Multiphase Chemical Multiphase Chemical Reactor EngineeringReactor Engineering

Quak Foo LeePh.D. Candidate

Chemical and Biological Engineering

The University of British Columbia

Different Types of Different Types of ReactorReactor

Fluidized Bed Reactor

Trickle Column ReactorSlurry Bubble Column ReactorBatch 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 Through Straight 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 Distillate Slurry Phase Distillate ReactorReactor

Packed Bed ReactorPacked Bed Reactor

CSTR CSTR

Agitator

Connection for heating or cooling jacket

Hand holes for charging reactor

CA,in

CA,out

Gas + solids

Plug Flow ModelPlug Flow Model

V

Ht

out,Ain,A CC

Particle surrounding by Particle surrounding by fluid of essential fluid of essential constant concentration, constant concentration, CCA,mA,m

Batch Mix Flow: Charge Batch Mix Flow: Charge ReactorReactor

Residence time Residence time distributiondistribution

Particle stays in the Particle stays in the reactor for certain reactor for certain length of timelength of time

Countercurrent FlowCountercurrent Flow

If solids are moving plug If solids are moving plug flow and we have constant flow and we have constant flow composition flow composition

Residence time of solids:Residence time of solids:

Heat Effects !! Heat Effects !!

V

Ht

AC

Heat Effects on Reactions Heat Effects on Reactions of Single Particlesof Single Particles

Normally (developed) dealing with exothermic and Normally (developed) dealing with exothermic and endothermic reaction.endothermic reaction.

If reaction occurs at a rate such that the heat absorbed If reaction occurs at a rate such that the heat absorbed (endothermic) or generated (for exothermic) can’t be (endothermic) or generated (for exothermic) can’t be transferred rapidly enough, then non-isothermal effects transferred rapidly enough, then non-isothermal effects become important: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 will increase and the rate of

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

Two conditions:Two conditions: i) Film i) Film ∆T (external ∆T) T∆T (external ∆T) Tff (bulk fluid) ≠ T (bulk fluid) ≠ Tp p

(particle)(particle) ii) Intraparticle ∆T (internal ∆T) Tii) Intraparticle ∆T (internal ∆T) Tr=Rpr=Rp ≠ T ≠ Tr=∞r=∞

Non-ReactingNon-Reacting

1.1. Small particles Small particles highly conductive highly conductive particlesparticles

2.2. Small particles Small particles volumetric volumetric reactionreaction

1)1)Small Particles: Small Particles: Highly Conductive Highly Conductive

ParticlesParticles Particle initially at uniform Particle initially at uniform

T = TT = Tpp

At t = 0, we drop it into our At t = 0, we drop it into our furnacefurnace

Fluid at Tf

Tp

Energy BalanceEnergy Balance

dt

dHmQQ radiationconvection

dt

TCdmTTTThR pp

pwmpfcv 4424

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

Where,Area of sphere = 4πR2

Hcv = convection coefficientσ = Stefan-Boltzman constantЄm = emissivity of the particle (wall has Є = 1)

Energy BalanceEnergy Balance

pF

pwmr TT

TTh

44

dt

dT

A

CmTThh ppp

pFrcv

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

Find hFind hcvcv

Have film: Have film: ∆H T∆H Tff ≠ T ≠ Tpp

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

31

21

602 PrRe.Nuk

dhp

f

pcv 31

21

602 PrRe.Nuk

dhp

f

pcv

;k

CPr;

VdRe

f

ppp

2. Small Particles: 2. Small Particles: Volumetric ReactionVolumetric Reaction

Small such that no Small such that no internal gradientsinternal gradients

fpprAvp TThAHrV

Heat generated by reaction = Heat transferred to surroundingHeat generated by reaction = Heat transferred to surrounding

Steady State:

Volume of particle Rate of

reaction

3

R

h

rHTT Avr

fp

Exothermic Rxn:-∆Hr = (+)-rAv = (+)

3. Large Particles:3. Large Particles:Possible Internal Particle Possible 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

TC

r

Tkr

rr s,pe

2

2

1

Rrpf

Rre TThdr

dTk

:Surface

Heat conducted into particle at r =Rp

Heat transferred into particleNote: 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

rr

T

p,pp T)r(T;TT;t 00

00

00

Rrrrr

rr

TT

RTT

Symmetry condition

Initial condition

Internal gradient

External gradientRrrf TT

Reacting SystemsReacting Systems

General equation for volumetric General equation for volumetric reactions reactions

(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

AvA

eA r

r

CDr

rrt

C

22

1

AvnS

mAr

rAvep

rCCk

Hrr

Tkr

rrt

TC

22

11

Continuity for A

Energy balance

AvnS

mAr rCCTk

(1)

(2)

(3)

Cou

pled

thr

ough

the

re

actio

n ra

te

In Steady State In Steady State Showed that for steady conditions:Showed that for steady conditions:

rA

ee Hdr

dCD

dr

dTk r

Aee H

dr

dCD

dr

dTk

rr,As,Ae

eSr HCC

k

DTT 00

rr,As,Ae

eSr HCC

k

DTT 00

Integrate at r = 0, r = R

For sphere

RrrS TT

Some NotesSome Notes If we know If we know CCA,sA,s (surface concentration) and (surface concentration) and CCA,r=0A,r=0 ( (CCAA

within pellet at r = 0), we can calculate temperature within pellet at r = 0), we can calculate temperature gradient, previous equation tell us either we need or gradient, 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 be Where isothermal (approach) approximation can be used and where internal T gradients must be used and where internal T gradients must be considered.considered.

Volumetric reaction for porous particles, heat is Volumetric reaction for porous particles, heat is generated in a volume.generated in a volume.

Shrinking Core: Non-Shrinking Core: Non-IsothermalIsothermal

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

In Steady State, In Steady State,

SolveSolve

t

TC

r

Tkr

rr s,pe

2

2

1

02

2

r

Tr

rr

ke

21111

11

r

TT

dr

dT;

TT

TT

cc

c

rR

sc

rR

rr

sc

c

R

r

rc

Ts

Tf

Tc

T ConditionsT Conditions

rr

Rrs

rrc

TT

TT

TTc

Boundary Condition 1: Boundary Condition 1: rr = = rrcc

Heat is generated = Heat conducted out through product layer Area

ce

rc,A,SrSC

rrerc,A,Sr

rRk

HCCakTT

dr

dTkHCCak

c

110

0

Boundary Condition 2: Boundary Condition 2: rr = = RR

Heat arriving by conduction = Heat removed forfrom within particle convection

crR

eSCfS

fSRr

e

RhR

kTTTT

TThdr

dTk

11

1

Bi-1Can be obtained from B.C. 1

SolutionSolution Combine equations and eliminate Combine equations and eliminate TTS S to get to get TTcc--TTf f

20

21111

crc,A,Sr

ce

fC rHCCak

hRRrk

TT

2

0

21111

crc,A,Sr

ce

fC rHCCak

hRRrk

TT

Recall from Isothermal Recall from Isothermal SC ModelSC Model

RBirrCakD

rCak

D

C

C

mcc,sr

e

c,Sr

e

f,A

c,A

111

11

0

20

Substitute CA,c into (Tc –Tf) equation

TTcc - - TTff

220

2

111111111RkrCakRrD

HC

hRRrk

TT

mc,Srce

rf,A

ce

fC

220

2

111111111RkrCakRrD

HC

hRRrk

TT

mc,Srce

rf,A

ce

fC

Conduction Convection Diffusion inProduct Layer

Reaction MassTransfer

Can Heat Transfer Control Can Heat Transfer Control the Rate in Endo- and the Rate in Endo- and

Exothermal Rxn?Exothermal Rxn? Consider Consider CCA,cA,c ≈≈ CCA,fA,f; initially rapid reaction; initially rapid reaction

a)a) EndothermicEndothermicwith poor heat transfer, heat will be consumed in reaction, with poor heat transfer, heat will be consumed in reaction, and if can’t transfer heat in, and if can’t transfer heat in, TTCC will drop will drop reaction rate reaction rate ↓↓ markedly and rate of reaction become markedly and rate of reaction become the slow step occurring at a rate dictated by the flow of the slow step occurring at a rate dictated by the flow of heat.heat.

b)b) ExothermicExothermic

initial rapid reaction and with poor initial rapid reaction and with poor QQ, , TTCC will increased, will increased, then then rate of reaction rate of reaction ↑↑ and eventually reach point where and eventually reach point where gaseous reactant can’t be transferred fast enough gaseous reactant can’t be transferred fast enough (external mass transfer or diffusion). Hence (external mass transfer or diffusion). Hence rate is limitedrate is limited..

Fixed Bed Fixed Bed ReactorReactor

Fixed Bed ReactorFixed Bed Reactor

Solids take part in reaction Solids take part in reaction unsteady state or semi-batch mode unsteady 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/C

A,in

Breakthrough curve

Isothermal Reaction:Isothermal Reaction:Plug Flow ReactorPlug Flow Reactor

Plug flow of fluid – no radial Plug flow of fluid – no radial gradients, and no axial dispersiongradients, and no axial dispersion

Constant density with positionConstant density with position

Superficial velocity remains Superficial velocity remains constantconstant

Plug Flow ModelPlug Flow Model

z + dz CA,f + dCA,f

z CA,f

U0 (m/s) superficial velocity 2

2

0 mA

s/mVU

xs

gas

Mass BalanceMass Balance

zCt

dzrdCCUCU f,AAvf,Af,Af,A

00

Input – Output – Reaction = Accumulation

Divide by ∂z and take the limits as ∂z 0

00

Avf,Af,A r

z

CU

t

C 00

Av

f,Af,A rz

CU

t

C

ε is void fraction in bed

f,A''v

A

rAv Ck

dt

dN

Vsreactorm

molr

1

13

0

t

C f,A

For first order reaction, fluid only:

For steady state:

Therefore,

010 f,A''v

f,A Ckdz

dCU

Volume of reactor

Void fraction

Conversion as a function Conversion as a function of Heightof Height

Integrating with CA,f = CA,f,in at z = 0

z

U

kexp

C

CX

''v

in,f,A

f,AA

0

111

z

U

kexp

C

CX

''v

in,f,A

f,AA

0

111

Note 1: Same equation as for catalytic reactor with 1st order reactionNote 2: Can be used in pseudo-homogeneous reaction

Balance on SolidBalance on Solid

aA (fluid) + S (solid) aA (fluid) + S (solid) Products Products Input – Output – Reaction = AccumulationInput – Output – Reaction = Accumulation Over increment of dz: input = 0, output Over increment of dz: input = 0, output

=0=0

zt

Czr s

sv

1

Volume fraction of solid = m3 of solid m3 of reactor volume

mol m3 of solid · s

Balance on SolidBalance on Solid

01

01

a

r

t

C

rar

rt

C

Avs

svav

svs

Solve These EquationsSolve These Equations

00

Avf,Af,A r

z

CU

t

C 00

Av

f,Af,A rz

CU

t

C

01

a

r

t

C Avs

01

a

r

t

C Avs

0

1

0

t

C

U

a

z

Csf,A

01

0

t

C

U

a

z

Csf,A

= 0 (In quasi steady state, we ignore the accumulation of A in gas)

Sub

stitu

te r Av

t,zfC

t,zfC

t

C

z

C

's

'f,A

's

'f,A

0

t,zfC

t,zfC

t

C

z

C

's

'f,A

's

'f,A

0

a)a) Shrinking Core ModelShrinking Core Modelb)b) Uniform reaction in porous particleUniform reaction in porous particle, zero order , zero order

in fluidin fluidc)c) Uniform reactionUniform reaction, 1, 1stst order in fluid and in solid order in fluid and in solidd)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 Pellet Evans 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)

a) In Shrinking Core a) In Shrinking Core ModelModel

o,Sc,AvAv CCakr 1

RBirrCakD

rCakD

C

C

mcco,Sr

e

co,Sv

e

f,A

c,A

111

11

2

3

R

rCC c

o,ss

Recall that

03

32

cc,Avc

c rCkR

t

rr 0

3

32

cc,Avc

c rCkR

t

rr

010

c,Ao,sv

f,A CCakz

CU 010

c,Ao,svf,A CCak

z

CU

Solid Phase

Liquid Phase

For SCM

SolveCA,f = f(z) rc = f(z,t)

Conversion vs TimeConversion vs Time

z

t = 0 t > 0

Overall Conversion of Overall Conversion of SolidSolid

L

cL

Lc

s dzrLR

dz

dzRr

X0

33

0

0

3

11

Height Vs time Height Vs time (Graphical)(Graphical)

z/L

t/

All CA has been reacted

Particles at bed entrance are completed reacted

Unreacted bed depth

Reaction zone

Completely reacted

b) Uniform Reaction in Porous b) Uniform Reaction in Porous ParticleParticle

and Zero Order in Fluidand Zero Order in Fluid

SS Xk

dt

dX 1

S,S

S

SS

dCC

dX

C

CX

0

0

1

1

where

0

01

0

SS

Sf,A

kCt

C

kCz

C

a

U

0

01

0

SS

Sf,A

kCt

C

kCz

C

a

U

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

Ss,Avs,A

Ss,Avf,A

SvAv

SAvAv

CCakt

C

CCakz

CU

Cakr

CCakr

Non-Isothermal Packed Non-Isothermal Packed Bed ReactorBed Reactor

For mass continuity For mass continuity did balance did balance on fluid and on solidon fluid and on solid

For energy balance, we do balance For energy balance, we do balance on each phaseon each phase

Non-Isothermal Packed Non-Isothermal Packed Bed ReactorBed Reactor

Assumptions:Assumptions:1)1) Adiabatic reaction – no heat lost through Adiabatic reaction – no heat lost through

shell to surroundings (no radial shell to surroundings (no radial temperature gradients) q = 0temperature gradients) q = 0

2)2) BiBiλλ is small – uniform T within particle (an is small – uniform T within particle (an exothermic reaction Texothermic reaction Tpp > T > Tgg))

3)3) Plug flow of gas and use TPlug flow of gas and use Trefref =0 for =0 for enthalpy calculationsenthalpy calculations

4)4) Assume an average density can be used Assume an average density can be used ((ρρgg = constant) = constant)

ModelingModeling

Tf + dTf

Tf

z + dz

z

Tf,0

U0

q =0

gUsm

kgG 02

Moving Bed ReactorMoving Bed ReactorSolids in

Solids out

Gas in

Gas out

U0

Vs

∆z

Moving Bed Reactor Moving Bed Reactor (MBR)(MBR)

Steady state reactor where solids moving at Steady 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 shaft Solid usually move downward (vertical shaft

reactor or furnace)reactor or furnace) Voidage is near that of a packed bedVoidage is near that of a packed bed

Slightly above random loose-packed Slightly above random loose-packed voidagevoidage

Solids move mainly in a plug floe, but region Solids 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 flowTrue counter-current flow Uniform residence time (essentially plug Uniform residence time (essentially plug

flow)flow) Reasonable Reasonable ∆P∆P Throughput variableThroughput variable Generally larger particle dGenerally larger particle dpp > 2-3 mm > 2-3 mm Difficulties coping with wide size Difficulties coping with wide size

distribution of particles (fines tend to distribution of particles (fines tend to block up the void spaces)block up the void spaces)