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  • © 2014

Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems

  • Self-contained introduction to the derivation of conservation, thermodynamic, and evolution equations for modeling multiphase porous media systems
  • Formulates entropy inequalities that can be used to guide the closure of governing equation systems
  • Includes detailed applications to formulate models for flow and transport consistent across scales
  • Presents a forward-looking discussion of open research problems in multi-scale porous medium systems
  • Includes supplementary material: sn.pub/extras

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxxiv
  2. Elements of Thermodynamically Constrained Averaging Theory

    • William G. Gray, Cass T. Miller
    Pages 1-36
  3. Microscale Conservation Principles

    • William G. Gray, Cass T. Miller
    Pages 37-85
  4. Microscale Thermodynamics

    • William G. Gray, Cass T. Miller
    Pages 87-134
  5. Microscale Equilibrium Conditions

    • William G. Gray, Cass T. Miller
    Pages 135-165
  6. Microscale Closure for a Fluid Phase

    • William G. Gray, Cass T. Miller
    Pages 167-199
  7. Macroscale Conservation Principles

    • William G. Gray, Cass T. Miller
    Pages 201-261
  8. Macroscale Thermodynamics

    • William G. Gray, Cass T. Miller
    Pages 263-300
  9. Evolution Equations

    • William G. Gray, Cass T. Miller
    Pages 301-326
  10. Single-Fluid-Phase Flow

    • William G. Gray, Cass T. Miller
    Pages 327-372
  11. Single-Fluid-Phase Species Transport

    • William G. Gray, Cass T. Miller
    Pages 373-420
  12. Two-Phase Flow

    • William G. Gray, Cass T. Miller
    Pages 421-463
  13. Modeling Approach and Extensions

    • William G. Gray, Cass T. Miller
    Pages 465-488
  14. Back Matter

    Pages 489-582

About this book

Thermodynamically constrained averaging theory provides a consistent method for upscaling conservation and thermodynamic equations for application in the study of porous medium systems. The method provides dynamic equations for phases, interfaces, and common curves that are closely based on insights from the entropy inequality. All larger scale variables in the equations are explicitly defined in terms of their microscale precursors, facilitating the determination of important parameters and macroscale state equations based on microscale experimental and computational analysis. The method requires that all assumptions that lead to a particular equation form be explicitly indicated, a restriction which is useful in ascertaining the range of applicability of a model as well as potential sources of error and opportunities to improve the analysis.

Authors and Affiliations

  • Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, USA

    William G. Gray, Cass T. Miller

Bibliographic Information

Buy it now

Buying options

eBook USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access