Chemical Reaction Engineering

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Chemical Reaction Engineering
Lecture 4
Lecturer ???
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This course focuses on how to establish the rate
laws.
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Collection and analysis of rate data

• Batch reactor
• for homogenous reactions
• measurement during the unsteady-state operation
• Differential reactor
• for solid-fluid reactions
• measurement during steady state operation
• product concentration is usually monitored for
  different feed conditions.

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Analysing methods

• Differential method
• Integral method
• Half-lives method
• Initial rate method
• Linear regression
• Non-linear regression

Batch reactors
Software packages
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Batch reactor

• Differential method of rate analysis
• When a reaction is irreversible, it is possible
  to obtain the specific rate constant by
  numerically differentiating concentration versus
  time data.
• For example decomposition reaction A ?
  products

What we measured
What we want to develop
Assuming the rate law as
What about A B ? products ?
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Method of excess

• A B ? products

Assuming the rate law as
Run in an excess of B, so that CB remains
essentially unchanged during the course of the
reaction
After determing ?, the reaction is run in an
excess of A
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Constant-volume batch reactor
constant volume
ln (-dCA/dt)
Slope ?
ln CA
Differential method
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Methods for the determination of the derivatives

• Graphical differentiation
• plotting ?CA/ ?t as a function of t
• using equal-area differentiation to obtain dCA/dt
• Numerical differentiaion
• when the data points in the independent variable
  are equally spaced
• weighted averaged ?CA
• Differentiation of a polynomial fit to the data
• Excel, Sigmaplot and other softwares can be used

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Differential method example
Gas-phase decomposition of di-tert-butyl peroxide
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Postulate a rate law
CA?? P
Mole balance
For a constant volume batch reactor
For isothermal operation and constant volume
For the reaction
12-1
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P
ln (dP/dt)
t
ln (3P0 -P)
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Analysing methods

• Differential method
• Integral method
• Half-lives method
• Initial rate method
• Linear regression
• Non-linear regression

Batch reactors
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Integral Method

• A trial-and-error procedure to find reaction
  order
• Guess the reaction order Integrate the
  differential equation
• This method is used most often when the reaction
  order is known and it is desired to evalue the
  specific reaction rate constants at different
  temperatures to determine the activation energy.
• We are looking for the appropriate function of
  concentration corresponding to a particular rate
  law that is linear with time.

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For the reaction A ? products
For a zero-order reaction - rA - k
For a first-order reaction - rA - k CA
For a second-order reaction - rA - k CA2
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Integral method example
Gas-phase decomposition of di-tert-butyl peroxide
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Differential method
Integral method
Assuming ?1
ln 2P0/(3P0-P)
Bingo!
t
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Analysing methods

• Differential method
• Integral method
• Half-lives method
• Initial rate method
• Linear regression
• Non-linear regression

Batch reactors
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Method of half-lives

• The half-life of a reaction, t1/2, is defined as
  the time it takes for the concentration of the
  reactant to fall to half of its initial value.
• By determining the half-life of a reaction as a
  function of the initial concentration, the
  reaction order and specific reaction rate can be
  determined.

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A ? products
ln (t1/2)
Slope 1- ?
ln CA0
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Analysing methods

• Differential method
• Integral method
• Half-lives method
• Initial rate method
• Linear regression
• Non-linear regression

Batch reactors
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Method of initial rates

• When the reaction is reversible, the method of
  initial rates can be used to determine the
  reaction order and the specific rate constant.
• A series of experiments is carried out at
  different initial concentrations and the initial
  rate of reaction is determined for each run. The
  initial rate can be found by differentiating the
  data and extrapolating to zero time.
• By various plotting or numerical analysis
  techniques relating -rA0 to CA0, we can obtain
  the appropriate rate law

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Initial rate method example
The dissolution of dolomite using hydrochloric
acid
4HCl CaMg(CO3)2 ? Mg2 Ca2 4Cl-2CO3 2H2O
The concentration of HCl at various times was
determined from atomic absorption
spectrophtometer measurements of the calcium and
magnesium ions
4 N HCl
CHCl
1 N HCl
p. 240
t
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Evaluating the mole balance on a constant-volume
batch reactor at t 0
ln -rHCl,0
Slope ?
ln CHCl
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Analysing methods

• Differential method
• Integral method
• Half-lives method
• Initial rate method
• Differential reactor
• Linear regression
• Non-linear regression

Batch reactors
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Differential reactors

• The criterion for a reactor being differential is
  that the conversion of the reactants in the bed
  is extremely small, as is the change in reactant
  concentration through the bed.
• The reactant concentration through the reactor is
  essentially constant (i.e. the reactor is
  considered to be gradientless)
• The rate of reaction is determined for a
  specified number of pre-determined initial or
  entering reactant concentrations.
• Determine the rate of reaction as a function of
  either concentration or partial pressure.

CA0 CA CAe
CA
CA0
CAe
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Differential reactors

• The reactor is considered to be gradientless
  (considered as a CSTR).
• They operate essentially in an isothermal manner.
• (Limitation) If the catalyst under investigation
  decays rapidly, the differential reactor is not a
  good choice because the reaction rate parameters
  at the start of a run will be different from
  those at the end of the run.

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Differential catalyst bed
The rate of reaction per unit mass of catalyst,
rA
flow rate in - flow rate out rate of generation
rate of accumulation
When constant flow rate, v0 v
Product concentration
The reaction rate can be determined by measuring
the product concentration, Cp
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Differential reactor example
The formation of methane from carbon monoxide and
hydrogen using a nickel catalyst at 500 F in a
differential reactor
3H2 CO ? CH4 2H2O
10 g catalyst exit volumetric flow rate 300
dm3/min
Product composition was monitored
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We can then relate the rate of reaction to the
exit methane concentration for each single run.
For constant hydrogen concentration, the rate law
?1
We observe (1) at low H2 concentration where
rCH4 increases as PH2 increases, the rate law
may be of the form rCH4 PH2 ?1 (2) at high H2
concentration where rCH4 decreases as PH2
increases, the rate law may be of the form rCH4
PH2 1/?2
We suggest that the rate law can be the form
?11/2 ?21
Actually, this is the typical form of the rate
law for heterogeneous catalysis. This predicts
that if the rate-limiting step in the overall
reaction is the reaction between atomic hydrogen
absorbed on the nickel surface and CO in the gas
phase.
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Analysing methods

• Differential method
• Integral method
• Half-lives method
• Initial rate method
• Differential reactor
• Linear regression
• Non-linear regression

Batch reactors
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Least-squares analysis

• If a rate law depends on the concentration of
  more than one species and it is not possible to
  use the method of excess, we may choose to use a
  linearized least-squares method.

Assuming a form of the rate law
Find the linear least-squares solution
Run N experiments
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Least-squares analysis example
The etching of semiconductors in the manufacture
of computer chips is an important solid-liquid
dissolution reaction. The dissolution of the
semiconductor MnO2 was studied using a number of
different acids and salts. The rate of
dissolution was found to be a function of the
reacting liquid solution redox potential relative
to the energy-level conduction band of the
semiconductor. It was found that the reaction
rate could be increased by a factor of 105simply
by changing the anion of the acid. From the data
below, determine the reaction order and specific
reaction rate for the dissolution of MnO2 in HBr.
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We assume a rate law of the form
Taking the ln of the both sides and using the
initial rate and concentration
A HBr
Substituting the experimental data in the the
equation and find the least squares equation
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Analysing methods

• Differential method
• Integral method
• Half-lives method
• Initial rate method
• Differential reactor
• Linear regression
• Non-linear regression

Batch reactors
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Nonlinear least-squares analysis

• In nonlinear least squares analysis we search for
  those parameter values and the calculated values
  for all the data points.
• Many software programs are available to find
  these parameter values and all one has to do is
  to enter the data.

I will leave this to you...
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Experimental planning
Fogler, 1999
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Evaluation of laboratory reactors
Also, p 267 for the selection of lab reactors
Fogler, 1999