Chapter 6 Design for Single Reaction

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Chapter 6 Design for Single Reaction

• In this chapter we deal with single reaction.
  These are reactions whose progress can be
  described and followed adequately by using one
  and only one rate expression coupled with the
  necessary stoichiometric and equilibrium
  expressions.
• For such reactions product distribution is fixed
  hence, the important factor in comparing design
  is the reactor size.

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6.1 Size Comparison of Single Reactors

• Batch reactor
• Batch reactor has the advantage of small
  instrumentation cost and flexibility of
  operation. It has the disadvantage of high labor
  and handling cost, often considerable shutdown
  time to empty, clean out, and refill, and poorer
  quality control of the product.

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• Regarding reactor size, for a given duty and a
  constant volume system, an element of fluid
  reacts for the same length of time in the batch
  and in the plug flow reactor. Thus, the same
  volume of these reactors is needed to do a given
  job.
• On a long-term production basis we must correct
  the size requirement estimate to account for the
  shutdown time between batches.

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• Mixed versus plug flow reactor, first- and
  second-order reaction
• Make a comparison for large class of reactions
  approximated by the simple nth-order rate law

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Above figure shows
Remember that the essential factor for reactor
size is reaction rate, which is controlled only
by concentration of reactant A, besides
temperature. The order of reaction, conversion,
expansion factor are all related to concentration.
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• Variation of reactant ratio for second-order
  reaction

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• General graphical comparison
• For a nth-order reaction(ngt0), it can be seen
  that mixed flow always needs a larger volume than
  does plug flow for any given duty.

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6.2 Multiple-Reactor System

• Plug flow reactors in series and/or in parallel
• N plug flow reactors in series with a total
  volume V gives conversion as a single plug flow
  reactor of volume V.
• For reactors in parallel V/F or t must be the
  same for each parallel line. Any other way of
  feeding is less efficient.

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• Equal-size mixed flow reactors in series
• In plug flow, the concentration of reactant
  decreases progressively through the system in
  mixed flow, the concentration drops immediately
  to a low value.

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Consider a system of N equal-size mixed reactors
connected in series. Density changes will be
assumed to be negligible.
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• First-order reactions

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• Second-order reactions
• With the same per-condition and same procedure,
  the performance of a second-order
  bimolecular-type reaction with no excess of
  either reactant can be found

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To double reactor size
Divide reactor to two
To lower conversion by increasing treatment rate
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• Mixed flow reactors of different sizes in series
• Two types of questions may be asked
• How to find the outlet conversion from a given
  reactor system?
• How to find the best setup to achieve a given
  conversion?

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• Finding the conversion in a given system

Note for a given system, ti is known
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• Determining the best system for a given
  conversion

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• Reactors of different types in series

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• Ideas for best arrangement

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6.3 Recycle reactor

• recycle ratio R

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Overlap graph for a comparison of recycled and
equal size mixed flow reactors
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• Rough Comparison of recycled and equal-sized
  mixed flow reactors in series

The data can be read from the overlap graph
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isolation
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Inner-recycle reactor
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6.4 Autocatalytic Reactions
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• Plug flow versus mixed flow reactors
• At low conversion, the mixed reactor is superior
  to the plug flow reactor.
• At high enough conversions the plug flow reactor
  is superior.

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• Optimum Recycle Operations
• Only autocatalytic reactions need to optimize
  recycle ratio.
• The optimum recycle ratio is found by
  differentiating
• with respect to R and setting to zero

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By selecting proper R, to make
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• Reactor combinations

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Chapter 7 Design for Parallel Reactions

• In this chapter, we discuss how to optimize the
  size of a reactor and product distribution with a
  pre-condition of constant volume.
• The two requirements, small size and maximization
  of desired product, may run counter to each
  other. In such a situation an economic analysis
  will yield the best compromise.

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• Qualitative Discussion About Product Distribution
• Consider the decomposition of A by either one or
  two path

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• Discussion
• CA is the only factor in this equation which we
  can adjust and control.
• If a1gta2 or the desired reaction is of higher
  order than unwanted reaction, high reactant
  concentration is desirable. As a result, a batch
  or plug flow reactor would favor formation of
  product R and would require a minimum reactor
  size.

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• If a1lta2 or the desired reaction is of lower
  order than unwanted reaction, we need a low
  reactant concentration to favor formation of
  product R. But this would also require large
  mixed flow reactor.
• If a1a2 or the two reactions are of same order.
• Product distribution is fixed by k1/k2 alone and
  is unaffected by type of reactor used.

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summarizing
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• Quantitative Treatment of Product Distribution
  and of Reactor Size
• For convenience in evaluating product
  distribution we introduce two terms

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• For mixed flow reactor in series
• Single reactor

CR,N
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• When there are two or more reactants involved,
  the fractional yield can be based on one of the
  reactants consumed, on all reactants consumed, or
  on products formed. It is simply a matter of
  convenience which definition is used. Thus in
  general, we define as the
  instantaneous fractional yield of M, based on the
  disappearance or formation of N.

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• The Selectivity
• The selectivity is defined as follow

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Chapter 8 Potpourri of Multiple Reaction

• In this chapter, we develop or present the
  performance equations of some of the simpler
  system and point out their special features such
  as maxima of intermediates

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• 8.1 Irreversible first-order reaction in series

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• Qualitative discussion about product distribution

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• The following rule governs product distribution
  for reactions in series
• For irreversible reactions in series the mixing
  of fluid of different composition is the key to
  the formation of intermediates. The maximum
  possible amount of any and all intermediates is
  obtained if fluids of different compositions and
  at different stages of conversion are not allowed
  to mix.

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why?
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Overlap graph for a comparison of recycled and
equal size mixed flow reactors
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• Quantitative treatment, plug flow or batch flow
  reactor

Chapter 3
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• Quantitative treatment, mixed flow reactor
• Material balance for reactant A
• inputoutputdisappearance by reaction
• FA0FA(-rA)V
• vCA0vCAk1CAV

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• 8.2 First-order followed by zero-order reaction

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why?
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• 8.3 Zero-order followed by first-order reaction

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• 8.4 Successive irreversible reaction of different
  order
• explicit solution are difficult to obtain,
  numerical methods provide the best tool for
  treating such reactions.
• As with reactions in parallel, a rise in reactant
  concentration of favors the higher-order
  reaction a lower concentration favors
  lower-order reaction.

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• 8.5 Reversible reactions
• Solution of the equations for successive
  reversible reactions is quite formidable even for
  the first-order case thus we illustrate only the
  general characteristics for a few typical cases.
  Consider the reversible first-order reactions

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• 8.6 Irreversible series-parallel reaction

Some examples shown on the text book
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• Two-step irreversible series-parallel reaction

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• Qualitative discussion about product distribution
• R is desired product, and S is unwanted.
• Image we have two beakers, one holding A and the
  other holding B.
• Mix them by three ways, add A slowly to B, add B
  slowly to A and mix A and B together rapidly.

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• (a) Add A slowly to B
• The result is that at no time during the slow
  addition will A and R be present in any
  appreciable amount.

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• (b) Add B slowly to A

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• (c) Mix A and B rapidly
• Same type of distribution curve as for the
  mixture in which B is added slowly to A can be
  found.
• In case (a), the performance is a reaction in
  series
• In case (b) and (c) , it looks like

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• From this discussion we propose the general rule
• Irreversible series-parallel reactions can be
  analyzed in term of their constituent series
  reactions and parallel reactions in that optimum
  contacting for favorable product distribution is
  the same as for the constituent reaction.

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• Quantitative treatment, plug flow or batch reactor

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• The solution of above differential equation is

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• Quantitative treatment, mixed flow

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Chapter 9 Temperature and Pressure Effects

• This is the only chapter which deals with heat.
• 9.1 Single Reaction
• Brief Review
• Heats of reaction from thermodynamics

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• Equilibrium Constants from Thermodynamics

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Equilibrium Conversion
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• General Graphical Design Procedure
• Temperature, composition and reaction rate are
  uniquely related for any single homogeneous
  reaction.

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For a given feed and using conversion of key
component as a measure of composition and extent
of reaction, the XA vs. T plot has the general
shape shown below
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• The size of reactor for a given duty and for a
  given temperature progression is found as follows
• 1. Draw the reaction path on the XA vs. T plot.
  This is the operating line for the operation.
• 2. Find the rates at various XA along this path.
• 3. Plot the 1/(-rA) vs. XA curve for this path.
• 4. Find the area under this curve. This gives
  V/FA0.

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• Optimum Temperature Progression
• We define the optimum temperature progression to
  be that progression which minimizes V/FA0 for
  given conversion of reactant. This optimum may be
  an isothermal or it may be a changing
  temperature in time for a batch reactor, along
  the length of a plug flow reactor, or from stage
  to stage for a series of mixed flow reactors. It
  is important to know this progression because it
  is the ideal which we try to approach with a real
  system. It also allows us to estimate how far any
  real system departs from this ideal.

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• Heat Effects
• If the reaction is exothermic and if heat
  transfer is unable to remove all of the liberated
  heat, then the temperature of the reacting fluid
  will rise as conversion rise.
• Adiabatic Operations
• ------The heat liberated (or absorbed) by
  reaction is only for heating (or cooling) the
  reacting fluid.
• In this situation, the conversion and temperature
  shows sole relationship.

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• Nonadiabatic Operation(not isothermal)
• Some heat add or remove from the reaction system

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Some true cases
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Exothermic Reactions in Mixed Flow Reactor---- A
Special Problem
VR
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• The heat generated by reaction

• The heat removed by heating the feed stream and
  cooling water

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Q
Q
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Igniting and extinguish points of a mixed flow
reactor
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Important line CD is doubtable for optimal
value.
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• Summarizing of above examples

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• 9.2 Multiple Reaction
• In multiple reactions both reactor size and
  product distribution should be considered.
• Product distribution and temperature

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Chapter 10 Choose the Right Kind of Reactor

• Six rules and some examples
• The summary of the first 9 chapters
• Nothing new