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CHEMICAL REACTION

ENGINEERING II

CHE 416

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CHEMICAL KINETICS AND REACTION

DESIGN:

Motivation for understanding chemical kinetics and

reaction design:

This is what makes us chemicalengineers the

reactor is the central feature of most chemical processes. Even if separation costs

dominate, the reactor often determines the

separation costs. Chemical reactions are ubiquitous in nature and

industry.

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COURSE OUTLINE:CHE416

IDEAL REACTORS

ASSUMPTIONS (IDEAL VS. REAL)

MATERIAL BALANCE / PERFORMANCE ORDESIGN EQUATIONS

COMPARISON OF IDEAL REACTORS

NONISOTHERMAL OPERATION

ENERGY BALANCE EQUATION

APPLICATION TO DESIGN

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OUTLINE:CHE416 CONTD.

REAL VERSUS IDEAL REACTORS

SOURCE OF DEVIATIONS

RESIDENCE TIME DSTRIBUTION RTD FUNCTIONS

CONVERSIONS-1ST ORDER RXNS

REACTOR MODELS

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ATTENTIVE IN CLASS

RE-READ NOTES

PRACTICE SOLVING QUESTIONSYOURSELF

ASK QUESTIONS TO BE SURE

YOU UNDERSTAND

BE READY FOR WEEKLY TESTS

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WHY IDEAL REACTORS?

Represent distinct extremes of mixing(100% in BR and CSTR; 0% in axialdirection for PFR)

Ideal reactors simpler to analyse [welldefined flow pattern of fluid in reactors]

More complex real reactors can be

examined in terms of ideal reactors For new designs ideal reactors help

determine

type of mixing that leads to better results

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WHY IDEAL REACTORS? Contd.

estimate the size of the required reactor syst.

Gives insight into:

the operation of the real reactors Effect of parameters on results

most important factors to control

Hence powerful models for chemical reactionsystems

much to gain from a study of ideal reactors.

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IDEAL REACTOR MODELS

Based on assumptions about mixing patterns

within them

One of the assumptions represent the best

way of contacting the reactants

Easy to treat mathematically

Insights obtained are significant for realreactors-type of mixing, important design

parameters, better control

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Ideal reactor types

1. batch reactor (BR) 100% mixing

2. Continuously(operated) stirredtank reactor (CSTR)

3. plug flow reactor (PFR)

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Batch Reactor (BR)

operates in a discontinuous way

reactants and any other substances

(catalyst, solvent etc.) are loaded into thereactor at beginning

Contents subjected to perfect mixing (and left

to react) for a certain period.

The resultant mixture is then discharged.

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Batch reactor: homogenous reaction

mixture

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Batch Reactor (BR)2

operates in unsteady mode with respect to time

at any position

Composition at any point in reactor changes

continuously wrt time 1st order reaction: CA=CA0e

-kt

operates in steady mode wrt space. Novariation from point to point because of perfect

mixing at any point in time

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CA VS t,

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CA VS t,p Fig

1

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Advantages/Disadvantages of BR

is simple,

needs little supporting equipments,

high flexibility-high conversions

through as high reaction time as

desired ideal for small-scale experiments

(kinetics studies).

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Advantages/Disadvantages of BR2

Industrially, a single unit may be used for the

manufacture of relatively small amounts of

material (drugs, dyes, cosmetic articles)-not

dedicated unit

Disadvantages are idle periods (for loading,

unloading, cleaning, heating etc).

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Design equation of BR

Obtained from the law of conservation of

matter.

Written for any component in the system [

reactant, product, inert]

Written in terms of limiting reactant ,A

Written for the whole volume of reactor

because of uniform conditions within it

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Control volume/element of

volume

Reactions occur in a localized region of space

Control volume is

any region of space that has a finite volumewith boundaries that clearly separate the

region from the rest of the universe.

real or abstract ,macrosized

Chosen according to the dictates of the

analysis that we are undertaking

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Law of conservation of mass

a

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Balance after t>0 Rate in=0 no inflow after charging

Rate out=0 no outflow after charging

Rate of disappearance by reaction=V(-rA) Rate of accumulation=dNA/dt

=dNA0(1-XA)/dt

= -NA0dXA/dtt=REACTION TIME

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1

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Substituting in equation

0-0-V(-rA)=-NA0dXA/dt

Integrating between: t=0, XA=0

Ae

Ae

X

A

A

A

X

A

A

A

t

rV

dXNt

rV

dXNdt

0

0

0

0

0

)(

)(

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For constant volume reaction mixture

This gives the time for a conversion of XA=XAe

as a function of the: rate law and the

initial concentration of A

AeX

A

A

A

rV

dXCt

0

0

)(

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Reaction time, t, is the natural

performance measure for a BR

Integral =area under the curve of [1/(-rA ) ]

vs.XA.

It may be evaluated

1.Analytically

2.Graphically

3.Numerically( minimum of 5 points consideredsufficient)

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x

3

12

x=(a+b)/2 b=XAea=0

f(x)

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CONTINUOUS STIRRED TANK

REACTOR (CSTR)

Continuousrefers to the inflow and outflowof materials. Hence CFSTR

Namemisses the essence of the

idealization completely ideality arises from assumption that the

reactor is perfectly mixed and hence

homogeneous Continuous perfectly mixed

reactor(=CPMR) is an even better name

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CSTR: Homogeneous reaction

mixture, constant inflow & outflow

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CSTR contd2.

mixing so perfect that concentration and

temperature are spatially uniform within

whole of reactor and

correspond to those of the exit stream;

operates in a steady mode wrt. time

[at all times, Ci

is same at any point]

operates in a steady mode wrt. space

Ci .is same at all points at any t]

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Design equation: CSTRelement of volume=total reactor

Rate in=FA0

Rate out=FAe

Rate of disappearance by reaction =V(-rA) Rate of accumulation =0 (steady state)

FA0 - FAe- V(-rA)=0

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CSTR contd.

*reactants continuously fed into thereactor

products continuously drawn fromreactorAlso called vat, backmix

reactor,mixed flow reactor100% back mixing

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Term In Square Brackets

=area of The Rectangle1/(-ra) By Xae

Rearranging to obtain the space time,

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VCSTR=[FA0/(-rA)] x XAe

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Space time and space velocity

= time required to process one reactor

volume of feed measured at specified

conditions, usually feed conditions

= V/vo = (reactor volume)/(volumetric feed

rate

=space time

Space velocity=1/space time

gas hourly Space velocity GHSV

liquid hourly Space velocity=LHSV

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APPLICATION OF CSTR.

For continuous production

WHEN INTENSE MIXING IS REQUIRED

CAN BE USED ALONE OR AS part OF BATTERY

of CSTRs

EASY TO MAINTAIN GOOD TEMPERATURE

CONTROL

CONVERSION OF REACTANT PER VOLUME IS

LOWEST OF THE FLOW REACTORS. LARGE

VOLUME IS REQUIRED

MOST LIQUID PHASE REACTIONS

Plug/Piston/ slug flow reactor [PFR]

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Plug/Piston/ slug flow reactor [PFR]

Continuous Tubular Reactors (CTRs).

Plug flow Tubular Reactors (PFTR) FLUID Flows orderly

No Element Of Fluid Mixing With Or

Overtaking Any Other Element Ahead Or

Behind.

May Be Lateral Mixing, No Diffusion

Along The Flow Path (0% Of Backmixing).

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Plug flow Tubular Reactors (PFTR)

CONTINUOUS OPERATION

reactants continuously fed into the reactor

products continuously drawn from reactor

operates in a steady mode wrt. time

[at all times, Ci is same at a given point]

Spatial variation in composition andtemperature from entrance to exit of reactor

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PFR or PFTR or CTRs

Variation in composition and temperaturealong the length of reactor

The PFR model works well for many fluids:

liquids, gases, and slurries. turbulent flow and axial diffusion cause a

degree of mixing in the axial direction in realreactors

PFR model is appropriate when these effectsare sufficiently small that they can be ignored.

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Design equation2

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DESIGN EQUATION: PFR

element of volume is a section of tube of

volume V, small enough for the rate of

reaction within it to be considered uniform.

Rate IN(moles / time) =FA

Rate out(moles / time) =FA + FA

Rate of disappearance by reaction = V(-rA

)

Rate of accumulation =0 (steady state)

Substituting in balance equation

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FA-(FA+FA)-(-rA)V=0

-FA=(-rA)V

FA/V=-(-rA)

As V0

In terms of XA,

dV =FA0 [dXA/(-rA)]

Integrating,

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From : FA= FA0(1- XA)

Separating variables and integrating

Applications: PFR

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Applications: PFR

Large-scale reactions

Homogeneous or heterogeneous reactions Continuous production

Most gas phase reactions

Relatively Easy to maintain(no moving parts)

Highest conversion per volume

Difficult to control temperature within the

reactor, hence hot spots for exothermic rxns

As one long tube or as a tube bank

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Actual residence time and space time

THE actual time a fluid element resides in the

reactor will be equal to the space time only if:

1. There is no change in the number of moles

during the reaction

2. There is no change in temperature

3. There is no change in pressure

4. =vo(1+XAA) [T /T0][P0/P]

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Actual residence time:PFR

the time to traverse and element of volume

dV, is dtr

From differential form of the design equation

Substituting for dV from above,

tr=Actual residence time of fluid in reactor,

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Actual residence time: PFR contd.

Integrating

SYSTEM OF REACTORS

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SYSTEM OF REACTORS

CSTR in a series

CSTR in series: nth reactor

INOUT-DISAPPEARANCE BY REACTION=0

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FA1;

CA1

FA0

CA0

FA2;

CA2

CA3

1

2 3

CSTRs in a series

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nth CSTR in a series

[ )/( )

1/(-rA)

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XA

[XA1-XA0)/(-rA1)1/(-rA2)

XA0 XA1 XA2 XA3

[XA3-XA2)/(-rA3)[XA2-XA1)/(-rA2)

/( A)

1/(-rA1)

1/(-rA3)

SIZE COMPARISON OF IDEAL

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SIZE COMPARISON OF IDEAL

REACTORS: for single reactions

Kind of reactors affects the Size of reactor

affects

and selectivity

BR PFR

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BR vs. PFR

*

CA0= NA0/V for BR ; CA0= FA0/0 for PFR

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PFR vs CSTR

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PFR vs. CSTR

For any conversion and for all positive

reaction orders, the CSTR is always larger thanthe PFR: VCSTR / VPFR > 1.

For any conversion, the ratio of volumes :

VCSTR/VPFR increases with the reactionorder.

For any positive reaction order, the ratio ofvolumes VCSTR/VPFR increases with theconversion

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Size comparison of single reactors:

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Size comparison of single reactors:

autocatalytic reactions

(1/rA) - A curve, a comparison of areas willshow which reactor is superior for a given job

positive nth order, the rate is maximum at high CA islows progressively as the reactant is consumed

in autocatalytic reactions, the rate at the start islow (little product is present), it increases to amaximum as product is formed and then it dropsagain as reactant is consumed.

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Size comparison of multi reactor

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Size comparison of multi-reactor

systems Instead of a single reactor

Reactors of the same or different

types,

different or equal size , arranged in

series or in parallel, can be used.

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PFR in svs.

A single

XA3XA0 XA1 XA2

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Design for parallel reactions

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Design for parallel reactions

A D; rD =k1CA1 ; A U; rU =k2CA

2

Summary of ideal reactor systems:

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Summary of ideal reactor systems:

general rules

a single, piston flow reactor will give higher conversion and better selectivitythan a CSTR.

combinations of isothermal reactors provide intermediate levels ofperformance compared with single reactors that have the same total volume

and flow rate.

parallel reactor system has an extra degree of freedom compared with aseries system.

A parallel reactor system at the same.T, total V and flowrate has noperformance advantages compared with a single reactor

When heat must be transferred to or from the reactants, identical smallreactors in parallel may be preferred because the desired operating

temperature is easier to achieve.

Summary of ideal reactor systems:

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Summary of ideal reactor systems:

general rules

A single, PFR will give higher

conversion and better selectivity

than a CSTR. combinations of isothermal reactors

provide intermediate levels of

performance compared with single

reactors that have the same total

volume and flow rate.

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GENERAL RULES CONTD1.

A parallel reactor system has an

extra degree of freedom compared

with a series system. A parallel reactor system at the

same T, total V and flowrate has no

performance advantages comparedwith a single reactor

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GENERAL RULES CONTD2

When significant amounts of heat

must be transferred to or from the

reactants, identical small reactors in

parallel may be preferred because the

desired operating temperature is easier

to achieve.

Autocatalytic reactions are exceptions

to both these statements.

N equal-size CSTR in series;

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N equal size CSTR in series;

1st order constant density reaction

At constant reaction T,

Same results as a single PFR with same Several CSTRs in series approaches

performance of a single PFR with same total V

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