Theory and Applications of Macroscale Models in Porous Media

Battiato, Ilenia; Ferrero V, Peter T.; O’ Malley, Daniel; Miller, Cass T.; Takhar, Pawan S.; Valdés-Parada, Francisco J.; Wood, Brian D.

doi:10.1007/s11242-019-01282-2

Title: Theory and Applications of Macroscale Models in Porous Media

Abstract

Systems dominated by heterogeneity over a multiplicity of scales, like porous media, still challenge our modeling efforts. The presence of disparate length- and time-scales that control dynamical processes in porous media hinders not only models predictive capabilities, but also their computational efficiency. Macrosopic models, i.e., averaged representations of pore-scale processes, are computationally efficient alternatives to microscale models in the study of transport phenomena in porous media at the system, field or device scale (i.e., at a scale much larger than a characteristic pore size). We present an overview of common upscaling methods used to formally derive macroscale equations from pore-scale (mass, momentum and energy) conservation laws. This review includes the volume averaging method, mixture theory, thermodynamically constrained averaging, homogenization, and renormalization group techniques. We apply these methods to a number of specific problems ranging from food processing to human bronchial system, and from diffusion to multiphase flow, to demonstrate the methods generality and flexibility in handling different applications. The primary intent of such an overview is not to provide a thorough review of all currently available upscaling techniques, nor a complete mathematical treatment of the ones presented, but rather a primer on some of the tools available for upscaling, themore »« less

Authors:

^[1]; Ferrero V, Peter T. ^[2];

^[3]; Miller, Cass T. ^[4]; Takhar, Pawan S. ^[5]; Valdés-Parada, Francisco J. ^[6]; Wood, Brian D. ^[2]

Stanford Univ., CA (United States)
Oregon State Univ., Corvallis, OR (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States)
Univ. of North Carolina, Chapel Hill, NC (United States)
Univ. of Illinois, Urbana-Champaign, IL (United States)
Metropolitan Autonomous Univ., Mexico City (Mexico)

Publication Date:: Mon Apr 15 00:00:00 EDT 2019

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program; Army Research Office (ARO); National Science Foundation (NSF)

OSTI Identifier:: 1511237

Report Number(s):: LA-UR-18-26414
Journal ID: ISSN 0169-3913

Grant/Contract Number:: 89233218CNA000001; W911NF-14-1-02877; 1619767; 1604314

Resource Type:: Accepted Manuscript

Journal Name:: Transport in Porous Media

Additional Journal Information:: Journal Volume: 13; Journal Issue: 1; Journal ID: ISSN 0169-3913

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; Earth Sciences; Mathematics; Upscaling; Porous media; Volume averaging method; Mixture theory; Thermodynamically constrained averaging theory; Homogenization theory; Renormalization group theory

Citation Formats


                    Battiato, Ilenia, Ferrero V, Peter T., O’ Malley, Daniel, Miller, Cass T., Takhar, Pawan S., Valdés-Parada, Francisco J., and Wood, Brian D. Theory and Applications of Macroscale Models in Porous Media.  United States: N. p., 2019. 
Web.  doi:10.1007/s11242-019-01282-2.

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                    Battiato, Ilenia, Ferrero V, Peter T., O’ Malley, Daniel, Miller, Cass T., Takhar, Pawan S., Valdés-Parada, Francisco J., & Wood, Brian D. Theory and Applications of Macroscale Models in Porous Media.  United States.  https://doi.org/10.1007/s11242-019-01282-2

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                    Battiato, Ilenia, Ferrero V, Peter T., O’ Malley, Daniel, Miller, Cass T., Takhar, Pawan S., Valdés-Parada, Francisco J., and Wood, Brian D. Mon .  
"Theory and Applications of Macroscale Models in Porous Media".  United States.  https://doi.org/10.1007/s11242-019-01282-2.  https://www.osti.gov/servlets/purl/1511237.

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@article{osti_1511237,

  title        = {Theory and Applications of Macroscale Models in Porous Media},

  author       = {Battiato, Ilenia and Ferrero V, Peter T. and O’ Malley, Daniel and Miller, Cass T. and Takhar, Pawan S. and Valdés-Parada, Francisco J. and Wood, Brian D.},

  abstractNote = {Systems dominated by heterogeneity over a multiplicity of scales, like porous media, still challenge our modeling efforts. The presence of disparate length- and time-scales that control dynamical processes in porous media hinders not only models predictive capabilities, but also their computational efficiency. Macrosopic models, i.e., averaged representations of pore-scale processes, are computationally efficient alternatives to microscale models in the study of transport phenomena in porous media at the system, field or device scale (i.e., at a scale much larger than a characteristic pore size). We present an overview of common upscaling methods used to formally derive macroscale equations from pore-scale (mass, momentum and energy) conservation laws. This review includes the volume averaging method, mixture theory, thermodynamically constrained averaging, homogenization, and renormalization group techniques. We apply these methods to a number of specific problems ranging from food processing to human bronchial system, and from diffusion to multiphase flow, to demonstrate the methods generality and flexibility in handling different applications. The primary intent of such an overview is not to provide a thorough review of all currently available upscaling techniques, nor a complete mathematical treatment of the ones presented, but rather a primer on some of the tools available for upscaling, the basic principles they are based upon, and their specific advantages and drawbacks, so to guide the reader in the choice of the most appropriate method for particular applications and of the most relevant technical literature.},

  doi          = {10.1007/s11242-019-01282-2},

  journal      = {Transport in Porous Media},

  number       = 1,

  volume       = 13,

  place        = {United States},

  year         = {Mon Apr 15 00:00:00 EDT 2019},

  month        = {Mon Apr 15 00:00:00 EDT 2019}

}

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Works referencing / citing this record:

Roughness Control on Multiphase Flow in Rock Fractures
journal, November 2019

Hu, Ran; Zhou, Chen‐Xing; Wu, Dong‐Sheng
Geophysical Research Letters, Vol. 46, Issue 21
DOI: 10.1029/2019gl084762

Toward a New Generation of Two-Fluid Flow Models Based on the Thermodynamically-Constrained Averaging Theory
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Bruning, Kelsey; Miller, Cass T.
Water, Vol. 11, Issue 11
DOI: 10.3390/w11112260

Comments on the Paper “Theory and Applications of Macroscale Models in Porous Media” by Ilenia Battiato et al
journal, August 2019

Auriault, Jean-Louis
Transport in Porous Media, Vol. 130, Issue 2
DOI: 10.1007/s11242-019-01327-6

Diffusion in Porous Media: Phenomena and Mechanisms
journal, March 2019

Tartakovsky, Daniel M.; Dentz, Marco
Transport in Porous Media, Vol. 130, Issue 1
DOI: 10.1007/s11242-019-01262-6

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FINAL REPORT: Mechanistically-Base Field Scale Models of Uranium Biogeochemistry from Upscaling Pore-Scale Experiments and Models

Technical Report Wood, Brian D.

Biogeochemical reactive transport processes in the subsurface environment are important to many contemporary environmental issues of significance to DOE. Quantification of risks and impacts associated with environmental management options, and design of remediation systems where needed, require that we have at our disposal reliable predictive tools (usually in the form of numerical simulation models). However, it is well known that even the most sophisticated reactive transport models available today have poor predictive power, particularly when applied at the field scale. Although the lack of predictive ability is associated in part with our inability to characterize the subsurface and limitations inmore »« less
https://doi.org/10.2172/1098131

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Effective parameters, effective processes: From porous flow physics to in situ remediation technology

Conference Pruess, K

This paper examines the conceptualization of multiphase flow processes on the macroscale, as needed in field applications. It emphasizes that upscaling from the pore-level will in general not only introduce effective parameters but will also give rise to ``effective processes,`` i.e., the emergence of new physical effects that may not have a microscopic counterpart. ``Phase dispersion`` is discussed as an example of an effective process for the migration and remediation of non-aqueous phase liquid (NAPL) contaminants in heterogeneous media. An approximate space-and-time scaling invariance is derived for gravity-driven liquid flow in unsaturated two-dimensional porous media (fractures). Issues for future experimentalmore » and theoretical work are identified.« less
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Title: Theory and Applications of Macroscale Models in Porous Media

Abstract

Citation Formats

Coupled transport and dispersion of multicomponent reactive solutes in rectilinear flows journal, November 1996

Proofs of the volume averaging theorems for multiphase flow journal, December 1982

Multiscale Mesoscopic Entropy of Driven Macroscopic Systems journal, November 2013

Stochastic Radon operators in porous media hydrodynamics journal, January 1997

Theorem for the local volume average of a gradient revised journal, January 1981

On constitutive equations for flow of fluid through an elastic solid journal, August 1966

Spatial–temporal nonlocal homogenization model for transient anti-plane shear wave propagation in periodic viscoelastic composites journal, December 2018

Multiscale modeling approach to determine effective lithium-ion transport properties conference, May 2017

Stochastic Diagrammatic Analysis of Groundwater Flow in Heterogeneous Porous Media journal, July 1995

Diffusion in Porous Media: Phenomena and Mechanisms journal, March 2019

Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems book, January 2014

Optimal design of nanoporous materials for electrochemical devices journal, April 2017

Modeling of core-annular and plug flows of Newtonian/non-Newtonian shear-thinning fluids in pipes and capillary tubes journal, June 2018

Upscaling pollutant dispersion in the Mexico City Metropolitan Area journal, February 2012

A deformation model for Case II diffusion journal, June 1980

Physics-based hybrid method for multiscale transport in porous media journal, September 2017

Transient flow in bounded randomly heterogeneous domains: 1. Exact conditional moment equations and recursive approximations journal, January 1998

Transport modeling of nonlinearly adsorbing solutes in physically heterogeneous pore networks: TRANSPORT OF REACTIVE SOLUTES journal, February 2005

Technical Notes on Volume Averaging in Porous Media I: How to Choose a Spatial Averaging Operator for Periodic and Quasiperiodic Structures journal, July 2017

Homogenization theory and digital imaging: A basis for studying the mechanics and design principles of bone tissue journal, March 1994

Dispersion of a chemically reactive solute in a spatially periodic model of a porous medium journal, January 1988

Diagrammatic theory of effective hydraulic conductivity journal, October 1997

Modeling Turbulent Flows in Porous Media journal, January 2020

Homogenizability conditions for multicomponent reactive transport journal, December 2013

Renormalization group methods in subsurface hydrology: overview and applications in hydraulic conductivity upscaling journal, December 2003

Beyond Onsager–Casimir Relations: Shared Dependence of Phenomenological Coefficients on State Variables journal, December 2018

Flow of viscoelastic fluids through porous media journal, November 1967

Universal scaling-law for flow resistance over canopies with complex morphology journal, March 2018

General conservation equations for multi-phase systems: 1. Averaging procedure journal, March 1979

On the Domain of Validity of Brinkman’s Equation journal, December 2008

Taylor dispersion in porous media: Analysis by multiple scale expansions journal, January 1995

The role of scaling laws in upscaling journal, May 2009

Noise propagation in hybrid models of nonlinear systems: The Ginzburg–Landau equation journal, April 2014

Filtration Law in Porous Media with Poor Separation of Scales journal, July 2005

A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage journal, August 1991

The use of renormalization for calculating effective permeability journal, February 1989

Moisture transport in shrinking gels during saturated drying journal, August 1997

Modeling multiscale transport mechanisms, phase changes and thermomechanics during frying journal, August 2014

Anomalous transit-time dispersion in amorphous solids journal, September 1975

Fluid flow through an array of fixed particles journal, January 1983

Accuracy of Hybrid Lattice Boltzmann/Finite Difference Schemes for Reaction-Diffusion Systems journal, January 2007

Algorithm refinement for stochastic partial differential equations: II. Correlated systems journal, August 2005

Multiphase transport equations: I - general equation for macroscopic statistical, local space-time homogeneity 1 journal, January 1983

A Guide through Available Mixture Theories for Applications journal, December 2013

Rigorous Upscaling of the Reactive Flow through a Pore, under Dominant Peclet and Damkohler Numbers journal, January 2006

A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles journal, December 1949

Homogenization of a Nonlinear Convection-Diffusion Equation with Rapidly Oscillating Coefficients and Strong Convection journal, October 2005

Thermodynamically Constrained Averaging Theory: Principles, Model Hierarchies, and Deviation Kinetic Energy Extensions journal, April 2018

Flow in porous media I: A theoretical derivation of Darcy's law journal, January 1986

Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen journal, January 1905

The dissolution kinetics of major sedimentary carbonate minerals journal, July 2002

Shouldn’t catalysts shape up? journal, January 2006

A primer on upscaling tools for porous media journal, August 2002

Hybrid mixture theory based modeling of transport mechanisms and expansion-thermomechanics of starch during extrusion journal, July 2015

Theoretical derivation of Darcy's law journal, September 1977

The use of mathematical modeling in the design of lithium/polymer battery systems journal, October 1995

Transport in ordered and disordered porous media II: Generalized volume averaging journal, February 1994

Hybrid models of reactive transport in porous and fractured media journal, September 2011

Calculation of effective diffusivities for biofilms and tissues journal, January 2002

A comparison of two physics-based numerical models for simulating surface water–groundwater interactions journal, April 2010

Multiscale fluid transport theory for swelling biopolymers journal, June 2003

Hybrid mixture theory based moisture transport and stress development in corn kernels during drying: Validation and simulation results journal, October 2011

Role of glycocalyx in attenuation of shear stress on endothelial cells: From in vivo experiments to microfluidic circuits conference, September 2017

Eulerian kinematics of flow through spatially periodic models of porous media journal, September 1989

Fickian dispersion is anomalous journal, December 2015

Vertical dispersion in vegetated shear flows: VERTICAL DISPERSION IN VEGETATED SHEAR FLOWS journal, October 2016

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 3. Single-fluid-phase flow journal, November 2006

Microstructural Characterization of Fried Potato Disks Using X‐Ray Micro Computed Tomography journal, January 2016

On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media journal, January 1982

A Priori Parameter Estimation for the Thermodynamically Constrained Averaging Theory: Species Transport in a Saturated Porous Medium journal, February 2018

NMR imaging of continuous and intermittent drying of pasta journal, January 2007

Homogenization and Porous Media book, January 1997

A volume averaging approach for asymmetric diffusion in porous media journal, May 2011

Taylor dispersion of chemically reactive species: Irreversible first-order reactions in bulk and on boundaries journal, January 1986

Modeling two-fluid-phase flow and species transport in porous media journal, February 2015

A comparison of measured and modeled velocity fields for a laminar flow in a porous medium journal, November 2015

A computational homogenization approach for Li-ion battery cells: Part 1 – formulation journal, April 2014

Coupled transport and dispersion of multicomponent reactive solutes in rectilinear flows
journal, November 1996

Proofs of the volume averaging theorems for multiphase flow
journal, December 1982

Multiscale Mesoscopic Entropy of Driven Macroscopic Systems
journal, November 2013

Stochastic Radon operators in porous media hydrodynamics
journal, January 1997

Theorem for the local volume average of a gradient revised
journal, January 1981

On constitutive equations for flow of fluid through an elastic solid
journal, August 1966

Spatial–temporal nonlocal homogenization model for transient anti-plane shear wave propagation in periodic viscoelastic composites
journal, December 2018

Multiscale modeling approach to determine effective lithium-ion transport properties
conference, May 2017

Stochastic Diagrammatic Analysis of Groundwater Flow in Heterogeneous Porous Media
journal, July 1995

Diffusion in Porous Media: Phenomena and Mechanisms
journal, March 2019

Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems
book, January 2014

Optimal design of nanoporous materials for electrochemical devices
journal, April 2017

Modeling of core-annular and plug flows of Newtonian/non-Newtonian shear-thinning fluids in pipes and capillary tubes
journal, June 2018

Upscaling pollutant dispersion in the Mexico City Metropolitan Area
journal, February 2012

A deformation model for Case II diffusion
journal, June 1980

Physics-based hybrid method for multiscale transport in porous media
journal, September 2017

Transient flow in bounded randomly heterogeneous domains: 1. Exact conditional moment equations and recursive approximations
journal, January 1998

Transport modeling of nonlinearly adsorbing solutes in physically heterogeneous pore networks: TRANSPORT OF REACTIVE SOLUTES
journal, February 2005

Technical Notes on Volume Averaging in Porous Media I: How to Choose a Spatial Averaging Operator for Periodic and Quasiperiodic Structures
journal, July 2017

Homogenization theory and digital imaging: A basis for studying the mechanics and design principles of bone tissue
journal, March 1994

Dispersion of a chemically reactive solute in a spatially periodic model of a porous medium
journal, January 1988

Diagrammatic theory of effective hydraulic conductivity
journal, October 1997

Modeling Turbulent Flows in Porous Media
journal, January 2020

Homogenizability conditions for multicomponent reactive transport
journal, December 2013

Renormalization group methods in subsurface hydrology: overview and applications in hydraulic conductivity upscaling
journal, December 2003

Beyond Onsager–Casimir Relations: Shared Dependence of Phenomenological Coefficients on State Variables
journal, December 2018

Flow of viscoelastic fluids through porous media
journal, November 1967

Universal scaling-law for flow resistance over canopies with complex morphology
journal, March 2018

General conservation equations for multi-phase systems: 1. Averaging procedure
journal, March 1979

On the Domain of Validity of Brinkman’s Equation
journal, December 2008

Taylor dispersion in porous media: Analysis by multiple scale expansions
journal, January 1995

The role of scaling laws in upscaling
journal, May 2009

Noise propagation in hybrid models of nonlinear systems: The Ginzburg–Landau equation
journal, April 2014

Filtration Law in Porous Media with Poor Separation of Scales
journal, July 2005

A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage
journal, August 1991

The use of renormalization for calculating effective permeability
journal, February 1989

Moisture transport in shrinking gels during saturated drying
journal, August 1997

Modeling multiscale transport mechanisms, phase changes and thermomechanics during frying
journal, August 2014

Anomalous transit-time dispersion in amorphous solids
journal, September 1975

Fluid flow through an array of fixed particles
journal, January 1983

Accuracy of Hybrid Lattice Boltzmann/Finite Difference Schemes for Reaction-Diffusion Systems
journal, January 2007

Algorithm refinement for stochastic partial differential equations: II. Correlated systems
journal, August 2005

Multiphase transport equations: I - general equation for macroscopic statistical, local space-time homogeneity ¹
journal, January 1983

A Guide through Available Mixture Theories for Applications
journal, December 2013

Rigorous Upscaling of the Reactive Flow through a Pore, under Dominant Peclet and Damkohler Numbers
journal, January 2006

A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles
journal, December 1949

Homogenization of a Nonlinear Convection-Diffusion Equation with Rapidly Oscillating Coefficients and Strong Convection
journal, October 2005

Thermodynamically Constrained Averaging Theory: Principles, Model Hierarchies, and Deviation Kinetic Energy Extensions
journal, April 2018

Flow in porous media I: A theoretical derivation of Darcy's law
journal, January 1986

Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen
journal, January 1905

The dissolution kinetics of major sedimentary carbonate minerals
journal, July 2002

Shouldn’t catalysts shape up?
journal, January 2006

A primer on upscaling tools for porous media
journal, August 2002

Hybrid mixture theory based modeling of transport mechanisms and expansion-thermomechanics of starch during extrusion
journal, July 2015

Theoretical derivation of Darcy's law
journal, September 1977

The use of mathematical modeling in the design of lithium/polymer battery systems
journal, October 1995

Transport in ordered and disordered porous media II: Generalized volume averaging
journal, February 1994

Hybrid models of reactive transport in porous and fractured media
journal, September 2011

Calculation of effective diffusivities for biofilms and tissues
journal, January 2002

A comparison of two physics-based numerical models for simulating surface water–groundwater interactions
journal, April 2010

Multiscale fluid transport theory for swelling biopolymers
journal, June 2003

Hybrid mixture theory based moisture transport and stress development in corn kernels during drying: Validation and simulation results
journal, October 2011

Role of glycocalyx in attenuation of shear stress on endothelial cells: From in vivo experiments to microfluidic circuits
conference, September 2017

Eulerian kinematics of flow through spatially periodic models of porous media
journal, September 1989

Fickian dispersion is anomalous
journal, December 2015

Vertical dispersion in vegetated shear flows: VERTICAL DISPERSION IN VEGETATED SHEAR FLOWS
journal, October 2016

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 3. Single-fluid-phase flow
journal, November 2006

Microstructural Characterization of Fried Potato Disks Using X‐Ray Micro Computed Tomography
journal, January 2016

On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media
journal, January 1982

A Priori Parameter Estimation for the Thermodynamically Constrained Averaging Theory: Species Transport in a Saturated Porous Medium
journal, February 2018

NMR imaging of continuous and intermittent drying of pasta
journal, January 2007

Homogenization and Porous Media
book, January 1997

A volume averaging approach for asymmetric diffusion in porous media
journal, May 2011

Taylor dispersion of chemically reactive species: Irreversible first-order reactions in bulk and on boundaries
journal, January 1986

Modeling two-fluid-phase flow and species transport in porous media
journal, February 2015

A comparison of measured and modeled velocity fields for a laminar flow in a porous medium
journal, November 2015

A computational homogenization approach for Li-ion battery cells: Part 1 – formulation
journal, April 2014

Application effective medium approximation approach for economic researching
journal, November 2003

Effect of Network Structure on Characterization and Flow Modeling Using X-ray Micro-Tomography Images of Granular and Fibrous Porous Media
journal, June 2011

Multiphase flow and transport modeling in heterogeneous porous media: challenges and approaches
journal, March 1998