Microscale Modeling of Fluid Flow in Porous Medium Systems

Proper mathematical description of macroscopic porous medium flows is essential for the study of a wide range of subsurface contamination scenarios. Existing mathematical formulations, however, demonstrate inadequacies that preclude the accurate description of many systems. Multi-scale models developed using thermodynamically constrained averaging theory (TCAT) rigorously define macroscopic variables in terms of more well-understood microscopic counterparts, permitting detailed analysis of macroscopic model forms based on microscale simulation and experiment. Within this framework, the primary objectives of microscale modeling are to elucidate important physical mechanisms and to inform both the form of macroscale closure relations as well as associated parameter values. In order to meet these goals, numerical tools must include: (1) simulations that provide accurate microscopic solutions for physical phenomena in large, complex domains; (2) morphological analysis tools that can be used to upscale simulation results to larger scales as dictated by the associated theoretical framework. Development of a numerical toolbox for microscale porous medium studies is considered in line with these objectives, including both implementation and optimization strategies. High-performance implementations of the lattice Boltzmann method are developed to simulate one- and two-phase flows using several computing platforms. A modified marching cubes algorithm is developed to explicitly construct all entities in a two-phase system, including all interfaces between the fluid and solid phases in addition to the three phase contact curve. These entities serve as a numerical skeleton for upscaling multiphase porous medium simulation results to the macroscale. Based on these tools, development of macroscopic constitutive laws is illustrated for a special case of anisotropic flow in porous media. In this example, microscale simulation is used to demonstrate a limitation of existing macroscopic forms for cases in which the momentum resistance depends on the flow direction in addition to the orientation. A modified macroscopic form is proposed in order to properly account for this phenomenon.