Design Equations 3

Ch E 441: Chemical Kineticsand Reaction Engineering

Mole Balances in Reacting Systems & Reactor Design EquationsDavid A. Rockstraw, Ph.D., P.E.New Mexico State UniversityChemical Engineering

Objectives• Describe photos of real reactors. • Define the rate of chemical reaction. • Apply a general mole balance to

– a batch reactor, – a continuous stirred tank reactor (CSTR), – a plug flow reactor (PFR), and – a packed bed reactor (PBR).

Industrial Reactors

Industrial Reactors

Industrial Reactors

Spherical Reactors

Industrial Reactors

Industrial Reactors

Industrial Reactors

Industrial Reactors

Industrial Reactors

Industrial Reactors

Industrial Reactors

Packed Bed ReactorPacked Bed Reactor in use for a Fisher-Tropsch synthesis reaction at Sasol Limited Chemical.

Moving Bed ReactorThis photo is of a catalytic cracker moving bed reactor. Only the disengager section of the reactor is visible in the picture - the reaction section is hidden behind the stair structure beneath the disengager.

The cracker is used for the catalytic cracking of gas oil into light aromatics and straight chain hydrocarbons, which are then separated in the distillation tower to the right of the photo.

The white unit to the left of the cat cracker is the catalyst regenerator,where coke deposits are burned off the catalyst. This is a highly exothermic operation, (1400°F), and so the boiler unit at the far left recovers the sensible heat of the regenerator exhaust to produce steam.

boilerdisengager

stillregenerator

Straight ThroughTransport Reactor

Straight Through Transport Reactor (STTR) in use for a Fisher-Tropsch synthesis reaction at Sasol Limited Chemical.

Industrial Reactors

Automotive Catalytic Converter

Industrial Reactors

Glass Lined Reactors

General Reactor Construction

Fluidized-Bed Reactor

Trickle-Bed Reactor

Wetlands

Chemical Vapor Deposition Reactor

reacting gas flows through annulus between outer edges of cylindrical wafers and the tube wall

Laboratory CSTR/Batch Reactor

Laboratory CSTR

RC1e Reaction Calorimeter

React IR 1000 (FTIR)

Which of the following is probablyNOT a chemical reactor?

A. a pan of boiling water containing pastaB. a jar of medication in the bathroom cabinetC. a public swimming poolD. a cup of coffee with cream and sugarE. a cow’s stomach and contents

Chemical Identity• A chemical species has reacted when it

has lost its chemical identity. The identity of a chemical species is determined by the kind, number, and configuration of that species' atoms.

Loss of Chemical Identity• Decomposition; AB A + B• Combination; A + B AB• Isomerization; A B• single displacement (substitution);

A + BC AC + B• double displacement (metathesis);

AB + CD AD + CB

Reaction Rate• The reaction rate is the rate at which a species

looses its chemical identity per unit volume. • 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.

• Reaction rates are associated with reaction stoichiometry, which describe molar relationships

Reaction Rate• Consider species A: ☞ rA = rate of formation of A per unit vol

☞ -rA = rate of a disappearance of A per unit vol

☞ For a catalytic reaction, -rA' is the rate of disappearance of species A on a per mass of catalyst basis.

☞ NOTE: dCA/dt is not the rate of reaction

Reaction Rate• Consider in general terms, species j…• The rate, rj is

– the rate of formation of species j per unit volume – a function of concentration, temperature, pressure,

and the type of catalyst (if any) – independent of the type of reaction system (batch,

plug flow, etc.) – an algebraic equation, not a differential equation

Which reaction type characterizes the combusion of ethane?

2 C2H6 + 7 O2 4 CO2 + 6 H2O

A. combinationB. isomerizationC. decompositionD. single displacement E. double displacement

Which statement is always false?

A.

B.

C.

D.

E.

What are the units of reaction rate?

A. mass / length / time

B. moles / volume / time

C. moles / catalyst mass / time

D. both A and B

E. both B and C

General Mole Balance Equation

GjGjFjo Fj

system within j of

onaccumulati of rate

system ofout j of

flow of rate

rxnby systemin j of

generation of rate

system into j of

flow of rate

dt

dNFGF j

jjjo where N is the moles of jin the system at time t.

General Mole Balance Equation

GjGjFjo Fj

system within j of

onaccumulati of rate

system ofout j of

flow of rate

rxnby systemin j of

generation of rate

system into j of

flow of rate

dt

dNFGF j

jjjo VrG jj if all variables are spatially uniform

General Mole Balance Equation• If rj varies with position in the system,

rj,1

V1

rj,2

V2

m

1iii,j

m

1ii,jj

11,j1,j

VrGG

VrG

0V ,m Let

V

jj dVrG

General Mole Balance Equation

dt

dNFGF j

jjjo V

jj dVrG

dt

dNFdVrF j

j

V

jjo

GjGjFjo Fj

GMBE Applied to Batch Reactors• For a batch reactor (no flows):

• GMBE reduces to:

0FF jo,j

dt

dNFdVrF j

j

V

jjo

dt

dNdVr jV

j

0 0

GMBE Applied to Batch Reactors• Assuming perfect mixing:

dt

dNdVr jV

j dt

dNdVr jV

j

Vrdt

dNj

j Batch ReactorDesign EquationBatch ReactorDesign Equation

GMBE Applied to Batch Reactors• For the simple reaction A products:

– In a constant volume reactor,

dt

dN

V

1r AA

dt

dC

dt

VNd

dt

dN

V

1r AAAA

GMBE Applied to Batch Reactors• For the simple reaction A products:

– In a constant pressure reactor,

dt

VlndC

dt

dC

dt

dV

V

C

dt

dC

dt

VCd

V

1

dt

dN

V

1r

AAAA

AAA

dt

dN

V

1r AA

Which is NOT a characteristic of an ideal batch reactor ?

A. Absence of concentration gradients (i.e., perfect mixing)

B. Steady state operationC. No material crosses system boundary

(i.e., no flows)D. Derivative with respect to time

GMBE Applied to Flow Reactors• Continuous Stirred-Tank Reactor (CSTR):

reactants

products

dt

dNFdVrF j

j

V

jjo 0

steadystate

0FVrF jjjo perfectmixing

j

jjo

r

FFV

jj CF

volumetricflow rate

GMBE Applied to Flow Reactors• Continuous Stirred-Tank Reactor (CSTR):

CSTRDesignEquation

CSTRDesignEquation

reactants

products j

jjo

r

FFV

dt

dNFdVrF j

j

V

jjo 0

steadystate

0FVrF jjjo perfectmixing

Which is NOT a characteristic of an ideal CSTR?

A. Absence of concentration gradients (i.e., perfect mixing)

B. Steady state operationC. Material crosses system boundary

(i.e., flows in and out)D. Derivative with respect to time

GMBE Applied to Flow Reactors• Tubular (Plug Flow) Reactor (PFR):

reactants products

yy+yy

VFj(y) Fj(y+y)

GMBE Applied to Flow Reactors• Tubular (Plug Flow) Reactor (PFR):

dt

dNFdVrF j

j

V

jjo

0steadystate

0FVrF jjjo spatiallyuniform V

VFj(y) Fj(y+y)

GMBE Applied to Flow Reactors• Tubular (Plug Flow) Reactor (PFR):

0yAryyFyF jjj uniformcross-section

dt

dNFdVrF j

j

V

jjo

0steadystate

0FVrF jjjo spatiallyuniform V

GMBE Applied to Flow Reactors• Tubular (Plug Flow) Reactor (PFR):

jj r

dV

Fd

PFRDesignEquation

PFRDesignEquation

dy

dVrAr

dy

Fdjj

j

Ar

y

yF-yyFj

jj

dx

df

x

xf-xxflim

0x

Which IS a characteristic of an ideal Plug Flow Reactor?

A. Absence of concentration gradients (i.e., perfect mixing)

B. Steady state operationC. Material crosses system boundary

(i.e., flows in and out)D. Derivative with respect to time

GMBE Applied to Packed Bed Reactors• PBR used for fluid/solid catalytic reaction:

FAo FA

WW+WW

WFA(W) FA(W+W)

GMBE Applied to Packed Bed Reactors• PBR used for fluid/solid catalytic reaction:

0WrWWFWF 'AA A

catalyst masscatalyst masstime

A molesWr '

A

dimensions of

generation term

WFA(W) FA(W+W)

GMBE Applied to Packed Bed Reactors• PBR used for fluid/solid catalytic reaction:

'AA

rdW

Fd

PBRDesignEquation

PBRDesignEquation

'AAA

rW

WF-WWF

dx

df

x

xf-xxflim

0x

When pressure drop and catalyst decay canbe neglected, integral form can be used:

A

AoA

F

F 'A

r

FdW

Which IS a characteristic of an ideal Packed Bed Reactor?

A. Absence of concentration gradients (i.e., perfect mixing)

B. Steady state operationC. No material crosses system boundary

(i.e., no flows)D. Derivative with respect to position

Design Equation Summary

Batch Vrdt

dNA

A

CSTR

PFR

PBR 'AA

rdW

Fd A

AoA

F

F 'A

r

FdW

jj r

dV

Fd

j

jjo

r

FFV

A

Ao

F

FA

A

r

FdV

A

Ao

N

NA

A

Vr

Ndt

Next Session• Define conversion and space time. • Write the mole balances in terms of conversion

for a batch reactor, CSTR, PFR, and PBR. • Size reactors either alone or in series once given

the molar flow rate of A, and the rate of reaction, -rA, as a function of conversion, X.