chapter 2 conversion and reactor sizing

Chemical Engineering Department

CDB2043 REACTION ENGINEERING

CHAPTER 2: CONVERSION AND REACTOR SIZING(part 1)

1

Basic

knowledge

Application

At the end of the lecture, students should be able to:

1. define conversion

2. developed the design equation for batch and flow reactor

3. apply the design equation to calculate the volume of reactors for a particular process

4. evaluate the best reactor arrangement

5. differentiate between space time and space velocity

3

Course Learning Outcome

4Overview 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

Batch CSTR PFR PBR

5

Recap from Lecture 1

Design Equation in terms of mole

dt

dNVr AA

How do we relate conversion with flow rate or moles of reactant?

What is conversion?

Consider the general equation (irreversible eqn)

aA + bB cC + dD

We will choose A as our basis of calculation

Da

dC

a

cB

a

bA

How do we define conversion?

Conversion

Conversion is define as:

feedA of moles

reactedA of molesAX

MAXIMUM CONVERSION?

Irreversible Reaction

X = 1

Reversible Reaction

X = Xe

8Relating conversion with moles of reactant

Batch reactor

Flow reactor (CSTR and PFR/PBR)

reactedA of Mole - fedA of Mole any timeat A of Mole t

XNNN AAA 00 -

XFFF AAA 00 -

outletat A of rate flowMolar

-inlet at A of rate flowMolar any timeat A of rate flowMolar t

Now, recap back our design equation:

9

Relating V to X

dt

dNVr AA

HOW TO RE-WRITE

V = f(X)

WHAT WE HAVE JUST DISCOVERED:

XNNN AAA 00 -

XFFF AAA 00 -

Develop Design Equation for batch reactor

Batch reactor

PFR CSTR

Develop Design Equation for flow reactor

Design Equation(Summary)

Reactor Differential Algebraic Integral

Batch

CSTR

PFR

PBR

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 knowN value of FA0:

14

Reactor Sizing for flow reactor

rA X FA0/-rAFA0/-rA

X


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

using Levenspiel plot

Consider the design equation for CSTR

A

0A

r

XFV

Consider the design equation of a PFR


A0A rdV

dXF

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?

17


XA -rA (mol/m3.s)

0.0 0.45

0.1 0.37

0.2 0.30

0.4 0.195

0.6 0.113

0.7 0.079

0.8 0.05

TABLE 2.1

Solution Ex 2-2: Sizing for CSTR

TABLE 2.1

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

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

(m3..s/mol)

0.0 0.45 2.22 0.89

0.1 0.37 2.70 1.08

0.2 0.30 3.33 1.33

0.4 0.195 5.13 2.05

0.6 0.113 8.85 3.54

0.7 0.079 12.70 5.06

0.8 0.05 20.00 8.00

XFr

V AA

0

1

DESIGN EQUATION OF CSTR!!

Solution Ex 2-2: Sizing for PFR

TABLE 2.1

XA -rA(mol/m3.s)

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

0.0 0.45 0.89

0.2 0.30 1.33

0.4 0.195 2.05

0.6 0.113 3.54

0.8 0.05 8.00

0.80

0

A

A

FV dX

r

DESIGN EQUATION OF PFR!!

Use 5-point quadrature formula:

4

00 1 2 3 44 2 4

3

X

X

hf X dX f f f f f

4 0

4

X Xh

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 theres no side reactors, conversion at any

reactor outlet is define as:

reactorfirst tofedA of mole

ipoint toup reactedA of moles totaliX

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

FA

0/-

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, XF

A0

/-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

02

4

6

8

10

0 0.2 0.4 0.6 0.8 1

Conversion, X

FA

0/-

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 Levenspielplot 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 0.8

FA0/-rA 0.89 1.09 1.33 2.05 3.54 5.06 8.0

02

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

FA

0/-

rA

3

1

3

1

3

4.0

0

8.0

4.00.2

0.2

mV

mV

mr

F

XA

A

332

12

2

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 Simpsons three-point rule

331

0001

4.0

0

01

551.005.233.1489.03

2.0

)4.0()2.0(4

)0(3

mmV

r

F

r

F

r

FXV

r

dXFV

A

A

A

A

A

A

A

A

331

0002

8.0

4.0

02

614.10.854.3405.23

2.0

)8.0()6.0(4

)4.0(3

mmV

r

F

r

F

r

FXV

r

dXFV

A

A

A

A

A

A

A

A

210 43

)(2

0

XfXfXfX

dXxf

X

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 Levenspielplot to show how to calculate the reactor volume

Reactors in series

2538595339-rA (kmol/m3.hr)

0.650.60.40.20X

Table 2-7

Reactors in series

V1

X1=0.2

X2=0.6

X3=0.65

Figure E2-7.1

33

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

FA

0/-

rA

1st CSTR 2nd CSTRPFR

CSTR PFR

Some further definitions

Relative rate of reaction

Obtained from stoichiometric ratio

Example:

d

r

c

r

b

r

a

r 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

V

vSV o

1

END OF LECTURE

37

chapter 2 conversion and reactor sizing

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