Thermodynamics/chemistry (Vapor and Liquid Phase Equilibra)
Abstract
This report is prepared to present the Pxy calculations and plots generated for the given binary system - ethane and pentane, and showcase the various equations, models, assumptions exercised. The primary results if the table and plot of Pxy for the binary system, while discussion of a comparison with experimental results and drawing conclusion on the efficacy of the used software MixProps is discussed and evaluated. Additionally,the knowledge of the phase equilibria of mixtures is important for numerous industrial applications. Soa chemical engineer should be capable to optimize,trouble shoot and to be well acquainted with the all numerical method, models and equations. Therefore, this technique is expected to provide significant skills about how to deal with real thermodynamic problems often take place in the industry.
Thermodynamics/Chemistry (Vapor and Liquid Phase Equilibra)
Introduction
Understanding the physical nature of the glassy state of matter, as well as the transition which separates it from the liquid, still presents a challenge to materials science. According to the thermodynamic viewpoint, the laboratory glass transition can be interpreted as the kinetically-controlled manifestation of an underlying phase transition associated with the vanishing of the con?gurational entropy of the supercooled liquid as temperature decreases. From this perspective, the existence of a limiting density, below which homogeneous inherent structures, and hence homogeneous glasses no longer exist, is particularly interesting, and may lead to a more fundamental understanding of the glass transition in general
Model and methods
The bubble point calculation for a given temperature is pressure variation as the composition of the liquid binary mixture is varied, whereas the dew point calculation is the pressure variation as the vapor composition is varied.
The liquid and vapor mixture mainly characterized by equation of state used for the vapor and liquid phase, the equation of state used, is SRK, which is described below and explained in all terms and parameters. The mixing rules are incorporated through the interaction coefficients of the binary species as given for the equation of state. The assumptions are the binary mixture follows Raoult's law for ideal vapor and liquid mixture, and is modified by use of the mentioned equation of state.
Soave Modification of the Redlich-Kwong Equation of State {}:
Peng-Robinson Equation of State {}:
Results and Discussion
Table 1
T=40 F, EoS = SRK, Pbubble
Table 2
T=40 F, EoS = SRK, Pdew
Xethane
Yethane
Pbubble
Xethane
Yethane
Pdew
0
0
4.276
0
0
4.276
0.1
0.8808118
35.241
1.563936E-03
0.1
4.751
0.2
0.9393287
67.359
3.516286E-03
0.2
5.346
0.3
0.960835
100.710
6.022254E-03
0.3
6.109
0.4
0.9721882
135.382
9.356195E-03
0.4
7.126
0.5
0.9793686
171.475
1.400958E-02
0.5
8.547
0.6
0.9844864
209.124
2.095872E-02
0.6
10.674
0.7
0.9885092
248.545
3.245785E-02
0.7
14.204
0.8
0.9920053
290.204
5.514459E-02
0.8
21.213
0.9
0.995481
335.443
0.1206913
0.9
41.789
1.0
1.0
389.861
1.0
1.0
389.858
Table 3
T=100 F, EoS = SRK, Pbubble
Table 4
T=100 F, EoS = SRK, Pdew
Xethane
Yethane
Pbubble
Xethane
Yethane
Pdew
0
0
15.555
0
0
15.555
0.1
0.7723315
69.488
3.328852E-03
0.1
17.310
0.2
0.8736656
126.099
7.484993E-03
0.2
19.505
0.3
0.9138436
185.667
1.282053E-02
0.3
22.329
0.4
0.9355788
248.523
1.992038E-02
0.4
26.097
0.5
0.9493912
315.069
2.983264E-02
0.5
31.379
0.6
0.9591554
385.841
0.0446402
0.6
39.316
0.7
0.9667205
461.648
6.915412E-02
0.7
52.578
0.8
0.9732259
544.064
0.1175412
0.8
79.217
0.9
0.9799309
637.588
0.2571127
0.9
159.738
1.0
1.0
785.243
1.0
1.0
785.243
Table 5
T=220 F, EoS = SRK, Pbubble
Table 6
T=220 F, EoS = SRK, Pdew
Xethane
Yethane
Pbubble
Xethane
Yethane
Pdew
0
0
96.262
0
0
96.262
0.1
0.4912601
204.226
0.0112437
0.1
108.119
0.2
0.6515186
318.092
2.538418E-02
0.2
123.130
0.3
0.7288634
438.162
0.0437142
0.3
142.756
0.4
0.7719533
564.424
6.843916E-02
0.4
169.532
0.5
0.7960213
695.979
0.1036727
0.5
208.301
0.6
0.8050276
829.164
0.1581614
0.6
269.710
0.7
0.7908739
949.086
0.2551921
0.7
383.582
0.8
0.8004321
1,374.207
0.5284457
0.8
733.988
0.9
0.9000674
1,777.915
0.8995396
0.9
1,011.362
1.0
1.0
2,186.612
1.0
1.0
2,186.612
Table 7
T=40 F, EoS = PR, Pbubble
Table 8
T=40 F, EoS = PR, Pdew
Xethane
Yethane
Pbubble
Xethane
Yethane
Pdew
0
0
4.385
0
0
4.385
0.1
0.8760601
34.784
1.634785E-03
0.1
4.873
0.2
0.9367354
66.353
3.675473E-03
0.2
5.482
0.3
0.9591197
99.180
6.294654E-03
0.3
6.265
0.4
0.9709575
133.362
9.778902E-03
0.4
7.308
0.5
0.9784543
169.014
1.464149E-02
0.5
8.766
0.6
0.9838039
206.289
2.190169E-02
0.6
10.947
0.7
0.9880136
245.432
3.391199E-02
0.7
14.568
0.8
0.9916756
286.947
5.759341E-02
0.8
21.754
0.9
0.9953134
332.215
0.1258968
0.9
42.844
1.0
1.0
386.726
1.0
1.0
386.726
Table 9
T=100 F, EoS = PR, Pbubble
Table 10
T=100 F, EoS = PR, Pdew
Xethane
Yethane
Pbubble
Xethane
Yethane
Pdew
0
0
15.615
0
0
15.615
0.1
0.7683297
68.672
3.401765E-03
0.1
17.378
0.2
0.8710374
124.473
7.649146E-03
0.2
19.582
0.3
0.9118879
183.318
1.310214E-02
0.3
22.420
0.4
0.9340218
245.565
2.035884E-02
0.4
26.207
0.5
0.9481036
311.663
3.049118E-02
0.5
31.518
0.6
0.9580739
382.207
0.0456297
0.6
39.502
0.7
0.9658126
458.105
7.069726E-02
0.7
52.853
0.8
0.9724933
541.093
0.1201959
0.8
79.712
0.9
0.9793878
635.971
0.2630638
0.9
161.207
1.0
1.0
785.243
1.0
1.0
785.243
Table 11
T=220 F, EoS = PR, Pbubble
Table 12
T=220 F, EoS = PR, Pdew
Xethane
Yethane
Pbubble
Xethane
Yethane
Pdew
0
0
95.033
0
0
95.033
0.1
0.4917789
202.865
1.117388E-02
0.1
106.788
0.2
0.6508021
316.889
2.524193E-02
0.2
121.691
0.3
0.7270637
437.430
0.0435045
0.3
141.211
0.4
0.7691019
564.467
6.818815E-02
0.4
167.910
0.5
0.7918753
696.963
0.1034687
0.5
206.714
0.6
0.7992577
830.703
0.1583077
0.6
268.572
0.7
0.7808691
948.302
0.2570375
0.7
384.831
0.8
0.8004149
1,363.872
0.7974875
0.8
987.656
0.9
0.9000595
1,783.246
0.8996916
0.9
1,010.099
1.0
1.0
2,186.612
1.0
1.0
2,186.612
The Average Absolute Deviations
The absolute average deviation for each case calculated in an excel workbook and shown in following tables. They are calculated using the excel formula =avdev ()
T = 40 F
PR
SRK
x,y
Pdew
Pbubble
Pdew
Pbubble
0
4.385
4.385
4.276
4.276
0.1
4.873
34.784
4.751
35.241
0.2
5.482
66.353
5.346
67.359
0.3
6.265
99.18
6.109
100.71
0.4
7.308
133.362
7.126
135.382
0.5
8.766
169.014
8.547
171.475
0.6
10.947
206.289
10.674
209.124
0.7
14.568
245.432
14.204
248.545
0.8
21.754
286.947
21.213
290.204
0.9
42.844
332.215
41.789
335.443
1
386.726
386.726
389.858
389.861
AAD
61.81931
102.649
62.38917
103.5842
T = 100F
PR
SRK
x,y
Pdew
Pbubble
Pdew
Pbubble
0
15.615
15.615
15.555
15.555
0.1
17.378
68.672
17.31
69.488
0.2
19.582
124.473
19.505
126.099
0.3
22.42
183.318
22.329
185.667
0.4
26.207
245.565
26.097
248.523
0.5
31.518
311.663
31.379
315.069
0.6
39.502
382.207
39.316
385.841
0.7
52.853
458.105
52.578
461.648
0.8
79.712
541.093
79.217
544.064
0.9
161.207
635.971
159.738
637.588
1
785.243
785.243
785.243
785.243
AAD
130.7186
199.4906
130.5497
199.7405
T = 220F
PR
SRK
x,y
Pdew
Pbubble
Pdew
Pbubble
0
95.033
95.033
96.262
96.262
0.1
106.788
202.865
108.119
204.226
0.2
121.691
316.889
123.13
318.092
0.3
141.211
437.43
142.756
438.162
0.4
167.91
564.467
169.532
564.424
0.5
206.714
696.963
208.301
695.979
0.6
268.572
830.703
269.71
829.164
0.7
384.831
948.302
383.582
949.086
0.8
987.656
1,363.87
733.988
1,374.21
0.9
1,010.10
1,783.25
1,011.36
1,777.92
1
2,186.61
2,186.61
2,186.61
2,186.61
AAD
479.2841
518.9558
445.4797
519.4959
Analysis results
The results obtained by both EoS are in good agreement, but these differ to around 10% from the experimental data ...