multi phases

8/8/2019 Multi Phases

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Multiphase ChemicalMultiphase Chemical

Reactor EngineeringReactor EngineeringQuak Foo Lee

Ph.D. Candidate

Chemical and BiologicalEngineering

The University of British Columbia



Different Types of Different Types of

ReactorReactor

Fluidized Bed Reactor

Trickle Column Reactor Slurry Bubble Column Reactor Batch Reactor

Fixed Bed Reactor



Fixed Bed RectorFixed Bed Rector

Fixed Bed Reactor that converts sulfur in diesel fuel to H2S



Fluidized Bed ReactorFluidized Bed Reactor

Fluidized Bed Reactor using H2SO4 as a catalyst to bond butanes

and iso-butanes to make high octane gas



Batch ReactorBatch Reactor

Stirring Apparatus



Straight ThroughStraight Through

Transport ReactorTransport Reactor

Riser

Standpipe

Settling

Hopper

The reactor is 3.5 m in diameter and 38 m tall.

Sasol/Sastech PT Limited



Slurry Phase DistillateSlurry Phase Distillate

ReactorReactor



Packed Bed ReactorPacked Bed Reactor



CSTRCSTR

Agitator

Connection for heating

or cooling jacket

Hand holes for charging

reactor



CA,in

CA,out

Gas + solids

Plug Flow ModelPlug Flow Model

ρ V

H t =

out , Ain , A C C ≅

Particle surrounding byParticle surrounding by

fluid of essential constantfluid of essential constantconcentration,concentration, CC A,m A,m



Countercurrent FlowCountercurrent Flow

If solids are moving plugIf solids are moving plug

flow and we have constantflow and we have constant

flow compositionflow composition

Residence time of solids:Residence time of solids:

Heat Effects !!Heat Effects !!

ρ V

H t =

AC



Heat Effects on ReactionsHeat Effects on Reactions

of Single Particlesof Single Particles Normally (developed) dealing with exothermic and endothermicNormally (developed) dealing with exothermic and endothermic

reaction.reaction.

If reaction occurs at a rate such that the heat absorbed (endothermic)If reaction occurs at a rate such that the heat absorbed (endothermic)

or generated (for exothermic) can’t be transferred rapidly enough,or generated (for exothermic) can’t be transferred rapidly enough,

then non-isothermal effects become important:then non-isothermal effects become important:The particle T The particle T ≠ the fluid T≠ the fluid T

For exothermic reaction, TFor exothermic reaction, Tpp will increase and the rate of reaction willwill increase and the rate of reaction will

increase above that expected for the isothermal case.increase above that expected for the isothermal case.

Two conditions: Two conditions:

i) Filmi) Film ∆T (external ∆T) T ∆T (external ∆T) Tf f (bulk fluid) ≠ T(bulk fluid) ≠ Tpp (particle)(particle) ii) Intraparticle ∆T (internal ∆T) Tii) Intraparticle ∆T (internal ∆T) Tr=Rpr=Rp ≠ T≠ Tr=∞r=∞



Non-ReactingNon-Reacting

1.1. Small particlesSmall particles highly conductivehighly conductive

particlesparticles

2.2. Small particlesSmall particles volumetricvolumetric

reactionreaction

1)1)S ll P i lS ll P ti l



1)1)Small Particles:Small Particles:

Highly ConductiveHighly Conductive

ParticlesParticles Particle initially at uniform TParticle initially at uniform T

= T= Tpp

At t = 0, we drop it into ourAt t = 0, we drop it into ourfurnacefurnace

Fluid at Tf

Tp



Energy BalanceEnergy Balance

dt

dH mQQ radiationconvection =+

( ) ( )[ ]( )dt

T C d mT T T T h R

p p

pwm p f cv =−∈+− 4424 σ π

Heat in by convection and radiation = change in enthalpy of particle

Where,

Area of sphere = 4πR2

Hcv = convection coefficient

σ = Stefan-Boltzman constant

Єm = emissivity of the particle (wall has Є = 1)



Energy BalanceEnergy Balance

( )( ) p F

pw

mr T T

T T h

−−

∈=44

σ

( ) ( )dt

dT

A

C mT T hh

p p p

p F r cv

ρ

=−⋅+

Can solve this equation to get Tp =f(t)



Find hFind hcvcv

Have film:Have film: ∆H T ∆H Tf f ≠ T≠ Tpp

Use mass transfer analogy to get hUse mass transfer analogy to get hcvcv

3

1

2

1

602 Pr Re. Nuk

d h p

f

pcv +==

ρ

µ ν

µ

ν === ;

k

C Pr ;

Vd Re

f

p p

p



2. Small Particles:2. Small Particles:

Volumetric ReactionVolumetric Reaction Small such that noSmall such that no

internal gradientsinternal gradients

( ) ( ) ( ) f p pr Av p T T hA H r V −=−⋅− ∆

Heat generated by reaction = Heat transferred to surrounding

Steady State:

Volume of particle Rate of

reaction

( ) ( ) ( )

⋅

−⋅−=−

3

R

h

r H T T Avr f p

∆

Exothermic Rxn:

-∆Hr = (+)

-r Av = (+)

3 L P ti l3 L P ti l



3. Large Particles:3. Large Particles:

Possible Internal ParticlePossible Internal Particle

GradientsGradients We have to solve the conduction equationWe have to solve the conduction equation

Non reacting particle: the conduction equation for sphere:Non reacting particle: the conduction equation for sphere:

t

T

C r

T

k r r r s , pe ∂∂

=

∂∂

∂∂

ρ 2

2

1

( ) Rr p f

Rr e T T hdr

dT

k

:Surface

== −=

Heat conducted into

particle at r =Rp

Heat transferred into particle

Note: accommodate radiation in the

definition of h if that is the case

Ke = effective thermoconductivity

within the particle∂T/∂r = 0 at steady state



Boundary ConditionsBoundary Conditions

0

0

=

=∂

∂

r r

T

p , p p T )r ( T ;T T ;t === 00

00

00

Rr r r r

r r

T T

RT T

== ≠

=≠=

Symmetry condition

Initial condition

Internal gradient

External gradient Rr r f T T =

≠



Reacting SystemsReacting Systems

General equation for volumetricGeneral equation for volumetric

reactionsreactions

(Reaction in porous particles)(Reaction in porous particles)

Recall continuity equation:Recall continuity equation:

continuity for Acontinuity for A



Solve (1), (2), (3)Solve (1), (2), (3)

TogetherTogether

Av A

e A r

r

C Dr

r r t

C −

∂∂

∂∂

=∂∂ 2

2

1ε

( ) ( )

( ) Av

n

S

m

Ar

r Ave p

r C C k

H r r

T k r

r r t

T C

−=

−+

∂∂

∂∂

=∂∂

− ∆ε ρ 2

2

11

Continuity for A

Energy balance

( ) ( ) Av

n

S

m

Ar r C C T k −=

(1)

(2)

(3)

Coupledthroug

hthe

reaction

rate



In Steady StateIn Steady State

Showed that for steady conditions:Showed that for steady conditions:

( )r A

ee H dr

dC D

dr

dT k ∆−=−

( ) ( ) ( )r r , A s , Ae

e

S r H C C k

D

T T ∆−⋅−=− == 00

Integrate at r = 0, r = R

For sphere

Rr r S T T =

=



Some NotesSome Notes

If we knowIf we know CC A,s A,s (surface concentration) and(surface concentration) and CC A,r=0 A,r=0 ((CC A A

within pellet at r = 0), we can calculate temperaturewithin pellet at r = 0), we can calculate temperature

gradient, previous equation tell us either we need orgradient, previous equation tell us either we need or

don’t need to worry about T gradient within particle.don’t need to worry about T gradient within particle.

Where isothermal (approach) approximation can beWhere isothermal (approach) approximation can be

used and where internal T gradients must beused and where internal T gradients must be

considered.considered.

Volumetric reaction for porous particles, heat isVolumetric reaction for porous particles, heat is

generated in a volume.generated in a volume.



Shrinking Core: Non-Shrinking Core: Non-

IsothermalIsothermal

Heat generated at reactionHeat generated at reaction frontfront, not throughout the volume, not throughout the volume

In Steady State,In Steady State,

SolveSolve

t

T C

r

T k r

r r s , pe ∂∂

=

∂∂

∂∂

ρ 2

2

1

02

2

=

∂∂

∂∂

r

T r

r r

k e

( )( ) ( ) 21111

11

r

T T

dr

dT ;

T T

T T

cc

c

r R

sc

r R

r r

sc

c

−−

=−

−=

−−

R

r

r c

Ts

Tf

Tc



T ConditionsT Conditions

r r

Rr s

r r c

T T

T T

T T c

=

=

=

=

=

=



Boundary Condition 1:Boundary Condition 1: r r == r r

cc

Heat is generated = Heat conducted out through product layer

Area

( )

( )

−⋅

−−

=−

−=−=

ce

r c , A ,S r

S C

r r

er c , A ,S r

r Rk

H C C ak

T T

dr dT k H C C ak

c

110

0

∆

∆



Boundary Condition 2:Boundary Condition 2: r r == RR

Heat arriving by conduction = Heat removed for

from within particle convection

( )

( ) ( )

−

−−=−

−=−=

cr R

e

S C f S

f S

Rr

e

RhR

k

T T T T

T T hdr

dT k

11

1

Bi-1Can be obtained

from B.C. 1



SolutionSolution

Combine equations and eliminateCombine equations and eliminate T T SS to getto get T T cc--T T f f

( ) 2

0

2

1111cr c , A ,S r

ce

f C r H C C ak

hR Rr k

T T ⋅−=+

−

− ∆



T T cc

-- T T f f

( )

22

0

2

111111111

Rk r C ak Rr D

H C

hR Rr k

T T

mc ,S r ce

r f , A

ce

f C

++

−

−=

+

−

− ∆

Conduction Convection Diffusion in

Product Layer

Reaction Mass

Transfer



Fixed Bed ReactorFixed Bed Reactor

Solids take part in reactionSolids take part in reaction unsteady state or semi-batch modeunsteady state or semi-batch mode

Over some time, solids either replaced or regeneratedOver some time, solids either replaced or regenerated

1 2

CA,in

CA,out

Regeneration

t

CA,out

/CA,in

Breakthroughcurve



Isothermal Reaction:Isothermal Reaction:

Plug Flow ReactorPlug Flow Reactor

Plug flow of fluid – no radialPlug flow of fluid – no radial

gradients, and no axial dispersiongradients, and no axial dispersion

Constant density with positionConstant density with position

Superficial velocity remains constantSuperficial velocity remains constant



( )f , A

' '

v A

r

Av C k dt

dN

V sreactor m

mol r ε −==

⋅

11

3

0→∂

∂

t

C f , A

For first order reaction, fluid only:

For steady state:

Therefore,

( ) 010

=−+ f , A

' '

v

f , AC k

dz

dC U ε

Volume of reactor

Void fraction



Balance on SolidBalance on Solid

( )

( ) ( )

( )0

1

01

=−

+∂∂

−⋅=−

=+∂∂

−

ε

ε

a

r

t

C

r ar

r t

C

Av s

svav

sv s



Solve These EquationsSolve These Equations

00 =+∂

∂

+∂

∂ Av

f , A f , A

r z

C

U t

C

ε

( )0

1=

−+

∂∂

ε a

r

t

C Av s

( )0

1

0

=∂

∂−−

∂

∂

t

C

U

a

z

C s f , A ε

= 0 (In quasi steady state, we ignore the

accumulation of A in gas)

S u b s t i t u

t e r A

v

( )

( )t , z f C

t , z f C t

C

z

C

'

s

'

f , A

'

s

'

f , A

=

=

=∂

∂+

∂

∂0



a)a) Shrinking Core ModelShrinking Core Model

b)b) Uniform reaction in porous particleUniform reaction in porous particle, zero order, zero orderin fluidin fluid

c)c) Uniform reactionUniform reaction, 1, 1stst order in fluid and in solidorder in fluid and in solid

d)d) Park et al., “An Unsteady State Analysis of Park et al., “An Unsteady State Analysis of Packed Bed Reactors for Gas-Solid Reactions”,Packed Bed Reactors for Gas-Solid Reactions”,

J. Chem. Eng. Of Japan, 17(3):269-274 (1984) J. Chem. Eng. Of Japan, 17(3):269-274 (1984)

e)e) Evans et al., “Application of a Porous PelletEvans et al., “Application of a Porous Pellet

Model to Fixed, Moving and Fluid Bed Gas-Model to Fixed, Moving and Fluid Bed Gas-Solid Reactors”, Ind. Eng. Chem. Proc. Des.Solid Reactors”, Ind. Eng. Chem. Proc. Des.13(2):146-155 (1974)13(2):146-155 (1974)

) I Sh i ki C) I Sh i ki C



a) In Shrinking Corea) In Shrinking Core

ModelModel

( ) o ,S c , Av Av C C ak r ε −= 1

R Bir r C ak

D

r C ak

D

C

C

mcco ,S r

e

co ,S v

e

f , A

c , A

111

11

2

−−

+

=3

= Rr C C c

o , s s

Recall that

03

3

2

=+∂∂ cc , Avc

c r C k R

t

r r

( ) 010

=−+∂

∂c , Ao , sv

f , AC C ak

z

C U ε

Solid Phase

Liquid Phase

For SCM

SolveCA,f = f(z)

r c = f(z,t)



O ll C i fO ll C i f



Overall Conversion of Overall Conversion of

SolidSolid

∫

∫

∫ =

=− L

c L

L

c

s dz r LR

dz

dz R

r

X 0

3

3

0

0

3

11

H i ht V tiH i ht V ti



Height Vs timeHeight Vs time

(Graphical)(Graphical)

z/L

t/τ

All CA has

been

reacted

Particles at bed

entrance are

completed reacted

Unreacted

bed depth

Reaction

zone

Completelyreacted

b) Uniform Reaction in Porousb) Uniform Reaction in Porous



b) Uniform Reaction in Porousb) Uniform Reaction in Porous

ParticleParticle

and Zero Order in Fluidand Zero Order in Fluid

( )S S X k

dt

dX −= 1

S ,S

S

S S

dC C dX

C

C X

0

0

1

1

=−

=−where

( )0

0

1

0

=+∂∂

=+

∂

∂⋅

−S

S

S

f , A

kC t

C

kC

z

C

a

U

ε



c) Uniform Reaction and 1c) Uniform Reaction and 1stst order in Fluid and in solidorder in Fluid and in solid

( )

( )

( )

( ) 01

01

1

1

0

=−+∂

∂

=−+

∂

∂

−=

−=

S s , Av

s , A

S s , Av

f , A

S v Av

S Av Av

C C ak t

C

C C ak

z

C U

C ak r

C C ak r

η ε

η ε

η ε

ε



Non-Isothermal PackedNon-Isothermal Packed

Bed ReactorBed Reactor For mass continuityFor mass continuity did balance ondid balance on

fluid and on solidfluid and on solid For energy balance, we do balanceFor energy balance, we do balance

on each phaseon each phase



ModelingModeling

Tf + dTf

Tf

z + dz

z

Tf,0

U0

q =0

g U sm

kg G ρ

02=



Moving Bed ReactorMoving Bed Reactor



Moving Bed ReactorMoving Bed Reactor

(MBR)(MBR) Steady state reactor where solids moving atSteady state reactor where solids moving at

near their packed bed voidagenear their packed bed voidage

Counter or co-current operationCounter or co-current operation

Solid usually move downward (vertical shaftSolid usually move downward (vertical shaftreactor or furnace)reactor or furnace)

Voidage is near that of a packed bedVoidage is near that of a packed bed

Slightly above random loose-packedSlightly above random loose-packed

voidagevoidage Solids move mainly in a plug floe, but regionSolids move mainly in a plug floe, but region

near wall have a velocity distributionnear wall have a velocity distribution



Advantages of MBRAdvantages of MBR

True counter-current flow True counter-current flow

Uniform residence time (essentially plug flow)Uniform residence time (essentially plug flow)

ReasonableReasonable ∆P ∆P

Throughput variable Throughput variable Generally larger particle dGenerally larger particle dpp > 2-3 mm> 2-3 mm

Difficulties coping with wide size distribution of Difficulties coping with wide size distribution of

particles (fines tend to block up the voidparticles (fines tend to block up the void

spaces)spaces)

multi phases

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