Chemical engineering volume 3 coulson and richardson’s

3.3.5 3.3.6 Catalyst de-activation and poisoning 3.5 Chemical kinetics of heterogeneous catalytic reactions 3.5.1 Adsorption of a reactant as the rate determining step 3.5.2 Surface reac

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reactions Reactor yield

1.10.1 Types of multiple reactions

1.10.2Yield and selectivity

1.10.3 Reactor type and backmixing

1.10.4 Reactions in parallel

1.10.5 Reactions in parallel-two reactants

1.10.6 Reactions in series

1.10.7 Reactions in series-two reactants

I.12 References

1.13 Nomenclature

2 Flow Characteristics of Reactors-Flow Modelling

2.1.1 Types of non-ideal flow patterns

2.1.4 Application of tracer information to reactors

2.3.2 Basicdifferential equation

2.3.3 Response to an ideal pulseinput of tracer

2.3.4 Experimental determination of dispersion coefficient from a pulseinput

2.3.5 Further development of tracerinjection theory

2.3.6 Values of dispersion coefficientsfrom theory and experiment

2.3.7 Dispersedplug-flow model with first-order chemical reaction

2.3.8 Applications and limitations of the dispersedplug-flow model

Models involving combinations ofthe basic flow elements

Mass transfer within porous solids

3.2.1 The effectivediffusivity

Chemical reaction in porous catalyst pellets

3.3.1

3.3.2

3.3.3

Effect ofintraparticle diffusion on experimental parameters

Non-isothermal reactionsin Dorous catalvst Dellets

43

43 44 47 49 50 51 52

52

54 55 56

57

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68

68 68

71

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71 71 73 75 78 80

80

83 84 88

93

96 98 102 104 105 105 106

108 108

111 112 115 116 122

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<.

3.3.5

3.3.6 Catalyst de-activation and poisoning

3.5 Chemical kinetics of heterogeneous catalytic reactions

3.5.1 Adsorption of a reactant as the rate determining step

3.5.2 Surface reaction asthe rate determining step

3.5 3 Desorptionof a product as the rate determining step

3.5.4 Rate determining steps for other mechanisms

3.5.5 Examples of rate equations forindustrially important reactions

3.6 1 Packedtubular reactors

3.6 2 Thermal characteristics of packedreactors

3.6.3 Fluidised bed reactors

3.7.2 Single particle unreacted core models

3.7 Gas-solidnon-catalytic reactors

4 Gas-Liquid and Gas-Liquid-Solid Reactors

4.1 1 Gas-liquid reactions

4 I 4 Choiceof a suitable reactor

4.1 7 High aspect-ratio bubble columns and multiple-impeller agitated tanks

4.1.8 Axial dispersion in bubble columns

4.1.9 Laboratory reactors forinvestigating the kinetics of gas-liquid reactions 4.2.I Gas-liquid-solid reactions

4.2.2 Mass transfer and reaction steps

4.2 3 Gas-liquid-solid reactor types: choosingareactor

The biological world and ecology

Biologicalproducts and production systems

151 151

172

180 181 182

183

186 190 190 192 196 196 196 196 197

202

204 205 216

218

223 229

229

230 231 235

248

248 249

252

252 254 255

256

257 259

260

262 265 269

270

5.3 Chemical composition of cells

5.3.2 Proteins

5.3.3 Physical properties of proteins

5.3.4 Protein purification and separation

5.4.4 Derivationof the Michaelis-Menten equation

5.4.5 The significance ofkinetic constants

5.4.6 The Haldane relationship

5.4.7 Transformationsof the Michaelis-Menten equation

5.4.8 Enzyme inhibition

5.4 9 The kinetics oftwo-substrate reactions

5.4.10 The effects of temperature and pHon enzyme kinetics and enzyme

5.6.1 Mutation and mutagenesis

5.6.2 Genetic recombination in bacteria

5.6.3 Genetic engineering

5.6.4 Recombinant DNA technology

5.6.5 Genetically engineered products

Cellularcontrol mechanisms and their manipulation

5.7 I The control of enzyme activity

5.7 2 The control of metabolicpathways

5.7.3 The control of protein synthesis

5.10.1 Effect ofexternal diffusion limitation

5.10.2 Effect of internal diffusion limitation

5.1 I.1 Enzyme reactors

5.11.2Batch growth of micro-organisms

5.11.3 Continuous culture of micro-organisms

Types of reactionsin metabolism Energetic aspects of biological processes

5.6 Strainimprovement methods

277

277 278 278

278

278 279 279 279 281

282

285 286 287

289

29I 294

295

298 298 298

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309

315 315 316

318

320 320

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326 326 327

334

337 339

342

342 345 352

354

356 360

364

364 365 367

386

386 393

5.13 Non-steady state microbial systems

5.13.I Predator-prey relationships

rapid-equilibrium assumption

Appendix 5.4 TheHaldane relationship

Appendix 5.5 Enzyme inhibition

402

405 405

409

410 410 416

6 Sensors for Measurement and Control

6.1Introduction

6.2 1 Methods dependent on relationship between pressure drop and flowrate

6.2.6 Flow profile distortion

6.3 2 Elastic elements

6.3.3

6.3.4 Differential pressure cells

6.4 The measurement of temperature

6.4 1 Thermoelectric sensors

6.4 2 Thermalradiation detection

6.5 The measurement of level

6.5 2 Techniquesusing hydrostatic head

6.5 3 Capacitivesensing elements

6.7. I Off-line measurement of viscosity

Electric transducers for pressuremeasurement

Radioactive methods (nucleonic level sensing)

Other methods oflevel measurement

6.6

The chromatograph as an on-line process analyser

418

419 421

425

431 431 433

437

437 438

438

439 445 448

448

449 452

452

454 454 463

465

466 468

473

478 479 480

481

482 484

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484 488 489

489

493 495

497

503 511 515

516

6.8 6 The detection ofwater 519

6.9.2 Thesampling of multiphase systems (isokinetic sampling) 528

6.10 The static characteristics of sensors

6.I1Signal conditioning

7.2 1 The block diagram

7.2 2 Fixed parameterfeedback control action

7.2.3 Characteristics ofdifferent control modes-offset

7.3 Qualitative approaches to simple feedbackcontrol system design

7.7 Transferfunctions of fixed parameter controllers

7.7 1 Ideal controllers

7.7 2 Industrial three term controllers

Responseof control loop components to forcing functions

7.8 I Common types offorcing function

7.8 2 Response to stepfunction

7.8.3 Initial and final value theorems

7.8 4 Response to sinusoidal function

7.8 5 Response to pulse function

7.9 Transfer functions of feedback control systems

7.9 1 Closed-looptransfer function between C and R

The degrees of freedom approach

Linearsystems and the principle of superposition

The polesand zeros of a transfer function

7.5

7.8

560

560 560 562

564

566 570

571

573

575 576 577

579

579 579

579

583 589 592

593

593 594

594

594 597 600

600

603 605

608

608

7.9.2 Closed-loop transfer function between C and V

7.9 3 Calculation of offsetfrom the closed-loop transfer function

7.9 4 The equivalent unity feedback system

7.10 1 The characteristic equation

7.10 3 Destablising a stable processwith a feedback loop

7.10.5 The Nyquist stability criterion

7.10.6 The log modulus (Nichols) plot

7.1 1.2 Process reaction curve methods

7.1I.3Direct search methods

7.12 2 Series compensation

7.14 Feed-forwardand ratio control

7.10 System stability and the characteristic equation

7.11 Common proceduresfor setting feedback controller parameters

7.14 1 Feed-forward control

7.14.2 Ratio control

7.15MIMO systems-interaction and decoupling

7.15.1 Interaction between control loops

7.15.2Decouplers and their design

7.16.1Linearisation using Taylor\342\200\231sseries

7.16.2 The describing function technique

7.17 1 Sampled data (discretetime) systems

7.17 2 Block diagram algebra for sampled datasystems

7.17 3 Sampled data feedback controlsystems

7.17 4 Hold elements (filters)

7.17.5 Thestability of sampled data systems

7.17 6 Discretetime (digital) fixed parameter feedback controllers

7.17 8 Responsespecification algorithms

7.18 1 Scheduled (programmed) adaptive control

7.18.2 Model reference adaptive control (MRAC)

7.18.3 Theself-tuning regulator (STR)

7.19 Computer control of asimple plant-the operator interface

7.19 1 Directdigital control (DDC) and supervisory control

7.19.2 Real time computer control

7.19 3 System interrupts

7.19 4 The operator/controller interface

7.20 2 Design ofdistributed computer control systems

7.20.3 DCCShierarchy

7.20.4 Data highway (DH) configurations

7.20 5 The DCCS operator station

7.20 6 System integrity and security

7.20 7 SCADA (Supervisory control and dataacquisition)

613 614 617 619

625

632 632 634

635

638 638

638

640 645 646

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653

654 658 660

661

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675 677 679

681

684 686

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692 692

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696 696 698

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698 700

703

703 708 708

709

709 711

7.22 Regulators and actuators (controllersand control valves)

7.22 1 Electronic controllers

7.22 2Pneumatic controllers

7.22 3 The control valve

7.22 4 Intelligent control valves

715

719 724

726

726 726 729

729

731

737 750

753

xiv PREFACE TO THIRDEDITION

various in-line techniques for measurement ofthe process variables which constitute

the essential inputs to the controlsystem of the plant The last chapter gives an

updated treatment of the principles and applications of process controland

concludes with a discussion of computer control of processplant.

Department of Chemical Engineering

PREFACE TO THE FIRSTEDITION xvii engineering problems forms the subject of a chapter Parallelwith the growth in

complexity of chemical plants has developedthe need for much closer control of

the authors are present or past members of the staff of the Chemical Engineering Department ofthe University College of Swansea W.J Thomas isnow at the Bath

University of Technology and J M.Smithis at the Technische Hogeschool Delft.

J M.C J.F.R D.G.P.

2 CHEMICAL ENGINEERING

(b) The physical condition of the reactants at theinlet to the reactor Thus, the

basic processing conditionsin terms of pressure,temperature and

specified as part of the original processdesign

Subsequently, the aim is to reach logical conclusionsconcerning the following

(a) The overall size of the reactor, its general configuration and the more important dimensionsofany internal structures.

(b) The exact composition and physical conditionofthe products emerging from

the reactor The composition ofthe products must of course lie within any limits set in the original specification of the process.

(c) Thetemperatures prevailing within the reactor and any provision which must

be made for heat transfer.

with the flow of the reaction mixture.

principal features ofthe reactor:

1.1 1 Byproducts and their Economic Importance

important question of whether any byproducts are formed in the reaction.

Obvious-ly, consumption of reactants to give unwanted,and perhaps unsaleable,byproducts

is wasteful and will directly affect the operating costsofthe process Apart from

this, however, the nature of any byproducts formed and their amounts must be

known sothat plant for separating and purifying the products from the reaction may be correctly designed The appearance ofunforeseen byproducts on start-up of

a full-scale plant can beutterly disastrous Economically, although the cost of the

reactormay sometimes not appear to be great comparedwith that of the associated

separation equipment such asdistillation columns, etc., it is the composition of the mixture of products issuing from the reactor which determines the capitaland

operating costs of the separation processes.

For example,in producing ethylene\342\200\230\342\200\235together with several other valuable

hydro-carbons like butadienefrom the thermal cracking of naphtha, the design of the

tubular reactor in which the conditions arevery carefully controlled As we shall see later, the designof a reactoritself can affect the amount of byproducts formed

and thereforethe size of the separation equipment required The design ofa reactor and its mode of operation can thus have profound repercussions on the remainder

of the plant.

In the following pages we shall see that reactor design involves all the basic

principles of chemical engineeringwith the addition of chemical kinetics Mass

transfer, heat transfer and fluid flow are all concerned and complications arise

and the reaction itself In a reactor it is essential to weigh up all the

various factors involved and,by an exercise of judgement, to place them in their

what is seen to be the most troublesomestep Itmay be the chemical kinetics; it

the need to ensure safe operation Forexample, in oxidising naphthalene or

o-xylene to phthalicanhydride with air, the reactor must be designed so that

ignitions, which are not infrequent, may be rendered harmless.Thetheory of reactor design is being extended rapidly and more precisemethods for detailed

successful,the major decisions taken at the outset must be correct Initially, a careful appraisal of the basic roleand functioning of the reactor is required and at this

stage the application of a little chemical engineering commonsensemay be invaluable.

1.2 CLASSIFICATION OF REACTORSAND CHOICE OF

1.2 1 Homogeneousand HeterogeneousReactors

heterogeneous In homogeneous reactors only one phase, usually a gas or a liquid,

is present.If morethan one reactant is involved, provision must of coursebe made

for mixing them together to form a homogenouswhole.Often, mixing the reactants

is the way of starting off the reaction, although sometimes the reactants are mixed and then brought to the required temperature.

In heterogeneous reactorstwo, or possibly three, phases are present, common examplesbeinggas-liquid, gas-solid, liquid-solid and liquid-liquid systems In cases

chemical reaction itself may be truly heterogeneous, but this is not necessarily so.

In a gas-solidcatalytic reactor, the reaction takes place on the surface of the solid

to dissolve the gasin the liquid where it then reacts homogeneously;the reaction is thus homogeneous but the reactor is heterogeneousin that it is required to effect contact between two phases-gas and liquid Generally, heterogeneous reactors

exhibit a greatervariety of configuration and contacting pattern than homogeneous

reactors.Initially, therefore, we shall be concerned mainly with the simpler

homo-geneous reactors, although parts of the treatment that follows can be extendedto heterogeneous reactorswith little modification.

4 CHEMICALENGINEERING

especially in large-scale operation, where considerable advantages accrueby rying out a chemical reaction continuously in a flow reactor.

car-Figure 1.1 illustrates the two basic types of flow reactor whichmay be employed.

In the tubular-flow reactor (b) the aim is to pass thereactants along a tube so that

there is aslittle intermingling as possible between the reactants entering the tube and the productsleaving at the far end In thecontinuous stirred-tank reactor (C.S.T R ) (c) an agitator isdeliberately introduced to disperse the reactants thoroughly into the reaction mixtureimmediately they enter the tank The product streamisdrawn

composition as the contentsof the tank In someways, using a C.S.T.R., or backmix reactor as it is sometimes called, seemsa curious method of conducting a reaction

becauseas soonasthe reactants enter the tank they are mixed and a portionleaves

employ anumber of stirred tanks connected in series as shownin Fig 1 Id.

The stirred-tank reactor is by its nature well suitedtoliquid-phase reactions The

choice for gas-phase reactions, even on a small scale.Usually the temperature or

catalyst is chosen sothat the rate of reaction is high, in which case acomparatively

small tubular reactor is sufficient to handle a highvolumetric flowrate of gas A few gas-phase reactions, examplesbeing partial combustion and certain chlorinations, are carried outin reactors which resemble the stirred-tank reactor; rapid mixingis

motion instead of by mechanical means.

(c) Continuous stirred-tank reactor (C.S T.R.)or\342\200\234backmixreactor\342\200\235

C.S.T R sin series as used

REACTOR DESIGN-GENERAL PRINCIPLES 5 1.2.3 Variations in Contacting Pattern - Semi-batch

Operation Another question which should be asked in assessingthe most suitable type of

reactor is whether there is any advantage to be gained by varying the contacting pattern Figure 1.h illustrates the semi-batch mode of operation The reaction

vessel hereisessentially a batch reactor, and at the start of a batchit is charged with one of the reactants A However, the second reactant B is not all addedat once,

way to carry outmany reactions For example, if a liquid has to be treatedwith a

at the rate atwhich it is used up in the reaction Another case is wherethe reaction

example, can be conveniently controlled by regulating the rate of addition of the

will be determinedby the rate of heat transfer.

A characteristic of semi-batch operation is that the concentration C, of the reactant addedslowly, B in Fig 1 2, is lowthroughout the course of the reaction.

reaction is favoured by a low value of C, Thus, the semi-batch method may be chosen for a further reason, that of improving the yield of the desiredproduct, as

Summarising, a semi-batch reactormay be chosen:

(a) to react a gaswith a liquid,

(b) to control ahighly exothermic reaction, and

(c) to improve productyield in suitable circumstances.

In semi-batch operation, whenthe initial charge of A has been consumed,theflow

of B is interrupted, the products discharged, and the cyclebegun againwith a fresh

retained but the reactorsystem designed for continuous flow of both reactants In

end

FIG.1 2 Examples of possiblevariations in reactant contacting pattern

(a) Semi-batchoperation

(b)Tubular reactor with divided feed

(in each casethe concentration of B, C,, islow throughout)

Products

6 CHEMEALENGINEERING

the tubular flow version (Fig 1.2b)and the stirred-tankversion (Fig 1 24, the feed

both cases C, is low throughout.

1.2.4 InfluenceofHeat of Reaction on Reactor Type

Associated with every chemical change there is a heat of reaction, and only in a

reactionoften has a major influence on the design of a reactor.With a strongly

mixture will take place unless provision is made for heat to be transferred as the reaction proceeds.It isimportant to try to appreciate clearly the relation between

reactionmixture; quantitatively this is expressed by an enthalpy balance (Section 1.5).Ifthe temperature of the reaction mixture is to remain constant (isothermal

must be transferred to or from the reactor If no heat is transferred (adiabatic operation),the temperature of the reaction mixture will rise or fall as the reac-

tion proceeds In practice, it may be most convenient to adopt apolicy intermediate

if strictly isothermal operation would involve an elaborate and costly control scheme.

(a) What is the heat of reaction?

temperature range can only be roughly specified;often the lower temperature limit

is determined by the slowing down of the reaction, and the upper temperature

mixturemay be permitted to vary?

Adiabatic Reactors

If it is feasible, adiabatic operation is to bepreferred for simplicity of design.

Figure 1.3 shows the reactorsection of a plant for the catalytic reforming of

petroleumnaphtha; this is an important process for improving the octane number

of gasoline The reforming reactions are mostly endothermic so that in adiabatic

reactor were made as one singleunit, this temperature fall would be too large, i.e

occur, or the reactionwould be incomplete because the temperature near the outlet would be too low.Theproblem is conveniently solved by dividing the reactor into three sections.Heat issupplied externally between the sections, and the intermediate

temperatures areraised sothat each section of the reactor will adiabatically.

REACTOR DESIGN-GENERALPRINCIPLES 7

FIG.1 3 Reactor system of apetroleum naphtha catalytic reforming plant. (The reactor

is divided into threeunits each of which operatesadiabatically, the heat required being

suppliedat intermediate stages viaan external furnace)

temperature can be adjusted independently of the inlet temperature; thus an optimum temperaturedistribution can be achieved In this example we can see that

the furnaces where heat istransferred and the catalytic reactors are quite separate

generally provides easeof control,flexibility of operation and often leads to a good overallengineering design.

Reactorswith Heat Transfer

If the reactor does not operate adiabatically, then its design must include provision for heat transfer Figure 1.4 shows some ofthe ways in which the contents

of a batch reactormay be heated or cooled In a and b the jacketand the coils form

part of the reactoritself, whereas in c an external heat exchangeris usedwith a recirculating pump If one of the constituentsof the reactionmixture, possibly a

FIG 1 4.Batch reactors showing different methods ofheating or cooling

(a) Jacket

(b) Internal coils (c) External heat exchangers

solvent, is volatile at the operating temperature,the external heat exchanger may be

Figure 1.5shows ways of designing tubular reactors to includeheattransfer If

to reactorvolume will be large, and the reactor will lookvery much like a heat

exchanger as in Fig 1.56 Ifthe reaction has to be carried out at a high temperature

and is strongly endothermic (for example, the productionofethylene by the thermal

cracking of naphtha or ethane-see alsoSection 1.7.1, Example 1.4), the reactor will

be directly fired by the combustion of oil orgas and will look like a pipe furnace

If a reaction requiresa relatively high temperature before it will proceed at a

reasonable rate, the products of the reaction will leave the reactor at a high temperature and, in the interestsof economy,heatwill normally be recovered from

them Since heat must besupplied to the reactants to raise them to the reaction temperature,a commonarrangement is to use the hot products to heat the incoming feed asshown in Fig 1.6~.If the reaction is sufficiently exothermic, enough heat

will be produced in the reactionto overcomeany losses in the system and to provide

used to describe such a systemwhich is completely self-supporting in its thermal

energy requirements.

The essential feature of an autothermal reactor systemis thefeedback of reaction heat to raise the temperatureand hence the reaction rate of the incoming reactant

stream Figure 1.6shows a number of ways in which this can occur.With a tubular

shownin Fig 1.6u, orby internal heat exchange as in Fig 1.66 Both of these are

Chapter3, Section 3.6 2.Being catalytic the reaction can only take place in that

of the reactor which holds the catalyst, so the has the form

in reactor

Position

in heat exchanger

10 CHEMICALENGINEERING

indicated alongside the reactor Figure I 6c showsa continuousstirred-tank reactor

products andrapid reaction occurs The combustion chamber of a liquidfuelled

rocket motor is a reactor of this type, the productsbeinghot gaseswhich are ejected

at high speed Figure 1.6dshows another type of combustion process in which a laminar flame of conical shape is stabilised at the orificeof a simplegas burner.In

opposite to theflow of the cold reaction mixture.

Another feature of the autothermal system is that, although ultimately it is

has to beignited by raising some of the reactants to a temperaturesufficiently high for the reaction to commence Moreover,a stable operatingstatemay be obtainable only over a limited range of operating conditions.This question of stability is

discussed further in connectionwith autothermal operation of a continuous tank reactor (Section 1.8 4).

The choice of temperature, pressure,reactantfeed rates and compositions at the

inlet to the reactor isclosely bound up with the basic design of the process as a whole.In arriving at specifications for these quantities, the engineeris guidedby

knowledge available on the fundamental physical chemistry of the reaction.Usually

he will also have results of laboratoryexperimentsgiving the fraction of the reactants converted and the productsformed under various conditions Sometimes he may have the benefit of highly detailed information on the performance of the process

from a pilot plant, or even a large-scaleplant.Although such direct experience of

reactor conditions may be invaluable in particular cases, we shall here be concerned

1.3.1.Chemical Equilibria and Chemical Kinetics

The two basic principlesinvolved in choosing conditions for carrying out a

reaction arethermodynamics, under the heading of chemical equilibrium, and

chemical kinetics.Strictly speaking, every chemical reaction is reversible and, no matter how fast a reaction takes place, it cannot proceed beyond the point of

chemicalequilibrium in the reaction mixture at the particular temperatureand

pressure concerned Thus, under any prescribed conditions, the principleof

other hand, the principle of chemicalkineticsdeterminesatwhat rare the reaction will proceed towards this maximum extent If the equilibriumconstantisvery large, then for all practical purposes the reactionmay be said to be irreversible However, even when a reactionis claimedto beirreversible an engineer would be very unwise not to calculate the equilibrium constant and check the position of equilibrium,

In deciding processconditions, the two principles of thermodynamic equilibrium

and kinetics needto beconsidered indeed, any complete rate equation for

REACTOR DESIGN-GENERAL PRINCIPLES 11

a reversible reaction will includethe equilibrium constant or its equivalent (see

Section 1.4.4)but complete rate equations are not always available tothe engineer.

take placeat a reasonablerate (in the presence, of course, of any catalyst which may have been developedfor the reaction)? The next step is to calculatevalues of

reader unfamiliar with this subject should consult a standard textbook\.)") The

by the relation:

where-AH is the heat of reaction The equilibrium constant is then used to

temperature,pressure and reactant compositions which appear to be most suitable 1.3.2 Calculation ofEquilibrium Conversion

mixture and, in general, on the pressure If the equilibrium constant isvery high,

however, it may be possible to obtain acceptable conversionsonly by using high or

low pressures Twoimportant examples are the reactions:

CzH4 + H2O *

C2HSOH

both of which involve a decreasein the number of moles as the reaction proceeds,

and therefore high pressures are used to obtain satisfactory equilibrium conversions Thus,in those cases in which reversibility of the reaction imposes a serious

limitation, the equilibrium conversionmust be calculated in order that the most

be seen in detail in the following example of the styrene process.A study of the

design of this process is alsovery instructive in showing how the basic features of the reaction,namely equilibrium, kinetics, and suppression of byproducts, have all

Let us supposethat we are setting out from first principles to investigate the dehydrogenation of

There is available a catalyst which will give a suitablerate of reaction at 560OC.At this temperature the

constant for the reaction aboveis:

the fractional conversion at equilibrium.

Solution

This calculation requires not only the use of theequilibrium constant, but also amaterial balance over the reactor Toavoid confusion, it is aswell to set out this material balance quite clearly even in this

First it is necessary to choose abasis; let this be I mole of ethylbenzene fed into the reactor: afraction

4 of thiswill be converted atequilibrium. Then, from the abovestoichiometric equation, a, mole styrene

pressure at the outlet ofthe reactor be Pwhich we shall later setequal to I bar.

TOTAL I+a,

-Temperature 560\302\260C= 833 K Pressure P (Ibar = 1.0 x Id Nlm')

1+a, LP

I +a,

Since for I mole of ethylbenzene entering, the total number of moles increases to I + a,, the mole

At a total pressure P,the partial pressures are given in column c (assuming ideal gasbehaviour) If the reaction mixture is at chemical equilibrium, these partial pressures must satisfy equation A above:

aP \"P

bar is only 30 percent; this is not very satisfactory (although it ispossible in some processes to operate

at low conversions by separating and recycling reactants) Ways of improving this figure are now sought.

Notethat equation B above showsthat as P decreases a, increases; this is thequantitative expression

of Le Chatelier's principle that, because the total number of moles increases in the reaction, the

decomposition ofethylbenzene is favoured by a reduction in pressure There are, however, disadvantages

in operating such a processat subatmospheric pressures One disadvantage isthat any ingress of air through kaks might result in ignition A bettersolution in this instance isto reduce the partial pressure

by diluting the ethylbenzene with an inert gas, while maintaining the total pressure slightly in excess of atmospheric Theinert most suitable forthis is steam: onereason for this isthat it can be

REACTOR DESIGN-GENERALPRINCIPLES 13 condensed easily in contrast to a gas such as nitrogen which would introduce greater problems in separation.

Part (ii)

with steam in the ratio 15 molessteam : 1 mole ethylbenzene, determine the new fractional conversion atequilibrium a:.

Solution

Again we setout the material balance in full, the basis being 1 moleethylbenzene into the reactor.

Temperature560\302\260C= 833 K PressureP(Ibar =I.Ox Id N/m2)

ThuswhenP=1bar,a: = 0.70;i.e the maximum possible conversion hasnow been raised to 70 per cent.

increasein ethylbenzene conversion The optimum steam:ethylbenzene ratio is thus determinedby an economic balance.

(-AH)=

worked out for this process (Fig 1.7).Most of thwteam, 90 percent of the total used, isheated separately from the ethylbenzene and to a higher temperature (71OOC)than is at the inkt tothe

ethylbenzene Operating pressure 1bar.Conversion per pass 0.40.Overall relative yield 0.90

reactor Theethylbenzene is heated in the heat exchangersto only 520\302\260Cand is then rapidly mixed with the hotter steamto give a temperature of 630'Cat the inlet to thecatalyst bed If the ethylbenzenewere

heated to 63OOC moreslowly by normal heat exchangedecomposition and coking of the heat transfer

the steam used is passed through the heat exchanger with the ethylbenzene The presence of a large

proportion of steam in the reactor also prevents cokedeposition on the catalyst. By examining the equilibrium constant ofreactions involving carbon such as:

C6Hj.CH2.CHI *

C+H2O+CO+H2

it may be shown that coke formation is not possibleat high steam: ethylbenzene ratios.

with the equilibrium conversion of 0.70 This actual conversion of 0.40 isdetermined by the role ofthe

reaction over the catalyst at the temperature prevailing in the reactor (Adiabaticoperation means that the temperaturefalls with increasing conversion and the reactiontends to be quenched at the outlet.) The

unreacted ethylbenzene is separated and recycledto the reactor The overallyield in the process, i.e moles

of ethylbenzene transformed into styrene per moleofethylbenzene supplied, is 0.90, the remaining 0.10 being consumed in unwanted side reactions Noticethat the conversion per passcould be increased byincreasing the temperature at theinlet to the catalyst bedbeyond 630\"C, but the undesirable sidereactions

would increase, and the overall yield of the process would fall The figure of 630\302\260Cfor the inlet

temperature is thus determined by an economic balance between the cost of separating unreacted ethylbenzene (which ishigh if the inlet temperatureand conversion per pass are low),and the cost of ethylbenzene consumedin wasteful side reactions (which is high if the inlet temperature is high).

1.3.3 Ultimate Choice of Reactor Conditions

can exercisea of ingenuity in reactor design The advantages conferred

REACTOR DESIGN-GENERAL PRINCIPLES 15 the steam may be summarisedas follows:

at sub-atmospheric pressures;

ethylbenzene heaters.

(a) itlowers the partial pressure of the ethylbenzenewithout the need to operate

(b) it provides an internal heat source for the endothermicheat of reaction,

As the styrene process shows, it is not generally feasible to operate a reactorwith

a conversion per pass equal to the equilibrium conversion The rate of a chemical reaction decreasesas equilibrium is approached, so that the equilibrium conversion

can only be attained if either the reactor is very large orthe reaction unusually fast.

The size of reactorrequired to give any particular conversion, which of course cannot exceedthe maximum conversion predicted from the equilibrium constant, is calculatedfrom the kinetics of the reaction For this purposewe need quantitative data on the rate of reaction,and the rate equations which describe the kineticsare consideredin the following section.

If there aretwo or more reactants involved in the reaction, both can beconverted

completely in a single pass only if they are fed to the reactor in the stoichiometric proportion.In many cases, the stoichiometric ratio of reactants may be the best,

but in some instances, where onereactant (especially water or air) is very much cheaper than the other, it may be economically advantageous to useit in excess For

a given size of reactor, the objectis to increasethe conversion of the more costly reactant, possiblyat the expense of a substantial decrease in the fraction of the

cheaper reactant converted Examination of the kinetics of the reaction is required

to determinewhether this can be achieved, and to calculatequantitatively the effects

of varying the reactant ratio. Another and perhaps more common reason for

departing from the stoichiometric proportions of reactants is to minimise the

Ultimately, the final choice of the temperature, pressure, reactant ratio and conversionatwhich the reactor will operate depends on an assessmentofthe overall economics of the process This will take into accountthe costofthe reactants, the cost of separating the products and the costs associated with any recycle streams.

plant In the course of making this economic assessment,a whole series of

cal-culations of operating conditions,final conversion and reactor size may be

these sets of conditionsmay be technically feasible, but the one chosenwill be that

When a homogeneousmixture of reactants is passed into a reactor, eitherbatch

or tubular, the concentrations of the reactants fall as the reaction proceeds.

Experimentally it has been found that, in general, the rate of the reaction decreases

asthe concentrations of the reactants decrease In order to calculatethe size of the

reactor required to manufacture a particular product at a desired overall rate of

16 CHEMICALENGINEERING

production, the design engineer therefore needs to knowhow the rate of reaction at any time or at any point in the reactor depends on the concentrations of the reactants.Sincethe reaction rate varies also with temperature, generally increasing

rapidly with increasing temperature, a rate equation, expressing the rate of reaction

reactor.

1.4.1 Definition of Reaction Rate, Order of Reaction and Rate Constant

Let us consider a homogeneous irreversible reaction:

vAA + v,B + vcC + Products

whereA, B, C are the reactants and vA, vg, vc the corresponding coefficients in the

stoichiometric equation.The rate of reaction can be measured as the molesofA

transformed per unit volume and unit time Thus, if nA is the number of moles of

A present in a volume V of reaction mixture, the rate of reactionwith respect to A

is defined as:

However,the rate of reactioncan alsobe measured as the moles of B transformed

perunit volume and unit time, in which case:

and aB= (Y~/v~)%~; similarly aC= (V~/V,)%,and so on.Obviously, when quoting

a reaction rate, care must betaken to specify which reactant is being considered,

in which the rate of reaction is measured.Appropriate units for %A can be seen quite

clearly from equation 1.2;they are kmol of A/m3s or Ib mol ofA/ft3 s.

concentra-tions of the reactants.Experimentally, it has been found that often (but not always)

CA(=n,/ V) being the molar concentration of A, etc The exponents p, q, r in this

expression arequite often (but not necessarily) whole numbers.When the functional

respect to reactant A, qwith respect to B and r with respect to C The order of the

reactionoverallis (p+ q + r).

The coefficient k in equation 1.4isby definition the rate consrant of the reaction.

units in which it is to be expressed may be inferredfrom the defining equation 1.4.

For example,if a reaction:

A + Products

REACTOR DESIGN-GENERAL 17

behaves as a simplefirst-order reaction, it has a rate equation:

If the rate of reaction is measuredinunits of kmol/m3 s and the concentration

C, in kmol/m3,then k, has the units s-I On the other hand,if the reaction above

behaved as a second-order reactionwith a rate equation:

the units of this rate constant, with 3, in kmol/m3s and C, in kmol/m3, are

chemicalliterature, the rate equation, for say a second ordergasphase reaction may

be written a, = kpP:,where PAis the partial pressure of A and may be measured

in N/m2, bar oreven in mm Hg This form of expressionresults in rather confusing

hybrid units for kp and isnot to be recommended.

If a large excess of one or more of the reactants is used, such that the

reaction,the effective order of the reaction is reduced.Thus,if in carrying out a

reaction which isnormally second-order with a rate equation a,,= k,C, C, an excess

of B is used,then C, remains constant and equal to the initial value CBo.The rate

equation may then bewritten a, = k,C, where kl =k2CB0and the reaction is now

said to be pseudo-first-order.

1.4.2 Influence of Temperature Activation Energy

well represented by the originalequationofArrhenius:

Experimentally, the influence of temperature on the rate constant of a reactionis

termed the activation energy, and d the frequency factor There are theoretical reasonstosuppose that temperature dependence should be more exactly described

energy because in the molecular theory of chemicalkinetics it is associated with an energy barrierwhich the reactants must surmount to form anactivated complex in the transition state Similarly,SP is associated with the frequency with which the

theory, it is associatedwith the frequency of collisions.

Values ofthe activation energy E are in J/kmol in the SIsystem but are usually

quoted in kJ/kmol (or J/mol); using thesevalues R must then be expressed as

kJ/kmol K Formost reactions the activation energy lies in the range 250,000kJ/kmol, which implies a very rapid increase in rate constantwith tempera-

l00OC and has an activation energy of 100,000 kJ/kmol, the reaction rate will be doubled for a temperature riseof 10OC.

Thus, the complete rate equation for an irreversible reaction normally has the form:

rathertrouble-sometohandle mathematically, both by analytical methods and numerical niques In reactor design this means that calculations for reactors which are not

tech-operatedisothermally tend to become complicated In a few cases,useful results can

be obtained by abandoning the exponentialterm altogether and substituting a linear variation of reaction ratewith temperature, but this approach is quite inadequate

1.4 3 Rate Equationsand Reaction Mechanism

One of the reasons why chemical kinetics is an important branch of physical

mechanism The engineerconcernedwith reactor design and development is not

interestedin reaction mechanism per se, but should be aware that an insight into

the mechanism of the reaction can provide a valuable clue to the kind of rate equationto beused in a design problem In the present chapter, it will be possible

to make only a few observations on the subject, and for further information the

The first point which must be made is that the overall stoichiometry of a reaction

is no guide whatsoever to its rate equation or to the mechanism of reaction A

stoichiometric equation is no morethan a material balance; thus the reaction:

KC103+ 6FeS0,+ 3H2S043 KCI + 3Fq(S04),+ 3H20

isin fact second order in dilute solution with the rate of reaction proportional to the concentrationsof Cl0,-and Fez+ions In the general case the stoichiometric

mechanism issimply the interaction between a molecule of Mand a molecule of N,

then the moleculartheory of reaction rates predicts that the rate of this elementary step is proportional to the concentrationof speciesM and the concentration of

species N, i.e it is second orderoverall The reaction is also said to bebimolecular

since two molecules are involved in the actual chemical transformation.

Thus, the reactionbetween H2 and I2 is known to occur by an elementary

H,+I,+2HI and the rate of theforward reaction corresponds to the equation:

%I2 = kf C\"2C*2

For many years the hydrogen-iodine reactionwas quoted in textbooks as being

reactions iodine atoms do occur.

REACTOR DESIGN4ENERAL 19

Whereas in the hydrogen-iodine reaction,atomiciodineplays only a minor part,

in the reaction betweenhydrogen and bromine, bromine and hydrogen atoms are

The kineticsof the reaction arequite different from those of the hydrogen-iodine

reaction althoughthe stoichiometricequation:

chain propagation 1

The rate ofthe last reaction, for example, is proportional to the concentration of

H and the concentration of Br2, i.e it is second order.When the rates of these

elementary steps are combinedinto an overall rateequation, this becomes:

elementary steps This rate equation has adifferent form from the usual type given

by equation 1.4,and cannot therefore be said to have any order because the

definition of order appliesonly to the usual form.

We shallfind that the rate equations of gas-solid heterogeneouscatalytic reactions (Chapter 3) also do not, in general, have the same form as equation 1.4.

said to be rate-determining.The kinetics of the overall reaction thus reflect the

1.4).Themain overall reaction is:

C2H6+CZH, + H2 Although there are complications concerningthis reaction, under most circum-

stances it is first order, the kinetics being largely determinedby the first step in a

20 CHEMICAL ENGINEERING

radical reactions also take placeto a lesserextent leading to the formation of CH, and some higherhydrocarbons among the products.

1.4.4 Reversible Reactions

For reactionswhich do not proceed virtually to completion, it is necessary to include the kinetics of the reverse reaction, orthe equilibrium constant, in the rate equation.

The equilibriumstate in a chemicalreactioncan beconsidered from two distinct

points of view Thefirst is from the standpoint of classical thermodynamics,and

leads to relationships between the equilibrium constantand thermodynamic

calculate equilibrium conversion The second is a kineticviewpoint, in which the

state of chemical equilibriumis regardedas adynamic balance between forward and

reverse reactions; at equilibriumthe rates of theforward reactions and of the reverse reaction are just equal to each other, making the net rate of transformation zero.

9 A+B+M+N 4

species Thehydrolysis of an ester such as ethyl acetate is an example

*

The rate of the forward reaction expressed with respect to A, a+,,is given by

= kfc,,cB, and the rate of the reverse reaction(again expressed with respect to

direction left to right is thus:

Consider a reversible reaction:

%A =%+A -%-A = k/cAcB -krCMCN

(1.10)

kfcAe cBe =krCMeCNe or:

We seefrom the above example that the forward and reverse rateconstants are

REACTOR DESIGN-GENERAL PRINCIPLES 21

turn is related to the thermodynamic free energy, etc.More detailedexamination of

reverse reactionsshows that, to be consistent with the thermodynamic equilibrium

constant, the form of the rate equationfor the reversereactioncannot be completely

phosgene:

The rate ofthe forward reaction is given by = kfCcoCA: This rate equation indicatesthat the chlorine concentration must also appear in the reverse rate equation.Letthis be

we must have:

co+c1, *coa,

But we know from the thermodynamic equilibrium constant that:

1.4.5 Rate Equationsfor Constant-Volume Batch Reactors

In applying a rate equation to a situation where the volume of a given reaction mixture (i.e the density) remains constant throughout the reaction, thetreatment is very much simplified if the equation is expressedin terms of a variable X, which is

of reaction mixture (e.g C,, - C,)at any instant of time r The quantity x isvery

similar to a molar concentration and has the sameunits By simple stoichiometry,

the moles of the other reactantstransformed and products generated can also be

expressedin terms of 2,and the rate of the reaction can be expressedasthe rate of

Vdt and if Vis constant this becomes:

(1.16)

(1.17)

x being the moles ofA which have reacted The general rate equation 1.4may then

be written:

(1.18)

where C,, etc arethe initial concentrations This equation may then in general, at

that the reaction time for any particular conversion can bereadily calculated.

physico-chemical aspects of chemical kinetics''.') Table 1.1 shows a summary of some

ofthe simpler cases; the integrated forms can beeasily verified by the reader if desired One particularpoint of interestis the expressionfor the halj lgeof a reaction t,,*; this is the time required for one half of the reactant in questionto disappear.A first order reaction is unique in that the hufffifeis independentof theinitial concentra- tion of the reactant This characteristicis sometimesused as a test of whether a

1

reactionreally is first order Also since tl,2 = - In 2, a first-order rate constant can

ofthe reaction.

the shapesof graphsofX (or fractional conversion XIC,, = a\") vs.time for reactions

of different orders p Figure 1.8shows a comparison between first and second-order

reactionsinvolving a single reactant only, together with the straight line for a

zero-order reaction.The rateconstants have been taken so that the curves coincide at 50

curve (as indicatedby equation 1.17) It may be seenthat the rate of the order reaction ishigh at first but falls rapidly with increasing time and, compared

second-with first-order reactions, longer reaction times are requiredfor high conversions The zero-order reaction is the only one where the reaction rate does not decrease

with increasing conversion Many biological systems have apparent reaction orders

kl

0

Time t FIG.1.8 Batch reactionsat constant volume: Comparison ofcurves for zero, first and

second-orderreactions

type Rate equation

24 CHEMICAL ENGINEERING

1.4 6 Experimental Determination of Kinetic Constants

The interpretation of laboratory scale experiments to determine orderand rate constant is another subject which is consideredat length in physical chemistry

texts0*') Essentially, it is a process of fitting a rate equation of the general form given by equation 1.4to a setofnumerical data The experiments which are carried out to obtain the kineticconstantsmay be of two kinds, depending on whether the

rate equation is to be used in its original(diflerentiul) form, or in its integrated form

(see Table 1.1).If the differential form is to be used, the experimentsmust be

without its concentration changing appreciably.With batch or tubular reactors this

has the disadvantagein practicethat very accurate measurements of C, must be

for a batch reactor, equation 1.17in finite difference form is 3, =

reactors do not suffer from this disadvantage; by operating in the steady state,

If the rate equation is to be employed in its integrated form, the problem of

in many ways equivalent totaking the design equations and working backwards Thus, for a batch reactorwith constant volume of reaction mixture at constant tempera- ture, the equationslistedin Table 1.1 apply For example, if a reactionis suspected

of being second orderoverall, the experimental results are plotted in the form:

If the points lie closetoa straight line, this is taken asconfirmation that a

second-order equation satisfactorily describesthe kinetics,and the value of the rate constant

Experi-ments using tubular and continuous stirred-tank reactorstodetermine kinetic constants are discussed in the sections describing these reactors(Sections 1.7 4 and 1.8.5).

Unfortunately, many of the chemical processeswhich are important industrially

are quite complex. A complete description of the kinetics of a process, including

consecut-ive manner Often the resultsoflaboratory experiments in such cases are ambiguous and,even if complete elucidation of such a complexreactionpattern is possible, it may

take several man-yearsof experimentaleffort Whereas ideally the design engineer would like tohave a complete set of rate equations for all the reactions involved in

a process, in practicethe data available to him often fall far short of this.

The starting point for the design of any type of reactor is the generalmaterial balance.This material balance can be carried out with respect to one of the reactants