Reactor design for multiple reactors

L9-1

Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9-1

XA AA0

A0dXt=N -r V

XA dXAV =FA0 -rA0

Review: Isothermal Reactor DesignV j

j0 j jdN

F F r dVdt

In Out- +Generation =Accumulation1. Set up mole balance for specific reactor

2. Derive design eq. in terms of XA for each reactor

Batch

A0 AA

F XV = -r

CSTR PFR

3. Put Cj is in terms of XA and plug into rA

j0 j A0 A 0 0j

A 0

C C X T ZPC1 X P T Z

n

A jr kC

nj0 j A0 A 0

AA 0

C C X TPr k1 X P T

4. Plug rA into design eq & solve for the time (batch) or V (flow) required for a specific XA or the XA obtained for given V , 0, time, etc

(We will always look conditions where Z0=Z)

Be able to rearrange equations & integrate for Q2

Reaction order needs to be determined.

L9-2


L9-2

Review: Analysis of Rate Data

• Constant-volume batch reactor for homogeneous reactions: make concentration vs time measurements during unsteady-state operation

• Differential reactor for solid-fluid reactions: monitor product concentration for different feed conditions during steady state operation

Goal: determine reaction order, a, and specific reaction rate constant, k

• Data collection is done in the lab so we can simplify BMB, stoichiometry, and fluid dynamic considerations

• Want ideal conditions → well-mixed (data is easiest to interpret)

Method of Excess Differential method Integral method Half-lives method Initial rate method Differential reactor More complex kinetics

L9-3


L9-3

Review: Method of ExcessA + B → products Suspect rate eq. -rA = kCA

aCBb

1.Run reaction with an excess of B so CB ≈ CB0

2.Rate equation simplifies to –rA = k’CAa where k’=kACB

b ≈ k’=kACB0b and a

can be determined

3.Repeat, but with an excess of A so that CA ≈ CA0

4.With excess A, rate simplifies to –rA = k’’CBb where k’’=kACA

a ≈ k’’=kACA0a

5.Determine kA by measuring –rA at known concentrations of A and B, where

13AA

A B

r 1k dm molsC C

a b

a b

L9-4


L9-4

Review: Differential Method

1. Plot DCA/Dt vs t

2. Determine dCA/dt from plot by graphical or numerical methodsa) Draw rectangles on the graph.

Then draw a curved line so that the area above the curve that is cut off of each rectangle approximately fills the unfilled area under the curve

b) -dCA/dt is read using the value where the curve crosses a specified time

3. Plot ln(-dCA/dt) vs ln CA

j0 j j jdF F r V Ndt

0 0

jj

dCr

dt Where –rA = kCA

a

alpha power

Average slope

AA l

dCl

tnkn

dlnCa

A

A

dC dtkC a

Curved line represents –dCA/dt

Slope of line = α

Insert α, –dCA,p/dt, & corresponding CA,p

L9-5


L9-5

Review: Integral Method

• A trial-and-error procedure to find reaction order• Guess the reaction order → integrate the differential

equation• Method is used most often when reaction order is known

and it is desired to evaluate the specific reaction rate constants (k) at different temps to determine the activation energy

• Looking for the appropriate function of concentration corresponding to a particular rate law that is linear with time

L9-6


For the reaction A products

For a first-order reaction - rA = k CAA

AdC kC

dt

A0

A

Cln kt

C

ln (CA0/CA)

t

2AA

dC kCdt

For a second-order reaction - rA = k CA2

A A0

1 1 ktC C

1/CA

t

For a zero-order reaction -rA = k AdC kdt

A A0C C kt

CA

t

AA

dC rdt

Plot of CA vs t is a straight

line

Plot of ln(CA0/CA) vs t is a straight

line

Plot of 1/CA vs t is a straight line

L9-7


L9-7

AA

dC kCdt

a A products

1 1A A0

1 1 1tk 1 C Ca aa

A A0 1 21C C at t = t2

1

1 2 1A0

2 1 1tk 1 C

a

aa

1

1 2 A02 1ln t ln 1 lnCk 1

aa

a

ln (t1/2)

ln CA0

Slope = 1- a

A Ar kC a

Plot ln(t1/2) vs ln CA0. Get a straight line with a slope of 1-α

Review: Method of Half-livesHalf-life of a reaction (t1/2): time it takes for the concentration of the reactant to drop to half of its initial value

L9-8


L9-8

Review: Method of Initial Rates• When the reaction is reversible, the method of initial rates

can be used to determine the reaction order and the specific rate constant

• Very little product is initially present, so rate of reverse reaction is negligible– A series of experiments is carried out at different initial

concentrations

– Initial rate of reaction is determined for each run

– Initial rate can be found by differentiating the data and extrapolating to zero time

– By various plotting or numerical analysis techniques relating -rA0 to CA0, we can obtain the appropriate rate law:

A0 A0r kC a

L9-9


L9-9

Conversion of reactants & change in reactant concentration in the bed is extremely small

Review: Differential Catalyst Bed

FA0

CpCA0

FAe

Fp

DW

DL

r’A: rate of reaction per unit mass of catalyst

flow in - flow out + rate of gen = rate of accum.

A0 Ae AF F r W 0 D

A0 Ae 0 A0 AeA

F F C Cr

W W

D D

When constant flow rate, 0 = :

0 p0 A0 AeA

CC Cr

W W

D D

Product concentration

The reaction rate is determined by measuring product concentration, Cp

L9-10


L9-10

L9: Reactor Design for Multiple Reactions

• Usually, more than one reaction occurs within a chemical reactor• Minimization of undesired side reactions that occur with the desired

reaction contributes to the economic success of a chemical plant• Goal: determine the reactor conditions and configuration that

maximizes product formation• Reactor design for multiple reactions

• Parallel reactions• Series reactions• Independent reactions• More complex reactions

• Use of selectivity factor to select the proper reactor that minimizes unwanted side reactions

L9-11


L9-11

Classification of Multiple Reactions

A B Ck1 k2

A

C

B

k2

k1

A Bk1 C Dk2

2) Series reactionsDesired product

3) Independent reactions Crude oil cracking

Desired product

4) Complex reactions k1A B C D k2A C E

1) Parallel or competing reactions

L9-12


L9-12

Parallel ReactionsPurpose: maximizing the desired product in parallel reactions

DkD

A+B

UkU

(desired)

(undesired)

1 1D AD Bkr C Ca b

2 2U AU Bkr C Ca b

Rate of disappearance of A: D UA rr r

Define the instantaneous rate selectivity, SD/U

Goal: Maximize SD/U to maximize production of the desired product

EDRT 1 1

D A B

EURT AUA

2 2BAA e C Cr e C C

a b a b

1 2 1 2 1 2 1 2D U A B D U A

E ED UD D RT

UB

U

k AS C C S e

kC C

Aa a b b a a b b

EDRT

AD1 1

D Br CA e Ca b

EURT

AU2 2

U Br CA e Ca b

E

RTk T Ae

DD U

U

rrate of formation of DSrate of formation of U r

D1 1

U2 2

ERT AU B

ERT

D A BD U

A e C C

A es

C C

a b

a b

L9-13


L9-13

Maximizing SD/U for Parallel Reactions: Temperature Control

E ED UD RT 1 2 1 2

D U A BU

AS e C CA

a a b b

What reactor conditions and configuration maximizes the selectivity?Start with temperature (affects k):

a) If ED > EU

E ED UD U RTE E

0 e 1RT

Specific rate of desired reaction kD increases more rapidly with increasing T

Use higher temperature to favor desired product formation

b) If ED < EU

E ED UD U RTE E

0 e 1RT

Specific rate of desired reaction kD increases less rapidly with increasing T

Use lower T to favor desired product formation (not so low that

the reaction rate is tiny)

L9-14


L9-14

Maximize SD/U for Parallel Reactions using Temperature

E ED UD RT 1 2

D U AU

AS e CA

a a

What reactor temperature maximizes the selectivity?ED = 20 kcal/mol, EU = 10 kcal/mol, T = 25 ◦C (298K) or 100 ◦C (373K)

SD/U is greater at 373K, higher temperature to favors desired product formation

cal cal20,000 10,000mol mol

cal1.987 298K8mol KD D1 2 1 2

D U A D U AU U

A AS e C S 4.6 10 CA A

a a a a

cal cal20,000 10,000mol mol

cal1.987 373K6mol KD D1 2 1 2

D U A D U AU U

A AS e C S 1.4 10 CA A

a a a a

A

U

D

kU

kD

kD/U

a) ED > EUT = 25 ◦C (298K):

T = 100 ◦C (373K):

L9-15


L9-15

Maximizing SD/U for Parallel Reactions: Concentration

1 2 1 2a) 0a a a a

E ED UD RT 1 2 1 2

D U A BU

AS e C CA

a a b b

What reactor conditions and configuration maximizes the selectivity?Now evaluate concentration:

→ Use large CA

1 2 1 2b) 0a a a a

→ Use small CA

1 2 1 2c) 0b b b b

→ Use large CB

1 2 1 2d) 0b b b b

→ Use small CB

How do these concentration requirements affect reactor selection?

DkD

A+B

UkU

1 2AC a a 1 2

AC a a

1 2BC b b 1 2

BC b b

L9-16


L9-16

Concentration Requirements & Reactor Selection

CA00

CB00

CA0

CB0

How do concentration requirements play into reactor selection?

CSTR: concentration is always at its lowest value (that at outlet)

PFR

PFR (or PBR): concentration is high at the inlet & progressively drops to the outlet concentration

CA(t)CB(t)

DkD

A+B

UkU

Batch: concentration is high at t=0 & progressively drops with increasing time

Semi-batch: concentration of one reactant (A as shown) is high at t=0 & progressively drops with increasing time, whereas concentration of B can be kept low at all times

CB0

CA

L9-17


DkD

A+BUkU

b1 b2

High CB favors

desired product

formation

b1 b2

High CB favors

undesired product

formation(keep CB

low)

a1 a2High CA favors desired

product formationa1 a2

High CA favors undesired product formation

(keep CA low)

PFR/PBR

Batch reactor

When CA & CB are low (end time or position), all rxns will be slow

High P for gas-phase rxn, do not add inert gas (dilutes reactants)

PFR/PBR w/ side streams feeding low CB CB

←High CA

Semi-batch reactor, slowly feed B to large amount of A

CB CB CBCSTRs in seriesB consumed before leaving CSTRn

CA00

CB00

CA0

CB0 CSTR

PFR/PBRPFR/PBR w/ high recycle

• Dilute feed with inerts that are easily separated from product

• Low P if gas phase

PFR/PBRSide streams feed low CA

←High CB

CASemi-batch reactor slowly feed A to large amt of B

CA CA CACSTRs in series

L9-18


L9-18

Different Types of Selectivityinstantaneous rate selectivity, SD/U

DD U

U

rrate of formation of DSrate of formation of U r

DD U

U

F molar flow rate of desired productSF molar flow rate of undesir

ExitE ed prx oductit

overall rate selectivity, D US

DD U

U

N moles of desired productSN moles of undes

Fiir

nalFi ed pr unal od ct

DD

A

rrate of formation of DYrate of consumption of A r

instantaneous yield, YD

(at any point or time in reactor)

overall yield, DY

DD

A0 A

FYF F

flowD

DA0 A

NYN N

batchEvaluated at outlet

Evaluated at tfinal

L9-19


L9-19

Series (Consecutive) Reactions

(desired) (undesired)A D U

k1 k2 Time is the key factor here!!!

Spacetime t for a flow reactor Real time t for a batch reactor

To maximize the production of D, use:

Batch

or PFR/PBR orn

CSTRs in series

and carefully select the time (batch) or spacetime (flow)

L9-20


L9-20

Concentrations in Series ReactionsA B C

k1 k2-rA = k1CA

rB,net = k1CA – k2CB

k1A A1 A

A00A 1

AdF dCdV dV

C C ek C k C t

How does CA depend on t?

How does CB depend on t?

1 AB

2 Bk CdF Cd

kV

k1A01

B2 B0 C ekdC

dk C

V t

kB 11 A0 2 B

dC k C e k Cd

tt

Substitute

kB 12 B 1 A0

dC k C k C ed

tt

Use integrating factor (reviewed

on Compass)

k2

B k k2 11 A0

d C ek C e

d

tt

t

k k1 2B 1 A0

2 1

e eC k Ck k

t t

0

V t

C A0 A BC C C C

L9-21


L9-21

The reactor V (for a given 0) and t that maximizes CB occurs when dCB/dt=0

k k1 A0B 1 21 2

2 1

k CdC k e k e 0d k k

t tt

1opt

1 2 2

k1 lnk k k

t

0

V t

so opt 0 optV t

AB

C

k1A A0C C e t

k k1 2B 1 A0

2 1

e eC k Ck k

t t

C A0 A BC C C C topt

Reactions in Series: Cj & Yield

Documents

Reactor design for multiple reactors