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Optimization ofChemical Reactors
ByProf. Dr. Javaid Rabbani Khan
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Reactors: A Quick Review
Every chemical reaction involves the transfer
of reactants and products of reaction along
with absorption or evolution of heat.
Physical design of the reactor depends upon: emperature
Pressure Rate of !hemical Reaction
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Modelling and Optimization of
Reactors "ptimi#ation in the design and operation of a
reactor focuses on: $ormulating a ob%ective function
&imited by type of reaction'reactor( li)e e*uilibriumconditions and catalyst activity
+athematical description of the reactor using
algebraic( ordinary differential and partial
differential e*uations. &imited by a set of constraints li)e( order and
molecularity of reaction limits rate e*uation
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Cont
$actors affecting modelling of reactors he number and nature of the phases present in
the reactor ,gas( li*uid( solid( and combinations - he method of supplying and removing heat
,adiabatic( heat echange mechanism( etc.- he geometric configuration ,empty cylinder(
pac)ed bed( sphere( etc.- Reaction features ,eothermic( endothermic(
reversible( irreversible( number of species(parallel( consecutive( chain( selectivity-
/tability he catalyst characteristics
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Mathematical Euations for
Reactors
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O!"ective #unction for
Reactors +aimi#e conversion ,yield- per volume with respect to time +aimi#e production per batch +inimi#e production time for a fied yield +inimi#e total production costs per average production costs with
respect to time per fraction conversion +aimi#e yield per number of moles of component per
concentration with respect to time or operating conditions Design the optimal temperature se*uence with respect to time
per reactor length to obtain ,a- a given fraction conversion( ,b- a
maimum rate of reaction( or ,c- the minimum residence time
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Cont
0d%ust the temperature profile to specifications ,via sum ofs*uares- with respect to the independent variables
+inimi#e volume of the reactor,s- with respect to certainconcentration,s-
!hange the temperature from oto fin minimum time sub%ect toheat transfer rate constraints +aimi#e profit with respect to volume +aimi#e profit with respect to fraction conversion to get optimal
recycle
"ptimi#e profit per volume per yield with respect to boundary perinitial conditions in time
+inimi#e consumption of energy with respect to operatingconditions
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Optimization $echniues for
Reactor 0ll of the various optimi#ation techni*ues
studied can be applied to one or more types
of reactor models.
he reactor model forms a set of constraints
so that most optimi#ation problems involving
reactors must accommodate steady1statealgebraic e*uations or dynamic differential
e*uations as well as ine*uality constraints
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Cont
2n considering a reactor by itself( )eep in
mind that a reactor will no doubt be only one
unit in a complete process( and that at least a
separator must be included in any economicanalysis
$igure 34.3 depicts the relation between theyield or selectivity of a reactor and costs
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#igure %&'%
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OPTIMAL DESIGN OF AN
AMMONIA REACTOR
/tatement
his eample based on the reactor described
by +urase et al. ,3567- shows one way to
mesh the numerical solution of the differential
e*uations in the process model with an
optimi#ation code. he reactor( illustrated in
$igure E34.8a( is based on the 9aberprocess.
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Cont
$igure E34.8b illustrates the suboptimal
concentration and temperature profiles
eperienced. he temperature at which the
reaction rate is a maimum decreases as theconversion increases
$eed gas composition ,mole -
;8: 83.6
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#igure E %&'(a
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#igure E %&'( !
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)otation and *ata
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Assumptions
0ssumptions made in developing the model are he rate epression is valid
&ongitudinal heat and mass transfer can be ignored
he gas temperature in the catalytic #one is also the
catalyst particle temperature
he heat capacities of the reacting gas and feed gas
are constant
he catalytic activity is uniform along the reactor ande*ual to unity
he pressure drop across the reactor is negligible
compared with the total pressure in the system
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*e+ning O!"ective #unction
he ob%ective function for the reactoroptimi#ation is based on the difference
between the value of the product gas
,heating value and ammonia value- and thevalue of the feed gas ,as a source of heat
only- less the amorti#ation of reactor capital
costs. "ther operating costs are omitted.
$inally it is :
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Constraints
E*uality constraints "nly 3 degree of freedom eists in the problem
because there are three constraints? is
designated to be the independent variable
2ne*uality constraints
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Energ, -alance
$or $eed @as
111111111 ,b-
$or Reacting @as
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Mass -alance .-asis of)itrogen/
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0artial 0ressure for Reacting
1pecies $or reaction in terms of ;nitrogen( the partial
pressure are given as:
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1olution 0rocedure
Because the differential e*uations must besolved numerically( a two1stage flow of
information is needed in the computer
program used to solve the problem. Eamine
$igure E34.8c
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Result of optimization
he code @enerali#ed Reduced @radient8
was coupled with the differential e*uation
solver &/"DE( resulting in the following eit
conditions: