Accelerated Deployment of CO 2 Capture Technologies— ODT Simulation of Carbonate Precipitation Review Meeting—University of Utah September 10, 2012 David.

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