Chemical Reaction EngineeringChemical Reaction Engineering

제제 11 장장Mole BalanceMole Balance

반응공학 반응공학 II                                      

Chapter 1. Mole Balance

1.1 Definition of the Rate of Reaction, -rA

1.2 The General Mole Balance Equation

1.3 Batch Reactors

1.4 Continuous-Flow Reactors

1.4.1 Continuous-Stirred Tank Reactor

1.4.2 Tubular Reactor

1.4.3 Packed-Bed Reactor

1.5 Industrial Reactors

                                     

The first step to knowledgeis to know that we are ignorant

Socrates (470-399 B.C.)

Chapter 1. Mole Balance

ObjectivesAfter completing Chapter 1, the reader will be able to:

Define the rate of chemical reaction.

Apply the mole balance equations to

a batch reactor, CSTR, PFR, and PBR.

Describe two industrial reaction engineering systems.

Describe photos of real reactors.

The identity of a chemical species

The species nicotine is made up of a

fixed number of a specific atoms in the

specific atoms in a definite molecular

arrangement or configuration. The

structure shown illustrates the kind,

number, and configuration of atoms in

the species nicotine on a molecular

level.

The identity of a chemical species

C=CH H

CH3 CH3

C=CH CH3

CH3 H

2-butene has four carbon atoms and eight hydrogen atoms;

however the atoms in this compound can form two different

arrangements.cis-2-butene trans-2-butene

As a consequence of the different configurations, these two

isomers display different chemical and physical properties.

Therefore, we consider them as two different species.

We say that chemical reaction has taken place when

a detectable number of molecules of one or more

species have lost their identity and assumed a new

form by a change in the kind or number of atoms in

the compound and/or by a change in structure or

configuration of these atoms.

The identity of a chemical species is determined by

the kind, number, and configuration of that species’

atoms.

When has a chemical reaction taken place?

Three basic chemical reactions:

1. Decomposition ( 분해반응 )2. Combination ( 결합반응 )3. Isomerization ( 이성질화반응 )

A species can lose its identity by 3 reactions

Three basic chemical reactions:

When has a chemical reaction taken place?

CH(CH3)2

+ C3H6

DecompositionDecomposition

CombinationCombination

CH2=C-CH2CH3

CH3

CH3C=CHCH3

CH3

IsomerizationIsomerization

IsomerizationIsomerization

분 자 가 그 들 의 화 학 적 동 일 성 을 잃 을 때 어 떤 특 정 화학성분의 분자의 일정 개수가 반응 또는 소실되었다고 말한다 .

Reaction rate

The rate of a reaction can be expressed as the rate of disappearance of a reactant or as the rate of appearance of a product.

Consider species A:

A A → B→ B rrAA: the rate of formation of species A per unit volume -r-rAA: the rate of disappearance of species A per unit

volume rrBB: the rate of formation of species B per unit volume

2C6H5Cl + CCl3CHO (C6H4Cl)2CHCCl3 + H2OChlorobenzene Chloral DDT (Dichloro Diphenyl-Trichloroethane)

What is –r A (–r´A )?

Solely a function of properties of reacting materials.

(Concentration, temperature, pressure, catalyst or solvent) An intensive quantity. An algebraic function of concentration. such as. for homogeneous system:

for heterogeneous system:

The numerical value of the rate of reaction, -rA, is defined as

the number of moles of chloral reacting (disappearing) per unit time per unit volume [mol/dm3·s].

A

AA

AA

AA

Ck

Ckr

kCr

kCr

2

1

2

1

Fuming H2SO4

l

gmol

sec

catg

gmol

sec

Sodium Hydroxide Concentration in Batch Reactor

NaOH CH3COOC2H5

NaOH + CH3COOC2H5 CH3COONa + C2H5OH

dt

dCr A

A Time

CA

Constant-volume batch reactor

Ethyl Acetate Sodium Acetate

Ideal Reactor Type

Batch ReactorBatch Reactor-uniform composition everywhere in the reactor-the composition changes with time

Continuous-Stirred Tank Reactor (CSTR)Continuous-Stirred Tank Reactor (CSTR)

-uniform composition everywhere in the reactor (well mixed)

-same composition at the reactor exit

Tubular Reactor (PFR)Tubular Reactor (PFR)

-fluid passes through the reactor with no mixing of earlier

and later entering fluid, and with no overtaking.

-It is as if the fluid moved in single file through the reactor

-There is no radial variation in concentration (plug-flow reactor)

Is Sodium Hydroxide Reacting?

NaOH CH3COOC2H5

C2H5OH,CH3COONa, andunreactedNaOH andCH3COOC2H5

NaOH + CH3COOC2H5 CH3COONa + C2H5OH

0dt

dCr A

A

CSTR

Steady state:Steady state: the product is continuously withdrawn from the product is continuously withdrawn from the tank at a rate equal to the total feed rate.the tank at a rate equal to the total feed rate.

CA @ 1P.M. = CA @ 3P.M.

Balance on control volume

A mole balance on species j, at any time, t, yields

Nj

Gj = rj · VFj0 Fj

control volume

Rate of flow of j into the

system (mole/time)

Rate of generation of j by chem. rxn within the system

(mole/time)

Rate of accumulation of j within the system

(mole/time)

Rate of flow of j out of the system

(mole/time)

- + =

in - out + generation = accumulation

dt

dNGFF j

jjj 0

volumevolumetime

moles

time

molesG j

molesN j

Rate of formation of species j by chem. rxn

rj1

rj2

V1V2 V

Suppose that the rate of formation of species j for the reaction varies with the position in the control volume. The rate of generation, Gj1, in terms of rj1 and sub-volume V1 is

M

iiji

M

ijij VrGG

11

If the total control volume is divided into M sub-volume, the total rate of generation is

111 V jj rG

By taking the appropriate limits (i.e., let M → and V → 0) and making use of the definition of integral, we can rewrite the foregoing equation in the form

V

jj dVrG

From this equation, we can see that r j will be an indirect function of position, since the properties of the reacting materials (e.g., conc., temp.) can have different values at difference locations in the reactor.

1.2 The General Mole Balance Equation

(GMBE)

dt

dNdVrFF jV

jjj 0

With this GMBE, we can develop the design equations for the various types of industrial reactors: batch, semi-batch, and continuous-flow. Upon evaluation of these equations we can determine the time (batch) or reactor volume (continuous-flow) necessary to convert a specified amount of reactants to products.

1.3 Batch Reactors

If 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 and write the GMBE in the form

dt

dNdVrFF jV

jjj 0

0 0

Vrdt

dNj

j

t

NAA → B

V

jj VrdVrNo spatial variations in the rate of reaction

(1-5)

NA0

What time is necessary to reduce the initial number of moles from NA0 to NA1?

Vrdt

dNA

A

Vr

dNdt

A

A

1

01

A

A

N

NA

A

Vr

dNt (1-6)

Integrating with limits that at t = 0, NA = NA0

at t = t1, NA = NA1

1.3 Batch Reactors

Vrdt

dNA

A

t

NA

NA0

A B

t

NB

NB1

t1t1

NA1

0

11

A

A

N

NA

A

Vr

dNt

Constant Volume or Constant Pressure

CH3-O-CH3 → CH4 + H2 + CO

Constant volume(variable pressure)

Constant pressure(variable volume)

dt

dN

Vr A

A

1

dt

dN

Vr A

A

1

VCN AA

dt

dV

V

C

dt

dCdt

VCd

Vr

AA

AA

)(1

dt

dCr A

A dt

VdC

dt

dCr A

AA

)(ln

1.4.1 Continuous-Stirred Tank Reactor (CSTR)

The CSTR is normally run at steady state and is assumed to be perfect mixed. - No temporal, spatial variations in conc., temp., or rxn rate throughout the vessel - Conc. and temp at exit are the same as they are elsewhere in the tank- Non-ideal mixing, residence-time distribution model is needed

dt

dNdVrFF jV

jjj 0

0

V

jj VrdVr

j

jj

r

FFV

0

j

jj

r

FFV

0

No spatial variations in the rate of reaction

Design Equation for a CSTR

Fj0

Fj

1.4.1 Continuous-Stirred Tank Reactor (CSTR)

j

jj

r

FFV

0

j

jj

r

FFV

0

time

volume

volume

moles

time

moles

vCF jj

Design Equation for a CSTRFj0

Fj

A

AA

r

vCCvV

00

A

AA

r

vCCvV

00

1.4.2 Tubular Reactor

- The reaction rate will also vary axially.- To develop the PFR design equation, we shall divide (conceptually) the reactor into a number of sub-volumes so that within each sub-volume V, the reaction rate may be considered spatially uniform.

0jF exitFj ,

)(yFj )( yyFj V

y

y yy

Let Fj(y) represent the molar flow rate of species j into volume V at y

Fj(y+y) represent the molar flow rate of species j out of volume V at (y+y)

In a spatially uniform sub-volume V,

VrdVrV

jj

1.4.2 Tubular Reactor

dt

dNdVrFF jV

jjj 0

0

rj is a function of reactant concentration, which is function of the position y down the reactor.

Steady state

0)()( VryyFyF jjj

yAV

(1-8)

Substitute V into Eq. 1-8 and divide by y to yield

jjj Ar

y

yFyyF

)()(

Taking the limit as y approaches zero, we obtain

jj Ar

dy

dF

Tubular Reactor

It is usually most convenient to have the reactor volume V rather than the reactor length y as the independent variable. Using dV=Ady,

jj r

dV

dF

The tubular reactor design equation can be applied to the PFR with variable and constant cross-sectional area.

Tubular Reactor

It is usually most convenient to have the reactor volume V rather than the reactor length y as the independent variable. Using dV=Ady,

jj r

dV

dF

The tubular reactor design equation can be applied to the PFR with variable and constant cross-sectional area.

Tubular Reactor

V

FA

FA0

A B

V

FB

FB1

V1V1

FA1

0

11

A

A

F

F A

A

r

dFV

AA r

dV

dF

Packed-Bed Reactor (PBR)For a fluid-solid heterogeneous system, the rate of reaction of a substance A is defined as

catalystg

reactedAgmolrA

sec

'

The mass of solid is used because the amount of the catalyst is what is important to the –r’A

0AF AF

)(WFA )( WWF A

WrA'

W

W WW

0)()( ' WrWWFWF AAA

In - out + generation = accumulation

A

A

F

FA

A

r

dFW

0' No pressure drop

No catalyst decay

The first-order reaction (liquid phase rxn)

A Bis carried out in a tubular reactor in which the volumetric flow rate, v0, is

constant.

(1) Derive an equation relating the reactor volume (V) to the entering concentration of A (CA0), the rate constant k, and the volumetric flow

rate v0.

(2) Determine the reactor volume necessary to reduce the exiting concentration (CA) to 10% of the entering concentration (CA0) when the

volumetric flow rate (v0) is 10 ℓ/min and the specific reaction rate, k, is

0.23 min-1.

Example 1-1 How large is it? (PFR)

CA0 v0 CAV

rA=-kCA

Example 1-1 How large is it? (PFR)

dVC

dC

k

v

kCrdV

dCv

rdV

dCv

dV

vCd

dV

dF

kCr

rdV

dF

A

A

AAA

AAAA

AA

AA

0

0

00 )(

ll

C

ClV

C

C

k

vV

dVC

dC

k

v

A

A

A

A

VC

CA

AA

A

10010ln23.0

10

1.0ln

min23.0

min/10

ln

0

01

00

0

0

0

(GMBE for tubular reactor)

(first-order reaction)

Tubular, 1st order rxn

The first-order reaction (liquid phase rxn)

A Bis carried out in a CSTR in which the volumetric flow rate, v0, is

constant.

(1) Derive an equation relating the reactor volume (V) to the entering concentration of A (CA0), the rate constant k, and the volumetric flow

rate v0.

(2) Determine the reactor volume necessary to reduce the exiting concentration (CA) to 10% of the entering concentration (CA0) when the

volumetric flow rate (v0) is 10 ℓ/min and the specific reaction rate, k, is

0.23 min-1.

P1-6B How large is it? (CSTR)

V

rA=-kCA

Fj0

Fj

For CSTR, the mole balance on species A was shown to be

P1-6B How large is it? (CSTR)

V

rA=-kCA

Fj0

Fj

3.391

)min23.0/(min)/10)(9(

1.0

9.0

1.0

min23.0min,/10,1.0

1

0

0

000

100

0000

k

v

kC

vCvCV

kandvCC

kC

vCvC

r

FFV

A

AA

AA

A

AA

A

AA

3.391

)min23.0/(min)/10)(9(

1.0

9.0

1.0

min23.0min,/10,1.0

1

0

0

000

100

0000

k

v

kC

vCvCV

kandvCC

kC

vCvC

r

FFV

A

AA

AA

A

AA

A

AA

The CSTR is almost 4 times larger than the PFR for getting 90% conversion

Reactor Differential Algebraic Integral

Mole Balance on Different Reactor

Vrdt

dNA

A

A

A

F

FA

A

r

dFV

0

AA r

dV

dF

AA r

dW

dF A

A

F

FA

A

r

dFW

0

A

A

N

NA

A

Vr

dNt

0

A

AA

r

FFV

0

Batch

CSTR

PFR

PBR

Homework

1. P1-7A

2. P1-9A

3. P1-11B

4. P1-15B

Due Date: Next Week