD2M at T = 298.15 K.
Table 18. Average Absolute Relative Deviations (AARDs) between Experimental and Correlated Thermal Conductivities for the Studied Siloxanes compound
AARD (%)
MM
0.7
MDM
0.5
MD2M
0.4
D4
0.3
D5
0.4
50% MDM þ 50% MD2M
0.6
Figure 7. Experimental dynamic viscosities for D4 (maroon circles, this work; blue diamonds, ref 12; þ's, ref 7) and D5 ('s, this work; red asterisks, ref 12; green triangles, ref 7).
4. CONCLUSIONS Because of the recent applications of siloxanes and their mixtures as working fluids in ORC processes, their transport properties (thermal conductivities and dynamic viscosities) are needed for the proper construction and design of these processes. In this article, the thermal conductivities as a function of temperature and pressure for five selected siloxanes and for a 50 mass % MDM þ 50 mass % MD2M mixture are presented. The measurements were performed using the transient hot wire method. The measured thermal conductivities data were correlated as a function of temperature and pressure using a polynomial relationship. Additionally, thermal conductivities as a function of temperature for MM, D4, D5, and MD2M were measured at atmospheric pressure with the transient hot wire method using a glass cell. Furthermore, dynamic viscosities for five siloxanes were measured using the rotational Stabinger viscometer. The obtained data are in good agreement with published data. ’ AUTHOR INFORMATION Corresponding Author
*Tel.: þ49 441 798 3831. Fax: þ49 411 798 3330. E-mail:
[email protected]. URL: http://www. uni-oldenburg.de/tchemie. Figure 6. Experimental dynamic viscosities for MDM (asterisks, this work; red circles, ref 8; blue diamonds, ref 9) and MD2M (þ's, this work; green triangles, ref 8).
Within the measured temperature range (from 290 to 520 K) and the measured pressure range (from 500 to 10000 kPa), the deviations between experimental and correlated thermal conductivities for the studied siloxanes are given in Table 18. The average absolute relative deviation (AARD) is defined as follows 1 n λcalc λexp ð2Þ AARD ¼ n i ¼ 1 λexp
∑
It can be seen that the correlated thermal conductivities and the experimental data are in good agreement. Figures 6 and 7 show a comparison between the experimental dynamic viscosities for MDM, MD2M, D4, and D5 obtained in this work and the available literature data.79,12 Good agreement is obtained between the measured and literature data.
’ ACKNOWLEDGMENT The authors thank the Arbeitsgemeinschaft industrieller Forschungsvereinigungen (AIF: 13885N) for financial support of this work. R.A. thanks Al-Baath University in Syria for the fellowship. ’ REFERENCES (1) Saleh, B.; Koglbauer, G.; Wendland, M.; Fischer, J. Working fluids for low-temperature organic Rankine cycles. Energy 2007, 32 (7), 1210–1221. (2) Tchanche, B. F.; Papadakis, G.; Lambrinos, G.; Frangoudakis, A. Fluid selection for a low-temperature solar organic Rankine cycle. Appl. Therm. Eng. 2009, 29 (1112), 2468–2476. (3) Colonna, P.; Nannan, N. R.; Guardone, A.; Lemmon, E. W. Multiparameter equations of state for selected siloxanes. Fluid Phase Equilib. 2006, 244 (2), 193–211. (4) Lai, N. A.; Wendland, M.; Fischer, J. Description of linear siloxanes with PC-SAFT equation. Fluid Phase Equilib. 2009, 283 (12), 22–30. 8762
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(5) Lai, N. A.; Wendland, M.; Fischer, J. Working fluids for hightemperature organic Rankine cycles. Energy 2011, 36, 199–211. (6) Bates, O. K. Thermal conductivities of liquid silicones. J. Ind. Eng. Chem. 1949, 41, 1966–1968. (7) Palczewska-Tulinska, M.; Oracz, P. Selected physicochemical properties of hexamethylcyclotrisiloxane, octamethylcyclotetrasiloxane, and decamethylcyclopentasiloxane. J. Chem. Eng. Data 2005, 50 (5), 1711–1719. (8) Hurd, C. B. Siloxanes. I. The specific volume and viscosity in relation to temperature and constitution. J. Am. Chem. Soc. 1946, 68, 364–370. (9) Sperkach, V. S.; Cholpan, P. F. Study of acoustic scattering in some siloxanes. Fiz. Zhidk. Sostoyaniya 1979, No. 7, 104–109. (10) Nieto de Castro, C. A.; Taxis, B.; Roder, H. M.; Wakeham, W. A. Thermal diffusivity measurement by the transient hot-wire technique: A reappraisal. Int. J. Thermophys. 1988, 9 (3), 293–316. (11) Product Presentation: Stabinger Viscometer. http://www. anton-paar.com/001/en/Web/Document/download/1603?clng=en (Accessed January 2010). (12) Dortmund Data Bank Software & Separation Technology. http://www.ddbst.de/ (Accessed January 2010).
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