CHEE 321: Chemical Reaction Engineering Module 4: Finding Rate Laws (Chapter 5, Fogler)

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CHEE 321 Chemical Reaction EngineeringModule
4 Finding Rate Laws(Chapter 5, Fogler)
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Topics to be covered in this module

• Rate law from batch reactor
• Differential Method
• Methods for calculating dCA/dt
• Method Excess
• Method of initial rates
• Integral Method
• Rate law from differential reactor
• Brief description of other reactor types employed
  for kinetics study

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Common Reactor Types for Obtaining Rate Laws

• Batch Reactor
• used primarily for homogeneous reactions
• Differential Reactor
• used primarily for heterogeneous (solid-fluid
  catalytic) reactions

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Rate Law from Batch Reactor
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Typical Experimental Data Available from Batch
Reactor Experiments
OR
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Rate Law from Batch Reactor

• There are two general methods for obtaining rate
  law from batch reactor
• Differential Method
• Batch reactor data in differential form, i.e.
  dCA/dt or dPA/dt, is analyzed.
• Integral Method
• Batch reactor data in integral form, i.e. C(t),
  is analyzed

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Differential Method of Determining Rate Law from
Batch Reactor
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Differential Method for Obtaining Rate Law from
Batch Reactor

• 1. General Mole Balance

2. Rate Law
3. Stoichiometry
4. Combine
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Rate Law from Batch Reactor - Differential Method
Taking the logarithm of combined equation
Reaction order (?) can be found from slope of
log-log plot of - dCA/dt and CA
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Typical Experimental Data Available from Batch
Reactor Experiments
OR
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Methods for Calculating dCA/dt
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Methods for Calculating dCA/dt from CA vs t
data
1. Graphical Method (Appendix A.2 of Fogler)
Step 1 Calculate ? CA and ?t
Step 3 Read - dCA/dt at t for which
corresponding CA has been measured
Step 2 Plot -? CA / ?t vs t
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Methods of Calculating dCA/dt from CA vs t data
2. Polynomial Fit Method
Step 1 Fit CA vs t data using a polynomial of
n th order CA ao a1t a2t2 an tn
Step 2 Calculate dCA /dt dCA /dt a1 2 a2t
(n-1) an tn-1
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Methods of Calculating dCA/dt from CA vs t data
3. Numerical Method (See Appendix A of Fogler)
Can be used when independent variable (in our
case t) is equally spaced, i.e. t1-t0
t2-t1t3-t2 tn-tn-1 ?t
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Integral Method of Determining Rate Law from
Batch Reactor
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Integral Method for Obtaining Rate Law from Batch
Reactor

• 1. General Mole Balance

2. Rate Law
3. Stoichiometry
4. Combine
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Integral Method for Obtaining Rate Law from Batch
Reactor
In the integral method, the reaction order is
hypothesized (or guessed) and the preceding
equation is then integrated. The hypothesis is
verified against experimental data. One
disadvantage of the method is that if the
reaction order is not known a priori, several
trial and errors may have to be done before an
acceptable solution is achieved.
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Reaction Order and Rate Constant
First-order
Zero-order
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Method of Excess and Method of Initial Rates
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Method of Excess - Rate Law for Reactions
Involving Two Reactants
Reaction A B ? Products
Method of Excess Experiment is carried out under
conditions such that one species is in excess.
The rate law can be written as follows
We follow the same method for determining k' and
? as we have discussed previously
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Method of Initial Rates

• For reversible reactions, both forward and
  backward reaction may become significant. In such
  case, the methods discussed earlier may not be
  suitable

Method of Initial Rates may provide the solution
Initially or at time t0, CACA0 and the rate is
given by(-rA0) kCA0?

• Methodology
• Conduct a number of experiments at various
  initial concentrations (CA0) is carried out
• Next, plot (-rA0) vs CA0
• The slope ?
• Knowing the slope, one can calculate the rate
  constant k

Slope ?
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Rate Law from Differential Reactor
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Differential Reactor

• Channeling must be avoided
• Volumetric flow rate, inlet and outlet
  concentrations must be monitored
• Heat release per unit volume is low, as such the
  reactor behaves isothermally.
• The reactor is assumed to be gradientless, i.e.,
  concentration is assumed to be uniform in the
  catalyst bed.

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Method for Obtaining Rate Law from Differential
Reactor
Reaction a A ? b B

• 1. General Mole Balance

- in terms of molar flow rates
- in terms of concentration
- in terms of conversion (X) and molar flow rate
of product (FB)
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Method for Obtaining Rate Law from Differential
Reactor
- For constant volumetric flow rates

• 2. Rate Law

Where,
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Method for Obtaining Rate Law from Differential
Reactor

• 3. Stoichiometery

4. Combine
Kinetic parameters, k and a, can be obtained by
fitting the experimental data
Known from experiment
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Other Types of Reactorsused inDetermining Rate
Laws
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Integral Fixed Bed Reactor

• Ease of construction
• less prone to rate data being affected by
  channeling/bypassing of some areas of catalyst bed

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Stirred Batch Reactor

• Catalyst dispersed as slurry
• Good fluid-solid contact
• Sampling can be problematic

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Stirred Contained Solids Reactor

• Also called spinning basket reactor
• Good fluid-solid contact