Pore-scale modeling of reactive and non-reactive transport: Upscaling and multiscale hybrid modeling Timothy Scheibe Pacific Northwest National Laboratory Computational Methods in Water Resources July 2008

Presentation Outline Motivation – Two Example Problems Pore-Scale Modeling Computational Fluid Dynamics Smoothed Particle Hydrodynamics Upscaling Pore-to-Darcy Scaling with Nonlinearity Error Analysis Hybrid Modeling A 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 ( ) 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): , Na 2 CO 3 CaCl 2

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: /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, , 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

Upscaling Pore-to-Darcy Upscaling of Non-Linear Reactions Volume averaging with direct numerical simulation effectiveness factor  Thiele modulus Wood, B. D., K. Radakovich, and F. Golfier, Effective reaction at a fluid–solid interface: Applications to biotransformation in porous media, Adv. Water Resour., 30:1630–1647, 2007.

Upscaling – Error Analysis When does upscaling fail? Analysis based on full pore-scale simulation of diffusion/reaction problem = + B’ + A’ + A’B’ A = + A’ 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.

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