RTD in CSTR

Experiment  –  4 Residence Time in Continuous Stirred Tank Reactor AIM: To study the residence time distribution in a CSTR and further to compare the results obtained with the expected theoretical results.

APPARATUS: 

An overhead tank in order to maintain constant flow rate



Continuous Stirred Flow Reactor to analyze



Tracer (NaOH)



Stop Watch



Conductivity measuring instrument.



Injection to inject tracer



A beaker to collect effluent

EXPERIMENTAL PROCEDURE: 1. Fill the overhead tank with water and adjust the input and output flow rate in the tank so that its level remains constant. 2. From the overhead tank start the supply of water into the CSTR. 3. Adjust the flow rate of water into the CSTR until it comes equal to 1 mL/sec. 4. Now inject the tracer (NaOH) into the reactor and as soon as the tracer is injected start the stop watch. 5. Now keep on measuring the conductivity of the solution present in CSTR. 6. Stop your readings when the effluent streams contain negligible amount of the tracer.

THEORY: Residence Time is the time spent by an atom in a reactor. In an ideal CSTR the concentration of any substance in the effluent stream is identical to the concentration throughout the reactor. Consequently, it is possible to obtain the RTD from conceptual considerations in a fairly straight forward manner. But as we know that no reactor in the world is ideal and hence all the atoms/molecules entering the reactor don’t spend the same amount of time. To measure the non-ideality in a reactor we plot a residence time distribution of atoms in the reactor. To define it, Residence Time Distribution (RTD) of a reactor is a characteristic of the mixing that occurs in the chemical reactor. Non ideality comes into the picture and d ue to some disturbances in mixing the concentration of the exit effluents is not the same as that is there in the reactor. Experimentally, RTD is determined by injecting a tracer (which is normally an inert substance) in the reactor at some time t = 0 and then by measuring the tracer concentration in the effluent stream as a function of time. Some typical characteristics of a tracer are:

 

The tracer used should be a nonreactive species that is easily detachable. Should have similar physical properties to those of the reacting mixture and be b e completely soluble in the mixture. This is required so that the tracer’s behavior will honestly reflect that of the material flowing



It should not adsorb on the walls or other surfaces in the reactor.



Colored and radioactive materials along with inert gases are the most common types of tracers.

Here in this experiment we would use a pulse input of the tracer where an amount of tracer is suddenly injected in one shoot into the feed stream entering the reactor in as short a time as possible. The outlet co concentration ncentration is then measured as a function of time. A material balance on an inert tracer that has been injected as a pulse at time t = 0 into a CSTR for t > 0

Integrating the above the above equation with C = C o at t = 0, we get

We would further take C (t) as the measure of concentration of tracer as a function of time. Moving on we define a quantity E (t) as the residence-time distribution function. It is the function that describes in a quantitative manner how much time different fluid elements have spent in the reactor. Th e quantity E(t)dt is the fraction of fluid exiting the reactor that has spent between time t and t + dt inside the reactor. Mathematically it can be defined as:

An alternative way of defining the residence time distribution function can be:

As we know that the fraction of all the material that has resided for a time t in the react or between t = 0 and t = ∞ is 1 therefore,

Coming to the concept of space time or mean residen ce time (τ) , we know τ = V/vo. Now no matter what RTD exists for a particular reactor, ideal or non-ideal, non-ideal, the nominal space time τ, is equal to the mean residence time t m. As is the case with other variables described by distribution functions, the mean value of the variable is equal to the first moment of the RTD function, E (t). Thus the mean residence time is

OBSERVATIONS: Flow Rate (Q)

= 1 mL/s

Volume of Reactor (V)

= 870 mL

Time Constant Constant (τ)

= V/ Q

= 870/1

= 870 sec

Observation Tablet

C(Observed)

C(Theoretical)

C(t)dt

E(t)

E(t)dt

tE(t)dt

Experimental

Experimental

Experimental

Experimental

0

45.58

45.58

20

45

44.58413427

900

0.00096749

0.019349891

0.386998

24

44.5

44.38769363

178

0.00095674

0.003826979

0.091847

32.6

44

43.96839225

378.4

0.00094599

0.008135554

0.265219

43.7

43.54

43.43329221

483.294

0.0009361

0.010390763

0.454076

55.1

43

42.89079047

490.2

0.00092449

0.010539241

0.580712

66.8

42.5

42.34135501

497.25

0.00091374

0.010690815

0.714146

77.2

42

41.85913255

436.8

0.00090299

0.009391147

0.724997

89.6

41.5

41.29165836

514.6

0.00089224

0.011063838

0.99132

101.8

41

40.7411751

500.2

0.0008815

0.01075424

1.094782

114.7

40.5

40.16744242

522.45

0.00087075

0.011232612

1.288381

125.8

40

39.6805292

444

0.00086

0.009545946

1.20088

137.6

39.5

39.16967701

466.1

0.00084925

0.010021094

1.378902

149.1

39

38.67843515

448.5

0.0008385

0.009642696

1.437726

163.5

38.5

38.07240069

554.4

0.00082775

0.011919533

1.948844

178

38

37.4722095

551

0.000817

0.011846434

2.108665

188.8

37.5

37.03162583

405

0.00080625

0.008707451

1.643967

201.5

37

36.52048102

469.9

0.0007955

0.010102793

2.035713

216.1

36.5

35.94201162

532.9

0.00078475

0.011457286

2.475919

229.1

36

35.43504305

468

0.000774

0.010061944

2.305191

244

35.5

34.86322018

528.95

0.00076325

0.011372361

2.774856

257.2

35

34.36475544

462

0.0007525

0.009932944

2.554753

273.5

34.5

33.75957169

562.35

0.00074175

0.012090457

3.30674

287.2

34

33.25961715

465.8

0.000731

0.010014644

2.876206

300.7

33.5

32.77460276

452.25

0.00072025

0.00972332

2.923802

314.2

33

32.29705636

445.5

0.0007095

0.009578196

3.009469

330.12

32.5

31.74334492

517.4

0.00069875

0.011124038

3.672267

346.8

32

31.17396744

533.76

0.000688

0.011475776

3.979799

361

31.5

30.69777414

447.3

0.00067725

0.009616896

3.471699

376

31

30.20312349

465

0.0006665

0.009997444

3.759039

393.5

30.5

29.6367075

533.75

0.00065575

0.011475561

4.515633

409.8

30

29.11928205

489

0.000645

0.010513441

4.308408

427.6

29.5

28.5652049

525.1

0.00063425

0.011289587

4.827427

442.6

29

28.10700752

435

0.0006235

0.009352448

4.139393

458

28.5

27.64473862

438.9

0.00061275

0.009436297

4.321824

478.2

28

27.0506601

565.6

0.000602

0.012160332

5.815071

493.17

27.5

26.61920895

411.675

0.00059125

0.008850963

4.365029

513.6

27

26.04224698

551.61

0.0005805

0.011859548

6.091064

532.7

26.5

25.51496315

506.15

0.00056975

0.010882164

5.796929

552

26

24.99378747

501.8

0.000559

0.010788639

5.955329

569.6

25.5

24.52849291

448.8

0.00054825

0.009649146

5.496153

588.3

25

24.04432324

467.5

0.0005375

0.010051194

5.913117

606.7

24.5

23.57797153

450.8

0.00052675

0.009692146

5.880225

629.2

24

23.02094759

540

0.000516

0.011609935

7.304971

650.3

23.5

22.51151113

495.85

0.00050525

0.010660715

6.932663

671.7

23

22.00729833

492.2

0.0004945

0.010582241

7.108091

693.4

22.5

21.50852569

488.25

0.00048375

0.010497316

7.278839

713.7

22

21.05306117

446.6

0.000473

0.009601846

6.852838

740.5

21.5

20.46780673

576.2

0.00046225

0.01238823

9.173485

760.6

21

20.04054648

422.1

0.0004515

0.009075099

6.90252

786.3

20.5

19.50843301

526.85

0.00044075

0.011327211

8.906586

809.4

20

19.04338277

462

0.00043

0.009932944

8.039725

834.5

19.5

18.55187153

489.45

0.00041925

0.010523116

8.78154

862.3

19

18.02378585

528.2

0.0004085

0.011356236

9.792483

887.4

18.5

17.56127028

464.35

0.00039775

0.009983469

8.85933

915.3

18

17.06257888

502.2

0.000387

0.010797239

9.882713

942.4

17.5

16.5932598

474.25

0.00037625

0.010196318

9.60901

972.4

17

16.09048641

510

0.0003655

0.010964938

10.66231

1001.1

16.5

15.62545755

473.55

0.00035475

0.010181268

10.19247

1031.6

16

15.14779148

488

0.000344

0.010491941

10.82349

1064.6

15.5

14.649489

511.5

0.00033325

0.010997188

11.70761

1096.1

15

14.19114823

472.5

0.0003225

0.010158693

11.13494

1129.9

14.5

13.71745223

490.1

0.00031175

0.010537091

11.90586

1164.2

14

13.25519836

480.2

0.000301

0.010324242

12.01948

1200.7

13.5

12.78290512

492.75

0.00029025

0.010594066

12.72029

1238.4

13

12.3154473

490.1

0.0002795

0.010537091

13.04913

1278.2

12.5

11.84344461

497.5

0.00026875

0.01069619

13.67187

1318.6

12

11.38590739

484.8

0.000258

0.010423141

13.74395

1361

11.5

10.92803079

487.6

0.00024725

0.010483341

14.26783

1403

11

10.49594965

462

0.0002365

0.009932944

13.93592

1452.8

10.5

10.00993463

522.9

0.00022575

0.011242287

16.33279

1501.9

10

9.557229631

491

0.000215

0.010556441

15.85472

1553.1

9.5

9.111599587

486.4

0.00020425

0.010457541

16.24161

1606.5

9

8.673932717

480.6

0.0001935

0.010332842

16.59971

1664.1

8.5

8.231006842

489.6

0.00018275

0.010526341

17.51688

1772.8

8

7.470971702

869.6

0.000172

0.018696295

33.14479

1784.2

7.5

7.396626434

85.5

0.00016125

0.00183824

3.279787

1849

7

6.992048991

453.6

0.0001505

0.009752345

18.03209

1921

6.5

6.576484751

468

0.00013975

0.010061944

19.32899

2070

5.5

5.818364213

819.5

0.00011825

0.017619151

36.47164

2170

5

5.377696367

500

0.0001075

0.01074994

23.32737

2273

4.5

4.973776277

463.5

9.6749E-05

0.009965194

22.65089

2391

4

4.566152904

472

8.6E-05

0.010147943

24.26373

2531

3.5

4.149047932

490

7.525E-05

0.010534941

26.66394

2704

3

3.718236566

519

6.45E-05

0.011158437

30.17241

2984

2.5

3.17935888

700

5.375E-05

0.015049916

44.90895

3763

2

2.339727553

1558

4.3E-05

0.033496812

126.0485

5400

1.8

1.848318453

2946.6

3.87E-05

0.063351544

342.0983

Integral[ C(t)dt ] Integral[ E(t)dt ] Residence Time

46511.889 1 1231.0796

Graph of C (t) vs time  –

50 45 40 35

   y    t    i    v    i    t    c    u    d    n    o    C

30 25

Observed Theoritical

20 15 10 5 0 0

10 00

20 00

30 00 Time

4 00 0

50 00

6 00 0

RESULT: The residence time for the flow reactor is observed to be 1231.08 seconds.

CONCLUSION: For a CSTR initially the concentration shoots up very fast and reaches a maximum and then starts decaying exponentially. The reason for the instant shoot up is that both the inlet and outlet pipes are at the same level and hence some of tracer injected gets immediately removed from the reactor and the rest is caught up in the mixture and exists slowly. In a CSTR it is very much possible that a volume such as dead volume develops where some of the material is trapped and is never able to exit from the reactor. This volume might be found at one of  the corners of the reactor.