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Utilization of OLI Thermodynamic Model
in Reactive Crystallization Modeling
Zhilong Zhu, You Peng,
Richard D. Braatz, Allan S. Myerson
Department of Chemical Engineering, MIT
OLI Conference Presentation, Oct 21st, 2014
Outline
• Introduction to crystallization
– Quality attributes: CSD, purity, polymorph, yield
– Modeling: population balance model and thermodynamic model
•Why OLI thermodynamic model?
– Mixed Solvent Electrolyte (MSE) model
• Application in reactive crystallization
– OLI databank construction and result
– Integration with Matlab
– Simulation result
Page 2
Introduction to crystallization
• Crystallization is an important separation and
purification process
• Key attributes in crystallization
– Crystal size distribution (CSD)
– Crystal purity
– Crystal polymorphs
– Crystal yield
Page 3
( )f x
# d
ensity
Crystal size
a b
x
# p a r t ic le s /v o l ( )b
a
f x d x
Crystallization methods
• Driving force: supersaturation
•Methods:
– Cooling
– Antisolvent addition
– Evaporation
– Chemical reaction
Page 4
s a t
s a t
( )
( )
c c TS
c T
Metastable zone
Temperature
Solubility curve
Metastable limit
Labile zone Nucleation
Growth
Undersaturated
A.S. Myerson, Handbook of Industrial Crystallization, 1993
Population Balance Model (PBM)
Conservation equation for number density, f
– spatially homogenous
– one independent crystal internal coordinate, x
– constant volume
– batch process
Page 5
G ffB
t x
1st order partial integro-differential equation
Nucleation rate
Crystal growth rate
Total mass = solute mass + crystal mass
PBM:
Crystals
Thermodynamic model in crystallization
Page 6
Nucleation rate
Crystal growth rate Supersaturation
~ driving force
For most simple organic system
Concentr
ation
Temperature
s a t
s a t
( )
( )
c c TS
c T
For multi-species, ionic, concentrated system
i
i
s p
a
Sk
,w h e re
i i ia m
Need a rigorous electrolyte model to predict i
Solubility / equilibrium
s a t( )c T
OLI Thermodynamic models
•We chose to use OLI Mixed Solvent Electrolyte (MSE) model because
– First-principles model
– Agrees better with our test cases
• The MSE models the excess Gibbs free energy
Page 7
e x e x e x e x
L R S R IIG G G G
Long Range
Short Range
Ionic Interaction
,, ,
ln
j j k
e x
k
k T P n
G
n R T
Integration with Matlab via Excel
Page 8
Solution composition
Speciation
Supersaturation (scaling tendency)
PBM ode45 solver
(iterative)
Matlab GUI
Initial values model file from OLI Analyzer
Update solution composition via Excel Macro
CSD plots Excel data storage
speed: ~25 seconds for 300 OLI calls
OLI application in reactive crystallization
Page 9
OLI Analyzer # of solids: 18 # of liquids: 27 # of parameters: 38
Existing OLI databank does not have all the parameters in the MSE model for our system
We carried out solubility experiments at various conditions
We did regression using OLIREG for missing parameters
Scaling Tendency for CaSO4.2H2O in OLI
Parity plot for CaSO4.2H2O solubility
Page 10
0.00
0.05
0.10
0.15
0.20
0.00 0.05 0.10 0.15 0.20
Mo
del
pred
icte
d s
olu
bilit
y
(w
t%)
Solubility from literature data (wt%)
(1) Taperova, A. A. Zh. Prikl. Khim 18 (1940): 643. (2) Taperova, A. A., and N. M. Shulgiva. Zh. Prikl. Khim 18 (1945): 521.
(3) Kurteva, O. I., and E. B. Brustkus. Zh. Prikl. Khim 34 (1961): 1714.
Batch reactive crystallization simulation
Provide C0 , T , and initial CSD
Transform the PDE into ODEs
( , )d x
G x td t
( , )
( , ) ( , ) , ,d f G x t
f x t B f x t x td t x
Solve the ODEs using Matlab
- calculate drop in concentration - update Excel - trigger OLI Engine - return scaling tendency - next time step
Page 11
Reactive crystallization simulation result
Page 12
Matlab GUI
Summary
•Model for reactive crystallization needs accurate
thermodynamics
• OLI MSE model provides a good supersaturation
prediction for our electrolyte system
• OLI Engine was coupled with Matlab via Excel to
simulate batch reactive crystallization
Page 13
