Slide Kinetics 001

8/2/2019 Slide Kinetics 001

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Chemical Reaction Engineering

Introduction, Mole Balances

. . .

Objectives

Define the rate of chemical reaction.

Apply the mole balance equations to a batch

reactor, CSTR, PFR, and PBR.

Text books

Elements of Reaction Engineering, 4th Edition,

H.Scott Fogler, Prentice Hall.

Chemical Reaction Engineering, 2nd or 3rd

Edition, Octave Levenspiel, John Wiley and

Sons.

Rate of Reaction

A number of moles of one chemical species are

being consumed to form another chemical

Chemical species refers to any chemicalcomponent or element with a given identity.

species.

The identity of a chemical species is determined

, ,

species' atoms.


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Rate of Reaction (cont.)

Chemical reaction -> a detectable number of

molecules of one or more species reacted have lost

their chemical identity.

Assumed a new form by a change in the kind or

number of atoms in the compound and/or by achange in structure or configuration of these atoms

ssume t at t e tota mass s ne t er create nor destroyed when a chemical reaction occurs.


The mass referred to is the total collective mass of

all the different species in the system.

The rate of disappearance of a species is the

number ofA molecules that lose their chemical

identity per unit time per unit volume through the

breaking and subsequent re-forming of chemicalbonds during the course of the reaction.

The rate of a reaction can be expressed as the

rate ofdisappearance of a reactant or as the

rate of appearance of a product.


Consider reaction (species A)

A + 2B C + DThe numerical value of the rate of disappearance

of reactant

A, -rA is a positive number(-rA = 4 mol A/dm

3s, rA = -4 mol A/dm3s

-rB = 8 mol A/dm3s, rC = 4 mol A/dm

3s)

Whats -rA ?

The rate of reaction, -rA is the number of moles of A

reacting (disappearing) per unit time per unit volume

(mol/dm3s)


Consider species j

r is the rate of formation of s ecies er unit

volume [e.g. mol/dm3s] r

jis a function of concentration, temperature,

pressure, and the type of catalyst

rj is independent of the type of reaction system(batch, plug flow, etc.)

j ,equation (-rA = kCA)

is not the rate of reaction

dt

dCA


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Example of Rate of Reaction

Consider reaction

A B

If B is being created 0.2 mole/dm3s

rB = 0.2 mol /dm3/s

Then A is disappearing at the same rate:

- = 3.

The rate of formation of A (Generation of A) :

rA = 0.2 mol /dm3s

General Mole Balance Equation

Mole balance on species j in a system volume (V),where species j represents the particular chemicalspecies of interest (such as NaOH, water)

GjFj FjV

General Mole Balance Equation (cont.)

Equation of mole balance on species j at any time (t)

Rate of flow

of j intosystem

(moles/time)

-Rate of flow

of j out of

system(moles/time)

Rate of

generation of j

by chemical

reaction withinsystem

(moles/time)

+Rate of

accumulation of

j within system(moles/time)

=

n u + enera on = ccumu a on

(1-1)

Where Nj = the number of moles of species j in system at t.

dt

dNGFF

j

jjj 0


The rate of generation of speciesj, Gj is the

product of the reaction volume (V) and the rate of

formation of species j, r

Gj = rjV

volumevolumetime

moles

time

moles


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The rate of formation of species j for the reactionvarious position in system volume

V1

V2rj1

rj2

The rate of generation, Gj1 in terms of rj1 andsubvolume V1 is

Gj1=rj1V1


The total rate of generation is the sum of all therates of generation in each of the subvolumes

M

i

iji

M

i

jij VrGG11

By taking limits (M and V0) and use ofdefinition of integral, the equation can rewrite in

V

jj dVrG


Replace Gj in the mole balance equation

dN

V

j

jjjdt

dNdVrFF

0

dtGFF jjj 0 -

(1-4)

This is the general mole balance equation, we can

develop the design equations for the various types

of reactors: batch, semibatch and continuous-flow.

Types of Ideal Reactors

Perfectly mixed batch reactor (Batch)

Continuous stirred tank reactor (CSTR) orBackmix reactor

Plug flow reactor (PFR)

Packed bed reactor (PBR)


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Mole Balance for Batch Reactor

A batch reactor has neither inflow nor outflow of

reactants or products while the reaction is being

carried out: Fj0= Fj= 0. The resulting general

mole balance on speciesj is

dt

dNGFF

j

jjj 0

V

j

jjdt

dNdVrG

Mole Balance for Batch Reactor (cont.)

The reaction mixture is perfectly mixed so that

there is no variation in the rate of reaction

throughout the reactor volume, we can take rj out

of the integral, integrate, and write the molebalance in the form.

VrdN

j

j (1-5)

Consider the reaction of species A in batch reactor

A B

Mole Balance for Batch Reactor (cont.)

As the reaction proceeds, the number of moles of

A (NA) decreases and the number of moles of B

(NB) increases as shown in Figure

NA0

NA

NA1

NB1

NB

0 tt10 tt1

Mole-time trajectories

Mole Balance for Batch Reactor (continue)

Consider time t1 to reduce NA0 to NA1. Applying the

mole balance equation

Vr

dt

A

AVr

dt

dNA

A

Integrating with limits that t = 0, then NA = NA0 and

t = t1, then NA = NA1

0

1

A

AN A

A

Vr

dNt

This equation is the integral form of the mole

balance on a batch reactor.

(1-6)


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Usage of Batch Reactor

Small scale

operation

Production of expensive products

Processes that are difficult to convert to

con nuous opera ons

Used for liquid phase reactions that require a fairly

long reaction time.

Advantage of Batch Reactor

High conversions can be obtained by leavingreactants in the reactor for long periods of time.

Low capital cost.

Versatile, can be used to make many

products consecutively.

products while still in testing phase.

Easy to clean

Disadvantage of Batch Reactor

High labour cost.

Difficult for large-scale production.

Long downtime for cleaning leads to

periods of no production.

Ideal CSTR

Normally operated at steady state, therefore

reaction rate is the same at every point, and time

inde endent.

Assumed to be perfectly mixed.

No time dependence or position dependence of

temperature, concentration, or reaction rate inside

CSTR no s atial variations . .j0

V


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Mole Balance for CSTR

CSTR operated at steady state or conditions donot change with time.

V

00

dtdN

dVrFFj

jjj

No spatial variation in the rate of reaction

jj

The design equation for CSTR

j

jj

r

FFV

0 (1-7)

Mole Balance for CSTR (cont.)

The CSTR design equation gives the reactor

volume V necessary to reduce the entering flow

rate of species j, from Fjo to the exit flow rate Fj,when species j is disappearing at a rate of rj.

The molar flow rate Fj is the product of the

concentration of species j and the volumetric flow

rate

vjj

time

volume

volume

moles

time

moles

(1-8)

Mole Balance for CSTR (cont.)

Rewrite the design equation for CSTR on speciesj as

j

jj

j

jj

r

vCCv

r

FFV

000

Fj0

(1-9)

FjV

Usage of CSTR

Usually employed for liquid phasereactions.

Use for two-phase reactions in

which a gas is bubbledcontinuously through the liquid.

Use when intense agitation is

required.


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Advantage & Disadvantage of CSTR

Relatively easy to maintain good temperaturecontrol with a CSTR because it is well mixed.

Advantage

Cheap to construct.

Interior of reactor is easily accessed.

Disadvanta e

Conversion of reactant per volume of reactor is the

smallest of the flow reactors - very large reactors

are necessary to obtain high conversions

Ideal PFR

Normally operated at steady state

The reactants are continuously consumed as

they flow down the length of the reactor.

The concentration various continuously in the

axial direction through the reactor.

No radial variation in reaction rate and the reactoris referred to as a plug-flow reactor (PFR)

Mole Balance for PFR

From the general mole balance equation

dNjV

dt

jjj0

The design equation of PFR at steady state can

be developed 2 ways: (1) directly form the general

equation or(2) form a mole balance on species j

in a differential segment of reactor volume V.

Mole Balance for PFR (cont.)

The differential volume, V, shown in Figure

Fj0 FjFjFj

V V+V

V

No spatial variations in reaction rate within thisvolume. Thus the generation term, Gj is

VrdVrG j

V

jj


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Mole Balance for PFR (continue)

Molar flowrate of jIn at V

-Molar flow

rate of j

Out at V+ V

Molar rate ofGeneration of j

within V+

Molar rate ofAccumulation of

j within V=

In Out + Generation = Accumulation

Fj|V Fj|V+V + rjV = 0 (1-10)

j

VjVVjr

V

FF


The term in brackets resembles the definitionof the derivative

Taking the limit as V approaches zero, weobtain the differential form of stead state mole

dx

df

x

xfxxf

x

0

lim

balance on a PFR.

j

jr

dV

dF (1-11)


Consider the reaction of species A in PFR

A B

FA0

FA

FA1

FB1

FB

0 VV10 VV1

Profiles of molar flow rates in a PFR.


What is the reactor volume (V) to reduce FA0 toFA1. Applying the mole balance equation

A

A

r

dFdV

Integrating with limits that V = 0, then FA = FA0 and

V = V1, then FA = FA1

0

10

1

A

A

A

A F A

A

F A

A

r

dF

r

dFV

This equation is the integral form of the mole

balance on a PFR

(1-13)


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Usage of PFR

A wide variety of applications in either gas orliquid phase systems.

Use for produces the highest conversion per

reactor volume of any of the flow reactors.

Common industrial uses of tubular reactors are in

gasoline production, oil cracking, synthesis of

.

Used as bioreactor.

Advantage of PFR

Relatively easy to maintain since there are no

moving parts.

g convers on rate per reactor vo ume.

Mechanically simple.

Unvarying product quality.

Good for large capacity processes.

Disadvantage of PFR

Reactor temperature difficult to control.

Hot spots may occur within reactor when used

for exothermic reactions.

Difficult to control due to temperature and

.

Packed-Bed Reactor (PBR)

The reaction takes place on the surface of the

catalyst.

The reaction is based on mass of solid catalyst(W) rather than on reactor volume.

The rate of reaction of a substance A is defined as

- =


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Mole Balance for PBR

The derivation of the design equation for PBR will

be carried out in a manner analogous to the

development of PFR, replace the volume

coordinate in equation with the catalyst weight (W)

FA0 FAFAFA

W W+W

In Out + Generation = Accumulation

FA|W FA|W+W + r AW = 0

No radial gradients in concentration, temperature,or reaction rate. The general mole balance as

(1-14)

Mole Balance for PBR (continue)

Differential with respect to W and rearrange

'AdFA

dW

F

Integral form of PBR design equation

-

0

10

''

A AA A F

A

F

A

rdF

rdFW (1-16)

Summary of Reactor Mole Balances

Reactor Comment Mole BalanceDifferential

Form

AlgebraicForm

Integral form

0ANvariations

CSTR No spatialvariations,

steady state- -

PFR Steady state

Vrdt

AA

A

AA

r

FFV 0

A rdF

1

1

AN A

A

Vrt

0AF

AdFV

PBR Steady state

dV

'

Ar

dV

dFA

1AF A

r

0

1

'1

A

A A

F

F

A

r

dFW

Industrial Reactor


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Equipment of Batch Reactor

The movie to the left shows the basic

operation of a batch reactor.

The reactants are placed into the

reactor and then allowed to react, and

products form inside the reactor.

The products and unreacted

reactants are then removed and the

process is repeated.

Equipment design

(Fogler, 2006 )

Equipment of CSTR

The movie to the left shows the

operation of a CSTR.

Reactants are fed continuously into

the reactor through ports at the top.

The contents of the tank are well

mixed by unit's stirring device.

Products are removal continuously.

Equipment design

(Fogler, 2006 )

Equipment of PFR

The movie to the left shows the

operation of a plug flow reactor.

Plugs of reactants are

continuously fed into the reactor

from the left.

As the plug flows down the

reactor the reaction takes place,

resulting in an axial

Equipment design

(Fogler, 2006 )

.

The products and unreacted

reactants flow out of the reactor

continuously.

Equipment of PBR

The animation on the left shows the

operation of a packed bed reactor.

The reactants (green) enter the reactor

on the top, then flow through.

Upon entering the reactor the reactantsflow through the packed bed of catalyst.

By contacting with the catalyst pellets,

Equipment design

(Fogler, 2006 )

(blue), which the exit the reactor on the

bottom.

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