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Chapter 6 Design for Single Reaction

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Title: Chapter 6 Design for Single Reaction


1
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
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