lecture 2 - mole balances

7/23/2019 Lecture 2 - Mole Balances

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Lecture 2

Mole Balances

Fall 2015

CHE 314

Chemical Reaction Engineering

1 Slides adapted from Foglers PowerPoint slides


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Reaction Rates

General Mole Balance Equation

Batch Reactor (BR)

Continuously Stirred Tank Reactor (CSTR)

Plug Flow Reactor (PFR)

Packed Bed Reactor (PBR)

Outline:


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For all our chemical reactions/processes mass and moles

will be conserved

We are transforming chemical species to other chemical

species.

Molecules change their chemical identity during achemical reaction.

The identity of a chemical species is determined by the

kind, number, and configurationof that species atoms.

1. Decomposition CH3CH3H2+ H2C=CH22. Combination N2+ O22 NO

3. Isomerization

Chemical Identity
http://en.wikipedia.org/wiki/File:Trans-2-Buten.svghttp://en.wikipedia.org/wiki/File:Cis-2-Buten.svg


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A mole balance will be used to keep track of the number of

moles of each species in the reactor as a function of time.

Concept of a rate of reaction

The rate of reaction of species j, rj, is the number of moles

of A reacting per unit time per unit volume (e.g. mol/dm3/s).

Reaction Rate

: .

: .


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The rate equation/term will sometimes have a different

basis

Heterogeneous catalysis

Rates are expressed as the rate of disappearance of areactant species or the rate of formation of a product

species.

- sign denotes species consumption.

Reaction Rate contd)

:

.

: .

(molj/gcat/s)

(molj/m2cat/s)


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General Mole Balance Equation

Fj0 FjGj

System

Volume, V

=

+

=+

=

+

time

mole

time

mole

time

mole

time

mole

dt

dNGFF

jSpeciesof

onAccumulati

RateMolar

jSpeciesof

Generation

RateMolar

outjSpecies

ofRate

FlowMolar

injSpecies

ofRate

FlowMolar

j

jjj

0


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General Mole Balance Equation contd)

If spatially uniform:

Gj=rjV

If NOT spatially uniform:

2V

2jr111

VrG jj =222

VrG jj =

1V

rj1

=


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General Mole Balance Equation contd)

General Mole Balance on System Volume V:

If uniform distribution:

dt

dN

dVrFF

onAccumulatiGenerationOutIn

j

jjj 0 =+

=+

dt

dNVrFF

j

jjj 0 =+


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Batch Reactor Mole Balance

0

0

0

==

=+ jj

j

jjj

FF

dt

dNdVrFF

Vrdt

dNj

j =

Batch

VrdVr jj =Well-Mixed

Batch reactor with singleexternal cooling jacketSource: Wikipedia
http://en.wikipedia.org/wiki/File:Batch_reactor.2.jpg


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Batch Reactor Mole Balance contd)

Vr

dNdt

j

j=Rearranging:

Time necessary to reduce the number of moles of j

from Nj0to Nj.

Integrating: =0j

j

N

N j

j

Vr

dNt

jj

jj

NNtt

NNt

==

==

00

NA

t


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CSTR Reactor Mole Balance

dt

dNdVrFF j

jjj 0 =+

0=dt

dNjSteady-State:

CSTR

VrdVr jj =Well Mixed:

j

jj

r

FFV

=

0

V is the CSTR volume needed toreduce the entering flowrate ofspecies j (Fj0) to the exit flowrateof species j (Fj)


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Plug Flow Reactor Mole Balance

Sulzer Mixer Reactor (SMR) post-polymerization reactor for polystyreneSpecial mixing design for better plug flow behaviour

https://www.sulzer.com/en/Products-and-Services/Process-Technology/Polymer-Production-Technology/Other-Polymer-Applications/Polymer-Reaction-Technology


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steady-state)

In a plug flow reactor the composition of the fluid varies from point to point along a flowpath; consequently, the material balance for a reaction component must be made for a

differential element of volume V.V

V VV +

VjF VVj

F+

0

0

=+

=

+

+

+

VrFF

VinGeneration

VVatOut

VatIn

jVVjVj

statesteady


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steady-state) contd)

jVjVVj

V

r

V

FF=

+

0

lim

Rearrange and take limit as V0

j

jr

dV

dF=

Volume necessary to reduce the entering molar flow rate

(mol/s) from Fj0to the exit molar flow rate of Fj:

=j

j

F

F j

j

r

dFV

0


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Packed-Bed Reactor Mole Balance

steady-state)

W

W WW +

WjF

WWj

F+

statesteady

jWWjWj WrFF

+

=+ 0'

j

WjWWj

Wr

W

FF=

+

0lim

'

j

jr

dW

dF=

PBR catalyst weight necessary to reduce the entering molar flow

rate Fj0to molar flow rate Fj:

=j

j

F

F j

j

r

dFW

0

'


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Reactor Mole Balances Summary

Reactor Differential Algebraic Integral

Vrdt

dNA

A = 0

=A

A

N

N A

A

Vr

dNtBatch

NA

t

dFA

dV= rA =

A

A

F

F A

A

r

dFV

0

PFR

FA

V

dFA

dW= rA =

A

A

F

F A

A

r

dFW

0

PBR FA

W

V=

FA 0 FArA

CSTR


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Batch Reactors

Advantages:

- Simple operation

- High conversion can be reached

Disadvantage:

- High operating cost- Temperature control difficult

- Non steady-state (not continuous)

- Batch-to-batch variations

Applied to:

- Small scale testing

- Manufacture of expensive products

- Testing new proceses


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CSTR Reactors

Advantages:

- Intense agitation- Good temperature control

- Steady-state, continuouslarge production scale

Disadvantage:- Lowest conversion of all reactor types (hence large

volume reactors needed.

Applied to:

- A variety of reaction types

- Very common for liquid-phase reactions


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Tubular/Plug Flow Reactors

Advantages:

- Easy to maintain (no moving part)- Highest conversion per volume of the reactors

- Steady-state, continuouslarge production scale

Disadvantage:- Fouling, plugging

- Temperature control (variation in location), hot spot, non

uniform

Applied to:

- A variety of reaction types

- Very common for gas-phase reactions


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Practice Problem P1-15)

The reaction

ABis to be carried out isothermally in a continuous flow reactor.

1) Calculate both the CSTR and PFR reactor volumes necessary

to consume 99% of A (i.e. CA= 0.01 CA0) when the entering

molar flow rate is 5 mol/h, assuming the reaction rate rAis:

-rA= k CA with k = 0.0001 s-1

2) Repeat the question to calculate the time necessary toconsume 99.9% of species A in a 1000 dm3constant volume

batch reactor with CA0= 0.5 mol/dm3.

Additional data: entering volumetric flow rate is 10 dm3/h

lecture 2 - mole balances

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