1 hybrid and multiscale modeling of subsurface flow and transport processes mesa c organizers:...

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Hybrid and Multiscale Modeling of Hybrid and Multiscale Modeling of Subsurface Flow and Transport Subsurface Flow and Transport

ProcessesProcesses

Mesa CMesa C

Organizers:Organizers:

Timothy Scheibe (PNNL)Timothy Scheibe (PNNL)Daniel Tartakovsky (UCSD)Daniel Tartakovsky (UCSD)

Hybrid and Multiscale Modeling of Hybrid and Multiscale Modeling of Subsurface Flow and Transport Subsurface Flow and Transport

ProcessesProcesses

Mesa CMesa C

Organizers:Organizers:

Timothy Scheibe (PNNL)Timothy Scheibe (PNNL)Daniel Tartakovsky (UCSD)Daniel Tartakovsky (UCSD)

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Hybrid Models for Multiscale Simulation of Subsurface Biogeochemical Processes

Tim Scheibe1

Daniel Tartakovsky2

Alexander Tartakovsky1

George Redden3

1Pacific Northwest National Laboratory 2University of California, San Diego3Idaho National Laboratory

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MotivationMotivationMotivationMotivationContinuum reactive transport models may not adequately describe localized coupled precipitation / transport / reaction processes in the presence of high concentration gradients.

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-40 -20 0 20 40

Distance from centerline (cm)

Sa

tura

tio

n In

de

x

Z = 40.5 cm

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A+B=C reactive system (Chopard et al., 1994).

Continuity equation

Momentum conservation

1( ) /n s

m

V D C n

x

2/A A A AB A BdC dt D C k C C 2/B B B AB A BdC dt D C k C C 2/C C C AB A BdC dt D C k C C

( )C C CeqD C k C C nSurface reaction

Surface growth

/d dt v

2/ 1/ / 1/ extd dt P v v F

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Uncoupled Precipitation SimulationUncoupled Precipitation SimulationUncoupled Precipitation SimulationUncoupled Precipitation Simulation

ABkt

BAB

ABkt

AAB

Concentration of “A”

(Concentration of “B” is mirror image)

Concentration of “Caq”

Concentration of “Cs”

Continuum simulation with no change in flow or transport properties. Grid refined to 1 cm in center of domain.

ABkt

AAB

)( eqCAB CCkABkt

C

)( eqCb

s CCkt

C

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Fully Coupled Continuum SimulationFully Coupled Continuum SimulationFully Coupled Continuum SimulationFully Coupled Continuum Simulation

Continuum simulation with modification of permeability and transverse dispersivity as a function of changes in porosity associated with precipitation.

Porosity reduction only from 0.37 to 0.23

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Smoothed Particle Hydrodynamics Lucy (1977), Gingold and Monaghan (1977)

SPH does not require structured computational mesh for calculation of special derivatives. Fluids and solids are replaced with a set of particles. The particles serve as interpolation points from which properties of the fluid can be calculated.

( , )ba b a b

b b

mA A W h

r r

( , )ba b a b

b b

mA A W h

r r

0lim ( , ) ( )a b a bh

W h

r r r r

The SPH particles are material particles which can be treated like any other particle system.

W

Spatial derivatives can be found by analytical differentiation of the kernel:

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SPH Extension to Precipitation/Dissolution Reactions:

• Rate of gain/loss of mass in the solid phase is approximated by

• The processes of precipitation and dissolution are modeled by tracking the masses, mi, of the solid particles. Once the mass of a solid particle reaches twice the original mass of the solid particle the nearest fluid particle ‘precipitates’, becoming a new solid particle• Similarly, if the mass of a solid particle reaches zero, the solid particle becomes a new fluid particle. Since the new fluid particles will be very close to the solid boundary, where the fluid velocity is very small, the initial velocity of a new fluid particle is set to zero.

ij eq ij

j fi

dm RC C i s

dt n

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Comparison of SPH and one-dimensional analytical solutions of the diffusion equation with reaction (adsorption)

at a fixed solid boundary.

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Position of a solid boundary (in units of h) as a function of time (in dimensionless SPH model time

units) obtained by SPH simulations and analytically.

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time

front positio

n, S

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SPH

analytical

Tartakovsky A. M., P. Meakin, T. D. Scheibe, and R. M. Eichler West, "Simulations of reactive transport and precipitation with smoothed particle hydrodynamics." Journal of Computational Physics, 222(2):654-672, 2007.

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Side-by-side injection of reacting solutions into two halves of a two-dimensional granular porous medium.

Na2CO3 CaCl2

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Steady state solubility product <CA><CB>. Non-reactive flow, Pe=2.8

Changes in solubility product <CA><CB> as result of precipitation. Reactive flow, Pe=2.8

t = 1000

t = 6000t = 3000t = 1000

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Rate of change of <CC> due to reaction between solutes A and B versus the product of the average concentrations <CA><CB> for two Peclet numbers.

Rate of change of <CC> due to precipitation as a function of <CC> - Ceq for two Peclet numbers.

Effective reaction rates

Generation of “C” Precipitation of “C”

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New Direction: Hybrid ModelingNew Direction: Hybrid ModelingNew Direction: Hybrid ModelingNew Direction: Hybrid Modeling

Conclusion: Pore-scale modeling provides a more fundamental description of these strongly-coupled processes (mixing and reaction) that are not well described at 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).

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Hybrid Modeling – BackgroundHybrid Modeling – BackgroundHybrid Modeling – BackgroundHybrid Modeling – Background

Hybrid multiscale models can be traced back to the early 1970’s (Gehlen et al. 1972) and have become widely used in some disciplines during the last decade.

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Hybrid multiscale models can be traced back to the early 1970’s (Gehlen et al. 1972) and have become widely used in some disciplines during the last decade. Materials Science:

“Modeling and simulation on various length and time scales have become a major field of Materials Science and Engineering in academia as well as in industrial research and development.”

(Multiscale Materials Modeling conference; http://www.mmm2006.org/cms/front_content.php)

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Hybrid multiscale models can be traced back to the early 1970’s (Gehlen et al. 1972) and have become widely used in some disciplines during the last decade. Materials Science:

Figures from Belytschko and Xiao, 2003 and Xiao and Belytschko, 2004.See also reviews by Csanyi et al., 2005; Wang and Zhang, 2006.

Bridging domain model of a nanotube

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Hybrid multiscale models can be traced back to the early 1970’s (Gehlen et al. 1972) and have become widely used in some disciplines during the last decade. Chemical Engineering (catalysis and reactor processes):

From Vlachos et al. 2006

Comparison of predictions for NH3 decomposition on Ru with and without adsorbate-adsorbate interactions.

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Hybrid multiscale models can be traced back to the early 1970’s (Gehlen et al. 1972) and have become widely used in some disciplines during the last decade. Chemical Engineering (catalysis and reactor processes):

From Vlachos 1999

Thin film deposition processes – multiple length scales encountered.

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Hybrid multiscale models can be traced back to the early 1970’s (Gehlen et al. 1972) and have become widely used in some disciplines during the last decade. Life sciences:

From Villa et al. 2005

Multiscale model of lac repressor – DNA complex. Grey box is MD domain; DNA loop outside the box is modeled by elasticity theory (see below).

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Hybrid multiscale models can be traced back to the early 1970’s (Gehlen et al. 1972) and have become widely used in some disciplines during the last decade. Hydrodynamics:

From Wijesinghe et al. 2004

Self-diffusion of Argon gas (two colors). Simulated using hybrid Direct Simulation Monte Carlo / Euler method.

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What about porous media? From Balhoff et al. 2007

Two porous media of contrasting permeability (e.g., sand-filled fracture and relatively impermeable matrix). Network pore model in pore-scale region; continuum model in matrix region.

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Current ResearchCurrent ResearchCurrent ResearchCurrent Research

Hybrid Numerical Methods for Multiscale Simulations of Subsurface Biogeochemical Processes SciDAC Science Application (with two Science Application

Partnerships) funded in FY2007-2010.

http://subsurface.pnl.gov

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Partnerships) funded in FY2007-2010. Objective: Develop a component-based parallel model of

groundwater flow and multicomponent reactive transport by directly coupling sub-pore-, pore-, and continuum-scale models.


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Partnerships) funded in FY2007-2010. Objective: Develop a component-based parallel model of

groundwater flow and multicomponent reactive transport by directly coupling sub-pore-, pore-, and continuum-scale models.

Current focus: Hybrid two-scale model of calcite precipitation problem


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Continuum ModelContinuum ModelContinuum ModelContinuum Model

Subsurface Transport Over Multiple Phases (STOMP) Multiphase flow (sat/unsat) with multicomponent reactions Common Component Architecture framework Weak scaling studies

Smoothed Particle Hydrodynamics Can be used at continuum scale also Paper in preparation

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Pore-Scale ModelPore-Scale ModelPore-Scale ModelPore-Scale Model

Smoothed Particle Hydrodynamics 2D code being used to test model coupling Parallel 3D code is being debugged and validated

Front-Tracking Method (FronTier) Collaboration with Xiaolin Li (SUNY Stony Brook) and Harold

Trease (PNNL) http://www.ams.sunysb.edu/~linli/art/crystal.html

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First Hybrid (Continuum-Pore) ModelFirst Hybrid (Continuum-Pore) ModelFirst Hybrid (Continuum-Pore) ModelFirst Hybrid (Continuum-Pore) Model

SPH at both scalesNo advection; mixing by diffusion only and heterogeneous reactionAlso working on a coupled SPH / FE model using “compatibility coupling” (Rabczuk et al 2006).

(Tartakovsky et al., in preparation)

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ConclusionsConclusionsConclusionsConclusions

Hybrid multiscale methods represent a potentially powerful approach to subsurface reactive transport simulations in which highly coupled, non-linear, localized processes predominate.There has been little work undertaken to date in this area but we can build from developments in other disciplines.We have initiated a project that is developing a component-based hybrid modeling framework for subsurface simulations.

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Other ContributorsOther ContributorsOther ContributorsOther Contributors

Bruce Palmer (PNNL): CCA SAP PIKaren Schuchardt (PNNL): Workflow / data SAP PIYilin Fang, Glenn Hammond, Mark White (PNNL): Continuum-scale reactive transport modelingVidhya Gurumoorthi (PNNL): CCA implementation

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AcknowledgmentAcknowledgmentAcknowledgmentAcknowledgment

Funding for this research was provided by the U. S. Department of Energy through the following programs: Laboratory-Directed Research and Development

(administered by PNNL through the Computational Science Initiative)

Office of Science, Biological and Environmental Research, Environmental Remediation Sciences Program (ERSP).

Office of Science, Biological and Environmental Research and Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program.

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