Chapter 2: Conversion and Reactor Sizing

CHEMICAL REACTION ENGINEERING (SKF3223)

WAN NORHARYATI WAN SALLEH

hayati@petroleum.utm.my

RAFIZIANA MD. KASMANI rafiziana@petroleum.utm.my

Conversion, X

To quantify how far a reaction has progressed

How many moles of C are formed for every mole A consumed

Consider :

The basis of calculation is always the limiting reactant

Irreversible reaction: Xmax = 1.0 (complete conversion)

Reversible reaction: Xmax = Xequilibrium (equilibrium conversion)

Da

d C

a

c B

a

b A

dD cC bB aA

CONVERSION

Batch system (X,t)

Flow system (X,V/W)

0

AA0 N-N

A

AN

X0

0

A

AAA

F

FFX

XNNmolN AAA 00)(

X = moles of A reacted / consumed

moles of A fed

XFFsmolF AAA 00)/(

FA0X= molar flow rate at which A is

consumed / reacted

NA0X= moles of A consumed

/ reacted

)1(0 XN A )1(0 XFA

BATCH REACTOR

For batch reactor , we are interested in determining how long to leave

the reactants in the reactor to achieve a certain conversion

From mole balance: From the conversion:

4

This is how the Design Equation derived from mole balance equation in

terms of conversion

dtVrA

AdNXNNN AAA 00

dt

dXN

dt

dNA

A00

Differentiating with respect of time:

NA0 = 0 : constant with respect of time

dt

dXNVr AA 0

X

A

AVr

dXNt

0

0dt

dXNVr AA 0

GAS FLOW SYSTEM

The entering molar flow rate, FA0 (mol/s)

0

00

0

00

0

3

3

000

system gasfor

.

RT

Py

RT

PC

C

s

dm

dm

mol

s

mol

CF

AAA

A

AA CA0= entering concentration,

mol/dm3

Ya0= entering mole fraction of A

P0= entering total pressure, kPa

T0=entering temperature, K

Pa0= entering partial pressure

R= ideal gas constant =

8.314k.Pa.dm3/mol.K

CSTR

A

AA

r

FFV 0

A

AAA

r

XFFFV

)( 000

From mole balance:

XFFF AAA 00

Design Equation:

From the conversion:

A

AAA

r

XFFFV 000

A

A

r

XFV 0

PFR

AA r

dV

dF

From mole balance:

Design Equation:

From the conversion:

XFFF AAA 00

dV

dXF

dV

dFA

A00

Differentiating with respect of volume:

FA0 = 0 : constant with respect of volume

dV

dXFr AA 0 dV

dXFr AA 0

X

A

Ar

dXFV

0

0

PBR

AA r

dW

dF'

From mole balance:

Design Equation:

From the conversion:

XFFF AAA 00

dW

dXF

dW

dFA

A00

Differentiating with respect of weight of catalyst:

dW

dXFr AA 0'

dW

dXFr AA 0'

X

A

Ar

dXFW

0

0'

DESIGN EQUATIONS

9

X

A

AOr

dXFW

0'

Design Equations for Isothermal Reactors

REACTOR DIFFERENETIAL ALGEBRAIC INTEGRAL

FORM FORM FORM

Vrdt

dXN AAO )(

X

A

AOVr

dXNt

0

)( AAO rdV

dXF

X

A

AOr

dXFV

0

CSTR ExitA

AO

r

XFV

)(

)(

BATCH

PFR

PBR )'( AAO rdW

dXF

REACTOR SIZING By sizing a chemical reactor we mean we're either determine the

reactor volume to achieve a given conversion or determine the conversion that

can be achieved in a given reactor type and size.

Normally, the process / experimental data will be given (X, -rA)

PFR

Simpson's One-Third Rule is one of the more common numerical

methods.

Other numerical methods (see Appendix A.4, pp 1013-1015):

(i) Trapezoidal Rule (2 data points)

(ii) Simpson's Three-Eighth's Rule (4 data points)

(iii) Five-Point Quadrature Formula (5 data points)

Reactor Sizing

PFR CSTR

Levenspiel Plot

REACTORS IN SERIES

Why?

Sometimes 2 CSTR reactor volumes in series is less than the

volume of 1 CSTR to achieve the same conversion.

Can model a PFR with a large number of CSTR in series.

In the case of PFR, whether you place 2 PFR in series or have 1

PFR, the total reactor volume required to achieve the same

conversion is identical.

REACTORS IN SERIES

X=0

FA0

X1 = conversion achieved in

the PFR

FA1

X2 = conversion achieved in

the PFR & CSTR

FA2

X3 = total

conversion

achieved by all

3 reactors

V1

V2

CSTR

V3

Valid only for NO side

streams:

PFR

PFR

FA3

3003

2002

1001

XFFF

XFFF

XFFF

AAA

AAA

AAA

(i) CSTR in series:

(ii) PFR in series:

V2

-rA2

X1

FA1

X2

FA2

X0

FA0

V1

-rA1

V1

V2

-rA2

-rA1

X1

FA1 X2

FA2

X0

FA0

1

101

A

A

r

XFV

1

0

01

X

A

Ar

dXFV

2

1

02

X

X A

Ar

dXFV

2

1202

)(

A

A

r

XXFV

V1

-rA1

V3

V2

-rA2

-rA3

X1

FA1 X2

FA2

X0

FA0

X3

FA3

(iii) CSTR + PFR in series:

1

101

A

A

r

XFV

2

12

02

X

X A

Ar

dXFV

3

2303

)(

A

A

r

XXFV

SPACE TIME,

The time necessary to process one reactor volume by

the volumetric rate entering the reactor

Also called the holding time or mean residence time

where 0 is entrance volumetric rate

timevolume

volumetime

V

/

0

16

SPACE VELOCITY (SV)

10

VSV

GHSV Gas Hourly Space Velocity, h-1

v0 at STP (standard temp. and pressure)

LHSV Liquid Hourly Space Velocity, h-1

v0 at some reference temperature

Reciprocal of the space time,

Two SV commonly used in industry:

Main Reference:

1. Fogler,H.S., “Elements of Chemical Reaction Engineering”, 4th

Edition,Prentice Hall, New Jersey, 2006.

Other References:

1. Davis, M.E and Davis, R.J, “Fundamentals of Chemical Reaction

Engineering”, Mc-Graw-Hill, New York, 2003

2. Schmidt, L.D, “The Engineering of Chemical Reactions”, Oxford,

New York, 1998

3. Levenspiel,O., “Chemical Reaction Engineering”, 3rd Edition,

Wiley,New York, 1998

4. Smith,J., “Chemical Engineering Kinetics”, 3rd Edition, McGraw-

Hill, New York, 1981

REFERENCES