Discrete network modeling for field-scale flow and transport through porous media

Natural soil is a discrete, heterogeneous porous material with many sizes of physical structure. These multi-scale discrete media resist description by differential equations with macroscopic parameters. This fact complicates measurement and numerical modeling in support of the selection, design, and operation of contaminant remediation schemes. Constitutive parameters may display an apparent scale dependence or the governing equations may exhibit non-physical behavior. To address these issues, a discrete-medium modeling philosophy is adopted that relies less on complex constitutive theory and more on computational resolution. Specifically, a stochastic, high-resolution, discrete network model is developed and explored for simulating macroscopic flow and conservative transport through macroscopic porous media. In contrast to most historical network models in porous media, each throat represents a path between two points in the medium, not a pore. Therefore, this model is suitable for simulation from the pore scale to the basin scale. Network results are interpreted by volume averaging over scales larger than individual network components.; Networks can be created to honor macroscopic porosity, effective conductivity, and apparent dispersivity estimates or to honor statistical distributions of small scale conductivities. Flow through a discrete network compares well with analytical solutions for macroscopic, Darcian fluid flow. Transport through a discrete network differs fundamentally from advection-dispersion theory. Network transport is modeled as pure advection in the throats and perfect mixing at throat junctions. However, network-predicted concentration profiles and breakthrough curves are consistent with historical observations of nearly-Gaussian concentration distributions. Dispersion in the network is a natural consequence of its discrete structure. Velocity correlation that drives early-time (pre-asymptotic) plume growth is simpler and more efficient to enforce with a network than with a highly-resolved, continuum-based, finite element or finite volume model. Comparison of network simulation to laboratory data shows acceptably close agreement. However, substantial resolution is needed to simulate a homogeneous laboratory packing because characteristic lengths in such a medium are very short. For immiscible flow, network models offer the potential to simulate capillary barriers and macroporous breakthrough phenomena.