When an exact formula is not enough: The counter-intuitive nature of gas flow in anisotropic porous media

Landfills are the most common method of waste management. Inside a landfill facility anaerobic waste decomposition releases gases – including methane and carbon dioxide – which can escape into the environment when mismanaged. Methane in sufficiently high concentrations is explosive, flammable, toxic, and is one of the major contributors to greenhouse gases. Therefore, it is vital to know how the gas flows within the solid waste matrix to allow for adequate collection, safe removal and control of emissions. In particular, a correctly working facility would aim to collect as much gas as possible to prevent inadvertent escape into the environment. Current practices rely on decades of experience; however, there is little to no mathematical analysis readily available. Designers and operators require access to gas flow information to build and manage landfills with efficiency and minimal environmental impacts. One of the important effects is the intrinsic heterogeneity of the waste matrix. Such types of media are known as anisotropic, since the heterogeneity means the resistance to fluid flow depends on the flow direction. Analytical solutions exist for anisotropic media, describing the fluid flow by giving pressure and velocity at any desired point in simplified geometric settings. However, since the pressure gradient (velocity) varies over four orders of magnitude from the perimeter of the landfill to the centre, traditional methods of visualization, such as isocontours for pressure or arrow representation for the velocity vector field, are ineffective. A custom code was developed in Octave/MATLAB to visualize a large set of configurations with an arbitrary number of sectors and distinct permeabilities. This code implements backward integration of pathlines with customized seeding of starting points and is focused on the ability to accurately locate any present stagnation points and visualize how the gas moves around them. The code’s robustness was verified by running it for a wide range of sector angles and landfill parameters. The success of these runs was then classified by the qualitative visual features present in each flow field, such as reasonable density, smoothness of pathlines, and efficient coverage of key points in the flow. The code was only deemed robust and ready to use by practitioners once it was able to integrate and plot pathlines for a wide range of parameters. These visuals will provide landfill designers and engineers with crucial information regarding the efficiency of landfill operations. Specifically, the code will make it possible to identify regions of recirculation and escape, subsequently aiding in the design and optimization of more efficient and environmentally conscious landfills.