Numerical Simulation of a Solubility Process
in a Stirred Tank Reactor
Hugo Hartmann; Jos J. Derksen; Harry E.A. Van den Akker
Delft University of Technology, The Netherlands
Computational Fluid Dynamics in Chemical Reaction Engineering IV, Barga, Italy
August
8, 2005
August
8, 2005
Kramers Laboratorium voor Fysische Technologie
Multi-Scale Physics Department
Outline
Introduction
- industrial mixing
- objective
Simulation approach
-
LES (lattice-Boltzmann)
scalar mixing (finite volume)
particle transport
flow system & settings
Results
- solids and scalar distributions
- particle size distribution
- solubility time
Conclusions and perspectives
August 8, 2005
2
Introduction
Industrial mixing
Multi-phase mixing
Products
competitiveness
product quality
process optimization, etc
Lack of insight in
hydrodynamic phenomena
heat & mass transfer
Turbulence
break-up/coalescence
particle /bubble/droplet motion
August 8, 2005
Need for information on …
agglomeration/attrition
chemistry
collisions
3
Introduction
Scalar mixing; objectives
Contribute to reliable numerical predictions of
complex, multi-phase processes
Focus: solid-liquid mixing including mass transfer
Complex geometry: Rushton turbine stirred tank
Applications: crystallization, solubility processes, …
Tools:
- LES flow solver (lattice-Boltzmann)
- Scalar transport solver (finite volume)
- Particle transport solver (extension of the work of Derksen(1))
August 8, 2005
(1)
Derksen (2003)
4
Simulation approach
Large Eddy Simulation (LES)
Realistic description of multi-phase/
chemical reacting processes
Instantaneous
Time-averaged
- Small scale mixing
- Time dependency flow
Large Eddy Simulation
Smagorinsky SGS model(1)
Lattice Boltzmann discretization(2)
August 8, 2005
(1) Smagorinsky
(1963)
(2) Somers (1993)
Colors: kinetic energy
5
Simulation approach, cont’d
Assessment stirred tank flow (LES), Re = ND2/ν = 7,300(1)
0.5 vtip
LDA
LES
1
0.4
z/T (-)
k/vtip2
LDA
0.66
z/T(-)
0.26
LES
0.4
z/T (-)
0.33
0
r/T (-)
August 8, 2005
(1) Hartmann
et al (2004)
0.5
0
0
r/T (-)
0.26
0.33
6
Simulation approach, cont’d
Scalar mixing
Explicit finite volume scheme (LES; small time steps)
Cartesian grid of the flow
Coupled to LES
Flux-limited convection scheme (TVD)
Staircase-shaped walls inaccurate
wall representation (impeller!)
Impose dc/dn = 0 by means of
ghost cells (2 nd order)
4
3
∆
1
∆
No cut cells; no stability problems
Scalar mass conservation not guaranteed
August 8, 2005
dc/dn=0
2
1
2 3 4
∆
∆
7
Simulation approach, cont’d
Assessment mixing time experiment, Re =
ND2/ν
=
Exp.
Sim.
24,000(1)
c/c∞ 5
c/c∞
5
1
c/c∞
0
5
0
99% Mixing time:
concentration fluctuations < 1% final concentration
Nθm,99% = 73 (26% overprediction)
August 8, 2005
(1) Distelhoff
et al (1997)
1
0
0
Nt
60
8
Simulation approach, cont’d
Particle transport(1)
Euler-Lagrange approach
‘Point’ particles; dp < ∆
Particle dynamics
- forces from single-particle
correlations (drag, lift, ...)
- collisions
- simple two-way coupling
limits the applicability to “low” φV
Particle-impeller and particle
wall collisions: fully elastic
August 8, 2005
(1)
Derksen (2003)
Re = 105
9
Simulation approach, cont’d
Solid-liquid mixing including mass transfer
Single-phase LES solver
Scalar mixing solver
Particle transport solver
mass transport
crystallization process
solubility process, …
Focus on solubility process
c
φm”
csat
source term FV code:
S = Σp φm
mass flux:
φm”=Shρp(Γ/dp)(csat – c)
August 8, 2005
10
Simulation approach, cont’d
Flow system, settings
Physical case
T = 0.23 m (10 liter vessel)
working fluid: water
Re = 105 → N = 16.5 rev/s
7·106 calcium-chloride beads
csat = 600 kg/m3
Γmol = 0.7·10-9 m2/s (calcium ions)
beads released in upper part (0.9T-T)
dp = 0.3 mm; ρp/ρliq = 2.15
φV = 10% (average 1%)
Njs = 11.4 rev/s
August 8, 2005
11
Results
Nt = 7
August 8, 2005
Nt = 20
Nt = 5
Nt = 2
dp / dp0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Nt = 10
Animation spatial particle distribution: 0 < Nt ≤ 60
The particles
are 5 times
enlarged
12
Results, cont’d
Animation concentration distribution: 0 < Nt ≤ 20
Nt = 10
Nt = 2
c / c∞
Nt = 20
Nt = 5
2
1.8
1.6
1.4
Nt = 7
1.2
1
0.8
0.6
0.4
0.2
0
August 8, 2005
13
0.6
Nt = 60
Snapshots spatial particle distributions (particles 10 times enlarged)
dp / dp0
dp / dp0
0.5
0.7
0.25
0.5
0.01
0.05
0
0
Np / N p0
Np / N p0
Nt = 26.5
Results, cont’d
0 0.5 1
dp / dp0
August 8, 2005
0.01
0.05
0
0 0.5 1
dp / dp0
14
Results, cont’d
Snapshot of spatial particle and concentration distribution at Nt = 15
dp / dp0
c / c∞
0.82
0.8
0.79
0.72
0.76
0.64
0.73
0.56
0.7
0.48
0.67
0.4
The particles are 10 times enlarged
August 8, 2005
15
Results, cont’d
Solubility stages
1
I
II
III
I: Mixing & Dispersing (0 ≤ Nt < 12)
II: Quasi steady-state (12 ≤ Nt < 24)
III: Resuspension (24 ≤ Nt < 42)
IV: Dissolution (Nt ≥ 42)
V: Homogeneous suspension (Nt ≥ 58)
IV
0.6
0.9T - T
1
0.4
0 – 0.1T
0.2
0
0
20
August 8, 2005
40
60
Nt (-)
Np / N p0 (-)
Np / N p0 (-)
0.8
V
80
100
0
0
Nt (-)
15
16
Results, cont’d
Evolution particle size distribution in time
Nt = 10
Np / N p0
100
Nt = 60
Nt = 5
Nt = 20
Nt = 80
10-3
Nt = 7
Nt = 40
Nt = 100
d32 / d p0 (-)
Nt = 2
1
0.8
Sauter diameter
0.6
0.4
0.2
0
0 20 40 60 80 100
Nt (-)
Sh = 2 + 0.6Rep0.5Sc0.33
dp → 0
Sh → 2
10-6
0 d /d 1
p
p0
August 8, 2005
(1)
Ranz and Marshall (1952)
d(dp )/dt ∝ dp-1
φm ∝ dp
17
(1)
Results, cont’d
Solubility time
1
Np / N p0 (-)
0.8
99% Solubility time
(Nt = 84)
0.6
0.4
0.2
0
August 8, 2005
50
60
70
80
Nt (-)
90
100
18
Results, cont’d
2
2
1.6
1.6
c / c∞ (-)
c / c∞ (-)
Concentration profiles
1.2
0.8
1.2
0.8
0.4
0.4
0
0
0
20 40 60 80 100
Nt (-)
0
20 40 60 80 100
Nt (-)
Unphysical mass increase: 0.12% each impeller revolution
Due to newly developed immersed boundary technique
August 8, 2005
19
Conclusions…
Solubility time at most one order of magnitude larger than
mixing time scale
Four stages identified: mixing and dispersing, quasi steady-state,
resuspension, dissolution
Decreasing particle inertia: streaky patterns disappear
Non-homogeneous mixing effects: development PSD
Scalar transport matches particle transport
Unphysical scalar mass increase is due to newly developed immersed
boundary technique
August 8, 2005
20
… and perspectives
LES including scalar mixing in conjunction with particle transport
has become a promising possibility to study multi-phase processes
in lab-scale reactors
Improvements:
- Collision algorithm
- Inclusion hydrodynamic interactions between particles
- Immersed boundary technique for scalars
Future direction: crystallization process
- Nucleation
- Attrition
- Agglomeration
August 8, 2005
21
Acknowledgement
This work was sponsored by the Netherlands National
Computing Facilities for the use of supercomputer
facilities, with financial support from the Netherlands
Organization for Scientific Research (NWO).
August 8, 2005
22