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