NUMERICAL INVESTIGATION OF MULTIPLE-, INTERACTING-SCALE VARIABLE-DENSITY GROUND WATER FLOW SYSTEMS

We present a new modeling approach for elucidating the nonlinear processes that are important for multiple-, interacting-scale flow and solute transport in subsurface environments. Our analyses focus on the influence of small-scale instability development on variable-density ground water flow behavior in large field-scale systems. We also examine the creation of instabilities in field-scale systems, porous media heterogeneity effects, and the relation between heterogeneity characteristics (e.g., permeability variance and correlation length scales) and the associated mixing scales that develop for varying degrees of unstable stratification. A three-dimensional adaptive mesh refinement (AMR) method is used to discretize the governing flow and transport equations. Fine grid spacing is automatically generated in regions of high gradients (e.g., concentration and/or velocity) using multiple levels of progressively finer “nested” 3D meshes. High-order, semi-Lagrangian methods are used to numerically solve the solute transport equation. Semi-Lagrangian methods eliminate Courant no. stability limitations and Peclet no. restrictions that are associated with traditional models. Because high-order accuracy numerical techniques are used to solve the advection component of the transport equation, the AMR code can simulate high-gradient/sharp-interface problems and more accurately model mixing processes because numerical dispersion is minimized. We present model results for high-resolution simulation of variable-density flow and transport: modeling of sharp interface movement and instability development for dense treatment fluid injection applications; saltwater-freshwater mixing problems; freshwater injection/extraction using Aquifer Storage and Recovery wells that are currently being evaluated at many sites for water supply purposes; and simulation of dense fluid mixing in heterogeneous porous media with fine-scale (e.g., 1-10 cm) permeability contrasts.