THERMODYNAMICS/CHEMISTRY

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 ...