CE20023 REACTION ENGINEERING 2 Background

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CE20023 - REACTION ENGINEERING 2Background

• This course concerns chemical reactor design.
• Reactors are initially designed on paper, or in a
  computer, using scientific knowledge and
  mathematics.
• This approach is a lot cheaper and safer than
  proceeding by trial and error experiments.
• The chemical engineers design for a chemical
  reactor starts off with a mathematical model of
  the physics and chemistry taking place in the
  reactor.
• The model consists of a set of mathematical
  equations.
• This course will teach you how to construct
  mathematical models of chemical reactors.

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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.

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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.

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

• REACTION
• MASS TRANSFER
• ENERGY TRANSFER
• MOMENTUM TRANSFER

SO2 1/2O2
SO3
SO2
V2O5 catalyst
Exothermic
Pressure drop
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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
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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
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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

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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

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Example 1
Tubular reactor
SO2 O2 N2 SO3
28 SO2 72 Air (by vol.)
Isothermal 227 oC, 14.85 bara
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SO2 1/2 O2 SO3
Basis 100 moles, total in (mol/h)
15.12 mol O2
72 Air
56.88 mol N2
28 SO2
28 mol SO2
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What is ySO in the output ?
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What is the partial pressure of SO3 in the output
?
ySO 28 x 0.5/93 0.1505
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pSO ySO PT
3
3
0.1505 x 14.85 2.23 bar
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SO2 1/2 O2 SO3
What is DHo298 ?
HoSO , 298 -296.9 kJ mol-1 HoO 298 0
2
2
HoSO ,298 -395.18 kJ mol-1
3
DHo298 -395.18 - (-296.9 0)
-395.18 296.9 -98.28 kJ mol-1 SO2
What is DHo500 ?
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Revision, Ka
2HCl 1/2 O2 H2O Cl2
fugacity
activity
fugacity at standard state ( 1 atm)
For an ideal gas
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units ?
Ka can be evaluated from
where
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-57,200 - 4,509 -61,709 kJ kmol-1 Cl2
1300 (-62.5 - 6.62) -89,856 kJ kmol-1 Cl2
DGo1300 28,147 kJ kmol-1 Cl2
0.074
and Kp 0.074 atm-1/2
In refs., K 0.025, why ? - we used mean heat
capacity - we assumed ideal gas Real situation
is more complicated
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Assume DHoT is independent of T and integrate y
ln K thus dy d(ln K) (1/K)dK
As DHoT -61,709 kJ kmol-1 Cl2, substitute
values if T2 gt T1 (an increase in temperature)
then K2 lt K1, this results in a decrease in the
amount of Cl2 Therefore the incinerator should
be operated at a high temperature.
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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
For the heterogeneous case the rate will depend
on - the mass of catalyst/solid - surface
area - the reactor volume etc.
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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
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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
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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
Let species A be a reactant
Element of volume
FA
FA0
e.g. FA0 100 mol s-1
input
output
accumulation term
rate of disappearance by chemical reaction
GA rA V or GA rA dV
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a) IDEAL BATCH - CONSTANT VOLUME
0
0
rA V
or
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APPLICATION - Ideal Batch Reactor
(constant V and T)
A to products
2A to products
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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
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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
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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
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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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
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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