CFD modeling of precipitation of nanoparticles in Confined
Impinging Jet ReactorsY. S. de Gelicourt, D. L. Marchisio, A. A.
Barresi, M. Vanni & G. Baldi
Dip. Scienza dei Materiali e Ingegneria Chimica –Politecnico di Torino
Computational Fluid Dynamics in Chemical Reaction Engineering Conference, 19-24 June 2005, Barga, Italy
Motivation and goals
• Organic actives are often dispersed in polymer structures forming nano-spheres and nano-capsules
• The main advantages of these particulate systems are:
• Possibility of release of actives insoluble in water
• Controlled drug-delivery
• Passive and active targeting
• Increased lifetime in bloodstream
• The polymer usually has to be hydrophilic, flexible and non-ionic
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
Motivation and goals
• Very often block co-polymers are used: poly(MePEGCA-co-HDCA) poly (methoxypolyethyleneglycole cyanoacrylate – co – hexadecyl cyanoacrylate)
• HDCA chains (hydrophobic) are inserted in the organic active core
• PEG chains (hydrophylic) are oriented towards the water phase, forming a flexible protective layer that reduces the absorption of plasmatic proteins
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
CN
CO
CH2C
OCH2
CH2
(CH2)13
CH3
CN
C)m(CH2
CO
O
CN
C
CO
n
O
O
O
OCH3
Preparation
• Nano-particles are produced by precipitation (solvent displacement)
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
Effect of mixing
• Mixing controls nucleation, molecular growth (and aggregation) rates and therefore controls the particle size distribution
• Mixing (and cohesion forces) control the mass ratio of organic active/polymer in each particle
• Generally speaking good product quality is obtained with very high mixing rates
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
Aim of this work
• Design, optimization and scale-up of a continuous process to produce significant amounts of particles with a certain size range (≅200 nm) and with a specific active-to-polymer ratio
• CFD is used to simulate the precipitation process and its interaction with turbulent mixing
• Reactor configuration: confined impinging jet reactor (CIJR)
• Reacting systems: • parallel reaction scheme
• barium sulphate precipitation
• Real system: acetone-PEG-doxorubicine + water
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
Confined Impinging Jet Reactor
• The flow regimes in the reactor are characterized by the jet Reynolds number
• In this work we investigated 300<Re<3000 for d=1mm/D=4.76 mm
• Flow field simulations were run with LES and RANS approaches in Fluent 6.1.22
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
• Different three dimensional unstructured grids were tested in order to find a grid independent solution
• LES: ≈ 500,000 cells for the full geometry
• RANS: ≈ 100,000 cells (with finer resolution near the walls)
Large Eddy Simulation
• Fluent: box filter with bandwidth ∆ equal to the cell size
• The residual stresses are closed by using the Smagorinsky model
• Next steps: implementation of a dynamic SGS model
• Cluster: 6 Xeon bi-processors 2400 (MHz)
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
j
rij
iii
i
j
jii
xxp
xxU
xUU
tU
∂
∂−
∂∂
−∂∂
∂=
∂∂
+∂
∂ τρ
ν 12
ijrrij Sντ 2−=
filtered Strain rate
( ) 12.010.008.0 2 −−=∆= sSr CSCν
Large Eddy Simulation• Laminar inlet conditions (parabolic profile)
• Instantaneous velocity magnitude for Re= 704 and Re=2696
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
Large Eddy Simulation
• Velocity magnitude for Re=3000
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
RANS
• Different turbulence models have been tested: k-ε, RNG k-ε, relizable k-ε, k-ω, RSM
• Different near wall treatments have been tested: standard wall function, non-equilibrium wall function, enhanced wall treatment
• Results show that RSM with enhanced wall treatment gives the best agreement with time-averaged LES velocities
• Further analysis needs experimental data or DNS data (Alfredo Soldati, University of Udine)
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
Step 1: Parallel chemical reaction
• In order to test mixing efficiency in the confined impinging jetreactor a parallel reaction has been used
• The system can be described with mixture fraction and progress reaction variables
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
( )ASCARBA +→+→+
A B+C
( )
( ) 22
211
111
11
11
Ycc
cccY
cc
cccY
cc
sCo
C
CoAo
Coss
Bo
B
BoAo
Boss
Ao
A
ξξ
ξξξ
ξξξ
−−−=
+=−−−=
+=−=
Step 1: Parallel chemical reaction
• Micro-mixing is modeled with the DQMOM-IEM model
• Functional form of the Probability Density Function:
• … where weights wα and weighted abscissas wαξα are calculated by solving their corresponding transport equations and forcing the moments of the PDF to be correctly predicted
• With two nodes (N=2)
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
( ) ( ) ( )[ ]ttptfN
,,,;1
xxx αα
α ξξδξ −= ∑=
( ) ( )( ) ( ) 3
223
11322111
222
2112210
, ,
, ,
ξξξξ
ξξ
pptmpptm
pptmpptm
+=+=
+=+=
xxxx
Step 1: Parallel chemical reaction
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
A
B+C Mixture fraction
Mixture fraction variance
A
B+C
Step 1: Parallel chemical reaction
• Comparison between DQMOM-IEM and beta-PDF for the mixture fraction PDF
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
0
0
0
0
0
1
1
1
1
1
1
0.00 0.20 0.40 0.60 0.80 1.00
0
0
0
1
1
1
1
0.00 0.20 0.40 0.60 0.80 1.00
0 .0 0
0 .2 0
0 .4 0
0 .6 0
0 .8 0
1 .0 0
0.00 0.20 0.40 0.60 0.80 1.00
Step 1: Parallel chemical reaction
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
• Transport equations for weights and weighted abscissas
( )
( ) ( ) ( ) ( ) ( )21
22111221
111111
12111 1 0
ξξcpcpξξpγp
xp
xxpu
tp
ppxp
xxpu
tp
it
iii
it
iii
−+
+−=
∂
∂Γ+Γ
∂∂
−∂
∂+
∂∂
−==
∂∂
Γ+Γ∂∂
−∂∂
+∂∂
ξξξ
εγ φ kC
2=
∂∂
∂∂
Γ=ii
t xxc 11
1ξξ
∂∂
∂∂
Γ=ii
t xxc 22
2ξξ
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 1 2 3 4 5
Cφ/2
X
Step 1: Parallel chemical reaction
• The reacting system is described by transport equations for:
• … and algebraic equations for:
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
εγ φ kC
2=
2,221,2122111 YpYpppp ξξ
∞∞−= 2,11,112 1 YYpp
Selectivity of the second reaction
No micromixing limit
0
0.1
0.2
0.3
0.4
0.5
0.6
0 500 1000 1500 2000 2500 3000Re
X
Step 1: Parallel chemical reaction
• Comparison with experimental data from Johnson & Prud’homme (2003) for the CIJR
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
2=φC
2.0=φC
( )1RefC =φ
R.O. Fox & Y. Liu (2005) AIChE J.
Step 2: barium sulphate precipitation
• Different jet Reynolds numbers (80<Re<2500)
• Different reactant concentration (Ba++, SO4=)
• Different reactant concentration ratio (Ba++/SO4=)
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
44 BaSOSOBa →+ =++
Ba++ SO4=
• The reaction is very fast and mixing sensitive
• Relevant phenomena involved: nucleation, molecular growth and aggregation
Step 2: barium sulphate precipitation
• Effect of Reynolds number Ba++:800 SO4=:100 mol/m3
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
10
100
1000
10000
0 500 1000 1500 2000 2500 3000Re
dmea
n (n
m)
FR=120 ml/min
FR=3ml/min
c1_15000FR=3ml/min -acetone
3 µm
b2_50000xFR=60 ml/min-acetone
800 nm
Step 2: barium sulphate precipitation
• The CFD model uses the DQMOM-IEM (N=2) for micromixing
• Standard kinetic expressions for nucleation and growth
• Brownian aggregation kernel
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
( )( )
ps
BApsAB
m
B
CLm
B
CLApsAB
kccS
LSMkShD
G
SV
TkV
TkSNkDB
±=−
=
−=
γρ
νγπγ
12
ln316exp5.1 2
2337
hom
( ) αµ
β
++=
2121
113
2LL
LLTkB
Step 2: barium sulphate precipitation
• The population balance equation is solved by using the QMOM (for the two reacting environments)
• The Particle Size Distribution is computed through the moments of the distribution (k=0,…,3)
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
( ) ( )10
, ; ,N
k kk i i
im t n L t L dL w L
+∞
=
= ≈ ∑∫x x
( ) ( )( ) ( ) ( )
( ) ( ) ( ) ( )∑ ∑∑ ∑∑= == ==
− −+++
=
∂
∂Γ
∂∂
−∂∂
+∂
∂
N
iji
N
jj
kii
N
iji
N
j
kjiji
N
i
kiii
k
i
kt
iki
i
k
LLwLwLLLLwwLwLGk
tJx
tmx
tmuxt
tm
1 11 1
333
1
1 . ,,
,0,,,
ββ
xxxx
Step 2: barium sulphate precipitation
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
Re=2696 cA0=cB0=100 mol/m3
Supersaturation Nucleation rate (1/m3s) Growth rate (m/s)
Step 2: barium sulphate precipitation
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
10
100
1000
10000
0 500 1000 1500 2000 2500 3000Re
d, n
m
α=0
α=0,2
α=0,5
• Effect of the aggregation efficiency on the final mean particle size
• Crystallite size from X-ray measurements ≈20-40 nm
Step 3: acetone-PEG-doxorubicine/water
• Thermodynamics data concerning polymer and active solubility
• Bivariate population balance equation: DQMOM
• Validation by comparison with Monte Carlo simulations
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
( ) 210 0
2121, , ξξξξξξ ddnm lklk ∫ ∫
∞ ∞
=
Step 3: acetone-PEG-doxorubicine/water
• Validation by comparison with Monte Carlo simulations
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
( ) 210 0
2121, , ξξξξξξ ddnm lklk ∫ ∫
∞ ∞
=
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100τ
Monte Carlo
DQMOM N=3
1.0
2.0
3.0
4.0
5.0
0 50 100τ
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100τ1.0
2.0
3.0
4.0
5.0
0 50 100τ
a b
c d
τ = t β(0)m00(0)
m00 m02
Coalescence
Aggregation and restructuring
Conclusions and next steps
• The flow field in the confined impinging jet reactor has been modeled with RANS and LES (further validation with DNS data)
• Micromixing is taken into account with the DQMOM-IEM model and validation is carried out by comparison with experimental data from literature
• The population balance is described with QMOM (monovariate) and DQMOM (bivariate) resulting in a small number of additional scalars (4-8)
• Simulation of the real process will be carried out when thermodynamic and kinetic expressions will be available
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
Acknowledgements
• Liliana Rivautella (BaSO4 precipitation experiments)
• Emmanuela Gavi (CIJR simulations)
• Funding from the European project PRATSOLIS
Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy
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