ekc337: reactor design & analysis core course for b.eng

EKC337: REACTOR DESIGN & ANALYSISCore Course for

B.Eng.(Chemical Engineering)Semester II (2009/2010)

Mohamad Hekarl Uzir, DIC.,MSc.,PhD.([email protected])

School of Chemical Engineering

Engineering Campus, Universiti Sains Malaysia

Seri Ampangan, 14300 Nibong Tebal, Seberang Perai Selatan, PenangEKC314-SCE – p. 1/164

Syllabus

1. External Diffusion:External diffusion effectsMass Transfer CoefficientDiffusion with chemical reaction

2. Internal Diffusion:Internal diffusion effectsEffective diffusivity

Diffusion and chemical reaction in a cylindrical pore

Thiele Modulus, φ and effectiveness factor, η

Falsified kinetics

EKC314-SCE – p. 2/164

Syllabus

3. Bioreactor Analysis and Operation:

Mixing and transfer of masses: Oxygen transfer andKla

Bioreactor kinetics: substrate consumption,biomass production, product formation and kineticsmodelsDesign of bioreactors

Role of transport processes in bioreactor design

EKC314-SCE – p. 3/164

Syllabus

4. Design of Multiple-Phase Reactors

Gas-liquid-solid reaction

Trickle-bed reactorSlurry reactor

Three-phase fluidised-bed reactors

5. Projects on COMPUTER APPLICATIONS (MATLABr)in REACTOR DESIGN

EKC314-SCE – p. 4/164

External & Internal Diffusion

1. Diffusion FundamentalsConsider a tubular-typed reactor, where the molarflow rate of reaction mixture in the z-direction isgiven by;

FAz= AcWAz

where WAzis the flux and Ac is the cross-sectional

area.Diffusion–spontaneous mixing of atoms ormolecules by random thermal motion which givesrise to the motion of the species relative to themotion of the mixture.

EKC314-SCE – p. 5/164


CA,b

CA,s

CA(r)

External

diffusion

Internal

diffusion

Porous catalyst

pellet

External

surface

EKC314-SCE – p. 6/164


1. Diffusion FundamentalsMolecules of a given species within a single phasewill diffuse from regions of higher concentrations toregions of lower concentrations (this gives aconcentration gradient per unit area between the 2regions).

External mass transfer:(a) Consider a non-porous particle where the entire

surface is uniformly accessible.(b) The average flux of reactant, CA to the fluid-solid

interface can be written as;

NA = kA(CA,b − CA)

EKC314-SCE – p. 7/164


1. Diffusion FundamentalsExternal mass transfer:

(b) where CA,b is the bulk concentration of reactant Aand CA is the concentration at the solid-liquidinterface and kA is the mass-transfer coefficient.

(c) let the reaction rate, rA follows first order reaction;

rA = kCA

where k is the first order rate constant. Therefore,at steady-state;

kCA = kA(CA,b − CA)

EKC314-SCE – p. 8/164


1. Diffusion FundamentalsExternal mass transfer:

(d) defining the dimensionless parameters;

x =CA

CA,b

Da =k

kA

thus;

Da =1− x

x

(e) where Da is defined as the ratio of reaction ratewith the convective/diffusive mass transfer rate.

EKC314-SCE – p. 9/164

Heterogeneous Reaction

Introduction to Heterogeneous and Multiphase Reactions

For pseudo-homogeneous assumption:Mass and heat transfer resistances betweendifferent phases are neglected–the reactor contentscan be treated as a single phase.Useful for preliminary design–truly homogeneoussystem.

For heterogeneous model –used when temperatureand concentration need to be distinguished betweenthe phases.

EKC314-SCE – p. 10/164



For real reactor : (multiphases–Multi-Phase Reactors)Should be heterogeneous typeNormally used for systems involving fluid-fluidinteractions [liquid-liquid or gas-liquid]

EKC314-SCE – p. 11/164



For solid state:solid as porous catalyst pellet:

1. not being consumed during reaction BUTchanges in physical & chemical states

2. pore blocking due to deposits of carbonaceousby-products [coking]

3. metal particles [active catalyst]–coalesce at hightemperature–therefore reduce surface area forreaction hence reducing rate constant [sintering]

EKC314-SCE – p. 12/164



For solid state:solid as non-catalyst:

1. dissolution of solid through reaction with fluid2. burning off coke in catalyst pellet for its

regeneration3. most common utilisation of solid catalyst in

fixed-bed catalytic reactor -FBCR4. it is a turbular reactor packed with catalyst

through which the fluid species flow

EKC314-SCE – p. 13/164



For solid state:Advantages of FBCR:

1. no solids handling2. little solids attribution3. high surface area through use of porous catalyst4. plug flow operation can be achieved5. no separation of catalyst from reaction products

needed

EKC314-SCE – p. 14/164



For solid state:Disadvantages of FBCR:

1. pressure drop2. complex arrangement (e.g. multitubular) for

reactions requiring high heat-exchange duties3. large down-time for catalyst which deactivate

rapidly

EKC314-SCE – p. 15/164


Interfacial gradient effects: Reaction at catalyst surface

CA

CsAs

CAs

Boundary layer Active centres

Concentration within the catalyst

Concentration at thecatalyst surface

Transfer flux

Bulk concentration

NA

z

FLUID SOLID0EKC314-SCE – p. 16/164

Transport Processes inHeterogeneous Catalysis

Interfacial gradient effects

For first order reaction:reaction rate at the catalyst surface:

rsAs = ksCsAs (1)

where ks is the rate constant at the catalyst surfaceand Cs

As is the concentration at the active surface atz = 0

at steady-state:

rsAs = NA = rA (2)

whereNA = kmc(CA − Cs

As) (3)EKC314-SCE – p. 17/164



For first order reaction:the mass-transfer coefficient can also be expressedin terms of mole fraction & pressure:

kmy =NA

(yA − ysAs)

and

kmp =NA

(pA − psAs)

and kmc = kmp = kmy

EKC314-SCE – p. 18/164



For first order reaction:substitute (3) into (1):

NA = ksCsAs

ksCsAs = kmc(CA − Cs

As)

CsAs =

kmcCA

ks + kmc

(4)

EKC314-SCE – p. 19/164



For first order reaction:substitute into (1) and upon rearrangement gives;

1

ko=

1

kmc

+1

ks(5)

where ko is the overall rate constant.Limiting cases :

1. kmc >> ks [rapid mass transfer]

ko ∼ ks

andCs

As ∼ CAEKC314-SCE – p. 20/164



For first order reaction:Limiting cases :

2. ks >> kmc [rapid reaction]

ko ∼ kmc

andCs

As ∼ 0

EKC314-SCE – p. 21/164



For Second order reaction:the rate of reaction is expressed by;

rsAs = ksCsAs

2 (6)

at steady-state;

ksCsAs

2 = kmc(CA − CAs)2

ksCsAs

2 + 2kmcCACsAs − kmcC

sAs

2 = kmcC2A

EKC314-SCE – p. 22/164



For Second order reaction:Limiting cases :

1. kmc >> ks:

rA ∼ ksC2A

[second order dependent ] overall is reactionrate controlled

2. ks >> kmc:

rA ∼ kmcCA

[first order dependent ] overall is diffusioncontrolled regime

EKC314-SCE – p. 23/164



For Complex reactions (analytical SOLUTION notusually possible):

mass-transfer can lead to difficulties inexperimentally determining rate coefficient & orderscan work under conditions:

1. reaction controlled:

kmc >> ks

[reduce TEMPERATURE (lower rate), increasefluid turbulence]

EKC314-SCE – p. 24/164



For Complex reactions (analytical SOLUTION notusually possible):

can work under conditions:2. diffusion controlled:

ks >> kmc

[increase temperature]

EKC314-SCE – p. 25/164



Determining the km value:usually defined as the mass-transfer coefficient ofequimolar counter diffusion, k◦

m

relationship between k◦

m and km1. Equimolar counter diffusion:

NA = −NB

the total mass flux of component A:

NA = NTyA + CDAB

dyAdz

(7)

EKC314-SCE – p. 26/164



Determining the km value:relationship between k◦

m and km1. since

NT = NA +NB = 0

thus

NA = CDAB

dyAdz

(8)

EKC314-SCE – p. 27/164




m and km1. upon integration of this leads to;

NA =CDAB

l(yA − ysAs) (9)

since

k◦

my =CDAB

l

and for equimolar counter diffusion;

k◦

my = kmy

EKC314-SCE – p. 28/164




my and kmy

1. which then gives;

kmc =kmy

C=

DAB

l(10)

2. For reaction in which total moles are notconserved

aA⇋ bB

EKC314-SCE – p. 29/164




my and kmy

2. which gives;

NB = − b

aNA (11)

substitute into Equation (7) leads to;

NAl = CDAB

a

bln

yAysAs

(12)

EKC314-SCE – p. 30/164




my and kmy

2. for NA = kmy(yA − ysAs) where

kmy =k◦

my

yfA

and

yfA =(1 + δAyA)− (1 + δAy

sAs)

ln(

1+δAyA1+δAys

As

)

where δA = (b−a)a

EKC314-SCE – p. 31/164




my and kmy

2. for general equation of the form;

aA + bB + . . .⇋ qQ + rR + . . .

therefore;

δA =(q + r + . . .)− (a+ b+ . . .)

a

forδA −→ 0, yfA −→ 1

EKC314-SCE – p. 32/164




my and kmy

2. thus; kmy = k◦

my

the j-factor:1. jD-factor:

defined as;

jD =k◦

mMm

GSc

23

k◦

m can be taken as k◦

my/k◦

mp, as long as;

k◦

m = kmyyfA = kmpPyfA = kmpPfA

EKC314-SCE – p. 33/164



the j-factor:1. for a flow in a packed-bed with spherical particles

and εb = 0.37;

jD = 1.66Re−0.51, for Re < 190

jD = 0.983Re−0.41, for Re > 190

2. jH-factor:defined as;

jH =hf

CpGPr

23

EKC314-SCE – p. 34/164



Concentration partial pressure differences acrossexternal film:1. if ∆CA/∆PA ∼ 0 that is (yA ∼ 0) where the mass

transfer is very fast, therefore, rA can be expressedas function of bulk CA or PA

rA = rsAs = ksCA

since CA ∼ CsAs

2. using differential definition of rA, thus;

r′A

(

mol

kgcat · s

)

EKC314-SCE – p. 35/164



Concentration partial pressure differences acrossexternal film:2. with the correction factor for area, am given by;

r′A = kmcam(CA − CsAs) (13)

but in terms of concentration (mole fraction);

r′A = amkmy(∆yA)

and upon rearrangement gives;

kmy =k◦

m

yfAEKC314-SCE – p. 36/164



Temperature differences across the external film:1. taking energy balance at steady-state;

r′A(−∆Hr) = hfam(Tss − T ) (14)

but it is known that, r′A = kmyam∆yA uponsubstitution gives;

∆T = −∆Hr

(

jDjH

)(

Pr

Sc

)23(

∆yAyfA

)(

1

MmCp

)

(15)

∆T increases with the increase of ∆yA. → whenmass-transfer resistances is HIGH.

EKC314-SCE – p. 37/164



Temperature differences across the external film:1. for gaseous flow in a packed-beds;

∆T ≈ 0.7

[

− ∆Hr

Mmcp

]

∆yAyfA

(16)

for maximum ∆T → ∆T |max occurs when ysAs = 0(for irreversible reaction)and for reversible reaction,

ysAs = yAequilibriumand yfA =

δAyAln (1 + δAyA)

EKC314-SCE – p. 38/164



Temperature differences across the external film:1. for maximum temperature difference, substitute the

above terms into Equation (17) then, ∆T |max gives;

∆T |max = 0.7

[

− ∆Hr

Mmcp

]

ln (1 + δAyA)

δA(17)

EKC314-SCE – p. 39/164


Mass Transfer on Metallic Surfaces:

for a packed bed, concentration gradient, ∆C variationis SMALL–usually negligible

mass transfer may be significant when catalyst is aMETALLIC SURFACE1. catalyst monolith/honeycomb–[e.g. catalytic

converter]2. wire gauze–[oxidation of NH3]

advantages of this unit:1. LOW ∆P (due to porous structure)2. particulate in feed (NO clog-up bed)

EKC314-SCE – p. 40/164


Intra-Particle Gradient Effects:

Catalyst internal structure:reaction rate α catalyst surface areaarea range : 10 – 200 m2/g

activated carbon : 800 m2/g

sand : 0.01 m2/g

EKC314-SCE – p. 41/164



Catalyst internal structure:high areas through highly porous structure give highsurface area to volume ratiopore sizes are not uniform–pore sizes distributionexistspore size classifications:

1. Micropores: dpore < 0.3nm2. Mesopores: 0.3nm < dpore < 20nm3. Macropores: dpore > 20nm

IN CALCULATION → use MEAN PORE SIZE!!some catalysts–have bimodal distribution of poresizes ZEOLITE CATALYST

EKC314-SCE – p. 42/164



Catalyst internal structure:non-ZEOLITE catalystsactive metal dispersedand supported within a macroporous support matrixsuch as SILICA and ALUMINAFURTHER COMPLICATION: DIFFUSION RATEAND MECHANISMS VARY WITH PORE SIZE!

Pore diffusion:for a gas diffusion through a single cylindrical pore⇒ ratio of dpore to mean free path, λthe ratio determines whether OR not pore wallaffects the diffusion behaviour

EKC314-SCE – p. 43/164



λ dpore

where λ is the distance between the two molecules of gasfor collision.

for dpore >> λ:1. molecular diffusion dominates–Fickian Diffusion2. for example; gases at HIGH pressure or liquids

EKC314-SCE – p. 44/164



for dpore << λ and dmolecule < λ:1. molecular interaction with pore wall dominates2. diffusion described by Knudsen’s Law of Diffusion3. for example; gases at LOW pressure but NOT

liquids (molecular structure of liquid is too high)

for dpore << λ and dmolecule ≃ λ:1. complex interaction of diffusing molecules with

force-fields of molecules making up the wall2. referred to Configurational Diffusion OR activated

diffusion3. very difficult to predict

EKC314-SCE – p. 45/164



for dpore << λ and dmolecule ≃ λ:4. for example:

(a) large hydrocarbon molecules [petroleumdesulphurisation]

(b) pores of VERY SMALL size [zeolite crystals andbiological cell walls]

EKC314-SCE – p. 46/164



dpore

when dpore << λ and dmolecule < λ:

dpore

when dpore << λ and dmolecule ≃ λ:

EKC314-SCE – p. 47/164


Correlations for Diffusion Coefficient:

For binary molecular diffusion; (for gases)

Dmi,kα

T32

P

Diffusion coefficient for the key component through amixture of the other components, Dmi,m

Ni = yi

Nc∑

k=1

Nk − CDmi,m

dyidz

EKC314-SCE – p. 48/164



With the Stefan-Maxwell equation for diffusion, Dmi,m

can be calculated from the actual binary diffusion datausing;

1

Dmi,m

=

∑Nc

k=11

Dmi,k

(yk − yivkvi)

1− yi∑Nc

k=1vkvi

where v is the stoichiometric coefficient.

The Knudsen diffusion coefficient, DK can becalculated using;

Dki α

(

T

Mmi

)12

· dporeEKC314-SCE – p. 49/164



AndDki 6= f(P )

when P ↑: transport regime can switch fromKnudsen to molecular diffusion.

Micropore diffusion coefficient – difficult to predict –and always relies on experimental measurement

For NON-zeolite catalysts – molecular & Knudsendiffusion dominate and the pore diffusion coefficient,Dp is a function of Dm and Dk

EKC314-SCE – p. 50/164



Where Dp ⇒ the pore diffusion coefficient for a singlepore

→ dporeλ

> 20

(molecular diffusion controlling) thus,

Dp = Dm

→ dporeλ

< 0.2

(Knudsen diffusion controlling) thus,

Dp = DkEKC314-SCE – p. 51/164



For intermediate values, both diffusion types areimportant.

Use the Bosanquet Equation to estimate Dp where;

1

Dp

=1

Dk

+1

Dm

EKC314-SCE – p. 52/164



If given Dp, the approximation of Deff is given by;

Deff =εDp

τp

where Deff is the effective diffusion coefficient, εp is theintraparticle void fraction and τp is the tortuosity factor.

EKC314-SCE – p. 53/164



Comparing diffusion in a single pore, (a) & diffusion ina porous pellet, (b):

ANA = -Dp dCA/dz

CA,1z CA,2

tortuous path

(a) (b)

EKC314-SCE – p. 54/164



The cross-sectional area available for diffusion = Aεp,thus, lower NA.

Tortuous molecules path and changing porecross-sectional area due to constrictions, thus dCA

dzis

reduced.

Therefore;

NA = −εDp

τp

dCA

dz

For zeolite;τp = 3 ∼ 10

EKC314-SCE – p. 55/164



NOTE:

τp =tortuosity

constriction factor

where;

tortuosity =actual diffusion path length

shortest radial pellet length

If Deff is given, then the combined diffusion & reactionwithin a catalyst pellet can be considered.

Reaction at the surface–diffusion & reaction take placesimultaneously rather than consecutively.

EKC314-SCE – p. 56/164


Diffusion and Reaction within a Catalyst Pellet:

Concentration profile for porous catalyst pellet:

Concentration

Position

significant external mass

transfer

negligible external mass

transfer

central axis of pellet

CA

TA

LY

ST

external

film

CsA,s

CA

bulk concentration

concentration

on the surface

CA,s concentration

within the catalyst

0rpr

EKC314-SCE – p. 57/164



The rate of reaction is measured under conditionswhere external and internal mass-transfer resistancesare negligible; ⇒ r∗A [use small particle!]

When mass-transfer is important;

CA > CAs

1. CANNOT use bulk concentration to calculate theactual (observed ) reaction rate.

2. NEED to relate rA to r∗A using the EffectivenessFactor :

η =rAr∗A

EKC314-SCE – p. 58/164



η < 1 for ISOTHERMAL or ENDOTHERMIC reaction.

η is useful for DESIGN CALCULATION

For rigorous calculations, particularly for COMPLEXREACTION KINETICS and NON-ISOTHERMALoperation, BETTER to solve the simultaneousequations governing diffusion and reaction.

EKC314-SCE – p. 59/164



For packed-bed–external film mass-transferresistances ⇒ SMALL

ASSUME: situation depicted by the solid line inprevious graphr∗A is the reaction rate measured if all of the pelletsgive concentration of Cs

As, thus;

r∗A = rAs[CsAs] = rsAs

andη =

rArsAs

EKC314-SCE – p. 60/164



Pseudo-First Order Reaction: [A → Product]consider material balance through the incrementalsection of a catalyst SLAB of area, a;

r = 0

r

r + ∆r

rp

∆r r

Incremental

section

NA

EKC314-SCE – p. 61/164



Pseudo-First Order Reaction: [A → Product]

IN−OUT = CONSUMPTION

(NA · a)|r+∆r − (NA · a)|r = rAsa∆r

dividing by a∆r and let lim∆r→0 gives;

dNA

dr= rAs = kvCAs

EKC314-SCE – p. 62/164



Pseudo-First Order Reaction: [A → Product]For no convective flow in pellet, Fick’s Law isobeyed;

NA = DeA

dCAs

dr

upon substitution gives;

DeA

d2CAs

dr2= kvCAs (18)

for constant DeA with respect to radius, r.

EKC314-SCE – p. 63/164



Pseudo-First Order Reaction: [A → Product]integrating Equation (18) using the followingboundary conditions;

r = rp : CAs = CsAs

r = 0 :dCAs

dr

gives;

CAs

CsAs

=cosh

(

r ·√

kvDeA

)

cosh(

rp ·√

kvDeA

) (19)

EKC314-SCE – p. 64/164



Pseudo-First Order Reaction: [A → Product]where Thiele Modulus can be defined as;

φslab = rp

√

kvDeA

EKC314-SCE – p. 65/164



Pseudo-First Order Reaction: [A → Product]

1.0

1.0 0.0

CA

s/C

sA

s

r/rp

φslab = 0

φslab = rp(kv/DeA)1/2

As φslab increases - the rate

constant becomes SMALLER

INCREASING

EKC314-SCE – p. 66/164



Pseudo-First Order Reaction: [A → Product]for spherical pellet, asphere = 4πr2

applying the same method as for SLAB; the finalequation leads to;

CAs

CsAs

=rpr

sinh(

r√

kvDeA

)

sinh(

rp√

kvDeA

) (20)

EKC314-SCE – p. 67/164



Pseudo-First Order Reaction: [A → Product]for cylindrical-shaped pellet, acylinder = 2πr(L+ r)

applying the same method as for SLAB; the ratiogives;

CAs

CsAs

=I1I0

r√

kvDeA

rp√

kvDeA

(21)

where I is the Bassel function given by;

In(r) = rn∞∑

m=0

(−1)mr2m

22m+nm!(n+m)!

EKC314-SCE – p. 68/164



Pseudo-First Order Reaction: [A → Product]GENERALLY;

1

rm

d

dr(rmNA) = rAs (22)

where;1. for SLAB; m = 02. for CYLINDER; m = 13. for SPHERE; m = 2

EKC314-SCE – p. 69/164



Effectiveness Factor , ηe (for First-order reaction)It is given by;

ηe =observed reaction rate

reaction rate at pellet surface conditions

⇒ ηe =rArAs

(23)

EKC314-SCE – p. 70/164



Effectiveness Factor , ηe (for First-order reaction)Isothermal and Endothermic reactions; rsAs gives amaximum reaction ratesince;

CsAs > CAs

AND[rsAs = kvC

sAs] ≥ [rA = kvCAs]

AND therefore;ηe ≤ 1

EKC314-SCE – p. 71/164



Effectiveness Factor , ηe (for First-order reaction)For a very HIGH diffusional resistances withincatalyst, NEGLIGIBLE penetration of reactant intopellet;

CAs = 0, rAs = 0, ηe = 0

thus, the range of ηe;

0 ≤ ηe ≤ 1

EKC314-SCE – p. 72/164



Effectiveness Factor , ηe (for First-order reaction)With the value of ηe, rA can be determined using;

rA = ηe · rsAs

⇒ rA = ηe(kvCsAs)

⇒ rA = ηe(kvCA)

NOTE: This is only for NEGLIGIBLE external filmmass transfer resistances!

EKC314-SCE – p. 73/164



Effectiveness Factor , ηe (for First-order reaction)FOR SLAB:The rate of reaction is given as;

rAs = kvCAs

substitute into the average rate of reaction gives rAwhich can be used to obtain ηeFinal solution for SLAB-type catalyst;

ηe =tanhφslab

φslab

(24)

EKC314-SCE – p. 74/164



Effectiveness Factor , ηe (for First-order reaction)FOR SLAB:NOTE:

φslab → 0, ηe → 1

φslab → ∞, ηe ∼1

φslab

EKC314-SCE – p. 75/164



Effectiveness Factor , ηe (for First-order reaction)FOR SPHERE:By applying Equation (20), the Effectiveness factorfor spherical shape is given by;

ηe =3

φsphere

{

1

tanhφsphere

− 1

φsphere

}

(25)

NOTE:φsphere → 0, ηe → 1

φsphere → ∞, ηe ∼3

φsphere

EKC314-SCE – p. 76/164



Effectiveness Factor , ηe (for First-order reaction)FOR CYLINDER:

ηe =I1(2φcylinder)

I0(2φcylinder)

1

φcylinder

(26)

NOTE:φcylinder → 0, ηe → 1

φcylinder → ∞, ηe ∼2

φcylinder

For a very SMALL φ, ηe will always converge toUNITY (1)!

EKC314-SCE – p. 77/164



The Effectiveness Factor for First Order Reaction:

η

φ10 20 30

1.0

cylinder

slab

sphere

EKC314-SCE – p. 78/164



Effectiveness Factor , ηe (for First-order reaction)The equations (ηe and φ) for sphere and cylinderare rather complexFrom the previous plot, the trend is similar only theline shift in the x-axisThiele Modulus can be redefined for any pelletgeometry such that ηe and φ curve coincide

EKC314-SCE – p. 79/164



Effectiveness Factor , ηe (for First-order reaction)Curve for sphere and cylinder coincide with slabcurve such that a relatively simple expressionreduces into;

ηe =tanhφ

φ

where φ is generally given by;

φ =Vp

Ap

√

kvDeA

(27)

EKC314-SCE – p. 80/164



Effectiveness Factor , ηe (General Order Reactions)For general order & reversible reactions;

φ =Vp

Ap

rsAs√2

{

∫ CsAs

C∗

As

DeArAsdCAs

}−12

(28)

where C∗

As is the equimolar concentration of thelimiting reactant (= 0 for an irreversible reaction)The above equation accounts for DeA varies withCAs

EKC314-SCE – p. 81/164



Effectiveness Factor , ηe (General Order Reactions)It also assumes HIGH differential resistances suchthat within the region of ηe ∼ 1

φ

ELSE, C∗

As in the above equation needs to becalculated using;

rp =

∫ CsAs

C∗

As

DeAdCAs[

2∫ C′

A

C∗

As

DeArAsdC ′

A

] (29)

EKC314-SCE – p. 82/164



Criteria for Intraparticle Diffusional Limitations:For known reaction kinetics ⇒ ηe can be calculated(ηe < 1 indicates diffusional limitation)The Weisz-Prater Criteria :Using;

φ =Vp

Ap

√

kvDeA

EKC314-SCE – p. 83/164



Criteria for Intraparticle Diffusional Limitations:upon rearrangement gives;

φ2

(

Ap

Vp

)2

DeA = kv

for First-order reaction;

rA = ηersAs = ηkvC

sAs

EKC314-SCE – p. 84/164



Criteria for Intraparticle Diffusional Limitations:eliminating kv gives;

Φ =rA

DeACsAs

(

Vp

Ap

)2

= ηeφ2 (30)

Φ is the Weisz-Prater ParameterCs

As ∼ CA under typical conditions.

EKC314-SCE – p. 85/164



Criteria for Intraparticle Diffusional Limitations:The RHS of Equation (30) is measurable, then;

1. NEGLIGIBLE diffusional limitations; when;

φ ≪ 1, ηe ∼ 1

therefore;Φ ≪ 1

EKC314-SCE – p. 86/164



Criteria for Intraparticle Diffusional Limitations:The RHS of Equation (30) is measurable, then;

2. CONSIDERABLE diffusional limitations; when;

φ ≫ 1, ηe ∼1

φ

therefore;Φ ≫ 1

The above method can be generalised to anyreaction scheme where appropriate for the ThieleModulus .

EKC314-SCE – p. 87/164


Temperature Gradient Within Catalyst Pellet:

Temperature gradient, ∆T can be calculated byconsidering simultaneously the intraparticle mass andenergy balances.

For spherical pellet; the mass balance is given by;

1

r2DeA

d

dr

(

r2dCAs

dr

)

= rAs

similarly for energy balance;

1

r2λe

d

dr

(

r2dTs

dr

)

= rAs ·∆Hr (31)

EKC314-SCE – p. 88/164



Equation (31) is known as Fourier’s Law where λe isthe effective thermal conductivity of the pellet.

By eliminating rAs and integrating twice leads to;

∆Ts = (Ts − T ss ) =

∆HrDeA

λe

(CAs − CsAs) (32)

For irreversible reaction, ∆Ts is maximum whenCAs = 0 (OR C∗

As for an equimolar reversible reaction)thus;

∆Ts|max =−∆HrDeA

λe

CsAs (33)

EKC314-SCE – p. 89/164



Equation (33) is applicable to all pellet catalystgeometries.

For many industrial applications;

∆Ts|max

T ss

< 0.1

that is for small ∆Ts, ∆T (external film) can be large.

EXCEPT for HIGHLY exothermic reactions such assome oxidation and hydrogenation reactions.

The effect of ∆Ts on ηe is complex since, it willinfluence DeA as well as kv.

EKC314-SCE – p. 90/164



Consider the First-order non-isothermal reaction on apellet; the mass balance is given by;

1

r2DeA

d

dr

(

r2dCAs

dr

)

= rAs

andrAs = kvCAs

where

kv = A0e

(

−E

RT0

)

EKC314-SCE – p. 91/164



Upon substitution gives;

1

r2DeA

d

dr

(

r2dCAs

dr

)

= A0e

(

−E

RT0

)

CAs

putting into dimensionless form leads to;

d2C

dr2= φ′Ceγ(1−T )

where

C =CAs

CsAs

T =Ts

T ss

r =r

rpEKC314-SCE – p. 92/164



and both φ′ and γ is defined as;

φ′ =r2pA0e

−γ

DeA

and

γ =E

RT ss

EKC314-SCE – p. 93/164



Similarly, for energy balance;

d2T

dr2= −βφ′2Ceγ(1−T )

where

β =(∆Ts)max

T ss

=−∆HrDeAC

sAs

λeT ss

EKC314-SCE – p. 94/164



β < 0:

β = 0:

β > 0: Exothermic

Isothermal

Endothermic

φ’

η

1.0

0.0010.1

EKC314-SCE – p. 95/164


Combined Interfacial [External] and Intraparticle [Internal]Resistances:

In the solution of intraparticle diffusional equation, CsAs

was assumed known;

CsAs = CA

and it remains constant.

When the external-film resistances are important, theBOUNDARY CONDITIONS for the solution of theintraparticle diffusion equation become;

r = rp : kmc(CA − CsAs) = DeA

∣

∣

∣

∣

dCAs

dr

∣

∣

∣

∣

rp

EKC314-SCE – p. 96/164



and;

r = 0 :

∣

∣

∣

∣

dCAs

dr

∣

∣

∣

∣

0

= 0

For slab pellet with a First-order reaction, the solutionwith the above boundary conditions gives;

CAs =CA cosh φr

rp

coshφ+DeA

φ

rpkmcsinhφ

EKC314-SCE – p. 97/164



Therefore, the Global Effectiveness Factor can bedefined as;

ηG =rate observed

rate at bulk fluid concentration

ηG =rA

rAsCA

EKC314-SCE – p. 98/164



Which then gives;

1

ηG=

1

η+

φ2

Bim(34)

where Bim is Biot number for mass-transfer given by;

Bim =kmcrpDeA

For Bim ≫ 1.0, ηG = ηe.

EKC314-SCE – p. 99/164



For the region of strong intraparticle diffusionallimitations, where;

φ → ∞and

ηe =1

φ

thus,1

ηG= φ+

φ2

Bim(35)

EKC314-SCE – p. 100/164

Fixed-Bed Catalytic Reactor Design

Describing the homogeneous models and modelsaccounting for interfacial and intrafacial gradientsusing;1. Effectiveness factor2. Actual pellet phase mass and energy balances

PLUG-FLOW REACTOR (PFR) model:the simplest PFR model is given by;

dni

dV= −ri = −r′iρb =

vi|vA|

r′Aρb (36)

EKC314-SCE – p. 101/164


PLUG-FLOW REACTOR (PFR) model:when ni = uaCi and dV = adz, thus, the equationreduces into;

d

dz(uCi) = −r′iρb =

vi|vA|

r′Aρb (37)

since u 6= constant, therefore momentum equationis required.

EKC314-SCE – p. 102/164


PLUG-FLOW REACTOR (PFR) model:Using the Ergun equation of the form;

dp

dz= −E1u− E2u

2 (38)

to find the pressure along the bed, where;

E1 =180µ(1− εb)

2

d2pε3b

and

E2 =1.8(1− εb)ρgMm

dpε3b

EKC314-SCE – p. 103/164


PLUG-FLOW REACTOR (PFR) model:If the flow is highly TURBULENT, E1 can beneglected.If the flow is LAMINAR, E2 can be omitted.While for a perfect gas;

∑

i

Ci =P

RT= ρg

For non-isothermal operation, energy balance isrequired to describe T–z variation

EKC314-SCE – p. 104/164


PLUG-FLOW REACTOR (PFR) model:Energy balance across a fix-bed reactor is given as;

dT

dV= (

∑

i

nicpi) + ρbr′

A∆r −Qav = 0 (39)

whereQ = U(Tc − T ) (J/m2s)

and av is the surface area per unit reactor volume,(m1), therefore;

dT

dz= (U

∑

i

nicpi) + ρbr′

A∆r −Qav = 0 (40)

EKC314-SCE – p. 105/164


PLUG-FLOW REACTOR (PFR) model:where; U is the overall heat transfer coefficient,(J/m2s.K)and Tc is the temperature of cooling fluid (K)For no-separation of reactor species due to differentrates of axial dispersion OR intra-particle diffusion,Ci can be related to CA using the reactionstoichiometry;

(nAo− nA) → mol A reacted

thus;

ni = nio +νi|nA|

(nAo− nA)

EKC314-SCE – p. 106/164

Fluidised-Bed Reactors

These involve catalyst beds which are not packed inrigid but either suspended in fluid (for fluidised-bedreactor) or flowing with the fluid (transport reactor)

Fluidisation Principles (Overview):Downward flow in packed bed–no relativemovement between particles

1. ∆P α u for LAMINAR flow2. ∆P α u2 for TURBULENT flow

EKC314-SCE – p. 107/164


Fluidisation Principles (Overview):Upward flow through bed ⇒ ∆P is the same asdownward flow at LOW flow rate:

when frictional drag on particles become equal totheir apparent weight (actual weight LESSbuoyancy)–particle rearrange and offer LESSresistance to flow–results in bed EXPANSION.as u increases, process continues until bedassumes its “loosest” stable form of packing.

MINIMUM fluidisation velocity, umf–is the velocity ata point where fluidisation occurs!

EKC314-SCE – p. 108/164


Fluidisation Principles (Overview):When superficial velocity > umf ;

1. LIQUID fluidisation;bed continues to EXPAND with uit maintains a uniform characterand AGITATION of particleincreases–particulate fluidisation

EKC314-SCE – p. 109/164


Fluidisation Principles (Overview):When superficial velocity > umf ;

2. GAS fluidisation;gas bubble formation within a continuousphase consisting of fluidised solids.continuous phase refers to as thedense/emulsion phase–aggregation fluidisationat HIGH inlet flow rate: flow in emulsion phaseto particulate remains approx. constant butbubbles may be more rigorous.at HIGH inlet flow rate and a deepbed–bubbles coalesce forming slugs of gasthat occupy the entire cross-section of the bed.

EKC314-SCE – p. 110/164


Fluidisation Principles (Overview):An increase of bubbles within the bed gives ↑ V andthis lowers the transfer area.HIGH volume of bubbles also gives high residencetime.It behaves like fluid–hydrostatic forces aretransmitted and solid objects FLOAT when;densities of objects < density of bed

Intimate mixing and rapid heat transfer → easy tocontrol the TEMPERATURE (even for highlyEXOTHERMIC reaction)Type of fluidisation depends on [i] the particle sizeand [ii] relative density of the particles (ρs − ρg)

EKC314-SCE – p. 111/164


WHY Fluidisation?Can achieve a GOOD control of TEMPERATURECan work with VERY FINE particles for which

ηe ∼ 1

As catalyst improves–the rates of reactionINCREASE resulted form higher kv BUT;

φ =rp3

√

kvDeA

when fv ↑, the ONLY way to keep φ SMALL and ηeclose to 1 is to decrease rp

EKC314-SCE – p. 112/164


WHY Fluidisation?NOTE: an increase of kv will increase φ, therefore itwill be MASS TRANSFER controlling and NOTkinetics (reaction) the possible way is to REDUCErp

EKC314-SCE – p. 113/164


∆P versus uo for fluidised bed:

hysterisis due to

pressure differentblown out particles

(initiation of

particle entrainment)

log ∆P

log uo

umf

EKC314-SCE – p. 114/164


∆P versus uo for fluidised bed:NOTE:

1. LAMINAR FLOW:

∆P

L= −E1uo

→ log (∆P ) = C + log uo

2. TURBULENT FLOW:

∆P

L= −E2u

2o

→ log (∆P ) = C + 2 log uo

EKC314-SCE – p. 115/164


∆P versus uo for fluidised bed:Calculation of ∆P across fluidised bed: Consider adiagram below;

A

L

P1

P2

F1

F2

uo

uo = superficial velocity

at bed inlet

ut = terminal velocity

when pellet are

blown out of the

bed

EKC314-SCE – p. 116/164


∆P versus uo for fluidised bed:Resolving forces on the bed;

F1 = F2

P1A = P2A+ (ρs − ρg)(1− ε)ALg

(P1 − P2) = (ρs − ρg)(1− ε)Lg

−∆P = (ρs − ρg)(1− ε)Lg (41)

As P1 ↑, ∆P also ↑, and therefore, ↑ ε as the bedexpendsOR ↓ resistance as the gas by-pass throughbubbling and ∆P remains the same.

EKC314-SCE – p. 117/164


Calculation of the minimum fluidisation velocity, umf ;For LAMINAR flow;Using the previously defined Ergun equation[Equation (38)];

∆Pmf

Lmf

= −E1umf

⇒ umf =(1− εmf)(ρs − ρg)g

E1(42)

where

E1 =180µ(1− εmf)

2

d2p · ε3mf

EKC314-SCE – p. 118/164


Calculation of the minimum fluidisation velocity, umf ;For LAMINAR flow;Substitute into Equation (40) and simplify gives;

umf =1

180

ε3mf · d2p(1− εmf)

(ρs − ρg)g

µ(43)

For εmf ∼ 0.4 ⇒ the bed is packed with isometricparticles.

EKC314-SCE – p. 119/164


Calculation of the minimum fluidisation velocity, umf ;For TURBULENT flow [usually for coarse particles];Similarly, applying the Ergun equation ;

∆Pmf

Lmf

= −E1umf − E2u2mf = −(1− εmf)(ρs − ρg)g

and solving for umf explicitly gives;

Ga = 180(1− εmf)

ε3mf

Remf +1.75

ε3mf

Re2mf (44)

EKC314-SCE – p. 120/164


Calculation of the minimum fluidisation velocity, umf ;For TURBULENT flow [usually for coarse particles];where

Ga =ρg(ρs − ρg)gd

3p

µ2

is the Galileo’s Number and

Remf =ρgumfdp

µ

is the Reynold’s Number for minimum fluidisation.in reality, expect Darcy’s Law and Ergun equationto overestimate ∆Pmf .

EKC314-SCE – p. 121/164


Calculation of the minimum fluidisation velocity, umf ;For LAMINAR flow, many investigations haveshown that it is more accurate to use a value of 120rather than 180 in Equation (41).Equation (42) for TURBULENT flow DOES NOTaccount for;

1. Channeling of fluid2. Electrostatic forces between particles3. Agglomeration of particles4. Friction between fluid and vessel walls.

EKC314-SCE – p. 122/164


Calculation of turbulent velocity, ut;

Force exerted by flowing gas

mg

when the drag force exerted on a spherical particleby the upflowing gas, the gravitational force (basedon the apparent density) on the particle, then theparticle will be BLOWN OUT of the bed!

EKC314-SCE – p. 123/164


Calculation of turbulent velocity, ut;this can be shown by;

Fdrag = Vp(ρs − ρg)g

but (FROM FLUID FLOW NOTES);

Fdrag =1

2ρgu

2tCD · Ap

where CD is the drag coefficient. with Ap =πd2p4

thus;

Fdrag =πd2p8

· ρgu2t · CD

EKC314-SCE – p. 124/164


Calculation of turbulent velocity, ut;upon rearrangement gives;

ut =

√

4dp(ρs − ρg)g

3CDρg(45)

for spherical particles and Re < 0.4 where

Re =ρgutdp

µ

EKC314-SCE – p. 125/164


Calculation of turbulent velocity, ut;and the Drag coefficient is given by;

CD =24

Re

and Equation (43) reduces into Stoke’s Law of theform;

ut =(ρs − ρg)gd

2p

18µ(46)

EKC314-SCE – p. 126/164


Calculation of turbulent velocity, ut;for 1 < Re < 103;the Drag coefficient is given by;

lnCD = −5.50 +69.43

lnRe + 7.99

and for Re > 103;the Drag coefficient CD = 0.43, which gives;

ut =

√

3.1dp(ρs − ρg)g

ρg

EKC314-SCE – p. 127/164


Fluidisation regimes:For COARSE PARTICLES:

bubbles appear as soon as umf is exceeded.in TURBULENT regimes–bubbles life time isSHORT due to bubbles burst. Bed is quiteuniform–short circuiting of gas through bubbles isless likely.umf and particle blow-out coincide.in FAST fluidisation regime–there is the netentrainment of solids.in TRANSPORT regime–there is solid flow in thedirection of gas flow.carry-over (entrainment) separates particles bysize.

EKC314-SCE – p. 128/164


Fluidisation regimes:For FINE PARTICLES:

bubbles DO NOT appear as soon as minimumfluidisation is reached–instead, there is a uniformexpansion of bed.bed is more coherent rather than particlesbehaving independently.TURBULENT regime sets in well after uo exceedsut of an individual particle, thus, operate at higheruo.carry-over DOES NOT separate particles bysize–a more cohesive bed.

EKC314-SCE – p. 129/164


Fluidised-Bed Reactors: The ApplicationsIt is useful for highly EXOTHERMIC systemsAND/OR systems requiring close temperaturecontrol such as oxidation reactions.In a classical fluidised-bed operation, catalystparticles are retained in bed–little catalystentrainment.Some of the systems of reactions that usefluidised-bed include:

1. Oxidation of napthalene into phtalic anhydride.2. Ammoxidation of propylene to acrylonitrile.3. Oxychlorination of ethylene to ethylene dichloride.4. Coal combustion (injection of limestone for the

in-situ capture of SO2).EKC314-SCE – p. 130/164


Fluidised-Bed Reactors: The ApplicationsSome of the systems of reactions that usefluidised-bed include:

5. Roasting of oresEven with classical fluidised-bed, region above thesurface of bed contains some solid concentration.This concentration becomes constant as it is movedaway from the surface.

EKC314-SCE – p. 131/164


Modelling of fluidised-bed reactors:Two-phase model:

the model is based on the interchange betweenthe two phases;

Bubble

phase

Emulsion

phase

uo, CAo

CAb|out CAe|out

CA

ub ue

CAb CAe

EKC314-SCE – p. 132/164



for ISOTHERMAL fluidised-bed in emulsionphase, the material balance is given by;for bubble-phase:

fbub

dCAb

dz+ kI(CAb − CAe) + fbgbr

′

A = 0 (47)

for emulsion-phase:

feue

dCAe

dz−feDze

d2CAe

dz2−kI(CAb−CAe)+(1−fb)ger

′

A = 0

(48)

EKC314-SCE – p. 133/164



also;uoCA = fbubCAb + feueCAe (49)

and the boundary conditions are;for bubble-phase:

z = 0 : CAb = CAo

EKC314-SCE – p. 134/164



for emulsion-phase:

z = 0 : −Dze

dCAe

dz= ue(CAo − CAe)

z = L :dCAe

dz= 0

EKC314-SCE – p. 135/164


Modelling of fluidised-bed reactors:Model simplification:

If ub ≫ ue, that is when ub ≫ umf , then theemulsion-phase∼closed (relatively negligible inletOR outlet flow). Thus Equation (46) reduces into;

kI(CAb − CAe) = (1− fb)ger′

A (50)

also neglecting the DISPERSION.The above equation assumes a stagnantemulsion phase BUT, CAe varies with bed lengthz.

EKC314-SCE – p. 136/164


Modelling of fluidised-bed reactors:Estimation of parameters appearing in thetwo-phase model:

1. ub: bubble velocity:this is given by;

ub = (uo − umf) + ubr

where ubr is the bubble rise velocity when there isa SWARM of bubbles. This is separately given by;

ubr = α√

dbg

EKC314-SCE – p. 137/164



1. ub: bubble velocity:where α = 0.64 for dt < 0.1m OR α = 1.6d0.4t for0.1m < dt < 1.0m OR α = 1.6 for dt > 1.0m

2. fb: bubble friction:this is given by;

fb =uo − umf

ub

EKC314-SCE – p. 138/164



2. fb: bubble friction:BUT for ub ≫ umf

fb ∼uo

ub

3. fe: emulsion friction:This is given by

fe + fb = εf

where εf is the VOIDAGE of a fluidised-bed.EKC314-SCE – p. 139/164



4. Lf and εf : length of bed and bed voidage:Given that the volume of solids constant, where;

Lf(1− εf) = Lmf(1− εmf) = L(1− εb)

⇒ 1− εf1− εmf

=Lmf

Lf

= 1− fb

given that fb and εmf ∼ 0.4, then Lf and εf can becalculated.

EKC314-SCE – p. 140/164



5. Dze : diffusion coefficient of emulsion phase:Using;

Dze = f(uo, dt)

6. ue: emulsion velocity:Using

ue =umf

εmf

EKC314-SCE – p. 141/164



7. gb and ge: mass of solid in bubble andemulsion phases respectively:Using;

fbgb + (1− fb)ge =m

A · Lf

8. kI : gas interchange coefficient:For two-phase models–kI often used as a fittingparameter such that model agrees with plantdata.

EKC314-SCE – p. 142/164


Modelling of fluidised-bed reactors:Three-phase model:

ub

ue

emulsion

cloud

bubble

EKC314-SCE – p. 143/164



there is an interchange of gas from bubble tocloud, then from cloud to emulsion in sequentialstepthis can be depicted in the diagram below;

kI,b

kI,e

CA,b CA,b CA,e

bubble cloud emulsion

EKC314-SCE – p. 144/164



different mixing regimes in different phases canbe assumed.Kunnii-Levenspiel Model (k-L) assumesemulsion phase with no net gas flow.this is usually achieved for

uo

umf

> 6

EKC314-SCE – p. 145/164


Modelling of fluidised-bed reactors:Example: k-L Model for First-order reaction

Consider the material balances:Bubble phase :

fbub

dCAb

dz+ kIb(CAb − CAc) + fbgbkCAb = 0

Emulsion phase :

kIe(CAc − CAe) = (1− fb − f ′

c)gekCAe

Cloud phase :

kIb(CAb − CAc) = kIe(CAc − CAe) + f ′

cgckCAc

EKC314-SCE – p. 146/164



fc is with the units of m3cloud

m3bed

gc is in the form of kgm3

cloudwhich is approx. equal to

ge =ρb

1− fb

and f ′

c is normally given by;

f ′

c · fb =1.17

1.17 ·+ub

ue

EKC314-SCE – p. 147/164



using equations for emulsion and could phasesand substitute into the bubble phase equationgives;

−ub

dCAb

dz= kCAb (51)

EKC314-SCE – p. 148/164



and K is given by;

K = k

gb +1

kfbkIb

+ 1gcf ′

c+1

kfbkIe

+ 1ge(1−fb−f ′c)

fb

which is the effective rate constant for athree-phase fluidised-bed model ⇒ k-L rateconstant.

EKC314-SCE – p. 149/164



Integration of Equation (49) with boundaryconditions;

z = 0; CAb = CAo

leads to;CAb

CAo

=CA

CAo

= e−Kτb (52)

where τb =Lf

ub

EKC314-SCE – p. 150/164


Modelling of Transport Reactor (Riser):Example: Fluid Catalytic Cracking⇒fast reactions(small τ required) and rapid catalyst deactivation.Velocity of SOLIDS ≈ velocity of GAS. That is, NOSLIP VELOCITYUsually employed FINE SOLIDS such that ηe ∼ 1

For NO catalyst DEACTIVATION , riser is very muchlike pseudo-homogeneous Plug-Flow reactor (PFR)but

ε > εb

EKC314-SCE – p. 151/164


Modelling of Transport Reactor (Riser):Calculation of ε:

Given that;

ε

(

m3g

m3b

)

=Auo

Auo +ms

ρp

(53)

where ρp is the pellet density with units of kgm3

pellet

Upon simplification of Equation (51) gives;

ε

(

m3g

m3b

)

=1

1 + msAuoρp

(54)

EKC314-SCE – p. 152/164



The diagram is given;

solidgasms (kg/s)uo (m/s)

A

ε

EKC314-SCE – p. 153/164



From Equation (52);

ms ≪ uo : ε → 1

ms ≫ uo : ε → 0

for Packed-Bed reactor; εb → 0.4For NO catalyst deactivation:

uo

dCA

dz= −r′A(1− ε)ρp (55)

EKC314-SCE – p. 154/164



Catalyst deactivation in Fluid-Catalytic Crackingis believed to arise from:

1. coke deposition2. adsorption of certain species present in the

feedThus will give a reduction in the reaction rate(s)and therefore with time, with DeactivationFunction given by;

ΦA =r′A(t)

r′A(0)= f(t) (56)

EKC314-SCE – p. 155/164



The function can be of the form;

Φ = 1− αt

ORΦ = e−αt

Therefore Equation (53) becomes;

uo

dCA

dz= −r′AΦA(1− ε)ρp (57)

EKC314-SCE – p. 156/164



Where t = zuo

(NO SLIP) and it represents thetime for a particular catalyst to have spent in theriser.Sometimes, Φ is given as a function of the cokeconcentration on the catalyst pellets. It is practicalto express the concentration in the form of;

Cc

(

kgcokekgcatalyst

)

EKC314-SCE – p. 157/164



And the rate of formation of coke is given by;

rc

(

kgcokekgcatalyst · s

)

where rc can itself be deactivated as the coke isbeing produced!The balances for coke deposition is given by;

ms

A· dCc

dz= rcΦcρp(1− ε) (58)

EKC314-SCE – p. 158/164



The energy balances for the ADIABATIC riser canbe written as;

mgcpg + mscpsA

dT

dz= [r′AΦA(−∆HA) + rcΦc(−∆Hc)]

× ρp(1− ε) (59)

where cpg and cps are the specific heat capacitiesof gas and solid respectively in kJ

kg−Kand mg is the

mass flow rate of gas in kgs

EKC314-SCE – p. 159/164



And mg is given by;

mg =AuopoRTo

Mg

EKC314-SCE – p. 160/164

Multiphase Reactors

Involved GAS and LIQUID phases in contact with aSOLID.

The SOLID may be of the form of;1. catalyst particles dispersed in the liquid phase (Eg.

SLURRY REACTOR)2. packing for liquid distribution (Eg. PACKED-BED

ABSORBER)3. packing for liquid distribution and catalyst support

(Eg. TRICKLED-BED REACTOR and PACKEDBUBBLE REACTOR)

4. plates for liquid-gas contact (Eg. DISTILLATIONCOLUMN)

EKC314-SCE – p. 161/164

Multiphase Reactors

Reactors can also be classified in terms of whichphase is continuous and which is dispersed.

Referring to the diagram below:

LIQUID: continuous

GAS: disperse

LIQUID: disperse

GAS: continuous

LIQUID: continuous

GAS: continuous

GAS GAS GAS

LIQUID

LIQUID

LIQUID

Bubble reactor

Slurry reactor

Fermentation vessel

Spray tower

Trickle-bed reactor

Packed-bed reactor

Wetted-wall reactor

(falling film)

EKC314-SCE – p. 162/164

Multiphase Reactors

If mass-transfer resistance located in the liquid-film,use DISPERSE–gas phase and CONTINUOUS–liquidphase.

If mass-transfer resistance located in the gas-film,use CONTINUOUS–gas phase and DISPERSE–liquidphase.

Residence time, τ of reactant and heat transferconsideration will also dictate the type of reactor;1. plate columns can achieve long contact times

between gas and liquid, BUT poor TEMPERATUREcontrol

EKC314-SCE – p. 163/164

Multiphase Reactors

Residence time, τ of reactant and heat transferconsideration will also dictate the type of reactor;2. stirred-tank (BUBBLE and SLURRY), will have large

LIQUID:GAS ratio, BUT yet, cope with HIGH GASflow rates and therefore GOOD TEMPERATUREcontrol.

Reactors can have co- OR counter- current flow ofGAS and LIQUID to utilise driving force for MASS andHEAT transfers.

Where reactors are employed for GAS purification,then it is referred to as ABSORBERS.

EKC314-SCE – p. 164/164

ekc337: reactor design & analysis core course for b.eng

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