CE20023 REACTION ENGINEERING 2

1
CE20023 - REACTION ENGINEERING 2

• Basic reactor designs batch, CSTR, plug flow.
• Application of stoichiometric tables chemical
  equilibrium.
• Definition of reaction rate elementary
  reactions and temperature dependence.
• Mass and energy balances appropriate to each
  reactor.
• Ideal batch reactor constant volume, variable
  volume, variable temperature and pressure.
• Expansion factor irreversible and reversible
  reactions.
• Performance comparison between batch, CSTR and
  plug flow.

2
CE20023 - REACTION ENGINEERING 2

• Optimisation multiple reaction parallel
  series series-parallel selectivity and yield
  optimum temperature isothermal, adiabatic and
  non-adiabatic modes of operation multiple
  reactions temperature effects, heterogeneous
  kinetics.

3
Reactions
Catalytic
Homogeneous (1 phase)
Heterogeneous (2 or more phases)
Non-catalytic
4
Reactors
Continuous Flow
CSTR
Tubular
Batch
5
The processes occurring in a reactor

• REACTION
• MASS TRANSFER
• ENERGY TRANSFER
• MOMENTUM TRANSFER

SO2 1/2O2
SO3
SO2
V2O5 catalyst
Exothermic
Pressure drop
6
Heterogeneous catalytic reaction -simplified
steps
B
A
(1) External diffusion
(2) Internal diffusion
(3) Adsorption/Desorption
(4) A B Reaction
A typical silica-alumina cracking catalyst
has - specific pore volume of 0.6 cm3g-1 -
pore radius of 4 nm - specific surface area of
300 m2g-1
7
Rate data
Tb Cb
Tp Cp
Intrinsic kinetics Data obtained under
conditions when the rate is not controlled by
external or internal mass transfer Cb
Cp also Tb Tp
8
Global rate data
Tb Cb
Tp Cp

• The measured rate is associated with bulk
  concentrations
• and temperatures.
• Simplifies modelling
• Care needs to be taken with scale-up
• Often used in industry

9
Example of variables

• Feed
• composition
• temperature
• flowrate

• Reactor
• size/geometry
• temperature
• pressure
• degree of mixing
• energy transfer
• residence time

• Modes of operation
• Isothermal or Non-isothermal
• Adiabatic or Non-adiabatic
• Complete mixing
• Plug flow
• Non-ideal flow

10
REACTION RATE
Homogeneous rA, is the number of moles of A
reacting per unit time per unit volume.
if j is a product - if j is a reactant
(N/V C at const. vol.)
For the heterogeneous case the rate will depend
on - the mass of catalyst/solid - surface
area - the reactor volume etc.
11
ELEMENTARY REACTIONS
The rate equation corresponds to stoichiometric
equation
rA k CA CB
or for
Reaction is 3rd order with respect to species B
rA k CA2 CB3
Reaction is 2nd order with respect to species A
But the overall order is 2 3 5
The rate of change of a species is related by the
stoichiometry
The molar extent of reaction, z, for a batch
reactor is
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ELEMENTARY REVERSIBLE REACTIONS
k1
A
2R
k2
Gas phase rf k1 pA
Forward reaction
Units, e.g. mol m-3 s-1
Reverse reaction
At equilibrium rf rr
Also
13
Batch Reaction Kinetics Equations
Rate expressions discussed below refer to the
situation where the reactants are added to a
vessel at time t 0, and then nothing more
is added to, or taken from, the vessel until it
is examined at a later time t.
Zeroth order reaction Rate equation
C concentration of reactant (units mol/m3) k
rate constant (mol/m3.s) r rate (mol/m3.s,
ALWAYS)
What has happened after time t has elapsed? -
integrate rate eq.
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Batch Reaction Kinetics Equations 2
First order reaction Rate equation
C concentration of reactant (units mol/m3) k
rate constant (s-1)
Integrate
Second order reaction Rate equation
C concentration of reactant (units mol/m3) k
rate constant (m3/mol. s)
Integrate
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REACTOR DESIGN
MATERIAL BALANCE
MOMENTUM BALANCE
ENERGY BALANCE
ARE LINKED
e.g. - As T increases reaction rate increases -
For gases, as T increases, volumetric flow
increases and DP increases
16
We start by writing an equation for an element of
volume
If the composition is uniform, then the whole of
the reactor is the volume element
If composition in the reactor varies, then we
consider a differential element of volume and
integrate across the reactor
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MATERIAL BALANCE
Master Equation and its application to Batch
Kinetics IN MADE OUT ACCUMULATION
0 Nothing is added during reaction
add kinetics x volume of reactor e.g. 1st
order reaction
0 Nothing is removed during reaction
Leads to
...as before
(Units of each term are mol/s (or molecules/s)
V volume of reactor (m3))
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MATERIAL BALANCE
Let species A be a reactant
Element of volume
FA
FA0
e.g. FA0 100 mol s-1
NA no. of moles of A within volume element
CA.V or CA.dV
input
output
accumulation term
rate of disappearance by chemical reaction -
rate of appearance N.B. beware definition of
terms and note where they appear in the
equations to determine signs
GA rA V or GA rA dV
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a) IDEAL BATCH - CONSTANT VOLUME
0
0
rA V
or
20
APPLICATION - Ideal Batch Reactor
(constant V and T)
A to products
2A to products
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CSTR Reactor for Liquid Phase Reaction
Reactor operates at outlet conditions. Reactor is
well- mixed, hence concentration of reactant
throughout is C
Reactant supply in Liquid flow rate v
m3/s Concentration C0 mol/m3
Remaining reactant out Liquid flow rate v
m3/s Concentration C mol/m3
Volume of reactor V m3
Reactor operates at steady-state - variables do
not change with t
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Material Balance for CSTR
Master Equation IN MADE OUT ACCUMULATION
0 at steady-state (no change with t) i.e. no
build up of material within the reactor
add kinetics x volume of reactor e.g. 1st
order reaction
v.C
v.C0
Leads to
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CSTR
rA V
0
Since FA0 v0 CA0
Case for constant volume V, concentration CA0 of
inlet stream
subst. for t
Most reactions in a CSTR are in the liquid phase
24
CSTR
Second order, reversible reaction in a CSTR with
constant volume
k1
A B
C D
Feed CA0, CB0, CC0 0, CD0 0
k2
From
25
CSTR
Mass balance
Substitute CB CA - CA0 CB0 CC CD CA0 -
CA
Solve for CA
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PLUG FLOW REACTOR
Since the composition within the reactor varies -
we take a balance over a differential element of
volume
DV
FA(yDy)
Faf XAf
FA0 XA0 0 v0
FA(y)
y
yDy
0
Concentration at point y is constant across
reactor cross-section
rA DV rA A Dy
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The basic limiting process of calculus states
that for any quantity FA, which is a smooth
continuous function of y
Taking the limit as Dy tends to 0
Usually we have V rather than y as the
independent variable Since dV A dy
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Liquid State Reaction in a PFR
Reactant supply in Liquid flow rate v
m3/s Concentration CA0 mol/m3
Remaining reactant out Liquid flow rate v
m3/s Concentration CA mol/m3
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CSTR vs. PLUG FLOWIsothermal
CSTR
General form of rate curve
1/rA
XA
PLUG FLOW
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CSTR VS Plug Flow

• A combination of PFRs giving a particular final
  conversion have the
• same volume as a single PFR which gives the same
  total conversion.
• A series of CSTRs can be useful to reduce the
  overall volume

1/rA
V1
V2
XAf
XAi
V2
0
V1
XA
XAi
XAf

• Other rate expressions
• rAkCAn - as n increases, PFR
• more favourable
• zero order reactions are
• reactor independent
• autocatalytic reactions
• A B rAkCACB

1/r
Rate low at low conversion due to low CB
VCSTR
VPFR
X
XIN
XCSTR
XOUT
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Ideal batch - variable volume
0
0
rAV
This two-term expression can be avoided if we use
fractional conversion and expansion factor
Expansion factor
For constant P and T
Thus
Volume varies linearly with conversion
32
From
Constant T P
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IDEAL BATCH
V, P T varying
From PV zNTRT get P0V0 z0 NT0RT0
(1)
Since
(Subst. for V from (1))
Then
Can be solved provided we know how P and T are
varying with time
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Comparison of CSTR vs. Plug Flow for nth order
reactions
100
n2
n1
10
n0.5
1
0.01
0.1
1.0
(1-XA)
Comments (1) n ve VCSTR gt VPFR (2) n 0
VCSTR VPFR (3) low XA flow type influence is
small (4) read Levenspiel 2nd edition p. 124-127
and make notes on expansion/density effects
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OPTIMIZATION-REACTOR DESIGN FOR MULTIPLE
REACTIONS

• They can be considered to be a combination of
  parallel and series reactions.
• Easier to deal with concentration rather than
  conversion.
• Eliminate time variable by dividing one rate by
  the other.
• The two requirements are
• minimum reactor size
• maximum of desired products
• may run counter to each other - then perform an
  economic analysis
• In general product distribution controls.
• We will ignore expansion effects.
• We consider isothermal reactions

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REACTIONS IN PARALLEL
k1
B
Desired product
A
(Isothermal, Irreversible)
C
k2
(2)
(1)
Dividing (2) by (1)
Ratio to be small
k1, k2, a, b are all constant. CA is the only
variable.
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• To keep CA
• Low - Use CSTR, maintain high XA, increase
  inerts in the feed, decrease pressure in a gas
  phase system.
• High - Use Batch/Plug Flow, maintain low XA
• If b-a is -ve high CA b-a is ve low
  CA ba - product distribution fixed -
  reactor volume important
• OTHER WAYS TO CHANGE PRODUCT DISTRIBUTION
• Change temperature and hence k2/k1 may vary (see
  later)
• Use a catalyst

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1st Order, Irreversible, Parallel, Constant Volume
Rate equations
t 0 CA CA0 CB CB0 CC CC0
k1
B
A
C
k2
Integrating rate equations using initial
conditions
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1.0
Cj /CA0
B
C
A
t
For plug flow reactor, replace t with t e.g.
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CSTR
CA0 CB0 CC0
k1
B
CA CB CC
A
C
k2
Thus
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For two competing reactions forming
D
Desired product
A
U
Unwanted product
Yield (A is reactant)
Selectivity
GENERAL
FLOW
BATCH
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Space time
(mean residence time)
Space velocity
GHSV Gas Hourly Space Velocity, h-1 v0 at STP
LHSV Liquid Hourly Space Velocity, h-1 v0 at
some reference temperature
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Temperature and Energy Effects in Chemical
Reactors

• Equilibrium yield
• Rate of reaction
• Product distribution (multiple)
• Reactions are generally accompanied by heat
  effects
• How will they change the temperature ?
• Economic considerations
• Identify optimum
• Reactor stability
• operating point

Affected by temperature
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(1) Effect of temperature on equilibrium
Endothermic
1.0
XA
Exothermic
VANT HOFF Exothermic (DHolt0) T rises, K
decreases Endothermic (DHogt0) T rises, K
increases
T
If DHo const. (not really)
(2) Effect of temperature on rate
k0
ARRHENIUS
k
Note Vant Hoff is thermodynamic and thus always
true. Arrhenius is an approximate model
T
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(3) Choice of operating temperature Endothermic H
igh T maximises the rate and the eqm.
conversion - thus choose as high a T as
possible Exothermic High T maximises the rate,
but Low T maximises the eqm. conversion -
compromise between kinetics and
thermodynamics (4) Effect of T on actual
conversion (a) Irreversible reaction - any
reactor type (batch, CSTR, PFR etc.) -
arbitrary kinetics
assymptote just less than 1
1
higher t
exhaustion of reactants
XA
S- shaped curve Note assymptote not XA 1
in general, as rate finite at T infinity thus
XAlt1, but can be treated as such.
lower t
T
dominated by Arrhenius
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(b) Reversible reaction Endothermic
1
XA
equilibrium conversion
lower t
T
Exothermic i.e. get a maximum in XA vs. T (for
a given t)
1
equilibrium
lower t
XA
T
47
(5) Temperature Effects in Isothermal Reactors
Definition Isothermal enthalpy removed from (or
added to) the reactor by cooling (or heating) so
that Tconst. within the reactor and equals the
feed temperature. (a) Irreversible Reactions Use
usual design equations with Arrhenius dependence
in rate constant (b) Reversible Reactions -
illustrate with a CSTR
Volumetric flowrate, v CA0 CB0
V
k1
v CA CB
A
B
Liquid phase
k-1
48
Reversible Reaction
CSTR design equation
Combine
If let CB0 0 then
In practice, we may have one rate constant (e.g.
k1) and eqm. const. K Assume and ideal mixture,
thus
Hence
i.e. we have XA as a func. of (T,t) or t(T,XA)
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Non-isothermal CSTR
v CA0 T0
A B irreversible - Heat transfer coefficient
h - Area A - Temperature TC - Kinetics (-rA)
kCA - Enthalpy change of reaction DH - Assume
CpA CpB const.
T
v CA
V
Cooling water h, A, TC
Mass balance
Subst. kinetics
50
Insert Arrhenius expression
Rate of reaction per unit volume
Energy balance Heat generated (exothermic) -
Heat evolved per mole reactant
Arrhenius -
Substitute for CA from above and rearrange Thus
in the limit -
Heat removed -
AT STEADY STATE Qr Qg
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Qr 1 2 3
Cases 1, 3 - single steady states
Qg, Qr
Qg
Case 2 - multiple steady states
Case 2 has three possibilities - which steady
state do we actually get ?
T
Stability of steady states Definition a steady
state is stable if, when subjected to a
perturbation, it returns to the steady state.
Steady state a - If Ta increases to Ta DT Qr
gt Qg thus T reduces - If Ta decreases to Ta - DT
Qr lt Qg thus T increases System acts to
eliminate the perturbation - thus steady state a
is stable.
Qr
Qg, Qr
c
Qg
b
a
Ta
Tb
Tc
T
52
Steady state b - If Tb increases to Tb DT Qr
lt Qg T increases further until steady state c is
reached - If Tb decreases to Tb - DT Qr gt Qg
thus T decreases further to Ta Steady state c as
per case a, i.e. stable
Implications for operability
Start up temperature, Ts If TsgtTi, QggtQr and the
reactor goes to the upper steady state (high T
implies high conversion). This is usually the
desired steady-state. This may not be desired
due to- high T encourages side reactions, or the
material of the reactor may not stand high T, or
the rate may become dangerously high.
Qr, Qg
Qr
Qg
Ti
T
If Ts lt Ti, Qg lt Qr and the reactor goes to the
lower steady-state (low conversion). May need to
pre-heat reactants at start-up even if reaction
is exothermic.
53
Example 1.1 Operation of a CSTR with Heat Effects
A first order reaction is to be carried out in a
CSTR. The conversion is required to be at least
75 and the reactor temperature must not
exceed 340 K. In order to facilitate start-up,
the reactor should have only one steady
state. Data V 10 m3 Three feed temperatures
are to be C0 5 kmol m-3 considered T0290 K,
300 K and v 10-2 m3s-1 310 K. DH -2x107 J
kmol-1 k 1013exp(-12000/T) s-1 r 850 kg
m-3 Cp 2200 J kg-1
54
(1) Can this reactor be operated adiabatically
? Fig. 1 shows the Qr and Qg curves for adiabatic
operation. The steady- state temperatures are
read from the graph. (in practice the heat
generation and heat removal equations would be
solved numerically.) The conversion, X, is
calculated from the heat generation equation. In
this case Qg C0X.v.(-DH) X.106 J/s Figure
1 The results are as follows T0 290 K one
steady state, T 291 K, X 0.01 (too low) T0
300 K lower steady state, T 303 K, X 0.06
(too low) upper steady state, T 349 K, X
0.92 (too hot) T0 310 K one steady
state, T 362 K, X 0.98 (too hot) Adiabatic
operation does not meet the temperature and
conversion constraints.
55
(2) A cooling coil is added. Can the requirements
be satisfied now ? Data hA 9x103 J s-1 K-1 Tc
310 K Fig. 2 shows the Qr and Qg curves with
the reactor with the cooling coil for Tc 310
K. With the cooling coil in operation, a single
steady state at T 339 K, X 0.82 is obtained,
which satisfies the requirements.
56
6. Adiabatic PFR
PFR design equation
T0 Molar flowrates nA0, nB0
T nA nB
Cant integrate because rA f(XA, T)
Energy balances
Steady state Input - Output Generated
0 Assume Cp const., i.e. Cp is not a function of
T
When XA 1, (T-T0) is often called the
ADIABATIC TEMPERATURE RISE, Dtad.
57
If capacity flowrate is constant (i.e. CpA
CpB in this case)
From above we have T f(XA), and reaction rate
is rA f(XA, T). Hence now have rA f(XA only)
and we can integrate the PFR design equation.
Example 1.2 Design of an Adiabatic PFR The
first order gas phase reaction A B is to be
carried out in an adiabatic PFR. Calculate the
size of reactor required for a conversion of 30
. The feed is 100 mol/s of pure A at 700 K and 2
bar. Data Forward rate constant k1
4.6x105exp(-12500/T) s-1 Reverse rate constant k2
7.7x106exp(-15000/T) s-1 DH -20000 J mol-1 Cp
40 J mol-1 K-1 for both species
58
Solution PFR design equation
Assume ideal gas conditions (OK because low P and
high T)
Introduce definition of conversion
k1 and k2 are given as functions of T in the
Arrhenius expressions above. Before V can be
evaluated, T must be found as a function of X by
an energy balance
Substituting for T0, DH and Cp T 700
500X
59
The integrand of the expression for V is now
known as a function of X. The equation is
integrated numerically giving the results shown
in the handout figure. Note that the maximum
conversion is restricted by chemical equilibrium
under these conditions, the maximum conversion is
47 . The volume required for a conversion of 30
is 37.9 m3. Isothermal and adiabatic
operations are extremes. How about
controlling the temperature profile so that the
reaction is neither isothermal nor adiabatic
?... 7. Optimal Temperature Profile From
section 4(b) Exothermic Reaction
XA
Decreasing t
Constant t (residence time)
Desired XA

Possible design strategy (1) Choose XA (2)
Choose T so that t is minimised for this XA ( on
diagram). BUT WE CAN DO BETTER !
T
T
60
k1
Exothermic
A
B
k2
(-rA)
Initial rate depends on kinetics
Better Design Strategy - Start with high T at low
XA and progressively reduce T as XA increases. -
At any XA, operate at T that gives the highest
rate, called OPTIMAL TEMPERATURE PROGRESSION
30 oC
20 oC
10 oC
XA
(-rA)
Maximum reaction rate
Max. conversion depends on eqm.
N.B. Initial rate is determined by max. allowable
T. Practically - metal mpt - undesired
side reactions
T decreasing
XA
61
Practical Schemes (1) PFR with heat removal rate
varying along the reactor (2) e.g. PFRs or CSTRs
with inter-coolers
10 oC
30 oC
20 oC
(3) Cold Shot Cooling
62
Design calculations for optimal T progression We
want max. rate at each XA
Example 1.3 Optimal Temperature Progression The
first-order gas phase reaction A B is to
be carried out in a PFR. Calculate the size of
the reactor required for a conversion of 50 , if
the temperature profile is optimal. The feed is 1
mol/s of A and 1 mol/s of B at 2 bar. The
reactor may not operate at more than 800
K. Data Forward rate constant k1
4.6x105exp(-12500/T) s-1 Reverse rate constant k2
7.7x106exp(-15000/T) s-1 DH -20000 J/mol Cp
40 J/mol K for both species.
63
Solution PFR design equation
Assume ideal gas under these conditions (OK
because low P and high T)
Introduce definition of conversion
For optimal temperature progression

Differentiation of the rate law and rearrangement
gives
The expression for V can now be evaluated to
give the value required for any conversion with
optimal temperature progression.
64
Thermal Runaway in Closed Systems
1. Useful references Coulson and Richardson
series, Denbigh and Turner, Chemical Reactor
Theory 2. Definitions and Examples Thermal
runaway is the sudden inflammation of a uniformly
heated mass (as opposed to that caused by a
spark etc. which is localised) e.g. peroxides,
haystacks (spontaneous combustion) 3. Aims - To
see how little self-heating can lead to thermal
runaway. - To explore heat balance equations and
to lay foundations for understanding other
instabilities. - To introduce useful
dimensionless variables and parameters.
65
Dimensionless Temperature
Reaction rate constants often have an Arrhenius
temperature dependence
Thus the group RT2/E is a natural yardstick of
temperature
where Ta is the ambient temperature, and T is the
temperature in a reactor, say.
66
Stationary States and Criticality (ignition)
Assumptions- - ignition has a thermal origin -
neglect- (i) reactant consumption (ii) T as a
function of position, thus assume a mean
temperature
Thermal diagram
Volume, V Surface Area, A Temperature inside,
T outside, Ta Reactant concentration,
CC0 Reaction rate constant, k Heat transfer
coefficient, h
A
T, V, C
67
Qr, Qg
Qg
T
Super-critical (Runaway)
Qr, Qg
Qg
B
Qr
C
Qr
A
Sub-critical
C
T
Ta
time
T
Ta
Stationary states A - stable B - unstable C -
critical point
No stationary state
For all stationary states (including C) Qr
Qg Thus hA(T - Ta) V(-DH)kC0 At point C
- defines the critical point, and thus TC
68
Thus T - Ta RT2/E at T TC (the critical
temperature) Solve the quadratic
..to find TC
Main result
typically 10-15 K, i.e. a small
difference, hence very little consumption is
needed (2 ), so our initial assumption of
negligible reactant consumption is reasonable.
From the definition of q, this equation also
implies that qC 1 for ignition. A single
dimensionless group encapsulates the criterion
for criticality.
69
8. Temperature Effects With Multiple
Reactions Product Distribution (a) Parallel
reactions
Assume reactions are of the same order We
want k1 large k2 small k k0exp(-E/RT)
R desired
(1)
A
S unwanted
(2)
If E1gtE2, (1) increases with T more rapidly than
(2) - Use high T If E1ltE2, (2) increases with T
more rapidly than (1) - Use low T (b) Series
Reactions If E1gtE2 use high T If E1ltE2 use low T
(1)
(2)
R
S
A
desired
70
(c) Mixed reaction scheme (i.e. series and
parallel elements)
(3)
(1)
(i) E1gtE2gtE3 - use high T (ii) E1gtE2, E1ltE3
A
R
S
(2)
desired
T
Want low T to minimise S
Want high T to maximise R
- Use falling temperature
T
(iii) E1ltE2 and E3 - use low temperature (iv)
E1ltE2, E1gtE3, use rising T (opposite of (ii))
71
The Rate-Limiting Step
It would be wrong to assume that the rate of
reaction is always the rate-limiting step. Mass
transfer may control. Consider A Z where
rZ kCA on the surface of a catalyst. Assume a
steady-state, the rate of mass transfer equals
the rate of reaction, thus the rate per unit area
is given by
pAi
pAbulk
Solid
Now
and
Gas film
where
72
So, in general, the rate of reaction is a
function of both kinetics and mass transfer. May
have a fast reaction rate or slow mass transfer,
then MASS TRANSFER controls the reaction. How
do you find this out ? - estimate kg from
correlations - find the temperature
dependence of the reaction In general
k// k0exp(-E/RT) For diffusion/mass
transfer E 30-50 kJ mol-1 For reactions E
gt 100 kJ mol-1
At low T, high E
Ln k//
At high T, low E
Solid line shows observed rate
1/T
Lowest rate controls and so is observed as k//
73
General Energy Balances
(2)
(1)
T Fi Hi
T0 Fi0 Hi0
Q
Ws
Rate of heat flow TO system from surroundings
Rate of accumulation of energy within the system
Rate of work done BY the system ON the
surroundings
74
Work done by system on surroundings
Energy of mass entering system
Energy of mass leaving system
Change in energy of system
Heat added to system

-
-

For steady state 0 Q - W (rQvE)1
(rQvE)2 where Q is in Watts, r is the mass
density, Qv is the volumetric flowrate, and E is
the specific energy. E U u2/2 gZ where
U is the internal energy, u2/2 is the kinetic
energy and gZ is the potential energy.
75

• In a reacting system the kinetic energy and
  potential energy are relatively
• small, thus EU.
• U consists of
• Sensible energy
• translational
• rotational
• vibrational
• Latent energy - change of phase
• Chemical bonds - chemical reaction

Affected by T
Viscous and frictional work
Flow work
Shaft work
W


(Wf )1 - (Wf )2
If we consider viscous/frictional work and shaft
work terms to be small, for a fluid entering the
system (Wf )1 (-PAu)1 (-PAQv/A)1
(-PQv)1 Wf is a negative quantity because the
fluid does work on the system. (u is velocity, A
is area of flow)
76
Q (PQv)1 -(PQv)2 (rQvU)1 - (rQvU)2 0 We
now introduce enthalpy, H U P/r thus Q
rQv(UP/r)1 - rQv(UP/r)2 Q rQvH1 -
rQvH2 0 Let DH H2 - H1 then Q - mTDH
0 If Q 0, then DH 0 and enthalpy of the
inlet stream is equal to the outlet stream. At
steady-state, under adiabatic conditions, and
neglecting work done by the system
where Fi is the molar flowrate and Hi is molar
enthalpy
Reminder
77
In a chemical reacting system this results in
For this adiabatic system, the heat released by
the chemical reaction must be used to raise the
temperature of the product stream. Simplification
Assume DHR(T) or...
assume
qi Fio/FA0
Mean value for feed
78
Mean value for feed
Note that for the general reaction
In general Cp is a function of temperature which
is generally correlated (e.g. Perry) in a form
If used in this form then
where Cpi is evaluated at the mean temperature
between T and TR