Synthesis of Crystallization-Based Separation Systems …cepac.cheme.cmu.edu/pasilectures/cisternas/Seminar Crystallization.pdf · Seminar - Synthesis of crystallization-based separation

Luis A. CisternasDepartamento de Ingeniería Química

Universidad de AntofagastaAntofagasta - Chile

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PASI 2005PASI 2005Pan American Advanced Studies Institute on Process Systems Engineering

Synthesis of Crystallization-BasedSeparation Systems

• Crystallization design problem overview• Fractional Crystallization• Fractional Crystallization with Heat

Integration & Cake Washing• Final Remark

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Outline

• Crystallization is extensively used in different industrial applications, including the production of a wide range of materials such as fertilizers, detergents, foods, and pharmaceutical products, as well as in the treatment of waste effluents

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Crystallization design problem overview

• The crystallization stages are usually accompanied by other separation techniques. Leaching.

• Various types of crystallization exist: cooling, evaporation, reactions, and drowning-out

• The characteristics of the product affects a series of other associated operations. filtration & washing.

• The separation is limited by multiple saturation points. Temperature changes & external chemical agents.

• Kinetic factors and metastability may affect the design.

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Problems

• The greatest advantages obtained in the use of the phase diagram are the possibilities for the visualization of the behavior of phase equilibria, describing the processes, and obtaining mass balances with the help of the lever arms rule.

• The phase diagrams, however, also have a series of limitations as a design tool

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Phase Diagram

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Phase Diagram

• Determine optimal stream configuration. • Determine operational conditions & flowrates.• Selection of equipment type.• Determine solid-liquid separation. Washing & Filtration.• Determine heat integration.

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Goals

• Basic Crystallization Separation• Relative Composition Diagram• Feasible Pathway Diagram• State Superstructure• Connectivity Matrix• Mathematical model• Examples

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Fractional Crystallization

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Basic Crystallization Separation

Isothermal CutKCl+NaCl+H2OKNO3+NaNO3+H2OL serine acid + L aspartic acid + water

p1

p2

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Basic Crystallization Separation

Basic Cycle

A S

B

bH

C

a

(a)

c

h

Heat and Evaporate

Cool and Dilute

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Relative Composition Diagram

RB

RC

RH

RA= 0S

H

F

C

a

(a)

8

RB > RC > RH > RA

A ofn CompositioWeight B ofn CompositioWeight

=R

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Feasible Pathway Diagram

RB

RC

RH

RA= 0S

H

F

C

a

(a)

8

RB > RC > RH > RA

RB > RC > RH > RA

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State Superstructure

F

S

C

H

A

S

B

RB > RC > RH > RA

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Connectivity Matrix

F

S

C

H

A

S

B

1

2

3

4

5 6

7

8

9

101096H

785C

43S1

21F

BAS2HC

RB > RC > RH > RA

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Mathematical model

F

S

C

H

A

S

B

1

2

3

4

5 6

7

8

9

10

SBAiwCxwxw

xwxwxwxwxwxwxwxwxwxwxwxw

wMin

l

Fiii

iiiiii

iiiiii

llw

,,;0,1,22,11

,1010,99,66,55,44,22

,88,77,55,66,33,11

=≥

=+

++=++

++=++

∑

General modelCisternas, L.A. (1999), Optimal design of crystallization-based separation schemes, AIChE J., 45, 1477-1487.

Production of potassium chloride from 100,000 ton/year of sylvinite (47.7% KCl, 52.3% NaCl).

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Examples-Sylvinite

Equilibrium Data

KCl+NaCl15.922.2100H1KCl+NaCl20.2511.730C1

NaClKClSolid Phase

WeightCompositionTemperature

[°C ]key

0.00.581.40∞

RNaClRC1RH1RKCl

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Examples-Sylvinite

Relative Composition Diagram

RKCl > RH1 > RC1 > RNaCl RKCl > RH1 > RC1 > RNaCl


Sylvinite

H2O

H1

C1

NaCl

H2O

Kcl

1

2

3

4

5 6

7

8

10

8

State Diagram

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Examples-Sylvinite

State Diagram

Sylvinite

H1

C1

NaCl

K

1

2

5 6

7

8Cl

Flow Sheet

LEACHING AT100 ‘C

LEACHING AT30 ‘C

Sylvinite

NaCl KCl

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Examples-Sylvinite

Sylvinite.gms

H

C

a

b

SD

NaCl

KCl

10090807060504030201000

10

20

30

40

50

60

70

80

90

100

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Examples-Astrakanite Equilibrium data for MgSO4+Na2SO4+H2O system.

0.377.9822.02SD3

0.854.1445.86SD2

0.842.4835.99SD1

0.2SD3 + Na26.95.88F397

0.8SD2 + SD319.1514.4F297

5.8Mg1 + SD25.5532.2F197

0.5SD1 + Na23.2511.98E250

6.6Mg6 + SD14.7431.32E150

0.9SD1 + Na1017.816.6D225

1.6Mg7 + SD11321.15D125

1.7Mg7 + Na1011.820.57C18.7

Na2SO4MgSO4RSolid phase

Saturated solution, % wkeysT ºC

Mg7=MgSO4.7H2O; Mg1=MgSO4.1H2O; Mg6=MgSO4.6H2O; Na10=Na2SO4.10H2O; Na=Na2SO4; SD1= Na2SO4.MgSO4.4H2O; SD2= Na2SO4.MgSO4; SD3= MgSO4.3Na2SO4

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Phase Diagram

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Isothermal Cuts

0102030405060708090

100

0 50 100

Na2SO4

MgS

O4

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Examples-AstrakaniteRelative Composition Diagram


4MgSOR > RE1 > RF1 > RC > RD1 > RD2 > RDS1= RDS2 > RF2 > RE2 > RDS3 > RF3 > 42SONaR

4MgSOR > RE1 > RF1 > RC > RD1 > RD2 > RDS1= RDS2 > RF2 > RE2 > RDS3 > > 42SONaR

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Examples-Astrakanite

astrakanite.gms

REACTIVECRYSTALLIZATION

18.7 ‘C

COOLING CRYSTALLIZATION

25 ‘C

Astrakanite

EVAPORATIVE CRYSTALLIZATION

50 ‘C

Astrakanite

Water Water

MgSO .6H O24Na SO .10H O2 4 2

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Examples-Astrakanite

REACTIVECRYSTALLIZATION

18.7 ‘C

COOLING CRYSTALLIZATION

25 ‘C

Astrakanite

EVAPORATIVE CRYSTALLIZATION

50 ‘C

Astrakanite

Water Water

MgSO .6H O24Na SO .10H O2 4 2

4MgSOR > RE1 > RF1 > RC > RD1 > RD2 > RDS1= RDS2 > RF2 > RE2 > RDS3 > > 42SONaR

C 18.7 °CD1 25 °CE1 50 °C

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Fractional Crystallization with Heat Integration & Cake Washing• State Superstructure • Task superstructure.• Heat integration.• Cake Washing

•Cisternas L.A., J.Y. Cueto and R.E. Swaney, “Flowsheet Synthesis of Fractional Crystallization Process with Cake Washing”, Computer and Chemical Engineering, 28, 613-623 ( 2004)• Cisternas L.A., C. Guerrero and R. Swaney,, “Separation System Synthesis of Fractional Crystallization Processes with Heat Integration”, Computer and Chemical Engineering, 25, 595-602 2001

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Task Superstructure

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wl (w + w h )m m mG

outt,mG

inl,t

Leaching

CrystallizationEvaporative

CoolingCrystallization

t

iΣn n,i(w + h x )

Task Network

MultipleSaturation

Points

ProductIntermed.

Solvent

Feed

Product

Solvent

Product

n

l m

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k−1

k

1

K

Rk−1

Rk

MultipleSaturation

Points

ProductIntermed.

Solvent

Feed

Product

Solvent

Product

Heat Integration

Papoulias S.A., & I.E. Grossmann (1983), A structural optimization approach to process synthesis-II. Heat recovery networks. Comp. and Chem. Engng., 7, 707

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Cake Washing

Parallel Options

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Mathematical Model

IiSsxhwxwxwhx MsSLqLwl

illlsSl

illsSl

illsSLql

iloutoutinin

∈∈=−⋅−⋅+ ∑∑∑∑∩∪∈∈∈∩∈

,0)()(

,)(

,)(

,)(

, '

Mass balance for each component in multiple saturation nodes (SM):

Mass balance for each component in intermediate product nodes (SI):IiSsxwxw I

sSLqlill

sSLqlill

outin

∈∈=⋅−⋅ ∑∑∩∈∩∈

,0)(

,)(

,

IiSsxhwhx IsSLql

illlsSLql

ilinout

∈∈=− ∑∑∩∈∩∈

,0)(

,')(

,

Iout

llIi

ilill SssSLqlymUhxxw ∈∩∈≤−+⋅∑∈

),(0)( ,,

IsSLql

l Ssymout

∈=−∑∩∈

01)(

Specification for feeds flow rates in feed nodes (SF):)(,,

)(, sIiSsCxw FF

Fis

sSlill

out

∈∈=⋅∑∈

State Superstructure

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Task Superstructure

Mass balance between the thermodynamic state network and task network

∑∑∈∈

∈∈=+)(

,, ),(,sTt

Minin

tlIi

ill SssSlGhxw

∑∈

∈∈=+)(

, ),(,sTt

Moutout

ltlll SssSlGhww

Mass balance in the task network:

∑∑∈∈

∈∈=)(

,)(

, ,,sSl

Moutlt

sSl

intl

outin

SsTtGG

Task selection and energy balance:

True)(

)(),(

0000

)(,)(2),(1,

,

,

,

,

,

,

,,,

,2,1,,,

)(,,,

,,

,

=

∈∈

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

====

¬

∨

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

∈=∈∈+=

==

∑∈

st

M

Sst

Cst

st

st

st

outs

outltst

Sst

ind

outd

intl

Dst

outlt

Cst

Cst

sSl

intlstst

stst

st

yg

sSssTt

QQ

VCFC

y

sSlGHSQsSlsSlGHQGHQQ

GVCFC

y

in

βα

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Cake Washing

Mass balance for each component in wash/reslurry stage:

0),(,0

,,,,,,,,,,

,,,,,,,,,,

=−−+

∈∈∈=−−+

elielielieleliel

elielielieleliel

nrrrymrzrnryprIiLwEeLwlnwrwymwzwnwypw

Efficiency constraint for wash/reslurry stage:

0),(,0

,,,,,,,,,,,,

,,,,,,,,,,,,

=+−−

∈∈∈=+−−

ielielielielieliel

ielielielielieliel

yprymryprErrrErIiLwEeLwlypwymwypwEwrwEw

Degree of impurity:

illiEl ILhy ,,, ≤ IiLwl ∈∈ ,

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Wash or reslurry/filter selection:

IiLwlLwEe

CvCfQrQw

zzrzwypwymwyprymr

yyyryw

QrCsQrCvfwQrCvrCv

CffCfrCfwhnrQr

Qwzzr

zwypwymw

yyprymry

yryw

QwCsQwCvwCv

CfwCfQr

whnwQw

zrzzw

yprymr

yypwymwy

yryw

el

el

el

el

ieliel

iel

iel

iel

iel

iel

ieliel

el

el

elel

lelel

el

llelel

el

ieliel

iel

iel

iel

ieliel

ieliel

el

el

el

elel

el

el

llelel

iel

ieliel

iel

iel

ieliel

ieliel

el

el

∈∈∈

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

=

=

=

=

=

=

=

=

=

=

¬

¬

∨

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+=

+=

=

=

=

=

=

=

=

=

¬

∨

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+=

=

=

=

=

=

=

=

=

=

¬

−−

,),(

0000

000

00

)(

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0

00

,

,

,

,

,,,,

,,

,,

,,

,,

,,

,,,,

,

,

,,

0,,

,

0,,

,

,,,,

,,

,,

,,

,1,,,

,,,,

,

,

,

,,

,

,

0,,

,,

,,,,

,,

,,

,1,,,

,,,,

,

,

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Heat Integration

Heat balance around each temperature interval k:

KkTCwTCwQQRRkkkk Cl

Clkpl

Hl

Hlkpl

Un

Un

Vm

Vmkk ∈∆−∆=+−− ∑∑∑∑

∈∈∈∈− )()(1

objective function minimizes the total venture cost:

∑∑∑∑∑ ∑∈∈∈∈ ∈

+++++++Lwl e

elelUn

Unn

Vm

Vmm

Sst

Sst

Cst

Cststst

Ss sTtCvCfQcQcQcQcVCFC

M

)()(min ,,,,,,,,)(

Objective Function

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Example: Sylvinite

The MILP formulation contains 299 equations, 218 continuous variables, and 27 binary variables.

Sylvinite.gmsSylvinite_heat.gmsSylvinite_wash.gmsSylvinite_wash_heat.gms

Sylvinite

cw

Leachingat 30ºC

Filtration

WashingWashsolvent

Washing

NaClCake

Water

St

Leachingat 100ºC

Filtration

Washsolvent

KClCake

Production of potassium chloride andmagnesium chloride from carnallite(KCl.MgCl2.6H2O).

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Examples-Carnallite

Equilibrium Data

Carnallite+MgCl2.6H2O40.751.07105H2KCl+Carnallite30.827105H1

Carnallite+MgCl2.6H2O35.170.1435C2KCl+Carnallite27.323.835C1

MgCl2KClSolid Phase

Weight CompositionTemperature[°C ]key

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Example: Carnallite

StCarnallite

Reactivecrystallization

at 105ºC

FiltrationFiltrationFiltration

Filtration

Filtration

Washsolvent

Carnallitecake

Washing

Reslurry

Reslurry

KClCake

Water

Coolingcrystallization

at 35ºC

Cw

CwSt

Washing

Washsolvent

Evaporativecrystallization

at 105ºC

Cw

MgCl 6H OCake

2 2.

KCl·MgCl2·6H2O

The MILP formulation contains 598 equations, 556 continuous variables, and 69 binary variables

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Example: Astrakanite

Astrakanite

Water Water

Reactivecrystallization

at 18.7ºC

Filtration

WashingWashsolvent

Washsolvent

Na SO .10H Ocake

2 4 2 MgSO .7H Ocake

4 2

Washing

Filtration Filtration

Coolingcrystallization

at 25ºC

R

StEvaporative

crystallizationat 50ºC

Astrakanitecake

MgSO4·Na2SO4·4H2O

The MILP formulation contains 1209 equations, 1201 continuous variables, and 145 binary variables. Solution time was 84 s for OSLv2 (GAMS) with a 1.7 GHz Pentium 4 processor.

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Final Remark• Complete examples • Complete list of references on design of separation based on

crystallization (metathetical salts, drowning-out, reactive

crystallization, wastewater systems, chiral crystallization)• Other papers• Links

Can be found on http://www.ingen.uantof.cl/webpages/Academicos%20Ing.%20Quimica/Luiscisternas/principal.htm

Orhttp://cepac.cheme.cmu.edu/pasifaculty.htm

Fin

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Rem

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Fractional Crystallization• Cisternas L.A., R.E. Swaney, 1998, Separation system synthesis for fractional crystallization from solution

using a network flow model, Ind. Eng. Chem. Res., 37, 2761-2769.• Cisternas L.A., D. F. Rudd, 1993, Process design for fractional crystallization from solution, Ind. Eng. Chem.

Res., 32, 1993-2005• Cisternas L.A., C.P. Guerrero, R.E. Swaney, 2001, Separation system synthesis of fractional crystallization

processes with heat integration, Comput. Chem. Engng., 25, 595-602.• Cisternas L.A., J. Cueto, R. E. Swaney, 2004, Flowsheet synthesis of fractional crystallization processes with

cake washing, Comput. Chem. Engng., 28, 613-623.• Cisternas L.A., 1999, Optimal design of crystallization-based separation schemes, AIChE J., 45, 1477-1487.• Dye S.R., D.A. Berry, K.M. Ng, 1995, Synthesis of crystallization-based separation schemes, AIChE

Symposium Series, 304, 91, 238-241.• Dudczak J., 1996, Synthesis of crystallization processes with multiple feeds, Inzynieria chemiczna I

procesowa, 17 (3), 339-353• Dudczak J., 2001, Synthesis of crystallization processes. Ternary systems with a single congruently soluble

double salt, Inzynieria chemiczna I procesowa, 22, 397-407.• Fitch, B., 1970, How to design fractional crystallization processes, Ind. Eng. Chem., 62, 6-33.• Fitch, B., 1976, Design of fractional crystallization processes involving solid solutions. AIChE Symps. Series,

72, 153. • Ng K. M., 1991, Systematic separation of a multicomponent mixture of solids base on selective crystallization

and dissolution, Separation Technology, 1, 108-120.• Rajagopal S., K.M. Ng, J.M. Douglas, 1992, A hierarchical procedure for the conceptual design of solids

processes, Computers Chem. Engng., 16 (7), 675-689.• Rajagopal S., K.M. Ng, J.M. Douglas, 1988, Design of solids processes: Production of Potash, Ind. Eng.Chem.

Res., 27(11), 2071-2078.• Schroer J.W., K.M. Ng, 2001, Simplify multicomponent crystallization, Chemical Engineering, December, 46-

53.• Wibowo C., K.M. Ng, 2000, Unified approach for synthesizing crystallization-based separation processes,

AIChE J., 46 (7), 1400-1421.• Wibowo C., W.C. Chang, K.M. Ng, 2001, Design of integrated crystallization systems, AIChE J., 47(11) 2474-

2492.

Fin

al

Rem

ark


Reactive Crystallization• Berry D.A., K.M. Ng, 1997a, Synthesis of reactive crystallization processes, AIChE J., 43 (7),

1737-1750.• Berry D.A., K.M. Ng, 1996, Separation of quaternary conjugate salt systems by fractional

crystallization, AIChE J., 42 (8), 2162-2174.• Cisternas L.A., M.A. Torres, M.J. Godoy, R.E. Swaney, 2003, Design of separation schemes

for fractional crystallization of metathetical salts, AIChE J., 49 (7), 1731-1742.• Kelkar V.V., K.M. Ng, 1999, Design of reactive crystallization systems incorporating kinetics

and mass-transfer effects, AIChE J., 45 (1), 69-81.

Hybrid Systems and Drowning-out

• Berry D.A., K.M. Ng, 1997b, Synthesis of crystallization-distillation hybrid separation processes, AIChE J., 43(7), 1751-1762

• Berry D.A., S.R. Dye, K.M. Ng, 1997, Synthesis of Drowning-Out crystallization-based separation, AIChE J., 43(1), 91-103

• Oosterhof H., C. Witkamp & C.M. Van Rosmalen, 2001, Antisolvent crystallization of anhydrous sodium carbonate at atmospherical conditions, AIChE J., 47, 602

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Environmental applications• Parthasarathy G., R.F. Dunn, M.M. El-Halwagi, 2001a, Development of Heat-Integrated

Evaporation and Crystallization Networks for ternary wastewater systems. 1. Design of the separation systems, Ind. Eng.Chem. Res., 40, 2827-2841.

• Parthasarathy G., R.F. Dunn, M.M. El-Halwagi, 2001b, Development of Heat-Integrated Evaporation and Crystallization Networks for ternary wastewater systems.2. Interception task identification for the separation and allocation network, 40,(13) 2843-2855.

• Parthasarathy G., R.F. Dunn, 2003, Graphical strategies for design of evaporation crystallization networks for environmental wastewater applications, Advances in Environmental Research, 8, 247-265..

Others

• Schroer J.W., C. Wibowo, K.M. Ng, 2001, Synthesis of chiral crystallization processes, AIChEJ., 47(2), 369-387.

• Thomsen K., P. Rasmussen, R. Gani, 1998, Simulation and optimization of fractional crystallization processes, Chem. Eng. Sci., 53(8), 1551-1564.

• Thomsen K., R. Gani, P. Rasmussen, 1995, Synthesis and analysis of processes with electrolyte mixtures, Comput. Chem. Engng., 19 (Suppl), S27-S32.

• Takano K., R. Gani, T. Ishikawa, P. Kolar, 2002, Conceptual design and analysis methodology for crystallization processes with electrolyte systems, Fluid Phase Equilibria, 194, 783-803.

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Acknowledgements

• Ross Swaney, University of Wisconsin-Madison

• Paola Guerrero• Jessica Cueto

Documents

Synthesis of Crystallization-Based Separation Systems …cepac.cheme.cmu.edu/pasilectures/cisternas/Seminar Crystallization.pdf · Seminar - Synthesis of crystallization-based separation