Chemical Reaction Engineering

CHEE 321: Chemical Reaction Engineering

6. Multiple Reactions; Reaction Networks and Pathways

6a. Multiple Reactions (Fogler Ch 6, Ch 8.8)

Course (Content) OrganizationIsothermal, Ideal Reactor (Single Reaction) Design

Mole Balance(Module-1,2)

In Out + Con = AccFA,in-FA,out+(rA)V = dCA/dt

Rate Law(Module-1)

(rA) = kCAn

Design Algorithm(Module-2)

1. GMBE, 2. Rate Law3. Stoich 4.Combine

Analysis of Rate law(Module-5)

Kinetics: How to obtain k and rxn order

Multiple Reactions(Module-6)

Selectivity, Yield

Non-Isothermal Reactor Design

dT/dz = ?

Tin-Tout =?

Output

Reactor Volume Reaction Time

Rate Constant

Conversion Product Composition

Energy Balance Heat Transfer Rate Equilibrium Reactions Multiple Steady State

(Module-3) Temperature Profile Heat Removal Heating Requirement

Output

Topics to be covered in this Module

Algorithm for Reactor Design of Multiple Reactions Mole Balance Net Rates of Reactions Stoichiometry Energy balances

Introduction to selectivity and yield

Qualitative Analyses (Parallel and Series Reactions) Maximizing the reactor operation for single reactant systems Maximizing the reactor operation for two reactant systems

Multiple ReactionsTypes of Multiple Reactions

1. Series Reactions

2. Parallel Reactions

3. Complex Reactions: Series and Parallel

4. Independent

CBA kk 21

CABA

k

k

2

1

DCACBA

k

k

++

2

1

DBCA

k

k

2

1

Use molar flow rates and concentrations; DO NOT use conversion!

Cannot use stoichiometric tables to relate change in CB to change in CA

VERY IMPORTANT!!!

Species Feed Flow Rate (mol/s)

Change within Reactor (mol/s)

Effluent Rate from Reactor (mol/s)

A 0AF 0( )A AF X 0 (1 )A A AF F X= B 0 0B B AF F=

0( )A Ab F Xa

0 ( )B A B AbF F Xa= C 0 0C C AF F=

0( )A Ac F Xa

0 ( )C A C AcF F Xa

= + D 0 0D D AF F=

0( )A Ad F Xa

0 ( )D A D AdF F Xa

= + I (inert) 0 0I I AF F= - 0I IF F= Total 0 0 (1

)T A B C

D I

F F

= + ++ +

0A AF X 0 0T T A AF F F X= +

Why not Stoichiometric Tables?Reaction: D

a

dC

a

c

a

b BA ++ Define 0 0/i i AF F =(Limiting reagent A)

1+=ab

ac

ad

Fogler 3.6

If you have multiple reactions:A + B C

andA + C D

then the consumption/generation rates of A, B, C and D are not simply coupled

Multiple Reactions: dont use Design Equations in terms of Conversion

'0 ( )A

AA

dXF rdW

=

IDEAL DIFFERENTIAL ALGEBRAIC INTEGRAL REACTOR FORM FORM FORM

0 ( )AA AdXN r Vdt

= 00

AX

AA

dXt Nr V

=

0 ( )AA AdXF rdV

= 0

0

AX

AA

dXV Fr

=

CSTR0 ( )

( )A A

A

F XVr

=

BATCH

PFR

PBR 0 '0

A

A

X

AdXW F

r=

If you have multiple reactions:A + B C

andA + C D

then the consumption/generation rates of A, B, C and D are not simply coupled

Therefore, we need to write individual equations for all species in the system.

Write these in terms of molar quantities, not fractional conversions

Multiple Reactions: Use these Design Equations, writing a balance for each species

DifferentialEquation

AlgebraicEquation

IntegralEquation Remarks

Vrdt

dNj

j )(=0( )

j

j

Nj

jN

dNt

r V=

Conc. changes with time but is uniform within the reactor. Reaction rate varies with time.

Batch(well-mixed)

CSTR(well-mixed at steady-state)

0

( )j j

j

F FV

r=

Conc. inside reactor is uniform. (rj) is constant. Exit conc = conc inside reactor.

PFR(steady-state flow; well-mixed radially)

jj r

dVdF =

0( )

j

j

Fj

jF

dFV

r= Concentration and hence reaction rates vary

spatially (with length).

Design Equation for Reactors Multiple Reactions

Gas-Phase Liquid Phase

Batch

Semi-Batch(B fed)

CSTR

PFR

PBR

NOTE the design equations are EXACTLY as for a

single reaction

but

Balances must be written for all components

Modification to the CRE Algorithm for Multiple Reactions

Mole balance on every species (not in terms of conversion) Rate Law: Net Rate of reaction for each species,

e.g., rA = ri where subscript i indicates the ith reaction Stoichiometry

a) Liquid Phase, incompressible: CA=NA/V=FA/v0b) Gas Phase use

Combine More difficult: set of algebraic or differential equations for A, B,

Fogler, 6.4

Variable volumetric flowrate; ideal gas

Net Rate of Reaction

For N reactions, the net rate of formation of species A is:

For a given reaction i ai A + bi B ci C + di D

This relationship is valid ONLY for reaction-i(i.e., it does not couple the OVERALL consumption ratesof A, B, C and D)

Example: Net Rate of Reaction

The following reactions follow elementary rate law:

Write net rates of formation of A, B and C

Fogler, 6.4.2; see Ex. 6-5

Note that the rate coefficients are associated with a particular component (-rA) for Rxn 1 and rD for Rxn 2

Example: Multiple Gas Phase Reactions in an Isothermal PFR

The complex gas phase reactions take place in a PFR. The feed is equal molar in A and B with FA0 = 10 mol/min and the volumetric flow rate is 100 dm3/min. The reactor volume is 1,000 dm3, there is no pressure drop, the total entering concentration is CT0 = 0.2 mol/dm3 and the rate constants are:

Plot FA, FB, FC, FD and as a function of V. (We will formulate, but not solve the differential equations. is selectivity of C relative to D, which we will talk about later.)

/C DS/C DS

Gas Phase Multiple Reactions - Algorithm

1. Mole Balance

Remember, unlike single-reactions, for multiple reactions

mole balance for each species must be written

A

B

C

D

rA, rB, rC, rD are all NET rates of reactions

Example (contd)2. Rate Laws

Species A

Species B

Species C

Species D

Example (contd)3. Stoichiometry

4. Combine

Solution

Also, see example 6-10

Energy Balance with Multiple Reactions

Steady-state PFR, Single Reaction

1

( ) ( ) ( ( ))a A rxnn

i pii

U a T T r H TdTdV F C

=

+ =

Steady-state PFR, Multiple Reaction (Nrxn)

,1

1

( ) ( ) ( ( ))rxnN

a ij rxn iji

n

i pii

U a T T r H TdTdV F C

=

=

+ =

Fogler, 8.8.1

Rxn-i rate and heat of reaction specified in terms of reactant-j

See Example 8-10

Energy Balance with Multiple Reactions

Steady-state CSTR, Single Reaction

Steady-state CSTR, Multiple Reaction (Nrxn)

Fogler, 8.8.2

Rxn-i rate and heat of reaction specified in terms of reactant-j

See Example 8-11

[ ]0 0 01

( ) ( ) ( )n

a A Rxn A A i pii

UA T T F H T X F C T T=

= [ ] 0 0

1( ) ( ) ( ) ( )

n

a Rxn A A i pii

UA T T H T r V F C T T=

+ = 0 ( )( )A A

A

F XVr

= but

, 0 01 1

( ) ( ) ( )rxnN n

a ij Rxn ij A i pii i

UA T T V r H T F C T T= =

+ =

Examples: Fogler Ex 6-5 and 6-6, 8-10 and 8-11

Know how to do set up this type of problem! Being able to formulate a model for a multiple reaction system is important. Usually they will be solved by computer.

Selectivity and YieldInstantaneous Global

U

DDU r

rS =U

DDU F

FS =~

A

DD r

rY =0 0

D DD

A A A A

F NYF F N N

= =

Selectivity

Yield

What should be the criterion for designing the reactor ? Is it necessary that reactor operates such that minimum amount of undesired

products are formed ?

Total Cost

Desired Reaction:

Undesired Reaction:

DA Dk

2

U

U

k

k

A UD U

C

o

s

t

Reactant Conversion

ReactorSystem

FA0FA

FDFU

FD

FU

SEPARATOR

FA

and/or

Fogler 6.1

Instantaneous vs. Global Yield

For a CSTR:

For proof, see Fogler Ex. 6-1 (pg 308)

For a PFR, concentrations and rxn rates are changing along reactor length:

instantaneous yield:

global yield

for v=v0:

DU DU

D D

S S

Y Y

==

D DD

A A

r dFYr dF

= =

0

D formedA reacted ( )

DD

A A

FYF F

= =

00

1( )

A

A

C

D D ACA A

Y Y dCC C

=

Series Reactions

, t=0 CA=CA0

Batch reactor, isothermal, incompressible

From Fogler website http://www.engin.umich.edu/~cre/06chap/frames_learn.htm

Series Reactions

See Appendix A3

Series Reactions

dCCdt = k 2CB , t = 0 CC = 0

What about byproduct C? This can be calculated by integration, or by stoichiometry

You would have the same set of equations for an isothermal PFR, replacing t with ; see Fogler Ex. 6-4

Parallel Reactions:Selectivity for Single Reactant Systems

Example (parallel reaction)

Desired Reaction:

Undesired Reaction:

DADD Ckr=

)( UDU

D

AU

D

AU

AD

U

DDU Ck

kCkCk

rrS

===

DA DkUA Uk UAUU Ckr =

Let us examine some reactor operating scenarios to maximize selectivity.

What is the net rate of reaction of A ??

Fogler, 6.2

Case 1: D-U >0

High CA favors D

How can we accomplish this?

)( UDA

U

D

U

DDU Ck

krrS ==

For gas phase reactions, maintain high pressures For liquid-phase reactions, keep the diluent to a minimum

Batch or Plug Flow Reactors should be used CSTR should NOT be chosen


Case 2: D-U < 0

Low CA favors D

How can we accomplish this?

For gas phase reactions, operate at low pressures For liquid-phase reactions, dilute the feed

CSTR is preferred

)( DUAU

D

U

DDU Ck

krrS ==

Reactant concentration maintained at low level

CA

CA

CA0


Case 3: D-U = 0Concentration cannot be used operating parameter for selectivity maximization What now?

U

D

U

DDU k

krrS ==

]/[exp]/[exp

RTEARTEA

UU

DD

=

(a) If ED > EU

(b) If EU > ED

Operate reactor at highest possible temperature

Operate reactor at lowest possible temperature


]/)([exp RTEEAA

UDU

D =

None of these discussions / strategies examine yield. Both must be considered in reactor design!

Parallel Reactions:Selectivity for Two Reactant Systems

Example

Desired Reaction:

Undesired Reaction:

11 BADD CCkr =DBA Dk+

UBA Uk+ 22 BAUU CCkr =

)()( 2121 == BAU

D

U

DDU CCk

krrS

Case 1: 1>2; 1 > 2

How can we accomplish this? Use Batch reactor Use Plug Flow reactor


For high SDU, maintain both A & B as high as possible

bB

aA

U

D

U

DDU CCk

krrS ==

Let, a = 1-2; b = 1 - 2

Case 2: 1>2; 1 < 2

How can we accomplish this? See Fogler Figure 6.3

Use semi-batch reactor where B is fed slowly Use Tubular reactor with side streams of B being fed continuously Use series of small CSTR with A fed only to first and B to each reactor


For high SDU, maintain concentration of A high and of B low

bB

aA

U

D

U

DDU C

Ckk

rrS ==

Let, a = 1-2; b = 2 - 1DBA Dk+UBA Uk+

11 BADD CCkr =

22 BAUU CCkr =

Case 3: 1

Case 4: 1 2

How can we accomplish this? Use semi-batch reactor where A is fed slowly Use Tubular reactor with side streams of A being fed continuously Use series of small CSTR with B fed only to first and A to each reactor


aA

bB

U

D

U

DDU C

Ckk

rrS ==

For high SDU, maintain concentration of B high and of A low

Let, a = 2-1; b = 1 - 2

Same as Case 2, with A and B switched

Why Semi-Batch Reactors?B

Aheat

B is slowly fed to A contained in the reactor.

Unwanted products can be minimized

exothermic reaction can be carried out at controlled rate

Product C is continuously removed

Higher conversion for reversible reactions can be obtained

C

A, B

Semi-Batch Reactors - GMBE

1. GMBE on a molar basis

Input - Output + Gen = Accu.

dtdNVr AA =+ )(00

0 0 ( ) BB BdNF r Vdt

+ =

BFB0v0

For Species A (present in reactor at t=0)

For Species B

Constant Density Systems

0 0V V v t= +

Constant Flowrate

Semi-Batch Reactors - GMBE2. GMBE on a concentration Basis

dtdNVr AA =+ )(00

0 0 ( ) BB BdNF r Vdt

+ =

B

For Species A (no inflow)

Similarly for Species B

][ AA CVN =

0( ) AA AdCr V V v Cdt

= + 0( )A A AvdC r Cdt V=

0 0 0[ ]B BF v C=

dtdVC

dtdCV

dtCVdVr AAAA +== )()(

Constant flow and density

0dV vdt

=0

0( ) ( )B B B BvdC r C C

dt V=

][ BB CVN =

FB0v0

What you should know

Qualitative Analyses (Parallel and Series Reactions) Maximizing the reactor operation for single reactant systems Maximizing the reactor operation for two reactant systems Consideration of selectivity and yield

Algorithm for Reactor Design of Multiple Reactions Mole Balance Net Rates of Reactions Stoichiometry Energy Balances Be able to derive the set of equations for the system

usually cannot be solved without computer programs be able to sketch the expected qualitative behaviour

CHEE 321: Chemical Reaction Engineering6. Multiple Reactions; Reaction Networks and Pathways6a. Multiple Reactions (Fogler Ch 6, Ch 8.8)Course (Content) OrganizationTopics to be covered in this ModuleMultiple ReactionsWhy not Stoichiometric Tables?Multiple Reactions: dont use Design Equations in terms of ConversionMultiple Reactions: Use these Design Equations, writing a balance for each speciesDesign Equation for Reactors Multiple ReactionsModification to the CRE Algorithm for Multiple ReactionsNet Rate of ReactionExample: Net Rate of ReactionExample: Multiple Gas Phase Reactions in an Isothermal PFRSlide Number 13Slide Number 14Slide Number 15SolutionEnergy Balance with Multiple ReactionsEnergy Balance with Multiple ReactionsExamples: Fogler Ex 6-5 and 6-6, 8-10 and 8-11Slide Number 20Instantaneous vs. Global YieldSeries ReactionsSeries ReactionsSeries ReactionsSlide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Semi-Batch Reactors - GMBESemi-Batch Reactors - GMBEWhat you should know

Chemical Reaction Engineering

Documents

Transcript of Chemical Reaction Engineering