Tray Efficiency versus Stripping Factor - American Chemical Society

ARTICLE pubs.acs.org/IECR

Tray Efficiency versus Stripping Factor Branislav M. Jacimovic and Srbislav B. Genic* Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11000 Belgrade, Serbia ABSTRACT: Estimation of the tray (plate) efficiency is the basis of trayed column design. A newly introduced parameter “normalized efficiency” (η) is compared to the stripping factor (λ) in order to derive a correlation which can be useful in engineering practice. The proposed correlation is based on the numerous data gathered from various literature sources describing distillation, absorption, and stripping (desorption) columns and covering sieve, tunnel, bubble-cup, uniflux, and jet trays, in the range λ = 0.03912196. The final form of this correlation is 8 1 > > < 1 þ 1:5λ0:9 for λ e 1 ηc ¼ λ0:3 > > for λ g 1 : 1:5 þ λ0:3 with correlation ratio Θ = 0.883 and standard deviation Δav = 13.1%.

1. INTRODUCTION Stagewise operations for gas (vapor)liquid contact, such as distillation, absorption, and stripping (desorption), can be carried out in trayed (plate) columns. Column diameter, tray (plate) spacing, and the number of actual trays are, as it is well-known, the most important parameters estimated in the trayed column design. In general, these parameters depend on the following: gas/vapor and liquid flow rates, physical properties of the phases in contact, tray type, and its geometrical characteristics. The number of actual trays (plates) is usually calculated using the number of theoretical stages and tray efficiency. Ever since Murphree’s definition of tray efficiency,1 a lot of attention has been given to the problems concerning the effects of tray design variables, two-phase flow regimes and physical properties on the intensity of mass transfer. Generally, all tray efficiency estimation methods can be divided into two groups: methods strictly based on experimental experience2 and various semitheoretical methods.3 Newly defined normalized efficiency 4 once again put the focus on the tray efficiency estimation problem. In this paper, a new correlation for the estimation of tray efficiency is presented. 2. MURPHREE TRAY EFFICIENCY VERSUS STRIPPING FACTOR Approximately at the same time (August 1996), two references have shown the major influence of the stripping factor on tray efficiency. The stripping factor is defined as the ratio of the slopes of equilibrium and operating lines λ¼m

G L

ð1Þ

where m is the slope of the equilibrium line; G, kmol/s, is the gas flow rate; L, kmol/s, is the liquid flow rate. Jacimovic and Genic2 r 2011 American Chemical Society

used the experimental data to establish a simple correlation in the form EMG ¼ aλb

ð2Þ

and the authors mention that the influence of all other parameters (i.e., viscosity, density, etc.) on tray efficiency can practically be neglected. Kunesh et al.5 gave the diagram EMG versus λ for their own measurements and stated that the “only physical property which has a major effect on EML is the liquid diffusivity”.

3. NORMALIZED EFFICIENCY VERSUS STRIPPING FACTOR IN GASLIQUID OPERATIONS Normalized efficiency η is defined4 as the ratio of real mass transfer rate on the tray and theoretically maximal mass transfer rate (obtained for the countercurrent plug-flow model for both phases in the case of an infinite contact surface). For onecomponent transfer between the phases in gasliquid operations, normalized efficiency is 8 y y xout xin in out > > < λyin yðxin Þ ¼ xðyin Þ xin for λ g 1 ð3Þ η¼ y yout 1 xout xin > > in ¼ for λ < 1 : λ xðyin Þ xin yin yðxin Þ where yin and yout are mole fractions of the transferred component in gas at the tray inlet and outlet, xin and xout are mole fractions of the transferred component in liquid at the tray inlet and outlet, and y* and x* are the equilibrium mole fractions of the transferred component. Received: May 7, 2010 Accepted: April 19, 2011 Revised: November 3, 2010 Published: May 02, 2011 7445

dx.doi.org/10.1021/ie101052f | Ind. Eng. Chem. Res. 2011, 50, 7445–7451

Industrial & Engineering Chemistry Research

ARTICLE

Table 1. Expected Range of Real Tray Efficiencies

Table 2. Experimental Tray Efficiency Data

λ

0.04

0.04

1

1

2000

2000

NTUG

2

0.5

2

0.5

2

0.5

NTUL

5

1

5

1

5

1

NTUOG

1.97

0.49

1.43

0.33

0.0025

0.0005

ηIM ηCC

0.65 0.85

0.32 0.38

0.37 0.59

0.20 0.25

0.83 0.99

0.50 0.63

no.

λ

EMG

η

mixture

1

0.0391

0.69

0.672

ammonia/water6

2

0.0793

0.69

0.654

ammonia/water6

3

0.07942

0.65

0.618

triethyleneglycol/natural gas þ water7

4

0.0986

0.69

0.646

ammonia/water6

5

0.158

0.69

0.622

ammonia/water6

The tray efficiency data are traditionally expressed in the open literature in the form of Murphree tray efficiency. The relationship between the normalized and the Murphree tray efficiency is4 8 EMG λ EML > > ¼ for λ g 1 < 1 þ EMG λ EML þ λ ð4Þ η¼ EMG EML λ > > ¼ for λ e 1 : EML þ λ 1 þ EMG λ

6

0.167

0.70

0.627

ammonia/water6

7 8

0.170 0.180

0.99 0.98

0.847 0.833

isopropyl alcohol/water8 isopropyl alcohol/water8

9

0.186

0.90

0.771

isopropyl alcohol/water8

10

0.187

0.94

0.799


11

0.188

0.91

0.777


12

0.192

0.92

0.782


13

0.203

0.94

0.790


14

0.205

1.04

0.857


where EMG and EML are Murphree tray efficiencies for gas and liquid phases, respectively. Normalized efficiency for the real cases of mass-transfer columns lies between the values calculated using idealized flow models:4 • For the countercurrent plug-flow model for both phases, normalized efficiency has a maximal value 8 1 exp½NTUOG ðλ 1Þ > > > for λ > 1 λ > > 1 λ exp½NTUOG ðλ 1Þ > > < NTUOG for λ ¼ 1 ηCC ¼ 1 þ NTUOG > > > > > 1 exp½NTUOG ðλ 1Þ > > for λ < 1 : 1 λ exp½NTU ðλ 1Þ OG

15 16

0.208 0.210

0.87 1.01

0.736 0.833


17

0.212

0.94

0.784


18

0.212

0.96

0.797


19

0.213

0.95

0.790


20

0.214

0.93

0.776


21

0.214

0.98

0.810


22

0.216

0.88

0.739


23 24

0.217 0.218

0.91 0.99

0.760 0.814


25

0.219

0.95

0.786


26

0.220

0.96

0.792


27

0.22

0.69

0.599

ammonia/water9

ð5Þ

28

0.222

0.91

0.757


29

0.224

0.85

0.714


30

0.230

0.94

0.773


31 32

0.232 0.233

0.94 0.90

0.772 0.744


33

0.236

0.91

0.749


34

0.237

0.92

0.755


35

0.240

0.93

0.760


36

0.241

0.85

0.706


37

0.241

0.86

0.712


38

0.243

0.84

0.698


39 40

0.244 0.245

0.96 0.82

0.778 0.683


41

0.245

0.83

0.690


42

0.245

0.81

0.676

dichloromethane/

• For the ideal phase mixing model for both phases, normalized efficiency has minimal value 8 λNTUOG > > for λ g 1 < 1 þ ðλ þ 1ÞNTU OG ηIM ¼ ð6Þ NTUOG > > for λ e 1 : 1 þ ðλ þ 1ÞNTU OG

where NTUOG is the overall number of transfer units for gas phase NTUOG ¼

1 1 λ þ NTUG NTUL

ð7Þ

dichloroethane10

and NTUG and NTUL are the numbers of transfer units for the gas and liquid phases, respectively. The majority of the published tray efficiency data fall within the range of λ = 0.042000, NTUG = 0.52, and NTUL = 15, and therefore, the expected normalized tray efficiencies should be within the range presented in Table 1. The data given in Table 2 were gathered from the open literature (ML is the molar mass of liquid in kilograms per kilomole), with the exception of the data marked with an asterisk, which are the data that the authors themselves have measured on an industrial distillation column (diameter 750 mm, uniflux trays,

43

0.247

0.85

0.702


44

0.255

0.89

0.725


45

0.257

0.83

0.684


46 47

0.258 0.259

0.85 0.95

0.697 0.763


48

0.260

0.83

0.683


49

0.26

0.57

0.496


50

0.26

0.88

0.716

dichloromethane/ dichloroethane10

7446

dx.doi.org/10.1021/ie101052f |Ind. Eng. Chem. Res. 2011, 50, 7445–7451


ARTICLE

Table 2. Continued no.

λ

Table 2. Continued EMG

η

no.

λ

8

mixture

EMG

η

mixture

51 52

0.262 0.264

0.94 0.97

0.754 0.772

isopropyl alcohol/water isopropyl alcohol/water8

103 104

0.367 0.368

0.76 0.86

0.594 0.653


53

0.267

0.82

0.673


105

0.368

0.85

0.648


0.789

8

106

0.378

0.97

0.710


8

107

0.383

0.91

0.675

dichloromethane/

54

0.267

1.00

isopropyl alcohol/water

55

0.274

0.83

0.676


56

0.274

0.83

0.676

isopropyl alcohol/water8 8

57

0.275

0.77

0.635


58

0.275

1.01

0.791


59

0.275

0.845

0.686


60

0.279

0.79

0.647 0.763

61 62 63 64 65

0.280 0.281 0.285 0.286 0.287

0.97 0.74 0.84 1.02 0.93

0.613 0.678 0.790 0.734

dichloroethane10 108

0.3959

0.60

0.485


109 110

0.401 0.42

1.00 0.78

0.714 0.588

isopropyl alcohol/water8 methanol/water11


111

0.427

0.85

0.624


8

112

0.43

0.82

0.606

methanol/water11

8

113

0.431

0.53

0.431

benzene/toluene12

8

114

0.432

0.54

0.438

benzene/toluene12

8

115

0.441

0.55

0.443

benzene/toluene12

8

116

0.442

0.64

0.499

benzene/toluene12

8

isopropyl alcohol/water isopropyl alcohol/water isopropyl alcohol/water isopropyl alcohol/water isopropyl alcohol/water

66 67

0.290 0.293

0.96 0.99

0.751 0.768


117

0.452

0.904

0.642


68

0.295

0.91

0.717


118

0.460

0.91

0.641


0.766

8

119

0.461

0.65

0.500

benzene/toluene12

8

120

0.461

0.64

0.494

benzene/toluene12

8

121

0.461

0.65

0.500

benzene/toluene12

8

122

0.472

0.90

0.632


8

123

0.478

0.66

0.502

benzene/toluene12

8

124 125

0.478 0.480

0.62 0.88

0.478 0.619

benzene/toluene12 isopropyl alcohol/water8

69 70 71 72 73

0.296 0.296 0.296 0.296 0.297

0.99 0.97 0.98 1.03 0.97

0.753 0.759 0.789 0.753

isopropyl alcohol/water isopropyl alcohol/water isopropyl alcohol/water isopropyl alcohol/water isopropyl alcohol/water

74 75

0.298 0.30

0.95 0.82

0.741 0.658

isopropyl alcohol/water dichloromethane/

126

0.48

0.7

0.524

methanol/water11

76

0.306

0.93

0.724


127

0.481

0.67

0.507

benzene/toluene12

77

0.310

0.91

0.710


128

0.482

0.91

0.633


78

0.312

1.05

0.791


129

0.486

0.87

0.612


79

0.319

0.93

0.717


130

0.50

1.0

0.667

ethanol/water14

80

0.327

0.89

0.689


131

0.514

0.67

0.498

benzene/toluene12

81 82

0.335 0.335

0.88 0.92

0.679 0.703


132 133

0.515 0.516

0.63 0.66

0.476 0.492

benzene/toluene12 benzene/toluene12

83

0.336

0.89

0.685


134

0.53

1.2

0.733


84

0.347

0.92

0.698


135

0.571

0.844

0.570

ethanol/water *

85

0.349

0.89

0.679


136

0.575

0.67

0.484

benzene/toluene12

86

0.353

0.88

0.671


137

0.607

0.61

0.445

benzene/toluene12

0.636

8

138

0.614

0.66

0.470

benzene/toluene12

8

139

0.625

0.65

0.462

benzene/toluene12

8

0.543 0.459

ethanol/water * benzene/toluene12

dichloroethane10

87 88

0.353 0.358

0.82 0.91

0.686

isopropyl alcohol/water isopropyl alcohol/water

89 90

0.358 0.361

0.88 0.79

0.669 0.615


140 141

0.626 0.642

0.823 0.65

91

0.362

0.88

0.667


142

0.654

0.846

0.545

ethanol/water *

92

0.362

0.83

0.638


143

0.658

0.62

0.440

ethanol/water12

93

0.363

0.86

0.656


144

0.658

0.62

0.440

ethanol/water12

0.602

8

145

0.660

0.63

0.445

ethanol/water12

8

146

0.661

0.62

0.440

ethanol/water12

8

147

0.669

0.75

0.499

ethanol/water12

8

94 95 96

0.364 0.364 0.365

0.77 0.88 0.82

0.666 0.631

isopropyl alcohol/water isopropyl alcohol/water isopropyl alcohol/water

97 98

0.365 0.365

0.82 0.85

0.631 0.649


148 149

0.675 0.685

0.62 0.75

0.437 0.495

ethanol/water12 benzene/n-heptane15

99

0.365

0.88

0.666


150

0.690

0.56

0.404

ethanol/water12

0.682

8

151

0.694

0.58

0.414

ethanol/water12

8

152

0.703

0.878

0.543

ethanol/water6

8

153

0.711

0.72

0.476

ethanol/water12

100 101 102

0.367 0.367 0.367

0.91 0.89 0.87

0.671 0.659

isopropyl alcohol/water isopropyl alcohol/water isopropyl alcohol/water

7447



ARTICLE


λ


η

mixture

154 155

0.713 0.719

0.752 0.62

0.489 0.429

methyl ethyl ketone/toluene ethanol/water12

156

0.736

0.74

0.479

ethanol/water12

157 158 159 160 161

0.737 0.742 0.747 0.748 0.749

0.69 0.68 0.894 0.76 0.66

0.457 0.452 0.536 0.485 0.442

16

12

168 169

0.792 0.810

0.809 0.877 0.67

0.497 0.517 0.434

209

0.952

0.890

0.482

methyl ethyl ketone/toluene16

ethanol/water

12

210

0.952

0.863

0.474


12

211

0.958

0.883

0.478

ethanol/water6

212 213

0.97 0.971

0.50 0.71

0.337 0.420

n-butane/1-butene10 ethanol/water12

214

0.973

0.399

0.287


benzene/toluene 12

11

215

0.973

0.769

0.440


methyl ethyl ketone/toluene

16

216

0.981

0.909

0.481



16

217

0.982

0.865

0.468



16

cyclohexane/n-pentane

ethanol/water

218

0.993

0.62

0.384

ethanol/water12

12

219

0.995

0.75

0.429

ethanol/water12

6

220 221

0.995 1.0

0.71 0.57

0.416 0.363

ethanol/water12 ethanol/water14

ethanol/water isopropyl alcohol/water8

172

0.819

0.74

0.461

ethanol/water12

174 175 176 177

0.825 0.827 0.827 0.827

0.735 0.69 0.655 0.661

0.458 0.439 0.425 0.427


ethanol/water

0.512 0.630 0.519

0.421


0.88 1.30 0.904

0.697

0.500

0.815 0.818 0.821

0.943

0.953

170 171 173

206

0.952


0.777

methyl ethyl ketone/toluene16 methyl ethyl ketone/toluene16

208

0.445

167

0.433 0.432

6

0.674

0.493

0.730 0.728

ethanol/water

0.765

0.799

0.942 0.942


164

0.777

204 205

0.420

ethanol/water benzene/toluene12

166

mixture

0.696

0.412 0.430 0.475

η

0.943

0.60 0.64 0.75

EMG

207

0.760 0.764 0.77

λ

12

benzene/toluene

162 163 165

no.

222

1.0

0.55

0.355

n-butane/1-butene10


16

223

1.004

0.928

0.482



16

224

1.004

0.921

0.481


225

0.983

0.5073

0.338

water/acetic acid18


16

226

1.045

0.700

0.422



16

227

1.049

0.56

0.370

benzene/toluene12

16

228 229

1.049 1.049

0.785 0.743

0.452 0.438


ethanol/water

12

178 179

0.827 0.83

0.638 0.56

0.418 0.382

methyl ethyl ketone/toluene n-butane/1-butene10

180

0.842

0.658

0.423


230

1.06

0.42

0.308

isobutane/1-butene10

181

0.842

0.760

0.463


231

1.062

0.70

0.426

n-heptane/toluene15

182

0.848

0.89

0.507

ethanol/water *

232

1.082

0.75

0.448

ethanol/water12

183

0.853

0.70

0.438

cyclohexane/n-heptane11

233

1.086

0.866

0.485


184

0.854

0.846

0.491


234

1.088

0.772

0.457


185

0.855

0.812

0.479


235

1.09

0.50

0.353

n-butane/1-butene10

186

0.856

0.69

0.372

2,2,4 trimethylpentane/ toluene17

236 237

1.092 1.137

0.58 0.78

0.388 0.470

benzene/toluene12 ethanol/water12

187

0.857

0.70

0.376

2,2,4 trimethylpentane/

238

1.160

0.721

0.455


239

1.182

0.47

0.357

benzene/toluene12

240

1.191

0.859

0.506


241

1.191

0.836

0.499


242

1.191

0.887

0.514


243

1.2

0.54

0.393

C3C6/oil (ML = 135)9

toluene17 188

0.862

0.74

0.388

2,2,4 trimethylpentane/ 17

toluene 189

0.864

0.56

0.327

2,2,4 trimethylpentane/ 17

toluene 190 191

0.869 0.869

0.835 0.845

0.484 0.487

methyl ethyl ketone/toluene methyl ethyl ketone/toluene16

244 245

1.242 1.28

0.71 0.60

0.469 0.434

ethanol/water12 methanol/water11

192

0.879

0.75

0.452

methanol/isopropanol15

193

0.889

0.813

0.472

16

246

1.289

0.78

0.501

ethanol/water12


16

247

1.293

0.73

0.485

ethanol/water12

16

248

1.327

0.478

0.388

methyl ethyl ketone/

194

0.890

0.583

0.384


195

0.891

0.925

0.507


196 197

0.894 0.907

0.91 0.632

0.502 0.402

toluene16 249

1.36

0.36

0.329

i-C4H8/heavy naphtha9


16

250

1.36

0.34

0.316


16

251 252

1.364 1.364

0.738 0.821

0.502 0.528


0.364

0.342

iso-C4H8/heavy naphtha6

ethanol/water

6

198 199

0.907 0.92

0.589 0.54

0.384 0.361

methyl ethyl ketone/toluene n-butane/1-butene10

200

0.924

0.60

0.386

acetic acid/water11

253

1.43

16

201

0.925

0.580

0.377


254

1.452

0.555

0.446

ethanol/water *

202

0.925

0.645

0.404


255

1.46

0.44

0.391

C3C6/oil (ML = 185)9

203

0.942

0.719

0.429


256

1.51

0.33

0.333


7448



ARTICLE


λ


η

mixture

257 258

1.54 1.575

0.45 0.41

0.409 0.392

C3C5/oil (ML = 135) acetic acid/water11

259

2.0

0.30

0.375

C3C6/oil (ML = 64)9

0.383

C3C6/oil (ML = 157)

260 261 262

2.0 2.5 2.564

0.31 0.50 0.74

9

11

6.25 7.79

0.18 0.131

7.94

0.11

307

126.0

0.021

0.73

CO2/water6

0.022

0.76

CO2/water6

310

142.4

0.035

0.833

toluene/water5

311

146.7

0.025

0.79

CO2/water6

heavy naphtha propene (C3H6)/

312 313

148.0 148.4

0.028 0.029

0.81 0.811

CO2/water6 toluene/water5

heavy naphtha6

314

157.6

0.022

0.78

CO2/water6

propene (C3H6)/

315

177.1

0.026

0.822

toluene/water5

6

heavy naphtha

316

178.9

0.024

0.811

toluene/water5

propene (C3H6)/

317

182.0

0.015

0.732

CO2/water9

0.462 0.504 0.540

318

185.3

0.024

0.816

CO2/water6

9

9

0.409

propene (C3H6)/gas oil

319

229.9

0.028

0.866

toluene/water5

0.529 0.505

C3C6/oil (ML = 201) propene (C3H6)/

320 321

235.2 278.7

0.019 0.029

0.817 0.890

CO2/water6 toluene/water5

322

282.9

0.029

0.891

toluene/water5

323

285.8

0.028

0.889

toluene/water5

324

341.9

0.031

0.914

toluene/water5

325

351.4

0.024

0.894

toluene/water5

326

372.1

0.015

0.848

CO2/water6

heavy naphtha6 271

CO2/water6

140.8

heavy naphtha 269 270

0.77

309

6

0.12

0.026

12

6

5.77

125.4

ethanol/water

propene (C3H6)/

268

306

0.655 0.417

0.216

CO2/water CO2/water6

CO2/water6

0.224

5.44

0.70 0.78

0.78

3.20

267

0.019 0.030

0.027

264

0.23

120.5 121.6

127.8

ethanol/water

4.42

304 305

308

0.658

266

mixture 6

12

0.69

0.240

η

methanol/water

2.785

3.57

EMG

0.556

263

265

λ

no. 9

0.466

propene (C3H6)/gas oil þ lube oil

9

272

10.0

0.18

0.643

C3C6/oil (ML = 206)

273

15.064

0.217

0.766

ethanol/water *

274

19.41

0.226

0.814

propene (C3H6)/

327

392.3

0.024

0.904

toluene/water5

6

9

275

42.6

0.029

0.55

heavy naphtha CO2/water6

328 329

460.9 484.0

0.028 0.018

0.928 0.897

toluene/water5 CO2/water9

276

49.4

0.032

0.61

CO2/water6

330

491.0

0.018

0.898

CO2/water6

277

58.6

0.035

0.67

CO2/water6

331

542.2

0.015

0.891

toluene/water5

278

58.8

0.027

0.61

CO2/water6

332

547.3

0.021

0.920

toluene/water5

279

61.8

0.021

0.56

CO2/water6

333

697.6

0.012

0.893

toluene/water5

280

66.5

0.026

0.634

CO2/water9

334

1185

0.0099

0.921

toluene/water5

281

66.7

0.022

0.595

CO2/water6

335

1533

0.012

0.948

toluene/water5

282 283

69.2 69.4

0.024 0.018

0.62 0.56

CO2/water6 CO2/water6

336 337

1882 2036

0.0081 0.008

0.938 0.942

toluene/water5 toluene/water5

284

70.5

0.020

0.59

CO2/water þ glycerol6

338

2196

0.0045

0.908

toluene/water5

6

285

79.2

0.033

0.72

CO2/water

286

79.6

0.026

0.674

CO2/water6

287

79.9

0.020

0.62

CO2/water6

288

80.0

0.035

0.737

CO2/water9

289

81.5

0.016

0.57

CO2/water þ glycerol

290

89.0

0.018

0.62

CO2/water6

291

90.4

0.017

0.606

CO2/water6

292

90.4

0.017

0.61

CO2/water6

293

90.8

0.032

0.74

CO2/water6

294

91.1

0.020

0.646

CO2/water þ glycerol9

295

92.9

0.018

0.63

CO2/water6

296

95.5

0.025

0.70

CO2/water6

297

102.7

0.015

0.61

CO2/water6

298

103.9

0.033

0.77

CO2/water6

299

109.7

0.019

0.68

CO2/water6

300

110.3

0.035

0.79

CO2/water6

301

110.8

0.018

0.67

CO2/water6

302

115.9

0.018

0.68

CO2/water6

303

120.2

0.036

0.812

toluene/water5

6

ethanolwater distillation). The data given in Table 2 cover all three gasliquid operations (distillation, absorption, and stripping) as well as a wide range of other influential parameters: • 338 experimental runs with more than 25 gasliquid systems (mixtures) • various tray designs: sieve, bubble-cup, tunnel, uniflux, jet • column diameter 50.82743 mm • column pressure range 133.4 bar • range of temperature 9.5120 °C • flood-factor from about 15% to 98% • stripping factor range λ = 0.03912196 (including two regimes with λ = 1). Figure 1 shows the data given in Table 2 and the lines for ηCC(NTUG = 2; NTUL = 5) and ηIM(NTUG = 0.5; NTUL = 1). It can be noticed that only 11 experimental runs fall outside of the field defined by lines for ηCC(NTUG = 2; NTUL = 5) and ηIM(NTUG = 0.5; NTUL = 1). 7449



ARTICLE

wide range of tray types, column diameter, and other tray variables, working conditions (pressure, temperature), various mixtures, and stripping factor in the range λ = 0.03912196, a new correlation was found in the form 8 > >
> : 1:5 þ λ0:3

Figure 1. Normalized efficiency experimental data vs stripping factor.

for λ e 1 for λ g 1

ð8Þ

The statistical parameters of eq 8 are so good (correlation ratio Θ = 0.883, standard deviation Δav = 13.1%) that we are assured that all the other parameters (such as the physical and transport properties and flow rates of both phases, tray geometrical parameters, etc.) have little or no influence on tray efficiency. Authors have already successfully used correlation 8 for the final design of a distillery for production of 4 m3 per day of refined ethanol from corn which was built in Kostojevici (Serbia) during 2007.

’ AUTHOR INFORMATION Corresponding Author

*Fax: þ381 11 3370364. Phone: þ381 11 3302360. E-mail: [email protected].

’ ACKNOWLEDGMENT We thank the Ministry of Science and Technological Development of Serbia for partial support of this study through Project of Energy Efficiency. ’ REFERENCES

Figure 2. Correlated normalized efficiency vs stripping factor.

Jacimovic and Genic4 have shown that tray efficiency has discontinuity for λ = 1, and so, the following correlation covers the whole range of λ 8 1 > > < 1 þ 1:5λ0:9 for λ e 1 ð8Þ ηc ¼ λ0:3 > > for λ g 1 : 1:5 þ λ0:3 Statistical parameters for correlation 8 are correlation ratio Θ = 0.883, standard deviation Δav = 13.1%, maximal deviation 41% and þ30%, 22 runs with deviation greater than (25%. The experimental data from Table 2 and correlation 8 are presented in Figure 2, accompanied by the (25% deviation field between the dashed lines.

4. CONCLUSION The introduction of normalized efficiency4 gave us one more opportunity to correlate tray efficiency versus stripping factor. By using 338 experimental data records gathered from the open literature for gasliquid mass transfer operations and for the

(1) Murphree, E. V. Rectifying Column Calculations. Ind. Eng. Chem. 1925, 17, 747. (2) Jacimovic, B.; Genic, S. Use A New Approach To Find Murphree Tray Efficiency. Chem. Eng. Progr. 1996, 92, 46–51. (3) Kafarov, V. V. Fundamentals of Mass Transfer; Mir Publishers: Moscow, 1985. (4) Jacimovic, B.; Genic, S. Normalized Efficiency For Stagewise Operations. Ind. Eng. Chem. Res. 2011in press. (5) Kunesh, J. G.; Ognisty, T. P.; Sakata, M.; Chen, G. X. Sieve Tray Performances for Steam Stripping Toluene from Water in a 4-ft Diameter Column. Ind. Eng. Chem. Res. 1996, 35, 2660–2671. (6) Walter, J. F.; Sherwood, T. K. Gas Absorption in Bubble-Cap Columns. Ind. Eng. Chem. 1941, 33, 493–501. (7) Oi, L. E. Estimation of Tray Efficiency in Dehydration Absorbers. Chem. Eng. Process. 2003, 42, 867–878. (8) Keyes, D. B.; Langdon, W. M. Plate Factors in Fractional Distillation of Isopropyl Alcohol-Water System. Ind. Eng. Chem. 1943, 35, 464–469. (9) Hobler, T. Mass Transfer and Absorbers; Pergamon: Oxford, 1966. (10) Bubble Tray Design Manual; AIChE: New York, 1958. (11) Afacan, A.; Chen, G. X.; Yang, N.; Chuang, K. T. Hydraulics and efficiency of screen trays for distillation. Chem. Eng. Commun. 2002, 189, 41–60. (12) Rhodes, F. H.; Slachman, P. G. Plate Efficiency and Entrainment in Distillation. Ind. Eng. Chem. 1937, 29, 51–54. (13) Hubner, W. Der Einfluss der Konzentration auf das Verst€arkungsverh€altnis von Rektifizierb€ oden. Chem. Ing. Technik 1972, 44, 546–552. (14) Shilling, G. D.; Beyer, G. H.; Watson, C. C. Efficiencies in Ethanol-Water Fractionation. Chem. Eng. Progr. 1953, 49, 128–134. 7450



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(15) Xu, Z. P.; Afacan, A.; Chuang, K. T. Prediction of packed sieve tray efficiency in distillation. Trans. Inst. Chem. Eng. 1996, 74(A), 893–900. (16) Rampacek, C. M.; Van Winkle, M. Efficiency Study on Jet Trays in a 6-Inch Diameter Laboratory Column. Ind. Eng. Chem. Proc. Des. Dev. 1968, 7, 313–318. (17) Manning, E.; Marple, S.; Hinds, G. P. A Plant-Scale Unit for Distillation Tray Research. Ind. Eng. Chem. 1957, 49, 2051–2054. (18) Pavlechko, V. N.; Minakhmetov, A. V.; Nikolaev, N. A. Analysis of Mass Exchange Efficiency in Rectifying Columns. Russ. J. Appl. Chem. 2009, 82, 435–438.

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Tray Efficiency versus Stripping Factor - American Chemical Society

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