IDEAL REACTOR TYPES - iauq.ac.irdrhojjat.iauq.ac.ir/assets/subdomains/drhojjat/file/Chemical... · Ideal Batch Reactor • It has neither inflow nor outflow of reactants orreactants

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IDEAL REACTOR IDEAL REACTOR TYPESTYPES

B t hBatchPlug flow

Steady-state flow

Mixed flow

Ideal Batch Reactor • It has neither inflow nor outflow of

reactants or products when the reaction isreactants or products when the reaction is being carried out.

• Uniform composition everywhere in the p yreactor (perfectly mixed)

• No variation in the rate of reaction th h t th t lthroughout the reactor volume

Batch Reactor• All reactants are supplied to the reactor at the outset. The

reactor is sealed and the reaction is performed. No addition f l f d d i h iof reactants or removal of products during the reaction.

• Vessel is kept perfectly mixed. This means that there will p p ybe uniform concentrations. Composition changes with time.

• The temperature will also be uniform throughout the• The temperature will also be uniform throughout the reactor - however, it may change with time.

• Generally used for small scale processes.

• Low capital cost. But high labour costs.Low capital cost. But high labour costs.

• Multipurpose, therefore allowing variable product specificationspecification.

Typical LaboratoryTypical Laboratory Glass Batch Reactor

Typical Commercial Batch Reactor

Ideal Mixed Flow Reactor • Normally run at steady state.• Uniformly mixed, same compositionUniformly mixed, same composition

everywhere within the reactor and at the exit.G ll d ll d h i ti l• Generally modelled as having no spatial variations in concentration, temperature, or reaction rate throughout the vessel

CONTINUOUS STIRRED TANK REACTOR (CSTR)BACKMIX REACTORBACKMIX REACTOR

Backmixed, Well mixed or CSTR

U ll l d f

,

•Usually employed for liquid phase

FA0(CA0)

reactions.FA(C )

•Use for gas phase usually in laboratory

(CA)CA

CA

usually in laboratory for kinetic studies.CA

Assumption: Perfect mixing occurs.

Characteristics• Perfect mixing: the properties of the reaction mixture are

uniform in all parts of the vessel and identical to the properties of the reaction mixture in the exit stream (i.e. CA, outlet = CA, tank)

• The inlet stream instantaneously mixes with the bulk of the reactor volume.A CSTR t i d t h t d t t• A CSTR reactor is assumed to reach steady state. Therefore reaction rate is the same at every point, and time independenttime independent.

• What reactor volume, Vr , do we take?– V refers to the volume of reactor contents– Vr refers to the volume of reactor contents.– Gas phase: Vr = reactor volume = volume contents

Liquid phase: V = volume contents– Liquid phase: Vr = volume contents

Cutaway view of aCutaway view of a CSTR/ Batch ReactorReactor

Ideal Plug Flow ReactorN ll t d t t d t t• Normally operated at steady state

• Fluid passes through the reactor with no mixing p g gof earlier and later entering fluid

• No radial variation in concentration• No radial variation in concentration • Referred to as a plug-flow reactor• The reactants are continuously consumed as

they flow down the length of the reactorthey flow down the length of the reactor.

PLUG FLOW REACTOR (PFR), TUBULAR REACTOR

– All fluid element have same residence time.

– Used for either gas phase or liquid phase reactions.

– The plug flow assumptions tend to hold when there is d di l i i ( hi d t hi h fl t Rgood radial mixing (achieved at high flow rates Re

>104) and when axial mixing may be neglected (when the length divided by the diameter of the reactor > 50the length divided by the diameter of the reactor > 50 (approx.))

Selection of Reactors• Batch

• Small scale• Production of expensive products (e g pharmacy)Production of expensive products (e.g. pharmacy)• High labor costs per batch• Difficult for large-scale production

• CSTR : most homogeneous liquid-phase flow reactors• When intense agitation is required• Relatively easy to maintain good temperature controlRelatively easy to maintain good temperature control• The conversion of reactant per volume of reactor is the smallest

of the flow reactors - very large reactors are necessary to obtain high conversionsg

• PFR : most homogeneous gas-phase flow reactors• Usually produces the highest conversion per reactor volume of

any of the flow reactorsany of the flow reactors• Difficult to control temperature within the reactor• Hot spots can occur

S i l h ti

The Rate EquationSuppose a single-phase reaction

The most useful measure of reaction rate for reactant A is then:

In addition, the rates of reaction of all materials are related by:, y

Experience shows that the rate of reaction is influenced by thecomposition and the energy of the materialcomposition and the energy of the material.By energy we mean the temperature (random kinetic energy ofthe molecules), the light intensity within the system (this maythe molecules), the light intensity within the system (this mayaffect the bond energy between atoms), the magnetic fieldintensity, etc.Ordinarily we only need to consider the temperature, so let usfocus on this factor. Thus, we can write

Rate constant, k

• It is strongly dependent on temperature• It is strongly dependent on temperature.– In gas-phase reactions

• It depends on catalysts and may be a function of total pressure.

I li id– In liquid system• It can be a function of total pressure.

It d d i i t th d h i f l t• It may depend on ionic strength and choice of solvent.

H id th t t l• Here, we consider the temperature only.

Rate of reaction and temperatureEmpirical Observations.

It was the Swedish chemist Svante Arrhenius who first suggested thatthe temperature dependence of the specific reaction rate constant, k,could be correlated by an equation of the type:

RTE

Ak

i

could be correlated by an equation of the type:

RTAek constant ratereaction Arrhenius Equation

Where :A= preexponential factor or frequency factor (1/time)A preexponential factor or frequency factor (1/time)E= Activation energy, J/mol or cal/molR= Gas constant, 8.314 J/mol K (or 1.987 cal/mol K)T= Absolute temperature, K

Arrhenius equation has been verified empirically to give thetemperature behaviour of most reaction rate constants (withinp (experimental accuracy) over fairy large experimental ranges.

Activation energy determined experimentally by carrying out theActivation energy determined experimentally by carrying out thereaction at several temperatures. After taking the natural logarithm ofthe Arrhenius equation :

E 1ln k -E/R

TR

EAk 1lnln

1/T

Example 3-1(Fogler) Calculate the activation energy for the first-order decomposition reaction of benzene diazonium chloride to pgive chlorobenzene and nitrogen:

ln kA

1/T

Arrhenius EquationArrhenius Equation

AE 1ln k ln AR T

E/RTAk (T) Ae R T

A ( )

A14017ln k 37.12 Aln k 37.12

T

kJ kJE (14017K)R (14017K) 8.314 116.5mol K mol

16 1A 1 32 10 s A 1.32 10 s

14017K Arrhenius Equation16A

14017Kk (T) 1.32 10 expT

Homogeneous Heterogeneousg g

Elementary Non-elementary

Single Multiple

Chemical Bio-chemicalClassification of Reactions

Reversible Irreversibleof Reactions

Exothermic Endothermic

Constant density Variable densityConstant density Variable density

Catalytic Non-catalyticCatalytic Non catalytic

When a single stoichiometric equation and single rate equationare chosen to represent the progress of the reaction we have aare chosen to represent the progress of the reaction, we have asingle reaction.

When more than one stoichiometric equation is chosen torepresent the observed changes, then more than one kinetic

i i d d t f ll th h i iti f ll thexpression is needed to follow the changing composition of all thereaction components, and we have multiple reactions.Multiple reactions may be classified as:Multiple reactions may be classified as:series reactions:

parallel reactions, which are of two types:

and more complicated schemes, an example of which is

Here, reaction proceeds in parallel with respect to B, but in series p p pwith respect to A, R, and S.

Order of reaction

One of the most general forms: a b dA B Dr k C C ....C

where k = velocity constant or specific rate constant.If C C = 1; then r = kIf CA, CB , …. = 1; then r = k

a , b … = reaction order with respect to CA , CB .a + b + ... +d = overall order (this treatment is only applicable to simple reactions).

Reaction order

• Power to which concentration is raised to make rate proportional to it.p p• It can only be determined experimentally.

Elementary reaction 

• Elementary reaction is one that evolves a single step. The stoichiometric coefficients in an elementaryThe stoichiometric coefficients in an elementary reaction are identical to the powers in the rate law:

OHOCHOHCHO 33 OHCHOOO CCkr3

• An elementary reaction has an elementary rate law.• Some reaction follows an elementary rate law is notSome reaction follows an elementary rate law is not an elementary reaction.

CCk2

2ONONONO CCkr

2 22NO O 2NO

HIIH 222 2222 IHHH CCkr

Molecularity• This is the number of atoms, ions, or molecules involved

(colliding) in a reaction.

Examples:

(i) 2HI IH Bimolecular reaction, since two species(i) 2HI 22 IH , pare involved in the reaction step.

(ii) Unimolecular4

2234

90238

92 HeThU

urianium-238 heliumthorium

Representation of an Elementary ReactionI i t i l t tIn expressing a rate we may use any measure equivalent to concentration (for example, partial pressure), in which case:

Whatever measure we use leaves the order unchanged; howeverWhatever measure we use leaves the order unchanged; however, it will affect the rate constant k.

For brevity elementary reactions are often represented by anFor brevity, elementary reactions are often represented by an equation showing both the molecularity and the rate constant. For example,

kp ,

represents a biomolecular irreversible reaction with second-order

1k2A 2R

represents a biomolecular irreversible reaction with second order rate constant k1, implying that the rate of reaction is

Representation of an Elementary Reaction

It would not be proper to write mentioned equation as:p p q1kA R

for this would imply that the rate expression is:

Thus, we must be careful to distinguish between the one particularequation that represents the elementary reaction and the manyequation that represents the elementary reaction and the manypossible representations of the stoichiometry.

Representation of an Elementary Reaction

Representation of a Nonelementary Reaction

A nonelementary reaction is one whose stoichiometry does notA nonelementary reaction is one whose stoichiometry does not match its kinetics.

Kinetic Models for Nonelementary Reactions

If the kinetics of the reaction:

Indicates that the reaction is nonelementary, we may postulate aseries of elementary steps to explain the kinetics, such as

Kinetic Models for Nonelementary ReactionsFree radicals

Types of intermediates

Ions and polar substances

Types of intermediates

Molecules

Transition complexes

Nonchain Reactions

Chain ReactionsChain Reactions

Examples ofExamples of mechanisms ofmechanisms of

i ki dvarious kinds

Free radicalschain reaction mechanism

1k2 2H Br 2HBr

22 2 k

H Br 2HBr

2221

1 BrH CCk

2

2

2 BrHBrf CCk

r

This is not a bimolecular reaction.This is not a bimolecular reaction.

Because the reaction occurs as follows:

2BrBr I iti ti2Br 2Br Initiation HHBr H 2Br rrH BHBrB 2 Propagation

rHH BHBr 22

2r Br2 BTermination

Each step has a molecularity, which must be an integer.Th d d l l it t ilThus, order and molecularity are not necessarilyidentical for a given reaction.

Molecular intermediates nonchain mechanism

The general class of enzyme catalyzed fermentation reactions:

with experimental ratep

is viewed to proceed with intermediate (A. enzyme)* as follows:

Transition complex nonchain mechanism

The spontaneous decomposition of azomethanep p

we hypothesize the existence of either of two types of intermediatesintermediates.

Type 1Type 1.

An unseen and unmeasured intermediate X usuallyAn unseen and unmeasured intermediate X usually present at very small concentration

This is called the steady-state approximation.

Type 2.

a homogeneous catalyst of initial concentration Co is present in two formsis present in two forms,

• free catalyst C • combined in an appreciable extent to form• combined in an appreciable extent to form intermediate X

Example 2.1 SEARCH FOR THE REACTION MECHANISM

The irreversible reaction

A+B=ABA+B=AB

has been studied kinetically, and the rate of formation of product y, phas been found to be well correlated by the following rate equation:

2AB A Br kC independent of C

What reaction mechanism is suggested by this rate expression ifthe chemistry of the reaction suggests that the intermediateconsists of an association of reactant molecules and that a chainreaction does not occur?

If this were an elementary reaction, the rate would be given by

AB A Br kC C k[A][B]

Model 1 1

2

k *2k

2A A

hi h ll i l f l t ti

3

4

k*2 k

A B A AB

which really involves four elementary reactions

1k *22A A

2k*2A 2A

3k*2A B A AB

4k *2A AB A B

*r k [A ][B] k [A][AB] AB 3 2 4r k [A ][B] k [A][AB]

2 * *1r k [A] k [A ] k [A ][B] k [A][AB]*2

1 2 2 3 2 4Ar k [A] k [A ] k [A ][B] k [A][AB]

2

r 0*2A

r 0

21 k [A] k [A][AB]21 4

*2

2 3

k [A] k [A][AB]2[A ]

k k [B]

2 3k k [B]

21 k k [A] [B] k k [A][AB]1 3 2 4

AB2 3

k k [A] [B] k k [A][AB]2r

k k [B]

2 3[ ]

21 3 2 4

1 k k [A] [B] k k [A][AB]2

AB

2 3

2rk k [B]

if k2, is very small, this expression reduces to

21 k k [A] [B] k k [A][AB]21 3 2 4

AB

1 k k [A] [B] k k [A][AB]2r

k k [B]

2 3k k [B]

21r k [A]AB 1r k [A]2

if k2, is very small, this expression reduces to2

1 3 2AB

(k k 2k )[A] [B]r1 (k k )[B]

AB3 21 (k k )[B]

Model 2Model 2

1k *2B B B

3

4

k*2 k

A B A AB

Example 2.2 SEARCH FOR A MECHANISM FOR THE ENZYMESUBSTRATE REACTION

Here, a reactant, called the substrate, is converted to product bythe action of an enzyme, a high molecular weight (MW > 10000)protein-like substance. An enzyme is highly specific, catalyzingone particular reaction, or one group of reactions. Thus,

EnzymeA R

Many of these reactions exhibit the following behavior:1. A rate proportional to the concentration of enzyme

introduced into the mixture [E ]introduced into the mixture [E0].

2. At low reactant concentration the rate is proportional to thet t t ti [A]reactant concentration, [A].

3. At high reactant concentration the rate levels off andb i d d t f t t t tibecomes independent of reactant concentration.

Propose a mechanism to account for this behavior.

Michaelis and Menten (1913) were the first to solve this puzzle.

1A E X

They guessed that the reaction proceeded as follows:

23

A E X

X R E

with the two assumptions

[E0]=[E]+[X][E0] [E] [X]

d[X] 0 0dt

d[R] k [X]3[ ] k [X]dt

d[X] k [A][E] k [X] k [X] 01 2 3[ ] k [A][E] k [X] k [X] 0dt

1 0k [A][E ][X] 3

d[R] k [X]dt

2 3 1

[X](k k ) k [A]

1 3 0 3 0

2 3 1 2 3 1

k k [A][E ] k [A][E ]d[R]dt (k k ) k [A] (k k ) k [A]

2 3 1 2 3 1

3 0k [A][E ]d[R]

dt [M] [A]

0[E ]d[A] d[R]

d[A] d[R] [A] when [A] [M]

dt dtis independent of [A]when [A] [M]

is independent of [A]when [A] [M]

TEMPERATURE-DEPENDENT TERM OF A RATE EQUATIONEQUATION

Temperature Dependency from Arrhenius' Law

i 1 2r f (temperature) f (composition)

2k f (composition) E RTk k E RT

0k k e

where k0 is called the frequency or pre-exponential factor and E

k E 1 1

0 q y p pis called the activation energy of the reaction

2 2

1 1 1 2

r k E 1 1ln lnr k R T T

provided that E stays constant.

TEMPERATURE-DEPENDENT TERM OF A RATE EQUATIONEQUATION

Comparison of Theories with Arrhenius' Law

m E RT0k k T e 0 m 1

summarizes the predictions of the simpler versions of the collisionand transition state theories for the temperature dependency ofhthe rate constant.For more complicated versions m can be as great as 3 or 4. Now,because the exponential term is so much more temperature-because the exponential term is so much more temperature-sensitive than the pre-exponential term, the variation of the latterwith temperature is effectively masked, thusp y ,

E RT0k k e 0

From Arrhenius' law a plot of ln k vs 1/T gives a straight line, withReactions with high activation energies are very temperature-Any given reaction is much more temperature-sensitive at a lowFrom the Arrhenius law, the value of the frequency factor k, doeslarge slope for large E and small slope for small E.sensitive; reactions with low activation energies are relativelytemperature-insensitive.temperature than at a high temperature.

q ynot affect the temperature sensitivity.

Example 2.3 SEARCH FOR THE ACTIVATION ENERGY OF A PASTEURIZATION PROCESS

Milk is pasteurized if it is heated to 63°C for 30 min, but if it isheated to 74°C it only needs 15 s for the same result. Find theactivation energy of this sterilization process.

assuming an Arrhenius temperature dependency

r t E 1 1 2 1

1 2 1 2

r t E 1 1ln lnr t R T T

1t30 E 1 1ln ln

E=422000 J/mol20.25 t 8.314 336 347