optimization of chemical reactors

7/24/2019 Optimization of Chemical Reactors

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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:

optimization of chemical reactors

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