Cre++++

Chemical Reactor Design-CHEM-E7135
Yongdan Li
The field that studies the rates and mechanisms of chemical
reactions and the design of the reactors in which they take place
Professor of Industrial Chemistry
Department of Chemical and
Metallurgical Engineering
School of Chemical Technology
Aalto University
Email: yongdan.li@aalto.fi
Kemistintie 1, E404

2. Performance of Ideal Reactors

3
Lecture 2.1 Introduction to Reactor Design
Broad classification of reactor types
Fig. 2.1 (a) The batch reactor. (b) The steady-state flow reactor. (c), (d), and (e) Various forms of
the semibatch reactor

4
Starting points Material balance Energy balance
Broad classification of reactor types

5
Material balance
Fig 2.2 Material balance for an element of volume of the reactor
Uniform composition
nonuniform composition
account over the whole reactor
account over a differential element
integration
i ii iii iv
Batch i, ii = 0
Steady-state flow iv = 0
Semibatch i, ii, iii, iv must be considered
Notes
(1)

6
Energy balances (nonisothermal operations)
Fig 2.3 Energy balance for an element of volume of the reactor
i ii iii iv
(2)
Uniform composition
nonuniform composition
account over the whole reactor
account over a differential element
integration
Eq.1 Eq.2iii
Heat effect is produced by the reaction itself

7
Symbols
Fig 2.4 Symbols used for batch reactors
Fig 2.5 Symbols used for flow reactors

8
Relationship between CA and XA
 Constant Density, Batch and Flow Systems
(3)
(4)

9
 Batch and Flow Systems or Gases of Changing
Density but with T and π Constant
density changes from the change
in moles during reaction
Requirement: the volume of a fluid element changes linearly with
conversion.
(5)
(6)

10
 Batch and Flow Systems for Gases in General (varying ρ, T, π)
For ideal gas
b) high-pressure nonideal gas behavior
z: compressibility factor
c) change to reactant B
a) liquids or isothermal gases with no
change pressure and density
(7)
For other systems

11
Three types of ideal reactors
Fig 2.6 The three types of ideal reactors: (a) batch reactor, or BR; (b) plug flow reactor, or PFR; and (c)
mixed flow reactor, or MFR.
At any instant the
composition throughout
the reactor is uniform
No back mixing or
diffusion along the flow
path. Residence time for
all elements is the same.
The contents are well
stirred and uniform
throughout. The exit
stream has the same
composition as it in the
reactor

12
Accounting about the whole reactor due to uniform composition
(8)
(9) (10)
General equation (isothermal or not, constant density or not)
Lecture 2.2 Ideal Batch Reactor

13
If the density of the fluid remains constant
(11)
Single gas-phase reactions with density changes
(V changes proportionately with XA)
(12)
Fig 2.7 Graphical representation of the performance equations for batch reactors, isothermal or not.
Lecture 2.2 Ideal Batch Reactor
10
11
11

14
Space-Time and Space-Velocity
reaction time t batch reactor
space time 
space velocity s
flow reactor
Space time
(13)
Space velocity
(14)
Lecture 2.3 Steady-State Mixed Flow Reactor

15
Space-Time and Space-Velocity
reaction time t batch reactor
space time 
space velocity s
flow reactor
Space time
(13)
(15)

16
Accounting about the whole reactor due to uniform composition
(16) (17)

17
FA0 , CA0 , XA0 = 0 FAi , CAi , XAi FAf , CAf , XAf
CAf , (-rA)f
When
(18)
For constant-density systems, XA=1-CA/CA0
(19)

18
In design
In kinetic studies, the rate information can be given without integration
Application of mixed flow performance equations
Fig 2.8 Graphical representation of the design equations for mixed flow reactor
(17)
(19)
be written out directly
F0 , -rA , XA ,V any one can be found from the other three
17
19

19
 first-order reaction
For constant-density systems, XA=1-CA/CA0
(20)
For linear expansion
(21)
 second-order reaction
(22)

20
In a plug flow reactor, the composition of the fluid varies from point to point along a flow
path. The material balance for a reaction component must be made for a differential ele-
ment of volume dV.
(23)
(24)
Lecture 2.4 Steady-state Plug Flow Reactor

21
(25)
FA0 , CA0 , XA0 = 0 FAi , CAi , XAi FAf , CAf , XAfPFR
When,
For the whole reactor,
(26)

22
For the constant-density systems
(27)(25)
Fig 2.9 Graphical representation of the performance equations for plug flow reactors
25
27

23
Application of Plug flow performance equations
In design v0 , -rA , XA ,V any one can be found from the other three
In kinetic studies, the rate information can be given with simple integration
based on Eqs. 25 and 27
 Zero-order homogeneous reaction
(28)
 First-order irreversible reaction
(29)
 First-order reversible reaction
(30)

24
 Second-order irreversible reaction
(31)
Where the density is constant, put A = 0
Comparison between batch and plug flow expressions
(1) For systems of constant density:
the performance equations are identical,
 for plug flow is equivalent to t for the batch reactor,
and the equations can be used interchangeably.
(2) For systems of changing density:
there is no direct correspondence between the batch and the plug flow equations,
and the correct equation must be used for each particular situation.

25
Mixed Versus Plug Flow Reactors
For the general case
Lecture 2.5 Size Comparison of Flow Reactors
(5)(1-27)
Mixed flow reactor: Eq. 17 gives
Plug flow reactor: Eq. 25 gives
(32)
(33)

26
Mixed Versus Plug Flow Reactors
With constant density, or ɛ = 0, this expression integrates to
Dividing we find that
(34)
(35) (36)
Identical feed composition CA0 and flow rate FA0 give directly the volume ratio.

27
Fig 2.10 Comparison of performance of single mixed flow and
plug flow reactors for the nth-order reactions
For any particular duty and for all
positive reaction orders the mixed
reactor is always larger than the plug
flow reactor. The ratio of volumes
increases with reaction order.
When conversion is small, the reactor
performance is only slightly affected
by flow type. The performance ratio
increases very rapidly at high
conversion; consequently, a proper
representation of the flow becomes
very important in this range of
conversion.
Density variation during reaction
affects design; however, it is normally
of secondary importance compared to
the difference in flow type.

28
For any particular duty and for all
positive reaction orders the mixed
reactor is always larger than the plug
flow reactor. The ratio of volumes
increases with reaction order.
When conversion is small, the reactor
performance is only slightly affected
by flow type. The performance ratio
increases very rapidly at high
conversion; consequently, a proper
representation of the flow becomes
very important in this range of
conversion.
Density variation during reaction
affects design; however, it is normally
of secondary importance compared to
the difference in flow type.
Mixed (18)
Plug (26)

Plug Flow Reactors in Series
X1, X2, . . . , XN
N plug flow reactors
the fractional conversion of component A leaving reactor 1, 2, . . . , N
For a number of reactors with total volume V
For the ith reactor
Lecture 2.6 Multiple-Reactor Systems
(37)
(38)
N plug flow reactors in series with a total volume V gives the same conversion as
a single plug flow reactor of volume V

Plug Flow Reactors in Parallel
X1, X2, . . . , XN
N plug flow reactors
the fractional conversion of component A leaving reactor 1, 2, . . . , N
In parallel, V/F or τ must be the same for each parallel line.
Any other way of feeding is less efficient. For the optimum
hook up of plug flow reactors connected in parallel or in any
parallel-series combination, we can treat the whole system as
a single plug flow reactor of volume equal to the total
volume of the individual units if the feed is distributed in
such a manner that fluid streams that meet have the same
composition.

Equal-Size Mixed Flow Reactors in Series
In plug flow
the concentration of reactant decreases progressively through the system.
In mixed flow
the concentration drops immediately to a low value.
Consider a system of N mixed flow reactors connected in series.
Fig 2.12 Concentration profile
through an N-stage mixed flow
reactor system compared with
single flow reactors.
31

32
Fig 2.13 Notation for a system of N equal-size mixed reactors in series
Quantitatively evaluate the behavior of a series of N equal-size mixed flow reactors.
ɛ = 0
First-Order Reactions
or
Vessel i
(18)
(39)

33
Now the space-time τ is the same in all the equal-size reactors of volume Vi
Treat the system as a whole
for N →∞
(40)
(41) (42)
Second-Order Reactions by a procedure similar to that of a first-order reaction
whereas for plug flow
(43)
(44)

34
Dimensionless reaction rate group

35
Dimensionless reaction rate group

36
Mixed Flow Reactors of Different Sizes in Series
Finding the Conversion in a Given System
Now from Eq. 19, noting that ɛ = 0, for the first reactor
For the ith reactor we may write
or
Fig 2.16 Notation for a series of unequal-size mixed flow reactors
(45)
(46)
ɛ = 0

37
Mixed Flow Reactors of Different Sizes in Series
Fig 2.17 Graphical procedure for finding compositions in a series of mixed flow reactors.

38
Determining the Best System for a Given Conversion
For the first reactor For the second reactor
Based on Eq. 18
(48)(47)
Find Vmin of two mixed flow reactors in series to achieve a specified XA
Smax of rectangle

39
Maximization of Rectangles
A = xy
dA = 0 = ydx + xdy
-dy/dx = y/x
Fig 2.19 Graphical procedure for
maximizing the area of a rectangle
For first-order reactions equal-size reactors are
best.
For n > 1, the smaller reactor should come first.
For n < 1, the larger should come first
Fig 2.20 Maximization of rectangles applied to find the optimum
intermediate conversion

40
Reactors of Different Types in Series
Fig 2.21 Graphical design procedure for reactors in series.
(49)

41
Reactors of Different Types in Series
(49)
For a reaction whose rate-concentration curve rises monotonically (any
nth-order reaction, n > 0) the reactors should be connected in series.
They should be ordered so as to keep the concentration of reactant as
high as possible if the rate-concentration curve is concave (n > 1), and
as low as possible if the curve is convex (n < 1). As an example, for the
case of Fig 2.21 the ordering of units should be plug, small mixed, large
mixed, for n > 1; the reverse order should be used when n < 1.

42
In certain situations it is found to be advantageous to divide the product stream from a plug
flow reactor and return a portion of it to the entrance of the reactor.
Let the recycle ratio R be defined as
Fig 2.22 Nomenclature for the recycle reactor
Across Eq. 26, plug flow gives
Lecture 2.7 Recycle Reactor
(50)
(51)

43
Now to the evaluation of XA1: from Eq. 5 we may write
On the other hand
(54)
(52)
(53)

44
Combining Eqs. 53 and 54
On replacing Eqs. 55 and 52 in Eq. 51
(55)
(56)
For the special case where density changes are negligible we may write this equation in
terms of concentrations
(57)

45
These expressions are represented graphically
Fig 2.23 Representation of the performance equation for recycle reactors
Any ɛ ɛ = 0
56
57

46
These expressions are represented graphically
Fig 2.23 Representation of the performance equation for recycle reactors
Any ɛ ɛ = 0
56
57
10
1
1 1
( 1) ( ) ( )
1 1
1 1
( ) ( )
1 1
Af
Af
Af
Af
X
A
RAf AfX
RA A
X
A
RAf Af Af dashed AfX
R A
Af average shadowed
dXV
R X X
F R r R
dX
X X X S X
r R R
X H S


  
  
   
  
  



47
Extremes of negligible and infinite recycle approach plug flow and mixed flow
For first-order reaction
For second-order reaction
ɛ = 0
(58)
(59)
0

48
Fig 2.24 Typical rate-concentration curve for autocatalytic reactions
In an autocatalytic reaction, the rate at the start is low because little product is present;
it increases to a maximum as product is formed and then drops again to a low value
as reactant is consumed.
Reactions with such rate-concentration curves lead to interesting optimization problems.
Lecture 2.8 Autocatalytic Reactions
(60)

49
Plug Flow Versus Mixed Flow Reactor, No Recycle
Fig 2.25 For autocatalytic reactions mixed flow is more efficient at low conversions, plug flow is
more efficient at high conversions.
1. At low conversion the mixed reactor is superior to the plug flow reactor.
2. At high enough conversions the plug flow reactor is superior.

50
Optimum Recycle Operations
The optimum recycle ratio is found by differentiating Eq. 56 with respect to R and setting
to zero, thus
(61)
Fig 2.26 Correct recycle ratio for an autocatalytic reaction compared with recycle ratios which
are too high and too low
Optimum:
KL=PQ

51
Reactor Combinations
Fig 2.27 (a) The best multiple reactor scheme. (b) The best scheme when unconverted reactant can
be separated and recycled
(If all sorts of reactor arrangements can be considered)

52
Isothermal and constant volume
Summary
Typical ideal reactors

53
1.We want to find how equilibrium composition and product distribution
are affected by changes in operating temperatures.
Temperature (T)Equilibrium Conversion (X)
2.We want to learn how the reactor size confirm through the XA versus T
plot.
3. How to choose the optimal temperature for some reactions ?
Purpose of this chapter:
Lecture 2.9 Temperature effect

54
THERMODYNAMICS REVIEW
Enthalpy change (ΔH) is variable quantity of the enthalpy (H), also the energy
liberation or the energy absorption can be expressed by the heat in a chemical
reaction process, and this heat is expressed by Enthalpy change (ΔH).
Thus, Enthalpy change (ΔH) usually has a direct relationship with heat
before and after a chemical reaction.
From macro perspectives: ΔH = H (product) - H (reactant). Thus,
(62)
Basically we often use ΔH to build relationship with the heat or temperature.

55
The first problem is to evaluate the heat of reaction at temperature T2 knowing the
heat of reaction at temperature T1. This is found by the law of conservation of energy
as follows:
(63)
In terms of enthalpies of reactants and products this becomes
(64)
reaction enthalpy
1. Find the relationship between the equilibrium composition and the
operating temperatures.
For

56
In terms of specific heats
where
(65)
(66)
(67)
When the molar specific heats are functions of temperatures as follows,

57
We obtain
(68)
(69)
where

58
Temperature (T)
Then we could build the relationship between the ΔH and the Equilibrium Conversion
(X), and that can be realized by a correlation between the ΔH and Equilibrium Constant
(K).
Enthalpies (ΔH)
Equilibrium Conversion (X) Equilibrium Constant (K)
The equilibrium composition, as governed by the equilibrium constant, changes with
temperature, and from thermodynamics the rate of change is given by
(70)Van't Hoff plot

59
When the heat of reaction Δ H, can be considered to be constant in the temperature
interval, integration yields
(71)
When the variation of ΔH, must be accounted for in the integration we have
where Δ Hr is given by a special form of Eq. 65 in which subscript 0 refers to the
base temperature
(72)
(73)

60
Replacing Eq. 73 in Eq. 72 and integrating, while using the temperature dependency for
Cp given by Eq. 67, gives
～Equilibrium Constant (K) Temperature (T)
(74)
*
Temperature (T)Equilibrium Conversion (X)
* ～
If
(75)
For example

61
2. How to find the reactor size through the XA versus T plot ?
1. Draw the reaction path on the XA versus T plot. This is the operating line
for the operation.
2. Find the rates at various XA along this path.
3. Plot the 1/(-rA) versus XA curve for this path.
4. Find the area under this curve. This gives V/FA
Fig 2.28 An example for plug flow reactor design (endothermic reaction, adiabatic operating)
Reactor size
equilibrium line of
endothermic reaction

62
Adiabatic Operation
Consider either a mixed flow reactor, a plug flow reactor, or a section of plug flow reactor, in
which the conversion is XA, as shown in Fig. 9.6.
Fig 2.29 Adiabatic operations with large enough heat effect to cause a rise in temperature (exothermic) or
drop in temperature (endothermic) in the reacting fluid.

63
With T1 as the reference temperature on which enthalpies and heats of reaction
are based we have enthalpy of entering feed:
Enthalpy of leaving stream:
Energy absorbed by reaction:
Replacing these quantities in the energy balance,
(76)
(77)
(78)
(79)

64
we obtain at steady state
By rearranging,
or, with Eq. 73
(81)
(80)
(82)
When C′p = C″p , the heat of reaction is independent of temperature, Eq. 82 reduce to
(83)

65
With Eq. 82 Draw the reaction path on the XA versus T plot.
Reactor size
equilibrium line of
endothermic reaction
Fig 2.30 Finding plug flow reactor size. (endothermic reaction, adiabatic operating)

66
Nonadiabatic Operation
parameters setting are the same with adiabatic operation:
Fig 2.31 Nonadiabatic operations with large enough heat effect to cause a rise in temperature (exothermic) or
drop in temperature (endothermic) in the reacting fluid.
Nonadiabatic operations

67
Let Q be the total heat added to a reactor per mole of entering reactant A, and let this heat also
include the losses to the surroundings. Then Eq. 80, the energy balance about the system, is
modified to:
which on rearrangement and with Eq. 73 gives:
and for C′p = C″p which often is a reasonable approximation
(80)
(85)
(86)
(84)
adiabatic operation

68
We define the optimum temperature progression to be that progression which minimizes
V/FA0 for a given conversion of reactant. The optimum temperature progression in any type
of reactor is as follows:
3. How to choose the optimal temperature for some reactions?
For single reaction
At any composition, it will always be at the temperature where the rate is a maximum. Rule
Fig 2.32 Operating lines for minimum reactor size.

69
A high temperature favors the reaction of higher activation energy,
a low temperature favors the reaction of lower activation energy.
 Rule
For multiple reactions
However, for the general series-parallel reaction we introduce two additional considerations.
First of all for parallel steps,
Second, for steps in series if an early step needs a high temperature and a later step needs a
low temperature, then a falling progression of temperatures should be used.
optimal temperature
(87)

70
Adiabatic Operations Nonadiabatic Operations
Temperature effect
Summary

Master thesis topics
Open but no salary funding
• Kinetic bahavior of single atom catalyst both in
convetional and electrochemical reactions
Post doc: Zhao Yingnan: yingnan.zhao@aalto.fi
• Photo catalytic water splitting
Ph.D. Candidate: Hou Xuelan: xuelan.hou@aalto.fi
• Ionic conductivity of semiconductors In batteries
Post-doc: Pan Zhengze: zhengze.pan@aalto.fi
In fuel cells
Visiting Ph.D. Candidate: Fan Lijun: lijun.fan@aalto.fi
• Lignin conversion to value added chemicals
Visiting Ph.D. Candidate: Cui Kai: kai.cui@aalto.fi

Yongdan Li
Professor of Industrial Chemistry
Department of Chemical and
Metallurgical Engineering
School of Chemical Technology
Aalto University
Email: yongdan.li@aalto.fi
Kemistintie 1, E404
Chemical Reactor Design
The field that studies the rates and mechanisms of chemical
reactions and the design of the reactors in which they take place

Cre++++

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