Computational Science Research and Education: Perspectives Evolving from Modeling Porous Medium Dynamics

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Computational Science Research and Education
Perspectives Evolving from Modeling Porous Medium
Dynamics

• C.T. Miller
• Department of Environmental Sciences
• and Engineering
• University of North Carolina-Chapel Hill

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Overview

• Modeling porous medium systems
• Motivation
• Example scientific issues
• Current challenges
• Computational science research and education
• Experiences
• Desirable skill set
• Useful educational components
• Funding considerations

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Some Motivating Problems

• Water supply
• Irrigation
• Drainage
• Infiltration
• Subsurface systems coupled to surface and
  atmospheric systems
• Domestic and industrial waste disposal

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Some Motivating Problems

• Nuclear waste disposal
• Contaminant remediation
• Risk assessment

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Environmental Modeling Framework
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Mechanistic Modeling Framework
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Standard Formulation Approach

• Conservation of mass for species
• Conservation of mass for a phase
• Conservation of energy
• Closure relations Darcys law, equations of
  state, capillary pressure-saturation-permeability
  relations, interphase exchange, and reactions

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Conservation Equations
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Identities
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Closure Relations
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Closure Relations
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Darcys Law
 
                                                                                                                        

Henry Darcy (1803-1858)
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Darcys Law
                                                
                                       Figure 1.
Darcy's data plotted as q versus H/e (Glenn
Brown).
 
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Multiscale Nature of Porous Medium Systems

• Range of scales is immense, lt10-6 to gt103 m
• Morphology and topology of pore structure is
  highly complex
• Impossible to represent detail at finest scale
• Must therefore represent smaller scale phenomena
  through appropriate closure schemes

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Natural Systems are Complex

• Heterogeneity exists across all observed scales
• Flow and transport process strongly influenced by
  heterogeneity
• Complete characterization is impossible
• Systems and models thus stochastic in nature
• Direct measurement of properties only one source
  of data

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Borden Site, Sudicky (1986, WRR)
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Subsurface Remediation Example
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Pump and Treat Modeling
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Microscale Heterogeneity
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Macroscale Heterogeneity

• Two-dimensional cell
• Heterogeneous porous medium
• TCE dyed with oil red
• Vertical gravity displacement
• Heterogeneous media effects dominant because of
  variation in capillary forces
• Brine layer establishment
• Vertical mobilization under gravity forces
• Surfactant added to reduce IFT
• TCE mobilized and collected from brine layer

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Immiscibile Instabilities

• From Imhoff et al.
• NAPL dissolution fingering
• Results from high-resolution finite volume
  simulator
• Length scale of features can be cm to meters
• At field scale very likely to be sub-grid scale
• Standard closure schemes based on laboratory
  experiments grossly in error

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Pore-Scale Modeling

• Need information at pore scale---either simulate
  or measure
• Solve equations with various levels of
  approximation at the pore scale
• Detailed information on flow and transport can be
  obtained

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Pore-Scale Modeling
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Standard LB Approach

• Memory waste
• For a typical porous medium, up to 70 of the
  memory is wasted
• Load imbalance due to
• Heterogeneity of porous media
• Use of large number of processors for homogeneous
  media

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Domain Decomposition Methods

• Regular domain decompositions 1D, 2D, 3D
• Rectilinear partitioning
• Orthogonal recursive bisection (ORB)

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Speedup as a Function of Number of Processors
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Current Challenges

• Existing multiphase porous medium modeling
  approaches suffer from many serious limitations
• No specific account for interfaces
• Lack of a direct relation to microscale
  properties
• No rigorous thermodynamic constraints applied
• Ad hoc and inconsistent closure relations for
  pressure-saturation-permeability relations

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Current Challenges

• Intent of evolving approach
• First principles set of balance equations
• Explicit link between microscale and macroscale
• All quantities rigorously defined
• Thermodynamic constraints imposed
• All assumptions explicit and changeable if model
  found to be inadequate

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Current Challenges

• Thermodynamically constrained model formulation,
  closure, and analysis
• Wettability, viscous coupling, transient psk, and
  interphase exchange in multiphase systems
• Multiscale closures
• Numerics, solvers, and optimization
• Spatial and spatial/temporal estimation
• Efficient modeling environments

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Computational Science Research and Education
Experiences

• Student backgrounds engineering, mathematics,
  computer science, physics, chemistry, and geology
• Student training porous medium physics,
  stochastic hydrology, environmental processes,
  numerical methods, applied mathematics, computer
  science, high-performance computing
• Graduates academic engineering, science, and
  mathematics departments, research, consulting
• Challenges rigor, cross-disciplinary
  requirements, disciplinary acceptance

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Computational Science Research and Education
Desirable Skill Set

• Science and engineering (10)
• Porous medium physics
• Stochastic hydrology
• Process dynamics and fluid dynamics
• Environmental sciences
• Thermodynamics
• Mathematics and statistics (15)
• Numerical methods including solvers, ODEs, PDEs
• Advanced and evolving methods for PDEs
• Analysis through functional analysis
• Probability

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Computational Science Research and Education
Desirable Skill Set

• Mathematics and statistics (continued)
• Mathematical statistics
• Random fields
• Spatial/temporal estimation
• Stochastic differential equations
• Computer science (5)
• Data structures
• Algorithms
• Parallel and distributed computing
• Compilers

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Computational Science Research and Education
Useful Educational Components

• Interdisciplinary curriculum
• Other identifiable skills (computer languages
  etc)
• Strong committee presence in science, math, and
  computer science
• At least an appreciation for all aspects
  experimental, theory, and computation
• Interdisciplinary research skills---demonstrated
  through publishing and presentations, and
  internship

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Computational Science Research and Education
Funding Considerations

• Fellowship programs
• Need for critical mass
• Focus
• Baseline support of sufficient duration is
  optimal