Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 9. Transition region models

2012 ◽  
Vol 42 ◽  
pp. 71-90 ◽  
Author(s):  
A.S. Jackson ◽  
I. Rybak ◽  
R. Helmig ◽  
W.G. Gray ◽  
C.T. Miller
Keyword(s):  
Porous Medium ◽  
Transition Region ◽  
Transport Phenomena ◽  
Averaging Theory ◽  
Theory Approach ◽  
Flow And Transport ◽  
Modeling Flow

Thermodynamically Constrained Averaging Theory Approach for Heat Transport in Single-Fluid-Phase Porous Medium Systems

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
William G. Gray ◽  
Cass T. Miller
Keyword(s):  
Porous Medium ◽  
Fluid Phase ◽  
Entropy Inequality ◽  
Averaging Theory ◽  
Local Thermal Equilibrium ◽  
Theory Approach ◽  
Equilibrium Conditions ◽  
Medium System ◽  
Closure Relations ◽  
Microscale Simulations

The recently developed thermodynamically constrained averaging theory is briefly summarized as a tool for the building of rigorous macroscale models of transport phenomena in complex systems. The specific case of thermal transport in a single-fluid-phase porous medium system is considered. Key results from the application of this theory are used to develop a simplified entropy inequality, which is in turn used to guide the development of closure relations. The decomposition of exchange terms is considered, and closed models for internal energy are derived for the case of nonequilibrium and local thermal equilibrium conditions. Since all variables are expressed in terms of precisely defined averages of microscale quantities, the resultant models can be compared with highly resolved microscale simulations to determine the range of validity of the upscaled models.

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