Chemical Reaction Engineering

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Chemical Reaction Engineering
Lecture 3
Lecturer ???
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This course focuses on isothermal ideal reactor
design.
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Design equations

• Batch
• The conversion is a function of the time the
  reactants spend in the reactor.
• We are interested in determining how long to
  leave the reactants in the reactor to achieve a
  certain conversion X.

?
?
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Design equations

• CSTR
• We are interested in determining the size of the
  reactor to achieve a certain conversion X.

?
?
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Design equations

• PFR
• We are interested in determining the size of the
  reactor to achieve a certain conversion X.

?
?
PBR
Generally, the isothermal tubular reactor
volume is smaller than the CSTR for the same
conversion
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Isothermal reactor design

• Design procedure
• mole balance
• rate laws
• stoichiometry
• combination of the above three procedures and
  solve ODE
• obtain the volume/reaction time for the reactor

Do not forget to add some other time required!
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Reactor design

• Batch
• constant volume, well-mixed
• CSTR
• constant volumetric flow rate

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Damköhler number

• ratio of the rate of reaction of A to the rate of
  convective transport of A at the entrance to the
  reactor
• estimation of the degree of conversion in a
  continuous reactor
• First order irreversible rxn
• Second order irreversible rxn
• Da 0.1 X 10 Da 10.0 X 90

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Example, const.-V, batch, 2nd order rxn,
isothermal

• mole balance
• rate laws
• Stoichiometry
• combination

some additional time for filling, heating, etc.
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Example 4-1 It is desired to design a CSTR to
produce 200 million pounds of ethylene glycol per
year by hydrolyzing ethylene oxide. However,
before the design can be carried out, it is
necessary to perform and analyze a batch reactor
experiment to determine the specific reaction
rate constant, k. Because the reaction will be
carried out isothermally, the specific reaction
rate will need to be determined only at the
reaction temperature of the CSTR. At high
temperature there is a significant by-product
formation, while at temperature below 40?C the
reaction does not proceed at a significant rate
consequently, a temperature of 55?C has been
chosen. Because the water is usually present in
excess, its concentration may be considered
constant during the course of the reaction. In
the laboratory experiment, 500 ml of a 2 M
solution of ethylene oxide in water was mixed
with 500 ml of water containing 0.9 wt sulfuric
acid, which is a catalyst. The temperature was
maintained at 55?C. The concentration of ethylene
glycol was recorded as a function of time,
determine the specific reaction rate at 55?C.
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Because water is present in such excess, the
concentration of water at any time t is virtually
the same as the initial concentration and the
rate law is independent of the concentration of
H2O. (CBCB0)
The reaction is first-order in ethylene oxide
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Batch design equation
Rate law
Stoichiometry
no volume change, VV0
Combination
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?
slope -k -0.311 min-1
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Example, liquid phase CSTR, 1st order rxn,
isothermal
or

• mole balance
• rate laws
• Stoichiometry
• combination

or
or
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Example, liquid phase CSTR, 2nd order rxn,
isothermal

• mole balance
• rate laws
• Stoichiometry
• combination

or
or
or
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CSTRs in series, 1st order rxn,
isothermal
CA0
CA1
CA2

• mole balance
• rate laws
• Stoichiometry
• combination

...
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CSTRs in parallel,
isothermal
FA01
FA0
FA02
. .
. .

• mole balance

same T, V, v
total volume
total molar flow rate
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CSTRs in series

• constant flow rate
• conversion as a function of the number of tanks
  in series Two equal-sized CSTRs in series will
  give a higher conversion than two CSTRs in
  parallel of the same size when the reaction order
  is greater than zero.

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CSTRs in parallel

• constant conversion and rate of reaction in each
  tank
• The sum of the volume of the tanks equals the
  total volume of a single large CSTR.
• The conversion achieved in any one of the
  reactors in parallel is identical to what would
  be achieved if the reactant were fed in one
  stream to one large reactor of volume V.
• Considering the degree of mixing and the room
  required, a large tank might not be appropriate.

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Example 4-2 Close to 12.2 billion metric tons of
ethylene glycol (EG) were produced in 2000, which
ranked it the twenty-sixth most produced chemical
in the nation that year on a total pound basis.
About one-half of the ethylene glycol is used for
antifreeze while the other half is used in the
manufacture of polyesters. In the polyester
category, 88 was used for fibers and 12 for the
manufacture of bottles and films. The 2004
selling price for ethylene glycol was 0.28 per
pound. It is desired to produce 200 million
pounds per year of EG. The reactor is to be
operated isothermally. A 1 lb mol/ft3 solution of
ethylene oxide (EO) in water is fed to the
reactor (shown in Figure E4-2.1) together with an
equal volumetric solution of water containing 0.9
wt of the catalyst H2SO4. The specific reaction
rate constant is 0.311 min-1, as determined in
Example 4-1.
The specified ethylene glycol (EG) production
rate
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(a) If 80 conversion is to be achieved,
determine the necessary CSTR volume.
CSTR Design equation
Rate law
Stoichiometry
Combination
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(b) If two 800-gal reactors were arranged in
parallel, what is the corresponding conversion?
CSTR Design equation
Rate law
Stoichiometry
Combination
The conversion exiting each of the CSTRs in
parallel is 81.
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(c) If two 800-gal reactor were arranged in
series, what is the corresponding conversion?
The two equal-sized CSTRs in series will give a
higher conversion than two CSTRs in parallel of
the same size when the reaction order is greater
than zero.
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PFR

• Gas-phase reactions are carried out primarily in
  tubular reactors where the flow is generally
  turbulent.
• Assuming no dispersion and there are no radial
  gradients in either temperature, velocity, or
  concentration.
• Should be aware of the change of the volume.

N.B. The majority of gas-phase reactions are
catalyzed by passing the reactant through a
packed bed of catalyst particles.
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PFR, 2nd order rxn, liquid phase, isothermal
No pressure drop

• mole balance
• rate laws
• Stoichiometry
• combination

No heat exchange
or
Damköhler number for 2nd-order reaction
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PFR, 2nd order rxn, gas phase, isothermal
No pressure drop

• mole balance
• rate laws
• Stoichiometry
• combination

No heat exchange
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Example 4-3 Ethylene ranks fourth in the Unite
States in total pounds of chemicals produced each
year, and it is the number one organic chemical
produced each year. Over 50 billion pounds were
produced in 2000, and it sold for 0.27 per
pound. Sixty-five percent of the ethylene
produced is used in the manufacture of fabricated
plastics, 20 for ethylene oxide, 16 for
ethylene dichloride and ethylene glycol, 5 for
fibers, and 5 for solvents. Determine the
plug-flow reactor volume necessary to produce 300
million pounds of ethylene a year from cracking a
feed stream of pure ethane. The reaction is
irreversible and follows an elementary rate law.
We want to achieve 80 conversion of ethane,
operating the reactor isothermally at 1100 K at a
pressure of 6 atm.
The activation energy is 82 kcal/g mol.
The molar flow rate of ethylene (B)
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PFR design equation
Rate law (elementary)
Stoichiometry
Combination
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(b) It was decided to use a bank of 2-in.
schedule 80 pipes in parallel that are 40 ft in
length. For pipe schedule 80, the cross-section
are, Ac, is 0.0205 ft2. The number of pipes
necessary is
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Pressure drop in reactors

• In gas-phase reactions, the concentration of the
  reacting species is proportional to the total
  pressure and proper accounting for the effects of
  pressure drop on the reaction system can be a key
  factor in the success or failure of the reactor
  operation (e.g. PBR).
• When accounting for the effects of pressure drop,
  the differential form of the mole balance must be
  used.

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PBR, 2nd order rxn, gas phase, isothermal

• mole balance
• rate laws
• Stoichiometry
• combination

or
What is the relationship between X and P? If PBR
Ergun equation
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Ergun equation

• Pressure drop in a porous bed

Dominant for turbulent flow
Dominant for laminar flow
constant mass flow rate
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Ergun equation (cont.)
Pressure drop in terms of Catalyst weight
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Gas phase, PBR with pressure change
Solve simultaneously!
Some special cases in the textbook!...
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Pressure drop in pipes without packing
constant mass flow rate
isothermal
integrate
fconst.
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PBR, 2nd order rxn, gas phase, isothermal

• mole balance
• rate laws
• Stoichiometry
• combination

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Spherical packed-bed reactors

• When small catalyst pellets are required, the
  pressure drop can be significant, and thus the
  conversion decreases.
• One type of reactor that minimises pressure drop
  and is also inexpensive to build is the spherical
  reactor, called an ultraformer.
• Spherical reactor the cross-sectional area and
  the weight of catalyst are functions of the
  position.
• In addition to the higher conversion, the
  spherical reactor has the economic benefit of
  reducing the pumping and compression cost because
  of higher pressure at the exit.

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Mole balance and rate laws

• Concentration f (conversion) We have done!
• There are a number of instances when it is much
  more convenient to work in terms of the number of
  moles (Ni) or molar flow rates (Fi) rather than
  conversion.
• Membrane reactors and multiple reactions taking
  place in the gas phase are two such cases where
  molar low rates rather than conversion are
  preferred.
• Concentration f (molar flow rate)

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Algorithm - liquid phase

• Liquid phase
• For liquid-phase reactions in which there is no
  volume change, concentration is the preferred
  variable.
• We have only to specify the parameter values for
  the system (CA0, vo, etc.) and for the rate law
  to solve the coupled ODEs for either PFR, PBR, or
  batch reactors, or to solve the coupled algebraic
  equations for a CSTR.

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Liquid phase mole balance
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Algorithm - gas phase

• Gas phase
• For gas-phase reactions in which there is volume
  change, molar flow rate is the preferred
  variable.
• The total molar flow rate is given as the sum of
  the flow rate of the individual species.
• A mole balance on each species has to be
  specified.

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Gas phase mole balance
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PBR, gas phase, isothermal, no ?P

• mole balance
• rate laws
• Stoichiometry
• combination

Solve
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Microreactors

• High surface area-to-volume ratio
• Reduce or eliminates heat and mass transfer
  resistances
• Shorter residence times narrower residence time
  distributions
• Production of lab-on-a-chip, chemical sensors
• Assume PFR or in laminar flow

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Thermodynamically limited rxns

• Catalytic membrane reactors can be used to
  increase the yield of reactions that are highly
  reversible over the temperature range of
  interest.
• The membrane can either provide a barrier to
  certain components, while being permeable to
  others, prevent certain components such as
  particulates from contacting the catalyst, or
  contain reactive sites and be a catalyst in
  itself.

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Membrane reactors

• The membrane reactor is another technique for
  driving reversible reactions to the right in
  order to achieve very high conversion.
• These high conversions can be achieved by having
  one of the reaction products diffuse out of a
  semipermeable membrane surrounding the reacting
  mixtures.
• Two main types
• inert membrane reactor with catalyst pellets on
  the feed side (IMRCF)
• Catalytic membrane reactor (CMR)

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Startup of a CSTR

• Determine the time necessary to reach
  steady-state operation
• Conversion does not have any meaning in the
  startup
• Use concentration rather than conversion as the
  variable in the balance equations.

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CSTR, 1st order rxn, liquid phase
const. .V

• mole balance
• rate laws
• combination

t 0
t ts
steady-state concentration
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Semi-batch reactors

• When unwanted side reactions occur at high
  concentration of reactant B, or the reaction is
  highly exothermic. Examples of reactions
• ammonolysis
• chlorination
• hydrolysis
• Reactive distillation Carrying out the two
  operations, reaction and distallation in a single
  unit results in lower capital and operating
  costs.
• acetylation reaction
• esterfication reaction (remove water) A

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Semi-batch reactor

• Write the reactor equations in terms of
  concentration / numer of moles of each species
• Write the mass balance of the vessel
• Write the rate laws

O.D.E solver
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Semi-batch, liquid phase

• mole balance (A)
• mole balance (B)
• V is not a constant
• combine

(overall mole balance)
..
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Example 4-9 The production of methyl bromide is
an irreversible liquid-phase reaction that
follows an elementary law. The reaction
CNBrCH3NH2?CH3BrNCNH2 is carried out
isothermally in a semibatch reactor. An aqueous
solution of methyl amine (B) at a concentration
of 0.025 mol/dm3 is to fed at rate of 0.05 dm3/s
to an aqueous solution of bromine cyanide (A)
contained in a glass-lined reactor. The initial
volume of fluid in a vat is to be 5 dm3 with a
bromine cyanide concentration of 0.05 mol/dm3.
The specific reaction rate constant is k 2.2
dm3/s?mol. Solve for the concentration of bromine
cyanide and methyl bromide and the rate of
reaction as a function of time.
Semi-batch reactor design equation
Rate law
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Combination
where
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Recycle reactors

• They are used when the reaction is autocatalytic,
  or when it is necessary to maintain nearly
  isothermal operation of the reactor or to promote
  a certain selectivity.
• They are used extensively in bio-chemical
  operations.
• Two conversions the overall conversion X0 and
  the conversion per pass Xs

Xs
Xo