Accelerated Deployment of CO 2 Capture Technologies— ODT Simulation of Carbonate Precipitation
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Accelerated Deployment of CO2 Capture
Technologies—
ODT Simulation of Carbonate
Precipitation
Review Meeting—University of Utah
September 10, 2012
David Lignell and Derek Harris
Objectives
• Year 2 Deliverables– Validation study of ODT with acid/base chemistry and population balance
against CO2 mineralization data identified in the scientific literature.
– Quantification of relevant timescale regimes for mixing, nucleation, and growth processes with associated identification of errors in LES models.
• Tasks– Implement acid/base chemistry and population balances in ODT code.
– Identification studies for active timescales: turbulent mixing, nucleation, growth.
– Quantification studies for influence of timescale approximations on particle sizes and polymorph selectivity.
– Investigation of implications of timescales on LES models.
Progress
• Focus on timescale analysis
– Chemical Kinetic timescales
– Mixing timescales in ODT
• Ongoing kinetic development with Utah group
– Heterogeneous nucleation
– Coagulation
• Beginning investigation of implications of timescales on
LES models.
Key Dynamics occur– mixing dependence
Basic Kinetic Processes
• Mix two aqueous streams
– Na2CO3, CaCl2
• Polymorphs:
– ACC, Vaterite, Aragonite, Calcite
• High super saturation ratio S causes precipitation
– ACC nucleates quickly, reduces S to 1
– As other polymorphs nucleate and grow, ACC dissolves, maintaining S
– When ACC is gone, S drops again, stepping through polymorphs.
• Nucleation rates are key– Set ratios of number densities, which then
grow/dissolve abundances
ACC Nuc, GrwACC Diss, Vat. Grw
Vat Diss, ACC. Grw
80% precipitation in 1 s.
Primarily ACC.
Basic Kinetic Processes
• 80% precipitation– Occurs withing 1 s
– Primarily ACC
• No new particles after ~1 s.
Basic Kinetic Processes
M0M3
Mo
men
tsR
ate
s
ACC VAT Cal
nuc
grw
Timescale Analysis
• Goal– Quantify timescales: Reaction Mixing
– Overlap of scales influences model development
• Turbulent flows contain a range of scales.
• Represented by the turbulent kinetic energy and scalar spectra.
LI
• Quantify large/small mixing scales: integral/Kolmogorov
• Where are the reactions?– rxn > mix no mixing model
– rxn < mix decoupled chemistry
– rxn ≈ mix T.C.I
Approach
Chemistry
• 0-D simulations
• Matlab code
• 4 polymorphs
• Nucleation, Growth
• Solve with DQMOM
• Analyze QMOM rates
Mixing
• ODT idealized channel
• ODT homogeneous turbulence
• Energy Spectra
• Timescales
Kinetic Analysis
• Timescales / Rates
• Several approaches– ODE integration
• Simple, global
– Direct rates from system• Scaled nucleation and
growth rates.
– Jacobian matrix• Components
• Eigenvalues
– Other approaches
Kinetic Analysis
• Timescales / Rates
• Several approaches– ODE integration
• Simple, global
– Direct rates from system• Scaled nucleation and
growth rates.
– Jacobian matrix• Components
• Eigenvalues
– Other approaches
• Solving with explicit Euler.– All Matlab solvers failed (long run times,
or no solution).
• Stable timesteps for
• Adjusting stepsize as
– Verified accuracy by comparison of coefficient 0.1, 0.01.
Kinetic Analysis
• Timescales / Rates
• Several approaches– ODE integration
• Simple, global
– Direct rates from system• Scaled nucleation and
growth rates.
– Jacobian matrix• Components
• Eigenvalues
– Other approaches 0
“Timescales” range from 1E-11 seconds to 1 second, during a 1 second simulation.
Kinetic Analysis
• Timescales / Rates
• Several approaches– ODE integration
• Simple, global
– Direct rates from system• Scaled nucleation and
growth rates.
– Jacobian matrix• Components
• Eigenvalues
– Other approaches
Lin and Segel “Mathematics applied to deterministic problems in the natural
sciences” 1998.
Direct Scales
• Timescales / Rates
• Several approaches– ODE integration
• Simple, global
– Direct rates from system• Scaled nucleation and
growth rates.
– Jacobian matrix• Components
• Eigenvalues
– Other approaches
Timescales from Eigenvalues
• Timescales / Rates
• Several approaches– ODE integration
• Simple, global
– Direct rates from system• Scaled nucleation and
growth rates.
– Jacobian matrix• Components
• Eigenvalues
– Other approaches
1-D
Multi-D
• Eigenvalues of Jacobian of RHS function are intrinsic rates, or inverse timescales.
Timescales from Eigenvalues
• Sawada compositions
• Timescale range – 1.2 s to O(>1000 s)
• Initial period is one of nucleation of particles.
• Variations as growth processes activate at times 10-8-10-5 s.
• Eigenvalue functions don’t preserve identities– sorting (“color jumping”)
• Fast dynamics occur up front: < 0.01 for t < 0.1
Lineart to 0.01 s
Logt to 10000 s
Vary Supersaturation Ratio
• Vary the range of
supersaturation ratios.
• 1-10x Sawada.
• Rates increase by (x100)
• Dynamics occur faster, at
earlier times.
Sawada
10*SSawada
Vary Temperature
• Vary temperature – 25 oC – 50 oC
• Rates are somewhat higher at higher temperature (but not much).
• Dynamics occur at similar times.
25 oC
50 oC
Other
• Diagonals of Jacobian are very similar to the eigenvalues.
• Investigaged and implemented eigenvalue tracking analysis– Kabala et al. Nonlinear Analysis, Theory, Methods, and Applications, 5(4) p 337-340 1981.
– To overcome sorting/identity problems, allowing mechanism investigation.
• Sensitivity analysis, CMC approaches
• PCA discussions with Alessandro
• DQMOM scales
• Coagulation considered. Very little changes (timescales).
• Heterogeneous nucleation
Summary
• Timescales can be tricky to compute and interpret
• Wide range of scales
• Will overlap with mixing scales
10-10 10-8 10-6 10-4 10-2 10-0 102 104
ODE integration
Direct Nucleation M0
Direct Growth M3
ACC V.A.C
Eigenvalues
Peak Init t=1s
Mixing Scales
• Mixer configuration—ODT – Sawada streams: m0/m1 = 0.4
– 1 inch Planar, temporal channel flow
– Re = 40,000
– Transport elemental mass fractions
– Sc = /D varies 120-1300 (H+, CaOH+)
Mixing Scales
• Mixer configuration—ODT – Sawada streams: m0/m1 = 0.4
– 1 inch Planar, temporal channel flow
– Re = 40,000
– Transport elemental mass fractions
– Sc = /D varies 120-1300 (H+, CaOH+)
Mixing Scales
LI
Integral Kolmogorov
Velocity
Length
Time
Mixing Scales
Integral Kolmogorov
Velocity
Length
Time
• Scalar Mixing– Sc > 1 gives fine structures
at high wavenumbers
• Batchelor scale
Mixing Scales
• Channel flow config is in progress.
• Challenging case– Non-homogeneous
– Energy spectra windowing.
• Full domain has a wide range of scales in channel flow
• Velocity and scalar dissipation is noisy (128 rlz).– Both decay in time, but velocity decays towards a
stationary value.
Velocity Dissipation Rate
Scalar Dissipation RateScalar RMSVelocity RMS
Mixing Scales
u
(s)
Time(s)
Scalar
Velocity
Time(s)
(s)
Scalar
Velocity
Integral
Kolmogrov, Batchelor
Homogeneous Turbulence
• Homogeneous turbulence simulations performed
• Faster turnaround, analysis.
• Initialize using Pope’s model spectrum
• Scalar transport with Sc=850 (the avg)
• Scalar initialized with scaled velocity field at Sawada average streams with peak mixf at 1.
• u’ = 0.3 (channel at 0.005 seconds, peak value)
• Li = 0.01 (~half channel); Ldom = 10Li Re = 206
• Velocity decays, scalar pushes to high wavenumberst=0.001 s t=0.02 s
Summary
• Mixing and reaction scales overlap
10-10 10-8 10-6 10-4 10-2 10-0 102 104
ODE integration
Direct Nucleation M0
Direct Growth M3
ACC V.A.C
Eigenvalues
Peak Init t=1 s
Mixing—Kolm./Batch
Mixing—Integral
u
u
MIXING
REACTION
Summary
• Wide range in reaction timescales
• Mixing and reaction timescales are not widely
disparate
• Test homogeneous mixing, vary mixing rates.
• LES model implications and testing