Relating porous media structure to the Darcy-Forchheimer model

• Main Author: Dupre, Kathleen R.
• Other Authors: Ryan, Emily M.
• Language: en_US
• Published: 2020
• Subjects: Mechanical engineering
• Online Access: https://hdl.handle.net/2144/41487

Flow in porous media is an important aspect of many systems, such as fluid separation, heat exchange, underground fluid transport, filtration, and purification. Computational modeling is used in all of these systems to increase the understanding of the system and enable researchers to make optimal decisions regarding the processes within the system. Current tools for modeling flow in porous media require calibration of each system individually, which reduces the quantity and efficiency of the information that simulations can provide. The most common method for modeling flow in porous media, is the Darcy-Forchheimer model. Although this model is accurate and robust, it relies on two coefficients which can only be determined through physical experiments on each individual porous media. These coefficients can be expressed as a product of the fluid properties and the properties of porous media structure; however the variables representing the structure of the porous media are still unable to be determined without physical experiments. For many years determining the relationship between porous media structure and the Darcy-Forchheimer model has been considered impractical, because the scale of porous media made it difficult if not impossible to measure the geometric properties of the material. Additionally, naturally occurring porous media have random structures; thus even if it were feasible to measure the porous media, it would have been difficult to determine the characteristics that most affect flow. Now researchers can both measure and manufacture porous media for specific purposes; however the models have not been updated to allow researchers to take advantage of this technology. Although researchers have the ability to control the exact structure of porous media, the models still lack the ability to help researchers create optimal designs for their systems. This research focuses on understanding the fundamental dynamics of flow in porous media, to enable complex systems to be modeled and developed more easily. Here computational upscaling is used to develop a revised Darcy-Forchheimer equation which includes a relation to the parameters of the porous media. The revised model was developed by simulating several homogeneous structured porous media. The porous media were studied by simulating a periodic unit cell of each porous media to understand the geometric effects. A primary porous media, made of stacked screens was used for the initial analysis. This porous media could be described in as little as two parameters, allowing multiple analyses to be completed without consideration of previous knowledge regarding how flow should behave in porous media. This analysis supported the long held assumption that the Darcy-Forchheimer equation can be divided into a viscous loss term and an inertial loss term. After this primary analysis several less ideal porous media were modeled and analyzed similar to the primary case. A more general relationship that can be used for a wide variety of homogeneous porous media was developed.