2.1. CONSTANT-VOLUME BATCH REACTOR
constant-density reaction system
Irreversible- 1st order
reaction
Irreversible – 2nd order
reaction
A+B→P
A→P
2A→P
Zero-Order Reactions
Overall Order of
Irreversible Reactions
from the Half-Life t1/2
Empirical Rate
Equations of nth Order
dCA
− rA = −
dt
n
= k CA
Irreversible Reactions
in Parallel
A → R, k1
A → S, k2
aA + bB → P
Irreversible
Reactions in Series
A→R→S
First-Order
Reversible Reactions
A
R
2.2. VARYING-VOLUME BATCH
REACTOR
1 dN i 1 d(Ci V) 1 VdCi + CidV
ri =
=
=
V dt
V dt
V
dt
dCi Ci dV
=
+
dt
V dt
V = V0 (1 +  A X A )
A =
VX A = 1 − VX A = 0
VX A = 0
A is the fractional change in volume of the system
Chapter 3
Ideal Reactors for a Single
Reaction
REACTOR DESIGN
In reactor design we want to know what size and type of
reactor and method of operation are best for a given job.
 Many factors must be accounted for in predicting the
performance of a reactor. How best to treat these factors is
the main problem of reactor design.

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REACTOR DESIGN
For the reaction aA +bB → rR, with inerts iI
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Figs. 4.4 and 4.5 show the symbols commonly used to tell what is happening
in the batch and flow reactors.
REACTOR DESIGN
For the reaction aA +bB → rR, with inerts iI
Special Case 1. Constant Density Batch and Flow Systems.
This includes most liquid reactions and also those gas reactions run at
constant temperature and density. Here CA and XA are related as follows:

To relate the changes in B and R to A we have:
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REACTOR DESIGN
For the reaction aA +bB → rR, with inerts iI
o
Special Case 2: Batch and Flow Systems of Gases of
Changing Density but with T and p constant
→The density changes because of the change in number of moles
during reaction. In addition, we require that the volume of a fluid
element changes linearly with conversion: V = Vo (1 + XA )
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2.3. TEMPERATURE AND REACTION
RATE
Arrheùnius
k = k0 e- E / RT
k0: frequency factor
E : activation energy, J/mol
R= 8,314 J/mol.K
T: K
1. Material and energy balances
The starting point for all design is the material balance expressed for any
reactant (or product).
Figure 3.1 Material
balance for an element
of volume of the reactor.
Thus, as illustrated in Fig. 3.1, we have
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In nonisothermal operations energy balances must be used in conjunction with
material balances.
Figure 3.2 Energy balance for
an element of volume
of the reactor.
Thus, as illustrated in Fig. 3.2, we have
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In this chapter we develop the performance equations for a single
fluid reacting in the three ideal reactors shown in Fig. 3.3. We call
these homogeneous reactions.
Figure 3.3 The three types of ideal reactors: (a) batch reactor, or BR; (b) plug
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flow reactor, or PFR; and (c) continuously stirred tank reactor, or CSTR.
2. Batch reactor (BR)
Make a material balance for any component A. Noting that no fluid enters or
leaves the reaction mixture during reaction, the material balance written for
component A is
or
(3.1)
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2. Batch reactor (BR)
(3.2)
By replacing these two terms in Eq. 3.1, we obtain
(3.3)
Rearranging and integrating then gives
(3.4)
If the density of the fluid remains constant, we obtain
with
(3.5)
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2. Batch reactor (BR)
For all reactions in which the volume of reacting mixture changes
proportionately with conversion, Eq. 3.4 becomes
(3.6)
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* V = const
t = CA0
XA

0
dX A
=
( − rA )
−
CA

CA0
dCA
( − rA )
* V = V0 (1 +  A X A )
t = N A0
XA
 (− r )
0
A
dX A
= C A0
V0 (1 +  A X A )
XA
 (− r )
0
A
dX A
(1 +  A X A )
21
𝑉
𝜏=
𝑣𝑜
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3. Continuously stirred tank reactor (CSTR)
Figure 3.4 Notation for a CSTR
Reactor in which the contents are well stirred and uniform throughout.
Thus, the exit stream from this reactor has the same composition as the
fluid within the reactor.
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3. Continuously stirred tank reactor (CSTR)
By selecting reactant A for consideration, material balance for a CSTR can be
written as follows
(3.7)
As shown in Fig. 3.4, if FA0 = v0CA0 is the molar feed rate of component A to
the reactor, then considering the reactor as a whole we have
Introducing these three terms into Eq. 3.7, we obtain
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(3.8)
which on rearrangement becomes
(3.9)
A space-time of 2 min means that every 2 min one reactor volume of feed at
specified conditions is being treated by the reactor.
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3. Continuously stirred tank reactor (CSTR)
More generally, if the feed on which conversion is based, subscript 0, enters
the reactor partially converted, subscript i, and leaves at conditions given by
subscript f, we have
(3.10)
For the case of constant-density systems XA = 1 – CA/CA0:
(3.11)
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3. Continuously stirred tank reactor (CSTR)
Figure 3.5 is a graphical representation of these mixed flow performance
equations.
3.9
3.11
Figure 3.5 Graphical representation of the design equations for CSTR.
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Example 3.2:
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Example 3.3:
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4. Plug flow tubular reactor (PFTR)
Figure 3.6 Notation for a plug flow tubular reactor.
At the steady-state, the material balance for reactant A becomes
(3.12)
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Referring to Fig. 3.6, we see for volume dV that
Introducing these three terms into Eq. 3.12, we obtain
Noting that
We obtain
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(3.13)
For the reactor as a whole the expression must be integrated. Grouping the terms
accordingly, we obtain
Thus
(3.14)
Equation 3.14 allows the determination of reactor size for a given feed rate and
required conversion.
Compare eq 3.9 and 3.14: The difference is that in plug flow rA varies, whereas
in mixed flow rA is constant.
(3.15)
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CSTR
(3.9)
PFR
(3.14)
Compare eq 3.9 and 3.14: The difference is that in plug flow rA varies, whereas
in mixed flow rA is constant.
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For a more general expression, if the feed on which conversion is based, subscript 0,
enters the reactor partially converted, subscript i, and leaves at a conversion designated by
subscript f, we have
For the special case of constant-density systems
We have
(3.16)
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3.14
3.16
Figure 3.7 Graphical representation of the performance equations for plug flow
tubular reactors.
Fig. 3.7 displays these performance equations and shows that the space-time
needed for any particular duty can always be found by numerical or graphical
Integration.
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These performance equations can be written either in terms of concentrations or
conversions. For systems of changing density it is more convenient to use
conversions; however, there is no particular preference for constant density
systems.
Whatever its form, the performance equations interrelate the rate of reaction, the
extent of reaction, the reactor volume, and the feed rate, and if any one of these
quantities is unknown it can be found from the other three.
(3.14)
(3.16)
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By comparing the batch expressions with these plug flow expressions we find:
BR * V = const
t = CA0
XA

0
dX A
=
( − rA )
−
CA

CA0
dCA
( − rA )
PFR
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By comparing the batch expressions with these plug flow expressions we find:
BR
* V = V0 (1 +  A X A )
t = N A0
XA
 (− r )
0
A
dX A
= C A0
V0 (1 +  A X A )
XA
 (− r )
0
A
dX A
(1 +  A X A )
PFR
(3.14)
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Example 3.4:
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* V = const
t = CA0
XA

0
dX A
=
( − rA )
−
CA

CA0
dCA
( − rA )
* V = V0 (1 +  A X A )
t = N A0
XA
 (− r )
0
A
dX A
= C A0
V0 (1 +  A X A )
XA
 (− r )
0
A
dX A
(1 +  A X A )
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Continuously stirred tank reactor (CSTR)
Figure 3.5 is a graphical representation of these mixed flow performance
equations.
3.9
3.11
Figure 3.5 Graphical representation of the design equations for CSTR.
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Plug flow tubular reactor (PFTR)
3.14
3.16
Figure 3.7 Graphical representation of the performance equations for plug flow
tubular reactors.
Fig. 3.7 displays these performance equations and shows that the space-time
needed for any particular duty can always be found by numerical or graphical
Integration.
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