Batch Reactor

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BATCH REACTOR Interpretation of rate data
A. SARATH BABU
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• Simplest reactor open / closed vessel
• Reactants are placed inside the reactor and
  allowed to react over time
• Products and unconverted reactants are removed
  and the process is repeated
• Closed system - unsteady state operation
• Fitted with a stirrer
• May have a jacket / cooling or heating coils
  inside the reactor
• Generally constant volume / some designed at
  constant pressure
• Materials of construction different linings

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• Used in variety of applications
• Typically for liquid phase reactions that
  require long reaction times
• Used only when small amount of product is
  required
• Favored when a process is in developmental
  stage or to produce expensive products
• Used to make a variety of products at different
  times

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Characteristics of a Batch Reactor
(1) Each batch is a closed system. (2) The total
mass of each batch is fixed. (3) The reaction
(residence) time t for all elements of fluid is
the same. (4) The operation of the reactor is
inherently unsteady-state for example, batch
composition changes with respect to time. (5)
It is assumed that, at any time, the batch is
uniform (e.g., in composition, temperature,
etc.), because of efficient stirring.
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• Advantages
• High conversions can be obtained
• Versatile, used to make many products
• Good for producing small amounts
• Easy to Clean

• Dis-advantages
• High cost of labor per unit of production
• Difficult to maintain large scale production
• Long idle time (Charging Discharging times)
  
• leads to periods of no production
• No instrumentation Poor product quality

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GUIDELINES FOR SELECTING BATCH PROCESSES
Production rates Sometimes batch process, if
the plants have production capacity less
than 10x106 lb/yr (5x106 kg/hr). Usually batch
process, if the plants have production
capacity less than 1x106 lb/yr (0.5x106
kg/hr). Where multiproduct plants are produced
using the same processing
equipment. Market forces Where products
are seasonal (e.g., fertilizers). Short
product lifetime (e.g., organic pigments).
Operational problems Long reaction times
(when chemical reactions are slow). Handling
slurries at low flowrates. Rapidly fouling
materials (e.g., materials foul equipment so
rapidly that shutdown and frequent cleaning are
required).
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General Mass Balance Equation Input output
accumulation
rate of disappearance
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General Mass Balance Equation Input output
accumulation
rate of disappearance
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Design Equation
General Mass Balance Equation Input output
accumulation rate of disappearance
0 0 dNA/dt (-rA) V

• General Design Equation
• (1/ V) dNA/dt (-rA)
• General Design equation in terms of conversion
• (NAo/ V) dxA/dt -rA

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• Design Eqn. for CVBR
• -dCA/dt -rA
• CAo dxA/dt -rA in terms of
  conversion

Design Eqn. for variable volume batch
reactor CAo/(1?AxA) dxA/dt -rA Design Eqn.
in terms of Total Pressure (1/?RT) dPT /dt
(-rA)
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Constant Volume Batch Reactor
t CA0 X area
t
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Stoichiometric Table Batch Systems
aA bB ? rR sS
Species Initial Change Final moles
A NA0 -NA0xA NA
NA0(1-xA)
B NB0 -(b/a)NA0xA NB
NA0(MB-(b/a)xA) R NR0
(r/a)NA0xA NR NA0(MR(r/a)xA) S NS0
(s/a)NA0xA NS NA0(MS(s/a)xA) I
NI0 0 NI NI0 Total NT0 NT NT0
NA0dxA Where MI NI0/NA0 d (r/a
s/a b/a 1)
For CVBR CA CA0(1-xA) CR CA0MR(r/a)xA
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Constant Volume Batch Reactor -rA -dCA/dt
CA0 dxA/dt
1. Zero Order Reaction -rA -dCA/dt k
CA0 - CA kt CA0xA kt
Strictly homogenous reactions do not follow zero
order. Apparently the reaction order is made zero
w.r.t. a reactant.
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2. First Order Reaction A ? Products -rA
-dCA/dt kCA
-ln (CA/CA0) kt -ln(1-xA) kt
Example N2O5 ? 2NO2 ½O2

• rA k CA0.6 CB0.4 ??
• Unimolecular Collision theory ??

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First Order Reaction kinetics Influence of k
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3. Second Order Reaction 2A ? Products A B
? Products CA0 CB0 -rA -dCA/dt kCA2
1/CA 1/CA0 kt xA/(1-xA) kCA0t
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4. Second Order Reaction A B ? Products CA0
? CB0 -rA -dCA/dt kCACB
K(CB0-CA0)
t
Example CH3COOC2H5 NaOH ? CH3COONaC2H5OH
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5. Third Order Reaction 3A ? Products
2A B ? Products CA0 2CB0 A B C ?
Products CA0 CB0 CC0 -rA -dCA/dt
kCACBCC k?CA3
Example 2NO H2 ? H2O N2O 2NO Cl2 ?
2NOCl
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6. Third Order Reaction 2A B ?
Products CA0 ? 2CB0 -rA -dCA/dt kCA2CB
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7. Third Order Reaction A B C ?
Products CA0 ? CB0 ? CC0 -rA -dCA/dt
kCACBCC
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8. nth Order Reaction nA ? Products
-rA -dCA/dt kCAn
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The reciprocal of rate approaches infinity as CA
? 0
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Integrated forms Constant density
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Note that for a II order reaction with a large
ratio of feed components, the order degenerates
to a first order (pseudo first order).
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Differential Method of analysis
CA
-rA
k
t
f(c)
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Differential Method of analysis
n
ln(-rA)
If rA kCAaCBb, how to use DM?
ln k

• Use stoichiometric ratio of reactants
• Use method of excesses
• Use method of least squares

ln(CA)
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• Integral Method of analysis
• Guess the reaction order
• Integrate and Derive the equation
• Check whether the assumed order is
• correct or not by plotting the necessary
• graph

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Differential Method
Integral Method

• Easy to use and is
• recommended for testing
• specific mechanism
• Require small amount of
• data
• Involves trial and error
• Cannot be used for
• fractional orders
• Very accurate

• Useful in complicated
• cases
• Require large and more
• accurate data
• No trial and error
• Can be used for
• fractional orders
• Less accurate

Generally Integral Method is attempted first and
if not successful, the differential method is
used.
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Method of Excesses

• Consider rA kCAaCBb
• Perform the experiment with CB0 gtgt CA0 and
• measure CA as a function of t.

rA kCAaCBb kCB0b CAa k?CAa Use either
differential method or integral method and
evaluate k a

• Perform the experiment with CA0 gtgt CB0 and
• measure CB as a function of t.

rA kCA0a CBb k?CBb Use either
differential method or integral method and
evaluate k b
Require multiple experiments
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Method of Half lives
(1-n)
ln(t1/2)
At t t1/2, CA CA0/2
K
ln(CA0)
For I Order reactions t1/2 ln(2)/k
t1/2 does not depend
on CA0
Require multiple experiments
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Check the value of dimensionless rate constant
kCA0(n-1)t for each order at t t½

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Method of Half lives
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Method of Fractional lives
The half-life, or half-period, of a reaction is
the time necessary for one half of the original
reactant to disappear.
At t t1/n, CA (1- 1/n) CA0
The ratio of any two fractional lives is
characteristic of the order.
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Method of Initial Rates
The order of the reaction with respect to an
individual component can be determined by making
an initial rate measurement at two different
initial concentrations of this species while
holding all other concentrations constant between
the two runs.
Advantage of the initial rate method is that
complex rate functions that may be extremely
difficult to integrate can be handled in a
convenient manner. Moreover, when initial
reaction rates are used, the reverse reactions
can be neglected and attention can be focused
solely on the reaction rate function for the
forward reaction.
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Method of Initial Rates
(CA0)1
(CA0)2
(-rA0)1 slope at (CA0)1, t 0
(-rA0)2 slope at (CA0)2, t 0
(CA0)3
(-rA0)3 slope at (CA0)3, t 0
Time, t
-rA0 k (CA0)n
ln(-rA0) ln(k) n ln(CA0)
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Method of Initial Rates
Slope gives order
ln (-rA0)
ln CA0
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CA/CA0
DA kCA0n-1 t
Comparison of Different order Reactions in a
Batch reactor
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Variable Volume Batch Reactor
Volume Change with time ??
Fractional Change in Volume or Expansion
factor(?A)
Expansion factor can be obtained if we know the
initial volume and the volume at any X. Similarly
X can be obtained given expansion factor.
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Example A ? 3R, starting with pure A Since
pure A, yAO 1. Also d 3/1 -1 3-1 2. ?A
(3 - 1)/1 2 With 50 inerts yAO 0.5 d
3/1 -1 2. ?A (4-2)/2 1 0.5
(3-1) 1
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Variable Volume Batch Reactor
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CVBR
VVBR
t / CA0
t
1 /-rA
CA0
CA
xA
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Variable Volume Batch Reactor
1. Zero Order Reaction
Ln(1?AxA)
k?A/CA0
t
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Variable Volume Batch Reactor
2. First Order Reaction
-ln(1-xA)
t
Performance equation is similar to that of CVBR
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Variable Volume Batch Reactor
3. Second Order Reaction
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Variable Volume Batch Reactor
4. Higher Order Reactions
Analytical integration would be
difficult. Resort to either graphical /
numerical integration.
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Constant Volume Batch Reactor (PT vs. t)
?A Fractional Volume / Pressure Change ??
Design equation for CVBR in terms of PT
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CVBR Concentrations in terms of PT
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CVBR Complex reactions
1. First Order Reversible ReactionA ? R
Integrating
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CVBR Complex reactions
2. Irreversible Reactions in parallel A ?
B A ? C
CA
CC
CB
Integrating
t
CB
K1/k2
CC
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CVBR Complex reactions
3. Homogenous Catalytic Reactions A ? R A
C ? R C

kobs
Integrating
t
kobs
k2
k1
CC
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CVBR Complex reactions
4. Auto Catalytic Reactions A R ? R R

kC0
Integrating
t
-rA
CA CR 0.5 C0
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CVBR Complex reactions
5. Irreversible Reactions in series A ? B ? C
CB0 CC0 0
CC/CA0
CA/CA0
CB/CA0
CB, max and topt - ??
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Integrating
Solving
If k1 k2, find topt and CR, max
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Consecutive I-order reactions Conc. vs. time for
various ratios of k2/k1
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Concept of Rate Determining Step (RDS)
Consider the irreversible reactions in series A
? R ? S
I. When k1 gtgt k2
Overall rate of product formation is dominated by
reaction - 2
II. When k2 gtgt k1
Overall rate of product formation is dominated by
reaction - 1
Overall rate of a reaction is always governed by
the slowest step, which is known as the rate
determining step (RDS).
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6. Reactions with shifting order A ? R
The order shifts from low to high (zero to
one) as the reactant concentration drops.
k1
-rA
t/(CA0-CA)
k2
CA
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7. Reactions with shifting order A ? R
The order shifts from high to low (one to
zero) as the reactant concentration drops.
CA
-rA
k2
k1
t
CA
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• Guggenheim's Method for First-Order Reactions
• A special method to obtain the rate constant for
  a first-order reaction when an accurate value of
  the initial reactant concentration is not
  available.
• Requires a series of readings of the parameter
  used to follow the progress of the reaction at
  times t1, t2, t3, etc. and at times t1 ?, t2
  ?, t3 ? etc.
• The time increment ? should be two or three times
  the half life of the reaction.
• For a I order reaction ln(1-xA) -kt ? xA 1 -
  e-kt

At t1 and t1 ?, (xA)t1 (xA)t1? e-kt1
(1-ek?)
Similar equations are valid at times t2, t3, etc.
In all cases, the right side will be a constant,
since the time increment is a constant.
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• applicable to systems that give apparent
  first-order rate constants.
• also applicable to irreversible first order
  reactions in parallel and reversible reactions
  that are first-order in both the forward and
  reverse directions.
• the technique provides an example of the
  advantages that can be obtained by careful
  planning of kinetics experiments instead of
  allowing the experimental design to be dictated
  entirely by laboratory convention and
  experimental convenience.
• Guggenheim's technique can also be extended to
  other order reactions, but the final expressions
  are somewhat cumbersome.

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Example
Note that k can be determined without a knowledge
of the dilatometer readings at times zero and
infinity.
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Batch reactors are charged with reactants,
closed, and heated to the reaction temperature,
maintained isothermally for the duration of the
reaction. After the reaction is completed, the
mixture cooled, and the reactor opened, the
product is discharged and the reactor is cleaned
for the next batch. In industrial operations, the
cycle time is constant from one batch to the
next. The time required for filling,
discharging, heating, cooling, and cleaning the
reactor is referred to as the turnaround time
(tt). The total batch cycle time tb is the
reaction tr time plus the turnaround time tt.
tb tr tt The total batch cycle time tb is
used in batch reactor design to determine the
productivity of the reactor.
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Design of Batch Reactor
What do you mean by Design ??
Can we Design the Batch Reactor using the Above
equation ??
How can you call the above equation as Design
equation of a Batch Reactor ??
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Design Problem
The reaction 2A ? R takes place in a batch
reactor. Pure A is to be taken initially in the
reactor. It is required to produce 3 tons of R
per day. The molecular weight of R is 120. The
density of A is 0.8 kg/lit. The expected
conversion of A is 75. A time of 30 min must be
allowed for filling the reactor and 45 min for
discharging and cleaning the reactor. Kinetic
calculations show that a reaction time of 4hr 45
min is needed for the required conversion. What
size reactor must be used??
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Solution
Total batch time ½ ¾ 4¾ 6 hrs. Number of
batches / day 4 Required production /batch ¾
tons 750kg 750 kg of A is required, if xA
100 For 75 conversion Amount of A to be
fed /batch 750/0.75
1000kg Volume of 1000
kg of A 1250 lit. ? Size of the vessel 1250
lit.
Is the above Design always valid ??
What is the use of the Design equation ??
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ANY CLARIFICATIONS ?
Gauss, Karl I have had my results for a long
time but I do not yet know how I am to arrive
at them.