Chemical Engineering DepartmentCCB3043 KINETICS AND REACTOR DESIGN

CHAPTER 2: CONVERSION AND REACTOR SIZING(part 1)

1

Basic knowledge

Application

3

1. Define conversion

2. Develop design equation for batch reactor

3. Develop design equation for flow reactor

4. Applying design equation to solve reactor problems

5. Applying design equation to reactors in series

6. Differentiate between space time and space

velocity

OBJECTIVES OF CHAPTER 2

4

Overview on Objective of Chapter 2

Re-write reactor sizing

in terms of conversion

Reactor sizing in terms of

mole balance

Relating mole balance to conversion

CHAPTER 1

CHAPTER 2

APPLYING DESIGN

EQUATION TO SOLVE

PROBLEMS RELATED TO FLOW REACTOR AND REACTOR IN SERIES

What is conversion?

• Consider the general equation (irreversible eqn)

aA + bB cC + dD

• We will choose A as our basis of calculation

DadC

acB

abA

How do we define

conversion?

Conversion

• Conversion is define as:

feedA of molesreactedA of moles

AX

MAXIMUM CONVERSION?

Irreversible ReactionX = 1

Reversible ReactionX = Xe

7

Conversion

How do we relate

conversion with flow rate or

moles of reactant?

8

Relating conversion with moles of reactant

Batch reactor

XNXN

A

A

0

0

.

reacted A of Mole

onversionC fed A of Moles reacted A of Mole

reacted A of Mole - fed A of Mole timeany at A of Mole t

XNNN AAA 00 -

0

0 - A

AA

NNNX

9

Relating conversion with molar flow rate

Flow reactor (CSTR and PFR/PBR)

XFXF

A

A

0

0

.

reacted A of flowrate Molar

onversionC fed A of flowrate Molar reacted A of flowrate Molar

t Molar flowrate A at any time Molar flowrate A fed - Molar flowrate A reacted

XFFF AAA 00 -

0

0 - A

AA

FFFX

10

Now, recap back our design equation:

Relating V to X

dtdN

Vr AA

HOW TO RE-WRITE

V = f(X)

WHAT WE HAVE JUST DISCOVERED:

0

0 - A

AA

NNNX

0

0 - A

AA

FFFX

Develop Design Equation for batch reactor

• Batch reactor

X

AA

AA

VrdXNt

Vrdt

dN

00

• PFR

0

AA

AA

A

dF rdV

dXV Fr

• CSTR

A

A

AAA

rXF

V

VrFF

0

0 0

Develop Design Equation for flow reactor

Design Equation(Summary)

Reactor Differential Algebraic Integral  

Batch                                                                               

CSTR                                               

PFR                                                                         

PBR                                                 

 

Example:

• E. 2-1: Using ideal gas law to calculate CAO and FA0

A gas of pure A at 830 kPa (8.2 atm) enters a reactor with a

volumetric flow rate, v0 of 2 dm3/s at 500K. Calculate the

entering concentration of A and its molar flow rate.

15

APPLYING DESIGN EQUATIONS TO SOLVE REACTOR PROBLEMS

For F LOW R EAC TO R , we can estimate the reactor

size using a L E V E N S P I E L P LOT .

What is LEVENSPIEL plot?

• From a given data of and X, and a know value of FA0:

16

Reactor Sizing for flow reactor

–rA X FA0/-rAFA0/-rA

X

Reactor Sizing for flow reactor

• Knowing –rA = f(XA), reactor size can be determine

using Levenspiel plot

• Consider the design equation for CSTR

A

0Ar

XFV

• Consider the design equation of a PFR

Reactor Sizing for flow reactor

A0A rdVdXF

19

Example 2-2 / 2-3: Sizing a CSTR / PFR

The gas phase reaction A B is carried out in a

CSTR and the entering molar flow rate of A is

0.4 mol/s. Using data in Table 2-1:

1. Calculate the volume required to achieve

80% conversion. Shade the area on the

Levenspiel plot that corresponds to this

conversion.

2. Re-do the problem if the reaction is carried

out in a PFR.

3. Any comment on the reactor size?

Reactor Sizing for flow reactor

XA -rA (mol/m3.s)0.0 0.450.1 0.370.2 0.300.4 0.1950.6 0.1130.7 0.0790.8 0.05

TABLE 2.1

Solution Ex 2-2: Sizing for CSTRTABLE 2.1

XA -rA (mol/m3.s) 1/-rA (m3..s/mol) FA0/-rA (m3..s/mol)

0.0 0.45 2.22 0.890.1 0.37 2.70 1.080.2 0.30 3.33 1.330.4 0.195 5.13 2.050.6 0.113 8.85 3.540.7 0.079 12.70 5.060.8 0.05 20.00 8.00

XFr

V AA

01

DESIGN EQUATION OF CSTR!!

Solution Ex 2-2: Sizing for PFRTABLE 2.1

XA -rA (mol/m3.

s)

FA0/-rA (m3..s/mol)

0.0 0.45 0.890.2 0.30 1.330.4 0.195 2.050.6 0.113 3.540.8 0.05 8.00

0.80

0A

A

FV dXr

DESIGN EQUATION OF PFR!!

Use 5-point quadrature formula:

4

00 1 2 3 44 2 4

3X

X

hf X dX f f f f f

4 0

4X X

h

Summary what we have learned:Important things to remember

Volume CSTR

Volume PFR

• General mole balance• Mole balance equations for

each reactor• Design equations for each

reactor• Conversion• Reactor sizing

Reactors in Series

• Knowing –rA = f(XA), we can design any sequence of

reactors

• Provided there’s no side reactors, conversion at any

reactor outlet is define as:

reactorfirst tofedA of moleipoint toup reactedA of moles total

iX

Reactors in series

Try and develop these design equations……..

2 CSTR in series

1 2

0

2

4

6

8

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Conversion, X

FA0/

-rA

FA2

X2=0.8

FA0

FA1

X1=0.4

2 PFR in series

0

2

4

6

8

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Conversion, XFA

0/-rA

1

2

FA0

FA1

X1=0.4

FA2

X2=0.8

CSTR in series = 1 PFR

54321

1 2 3 4 5

Equals to

As no. of CSTR in series increases, the total volume required for a given conversion is similar to the volume of one PFR

0

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1

Conversion, X

FA0/

-rA

CSTR in series = 1 PFR

CSTR 1CSTR 2

CSTR 3

CSTR 4

CSTR 5

PFR

Reactors in series• Example 2-5: Comparing volumes for CSTR in

series– From data below, calculate the volume of CSTR if 2 CSTR in series

is use for the reaction. Given that the intermediate conversion is 40% and the final conversion is 80%. Then, use the Levenspiel plot to help you explain on the difference of the reactor volume for single CSTR and CSTR in series.

– Will there be any difference in volume if the reaction is carried out in 2 PFR in series? Use the Levenspiel plot to explain your answer.

X 0.0 0.1 0.2 0.4 0.6 0.7 0.8FA0/-rA

0.89 1.09 1.33 2.05 3.54 5.06 8.0

0

2

4

6

8

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Conversion, X

FA0/

-rA

3

1

31

3

4.0

0

8.0

4.00.2

0.2

mV

mV

mr

F

XA

A

332

122

02

3

8.0

0

2.34.08.00.8

0.8

mmV

XXr

FV

mr

F

A

A

XA

A

VT = V1 +V2 = 0.82 + 3.2 = 4.02 m3

Answer Example 2-5

Reactors in series

• Example 2-6: Sizing plug flow reactors in series

– Redo Example 2-5 but using 2 PFR in series. The

intermediate and final conversion remains the same.

The flow rate, FA0, also remains the same.

Answer Example 2-6

• Use Simpson’s three-point rule

331

0001

4.0

001

551.005.233.1489.032.0

)4.0()2.0(4

)0(3

mmV

rF

rF

rFXV

rdXFV

A

A

A

A

A

A

AA

331

0002

8.0

4.002

614.10.854.3405.232.0

)8.0()6.0(4

)4.0(3

mmV

rF

rF

rFXV

rdXFV

A

A

A

A

A

A

AA

210 43

)(2

0

XfXfXfXdXxfX

X

3321 165.2614.1551.0 mmVVVT

This is the same volume if we were to calculate for a single PFR to achieve the same conversion.

•Example 2.7 – An adiabatic liquid phase isomerisation

The isomerisation of butane was carried out adiabatically in the liquid phase and the data in Table 2-7 was obtained. The entering molar flow rate of n-butane of 50 kmol/hr.

Given the reactor scheme in Figure E 2-7.1, use Levenspiel plot to show how to calculate the reactor volume

Reactors in series

2538595339-rA (kmol/m3.hr)

0.650.60.40.20XTable 2-7

Reactors in series

V1

X1=0.2

X2=0.6

X3=0.65

Figure E2-7.1

35

Levenspiel plot for adiabatic reactors in series

0.00

0.50

1.00

1.50

2.00

2.50

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Conversion, X

FA0/

-rA

Can you suggest a better reactor combination?

1st CSTR 2nd CSTRPFR

CSTR PFR

Some further definitions

• Relative rate of reaction– Obtained from stoichiometric ratio– Example:

dr

cr

br

ar DCBA

Space time

ReactorFluid

•Also know as Mean Residence Time or Holding Time •Defined as the time necessary to process one reactor volume of fluid based on entrance condition (volumetric flow rate)

0 V

Volume of reactor

Volumetric flowrate

Space time = time it for the fluid to enter the reactor completely

• Space velocity (SV)– 2 common measures of space velocity

• Liquid hourly space velocity (LHSV)–Liquid flowrate measured at 60 - 70oF

• Gas hourly space velocity (GHSV)–Gas flow rate measured at STP

– Given by:

Some further definitions

Vv

SV o1

39

END OF LECTURE