catalytic three-phase reactors gas, liquid and solid catalyst

Catalytic three-phase reactors

Gas, liquid and solid catalyst

Function principle

Some reactants and products in gas phaseDiffusion to gas-liquid surfaceGas dissolves in liquidGas diffuses through the liquid film to the liquid

bulk Gas diffuses through the liquid film around the

catalyst particle to the catalyst, where the reaction takes place

Simultaneous reaction and diffusion in porous particle

Three-phase reactors – catalyst

Small particles (micrometer scale < 100 micrometer)

Large particles (< 1cm)

Catalyst design

Reactors

Bubble column

Flow pattern in bubble column

Tank reactor

Often called slurry reactor

Packed bed – trickle bed

Trickle bedLiquid downflow – trickling flow

Packed bed, if liquid upflow

Packed bed- fixed bed – trickle bed

Flow chart: trickle bed

Trickle flow

Packed bed

Three-phase fluidized bed

Fluidized bed – flow chart

Monolith catalysts

Flow in monoliths

Monolith channel

Three-phase monolith reactor

Three-phase reactorsMass balancesPlug flow and axial dispersion

Columnr eactorTube reactor Trickle bedMonolith reactor

BackmixingBubble columnTank reactor

Three-phase reactorMass balancesMass transfer from gas to liquid, from

liquid to catalyst surface Reaction on the catalyst surface In gas- and liquid films only diffusion

transport Diffusion flow from gas to liquid

GiLi

i

bLii

bGib

Li

kkK

cKcN

1

Three-phase reactorMass transfer

Three-phase reactorMass balancesFor physical absorption the fluxes through

the gas- and liquid films are equal

Flux from liquid to catalyst particle = component generation rate at steady state

bGi

sGi

sLi

bLi NNNN

0 pipsLi mrAN

Three-phase reactorMass balancesFlux through the liquid film defined with

concentration difference and liquid-film coefficient

Catalyst bulk density defined by

sLi

bLi

sLi

sLi cckN

RL

cat

L

catB V

m

V

m

Three-phase reactorMass balances

ap = total particle surface/reactor volume

iBLpsLi

bLi

sLi

sLi racckN

Three-phase reactorMass balancesIf diffusion inside the particle affects the

rate, the concept of effectiviness factor is used as for two-phase reactor (only liquid in the pores of the particles)

The same equations as for two-phase systems can be used for porous particles

)('Bjejj cRR

Three-phase reactor – plug flow

Three-phase reactorplug flow, liquid phaseFor volume element in liquid phase

Liquid phase

psLiutLi

bLiinLi ANnANn

,,

psLiv

bLi

R

LiaNaN

dV

nd

Three-phase reactorPlug flow - gas phaseFor volume element in gas phase

Gas phase

- concurrent+ countercurrent

ANnn bGiutGiinGi

,,

vbLi

R

GiaN

dV

nd

Three-phase reactorPlug flowInitial conditions

Liquid phase

Gas phase, concurrent

Gas phase, countercurrent

0,0

RLiLi Vnn

0,0

RGiGi Vnn

RGiGi VVnn

,0

Three-phase reactorplug flow modelGood for trickle bedRather good for a packed bed , in which liguid

flows upwards For bubble column plug flow is good for gas

phase but not for liquid phase which has a higher degree of backmixing

Three-phase reactor- complete backmixingLiquid phase

Gas phase

psLv

bL

R

LiLiaNaN

V

nn

0

vbL

R

GiGiaN

V

nn

0

Three-phase reactor- semibatch operationLiquid phase in batchGas phase continuous

Initial condition

RpsLv

bL

Li VaNaNdt

dn

GiGi nVaNndt

dnRv

bLi

Gi0

0

0

0

0

tnn

tnn

GiGi

LiLi

Parameters in three-phase reactors

Gas-liquid equilibrium ratio (Ki) fromThermodynamic theoriesGas solubility in liquids (Henry’s constant)

Mass transfer coefficients kLi, kGi

Correlation equations

G

GiGi

L

LiLi

Dk

Dk

Numerical aspects

CSTR – non-linear equationsNewton-Raphson method

Reactors with plug flow (concurrent)Runge-Kutta-, Backward difference -methods

Reactors with plug flow (countercurrent) and reactors with axial dispersion (BVP)orthogonal collocation

Examples

Production of SitostanolA cholesterol suppressing agentCarried out through hydrogenation of Sitosterol

on Pd catalysts (Pd/C, Pd/Zeolite)

Production of XylitolAn anti-caries and anti-inflamatory componentCarried out through hydrogenation of Xylose on

Ni- and Ru-catalysts (Raney Ni, Ru/C)

Exemple: from cholesterol tol sitostanol

Reaction scheme

A superficially complicated scheme

From laboratory scale to industrial scale

Slurry, three-phase reactor

Lab reactor, 1 liter, liquid amount 0.5 kg

Large scale reactor, liquid amount 8080 kg

Simulation of large-scalle reactor based on laboratory reactor

Catalytic reactor

Semi-batch stirred tank reactorWell agitated, no concentration differences appear in

the bulk of the liquid Gas-liquid and liquid-solid mass transfer resistances

can prevailThe liquid phase is in batch, while gas is continuously

fed into the reactor. The gas pressure is maintained constant. The liquid and gas volumes inside the reactor vessel

can be regarded as constant

Mathematical modelling

dr

rNdrr

dt

dc SiS

pipi 1

j

jjiji aRr

Reaction, diffusion and catalyst deactivation in porous particles

Particle model

Rates

Model implementation

dr

dcDN i

eii

dr

dc

r

s

dr

cdDaR

dt

dc iieijjijpp

i2

21

, where Dei=(p/p)Dmi

0dr

dci 0r

Rcckdt

dcD iiLi

Rr

iei

Rr

Boundary conditions

Catalytic reactor, mass balances

GLGLipii aNaN

dt

dc

RcckN iiLii

GiLi

i

bLii

bGi

GLi

kk

KcKc

N1

Liquid phase mass balance

Liquid-solid flux

Gas-liquid flux

Numerical approach

PDEs discretizied with finite difference formulae

The ODEs created solved with a stiff algorithm (BD, Hindmarsh)

Rate equations

Surface reaction, rate determiningEssentially non-competetive adsorption of hydrogen and organics

Kinetics in laboratory scale

Concentrations as a function of reaction time

Kinetics in plant scale

Hydrogen concentration in liquid phaseConcentration of organics

Comparison of lab and plant scale

Laboratory Factory

Hydrogen concentration in liquid phase in plant scale

Hydrogenation of Xylose

=O

OH

HOOH

OH

D -Xylose(aldehyde form)

Xylitol

OHHO

OH

CH2OH

CH2OH

CH2OH

OH

HO

O

OH

D-Xylulose

OH

HO

OH

CH2OH

CH2OH

D-arabinitol

isomerization

hydrogenation

hydrogenationIsomerization

hydrogenation

=O

OH

HOOH

OH

=O

OH

HOOH

OH



Xylitol

OHHO

OH

CH2OH

CH2OH

OHHO

OH

CH2OH

CH2OH

CH2OH

OH

HO

O

OH

CH2OH

OH

HO

O

OH

D-XyluloseD-Xylulose

OH

HO

OH

CH2OH

CH2OH

OH

HO

OH

CH2OH

CH2OH

D-arabinitol

isomerization

hydrogenation

hydrogenationIsomerization

hydrogenation

Modelling resultsXylose hydrogenation

Heavy mass-transfer limitations

0

5

10

15

20

25

30

35

40

45

50

0 23 46 69 92 115

138

161

184

207

230

253

276

299

t/min

con

c. /

wt-

%

D-xylose

xylitol

D-xylulose

D-arabitol

Moderate mass-transfer limitations

0

10

20

30

40

50

60

0 23 46 69 92 115

138

161

184

207

230

253

276

299

t/min

con

c. /

wt-

%

D-xylose

xylitol

D-xylulose

D-arabitol

Heavy mass-transfer limitations and moderately deactivated catalyst

0

5

10

15

20

25

30

35

40

45

50

0 24 48 72 96 120

144

168

192

216

240

264

288

t/min

con

c. /

wt-

%

D-xylose

xylitol

D-xylulose

D-arabitol

Light mass-transfer limitations

0

5

10

15

20

25

30

35

40

45

50

0 23 46 69 92 115

138

161

184

207

230

253

276

299

t/minco

nc.

/ w

t-%

D-xylose

xylitol

D-xylulose

D-arabitol

Heavy mass transfer

Heavy mass transfer andModeratly deactivated

Moderate mass transfer

Light mass transfer

Effect of external mass transfer

Gas-liquid reactors

Gas-liquid reactors

Non-catalytic or homogeneously catalyzed reactionsGas phase Liquid phase ( + homogeneous catalyst)

Components i gas phase diffuse to the gas-liquid boundary and dissolve in the liquid phase

Procukt molecules desorb from liquid to gas or remain in liquid

Gas-liquid reactions

Synthesis of chemicals Gas absorption, gas cleaningVery many reactor constructions used,

depending on the application

Gas-liquid reaction: basic principle

Gas-liquid reactor constructions

Spray columnWetted wall columnPacked column Plate column Bubble columnsContinuous, semibatch and batch tank reactorsGas lift reactorsVenturi scrubbers

Gas-liquid reactors - overview

Tank reactor

Gas-liquid reactors

Packed columnAbsorption of gasesCountercurrent principle: gas upwards, liquid

downwardsColumn packings

enable a large gas-liquid contact areamade of ceramics, plastics or metalgood gas distribution because of packingschanneling can appear in liquid phase; can be

handled with distribution plates

Plug flow in gas and liquid phases

Gas-liquid reactors

Plate column Absorption of gases Countercurrent Various plates used as in distillation, e.g.

Bubble capPlate column

Packed column Absorption of gases Countercurrent A lot of column packings available; continuous development

Bubble column

Gas-lift -reactor

Bubble column – design examples

Bubble column

Packed column

Packings

Plate column

Gas-liquid reactors

Gas scrubbersSpray tower

Gas is the continuous phaseIn shower !

Venturi scrubber Liquid dispergation via a venturi neck

For very rapid reactions

Spray tower

Venturi scrubber

Gas-liquid reactors

Selection criteriaBubble columns for slow reactionsSckrubbers or spray towers for rapid reactionsPacked column or plate column if high reatant

conversion is desired

Mass balances

22

msm

molAN i

Gas-liquid reactors Mass balancesPlug flow

Liquid phase

Gas phase

av =gas-liquid surface area/reactor volumeL = liquid hold-up

utLiLibLiinLi nVrANn ,,

iLvbLi

R

Li raNdV

nd

vbGi

R

Gi aNdV

nd

Gas-liquid reactionsMass balancesComplete backmixing

Liquid phase

Gas phaseav =gas-liquid surface area/reactor volume

L = liquid hold-up

utLiLibLiinLi nVrANn ,,

iLvbLi

R

LiLiraN

V

nn

0

vbGi

R

GiGiaN

V

nn

0

Gas-liquid reactorsMass balancesBatch reactor

Liquid phase

Gas phaseav =interfacial area/reactor volumeL = liquid hold-up

RiLvbLi

Li VraNdt

dn

RvbGi

Gi VaNdt

dn

Gas-liquid reactors- Gas-liquid filmFluxes in gas-liquid films

NbLi Nb

Gi

Two-film theoryChemical reaction and molecular diffusion proceed

simultaneously in the liquid film with a thickness of L

Only molecular diffusion in gas film, thickness G

Fick’s law can be used:Gz

GiGi

bGi dz

dcDN

Lz

LiLi

bLi dz

dcDN

Gas-liquid reactorsGas film Gas film, no reaction

Analytical solution possibleThe flux depends on the mass transfer

coefficient and concentration difference

Adz

dcDA

dz

dcD

ut

GiGi

in

GiGi

02

2

dz

cdD Gi

Gi sGi

bGiGi

bGi cckN

Gas-liquid reactorsLiquid filmDiffusion and reaction in liquid film:

Boundary conditions:

Adz

dcDzArA

dz

dcD

ut

LiLii

in

LiLi

02

2

iLi

Li rdz

cdD

LbLiLi

LibGi

zvidcc

zvidNN

0

Gas-liquid reactorsLiquid filmLiquid film

Equation can be solved analytically for isothermas cases for few cases of linear kinetics; in other case numerical solution should be used

Reaction categoriesPhysical absorption

No reaction in liquid film, no reaction in liquid bulk

Very slow reactionThe same reaction rate in liquid film and liquid bulk –

no concentration gradients in the liquid film, a pseudo-homogeneous system

Slow reactionReaction in the liquid film negligible, reactions in the

liquid bulk; linear concentration profiles in the liquid film

Reaction categories

Moderate ratesReaction in liquid film and liquid bulk

Rapid reactionChemical reactions in liquid film, no reactions in bulk

Instantaneous reactionReaction in liquid film; totally diffusion-controlled

process

Concentration profiles in liquid film

Enhancement factor

Real flux/flux in the presence of pure physical absorption

EA 1

GALA

A

bLAA

bGA

sLA

A

kkK

cKc

NE

1

Gas-liquid reactors - very slow reactionNo concentration gradients in the liquid

film Depends on the role of diffusion

resistance in the gas film

bLA

bGA

AbLA

sGA

A c

cK

c

cK

bLAA

bGAGA

bLA

bGA cKckNN

Gas-liquid reactors - slow reactionDiffusion resistance both in gas- and liquid- film

retards the adsorption, but the role of reactions is negligible in the liquid film

sGA

bGAGA

bGA cckN

bLA

sLALA

bLA cckN

GALA

A

bLAA

bGAb

LA

kk

KcKc

N1

Gas-liquid reactors - moderate rate in liquid film

Chemical reactions in liquid film

The transport equation should be solved numerically

sLA

sGA

bGA

bLA

bGA

NNN

NN

sLA

sGA

Ac

cK 0

2

2

ALA

LA rdz

cdD

Reaction in liquid film

No reaction in gas film

Moderate rate in the liquid film

Transport equation can be solved analytically only for some special cases:

isothermal liquid film – zero or first order kinetics

Approximative solutions exist for rapid second order kinetics

Moderate rate…

Zero order kinetics

LA

ALA

D

k

dz

cd

2

2

GALA

A

bLAA

bGAs

LA

kk

KMcKc

N1

1

bLALA

LAA

ck

kDM

22

Moderate rate…

First order kinetics

Hatta number Ha=(compare with Thiele modulus)

LA

LAALA

D

kc

dz

cd

2

2

GALA

A

bLAAb

GAsLA

kk

K

M

M

M

cKc

N1tanh

)cosh(

2

2 LLA

A

LA

LAA

D

k

k

kDM

Rapid reactions

Special case of reactions with finite rateAll gas components totally consumed in

the film; bulk concentration is zero, cbLA=0

Instantaneous reactions

Components react completely in the liquid film

A reaction plane exists

Reaction plane coordinate

02

2

dz

cdD LA

LA

sLBLB

BsLALA

A

LBLB

LB

cDcD

cDz

'


Enhancement factor:

Flux at the interface:

Coordinate of the interface:

02

2

dz

cdD LA

LA

GALA

A

bLBA

LAB

LBAbGA

sLA

kk

K

cKD

Dc

N1

bGALAB

AbLBLBA

AcD

KcDE

1


Flux

Only diffusion coeffcients affect !For simultaneous reactions can several

reaction planes appear in the film

GALA

A

bLBA

LAB

LBAbGA

sLA

kkK

cKDD

c

N1

Fluxes in reactor mass balances

Fluxes are inserted in mass balances

For reactants:For slow and very

slow reactions: (no reaction in liquid film)

sLi

sGi

bGi NNN

sLi

bLi ΝΝ

sLi

bLi ΝΝ

General approach

We are left with the model for the liquid film:

Lz

LiLi

bLi dz

dcDN

02

2

iLi

Li rdz

cdD

Solution of mass balances

Numerical strategy:Algebraic equations

Newton-Raphson method

Differential equations, initial value problem (IVP)Backward difference- and SI Runge-Kutta-methods

Differential equations, BVPorthogonal collocation or finite differences

Number of equations

N = number of components in the system

N eqs for liquid phase; N eqs for gas phaseN eqs for the liquid filmEnergy balances

1 for gas phase1 for liquid phase

3N+2 equations in total

Mass transfer coefficients

Flux through the gas film

Partial pressures often used:

Ideal gas law gives the relation:

sGA

bGAGA

sGA

bGA cckNN

sAAGA

sGA

bGA ppkNN '

RTkk GAGA '

Gas-liquid equilibria

Definition

For sparingly soluble gases:

Relation becomes

KA from thermodynamics; often Henry’s constant is enough

sLA

sGA

A c

cK

sLA

sA

A c

pHe

RT

HeK A

A

sLA

sA

A x

pHe '

Simulation example

Chlorination of p-kresolp-cresol + Cl2 -> monocloro p-kresol + HCl

monocloro p-kresol + Cl2 -> dichloro p-kresol + HCl

CSTRNewton-Raphson-iteration

Liquid filmOrthogonal collocation

Chlorination of para-cresol in a CSTR

Fluid-solid reactions

Three main types of reactions:Reactions between gas

and solidReactions between

liquid and solidGas-liquid-solid

reactions


The size of the solid phaseChanges:

Burning oc charcoal or wood

Does not change:oxidation av sulfides, e.g. zinc sulphide --> zinc

oxide

Reactors for fluid-solid reactions

Reactor configurationsFluidized bedMoving bedBatch, semibatch and continuous tank reactors

(liquid and solid, e.g. CMC production, leaching of minerals)

Processes and reactors

Fluid-solid reaction modelling

Mathematical models usedPorous particle model

Simultaneous chemical reaction and diffusion throughout the particle

Shrinking particle modelReaction product continuously removed from the surface

Product layer model (shrinking core model)A porous product layer is formed around the non-reacted

core of the solid particleGrain model

The solid phase consists of smaller non-porous particles (rasberry structure)


Solid particles react with gases in such a way that a narrow reaction zone is formed

Shrinking particle model can thus often be used even for porous particles

Grain model most rrealistic but mathematically complicated

Product layer

Product layer

Concentration profiles in the product layer

Shrinking particle

Grain model


Particle with a porous product layerGas or liquid film around the product layerPorous product layerThe reaction proceeds on the surface of non-

reacted solid materialGas molecules diffuse through the gas film and

through the porous product layer to the surface of fresh, non-reacted material


Reaction between A in fluid phase and B in solid phase

R=reaction rate, A=particle surface areaGenerated B= Accumulated B

22

()() msm

molRA

sB

PB

cRx

M

dt

dr


Diffusion through the porous product layer (spherical particle)

Solution gives NA=DeA(dcA/dr):

0)2

(2

2

dr

dc

rdr

cdD AA

EA

)(

111

sA

M

sA

bAEA

A cR

BiR

rr

ccDN


Fick’s law is applied for the diffusion in the product layer gives the particle radius

Surface concentration is obtained from

AMA

sA

bAeAB

pB

BiRr

r

ccD

x

M

dt

dr

111

)(

111

si

iM

si

biei cR

BiRr

r

ccD

For first-order kinetics an analytical solution is possible

Four cases – rate limiting stepsChemical reactionDiffusion through product layer and fluid filmDiffusion through the product layerDiffusion through the fluid film



Reaction time (t) and total reaction time (t0 ) related to the particle radius (r)

Limit casesChemical reaction controls the process –

Thiele modulus is small -> Thiele modulus small

Diffusion through product layer and fluid film rate limiting -> Thiele modulus large

Reaktorer med reaktiv fast fas

Diffusion through the product layer much slower than diffusion through the fluid -> BiAM=

Diffusion through fluid film rate limiting -> BiAM=0


Shrinking particleShrinking particle

Phase boundaryFluid film around particles

Product molecules (gas or liquid) disappear directly from the particle surface

Mass balance

In via diffusion through the fluid film + generated = 0


First order kineticsSurface reaction rate limitingDiffusion through fluid film rate limiting

Arbitrary kineticsA general solution possible, if diffusion through

the fluid film is rate limiting

Semibatch reactor

An interesting special case

Semibatch reactorHigh throughflow of gas so that the concentrations in

the gas phase can be regarded as constant; used e.g. in the investigation of gas-solid kinetics (thermogravimetric equipment)

Complete backmixing locally simple realtions between the reaction time and the

particle radius obtained

Reaction time and particle radius

Thiele modulus, φ=-νAkR/DeA and Biot number, BiM=kGAR/DeA

Special cases – large Thiele modulus φ; control by product layer and fluid film

M

M

Bi

BiRrRr

t

t

/21

)/11)()/(1(2))/(1(3 32

0

)/21(6

)/11)()/(1(2))/(1(3)/(1(6 32

0 M

M

Bi

BiRrRrRr

t

t


Product layer model

Large Thiele modulus, φ=-νAkR/DeA and large Bi - control by product layer

Large Thiele modulus, φ=-νAkR/DeA and small Bi - control by film

3

0

)/(1 Rrt

t

32

0

)/(2))/(31 RrRrt

t


Product layer model

Small Thiele modulus, φ=-νAkR/DeA and large Bi - control by chemical reaction

)/(10

Rrt

t


Shrinking particle model

Small Bi - control by film diffusion

Large Bi - control by chemical reaction

)/(10

Rrt

t

2

0

)/(1 Rrt

t

Packed bed

Packed bed – operation principleGas or liquid flows through a stagnant bed of

particles, e.g. combustion processes or ion exchangers

Plug flow often a sufficient description for the flow pattern

Radial and axial dispersion effects neglected

Simulation of a packed bed

Mechanistic modelling of kinetics and mass transfer

for a solid-liquid system:Leaching of zinc with ferric iron

Tapio Salmi, Henrik Grénman, Heidi Bernas, Johan Wärnå, Dmitry Yu. Murzin

Laboratory of Industrial Chemistry and Reaction Engineering,

Process Chemistry Centre, Åbo Akademi, FI-20500 Turku/Åbo, Finland

Reaction system

ZnS(s) + Fe2(SO4)3 ↔ S(s) + 2FeSO4 + ZnSO4

SEM

Experimental system

Isothermal batch reactor

Turbine impeller

Ultrasound input

SIA – analysis of Fe3+

Experimental data of Bernas (Markus) & Grénman

Markus et al, Hydrometallurgy 73 (2004) 269-282,Grénman et al, Chemical Engineering and Processing 46 (2007) 862-869

Multi-transducer ultradound reactor

Generator (0-600W)

20 kHz

Reactor pot inserted

6 transducers

A time-variable

power input

Experimental results - Stirring speed

0

0.05

0.1

0.15

0.2

0 25 50 75 100 125 150

Time (min)

Fe

3+ (

mo

l/L)

200 rpm350 rpm500 rpm700 rpm

T = 85°C , Sphalerite : Fe3+ = 1.1:1

The effect of the stirring speed on the leaching kinetics.

Experimental results

T = 85°C, C0Fe(III) = 0.2 mol/L

0

0.05

0.1

0.15

0.2

0 50 100 150 200

Time (min)

Fe

3+ (

mo

l/L)

Stoic. 0.5:1Stoic. 0.9:1Stoic. 1.1:1Stoic. 1.6:1Stoic. 2.1:1

The effect of the zinc sulphide concentration on the leaching kinetics.


T = 95°C, Sphalerite : Fe3+ = 1.1:1

0

0.1

0.2

0.3

0 25 50 75 100 125 150

Time (min)

Fe

3+ (

mo

l/L)

The effect of the ferric ion concentration on the leaching kinetics.


T = 95°C, Sphalerite : Fe3+ = 1.1:1

0

0.05

0.1

0.15

0.2

0 50 100 150 200

Time (min)

Fe

3+ (

mo

l/L)

0.2 mol/L0.4 mol/L0.6 mol/L0.8 mol/L1.0 mol/L

The effect of sulphuric acid on the leaching kinetics.

Experimental results - Temperature effect

Sphalerite : Fe3+ = 1.1:1

0

0.05

0.1

0.15

0.2

0 50 100 150 200

Time (min)

Fe

3+ (

mo

l/L)

75°C

85°C

95°C

The effect of temperature on the leaching kinetics.

Experimental results - Ultrasound effect

T = 85°C Stirring rate 350 rpm

0

0.05

0.1

0.15

0.2

0 25 50 75 100 125 150

Time (min)

Fe

3+ (

mo

l/L)

0 W

60 W

120 W

180 W

The effect of ultrasound on the leaching kinetics.

Reaction mechanism and rate equations

Surface reaction

Stepwise process( first reacts one Fe3+, then the second one! )

Rough particles

Three-step surface reaction mechanism

ZnS(s) + Fe3+ ↔ I1 (I)

I1+ Fe3+ ↔ I2 (II)

I2 ↔ S(s) + 2 Fe2+ + Zn2+ (III)

ZnS(s) + 2Fe3+ ↔ S(s) + 2 Fe2+ + Zn2+

rates of steps (I-III)

cI1, cI2 and cI3 = surface concentrations of the intermediates.

1111 Icaar

22122 II cacar

3233 acar IZnIIFeIII

FeIII

FeIII

ccka

ka

ka

cka

ka

cka

2

33

33

22

22

11

11

Development of rate equations

Pseudo-steady state hypothesis

rrrr 321

Rate equation

323121

321321

aaaaaa

aaaaaar

Back-substitution of a1….a-3 gives

D

cckkkckkkr ZnIIFeIIFeIII

2321

2321

D

Kccckr ZnIIFeIIFeIII )/( 22

D = k-1k-2+k-1k+3+k+2k+3cFeIII

Rate equations

Final form

FeIII

FeIII

c

ckr

21

where β = (k-1k-2+k-1k+3)/(k+2k+3)

An alternative rate equation

FeIIIH

FeIIIH

cc

cckr

21 NOT VALID FOR THIS CASE!

Area & Shape factor

Development of a general approach

The surface area (A) can be expressed with a generalized equation

n = amount of solid n0= initial amount of solidShape factor (a=1/x)

xx

P

nnR

aMA 1

00

0RV

Aa

P

P PP

P

V

mRa

0

00/ aanMnA /11/1

0

Area & Shape factor

Geometry Shape factor (a) x 1-x

Slab 1 1 0

Cylinder 2 1/2 1/2

Sphere 3 1/3 2/3

Irregular,

‘rough’ particle high value 0 1

Reaction order can vary between 0 and 1!

Mass balance for batch reactor

rcx

M

dt

dcZnS

ZnS

ZnSZnS

0

rc

x

M

dt

dcZnS

ZnS

FeIIIFeIII

0

FeIII

FeIIIZnS

RTE

c

ccer

a

2/

' γ=(k1σM / x0ZnS)

'rdt

dci

i

, where

Parameter estimation

Nonlinear regression applied on intrinsic kinetic data

Estimated Parameter Parameter value Est. Std. Error %

γ (L / mol min) 0.331 4.5

Ea (J / mol) 53200 4.8

β (mol / L) 0.2 24.9

Intrinsic kinetics - Model fit

0

0.05

0.1

0.15

0.2

0 25 50 75 100Time (min)

Fe

3+ (

mo

l/L)

0.5:1

0.9:1

1.1:1

1.6:1

T = 85°C

The effect of the ratio sphalerite : FeIII on the kinetics

Intrinsic kinetics - Model fit

0

0.05

0.1

0.15

0.2

0 25 50 75 100 125 150Time (min)

Fe

3+ (

mo

l/L)

75°C

85°C

95°C

Temperature effect on the kinetics.

Mass transfer limitations in Batch reactor

0 rAAN is

Li

where ri=νir The mass transfer term (NLis) is described by Fick’s law

*

**)(

21

i

iiiiLi c

ckcck

The solution becomes

1'')1'(4)1'(

'2/*

2

ii cc

*

*21

FeIII

FeIII

c

ckr

β’=β/ci, γ’=(-νik1ci/kLi), y=ci*/ci

Liquid-solid mass transfer coefficient

General correlation

3/12/1Re ScbaSh

iLi DdkSh /

3/1

3

4

Re

d

iDSc /

3/16/1

3

4

i

iLi D

dba

d

Dk

3/16/1

3

3/440

3/10 i

iLi D

zdba

zd

Dk

where z=cZnS/c0ZnS. The index (i) refers to Fe(III) and Fe(II)

Correlations in rate equation

9/23/1

0

'2 zbzd

Dk i

Li b’=b(ε d04/ υ 3)1/6(υ/Di)1/3

IF b’z2/9 >> 2 under stirring,

9/19/10

'''

z

b

zd

bDk i

Li γ’=-νFeIII x0ZnS γ cFeIIIz1/9/(σMb’’FeIII)

))/(/( 3/26/13/1

00 FeIIIZnS DMbdx

9/10 )/(

'ZnSZnS

FeIIIFeIII

cc

c

The surface concentration:

FeIIIFeIIIFeIII

FeIIIFeIII

ccc

cc

)1'(4)(

2*

2

The rate:

*

*'

2

FeIII

FeIIIZnS

c

ccr

Determination of mass transfer parameter (ω)

Agitation rate & US effect ω (mol min / m3)

200 rpm 50

350 rpm 14

500 rpm 2.4

350 rpm US 0 W 14

350 rpm US 60 W 6.8

350 rpm US 120 W 5.8

350 rpm US 180 W 1.67

Modelling of kinetics and mass transfer

0

0.05

0.1

0.15

0.2

0 25 50 75 100 125 150Time (min)

Fe

3+ (

mo

l/L)

200 rpm

350 rpm

500 rpm

External mass transfer limitations – modelling of individual mass transfer parameters at different agitation rates.

Modelling of kinetics and mass transfer

0

0.05

0.1

0.15

0.2

0 25 50 75 100 125 150

Time (min)

Fe

3+ (m

ol/L

)

0 W

60 W

120 W

180 W

External mass transfer limitations – modelling of individual mass transfer parameters at different ultrasound inputs.

Mass transfer parameter

0

10

20

30

40

50

60

150 200 250 300 350 400 450 500 550

rpm (1/min)

ω

0

2

4

6

8

10

12

14

16

0 50 100 150 200US (W)

ω

Normal agitation

Ultrasound

The real impact of mass transfer limitations

0

20

40

60

80

100

120

0 25 50 75 100 125 150

Time (min)

(Fe

3+su

rfac

e /

Fe

3+b

ulk

)*1

00

500 rpm

350 rpm

200 rpm

The difference in the model based surface concentrations and measured bulk concentrations of Fe3+ at different stirring rates.

The real impact of mass transfer limitations

0

20

40

60

80

100

120

0 25 50 75 100 125 150Time (min)

(Fe

3+su

rfac

e /

Fe

3+b

ulk

)*1

00

180 W

60 W

0 W

The difference in the model based surface concentrations and measured bulk concentrations of Fe3+ at different ultrasound inputs.

Conclusions

A new kinetic model was proposed

A general treatment of smooth, rough and porous surfaces was developed

The theory of mass transfer was implemented in the model

Model parameters were estimated

The model works

Modelling and simulation of porous, reactive particles in

liquids: delignification of wood

Tapio Salmi, Johan Wärnå, J.-P. Mikkola, Mats Rönnholm

Åbo Akademi Process Chemistry Centre,

Laboratory of Industrial ChemistryFIN-20500 Turku / Åbo Finland,

[email protected]

Typical view of Finland

338000 km2 of which 70% forest

Papermaking

Wood chipsThis is where paper

making begins. A typical wood chip

measures 40 x 25 x 10 mm.

Wood

Each chip comprises water, cellulose wood fibres and the binding agent lignin.

.

Pulp

To make paper, we need to first make pulp, which is the process of breaking the wood structure down into individual fibers

DigesterChips

Reactions

The reactions in chemical pulping are numerous. Typical pulping chemicals are NaOH and NaHS

cellulose

Overall process:

Lignin+Cellulose+Carbohydrates+Xylanes+OH+HS -> Dissolved components

Part of Ligninmolecule

Kinetic modelling of wood delignification

Purdue model (Smith et.al. (1974) Christensen et al. 1983), 5 pseudocomponents

Gustafson et al. 1983, 2 wood components Lignin and Carbohydrate, 3 stages

Andersson 2003, 15 pseudocomponents

Very few models available!

Wood chip structure

Wood material is built up of fibres

We can expect different diffusion rates in the fibre direction and in the opposite direction to the fibres.

Existing models

The existing models for delignification of wood consider a 1 dimensional case with equal diffusion rates in all directions

Is a 2- or 3-dimensional model needed ?

Characteristics of our model

Time dependent dynamic modelComplex reaction network includedMass transfer via diffusion in different

directionsStructural changes of the wood chip

includedAll wood chips of equal sizePerfectly mixed batch reactor assumed

Mathematical model,volume element

3D –model for a wood chip

x

yz

xy

z

dt

dn+AN+AN+AN

ΔVr+AN+AN+AN

i

outxyizoutxziyoutyzix

'ixyizxziyyzix =

ininin

Mass balance for a wood chip

tr

dz

cdε+

dy

cdε+

dx

cdε

t

D

dt

dc

p

ii'z

i'y

i'x

p

ii

'

2

2

2

2

2

2

3 '''zyxp t

px

xx

'

Porosity

Boundary conditions

The concentrations outside the wood chip are locally known

ci=cLi

at the centre of the chip (symmetry)

dci/dx=dci/dy=dci/dz=0

Reactor model

Lx=x

ii

'xix dx

dcDε=N

ixyizxziyyxixLi r+aN+aN+aN=

dt

dc

Ly=y

ii

'yix dy

dcDε=N

Lz=z

ii

'ziz dz

dcDε=N

Fluxes from wood chip

Batch reactor model, ideal flow

Structural changes of the wood chip

Generally one can state that the porosity of the chip increases during the process, since lignin and hemicelluloses are dissolved

p 0 p 0 p 1 1 l

'l

l

l

lll c

c=

c

cc=η

00

0 1

Change of porosity as a functionof the lignin conversion

Kinetic models

)()()( 0"' CCHSOHkOHk

dt

dC baii

Purdue model (Christensen et al), 5 wood pseudocomponents

iHSOHi Wkcckr 21

Andersson model, 12 wood pseudocomponents

Gustafsson model, 2 wood components, 3 stagesInitial stage, >22% Lignin, Bulk stage , 22% > Lignin > 2%Residual stage < 2% Lignin

LeTdt

dL T 69.4807

5.02.36

dt

dLOH

dt

dC 11.053.2

LSOHeOHedt

dL TT

4.05.014400

23.2917200

19.35

LOHedt

dL T 7.0

1080464.19

Diffusion models

Del 373.15( ) 2.13 109

m2

s

380 400 420 440 4600

1 108

2 108

3 108

McKibbinsWilke-ChangNernst-Haskell

Temperature [K]

Dif

fusi

vity

[m

^2/s

]

6.0

12104.7

AB

BAB

V

TMD

zz

zzTDo

00

001410931.8

TOHNaOH eTD

9872.1

48708

, 10667.52

McKibbins

Wilke-Chang

Nernst-Haskel (infinite dillution)

Kappa number

5500

CHL

L

The progress of delignification is by pulp professionals described by the Kappa number

L = Lignin on wood, CH = Carbohydrates on wood

Numerical approach

Discretizing the partial differential equations (PDEs) with respect to the spatial coordinates (x, y, z).

Central finite difference formulae were used to approximate the spatial derivatives

Thus the PDEs were transformed to ordinary differential equations (ODEs) with respect to the reaction time with the use of the powerful finite difference method.

The created ODEs were solved with the backward difference method with the software LSODES

Simulation results, profiles inside wood chip

0

5

10

15 0

5

10

15

0.5

0.51

0.52

0.53

0.54

0.55

y

Porosity y

x

centre

0

5

10

15

0

5

10

1517

17.5

18

18.5

19

x

L1

y

centre

0

5

10

15

0

5

10

1576

78

80

82

84

86

x

Kappa

y

centre

Lignin content

Porosity

Kappa value

T=170 ºCC0,NaOH=0.5 mol/l

The impact of 2-D model

Red line, different diffusion rates in x and y directionsBlue line, same diffusion rates in x and y direction(Andersson kinetic model)

0 2 4 6 8 10 1217

17.2

17.4

17.6

17.8

18

18.2

18.4

18.6

18.8

19

x-node

Lign

in (

w%

)

0 2 4 6 8 10 1217.8

18

18.2

18.4

18.6

18.8

19

y-node

Lign

in (

w%

)

surface centre surface centre

y

x

Content of lignin on wood as a function of reaction time

Lignin concentration (w-%) in wood chip as a function of reaction time (min) with Andersson kinetic model (left) and Purdue kinetic model (right).

Simulation software

2-D model for a wood chip in a batch reactorDifferent kinetic and diffusion models availableStructural change model included (porosity)Dynamic model

all results can be presented as a function of reaction time

Temperature and alkali concentrationprofiles can be programmed as a function of reaction time

Conclusions

A general dynamic model and software for the description of wood delignification

Solved numerically for example cases, which concerned delignification of wood chips in perfectly backmixed batch reactors.

Structural changes and anisotropies of wood chips are included in the model.

The software utilizes standard stiff ODE solvers combined with a discretization algorithm for parabolic partial differential equations.

Example simulations indicated that the selected approach is fruitful, and the software can be extended to continuous delignification processes with more complicated flow patterns.

catalytic three-phase reactors gas, liquid and solid catalyst

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