Thomas Model to Batch Column Experiments

The linearised Thomas models for the data in this work are shown in Figs. 60, 61 and 62 at varying bed heights, varying input volume and varying initial dye

Fig. 61 Linearised Thomas model of RR158 adsorption on CAC's for varying input volume. Experimental conditions: concentration of dye: 60 mg/L, pH: 2 and bed height: 6 cm
Thomas Model For Column
Fig. 62 Linearised Thomas model of RR158 adsorption on CAC's for varying initial dye concentration. Experimental conditions: volume of dye solution: 150 mL, pH: 2 and bed height: 6 cm

concentration respectively. A summary of the results of the Thomas parameters determined from the Thomas model is displayed in Table 13. It was observed that the Thomas constant was directly proportional to both the bed height and the input

Table 13 Summary of results of Thomas model parameters

Present study

Table 13 Summary of results of Thomas model parameters

Present study

Bed height/cm

Effect

of bed height

8

0.190

2.432

0.446

10

0.329

4.837

0.272

12

0.989

15.435

0.157

Input volume/mL

Effect

of input volume

100

0.518

17.292

0.105

150

0.525

14.083

0.121

200

0.825

16.922

0.105

250

0.669

20.826

0.071

Initial dye concentration (mg/L)

Initial

dye concentration (mg/L)

60

0.525

14.083

0.093

80

0.955

12.073

0.099

100

0.888

10.566

0.105

120

0.917

5.438

0.146

R2

kT (L/min mg) x 10-3

q0 (mg/g)

From literature [1]

Initial dye concentration/mg/L

57.0

0.991

5.19

14.12

79.0

0.996

3.30

20.96

100.0

0.989

2.04

24.58

Mass of adsorbent/g

0.1

0.986

22.71

5.49

0.2

0.993

22.33

7.04

0.3

0.998

13.51

8.77

Flow rate (mL/min)

6.82

0.998

10.10

10.10

5.19

0.994

7.51

12.08

3.77

0.991

5.19

14.12

volume of dye solution. The kT values increased from 2.432E-05 L/min mg to 15.435E-05 L/min mg as bed height increased from 6 to 10 cm and from 14.083E-05 to 20.826E-05 L/min mg when the input volume of dye increased from 150 to 250 mL.

However, as far as the initial dye concentration was concerned, the Thomas constant was inversely relative such that the kT values decreased from 14.083E-05 to 5.438E-05 L/min mg as dye concentration increased from 60 to 120 mg/L. The calculated q0 values were inversely proportional to the bed heights and input volume but directly relative to initial dye concentration. The q0 values increased from 0.093 to 0.146 mg/g for rise in dye concentration from 60 to 120 mg/L, and decreased from 0.446 to 0.157 mg/g for rise in bed height from 6 to 10 cm and decreased from 0.105 to 0.071 mg/g for rise in input volume from 100 to 250 mL.

Table 14 Summary of results of Langmuir model and DR model

Dye concentration (mg/L)

SAE ARE Langmuir model

RSS

DR model

ARE

RSS

20

Adsorbent dosage: 0.346 0.995

0.120

0.190

0.546

0.036

40

0.614

0.919

0.377

0.444

0.664

0.197

60

1.509

0.802

2.277

0.671

0.356

0.450

80

1.606

0.827

2.580

0.440

0.227

0.194

100

1.986

0.865

3.944

1.670

0.727

2.788

120

3.469

0.787

12.033

3.104

0.704

9.632

20

Adsorbent dosage: 0.334 0.847

0.111

0.362

0.920

0.131

40

0.430

0.969

0.185

0.444

1.000

0.197

60

0.627

0.941

0.394

0.665

0.996

0.442

80

1.249

0.815

1.561

1.366

0.891

1.865

100

1.987

0.686

3.947

1.964

0.678

3.855

120

2.594

0.784

6.730

2.710

0.818

7.344

20

Adsorbent dosage: 0.332 0.848

0.110

0.361

0.923

0.130

40

-

-

-

1.356

0.954

1.839

60

0.797

0.712

0.636

1.057

0.944

1.117

80

0.806

0.996

0.650

0.809

1.000

0.654

100

1.081

0.721

1.168

1.156

0.772

1.336

120

1.213

0.958

1.472

1.264

0.997

1.596

20

Adsorbent dosage: 0.245 0.836

0.060

0.265

0.904

0.070

40

0.841

0.898

0.708

0.701

0.748

0.491

60

1.042

0.756

1.086

1.036

0.752

1.073

80

0.856

0.840

0.733

0.934

0.917

0.872

100

1.564

0.946

2.445

1.620

0.980

2.623

120

0.993

0.760

0.986

1.094

0.837

1.197

20

Adsorbent dosage: 0.615 0.881

0.378

0.629

0.901

0.395

40

0.800

0.878

0.640

0.824

0.904

0.679

60

0.729

0.713

0.531

0.792

0.775

0.627

80

0.820

0.762

0.673

0.866

0.805

0.750

100

0.895

0.792

0.801

0.966

0.855

0.933

120

0.687

0.784

0.472

0.778

0.889

0.606

20

Adsorbent dosage: 20 g/L 1.262 0.713 1.594

1.149

0.649

1.320

40

2.257

0.891

5.095

2.279

0.900

5.194

60

2.450

0.745

6.003

2.448

0.744

5.992

80

3.132

0.906

9.812

3.200

0.925

10.242

100

1.828

0.715

3.342

1.940

0.759

3.762

120

3.079

0.760

9.481

3.236

0.799

10.470

Table 15 Summary of results of error analysis of Pseudo first and second order

Dye concentration (mg/L)

SAE ARE Pseudo first order

RSS

SAE ARE Pseudo second order

RSS

20

Adsorbent dosage: 0.181 0.519

0.033

0.020

0.058

0.000

40

0.598

0.895

0.357

0.139

0.209

0.020

60

1.803

0.959

3.252

0.060

0.032

0.004

80

1.922

0.990

3.695

0.031

0.016

0.001

100

2.132

0.929

4.547

0.161

0.070

0.026

120

4.326

0.982

18.713

0.180

0.041

0.032

20

Adsorbent dosage: 0.104 0.263

0.011

0.064

0.161

0.004

40

0.015

0.034

0.000

1.187

2.674

1.410

60

0.000

0.000

0.000

0.274

0.410

0.075

80

0.948

0.619

0.899

0.212

0.138

0.045

100

1.257

0.434

1.581

0.342

0.118

0.117

120

2.652

0.801

7.032

0.186

0.056

0.034

20

Adsorbent dosage: 0.195 0.498

12.5 g/L 0.038

0.099

0.252

0.010

40

0.269

0.189

0.072

3.186

2.241

10.153

60

0.001

0.001

0.000

0.228

0.203

0.052

80

0.180

0.222

0.032

0.619

0.765

0.383

100

1.055

0.705

1.114

0.467

0.312

0.218

120

0.001

0.001

0.000

2.437

1.923

5.938

20

Adsorbent dosage: 0.053 0.181

0.003

0.135

0.460

0.018

40

0.291

0.311

0.085

1.164

1.242

1.354

60

0.001

0.001

0.000

0.115

0.083

0.013

80

0.000

0.000

0.000

0.029

0.029

0.001

100

0.464

0.281

0.215

6.681

4.044

44.640

120

1.307

1.000

1.708

0.420

0.321

0.176

20

Adsorbent dosage: 0.212 0.303

17.5 g/L 0.045

2.592

3.713

6.716

40

0.277

0.304

0.077

2.725

2.992

7.428

60

0.758

0.741

0.574

0.033

0.032

0.001

80

0.366

0.341

0.134

0.010

0.0010

0.000

100

0.171

0.151

0.029

0.091

0.081

0.008

120

0.488

0.557

0.238

0.866

0.989

0.750

20

Adsorbent dosage: 0.421 0.238

0.177

0.955

0.539

0.912

40

1.184

0.467

1.402

3.349

1.322

11.218

60

1.648

0.501

2.717

0.843

0.257

0.711

80

0.596

0.172

0.355

2.602

0.752

6.768

100

1.011

0.395

1.022

1.261

0.493

1.590

120

0.003

0.001

0.000

0.392

0.097

0.154

4 Results and Discussions

63

Table 16 Summary of results of error

analysis of Thomas model

SAE

ARE

RRS

Effect of bed height (cm)

6 0.348

3.551

0.121

8 0.192

2.400

0.037

10 0.080

1.039

0.006

Effect of input volume (mL)

100 0.081

3.375

0.007

150 0.083

2.184

0.007

200 0.059

1.283

0.003

250 0.029

0.690

0.001

Initial dye concentration (mg/L)

60 0.055

1.447

0.003

80 0.058

1.415

0.003

100 0.055

1.100

0.003

120 0.088

1.517

0.008

0 0

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