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Critical parameters for isobutane determined by the image analysis
J. Chem. Thermodynamics 38 (2006) 1711–1716 www.elsevier.com/locate/jct
Critical parameters for isobutane determined by the image analysis G. Masui, Y. Honda, M. Uematsu
*
Center for Multiscale Mechanics and Mechanical Systems, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan Received 11 November 2005; received in revised form 2 March 2006; accepted 12 March 2006 Available online 22 March 2006
Abstract (p, q, T) Measurements and visual observations of the meniscus for isobutane were carried out carefully in the critical region over the range of temperatures: 15 mK 6 (T Tc) 6 35 mK, and of densities: 7.5 kg Æ m 3 6 (q qc) 6 7.5 kg Æ m 3 by a metal-bellows volumometer with an optical cell. Vapor pressures were also measured at T = (310, 405, 406, 407, and 407.5) K. The critical point of Tc and qc was determined by the image analysis of the critical opalescence which is proposed in this study. The critical pressure pc was determined to be the pressure measurement at the critical point. Comparisons of the critical parameters with values given in the literature are presented. 2006 Elsevier Ltd. All rights reserved. Keywords: Critical parameters; Image analysis; Isobutane; (p, q, T) Measurements; Vapor pressure
1. Introduction In previous publications [1,2] we reported measurements of thermodynamic properties of isobutane in the compressed liquid phase between the temperatures (280 and 440) K at pressures up to 200 MPa by a metal-bellows variable volumometer. In this paper, the results of (p, q, T) measurements and visual observations of the meniscus for isobutane in the critical region using an optical cell and a metal-bellows volumometer are presented. The critical parameters were determined by the image analysis of the critical opalescence. Comparisons of the critical parameters with values given in the literature are also reported. 2. Experimental 2.1. Materials The isobutane was supplied by the Takachiho Chemical Industrial Co., Ltd., Ibaragi, Japan, and its volume fraction purity was specified by the supplier to be 0.9999. *
Corresponding author. Tel.: +81 45 566 1497; fax: +81 45 566 1495. E-mail address: [email protected] (M. Uematsu).
0021-9614/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2006.03.008
The sample to be loaded was degassed five times by freeze–thaw cycling with liquid nitrogen before loading. The sample loaded in this study is supplied by the same cylinder as the previous work [1,2] used. 2.2. Apparatus and experimental procedure The measurements were carried out using an optical cell and a metal-bellows volumometer in a pressure vessel. The apparatus and experimental procedures have been described in detail in our previous publications [3,4]. A sample of known mass was loaded into the optical cell and the metal-bellows volumometer. Nitrogen gas from a pressure-measurement system was supplied to the outside of the bellows in the pressure vessel to compress or expand the bellows. The inner volume of the optical cell and the volumometer as well as its variation with the bellows displacement, temperature, and pressure were calibrated with the known density of water. The inner volume can change from 18 cm3 to 12 cm3. The sample density q was calculated from the mass of the sample loaded and the inner volume of the optical cell and the volumometer. The uncertainty in the resulting density measurements was estimated to be less than ±0.8 kg Æ m 3 at a 95% confidence level.
G. Masui et al. / J. Chem. Thermodynamics 38 (2006) 1711–1716
The optical cell and the volumometer were immersed in the thermostatted bath filled with silicon oil. The temperature that was detected at the well drilled in the body of the volumometer was measured with a 25 X platinum resistance thermometer (Chino: model R 800-2) and a thermometer bridge (Tinsley: type 5840) on the International Temperature Scale of 1990 (ITS-90) [5]. The resistance of the thermometer at the triple-point temperature of water was measured periodically. The uncertainty in the temperature measurements was estimated to be less than ±7 mK at a 95% confidence level. The pressure of the nitrogen gas was measured with an air-piston pressure gauge (Raska: model 2465-753). The pressure of the sample was obtained by subtracting the difference between the internal and external pressures of the bellows from the pressure of the nitrogen gas outside the bellows. This pressure difference was calibrated as a function of the bellows displacement, temperature, and pressure. The uncertainty in the pressure measurements was estimated to be less than ±1.6 kPa at a 95% confidence level. Through the 8 mm diameter windows, which were set on two sides of the optical cell, the meniscus at the vapor–liquid interface of the sample and its critical opalescence were observed by a CCD camera. The pictures were monitored on a display and recorded by a video tape recorder. Each window was sealed by a synthetic sapphire, whose dimensions were 12 mm in thickness and 16 mm in diameter. The height of the space where the sample was loaded in the optical cell and volumometer was designed to be as small as possible. Two windows were also set on two sides of the thermostatted oil bath. 2.3. Determination of the critical point by the image analysis In our previous publications [3,4] the critical point of fluids and fluid mixtures was visually determined using the pictures taken by the CCD camera as the state where the critical opalescence is observed the most intensely with disappearance of the vapor–liquid interface. In this study we introduced image analysis for the pictures into the determination of the critical point. The picture taken by the CCD camera was a rectangle of 320 · 240 pix. We cut a round image of 52 pix in diameter, in which the behavior of the sample was taken, from the picture. A color image was then transformed into monochromatic image for determination of relative brightness (LR) of each picture. The relative brightness at each point in the picture is determined in comparison with the scale on which black and white are assigned the values of 0 and 255, respectively. Figure 1(a) shows six pictures taken by the CCD camera for isobutane at a density of 228.0 kg Æ m 3 with increasing temperature by 10 mK from T = (407.870 to 407.920) K. Each picture was taken after the temperature and density were kept constant at least for 10 h. We can clearly distinguish the existence of the meniscus at the center of the picture at T = 407.870 K.
1
2
3
4
5
6
5
6
(a)
y / pix
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30 20 10 0 -10 -20 -30
(b)
3
2
4 1
0
50
100 LR
FIGURE 1. (a) Pictures of the critical opalescence for isobutane at q = 228.0 kg Æ m 3. 1, +, T = 407.870 K; 2, ·, T = 407.880 K; 3, s, T = 407.890 K; 4, h, T = 407.900 K; 5, n, T = 407.910 K; 6, d, T = 407.920 K. (b) Distribution of the relative brightness along the vertical axis of each picture by the image analysis.
No significant differences in darkness can be found in two pictures at T = (407.880 and 407.890) K, and the meniscus can be hardly found in these pictures. The picture at T = 407.900 K is brighter than the picture at T = 407.890 K. As temperature increases, pictures at T = (407.910 and 407.920) K become brighter. Figure 1(b) shows distribution of relative brightness (LR) along the vertical axis (y) for the pictures shown in figure 1(a) by the present image analysis. The center in the picture shown in figure 1(a) is assigned the value of 0 in figure 1(b). The distribution of relative brightness at T = 407.870 K shows minimum at the center of the picture, which corresponds to the position of the meniscus shown in figure 1(a). The distribution of relative brightness at T = 407.880 K shows also minimum at the center of the picture, though it is not much difference in relative brightness from that at T = 407.890 K. Based on the distribution of relative brightness at 407.880 K, it is clear that there is a meniscus in the picture at this temperature. The distribution of relative brightness in the picture at T = 407.890 K shows maximum, and it is different from that at T = 407.880 K. The distributions of relative brightness at T = (407.900, 407.910, and 407.920) K show also maximum, and their values of relative brightness increase with temperature, which corresponds to the variation of darkness in the pictures shown in figure 1(a). It becomes easily concluded that the meniscus disappears between T = (407.880 and 407.890) K. On the basis of these results, it may be concluded that the critical point of fluids and fluid mixtures can be determined by the present image analysis. The critical point can be determined as the state where the relative brightness (LR) is the smallest and its distribution along the vertical axis (y) shows no position dependence. Critical pressure pc can be determined to be the pressure measurement at the critical point of Tc and qc.
G. Masui et al. / J. Chem. Thermodynamics 38 (2006) 1711–1716
3. Results and discussion We measured the vapor pressures of isobutane at T = (310.000, 405.000, 406.000, 407.000, and 407.500) K with different positions of the meniscus to confirm no impurity effect. The results are given in table 1. The mean values of these measurements are 489.3 kPa at T = 310.000 K, 3468.7 kPa at T = 405.000 K, 3526.9 kPa at TABLE 1 Experimental results of the vapor pressure ps of isobutane at T (ITS-90) T/K
q/(kg Æ m 3)a
ps/kPa
310.000 310.000 310.000 310.000 310.000 310.000 405.000 405.000 405.000 405.000 405.000 405.000 405.000 406.000 406.000 406.000 406.000 406.000 406.000 407.000 407.000 407.000 407.000 407.000 407.000 407.000 407.000 407.000 407.500 407.500 407.500 407.500 407.500 407.500 407.500 407.500 407.500
190.5 202.9 217.0 233.4 252.0 274.2 220.0 227.5 227.6 227.6 239.9 249.9 250.0 220.0 224.1 227.4 227.5 239.9 249.9 201.9 210.3 215.6 220.0 227.4 231.8 239.6 249.7 250.4 220.0 220.3 227.3 227.5 239.9 240.0 249.9 250.1 250.1
488.7 489.6 489.7 489.4 489.0 489.5 3468.3 3468.3 3468.4 3468.9 3468.6 3468.8 3469.3 3526.7 3526.6 3526.8 3527.2 3527.1 3527.0 3584.8 3585.2 3585.3 3585.5 3586.0 3585.2 3586.4 3585.9 3585.2 3618.6 3618.9 3618.9 3618.8 3619.0 3618.9 3619.1 3619.1 3619.5
a Densities are mean values of the mixture of liquid and its coexisting vapor.
TABLE 2 Comparison of the vapor pressure measurements for isobutane T/K
ps/kPa This work
310.000 405.000 406.000 407.000 a
a
489.3 3468.7a 3526.9a 3585.5a
e/kPab Miyamoto et al. [1] 488.4 3466.2 3524.7 3584.3
488.6
488.2
0.9 2.5 2.2 1.2
0.7
1.1
Mean value of the present measurements given in table 1. Pressure deviation of the experimental data by Miyamoto et al. [1] from mean values of the present measurements given in table 1. b
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T = 406.000 K, 3585.5 kPa at T = 407.000 K, and 3619.0 kPa at T = 407.500 K. The largest standard deviation of the present measurements from the mean values is TABLE 3 Experimental results for the (p, q, T) properties of isobutane in the onephase region at T (ITS-90) and q T/K
q/(kg Æ m 3)
p/kPa
405.000 405.000 405.000 405.000 405.000 405.000 406.000 406.000 406.000 407.000 407.000 407.500 407.500 407.500 407.500 407.890 407.890 407.890 407.890 407.890 407.890 407.890 407.890 407.890 408.000 408.000 408.000 408.000 408.000 408.000 408.000 408.000 408.000 408.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 410.000 410.000 410.000 410.000 410.000 410.000 410.000 410.000 410.000 410.000 410.000 410.000
185.0 199.9 200.0 200.0 200.0 264.9 184.9 199.9 264.9 185.4 200.3 185.0 199.9 200.4 265.0 184.9 200.1 240.0 241.4 250.0 250.2 250.5 263.7 264.9 184.1 184.9 200.0 200.4 220.0 220.1 227.5 240.0 249.9 265.5 184.7 184.9 200.0 200.4 219.8 219.9 220.4 224.2 227.4 239.9 250.0 250.4 265.0 185.0 200.0 200.0 210.0 220.0 227.4 228.1 240.0 250.0 250.4 265.0 265.2
3464.7 3467.3 3467.3 3468.4 3468.0 3469.9 3523.7 3525.7 3528.1 3582.1 3585.0 3613.8 3617.5 3617.7 3620.6 3632.3 3637.6 3640.5 3640.9 3640.6 3640.8 3641.3 3644.5 3644.6 3635.8 3638.1 3643.7 3644.2 3645.6 3646.8 3646.4 3646.6 3647.4 3652.4 3692.1 3692.8 3702.2 3702.8 3708.3 3708.5 3708.9 3709.7 3710.5 3713.6 3717.7 3718.4 3729.0 3745.3 3757.5 3758.2 3764.3 3769.4 3772.2 3772.5 3779.4 3785.9 3786.3 3802.3 3802.8
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G. Masui et al. / J. Chem. Thermodynamics 38 (2006) 1711–1716
0.47 kPa being smaller than the uncertainty in the present pressure measurements of ±1.6 kPa. Comparison of mean values of the present measurements with the experimental data by Miyamoto et al. [1] is given in table 2. The present ρ /(kg•m-3)
220.0
221.0
222.0
223.0
224.0
225.0
226.0
values are in good agreement with the data by Miyamoto et al. within the sum of both uncertainties of 2.7 kPa. (p, q, T) Measurements are also carried out in the one-phase region at T = (405 to 410) K and densities from (185 to
227.0
228.0
229.0
230.0
231.0
232.0
233.0
234.0
235.0
p / kPa
T /K
407.920 3640.0
3639.8
3640.3
3640.1
3640.3
3639.6
3640.9
3 6 40 .8
3640.6
3640.7
3640.7
3640.7
3639.7
3639.7
3639.6
3640.3
3639.6
3639.9
3640.0
3640.2
3640.0
3639.8
3640.5
3640.1
3639.3
3639.4
3639.8
3639.7
3639.9
3639.9
3639.8
3640.0
3638.5
3639.1
3639.5
3639.4
3640.2
3639.6
3638.7
3639.8
3639.9
3639.4
3637.8
3638.3* 3639.0* 3639.1* 3638.9* 3639.3* 3638.4
3639.2
3639.1
3639.3
3637.3
3637.9* 3637.9* 3638.3* 3638.2* 3638.4* 3638.0* 3638.4* 3638.7
3638.5
407.910 3640.0
3640.2
3639.8
3640.1
407.900 3640.4
407.890
407.880
407.870
FIGURE 2. Experimental results for the (p, q, T) properties and pictures of the critical opalescence for isobutane at T = (407.870 to 407.920) K and at q = (220.0 to 235.0) kg Æ m 3. , pictures observed with meniscus.
ρ /(kg•m-3) •
100 L 200 R
100 L 200 R
0
100 L 200 R
0
0
100 L 200 R
0
y / pix
y / pix y / pix
y / pix 0
100 L 200 R
0
100 L 200 R
0
100 L 200 R
0
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30 0
0
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
100 L 200 R
y / pix
y / pix
y / pix
0
y / pix
y / pix
0
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
y / pix
100 L 200 R
0
0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
y / pix 0
y / pix 0
30 20 10 0 -10 -20 -30
0
y / pix 0
235.0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
0
y / pix
y / pix 0
30 20 10 0 -10 -20 -30
100 L 200 R
100 L 200 R
0
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
230.0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
y / pix
y / pix
0
y / pix 0
0
y / pix
y / pix
0
100 L 200 R
30 20 10 0 -10 -20 -30
y / pix
y / pix y / pix
y / pix
y / pix
0
229.0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
y / pix 0
y / pix 0
0
y / pix 0
30 20 10 0 -10 -20 -30
100 L 200 R
0
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
228.0
y / pix
0 30 20 10 0 -10 -20 -30
0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
y / pix
y / pix y / pix
0
y / pix
y / pix
0
y / pix 0
0
30 20 10 0 -10 -20 -30
100 L 200 R
227.0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
0
y / pix 0
y / pix
y / pix
y / pix y / pix
0
407.870
0
100 L 200 R
30 20 10 0 -10 -20 -30
226.0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30 0
407.880
100 L 200 R
30 20 10 0 -10 -20 -30 0
407.890
0 30 20 10 0 -10 -20 -30
y / pix
y / pix
0
407.900
100 L 200 R
30 20 10 0 -10 -20 -30
y / pix
y / pix
0
407.910
225.0 30 20 10 0 -10 -20 -30
y / pix
30 20 10 0 -10 -20 -30
y / pix
407.920
y / pix
220.0
y / pix
T /K
100 L 200 R
30 20 10 0 -10 -20 -30 0
FIGURE 3. Distribution of the relative brightness along the vertical axis of pictures shown in figure 2 by the image analysis.
100 L 200 R
G. Masui et al. / J. Chem. Thermodynamics 38 (2006) 1711–1716
265) kg Æ m 3. These measurements cover the pressure range from (3464.7 to 3802.8) kPa. The results are given in table 3. Measurements of the (p, q, T) properties and observations of the critical opalescence for isobutane in the critical region have been carried out at six temperatures from (407.870 to 407.920) K and 16 densities from (220.0 to 235.0) kg Æ m 3. These measurements cover the pressure range from (3637.3 to 3640.7) kPa. The (p, q, T) measurements and pictures are shown in figure 2. Figure 3 shows the distribution of relative brightness of the pictures shown in figure 2 along the vertical axis at six temperatures as a function of density by the present image analysis. Based on the examination of these figures, we added measurements and observations at five states of temperatures and densities to determine the critical point. The results are shown in figure 4. Based on these results, the critical point has been determined to be the state at Tc = (407.885 ± 0.012) K and qc = (227.5 ± 1.3) kg Æ m 3. The critical pressure is determined to be pc = (3639.0 ± 1.6) kPa from the pressure measurement at the critical point. ρ / (kg m-3)
227.0
.
1715
Daubert [6] reviewed in 1996 on the critical parameters for isobutane, and proposed the recommended values; Tc = (407.8 ± 0.5) K, qc = (224 ± 3) kg Æ m 3, and pc = (3640 ± 50) kPa. Our Tc is larger than the recommended value by 0.085 K, our qc is larger than the recommended value by 3.5 kg Æ m 3, and our pc is smaller than the recommended value by 1 kPa. Our critical parameters are compared with values given in the literature [7–10] as shown in table 4. Two papers in the literature except three early works before 1940 [6], in which the critical point was visually determined, are found, i.e., by Connolly in 1962 [8] and by Levelt Sengers et al. in 1983 [10]. Tc measured by Connolly is smaller than our Tc by 735 mK, while Tc by Levelt Sengers et al. agrees with our Tc with the difference of 75 mK. Tc by Beattie et al. [7] is larger than our Tc by 225 mK, and that by Goodwin and Haynes [9] is smaller by 65 mK. qc of Beattie et al., Goodwin and Haynes, and Levelt Sengers et al. are smaller than our qc by (6.5, 3.14, and 2) kg Æ m 3 (2.9%, 1.4%, and 0.9%), respectively. pc of Levelt Sengers et al. is smaller than our pc by 10 kPa (0.27%), whereas that of Beattie et al., that of Connolly, 227.5
228.0
y / pix 10
20
0
10
20
407.880
40
LR
0
3639.1*
10
20
LR
0
10
20
3639.5
30
40
30 20 10 0 -1 0 -2 0 -3 0
0
10
20
3639.0 y / pix
y / pix
3639.0 30 20 10 0 -1 0 -2 0 -3 0
30
y / pix
y / pix
407.885
30 20 10 0 -1 0 -2 0 -3 0
LR
30
40
30 20 10 0 -1 0 -2 0 -3 0
LR
30
40
LR
0
10
3638.9*
20
LR
30 20 10 0 -1 0 -2 0 -3 0
0
10
20
10
20
10
20
3640.2 y / pix
0
3639.4
30 20 10 0 -1 0 -2 0 -3 0
30
40
30 20 10 0 -1 0 -2 0 -3 0
0
3639.3 y / pix
y / pix
407.890
30 20 10 0 -1 0 -2 0 -3 0
y / pix
p / kPa
T /K
30
40
30 20 10 0 -1 0 -2 0 -3 0
0
3638.9*
LR
LR
LR
30
40
30
40
30
40
FIGURE 4. (p, q, T) Measurements, pictures of the critical opalescence and distribution of the relative brightness along the vertical axis of each picture in the vicinity of the critical point for isobutane at T = (407.880, 407.885, and 407.890) K and at q = (227.0, 227.5, and 228.0) kg Æ m 3. , pictures observed with meniscus. TABLE 4 Comparison of the critical parameters for isobutane First author
Year
Tc/Ka
qc/(kg Æ m 3)
pc/kPa
Methodb
Reference
Beattie Connolly Goodwin Levelt Sengers This work
1949 1962 1982 1983
408.11 407.15 407.82 407.81 407.885
221
3647 3700 3640 3629 3639.0
2 1 2 1 1
[7] [8] [9] [10]
a b
224.36 225.5 227.5
Temperatures on ITS-90. Determination of the critical temperature, 1: meniscus observation, 2: PVT properties.
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G. Masui et al. / J. Chem. Thermodynamics 38 (2006) 1711–1716
and that of Goodwin and Haynes are larger than our pc by (8, 61, and 1) kPa (0.22%, 1.68%, and 0.03%), respectively. References [1] H. Miyamoto, J. Takemura, M. Uematsu, J. Chem. Thermodyn. 36 (2004) 919–923. [2] H. Miyamoto, M. Uematsu, J. Chem. Thermodyn. 38 (2006) 360–366. [3] Y. Suehiro, M. Nakajima, K. Yamada, M. Uematsu, J. Chem. Thermodyn. 28 (1996) 1153–1164.
[4] M. Sato, G. Masui, M. Uematsu, J. Chem. Thermodyn. 37 (2005) 931–934. [5] H. Preston-Thomas, Metrologia 27 (1990) 3–10. [6] T.E. Daubert, J. Chem. Eng. Data 41 (1996) 365–372. [7] J.A. Beattie, D.G. Edwards, S. Marple, J. Chem. Phys. 17 (1949) 576–577. [8] J.F. Connolly, J. Phys. Chem. 66 (1962) 1082–1086. [9] R.D. Goodwin, W.M. Haynes, NBS Technical Note 1051 (1982). [10] J.M.H. Levelt Sengers, B. Kamgar-Parsi, J.V. Sengers, J. Chem. Eng. Data 28 (1983) 354–362.
JCT 05-282
Critical parameters for isobutane determined by the image analysis G. Masui, Y. Honda, M. Uematsu
*
Center for Multiscale Mechanics and Mechanical Systems, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan Received 11 November 2005; received in revised form 2 March 2006; accepted 12 March 2006 Available online 22 March 2006
Abstract (p, q, T) Measurements and visual observations of the meniscus for isobutane were carried out carefully in the critical region over the range of temperatures: 15 mK 6 (T Tc) 6 35 mK, and of densities: 7.5 kg Æ m 3 6 (q qc) 6 7.5 kg Æ m 3 by a metal-bellows volumometer with an optical cell. Vapor pressures were also measured at T = (310, 405, 406, 407, and 407.5) K. The critical point of Tc and qc was determined by the image analysis of the critical opalescence which is proposed in this study. The critical pressure pc was determined to be the pressure measurement at the critical point. Comparisons of the critical parameters with values given in the literature are presented. 2006 Elsevier Ltd. All rights reserved. Keywords: Critical parameters; Image analysis; Isobutane; (p, q, T) Measurements; Vapor pressure
1. Introduction In previous publications [1,2] we reported measurements of thermodynamic properties of isobutane in the compressed liquid phase between the temperatures (280 and 440) K at pressures up to 200 MPa by a metal-bellows variable volumometer. In this paper, the results of (p, q, T) measurements and visual observations of the meniscus for isobutane in the critical region using an optical cell and a metal-bellows volumometer are presented. The critical parameters were determined by the image analysis of the critical opalescence. Comparisons of the critical parameters with values given in the literature are also reported. 2. Experimental 2.1. Materials The isobutane was supplied by the Takachiho Chemical Industrial Co., Ltd., Ibaragi, Japan, and its volume fraction purity was specified by the supplier to be 0.9999. *
Corresponding author. Tel.: +81 45 566 1497; fax: +81 45 566 1495. E-mail address: [email protected] (M. Uematsu).
0021-9614/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2006.03.008
The sample to be loaded was degassed five times by freeze–thaw cycling with liquid nitrogen before loading. The sample loaded in this study is supplied by the same cylinder as the previous work [1,2] used. 2.2. Apparatus and experimental procedure The measurements were carried out using an optical cell and a metal-bellows volumometer in a pressure vessel. The apparatus and experimental procedures have been described in detail in our previous publications [3,4]. A sample of known mass was loaded into the optical cell and the metal-bellows volumometer. Nitrogen gas from a pressure-measurement system was supplied to the outside of the bellows in the pressure vessel to compress or expand the bellows. The inner volume of the optical cell and the volumometer as well as its variation with the bellows displacement, temperature, and pressure were calibrated with the known density of water. The inner volume can change from 18 cm3 to 12 cm3. The sample density q was calculated from the mass of the sample loaded and the inner volume of the optical cell and the volumometer. The uncertainty in the resulting density measurements was estimated to be less than ±0.8 kg Æ m 3 at a 95% confidence level.
G. Masui et al. / J. Chem. Thermodynamics 38 (2006) 1711–1716
The optical cell and the volumometer were immersed in the thermostatted bath filled with silicon oil. The temperature that was detected at the well drilled in the body of the volumometer was measured with a 25 X platinum resistance thermometer (Chino: model R 800-2) and a thermometer bridge (Tinsley: type 5840) on the International Temperature Scale of 1990 (ITS-90) [5]. The resistance of the thermometer at the triple-point temperature of water was measured periodically. The uncertainty in the temperature measurements was estimated to be less than ±7 mK at a 95% confidence level. The pressure of the nitrogen gas was measured with an air-piston pressure gauge (Raska: model 2465-753). The pressure of the sample was obtained by subtracting the difference between the internal and external pressures of the bellows from the pressure of the nitrogen gas outside the bellows. This pressure difference was calibrated as a function of the bellows displacement, temperature, and pressure. The uncertainty in the pressure measurements was estimated to be less than ±1.6 kPa at a 95% confidence level. Through the 8 mm diameter windows, which were set on two sides of the optical cell, the meniscus at the vapor–liquid interface of the sample and its critical opalescence were observed by a CCD camera. The pictures were monitored on a display and recorded by a video tape recorder. Each window was sealed by a synthetic sapphire, whose dimensions were 12 mm in thickness and 16 mm in diameter. The height of the space where the sample was loaded in the optical cell and volumometer was designed to be as small as possible. Two windows were also set on two sides of the thermostatted oil bath. 2.3. Determination of the critical point by the image analysis In our previous publications [3,4] the critical point of fluids and fluid mixtures was visually determined using the pictures taken by the CCD camera as the state where the critical opalescence is observed the most intensely with disappearance of the vapor–liquid interface. In this study we introduced image analysis for the pictures into the determination of the critical point. The picture taken by the CCD camera was a rectangle of 320 · 240 pix. We cut a round image of 52 pix in diameter, in which the behavior of the sample was taken, from the picture. A color image was then transformed into monochromatic image for determination of relative brightness (LR) of each picture. The relative brightness at each point in the picture is determined in comparison with the scale on which black and white are assigned the values of 0 and 255, respectively. Figure 1(a) shows six pictures taken by the CCD camera for isobutane at a density of 228.0 kg Æ m 3 with increasing temperature by 10 mK from T = (407.870 to 407.920) K. Each picture was taken after the temperature and density were kept constant at least for 10 h. We can clearly distinguish the existence of the meniscus at the center of the picture at T = 407.870 K.
1
2
3
4
5
6
5
6
(a)
y / pix
1712
30 20 10 0 -10 -20 -30
(b)
3
2
4 1
0
50
100 LR
FIGURE 1. (a) Pictures of the critical opalescence for isobutane at q = 228.0 kg Æ m 3. 1, +, T = 407.870 K; 2, ·, T = 407.880 K; 3, s, T = 407.890 K; 4, h, T = 407.900 K; 5, n, T = 407.910 K; 6, d, T = 407.920 K. (b) Distribution of the relative brightness along the vertical axis of each picture by the image analysis.
No significant differences in darkness can be found in two pictures at T = (407.880 and 407.890) K, and the meniscus can be hardly found in these pictures. The picture at T = 407.900 K is brighter than the picture at T = 407.890 K. As temperature increases, pictures at T = (407.910 and 407.920) K become brighter. Figure 1(b) shows distribution of relative brightness (LR) along the vertical axis (y) for the pictures shown in figure 1(a) by the present image analysis. The center in the picture shown in figure 1(a) is assigned the value of 0 in figure 1(b). The distribution of relative brightness at T = 407.870 K shows minimum at the center of the picture, which corresponds to the position of the meniscus shown in figure 1(a). The distribution of relative brightness at T = 407.880 K shows also minimum at the center of the picture, though it is not much difference in relative brightness from that at T = 407.890 K. Based on the distribution of relative brightness at 407.880 K, it is clear that there is a meniscus in the picture at this temperature. The distribution of relative brightness in the picture at T = 407.890 K shows maximum, and it is different from that at T = 407.880 K. The distributions of relative brightness at T = (407.900, 407.910, and 407.920) K show also maximum, and their values of relative brightness increase with temperature, which corresponds to the variation of darkness in the pictures shown in figure 1(a). It becomes easily concluded that the meniscus disappears between T = (407.880 and 407.890) K. On the basis of these results, it may be concluded that the critical point of fluids and fluid mixtures can be determined by the present image analysis. The critical point can be determined as the state where the relative brightness (LR) is the smallest and its distribution along the vertical axis (y) shows no position dependence. Critical pressure pc can be determined to be the pressure measurement at the critical point of Tc and qc.
G. Masui et al. / J. Chem. Thermodynamics 38 (2006) 1711–1716
3. Results and discussion We measured the vapor pressures of isobutane at T = (310.000, 405.000, 406.000, 407.000, and 407.500) K with different positions of the meniscus to confirm no impurity effect. The results are given in table 1. The mean values of these measurements are 489.3 kPa at T = 310.000 K, 3468.7 kPa at T = 405.000 K, 3526.9 kPa at TABLE 1 Experimental results of the vapor pressure ps of isobutane at T (ITS-90) T/K
q/(kg Æ m 3)a
ps/kPa
310.000 310.000 310.000 310.000 310.000 310.000 405.000 405.000 405.000 405.000 405.000 405.000 405.000 406.000 406.000 406.000 406.000 406.000 406.000 407.000 407.000 407.000 407.000 407.000 407.000 407.000 407.000 407.000 407.500 407.500 407.500 407.500 407.500 407.500 407.500 407.500 407.500
190.5 202.9 217.0 233.4 252.0 274.2 220.0 227.5 227.6 227.6 239.9 249.9 250.0 220.0 224.1 227.4 227.5 239.9 249.9 201.9 210.3 215.6 220.0 227.4 231.8 239.6 249.7 250.4 220.0 220.3 227.3 227.5 239.9 240.0 249.9 250.1 250.1
488.7 489.6 489.7 489.4 489.0 489.5 3468.3 3468.3 3468.4 3468.9 3468.6 3468.8 3469.3 3526.7 3526.6 3526.8 3527.2 3527.1 3527.0 3584.8 3585.2 3585.3 3585.5 3586.0 3585.2 3586.4 3585.9 3585.2 3618.6 3618.9 3618.9 3618.8 3619.0 3618.9 3619.1 3619.1 3619.5
a Densities are mean values of the mixture of liquid and its coexisting vapor.
TABLE 2 Comparison of the vapor pressure measurements for isobutane T/K
ps/kPa This work
310.000 405.000 406.000 407.000 a
a
489.3 3468.7a 3526.9a 3585.5a
e/kPab Miyamoto et al. [1] 488.4 3466.2 3524.7 3584.3
488.6
488.2
0.9 2.5 2.2 1.2
0.7
1.1
Mean value of the present measurements given in table 1. Pressure deviation of the experimental data by Miyamoto et al. [1] from mean values of the present measurements given in table 1. b
1713
T = 406.000 K, 3585.5 kPa at T = 407.000 K, and 3619.0 kPa at T = 407.500 K. The largest standard deviation of the present measurements from the mean values is TABLE 3 Experimental results for the (p, q, T) properties of isobutane in the onephase region at T (ITS-90) and q T/K
q/(kg Æ m 3)
p/kPa
405.000 405.000 405.000 405.000 405.000 405.000 406.000 406.000 406.000 407.000 407.000 407.500 407.500 407.500 407.500 407.890 407.890 407.890 407.890 407.890 407.890 407.890 407.890 407.890 408.000 408.000 408.000 408.000 408.000 408.000 408.000 408.000 408.000 408.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 409.000 410.000 410.000 410.000 410.000 410.000 410.000 410.000 410.000 410.000 410.000 410.000 410.000
185.0 199.9 200.0 200.0 200.0 264.9 184.9 199.9 264.9 185.4 200.3 185.0 199.9 200.4 265.0 184.9 200.1 240.0 241.4 250.0 250.2 250.5 263.7 264.9 184.1 184.9 200.0 200.4 220.0 220.1 227.5 240.0 249.9 265.5 184.7 184.9 200.0 200.4 219.8 219.9 220.4 224.2 227.4 239.9 250.0 250.4 265.0 185.0 200.0 200.0 210.0 220.0 227.4 228.1 240.0 250.0 250.4 265.0 265.2
3464.7 3467.3 3467.3 3468.4 3468.0 3469.9 3523.7 3525.7 3528.1 3582.1 3585.0 3613.8 3617.5 3617.7 3620.6 3632.3 3637.6 3640.5 3640.9 3640.6 3640.8 3641.3 3644.5 3644.6 3635.8 3638.1 3643.7 3644.2 3645.6 3646.8 3646.4 3646.6 3647.4 3652.4 3692.1 3692.8 3702.2 3702.8 3708.3 3708.5 3708.9 3709.7 3710.5 3713.6 3717.7 3718.4 3729.0 3745.3 3757.5 3758.2 3764.3 3769.4 3772.2 3772.5 3779.4 3785.9 3786.3 3802.3 3802.8
1714
G. Masui et al. / J. Chem. Thermodynamics 38 (2006) 1711–1716
0.47 kPa being smaller than the uncertainty in the present pressure measurements of ±1.6 kPa. Comparison of mean values of the present measurements with the experimental data by Miyamoto et al. [1] is given in table 2. The present ρ /(kg•m-3)
220.0
221.0
222.0
223.0
224.0
225.0
226.0
values are in good agreement with the data by Miyamoto et al. within the sum of both uncertainties of 2.7 kPa. (p, q, T) Measurements are also carried out in the one-phase region at T = (405 to 410) K and densities from (185 to
227.0
228.0
229.0
230.0
231.0
232.0
233.0
234.0
235.0
p / kPa
T /K
407.920 3640.0
3639.8
3640.3
3640.1
3640.3
3639.6
3640.9
3 6 40 .8
3640.6
3640.7
3640.7
3640.7
3639.7
3639.7
3639.6
3640.3
3639.6
3639.9
3640.0
3640.2
3640.0
3639.8
3640.5
3640.1
3639.3
3639.4
3639.8
3639.7
3639.9
3639.9
3639.8
3640.0
3638.5
3639.1
3639.5
3639.4
3640.2
3639.6
3638.7
3639.8
3639.9
3639.4
3637.8
3638.3* 3639.0* 3639.1* 3638.9* 3639.3* 3638.4
3639.2
3639.1
3639.3
3637.3
3637.9* 3637.9* 3638.3* 3638.2* 3638.4* 3638.0* 3638.4* 3638.7
3638.5
407.910 3640.0
3640.2
3639.8
3640.1
407.900 3640.4
407.890
407.880
407.870
FIGURE 2. Experimental results for the (p, q, T) properties and pictures of the critical opalescence for isobutane at T = (407.870 to 407.920) K and at q = (220.0 to 235.0) kg Æ m 3. , pictures observed with meniscus.
ρ /(kg•m-3) •
100 L 200 R
100 L 200 R
0
100 L 200 R
0
0
100 L 200 R
0
y / pix
y / pix y / pix
y / pix 0
100 L 200 R
0
100 L 200 R
0
100 L 200 R
0
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30 0
0
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
100 L 200 R
y / pix
y / pix
y / pix
0
y / pix
y / pix
0
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
y / pix
100 L 200 R
0
0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
y / pix 0
y / pix 0
30 20 10 0 -10 -20 -30
0
y / pix 0
235.0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
0
y / pix
y / pix 0
30 20 10 0 -10 -20 -30
100 L 200 R
100 L 200 R
0
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
230.0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
y / pix
y / pix
0
y / pix 0
0
y / pix
y / pix
0
100 L 200 R
30 20 10 0 -10 -20 -30
y / pix
y / pix y / pix
y / pix
y / pix
0
229.0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
y / pix 0
y / pix 0
0
y / pix 0
30 20 10 0 -10 -20 -30
100 L 200 R
0
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
228.0
y / pix
0 30 20 10 0 -10 -20 -30
0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
y / pix
y / pix y / pix
0
y / pix
y / pix
0
y / pix 0
0
30 20 10 0 -10 -20 -30
100 L 200 R
227.0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
0
y / pix 0
y / pix
y / pix
y / pix y / pix
0
407.870
0
100 L 200 R
30 20 10 0 -10 -20 -30
226.0 30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30
100 L 200 R
30 20 10 0 -10 -20 -30 0
407.880
100 L 200 R
30 20 10 0 -10 -20 -30 0
407.890
0 30 20 10 0 -10 -20 -30
y / pix
y / pix
0
407.900
100 L 200 R
30 20 10 0 -10 -20 -30
y / pix
y / pix
0
407.910
225.0 30 20 10 0 -10 -20 -30
y / pix
30 20 10 0 -10 -20 -30
y / pix
407.920
y / pix
220.0
y / pix
T /K
100 L 200 R
30 20 10 0 -10 -20 -30 0
FIGURE 3. Distribution of the relative brightness along the vertical axis of pictures shown in figure 2 by the image analysis.
100 L 200 R
G. Masui et al. / J. Chem. Thermodynamics 38 (2006) 1711–1716
265) kg Æ m 3. These measurements cover the pressure range from (3464.7 to 3802.8) kPa. The results are given in table 3. Measurements of the (p, q, T) properties and observations of the critical opalescence for isobutane in the critical region have been carried out at six temperatures from (407.870 to 407.920) K and 16 densities from (220.0 to 235.0) kg Æ m 3. These measurements cover the pressure range from (3637.3 to 3640.7) kPa. The (p, q, T) measurements and pictures are shown in figure 2. Figure 3 shows the distribution of relative brightness of the pictures shown in figure 2 along the vertical axis at six temperatures as a function of density by the present image analysis. Based on the examination of these figures, we added measurements and observations at five states of temperatures and densities to determine the critical point. The results are shown in figure 4. Based on these results, the critical point has been determined to be the state at Tc = (407.885 ± 0.012) K and qc = (227.5 ± 1.3) kg Æ m 3. The critical pressure is determined to be pc = (3639.0 ± 1.6) kPa from the pressure measurement at the critical point. ρ / (kg m-3)
227.0
.
1715
Daubert [6] reviewed in 1996 on the critical parameters for isobutane, and proposed the recommended values; Tc = (407.8 ± 0.5) K, qc = (224 ± 3) kg Æ m 3, and pc = (3640 ± 50) kPa. Our Tc is larger than the recommended value by 0.085 K, our qc is larger than the recommended value by 3.5 kg Æ m 3, and our pc is smaller than the recommended value by 1 kPa. Our critical parameters are compared with values given in the literature [7–10] as shown in table 4. Two papers in the literature except three early works before 1940 [6], in which the critical point was visually determined, are found, i.e., by Connolly in 1962 [8] and by Levelt Sengers et al. in 1983 [10]. Tc measured by Connolly is smaller than our Tc by 735 mK, while Tc by Levelt Sengers et al. agrees with our Tc with the difference of 75 mK. Tc by Beattie et al. [7] is larger than our Tc by 225 mK, and that by Goodwin and Haynes [9] is smaller by 65 mK. qc of Beattie et al., Goodwin and Haynes, and Levelt Sengers et al. are smaller than our qc by (6.5, 3.14, and 2) kg Æ m 3 (2.9%, 1.4%, and 0.9%), respectively. pc of Levelt Sengers et al. is smaller than our pc by 10 kPa (0.27%), whereas that of Beattie et al., that of Connolly, 227.5
228.0
y / pix 10
20
0
10
20
407.880
40
LR
0
3639.1*
10
20
LR
0
10
20
3639.5
30
40
30 20 10 0 -1 0 -2 0 -3 0
0
10
20
3639.0 y / pix
y / pix
3639.0 30 20 10 0 -1 0 -2 0 -3 0
30
y / pix
y / pix
407.885
30 20 10 0 -1 0 -2 0 -3 0
LR
30
40
30 20 10 0 -1 0 -2 0 -3 0
LR
30
40
LR
0
10
3638.9*
20
LR
30 20 10 0 -1 0 -2 0 -3 0
0
10
20
10
20
10
20
3640.2 y / pix
0
3639.4
30 20 10 0 -1 0 -2 0 -3 0
30
40
30 20 10 0 -1 0 -2 0 -3 0
0
3639.3 y / pix
y / pix
407.890
30 20 10 0 -1 0 -2 0 -3 0
y / pix
p / kPa
T /K
30
40
30 20 10 0 -1 0 -2 0 -3 0
0
3638.9*
LR
LR
LR
30
40
30
40
30
40
FIGURE 4. (p, q, T) Measurements, pictures of the critical opalescence and distribution of the relative brightness along the vertical axis of each picture in the vicinity of the critical point for isobutane at T = (407.880, 407.885, and 407.890) K and at q = (227.0, 227.5, and 228.0) kg Æ m 3. , pictures observed with meniscus. TABLE 4 Comparison of the critical parameters for isobutane First author
Year
Tc/Ka
qc/(kg Æ m 3)
pc/kPa
Methodb
Reference
Beattie Connolly Goodwin Levelt Sengers This work
1949 1962 1982 1983
408.11 407.15 407.82 407.81 407.885
221
3647 3700 3640 3629 3639.0
2 1 2 1 1
[7] [8] [9] [10]
a b
224.36 225.5 227.5
Temperatures on ITS-90. Determination of the critical temperature, 1: meniscus observation, 2: PVT properties.
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G. Masui et al. / J. Chem. Thermodynamics 38 (2006) 1711–1716
and that of Goodwin and Haynes are larger than our pc by (8, 61, and 1) kPa (0.22%, 1.68%, and 0.03%), respectively. References [1] H. Miyamoto, J. Takemura, M. Uematsu, J. Chem. Thermodyn. 36 (2004) 919–923. [2] H. Miyamoto, M. Uematsu, J. Chem. Thermodyn. 38 (2006) 360–366. [3] Y. Suehiro, M. Nakajima, K. Yamada, M. Uematsu, J. Chem. Thermodyn. 28 (1996) 1153–1164.
[4] M. Sato, G. Masui, M. Uematsu, J. Chem. Thermodyn. 37 (2005) 931–934. [5] H. Preston-Thomas, Metrologia 27 (1990) 3–10. [6] T.E. Daubert, J. Chem. Eng. Data 41 (1996) 365–372. [7] J.A. Beattie, D.G. Edwards, S. Marple, J. Chem. Phys. 17 (1949) 576–577. [8] J.F. Connolly, J. Phys. Chem. 66 (1962) 1082–1086. [9] R.D. Goodwin, W.M. Haynes, NBS Technical Note 1051 (1982). [10] J.M.H. Levelt Sengers, B. Kamgar-Parsi, J.V. Sengers, J. Chem. Eng. Data 28 (1983) 354–362.
JCT 05-282