Week 1 CYJ Mole Balance-Print

Reactor Design H83RED

Course Syllabus

Lectures: 2-hour Lecture and 1-hour Example class per week

•Tuesday, 11-1 pm @ F1A15

•Thursday, 4-5 pm @ F3A12

Assessment: 10% quizzes; 20% coursework; 70% final exam (two hours)

Aims:

To learn how to apply the fundamental principles of chemical kinetics, along with heat and

mass transfer transport, to the design of chemical reactors for both homogenous and

heterogeneous cases. Emphasis will be placed on developing basic concepts which will then

be used to analyze problems of increasing sophistication including non-isothermal and

catalytic reactors.

Convener: Dr Chan Yi Jing [email protected]


Course Structure

The course is made of 8 topics, which are detailed as below. The course consists of lectures,

which will include problem solving, tutorials, and a week long game based on designing a

reactor. Problems are to be worked primarily at home by the students. We will closely follow

the textbook Fogler, H. Scott. “Elements of chemical reaction engineering” 3rd ed., Prentice

Hall, 2000.

Course Schedule (This might change as we move through the course)

Week 1 – Introduction to module, rate of reaction, mole balance

Week 2 – Design equations

Week 3 – Stoichiometry

Week 4 – Stoichiometry

Week 5 – Isothermal reactors

Week 6 – Isothermal reactors

Week 7 – Non-isothermal reactors

Week 8 – Non-isothermal reactors

Week 9 – Multiple reactions

Week 10 – Catalysts and Catalytic reactors

Week 11 – Catalysts and Catalytic reactors

Week 12 – Student study


Learning Outcomes:

A student who has successfully completed this module will be able to:

•Perform material balances to derive general reactor design equations

•Use the appropriate reaction kinetics in the reactor design equations

•Express concentrations and molar flow rate in terms of conversion

•Perform energy balances for the basic reactor types

•Use the energy balances for reactor design

•Calculate the parameters corresponding to optimal reactor design

•Extend these operations to the case of multiple reactions and reactor sequences

Summary:

Combine material balance, rate law, stoichiometry, energy balance for optimal reactor design

and operation

Reactor Design Outline

1. Introduction

2. The Place of “Reactor Design” in Chemical Engineering

3. Type of Reactors: Batch, Continuous

4. Definition of Rate of Reaction, - rA

5. The General Mole Balance Equation

6. Mole Balances for PFR, CSTR, PBR, and Batch Reactors

Outline

Reactor Design Introduction

The Place of “Reactor Design” in Chemical Engineering

ProductsRaw

materials

Chemical

Reactions

Physical

treatment

steps

Physical

treatment

steps

Recycle

Typical chemical process

Chemical treatment steps are carried out in chemical reactors.

Reactor design based on information, knowledge and experience from a variety of

areas:

Thermodynamics

Chemical kinetics

Fluid Mechanics

Heat Transfer

Mass Transfer

Economics

Knowledge of chemical kinetics and reactors design distinguishes the chemical

engineer from both chemists and other engineers


Types of Reactors

Relatively Small Scale (a few thousands of tons per year)

High Flexibility

Low Cross-contamination

Short Period for Reactor Start-up

Batch Reactors

Description

Reactants are charged into the vessel, react for a

specific period of time. Products are discharged after

the reaction.

Applicability

Advantages Disadvantages

High demands in manpower

Lower efficiency of services (heating & cooling)

Complicated automatic control

http://upload.wikimedia.org/wikipedia/commons/1/15/Batch_reactor_STR.svg


Types of Reactors

Large Tonnage Production (tens or hundreds of

thousands tons per year)

Steady-State Operation

Lower demands in manpower

Easy automatic control

Efficient services

Continuous Reactors

Description

Reactants flow continuously into the vessel, and

products flow continuously out of the reactor

Applicability

Advantages Disadvantages

Long Start-up

High cost of halting operation

Low flexibility

Continuous

Stirred Tank

Reactor

(CSTR)

Tubular or

Packed Bed

Reactor

Reactants

Products

Reactor Design Definition of rate of reaction

Definition of rate of reaction

(Homogeneous reaction systems)

Rate of reaction, - rA, is the rate of disappearance of species A per unit volume or

it is the number of moles of species A reacted per unit time per unit volume

Units:

Consider the reaction: A B

Rate of reaction, rB, is the rate of formation of species B per unit volume or it is the

number of moles of species B formed per unit time per unit volume

- rA = rB timevolume

moles

Rate of reaction, - r’A, is the number of moles of species A reacted per unit time per

unit mass of catalyst (or per unit surface area of catalyst), (or per unit volume of

catalyst)


over a catalyst

timecatalyst mass

moles

Definition of rate of reaction

(Heterogeneous reaction systems)

timecatalyst area surface

moles

timecatalyst volume

moles

Units:

- r’A = r’B

Reactor Design Definition of rate of reaction

Source of confusion

dt

dCr A

A

NaOH CH3COOC2H5

C2H5OH

CH3COONa

unreacted:

CH3COOC2H5

NaOH

CH3COOC2H5 + NaOH CH3COONa + C2H5OH

Perfect mixing and steady-state operation

result in identical concentration of each

species in any point:

0dt

dCA Wrong for continuous

systems

In flow system the differential form :

dt

dCr A

A

does not represent the rate of reaction


Constant volume batch reactorA

C

Time

A

B

Reactor Design The rate law

The chemical reaction rate:

• An intensive quantity

•Depends on the properties of the reacting materials (concentration, temperature,

pressure, type of catalysts) at a point in the system

• Independent of the type of system (i.e. batch or continuous flow) in which the

reaction is carried out.

Different forms of the dependencies of the reaction rate on concentration:

AA kCr 2

AA kCr

A

AA

Ck

Ckr

2

1

1

The reaction rate is essentially an algebraic equation involving

concentration, not a differential equation.

The rate law

Consider the reaction: A products

Reactor Design Mole balance

General Mole Balance Equation

Main Task of Reactor Design: to determine the degree of conversion of a particular

reactant, or to determine the reactor volume to achieve a particular conversion.

The system volume is defined as the volume enclosed by physical boundaries

of the reactor. System

Volume

GjFj0 Fj

Focus on species which are able to participate in a chemical reaction or are

generated as a result of it. Molar fluxes of such components must be balanced

A mole balance on species j at any instant of time, t:

)/(

j

onaccumulati

)/(

outj

)/(

j

generation

)/(

intoj

timemoles

systemthe

withinof

ofrate

timemoles

systemthe

of

flowofrate

timemoles

systemthe

withinreaction

chemicalbyof

ofrate

timemoles

systemthe

of

flowofrate

in + generation out = accumulation


General Mole Balance

If all the system variables are spatially uniform throughout the system volume, the

rate of generation of species j, Gj:

in + generation out = accumulation

dt

dNFGF

j

jjj 0(1)

VrG jj (2)

)/(

j

onaccumulati

)/(

outj

)/(

j

generation

)/(

intoj

timemoles

systemthe

withinof

ofrate

timemoles

systemthe

of

flowofrate

timemoles

systemthe

withinreaction

chemicalbyof

ofrate

timemoles

systemthe

of

flowofrate

volumetimevolume

moles

time

moles


General Mole Balance

The rate of reaction could vary through the system volume due to variation of

concentration, temperature, etc.. This means that rate of generation of species j is

dependant on the location within the system volume.

Consider indefinitely small volumes, Vi,

so that the rate of reaction

Using equation (2):

V1

V2

rj1

rj2

V

rj1 in V1; rj2 in V2 … rji in Vi

ijiji VrG (3)

Total rate of generation within the system

divided into M sub-volumes :

M

i

iji

M

i

jij VrGG11

Let M and V0:

V

jj dVrG0

Returning to the equation of mole

balance (1):

(4)

(5)

Vj

jjjdt

dNdVrFF

0

0(6)


Reactor Design Mole balance (Batch reactor)

Mole Balance for Batch Reactors

A batch reactor has neither inflow nor outflow of reactant or products in the

course of reaction

If the reaction mixture is perfectly mixed (rj = const)

General mole balance on species j:

(8)

Vj

jjjdt

dNdVrFF

0

0

V

j

jdVr

dt

dN

0

(7)

Vrdt

dNj

j

Reactor Design Mole balance (Batch reactor)

Mole Balance for Batch Reactors

Vrdt

dNA

A Consider the reaction: A B

NA

t

NA0

t1

NA1

Question:

Time, t1 necessary to reduce the initial number of moles

from NA0 to a final desired number NA1?

Vrdt

dNA

A

Rearranging,

Vr

dNdt

A

A

Integrating with limits at t=0, then NA=NA0, and t=t1, then NA=NA1,

Time, t1 necessary to reduce the number of moles from NA0 to NA1 is:

0

1

A

A

N

N A

A

Vr

dNt

(8)

Mole balance (Batch reactor)Reactor Design

Batch Reactor

Constant Volume or Constant Pressure:

Does it make a difference?Vr

dt

dNA

A

Constant volume Constant pressure

Consider the reaction:

(CH3)2O CH4 + H2 + CO

A M + H + C

Vrdt

dNA

A AA r

dt

dN

V

1

Perfectly mixed No spatial variation of rate

Constant-volume batch reactorA

AAA rdt

dC

dt

VNd

dt

dN

V

)/(1

Constant-pressure batch reactor

AAAAA r

dt

dV

V

C

dt

dC

dt

VCd

Vdt

dN

V

)(11

VCN AA

AAA r

dt

VdC

dt

dC

)(ln

Mole Balance (CSTR)Reactor Design

Mole Balance for CSTR

CSTR are operated at steady state:

The CSTR is a well mixed reactor operated continuously

There are no spatial variations in concentration,

temperature, or reaction rate throughout the tank

(9)

(10)

Vj

jjjdt

dNdVrFF

0

0

(11)0dt

dN j

and rj = const

V

jj VrdVr0

Using equations (9) and (10):

00 jjj VrFF

Design equation for a CSTR

(12)

Reactants

Products

The molar flow rate Fj is just the product of concentration

of species j and the volumetric flow rate v

vCF jj

j

jj

r

FFV

0

time

volume

volume

moles

time

moles

Reactor Design Mole Balance (PFR)

Mole Balance for Tubular Reactors

Tubular reactors consist of a cylindrical pipe and are

normally operated at steady state

Fj(V) - the molar flow

rate of species j into

subvolume V

Vj

jjjdt

dNdVrFF

0

0

Fj0 Fj,exitV

VFj(V) Fj(V+V)

(13)

In spatially uniform subvolume V:

V

jjj VrdVrG0

- steady state operation: 0dt

dN j

Fj(V+V) the molar flow

rate of species j out of

the subvolume

Model of a plug-flow reactor (PFR)

Highly turbulent flow

No radial variations in concentrations

(16)

(15)

(18)

General mole balance for the

subvolume:

(14)

0VrFF jVVjVj

After rearranging:

jVjVVj

rV

FF

taking the limit as V0

dV

dF

V

FFlim

jVjVVj

0V


(17)or

Differential Integral

j

jr

dV

dF

j

j

F

F j

j

r

dFV

0

Reactor Design Mole Balance (PFR)

Mole Balance for Packed-Bed Reactors

Packed-Bed Reactors are designed to carry out

heterogeneous reaction.

(19)

Wj

jjjdt

dNdVrFF

0

'

0

(21)

Differential form of the general mole

balance for PBR:

(20)

PBR Features

Replacing volume coordinate with the

catalyst weight coordinate and assuming

that there are no radial gradients in

concentration, temperature, or reaction

rate:

W

Fj0 Fj,exitW

W

Fj(W) Fj(W+W)

Reactor volume is filled with catalysts

Reaction kinetics is dependant on a quantity of catalyst

timecatalystofmass

A moles'

jr

After rearranging:

If the limit is W0

Integral form of the general mole

balance for PBR:

j

jr

dW

dF

j

j

F

F j

j

r

dFW

0

0WrFF jWWjWj

jWjWWj

rW

FF

Reactor Design Mole Balance

Mole Balance for Different Types of Reactors

Vrdt

dNA

A

Reactor Type Differential Algebraic Integral

Batch

CSTR

PFR

PBR

AA r

dV

dF

AA r

dW

dF

j

jj

r

FFV

0

A

A

N

N A

A

Vr

dNt

0

0A

A

F

F A

A

r

dFV

0A

A

F

F A

A

r

dFW

Reactor Design Mole Balance (Example 1-3)

Example 1: The first-order reaction A B is carried out in a tubular reactor in which the

volumetric flow rate, v, is constant.

Derive an equation relating the reactor volume to the entering and exiting concentrations of A, the rate constant k, and the volumetric flow rate v.

Determine the reactor volume necessary to reduce the exiting concentration to 10% of the entering concentration when the volumetric flow rate is 10 dm3/min and the specific reaction rate, k, is 0.23 min-1.

Solution

The mole balance on species A in tubular

reactor is:

AA r

dV

dF

Molar flow of the species A into reactor is:

AA CvF For a first-order reaction, the rate law is:

-rA = kCATherefore

dV

dCv

dV

Cvd

dV

dF AAA

)(

Reactants Products


Solution (continuation)



Derive an equation relating the reactor volume to the entering and exiting concentrations of A, the rate constant k, and the volumetric flow rate v.

Substitutions into molar balance equation results in:

AA kC

dV

dCv

Rearranging gives:

dVC

dC

k

v

A

A

Using the conditions at the entrance of the reactor that when V=0, CA=CA0

VC

C A

A dVC

dC

k

v A

A 00

After integration:

A

A

C

C

k

vV 0ln


Solution (continuation)




Substituting v=10 dm3/min; k=0.23 min-1; CA=0.1CA0:

A

A

C

C

k

vV 0ln

Reactor Design Mole Balance (Example P1-3)

Solution

Example 2: The first-order reaction A B is carried out in a CSTR in which the



The mole balance on species A in CSTR

is:

Molar flow of the species A into reactor is:

AA CvF

For a first-order reaction, the rate law is:

-rA = kCA

A

AA

r

FFV

0

Reactants

Products

Reactor Design Mole Balance (Example P1-4)

Solution

Example 3: The first-order reaction A B is carried out in a Constant Volume Batch

Reactor.

Determine the time necessary to reduce the number of moles of A to 10% of its initial value when the specific reaction rate, k, is 0.23 min-1.

The mole balance on species A in Batch

reactor is:

The moles of A into reactor is given by:

VCN AA

For a first-order reaction, the rate law is:

-rA = kCA

Vrdt

dNA

A

VkCdt

VCdA

A )(

Week 1 CYJ Mole Balance-Print

Documents

Transcript of Week 1 CYJ Mole Balance-Print