CFD modeling of precipitation of nanoparticles in Confined...
Transcript of CFD modeling of precipitation of nanoparticles in Confined...
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