Pore-scale modeling of reactive and non-reactive transport: Upscaling and multiscale hybrid

modeling

Timothy Scheibe Pacific Northwest National Laboratory

Computational Methods in Water ResourcesJuly 2008

Presentation Outline

Motivation – Two Example ProblemsPore-Scale Modeling

Computational Fluid Dynamics

Smoothed Particle Hydrodynamics

UpscalingPore-to-Darcy Scaling with Nonlinearity

Error Analysis

Hybrid ModelingA Two-Scale SPH Model of Diffusion and Reaction

Coupling Particle and Mesh Methods

Motivation – Mass Transfer Controls on Transport of Uranium

Uranium historically disposed to trenches and ponds at the Hanford Site 300 Area (1943-1994)After initial sharp decline, the plume has persisted at near-constant concentrations and extent

Motivation – Mass Transfer Controls on Transport of Uranium

Subsequent studies have shown that uranium is in the form of mineral precipitates in intragranular fractures in a small fraction (4%) of grains and its transport is controlled by kinetics of dissolution and diffusion-limited mass transfer.

Back-scattered electron SEM images showing intragrain distribution of U(VI) precipitates (white) within a feldspar grain.

Liu, C. X., Zachara, J. M., Yantasee, W., Majors, P. D. & McKinley, J. P. Microscopic reactive diffusion of uranium in the contaminated sediments at Hanford, United States. Water Resources Research 42 (2006).

Motivation – Mass Transfer Controls on Transport of Uranium

Upscaling Issues:Spatial distribution of grains with uranium precipitates (relative to dominant flow paths)

Effective mass transfer rates related to dissolution and diffusion rates within microfractures (with non-linear dissolution reaction kinetics)

Dispersion in complex pore geometry

Local (reacting) concentrations do not equal bulk (average) concentrations

Motivation – Mixing-Controlled Precipitation Reaction

Interest in controlling calcium carbonate precipitation for in-situ sequestration of strontium (Fujita et al. 2004)

Fujita, Y., G. D. Redden, J. C. Ingram, M. M. Cortez, F. G. Ferris, and R. W. Smith, Strontium incorporation into calcite generated by bacterial ureolysis, Geochim. et Cosmochim. Acta, 68(15): 3261-3270, 2004.

Na2CO3 CaCl2

Motivation – Mixing-Controlled Precipitation Reaction

Scaling Issues:Highly localized reaction (local – reacting – concentrations do not equal bulk – average – concentrations)

Strongly coupled transport and reaction

Variable / hysteretic reaction rates

Tartakovsky, A., G. Redden, P. C. Lichtner, T. D. Scheibe, and P. Meakin (2008), Mixing-Induced Precipitation: Experimental Study And Multi-Scale Numerical Analysis, Water Resources Research, 44, W06S04, doi:10.1029/2006WR005725, 2008.

Pore-Scale Modeling

“…It is important to have a reliable physically based tool that can provide plausible estimates of macroscopic properties. Any theoretical or numerical approach to this problem not only needs a detailed understanding of mechanisms at the pore level but also an accurate and realistic characterization of the structure of the porous medium.”

Piri and Blunt, Phys. Rev. E, 026310, 2005

Pore-Scale Modeling Approaches

Computational Fluid Dynamics (CFD)Development of efficient computational mesh is significant effort

Parallel code for efficiency

3D visualization

Pore-Scale Modeling Approaches

Computational Fluid Dynamics (CFD)Application to micromodel experiments

Pore-Scale Modeling Approaches

Movie Clip

Pore-Scale Modeling Approaches

Computational Fluid Dynamics (CFD)Upscaling by numerical solution of volume averaging closure

Pore-Scale Modeling Approaches

Smoothed Particle Hydrodynamics (SPH)

3D parallel SPH code runs on Environmental Molecular Sciences Laboratory supercomputer (fluid flow and solute advection/diffusion) using 500+ processors and 7 million particles

Cross-validation with CFD model (fluid flow only) and possibly others (LB / Front Tracking)

Currently developing capability for intragranular diffusion and surface sorption of uranium

SPH simulation by Bruce Palmer (PNNL); particle visualization by Kwan-Liu Ma,(UC Davis)

Pore-Scale Modeling Approaches

Smoothed Particle Hydrodynamics (SPH)Correlation of local velocities

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Upscaling

Pore-to-Darcy Upscaling of Non-Linear ReactionsVolume averaging with direct numerical simulation

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Thiele modulus

Wood, B. D., K. Radakovich, and F. Golfier, Effective reaction at a fluid–solid interface: Applications tobiotransformation in porous media, Adv. Water Resour., 30:1630–1647, 2007.

Am

Aeff

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Upscaling – Error Analysis

When does upscaling fail?Analysis based on full pore-scale simulation of diffusion/reaction problem

<AB> = <A><B> + <A>B’ + A’<B> + A’B’

A = <A> + A’B = <B> + B’

Hybrid Multiscale Modeling

Conclusion: In some situations, pore-scale modeling provides a more fundamental description of mixing-controlled reactions that are not straightforward to upscale to the continuum scale.Problem: Pore-scale modeling is extremely computationally intensive. Simulation at application-relevant scales is impractical.Potential Solution: Hybrid multiscale modeling – directly couple simulations at two scales (pore and continuum).

Hybrid Modeling

Hybridization methods:Diffusion-reaction problem – SPH/SPH multiscale coupling

Tartakovsky, A. M., D. M. Tartakovsky, T. D. Scheibe and P. Meakin, "Hybrid simulations of reaction-diffusion systems in porous media,“ accepted April 2008 for publication in SIAM Journal on Scientific Computing, in press.

Hybrid Modeling

Hybridization methods:Diffusion example – SPH/FE multiscale coupling

Poster by Yilin Fang and others was presented Monday evening.

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Hybrid Modeling

Hybridization methods:SPH/FE multiscale coupling with advection / diffusion / reaction

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Nie et al.,J. Fluid Mech.500:55-64, 2004

Summary

Pore-scale modeling provides qualitative insights and quantitative support for modeling at larger scales

A variety of methods have been developed for pore-scale modeling

Upscaling / averaging approaches are applicable when fine-scale information can be “thrown away”

Numerical simulation of closure equations allows generalization to complex pore geometries

When fine-scale information is important, a hybrid multiscale approach can be utilized