Hybrid Numerical Methods for Multiscale Simulation of Subsurface Biogeochemical Processes

1. Interagency Steering Committee on Multimedia Environmental Modeling (ISCMEM) Annual Public Meeting November 28, 2011 Hybrid Numerical Methods for Multiscale Simulation of Subsurface Biogeochemical Processes Tim Scheibe Pacific Northwest National Laboratory tim.scheibe@pnl.gov

2. Acknowledgments • Work presented here was mostly funded by the Office of Science, Biological and Environmental Research, Subsurface Biogeochemistry Research (SBR) Program: • PNNL-led SciDAC project (Scientific Discovery through Advanced Computing) • PNNL’s SBR Subsurface SFA (Scientific Focus Area) • MAP flowchart was developed during planning stages of a PNNL initiative in Energy Systems Simulation (LDRD – Laboratory Directed Research and Development)

3. What is the appropriate level of complexity in reactive transport modeling? (Thanks to Chris Green, USGS) “Entities should not be multiplied beyond necessity.” William of Ockham (c. 1320) “The variety of beings should not rashly be diminished.” Immanuel Kant (c. 1800) “A model should be as simple as possible, but no simpler.” Albert Einstein (c. 1940) “The secret to successful solute-transport modeling may simply be to lower expectations.” Leonard Konikow (2011 Ground Water)

4. What is the appropriate level of complexity in transport modeling? Descriptive Phenomenological (empirical) physics/chemistry Predictive Fundamental (first-principles) physics/chemistry Technology-driven Problem-driven 2 1 Complex Simple Solid/Fluid Dynamics (pore scale) Quantum Mechanics (electron scale) Calibrated aquifer model (field scale) Darcy’s Law / ADE (porous medium scale) Molecular Dynamics (molecular scale) Two Questions: Where do you need/want to be? (level of predictive power) Where can you be in practical terms? Satisfaction occurs when (1) and (2) coincide

5. Problems… • We often don’t know how to answer question 1 (and may not even give it any thought) • If we do think carefully about question 1, we are often limited by characterization, fundamental understanding, and/or computation such that we cannot achieve satisfaction Solutions… • Lower our expectations (and communicate clearly) • Develop rigorous tools for analyzing multiscale problems, and apply ongoing technology advances to bring questions 1 and 2 into harmony

6. Problems… • We often don’t know how to answer question 1 (and may not even give it any thought) • If we do think carefully about question 1, we are often limited by characterization, fundamental understanding, and/or computation such that we cannot achieve satisfaction Solutions… • Lower our expectations (and communicate clearly) • Develop rigorous tools for analyzing multiscale problems, and apply ongoing technology advances to bring questions 1 and 2 into harmony

7. Multiscale Analysis Platform - MAP Q0 Q1 Complete Fine Scale Solution? Q2 Degree of Coupling? What is the first principle model for your problem? Motif C: Numerical Upscaling/Parameterization Loosely Coupled No Tightly Coupled Q7 Macro- scopic Model Known? Q5 Temporal Scale Separation? (relaxation times) Q4 Self Similar? Q6 Small % of Domain? Q3 Spatial Scale Separation? Yes Q8 Macroscopic Model Known? Fully Decoupled Motif A: Multiresolution Solvers Motif B: Formal Upscaling with Closure Insufficient/None Sufficient Long Relaxation Time at Microscale Short Relaxation Time at Microscale Motif F: Hierarchical Hybrid Multiscale – Time Bursts Yes No Motif D: Fractal Methods No Yes ? Q8 Macro- scopic Model Known? Yes No Yes No Yes No Motif H: Time-Parallel Hierarchical Hybrid Multiscale Motif G: Hierarchical Hybrid Multiscale – Gap Tooth Motif E: Concurrent Hybrid Multiscale F1: Top Down F2:Bottom Up

8. Mixing-Controlled Mineral Precipitation Mixing-controlled calcium carbonate precipitation (Zhang et al., ES&T 44(20), 2010).

9. Mixing Controlled Mineral Precipitation Appropriate level of complexity: Darcy-scale simulation with effective process models and parameters Feasible level of complexity: Darcy-scale simulation with effective process models and parameters Battiato et al. Hybrid models of reactive transport in porous and fractured media. Adv Water Resour (2011), doi:10.1016/j.advwatres.2011.01.012

10. Pore-Scale Modeling and Upscaling Piri and Blunt, Phys. Rev. E, 026310, 2005 • Why 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… mechanismsat the pore level but also an accurate and realistic characterization of the structure of the porous medium.” (emphasis added)

11. Pore-Scale Modeling and Upscaling (X-ray CT Geometry Courtesy John Zachara, PNNL) (MRI Data Courtesy Joe Seymour, Montana St. U.) (Pore-scale Visualization by Chad Jones, UC Davis) Computationally intensive Multiple numerical approaches Makes use of advanced characterization techniques

12. Pore-Scale Dispersion • Particles from inlet face (“..zselect_points”) Simulations by Bruce Palmer, PNNL Animations by Chad Jones and Kwan-Liu Ma, UC Davis Nature of pore-scale dispersion

13. Direct Numerical Upscaling t = 600 t = 300 Example: Intragranular Diffusion No IGD With IGD Simulations by Zhangshuan Hou, PNNL • Explicit pore-scale simulation using SPH method • Two time snapshots • With and without intragranular diffusion • Effective measure: Breakthrough curve • Fit with 1) ADE and 2) MRM

14. 3D Pore-Scale Velocity Benchmark • Based on MRI experiments by Joe Seymour, Montana State University

15. Mixing Controlled Mineral Precipitation Appropriate level of complexity: Pore-scale resolution of flow and reactive transport Feasible level of complexity: Darcy-scale simulation with effective process models and parameters Battiato et al. Hybrid models of reactive transport in porous and fractured media. Adv Water Resour (2011), doi:10.1016/j.advwatres.2011.01.012

16. Hybrid Multiscale Simulation Reaction at each discretization point i Averaged reaction over all i Define mixing coefficient (equals unity if fully mixed) Macroscopic equation – must be “closed” by computing m from pore-scale information

17. Hybrid Multiscale Simulation (figure after Kevrekidis et al. 2003) Tartakovsky and Scheibe, “Dimension reduction method for advection-diffusion-reaction systems,” Advances in Water Resources, 34(12): 1616-1626, doi:10.1016/j.advwatres.2011.07.011, 2011. • Multiscale dimension reduction approach • Reduce degrees of freedom (number of time steps) solved in microscale simulation by iterating between microscale and macroscale • Perform numerical closure on microscale with short bursts of pore-scale simulation where insufficient general closure exists

18. Hybrid Multiscale Simulation Complete Pore-Scale Solution Dimension Reduction Solution Multiscale dimension reduction approach

19. Conclusions • “…as simple as possible” depends on the problem at hand • Rigorous analysis approaches are needed to define the necessary level of complexity for specific problems • Where the necessary level of complexity exceeds technological capabilities, new methods are needed to close this gap • Hybrid multiscale simulation methods offer a means for solving complex problems (in which pore- and Darcy-scale processes are tightly coupled) in a computationally efficient manner • Multiphase flow (e.g., CO2 sequestration) • Microbial dynamics (biofilms, chemotaxis, transport)

20. Questions? http://subsurface.pnnl.gov/