# Presentation: 694461

## 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 (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.

## 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

## Upscaling

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

- 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

- <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.

## 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