CHE 309: Chemical Reaction EngineeringCHE 309: Chemical Reaction Engineering

LectureLecture--22LectureLecture--22

Module 1: Mole Balances, Conversion & Reactor Sizing(Chapters 1 and 2, Fogler)

Module 1: Mole Balances, Conversion & Reactor Sizing

• Topics to be covered in Module 1 (Lectures 2-6):– General definitions for homogeneous/heterogeneous reactions

– Reaction rate.

– Common Industrial and Laboratory Reactor types and their key

characteristicscharacteristics

– Development of general mole balance and its application to common

industrial reactors (batch and continuous)

– Development of reactor design equations in terms of conversions

– Application of design equations in reactor sizing

Topics to be covered in today’s lectureTopics to be covered in today’s lecture

• Homogeneous and Heterogeneous reactions

– Reaction Rates and Definitions [Fogler Section 1.1]

• General Mole Balance Equation (GMBE) [Fogler Section 1.2]

• Common Reactor Types and Their Characteristics

• GMBE for a Batch Reactor [Fogler Section 1.3]

Homogeneous Reactions: reactions that occur in a single

phase (gas or liquid)

NOx formation

NO (g) + O2 (g) ↔ NO2 (g)

Ethylene Production

C2H6 (g) ↔ C2H4 (g) + H2 (g)

Homogeneous & Heterogeneous Reactions

Heterogeneous Reactions: reactions that require the presence of

two distinct phases

Coal combustion

C (s) + O2 (g) ↔ CO2 (g)

SO3(for sulphuric acid production)

SO2 (g) + 1/2 O2 (g) ↔ SO3 (g) Vanadium catalyst (s)

Classification of chemical reactions useful in rxn design

Non-catalytic Catalytic

Homogeneous Most gas-phase rxn Most liquid phase rxn

Fast rxns such as

burning of flame

Rxns in colloidal

systems Enzyme and

microbial rxnsmicrobial rxns

Heterogeneous Burning of coal

Roasting of ores

Attack of solids by

acids

Gas-liquid absorption

with rxn

Reduction if iron ore

to iron and steel

Ammonia synthesis

Oxidation of ammonia to

produce nitric acid

Cracking of crude oil

Oxidation of SO2 to SO3

On Reaction Rates

Design of a reactor requires that reaction rates of participating

species be specified.

(– rA) = rate of consumption of species A

= moles of A consumed per unit volume (mass) per unit time

(rA) = rate of formation of species A

Note: “minus” sign denotes consumption or disappearance.

Reaction Rate (Reaction Rate (--rrAA) for Homogeneous Reactions) for Homogeneous Reactions

Note: “minus” sign denotes consumption or disappearance.

Units of (rA) or (– rA)

• moles per unit volume (mass) per unit time

• mol/L-s or kmol/m3-s, mol/g-s, kmol/kg-s

* Caution

Customarily, we use rA = dCA/dt. But rA & dCA/dt come from different

concepts. As will be shown later, rA = dCA/dt is valid for only a constant

volume batch reactor system with perfect mixing.

Intrinsic Specific

Reaction Rate for Heterogeneous ReactionsReaction Rate for Heterogeneous Reactions

For a heterogeneous reaction, rate of consumption of species

A is denoted as (-rA')

Heterogeneous reactions of interest are primarily catalytic in

nature. Consequently, the rates are defined in term of mass of

catalyst present.catalyst present.

Units of (-rA')

•mol per unit time per mass of catalyst

•mol/s-g or kmol/hr-kg catalyst

Is (Is (--rrAA) = dC) = dCAA/dt always true?/dt always true?

Neither CAO nor CA are

changing with time

Let us consider the example of this flow reactor and evaluate if

dCA/dt is equal to (rA).

Ethylene Oxide

CCAO CA

Steady State Operation

- no change with time

CAO

CA

CAO CA

(mol/L) (mol/L)

10:00 am 50.0 10.0

12:00 pm 50.0 10.0

3:00 pm 50.0 10.0

5:00 pm 50.0 10.0

More on …. Reaction RateMore on …. Reaction Rate

Reaction rate (intrinsic)• function of temperature and reactant concentrations

• independent of reactor type

• described by a kinetic expression or rate law.

Rate Law (Rate Equation)

Note: a more appropriate description of functionality should be in terms

of “activities” rather than concentration.

Rate Law (Rate Equation)rate law is an algebraic equation that relates reaction rate to species

concentration via a reaction rate constant --- a constitutive relationship.

(-rA) = k ·[concentration terms]

e.g. (-rA) = k CA or (-rA) = k CA2 where, k is rate constant [k=f(T)]

Reactor Types

Common Industrial & Laboratory Reactor TypesCommon Industrial & Laboratory Reactor Types

• Batch Reactor

• Continuous-Flow Reactors

– Continuous-Stirred Tank Reactor (CSTR)

– Tubular Reactor ⊃ Plug Flow Reactor (PFR)– Tubular Reactor ⊃ Plug Flow Reactor (PFR)

– Packed Bed Reactor (PBR)

• Other Reactor Types

– Membrane Reactor

– Fluidized Bed Reactor

Characteristics of Key Reactor TypesCharacteristics of Key Reactor Types

• Batch Reactor

– mainly used for small scale operation

– suitable for slow reactions

– mainly used for liquid-phase reaction

– charge-in/clean-up times can be large

• CSTR (Continuous-Stirred Tank Reactor)

– steady state operation; used in series

Loading

(t < 0)Reaction

(t ≥ 0)

Discharge

(t = tf)

– steady state operation; used in series

– good mixing leads to uniform conc. and temp.

– mainly used for liquid phase reaction

– suitable for viscous liquids

• PFR (Plug Flow Reactor)

– suitable for fast reaction

– gas phase reaction

– temperature control is difficult

– there are no moving parts

CAO

CA

Reactants Products

Characteristics of Other Reactor TypesCharacteristics of Other Reactor Types

• Membrane Reactor

– Perfect solid-liquid separation

– Short hydraulic retention time

– Long solid retention time

– Facility compactness

– Suitable for coating, combustion process– Suitable for coating, combustion process

Characteristics of Other Reactor TypesCharacteristics of Other Reactor Types

• Fluidized Bed Reactor

– The smooth, liquidlike flow of particles

– Easy handling

– Isothermal condition

– Large-scale operation

– Suitable for coating, combustion process– Suitable for coating, combustion process

Spraying Wetting Solidifying

coating droplets

particle coated particle

Drag force by upward moving gas = Weight of particles

[Ref.] Daizo Kunii & Octave Levenspiel, “ Fluidization Engineering”, John Wiley & Sons, Inc

General Mole Balance

w.r.t. RATE (≡Amount / Time)

Reactant enters Reactant leaves

Element of reactor volume

Reactant disappears by

chemical rxn within the

elementReactant accumulates

within the element

General Mole Balance Equation (GMBE)General Mole Balance Equation (GMBE)

INPUT Rate – OUTPUT Rate + Rate of GENERATION – Rate of Consumption =

Rate of ACCUMULATION

General mole balance equation is the foundation of reactor design.

You have used the following form of mole balance

Rate of ACCUMULATION

{ rate of reactant flow into element of volume} –{rate of reactant flow out element of

volume} +{rate of reactant loss due to chemical rxn within the element of volume}

={rate of accumulation of reactant in element of volume}

{ rate of heat flow into element of volume} –{rate of heat flow out element of volume}

+{rate of disapperance due to chemical rxn within the element of volume}

={rate of accumulation of heat in element of volume}

General Mole Balance EquationGeneral Mole Balance Equation

INPUT Rate - OUTPUT Rate + Rate of GENERATION =

Rate of ACCUMULATION

FA

dt

dN AFAO=GA

+FA−

Control Volume = V

FAO

FA

GA = (rate of Generation of A) · V

= (rA)·VIn case of perfect mixing

In a general case Vd r∆V rlim∆GlimG

V

Ai

M

1i

jiM

M

1i

jiM

A ∫∑∑ ====

∞→=

∞→

General Mole Balance for a Batch ReactorGeneral Mole Balance for a Batch Reactor

Reaction: A → Products

General Mole Balance Equation (GMBE) for Batch Reactor may be

written in differential form as

written in integral form as

FA0 = FA = 0 and GA = (rA)·V (as a result of perfect mixing)

1

Key information: Time to reduce NA from NA0 to NA1.