CHEE 321: Chemical Reaction Engineering

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

Module 1: Mole Balances, Conversion & Reactor Sizing

• Topics to be covered:– Basic elements of reactor design, terminology/notation

– Development of general mole balance equation with reaction

– Key characteristics and mole balance equations for common industrial reactors (batch, CSTR, PFR, PBR)

– Reactor design for single-reaction systems• Definition of conversion• Levenspiel Plots

Basic Elements of Reactor Design• Reactor design usually involves the following:

– Knowledge of nature of reaction • Catalytic or Non-Catalytic• Homogeneous or Heterogeneous• Reversible or Irreversible

– Selection of operating conditions• Temperature, Pressure, Concentrations• Type of catalyst (if applicable)• Flow rates

– Selection of reactor type for a given application– Estimation of reactor volume required to process given amount

(moles or molar rate) of raw material to desired amount of products• How fast the reaction occurs (reaction rates) dictates how large the

reactor volume will be

Our approach to reactor design• Operation of most reactors are relatively complex

– Temperature is not uniform and/or constant– Multiple reactions can occur– Flow patterns are complex

• To gain an insight into basic concepts relevant to reactor design, we will first consider simplified and/or ideal reactor systems.

• Design of isothermal reactors involves solution of MOLE BALANCE equation only– In some cases, pressure drop must also be calculated

• Let us first familiarize ourselves with some common terminology and notation that we will be using throughout the course

Monomer Feed

Initiator

Feed

- A multi-zone Autoclave is a vertical cylindricalvessel with large L/D of 10-20. The reactionmixture is intensely mixed by a stirrer shaft.

- Reactor is divided into separated reaction zones.

- Reactor (and each zone) is considered as well-mixed CSTR in perfect mixing model approach.

- Imperfect mixing of initiator feed can occur dueto very fast initiator decomposition rate, despiteintense agitation

Ethylene Low Density Polyethylene

Reversible and Irreversible Reactions

Irreversible Reactions: Reactions that proceed uni-directionally under the conditions of interest

Reversible Reactions: Reactions that proceed in both forward and reverse directions under conditions of interest.

SO2 + 0.5 O2 ⇄ SO3

CH4 + 2O2 CO2+2H2O

H2S⇄ H2 + 1/xSx

Thermodynamics tells us that all reactions are reversible.However, in many cases the reactor is operated such that therate of the reverse reaction can be considered negligible.

Homogeneous Reactions: reactions that occur in a single-phase (gas or liquid)NOx formationNO (g) + 0.5 O2 (g) ↔ NO2 (g)Ethylene ProductionC2H6 (g) ↔ C2H4 (g) + H2 (g)

Heterogeneous Reactions: reactions that require the presence of two distinct phases

Coal combustionC (s) + O2 (g) ↔ CO2 (g)

SO3(for sulphuric acid production) SO2 (g) + 1/2 O2 (g) ↔ SO3 (g) Vanadium catalyst (s)

Homogeneous & Heterogeneous Reactions

Material Balances: It all starts from here!

Rate of INPUT – Rate of OUTPUT + Rate of GENERATION – Rate of CONSUMPTION

= Rate of ACCUMULATION

Input RateOutput Rate

Note: Rates refer to molar rates (moles per unit time).

Before we get into the details of the mole balance equation, we must introduce definition for reaction rate as well as associated notation.

System with Rxn: use mole balances

(– rA) = rate of consumption of species A (A is a reactant)= moles of A consumed per unit volume per unit time

(rA) = rate of formation of species A (A is a product)

Units of (rA) or (– rA)• moles per unit volume per unit time• mol/L-s or kmol/m3-s

Notation: Reaction Rate for Homogeneous Reactions

A + B C

D A

Notation: Reaction 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

Units of (-rA')•mol per unit time per mass of catalyst•mol/(g cat)-s or kmol/(kg cat)-h

Reaction Rate and Rate LawReaction Rate• Rate of reaction of a chemical species will depend on the local conditions

(concentration, temperature) in a chemical reactor

Rate Law• Rate law is an algebraic equation (constitutive relationship) that relates reaction

rate to species concentrations.• Rate law is independent of reactor type

(-rA) = k ·[concentration terms]

e.g. (-rA) = k CA or (-rA) = k CA2

where, k is the rate coefficient [k=f(T)]

Note: a more appropriate description of functionality should be in terms of “activities” rather than concentration.

We’ll learn more about rate laws in Modules 2 and 4.

General Mole Balance Equation (GMBE)

Rate of INPUT – Rate of OUTPUT + Rate of GENERATION/CONSUMPTION = Rate of ACCUMULATION

System volume VFA0

FA

GA = (rate of generation of A) · V

dtdN AFA0 =GA+FA−

General mole balance equation is the foundation of reactor design.

If A is consumed, add a –ve sign

All terms with units of mol/s

V

Ar dV ′= ∫Need to integrate over reactor volume, as reaction conditions (T, CA ) may vary with position

Common Reactor Types

• Batch Reactor

• Flow Reactors– Continuous-Stirred Tank Reactor (CSTR)– Plug Flow Reactor (PFR)– Packed Bed Reactor (PBR)

• Other Reactor Types– Semibatch Reactors– Fluidized Bed Reactor, Trickle Bed Reactor, Membrane

Reactor, …

Batch Reactor

Key Characteristics• No inflow or outflow of material• Unsteady-state operation (by definition)• Mainly used to produce low-volume high-value

products (e.g., pharmaceuticals)• Often used for product development• Mainly (not exclusively) used for liquid-phase

reactions• Charging (filling/heating the reactor) and clean-

out (emptying and cleaning) times can be large

For an ideal batch reactor, we assume no spatial variation of concentration or temperature. i.e.; lumped parameter system (well-mixed)

General Mole Balance for an Batch Reactor

If well-mixed (no temperature or concentration gradients in reactor):

differential form integral form

Input = Output = 0

0

;

at 0

AA

A A

dN r Vdt

N N t

=

= = 0

A

A

NA

AN

dNtr V

′= ∫

VA

AdN r dVdt

′= ∫

Class exercise: Derive concentration vs. t profiles for A and B for A B with rB=-rA=kCAfor a well-mixed constant-volume isothermal batch reactor. At t=0, CA=CA0 and CB=0

Continuous Stirred Tank Reactor (CSTR)

• Can be used in series• Mainly used for liquid phase

reaction, high-volume products• Suitable for viscous liquids

Picture Source: http://www-micrbiol.sci.kun.nl/galleries/two.html

FA0

FA

For an ideal CSTR, we assume no spatial variation of concentration or temperature. i.e.; lumped parameter system (well-mixed)

0

VA

A A AdN F F r dVdt

′= − + ∫

0A

A A AdN F F r Vdt

= − +

For an ideal CSTR operating at steady-state (no time variation of flows, concentrations, temperature) 0 0A A AF F r V− + =

General Mole Balance for Ideal CSTR at Steady-State

FA0=v0CA0

Class exercise: Derive expressions for concentration of A and B for A B with rB=-rA=kCA for a well-mixed steady-state CSTR with inlet concentrations CA=CA0 and CB=0, assuming no density change.

CSTRs are also known as “back-mix” reactors, as concentrations in the outlet stream are the same as concentrations in the reactor (a consequence of being well-mixed)

FA=vCANA=VCA

v0, v= volumetric flowrates (L/min, m3/s) of inlet and exit; if at steady-state and constant density, v0 = v

Average residence or space time of fluid in vessel based on inlet conditions τ = V/v0

Class Problem

Calculating Reaction Rate in a CSTR1.0 L/min of liquid containing A and B (CA0=0.10 mol/L, CB0=0.01 mol/L) flow into a mixed flow reactor of volume 1.0 L. The materials in the reactor interact (react) in a complex manner for which the stoichiometry is unknown.

The outlet stream from the reactor contains A, B and C at concentrations of CA= 0.02 mol/L, CB=0.03 mol/L and CC=0.04 mol/L.

Find the rate of reactions of A, B and C at conditions of the reactor.

Plug Flow Reactor (PFR)

Key Characteristics• Generally a long cylindrical pipe with no moving parts (tubular reactor)• Suitable for fast reactions (good heat removal), mainly used for gas phase

systems• Concentrations vary along the length of the tube (axial direction)

0

VA

A A AdN F F r dVdt

′= − + ∫

For an ideal PFR, we assume: - constant flowrate - no variation of fluid velocity or species concentration in radial direction

We also generally assume reactor is operating at steady-state: i.e.; no variation in properties with time at any position along reactor length

General Mole Balance for Ideal PFR at Steady-State

Infinitesimally small control volume

ΔV A V VF

+ΔA VF

0A A AV V VF F r V

+Δ− + Δ =At steady state:

0

;

at 0

AA

A A

dF rdVF F V

=

= =

differential form

integral form

0

A

A

FA

AF

dFVr′

= ∫

Class exercise: Derive concentration profiles for A and B for A B with rB=-rA=kCA for a isothermal PFR at steady-state, assuming constant volumetric flowrate. At the reactor inlet, CA=CA0 and CB=0

Packed Bed Reactor (PBR)

FA0 FA

Key Characteristics• Can be thought of as PFR packed with solid particles, usually

some sort of catalyst material.• Mainly used for gas phase catalytic reaction although examples for

liquid-phase reaction are also known.• Pressure drop across the packed bed is an important consideration.• This is the reactor type used in your integrated design project.

Mole Balance for PBR

FA0 FA

Let W = Weight of the packing

Making the same assumptions as for a PFR:- no variation of fluid velocity or species concentration in radial direction- operating at steady-state

integral form

0

A

A

FA

AF

dFWr′

=′∫

0

;

at 0

AA

A A

dF rdWF F W

′=

= =

differential form

Same as PFR, but with rate (r ) specified per mass of catalyst (instead of per unit volume) and using catalyst wt (W) instead of V as the coordinate

Summary - Design Equations of Ideal Reactors

DifferentialEquation

AlgebraicEquation

IntegralEquation Remarks

Vrdt

dNj

j )(=0( )

j

j

Nj

jN

dNt

r V′

= ∫Conc. changes with time but is uniform within the reactor. Reaction rate varies with time.

Batch(well-mixed)

CSTR(well-mixed at steady-state)

0

( )j j

j

F FV

r−

=−

Conc. inside reactor is uniform. (rj) is constant. Exit conc = conc inside reactor.

PFR(steady-state flow; well-mixed radially)

jj r

dVdF

=

0( )

j

j

Fj

jF

dFV

r′

= ∫Concentration and hence reaction rates vary spatially (with length).

Human Body as a System of Reactors

MouthStomach

Small IntestineLarge

Intestine

What reactor type can we represent the various body parts with?

Food

• We can often approximate behaviour of complex reactor systems by considering combinations of these basic reactor types (batch, PFR, CSTR)

• Next step (Fogler Ch 2): Formulate design equations in terms of conversionApply to reactor sizing

Feed

Recycle from

the next zone

CSTR segment

Plug flow

segment

Recycle to

previous zone

Each reaction zone is considered as a CSTR section followed by a plug flow section. The plug flow is considered as a series of CSTR’s in series due to complex mathematical difficulties. Recycle streams show the effects of imperfect mixing.

Chan ,W., Gloor, P. E., & Hamielec, A. E., AIChE J. 39, 111 (19xx).

Marini, L., Georgakis, C., AIChE J. 30, 401 (1984).

Each reaction zone is considered as a set of interconnected three CSTR’s. Recycle flow models the effect of imperfect mixing in initiator injection point and backmixing in the reaction space. The model parameters are based on geometrical and flow dynamic of the industrial system.

V3

V2

V1

Flow from previous zone

Flow of initiator and side feed

Recycle

flow

Compartments model

Segments model

Approaches in modeling imperfect mixing in LDPE Autoclave Reactors

Monomer Feed

Initiator

Feed

Conversion (X) [Single Reaction System]

• Quantification of how far a reaction has progressed

Batch Reactors

0

0

mols of species- reactedmols of species- fedj

j j

j

jXj

F FF

=

−=

Continuous (or Flow) Reactors

0

0

mols of species- reactedmols of initial species- j

j j

j

jXj

N NN

=

−=

A + B C + D

A + B C + D

a b c db c da a a

→

→

• Defined in terms of limiting reactant

Reactants Products

Assume “A” is our limiting reactant

Design Equation in Terms of Conversion(limiting reactant A)

IDEAL DIFFERENTIAL ALGEBRAIC INTEGRAL REACTOR FORM FORM FORM

0 ( )AA A

dXN r Vdt

= − 00

AXA

AA

dXt Nr V′

=−∫

0 ( )AA A

dXF rdV

= − 00

AXA

AA

dXV Fr′

=−∫

CSTR

PFR

0 ( )( )A A

A

F XVr

=−

BATCH

These equations can be used to size reactors required to achieve a desired conversion for a single-reaction system

Levenspiel Plots (Fogler, Ch 2.4-2.5)

Octave Levenspielconsidered to be one of the founders of Chemical Reaction Engineering

Basic idea: use plot of vs. X to calculate V

0

0

PFRXA

PFRA

FV dXr

=−∫

X

)(0

A

A

rF−

][])(

[ 0CSTR

A

ACSTR X

rFV ×−

=

Plug Flow Reactor (PFR)

Continuous Stirred Tank Reactor (CSTR)

)(0

A

A

rF−

XEvaluated at X=XCSTR

XPFR

XCSTR

)(0

A

A

rF−

Class Problem

The following reaction is to be carried out isothermally in a continuous flow reactor operating at steady-state:

A → B

Compare the volumes of CSTR and PFR that are necessary to consume 90% of A (i.e. CA=0.1 CA0). The entering molar and volumetric flow rates are 5 mol/h and 0.5 L/h, respectively. The reaction rate for the reaction follows a first-order rate law:

(-rA) = kCA where, k=0.0001 s-1

For same conversion, is the CSTR volume always higher than PFR volume ?

FA0-rA

X

For most cases yes, provided that rA decreases as X increases.

See Fogler Section 2.4 (Ex. 2-2 to 2-4) for using Levenspiel plots to size reactors (PFR vs. CSTR)

The real power of Levenspiel plots is for reactor networks (reactor in series)

PFR in Series

X

FA0-rA

Let us compare two scenarios

(i) Single reactor achieving X3(ii) 3 reactors in series achieving X3

• How is the total volume of 3reactors in series related to single reactor ??

FA0

X=0FA1

X=X1

FA2

X=X2 FA3; X=X3

CSTR in Series

FA0

X=0 FA1

X=X1FA2

X=X2FA3; X=X3

FA0-rA

XWe can model a PFR as a series of

“n” equal volume CSTRs

Compare volume for the following 2 cases

(i) A single reactor achieving X3(ii) 3 reactors in series achieving X3

How is the total volume of 3 reactors in series related to single reactor ??

See Fogler 2.5.1

If you could replace one of the CSTRs with a PFR, which one would you choose to minimize the total volume of the reactor system

Closing Thoughts on Levenspiel Plots

• Levenspiel Plots are useful means to illustrate the difference between PFR and CSTR behavior– If the rate law is given in terms of conversion (-rA) = f(X) or can be

generated/derived by intermediate calculations, one can size PFR, CSTRs, and batch reactors.

– PFR can be modeled as many CSTR in series (strategy used in UNISIM design software)

• Levenspiel plots are seldom used to design ‘real world’ reactors– Restrictive conditions: no secondary side streams, single reaction– Can only be used for scale-up if reaction conditions are kept identical: i.e.;

(-rA) varies with conversion identically in the full-size reactors as in the lab

Class ProblemThe following aqueous-phase reaction is carried out isothermally in both a laboratory-scale reactor and an industrial-scale continuous stirred tank reactor:

A → B The reaction rate follows a first-order rate law:

(-rA) = kCA where, k=0.1 min-1 at 50 oC

The operating conditions of the reactors are provided below

Industrial CSTR Lab CSTR

Feed concentration 10%A in solution 2% A in solution

Reactor volume 3600 L 63 mL

Volumetric flow rate 40 L/min 0.7 mL/min

The two reactors, vastly different in scale, and with different feed concentrationsyield similar conversion. Why?

Time is of the Essence

• The extent of conversion of reactants in a chemical reactor is related to the time the chemical species spend in the reactor.

• Remember the definition: Average residence or space timeof fluid in vessel is τ = V/v0– Space time is often used as a scaling parameter in reactor design

• Residence time is chosen to achieve desired conversion (different for PFR and CSTR!), and can vary from a few seconds to several hours, depending on the rate of reaction – See Fogler Table 2.5

Reaction Rates of Some Known Systems

Slow reaction Fast Reaction(requires large residence time) (short residence time)