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Accelerated Deployment of CO 2 Capture Technologies— ODT Simulation of Carbonate Precipitation. Review Meeting—University of Utah September 10, 2012. David Lignell and Derek Harris. Objectives. Year 2 Deliverables

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Accelerated deployment of co 2 capture technologies odt simulation of carbonate precipitation
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
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
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.


Basic kinetic processes
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, Grw

ACC Diss,

Vat. Grw

Key Dynamics occur– mixing dependence

Vat Diss, ACC. Grw

80% precipitation in 1 s.

Primarily ACC.


Basic kinetic processes1
Basic Kinetic Processes

  • 80% precipitation

    • Occurs withing 1 s

    • Primarily ACC

  • No new particles after ~1 s.


Basic kinetic processes2
Basic Kinetic Processes

M3

M0

Moments

VAT

ACC

Cal

nuc

grw

Rates


Timescale analysis
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.

  • Quantify large/small mixing scales: integral/Kolmogorov

  • Where are the reactions?

    • trxn > tmix  no mixing model

    • trxn < tmix  decoupled chemistry

    • trxn ≈ tmix  T.C.I

h

LI


Approach
Approach

Chemistry

Mixing

ODT idealized channel

ODT homogeneous turbulence

Energy Spectra

Timescales

  • 0-D simulations

  • Matlab code

  • 4 polymorphs

  • Nucleation, Growth

  • Solve with DQMOM

  • Analyze QMOM rates


Kinetic analysis
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 analysis1
Kinetic Analysis

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.

  • Timescales / Rates

  • Several approaches

    • ODE integration

      • Simple, global

    • Direct rates from system

      • Scaled nucleation and growth rates.

    • Jacobian matrix

      • Components

      • Eigenvalues

    • Other approaches


Kinetic analysis2
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 analysis3
Kinetic Analysis

Lin and Segel “Mathematics applied to deterministic problems in the natural sciences” 1998.

  • Timescales / Rates

  • Several approaches

    • ODE integration

      • Simple, global

    • Direct rates from system

      • Scaled nucleation and growth rates.

    • Jacobian matrix

      • Components

      • Eigenvalues

    • Other approaches

t


Direct scales
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 from Eigenvalues

1-D

Eigenvalues of Jacobian of RHS function are intrinsic rates, or inverse timescales.

  • Timescales / Rates

  • Several approaches

    • ODE integration

      • Simple, global

    • Direct rates from system

      • Scaled nucleation and growth rates.

    • Jacobian matrix

      • Components

      • Eigenvalues

    • Other approaches

Multi-D


Timescales from eigenvalues1
Timescales from Eigenvalues

Linear

t to 0.01 s

  • Sawada compositions

  • Timescale range

    • 1.2 ms 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:

    t < 0.01 for t < 0.1

Log

t to 10000 s


Vary supersaturation ratio
Vary Supersaturation Ratio

Sawada

  • Vary the range of supersaturation ratios.

  • 1-10x Sawada.

  • Rates increase by (x100)

  • Dynamics occur faster, at earlier times.

10*SSawada


Vary temperature
Vary Temperature

25 oC

  • Vary temperature

    • 25 oC – 50 oC

  • Rates are somewhat higher at higher temperature (but not much).

  • Dynamics occur at similar times.

50 oC


Other
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
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

V.A.C

ACC

Eigenvalues

Peak

Init

t=1s


Mixing scales
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 = n/D varies 120-1300 (H+, CaOH+)


Mixing scales1
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 = n/D varies 120-1300 (H+, CaOH+)


Mixing scales2
Mixing Scales

Kolmogorov

Integral

Velocity

Length

Time

h

LI


Mixing scales3

Scalar Mixing

Sc > 1 gives fine structures at high wavenumbers

Batchelor scale lf

Mixing Scales

Kolmogorov

Integral

Velocity

Length

Time


Mixing scales4
Mixing Scales

Velocity Dissipation Rate

  • 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 RMS

Scalar RMS

Scalar Dissipation Rate


Mixing scales5
Mixing Scales

Integral

Scalar

tu, tf (s)

Velocity

Kolmogrov, Batchelor

Time(s)

Scalar

th, tl (s)

Velocity

Time(s)


Homogeneous turbulence
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 Rel = 206

  • Velocity decays, scalar pushes to high wavenumbers

t=0.001 s

t=0.02 s


Summary1
Summary

u

Mixing—Integral

MIXING

f

  • Mixing and reaction scales overlap

Mixing—Kolm./Batch

f

u

10-10

10-8

10-6

10-4

10-2

10-0

102

104

ODE integration

Direct Nucleation M0

REACTION

Direct Growth M3

V.A.C

ACC

Eigenvalues

Peak

Init

t=1 s


Summary2
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


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