===affil2:
North Carolina State University
===firstname:
Deena
===firstname4:
W.G.
===firstname3:
C.T.
===lastname2:
Kelley
===keyword1:
Applications/Environmental
===lastname:
Giffen
===firstname5:
P.
===affil6:

===lastname3:
Miller
===email:
dhannou@ncsu.edu
===keyword2:
OTHER
===keyword_other2:
Optimization
===lastname6:

===affil5:
University of North Carolina
===otherauths:

===lastname4:
Gray
===affil4:
University of North Carolina
===lastname7:

===competition:
no
===affil7:

===firstname7:

===postal:
3212 Enchanting Way
Raleigh, NC 27616
===firstname6:

===ABSTRACT:
We seek to capture the behavior of a dense brine as it travels through porous media.  While the traditional model for single-fluid phase flow through porous media is so well-established that it is near universal, it has several notable deficiencies that lead us to consider alternate formulations.  We improve upon the classical  model with a method that utilizes the laws of thermodynamics.  This method, known as thermodynamically constrained averaging theory (TCAT), provides a basis for which we can accurately simulate transport and diffusion of a high-concentration solution through porous media.  The TCAT model is nonlinear and is comprised of two PDEs as well as a number of closure relations.  We begin by rewriting the PDEs as a system of partial differential-algebraic equations (PDAEs).  We then use the method of lines to transform our PDAEs into a large system of ODEs.  From there, we use a stiff temporal integrator to solve for the time derivative and arrive at a 1D numerical solution.  As this model is both nonlinear and nonsmooth, we will discuss results and numerical difficulties.
===affil3:
University of North Carolina
===keyword_other1:

===lastname5:
Schultz
===affilother:

===title:
Simulating Non-Dilute Transport in Porous Media Using a TCAT-Based Model
===firstname2:
C.T.