The Engineering of

Chemical Reactions

Chapter 3. Single reactions in continuous

isothermal reactors

Learning Objective & Overview

1. To understand the CSTR and PFTR

2. To understand batch processes are also ideal to measure rates and kinetics

in order to design continuous processes

Learning Objective

1. Mass balance & Energy balance

2. Conversion, X

3. CSTR and PFTR

4. Chemical reactors in series

Overview

Chapter 3. Single reactions in continuous

isothermal reactors

The Continuous Stirred Tank Reactor

Chapter 3. Single reactions in continuous

isothermal reactors

• CSTR (Continuous Stirred Tank Reactor)

• ‘stirred tank’ or ‘backmix reactor’

• In this situation the crucial feature is that the composition is identical

everywhere in the reactor and in the exit pipe

• Mass balance : .... GenOutInAccum

jojo CF 0

jj CF

V

The Continuous Stirred Tank Reactor

Chapter 3. Single reactions in continuous

isothermal reactors

ⅰ) Steady state :

reactor residence time :

ⅱ)

I. Steady state vs. non-Steady state

II. ↔

Conversion in a constant-density CSTR

Chapter 3. Single reactions in continuous

isothermal reactors

If,

If ,

νj = 1

• Irreversible Reactions

Conversion in a constant-density CSTR

Chapter 3. Single reactions in continuous

isothermal reactors

• Irreversible Reactions

<Example 3-1>

sol’n

X

X

X

X X

Conversion in a constant-density CSTR

Chapter 3. Single reactions in continuous

isothermal reactors

• Irreversible Reactions

<Example 3-2>

,

Sol’n

, conversion is 90%,

,

Conversion in a constant-density CSTR

Chapter 3. Single reactions in continuous

isothermal reactors

• Fractional Conversion, X

Example 3-1

( Assumed )

Conversion in a constant-density CSTR

Chapter 3. Single reactions in continuous

isothermal reactors

• Reversible reactions

<cf.> first-order reaction

The Plug-Flow Tubular Reactor

Chapter 3. Single reactions in continuous

isothermal reactors

• PFTR

0 LZ Z+△Z

0jF jF

The Plug-Flow Tubular Reactor

Chapter 3. Single reactions in continuous

isothermal reactors

• PFTR

0 z L

jj CF 000 jj CF

jtjj CuACzF )(

Tube of length L ; the molar flow rate of species j is Fj

The Plug-Flow Tubular Reactor

Chapter 3. Single reactions in continuous

isothermal reactors

• Mass balance

.... GenOutInAccum

, ( = volumetric flow rate,

D = diameter)

Δ

Δ

The Plug-Flow Tubular Reactor

Chapter 3. Single reactions in continuous

isothermal reactors

To assume Steady-state

,

Therefore, the mass balance on species j becomes

We next make a Taylor series expansion of the difference in Cj between z and z+dz

and let dz → 0, keeping only the lead term.

The Plug-Flow Tubular Reactor

Chapter 3. Single reactions in continuous

isothermal reactors

• Note again that this expression assumes

ⅰ) plug flow ~ no dispersion

ⅱ) steady state ~ no accumulation

ⅲ) constant density ~ =constant

ⅳ) constant tube diameter ~ At=constant

ⅴ) a single reaction ~ no summation in r

• This equation is not appropriate if all five of these conditions are not met

Taking the limit and dividing by

Conversion in a Constant-Density PFTR

Chapter 3. Single reactions in continuous

isothermal reactors

After separation we obtain the differential equation

,

• Irreversible Reactions

Conversion in a Constant-Density PFTR

Chapter 3. Single reactions in continuous

isothermal reactors

• Irreversible Reactions

<Example 3-3>

, , ,

,

sol’n

cf. 18min for CSTR

cf. 72 for CSTR

Conversion in a Constant-Density PFTR

Chapter 3. Single reactions in continuous

isothermal reactors

• Irreversible Reactions

<Example 3-3>

, , ,

,

sol’n

How long a 2cm diameter tube would be required for this conversion and

what would be the fluid velocity?

∴

Conversion in a Constant-Density PFTR

Chapter 3. Single reactions in continuous

isothermal reactors

• While the PFTR reactor volume is much smaller than the CSTR for this

conversion, the PFTR tube length may become impractical, particularly

when pumping costs are considered.

• Batch :

• PFTR :

Conversion in a Constant-Density PFTR

Chapter 3. Single reactions in continuous

isothermal reactors

• Irreversible Reactions

<Example 3-4>

sol’n

, Conversion 90%

Comparison between Batch,

CSTR, and PFTR

Chapter 3. Single reactions in continuous

isothermal reactors

cf.) first-order irreversible reaction, ρ= constant, steady-state

Comparison between Batch,

CSTR, and PFTR

Chapter 3. Single reactions in continuous

isothermal reactors

• Comparisons of Possible Advantages (+) and Disadvantages (-) of Batch, CSTR, and PFTR

Batch CSTR PFTR

Reactor size for given conversion + - +

Simplicity and cost + + -

Continuous operation - + +

Large throughput - + +

Cleanout + + -

On-line analysis - + +

Product certification + - -

Comparison between Batch,

CSTR, and PFTR

Chapter 3. Single reactions in continuous

isothermal reactors

• Ratio of Residence Times and Reactor Volumes in CSTR and PFTR versus Conversion for a

First-Order Irreversible Reaction

0.0 1.0

0.5 1.44

0.9 3.91

0.95 6.34

0.99 21.5

0.999 145

00 AAA CCCX /)( PFTRCSTR /

• X ↑, ↑ pC /

Chapter 3. Single reactions in continuous

isothermal reactorsThe 1/r Plot

AAo CC AAo CC 0

r

1

• From the preceding arguments it is clear that the PFTR usually requires a

smaller reactor volume for a given conversion, but even here the CSTR may

be preferred because it may have lower material cost(pipe is more expensive

than a pot).

Chapter 3. Single reactions in continuous

isothermal reactorsSemibatch Reactors

• It is of course possible to add feed or withdraw product continuously in a

“batch” process, and we call this a semibatch reactor.

if

: CSTR + Batch reactor

cf.) now the volume V of the reactor contents increases linearly with time

must be solved numerically

Chapter 3. Single reactions in continuous

isothermal reactorsVariable-density reactor

reactants : A, steady state

∴

:

• CSTR

Chapter 3. Single reactions in continuous

isothermal reactorsVariable-density reactor

∴

• PFTR

Chapter 3. Single reactions in continuous

isothermal reactorsVariable-density reactor

AC

AoC

)(

1

ACr

X

)(

1

Xr

0AF

V

• vs.

Chapter 3. Single reactions in continuous

isothermal reactorsVariable-density reactor

<Example 3-6>

, ,

Ideal gas

Chapter 3. Single reactions in continuous

isothermal reactorsVariable-density reactor

<Example 3-6>

, ,

Chapter 3. Single reactions in continuous

isothermal reactorsVariable-density reactor

1

10 15 20 25

0.6

0.8

5 30

0.2

0.4

00

V (liters)

X

PFTR

•

nB = 2

nB = 0.5• •

nB = 1

1

40 60 80 100

0.6

0.8

20 120

0.2

0.4

00

V (liters)

X

CSTR

140

nB = 0.5• ••

nB = 2nB = 1

• Plot of conversion versus reactor volume V for the reaction 𝐴 → 𝑛𝐵𝐵, 𝑟 = 𝑘𝐶𝐵 ,

with ideal gases for 𝑛𝐵 = 2,1, and1

2. The times are all close until the

conversion becomes large, when the product dilutes the reactant for 𝑛𝐵 = 2and slows the reaction.

Chapter 3. Single reactions in continuous

isothermal reactorsVariable-density reactor

• The constant-density approximation is frequently used even when it does

not apply exactly because it is much simpler to solve the equations, and the

errors are usually not large.

• We note finally that none of these formulations gives an accurate

description of any reactor in which there is a pressure drop in gases flowing

through the reactor.

• Another rather complex type of problem involves nonideal gases and gas

mixtures because then only numerical solutions are possible.

Chapter 3. Single reactions in continuous

isothermal reactorsSpace Velocity and Space Time

ⅰ) gas hourly SV (GHSV)

ⅱ) liquid hourly SV (LHSV)

0v

VST =

STv

VSV

1

0

== SV = space velocity

ST = space time

Chapter 3. Single reactions in continuous

isothermal reactorsChemical Reactors in Series

,,,AoC 1AC

2AC

3AC

AnC

1

2

3

4

• CSTRs in series

Tanks-in-series (cf. Levenspiel)

Sketch of ideal chemical reactors in series with 𝐶𝐴𝑛, the product from

reactor n, which is also the feed into reactor n+1

Chapter 3. Single reactions in continuous

isothermal reactorsChemical Reactors in Series

• CSTRs in series

For first-order kinetics with equal-volume CSTR reactors(and therefore for

all τs equal)

Chapter 3. Single reactions in continuous

isothermal reactorsChemical Reactors in Series

• CSTRs in series

n→∞ : total τ of CSTR = τ of PFTR

τ i

Chapter 3. Single reactions in continuous

isothermal reactorsChemical Reactors in Series

• CSTRs in series

<Example 3-8>

, residence time = τ, conversion = 90%, Equal volume CSTRs in series

What residence times and reactor volumes will be required for n=1,2,3, and 4.

Sol’n

We rearrange the equation for n equal volume CSTRs in series,

Chapter 3. Single reactions in continuous

isothermal reactorsChemical Reactors in Series

• CSTRs in series

<Example 3-8>

, residence time = τ, conversion = 90%, Equal volume CSTRs in series

What residence times and reactor volumes will be required for n=1,2,3, and 4.

τ decreases with n to approach the

PFTR for which τ = 4.61min

Chapter 3. Single reactions in continuous

isothermal reactorsChemical Reactors in Series

• CSTRs in series

<Example 3-8>

, residence time = τ, conversion = 90%, Equal volume CSTRs in series

What residence times and reactor volumes will be required for n=1,2,3, and 4.

The reactor volumes are 𝑉 = 𝜈𝜏𝑛, which are 72, 34.6, 27.7, and 24.9

liters, respectively. An infinite number of CSTRs in series would

require the total volume of a PFTR, which is 4 × 4.61 = 18.4 liter s

to run this reaction to this conversion.

Chapter 3. Single reactions in continuous

isothermal reactorsChemical Reactors in Series

• PFTR + CSTR

PFTR + CSTR

CSTR + PFTR

For first-order kinetics

i) PFTR + CSTR ii) CSTR + PFTR

For two equal-volume reactors(𝜏1 = 𝜏2) with first-order kinetics the

expression are identical for both configurations.

Chapter 3. Single reactions in continuous

isothermal reactorsChemical Reactors in Series

In general it is a common strategy to use a CSTR first where the conversion is low and

then switch to a PFTR as the conversion become high to minimize total reactor volume.

The total residence time from CSTR+PFTR in series is indicated by the 1/r plots

PFTR + CSTR CSTR + PFTR

Chapter 3. Single reactions in continuous

isothermal reactorsAutocatalytic reactions

A+B → B+B,

The rate of the forward reaction is enhanced by the concentration of a product.

Chapter 3. Single reactions in continuous

isothermal reactorsAutocatalytic reactions

P

F

T

R

If → 𝜏 = ∞

CAoCAo - CA CAo - CACAo

PFTR

CSTR

C

S

T

R

Chapter 3. Single reactions in continuous

isothermal reactorsAutocatalytic reactions

Fermentation

Combustion reactions

▶ sugar + enzyme → alcohol + 2enzyme(A) (B)

▶

▶A + R → 2R

radical

Chapter 3. Single reactions in continuous

isothermal reactorsReversible Reactions

• For a reversible reaction the rate goes to zero before the reaction reaches

completion, and 1/r therefore goes to infinity.

AACC

0 AACC

0

0ACAeC

r r

1

0

1

r

0r

AeC 0AC0 0

Irreversible

reversible

Irreversible

reversible

Chapter 3. Single reactions in continuous

isothermal reactorsReversible Reactions

What is Residence of CSTR and PFTR ?X=0.5

sol’n

CSTR

<Example 3-9>

Chapter 3. Single reactions in continuous

isothermal reactorsReversible Reactions

What is Residence of CSTR and PFTR ?X=0.5

sol’n

PFTR

<Example 3-9>

Chapter 3. Single reactions in continuous

isothermal reactorsTransients in Continuous Reactors

• non-steady state

In the case of CSTR (𝑉, 𝜐0 = constant)

Chapter 3. Single reactions in continuous

isothermal reactorsTransients in Continuous Reactors

• non-steady state

In the case of CSTR (𝑉, 𝜐0 = constant)

Chapter 3. Single reactions in continuous

isothermal reactorsTransients in Continuous Reactors

• Solvent replacement

no reaction

at t = 0, CA = CAi

(Note carefully here the difference between 𝐶𝐴𝑖 and 𝐶𝐴0)

Chapter 3. Single reactions in continuous

isothermal reactorsTransients in Continuous Reactors

• Reaction

ODE

: first-order irreversible reactions

at t = 0, CA = CAi

, : CSTR of steady state

Chapter 3. Single reactions in continuous

isothermal reactorsTransients in Continuous Reactors

• PFTR

process of induction

.... GenOutInAccum

Divide by ,

∴

Chapter 3. Single reactions in continuous

isothermal reactorsTransients in Continuous Reactors

0AC

AsC

0

AC

0t

0t 0t

0 0t

0AC

AsC

AC

Possible transients in CSTR reactors. left picture shows the situation starting with

pure solvent (𝐶𝐴 = 0) in the reactor initially, 𝐶𝐴 = 𝐶𝐴0 at t=0 with no reaction. right

picture shows the situation where the reactor initially contains pure reactant at 𝐶𝐴0,

and at t=0 reactant flow at 𝐶𝐴0 is begun and eventually approaches a steady-state

concentration 𝐶𝐴𝑠

• CSTR