Skip to main content

Abstract

In the preceding chapter, we demonstrated how the elements of the TCAT approach, as depicted in Fig. 5.1, are used to obtain a closed set of microscale equations. The procedure for the development of macroscale equations is similar. However, an additional step is required to transform the microscale relations to the macroscale prior to applying the closure procedure.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
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

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gray WG, Miller CT (2006) Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 3. Single-fluid-phase flow. Adv Water Resour 29(11):1745–1765

    Google Scholar 

  2. Gray WG, Miller CT (2009) Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 5. Single-fluid-phase transport. Adv Water Resour 32(5):681–711

    Google Scholar 

  3. Gray WG, Miller CT (2010) Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 8. Interface and common curve dynamics. Adv Water Resour 33(12):1427–1443, DOI 10.1016/j.advwatres.2010.01.010

  4. Gray WG, Miller CT (2011) On the algebraic and differential forms of Darcy’s equation. J Porous Media 14(1):33–50

    Google Scholar 

  5. Gray WG, Leijnse A, Kolar RL, Blain CA (1993) Mathematical Tools for Changing Spatial Scales in the Analysis of Physical Systems. CRC Press, Boca Raton

    Google Scholar 

  6. Gray WG, Miller CT, Schrefler BA (2013) Averaging theory for description of environmental problems: What have we learned? Adv Water Resour 51:123–138, DOI 10.1016/j.advwatres.2011.12.005

    Google Scholar 

  7. Jackson AS, Rybak I, Helmig R, Gray WG, Miller CT (2012) Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 9. Transition region models. Adv Water Resour 42:71–90, DOI 10.1016/j.advwatres.2012.01.006

  8. Miller CT, Gray WG (2008) Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 4. Species transport fundamentals. Adv Water Resour 31(3):577–597

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to William G. Gray .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Gray, W.G., Miller, C.T. (2014). Macroscale Conservation Principles. In: Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems. Advances in Geophysical and Environmental Mechanics and Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-04010-3_6

Download citation

Publish with us

Policies and ethics