Pore network models to determine the flow statistics and structural controls for single-phase flow in partially saturated porous media

We study the abilities of pore network models of different complexities to determine the flow statistics and structural controls for single-phase flow in partially saturated porous media. The medium permeability and hydraulic tortuosity are the basic parameters for upscaling flow problems from the pore to the Darcy scale. They represent average flow properties. However, upscaling and predicting dispersion and anomalous solute transport from the pore to the continuum scale requires knowledge of the velocity distribution, not only its mean values. Considering four different network models of increasing complexity, we analyze the statistical and structural properties of the fluid-filled pore space that determines the flow statistics. We consider statistical network models based on regular lattices with the same statistical properties as the porous medium regarding coordination number and pore-size distribution. We consider regular lattices which are characterized by uniform coordination, and diluted lattices, and random lattices, which are characterized by a distribution of coordination numbers. Furthermore, we consider a detailed network model, which accounts for the spatial location of pores, their coordination numbers, and the sizes of pore bodies and throats. The flow behaviors estimated from these network models are compared to direct numerical single-phase flow simulations in the digitized images of a fully and partially saturated two-dimensional porous medium and different saturation degrees. We find that the statistical network models can capture the saturation dependence of permeability and tortuosity but are not able to reproduce velocity statistics of even the velocity range observed in the direct flow simulations. The detailed network models, in contrast, provide excellent estimates for all flow statistics. This indicates that the configuration and correlation of the fluid phase are crucial structural controls of the observed distribution of flow velocities.

Plain Language Summary

Conceptualizing a porous media as a network of conductors sets a compromise between the oversimplifying conceptualization of the media as a bundle of capillary tubes and the computationally expensive and unobtainable detailed description of the media’s geometry needed for direct numerical simulations. These models are abundantly being used to evaluate single and multiphase flow characteristics. The different flow characteristics are valuable in evaluating phenomena that may or may not be relevant for different applications. Here, we evaluate how different information about the pore space affects the ability of the network model to evaluate different flow characteristics.

We found that the resistance of a media to the fluid flow can be estimated by the general stochastic features of the media (its size and connectivity). However, to account for more complex phenomena, such as solute transport and dispersion through the media, a piece of detailed information about the spatial location of the fluids is needed.