Modelling and Simulation in Chemical Engineering: Tools for

Modelling and Simulation in Chemical Engineering: Tools for Process Innovation

Alírio E. Rodrigues | LSRE | DEQ | FEUP

ESCAPE-14 Lisbon, Portugal 17 | MAY | 2004


A. E. Rodrigues

ESCAPE-14May 16-19, 2004

Fundação Calouste GulbenkianLisbon, Portugal




OUTLINEINTRODUCTIONTHE “ART” OF MODELLINGMODELS OF 10$, 100$ and 1000$PROCESS SIMULATIONPERFUSION CHROMATOGRAPHYSIMULATED MOVING BED (SMB)HYBRID PROCESS-SMB REACTOR

CONCLUSIONS




BSL




Ingredients for Process Innovation

Science Technology

Process




Increaseddiffusivity byconvection

Adsorbents (Materials)

Perfusion chromatography




SMB conceptModellingSimulation

Adsorbent(Materials)

Technology(rotary valve)

Sorbex processes (UOP)




ChE MethodologyLe Goff (1970)

Conservation equations (mass, energy, momentum, electric charge)

Equilibrium laws at the interface (s)Constitutive laws (e.g., ideal gas law)Kinetic laws of transport and reactionInitial and boundary conditionsOptimisation criterion







Surface diffusion

Pore diffusion External film diffusion

Axial dispersion (bulk)

Surface diffusion

Pore diffusion External film diffusion

Axial dispersion (bulk)

THE “ART” OF MODELLING




Scaling and dimensionless groups

constant time reactionconstant time diffusion

rate diffusionrate reactionDa

Dkc

IIe

niS ====

−2

12 φl

02

2=− n

ii

e kcdz

cdD

iSi

i

cczdzdcz

==

==

,

0,0

l

01

22

2=−

−n

ie

niSi f

Dkc

dx

fdl

lzx =

iS

ii c

cf =




Averaging

LDF

cicis

qis qis

<qi><qi>

qi(R)

⎟⎠⎞

⎜⎝⎛=

Rq

RRR

Dt

q ih

i∂∂

∂∂

∂∂ 2

21

)(,

0,0

iiSp

i

cfqRRRq

R

==

==∂∂

) )(( ⟩⟨−=⟩⟨−=⟩⟨−

==⟩⟨

iiShiiSh

p

iiS

p

h

R

i

p

hi qqkqqR

DR

qqRD

Rq

RD

tq

pp2

1533α∂

∂∂

∂




Choice of variables

00ˆ,ˆ

i

ii

i

ii q

qq

cc

c ==

i

ii cK

cKq

ˆ)1(1ˆ

ˆ−+

=

0ˆ1ˆˆ

=−

++t

qcq

tc

zc

u i

io

ioiii ∂

∂ε

ε∂

∂∂∂

KTKKTK

ci 1,1

1ˆ ≤≤

−

−=

⎟⎠⎞

⎜⎝⎛ −= 11

ztuT i

mξ




From model results to real life

eiS

obsDc

r 22 l

=ηφφφη tanh

=

0.1

1

0.1 1 10φi

η

η≈1

η≈1/φ

0

1

0.01 0.1 1 10 100

η φ2

η




Obtaining useful relations between dependent variables

)()(

iiSe

es cc

HDTT −

∆−=−

λ

0)(2

2=− i

ie cTk

dzcd

D

0)()(2

2=∆−+ ie cTkH

dzTdλ

0,0 ===dzdT

dzdc

z i

siSi TTccz === ;,l

cis

ci(R)

cis

Ts

T(R)Ts




⎟⎟⎠

⎞⎜⎜⎝

⎛+=++

Ω−=⎟⎟⎠

⎞⎜⎜⎝

⎛+

−==

⎟⎟⎠

⎞⎜⎜⎝

⎛ Ω+

Ω=

Ω+

Ω

2

2

2

2

2

2

2

2

2

2

2

2

)()(

;

)()(

yC

xCD

yuC

xuC

tC

yx

xv

yu

yxyv

xu

∂∂

∂∂

∂∂

∂∂

∂∂

∂ψ∂

∂ψ∂

∂∂ψ

∂∂ψ

∂∂

∂∂ν

∂∂

∂∂

MODELS OF 10$, 100$ AND 1000$




10$ models:Equilibrium theory for adsorption columns

0)1(0 =⟩⟨

−++tq

tc

zc

u iii∂

∂ε

∂∂

ε∂∂

)(*iii cfqq ==⟩⟨

i

i

ish

cq

uu

∆∆−

+=

εε11)(11 '

i

i

cc

cf

utzu

ii

εε∂

∂−

+=⎟

⎠⎞

⎜⎝⎛=

dispersive front compressive front




100$ models:Diffusion, convection and reaction in isothermal catalysts

reaction A → B in slab catalysts

042 22

2=−− f

dxdf

dx

fdSm φλ

eS D

kl=φ

em D

v l0=λ

Thiele modulus

intraparticlePeclet number

)( 12

)12(1

)12(2 21

αααα αα

−−

=−−

shesheshf

xx

24 22

2,1Smm φλλ

α+±

=




21

21cothcoth

/1/1αα

ααη

−−

=dc

S

Sd φ

φη

tanh=

0=mλ

when convection is not important

eS D

kl=φ




1000$ models:Computational Fluid Dynamics (CFD)

L

H

ux (y) 0.2 H

0.7 H

0.1 H

y

x




PROCESS SIMULATION




Increased diffusivity by convection



Increased diffusivity by convection



Perfusion Chromatography







Perfusion Chromatography

“Old” resin producer: Rohm & Haas2003 -criou Advanced Biosciences

Amberchrom chromatographic media, Amberlite XAD (biopharmaceuticals), Ambersynth CTC resin

“New” : PerSeptive Biosystems(1990)

…Now Applied Biosystems




Chromatography Pioneers

V

A

R

1

e

f

d

ba

c

M. Tswett D. T. Day




Factors governing the behaviour of an adsorptive process

IntraParticle Convection

IntraParticle Diffusion

Film Mass Transfer

Hydrodynamics (RTD)

Equilibrium Data




Concept behind Perfusion chromatography

)(1~λf

DD ee =

1

10

100

1 10 100

De

De~

λ

1/f( )λ

Enhancement factor for diffusivity due to convection, 1/f(λ)




HETP= A + B/u + Cu

uCfuBAHETP )(λ++=




How to decrease intraparticle mass transfer resistance?




Porous materials

POROSHELL (Agilent Technologies)POROS packing Silica Monolith












SimulatedSimulated MovingMoving BedBed




Simulated Moving Bed - (SMB)

http://books.nap.edu/books/0309039398/html/57.html




SMB Technology

“Old” : UOP(1961)Sorbex Processes: PAREX, SAREX, MOLEX…

“New” : NovasepFirst SMB in pharmaceutical industry

(UCB Pharma, 1999)




“Old” and “New”

• ParexProductivity 120 Kg/m3 hAdsorbent capacity 200 Kg/m3

• Chiral separationsProductivity 1-10 Kg/m3 hAdsorbent capacity 10 Kg/m3




UOP Parex

AC=adsorbent chamber; RV=rotary valve; EC=extract column; RC=raffinate column.Lines: 2-desorbent; 5-extract; 9-feed; 12-raffinate.




NOVASEP-chiral separation

The largest unit in operation for chiral separations has only 6 columns (Blehault et al., AIChE Meeting, Chicago, March 2001).




SMB unit at

Licosep 12-26 (Novasep)




TMB concept

Desorbent(D)

Feed (A+B)

Extract(A+D)

Raffinate (B +D)

A B

liquid circulation

Zone 1 Zone 2 Zone 3 Zone 4

solid circulation

A A B

B

regeneration of the adsorbent

regeneration of the desorbent

desorption of B adsorption of A




SMB concept

Desorbent (D) Extract (A+D)

Feed (A+B) Raffinate (B+D)

Port switching direction

Desorbent (D)

Raffinate (B+D)

Extract (A+D)

Feed (A+B)

Zone 1

Zone 3

Zone

4 Zone 2

B more strong adsorbedA more strong adsorbed

Extract (A+D)Desorbent (D)

Feed (A+B)Raffinate(B+D)

Desorbent (D)

Extract (A+D)

Feed (A+B)

Raffinate(B+D)




SMB-TMB equivalence

Solid phase Liquid phase

SMB 0 ∗jv

TMB ∗=tLu c

s sjj uvv −= *




Concentration profiles in TMB

EE XX FF RR




SMB Cyclic steady state

00.20.40.60.8

11.21.41.61.8

2

0 50 100 150 200 250

t ( min)

c (g

/l)

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8

c, g

/l

E X F R

0%

50%

100%

B

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8

c, g

/l

E X F R

0%

50%

100%

A

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8

c, g

/l

E X F RE X F R

0%

50%

100%

A

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250

t ( min)

c (g

/l)

A

B

EXTRACT

A

B

RAFFINATE




Design of SMBSeparation constraints - equivalent TMB

1>IAS

IAIqQcQ

1>IIBS

IIBIIqQcQ

1<IIAS

IIAIIqQcQ

Zone I

Zone II

1<IIIAS

IIIAIIIqQcQ

1>IIIBS

IIIBIIIqQcQZone III

1<IVBS

IVBIVqQcQ

Zone IV




Separation regions-Equilibrium theory

linear isotherms nonlinear isotherm

m1>KA KA< m2 m3<KB and m4<KB




no masstransfer

resistance

masstransfer

resistance

Influence of the mass transfer resistance




“Triangle theory” “Separation volume”

Design 100% product purities any product purities

Design parameters

flow rates-zone 2 and 3 flow rates-zone 2, 3 and 1 (or 4)

Mathematical model

equilibrium model general rate model

Design result two dimensional three dimensional

Optimal point vertex vertexes

Triangle theory vs. Separation volume methodology




Design of SMB: ”separation volume” methodology

Influence of γ4 on the separationregion

Influence of γ1 on the separationregion




Optimization procedure concept

constant γ4

productivity unchanged

desorbent consumption increases

productivity increases

violation of separation requirements

constant γ1

violation of separation requirements

productivity unchanged

desorbent consumption decreases

max (γ3−γ2)=max(QF)=max(productivity)

min (γ1−γ4)=min(QD)=min(desorbent consumption)




SMBREluent (E) Extract (B+E)

Feed (A) Raffinate (C+E)


Eluent (E)

Raffinate (C+E)

Extract (B+E)

Feed (A)

Zone 1

Zone 3

Zone

4 Zone 2

A B + C

)

Extract (B+E)

Extract (B+E)

Eluent (E) Eluent (E)

Raffinate (C+E)

Raffinate (C+E) Feed (A) Feed (A)

A → B + C





SMBR movie




SMBR-inversion of fructose

sucrose → fructose + glucose




Cashew apple juice chromatograms




Separation regions: multicomponent mixturesin the frame of the equilibrium theory




JO Process

IVQ4 QS

IIIQ3 QS

IIQ2 QS

IQ1 Q S

QR

QF

QX

QEl

IVQ4

IIIQ3

IIQ2

IQ1

QFQI

QEl1

IVQ4 QS

IIIQ3 Q S

IIQ2 Q S

IQ1 Q S

QR

QX

True Moving Bed Pseudo-SMBSTEP 1 STEP 2

QEl2

V. G. Mata, A. E. Rodrigues, J. Chromatography, 2001




CONCLUSIONS

Modelling/Simulation - second paradigm of ChE

Molecular transformation? third paradigm of ChE

Astarita: “the amount of information available grows continuously but the amount of information

that any one of us can usefully digest does not grow".




Documents

Modelling and Simulation in Chemical Engineering: Tools for