modelling across the length scales

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modelling across the length scales

• Computational Modelling Group (CoMo) Cambridge,
  14th February 2007

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the CoMo group at Cambridge
Founded in 1999, the CoMo group led by Dr. Markus
Kraft currently has 20 members
We develop and apply modern numerical methods to
problems arising in Chemical Engineering Overall
aim
to shorten the development period from research
bench to the industrial production stage by
providing insight into the underlying physics and
supporting the scale-up of processes to
industrial level
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research themes

• Common applications currently researched within
  the group include

particle processes
nanoparticles
engines

• Novel Methods researched include Numerics, CFD
  and Quantum Chemistry

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a hierarchy of scales

• Modelling takes place across a hierarchy of
  scales

• Modelling takes place across a hierarchy of
  scales
• Micro- and meso-scale modelling directly feeds
  into macro-scale models of industrial processes

• All models validated against experimental data

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micro-scale models

• Micro-scale simulation is modelling at the very
  smallest quantum scale
• Can provide parameters when experiments are
  impractical or impossible

• All models validated against experimental data

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micro-scale TiO2 production

• 4 million tonnes per year of TiO2
• Main use opacifier
• Particle size distribution of product is
  important

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chloride process
TiCl4(l)
TiO2(s)
Chlorination
Oxidation
Milling
Purification

• TiO2 made by oxidising TiCl4(g) at high temp
• Milling breaks down agglomerates

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example un-milled product
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why model the micro-scale?

• Particle inception is critical
• Detailed population balance model requires
  chemical mechanism information
• Thermodynamic information for intermediate
  species
• Rates of reaction between species

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existing data guessed in 1963

• TiOCl2 from JANAF tables
• guessed in 1963

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quantum chemistry

• Solve the Schrödinger wave equation
• Cant solve for multi-electron molecules
• Density Functional Theory (DFT)
• good results in reasonable time

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quantum calculations

• Electronic energy
• Geometry optimisation
• Rotational constants
• Vibrational frequencies
• Find temperature variation of Cp, H, S through
  Statistical Mechanics

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transition states
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reaction mechanism
reaction mechanism
CoMo Group http//como.cheng.cam.ac.uk
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gas phase chemistry

• Qualitatively correct TiCl4 into dimer

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gas phase chemistry

• Qualitatively correct TiCl4 into dimer
• Details of intermediate species

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gas phase chemistry

• Qualitatively correct TiCl4 into dimer
• Details of intermediate species
• Principle pathways

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gas phase chemistry

• Qualitatively correct TiCl4 into dimer
• Details of intermediate species
• Principle pathways
• Sensitivity analysis what needs work?

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rutile (110) surfaces
Defective, partially reduced TiO2110 surface
Reduced Surface TiO2110
Stoichiometric Surface TiO2110
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surface growth reactions
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adsorption energies
Defective, partially reduced TiO2110 surface
Reduced Surface TiO2110
Stoichiometric Surface TiO2110
-3.0 eV
-1.88 eV
0.59 eV
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diffusion and desorption

• Locate transition states with DFT
• Model diffusion and desorption using microkinetic
  simulations

Reduced Surface TiO2110
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meso-scale models

• Meso-scale modelling involves
• physically motivated descriptions of the
  behaviour of individual particles,
• e.g. single droplet drying in spray dryers
• describing the evolution of populations of such
  particles,
• e.g. soot, agglomeration

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micro/meso-scale nanoparticles
To model nano-particle production it is necessary
to consider

• Gas phase reactions
• Particle inception
• Surface reactions
• Particle agglomeration
• Sintering

• for a population of particles
• in an industrial reactor!

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solving it all at once

• Operator Splitting
• Chemistry Deterministic ODE solver
• Particles Stochastic population balance solver
• Benefit of stochastic solver track many particle
  properties
• e.g. primary particle sizes

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meso-scale - nanoparticles
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0.5 seconds
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0.5 seconds
0.75 seconds
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0.5 seconds
0.75 seconds
1 second
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0.5 seconds
5 seconds
0.75 seconds
1 second
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0.5 seconds
5 seconds
10 seconds
0.75 seconds
1 second
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full 3D geometry tracking
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meso-scale models

• Physically motivated model for single droplet
  drying
• Goal to produce a meso-scale model for
  incorporation into a macro-scale model of an
  industrial spray dryer
• Requirements of the final macro-scale simulation
  dictate the properties and features incorporated
  in the individual droplet model

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meso-scale droplet drying

• Physically motivated model for single droplet
  drying
• Goal to produce a meso-scale model for
  incorporation into a macro-scale model of an
  industrial spray dryer
• Requirements of the final macro-scale simulation
  dictate the properties and features incorporated
  in the individual droplet model

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modelling approach

• Adopt an Eulerian-Lagrangian framework

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droplet drying model system

• Model developed for detergent drying, but can be
  used for other systems, e.g.
• Powdered milk
• Coal-water slurrys ? burning
• Pharmaceuticals ? encapsulation
• All complex mixtures ? assumptions necessary for
  modelling
• Three component system
• Spherical particles, 1D model
• Single centrally located bubble
• Small Biot number ? uniform particle temperature

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droplet drying model system

• Population balance for solids

• Volume-averaged transport equations for the
  continuous phase

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droplet drying deliverables

• Droplet drying model capable of
• Predicting drying curves (moisture v. time)
• predicting spatially resolved solids and moisture
  profiles
• Describing evolving particle morphology

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meso-scale granulation

• Granules particle mixture on meso-scale
• better handling
• costumer benefits (e.g. delivery of active
  component)
• model process for prediction of product quality
• study influence of process conditions and
  composition
• faster formulation change due to reduced number
  of experiments for production approval

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meso-scale granulation

• Granules particle mixture on meso-scale
• better handling
• costumer benefits (e.g. delivery of active
  component)
• model process for prediction of product quality
• study influence of process conditions and
  composition
• e.g. faster formulation change due to reduced
  numberof experiments for production approval

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granulation approach

• use population balance equations (PBE)
• evolution of particles
• multi-dimensional particle description
• incorporation of various subprocesses
• current framework in more details

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granulation particle description

• composition of a granule
• solid material
• binder on solid
• pores
• binder in pores
• reaction products
• spherical particles
• 5 independent variables for particle
  description

solid material
reaction products
binder on solid
binder in pores
pores
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granulation transformations

• Addition of binder
• Coalescence
• Compaction
• Breakage
• Penetration
• Reaction

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meso-scale summary

• promising results for comparison of bench scale
  experiment and simulation
• Future
• more complex particle description
• study influence of subprocesses (sensitivity)
• more than one control volume (flowsheet)
• use in plant control

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meso/macro-scale

• Many applications necessitate modelling particles
  flowing through complex geometries
• Such problems lie in the intersection between
  meso and macro-scales
• Bridge these scales by developing strategies for
  coupling the solution methods from each

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from meso to macro

• Many applications necessitate modelling particles
  flowing through complex geometries
• Such problems lie in the intersection between
  meso and macro-scales
• Bridge these scales by developing strategies for
  coupling the solution methods from each

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applications

• Typical applications involve particles with a
  large number of internal coordinates
• Several examples already discussed
• Nano particles mass, volume, surface area,
  number of primary particles
• Detergent powders solid, binder, pores, binder
  in pores, reactants
• There are many more

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what do we want?

• Fully spatially resolved particle size
  distribution (PSD).
• The ability to track multiple internal
  coordinates e.g., diameter, temperature, moisture
  content.
• Quick and efficient algorithms.

All of these problems necessitate the solution of
population balance equations
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population balances

• Used whenever considering the interaction of a
  large number of particles
• The general form is
• Generally difficult to solve, so stochastic
  methods are appealing

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stochastic solutions
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stochastic solutions
Initialise solution
Coagulation
Select 2 particles
Calculate total rate of all processes
Perform Coagulation
Sintering
Wait exponentially distributed time ?t t ? t ?t
Select particle
Perform sintering
Yes
Surface growth
Is t tstop?
Select particle
Perform Surface Growth
No
Update solution incl. chemistry
Select event to perform
Inception
Perform Inception
STOP
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stochastic solutions
Calculate total rate of all processes
Initialise Solution
Update solution (including chemistry)
Wait exponentially distributed time ?t t ? t ?t
Perform particle processes, e.g., coagulation,
sintering, surface growth, inception, breakage
Is t tstop?
STOP
Yes
No
Select event to perform based on rates
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meso/macro-scale bridge

• Macro-scale modelling involves
• Predicting product properties from large scale
  simulations
• Combining multiple sub-models from the meso-scale
• Goal To develop useful industrial tools enabling
  a wide class of two-phase flow problems to be
  analysed

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coupling to CFD
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CFD results
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CFD results

• Velocity profiles from CFD simulation of test bed
  spray drying tower

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CFD results (3)
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CFD results (3)
For trivial kernels we can compare with the
method of moments
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case study - engines

• Engines continue to be a major research interest
  of the CoMo group
• Demonstrates
• Multiscale modelling
• Industrial collaboration

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engine modelling

• Industrial collaborators

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engine modelling macro-scale

• Full-cycle 1D CFD

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engine modelling macro-scale

• 3D CFD

• Li Cao

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engine modelling macro-scale

• HCCI knock

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engine modelling meso-scale

• Prediction of soot aggregates (work in progress)

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engine modelling micro-scale

• Prediction of trace species (emissions)

SAE 2006-01-1362
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thank you for listening