Chaotic advection at the pore scale: Mechanisms, upscaling and implications for macroscopic transport

• Published in: Advances in water resources 2016-11, Vol.97, p.175-192
• Main Authors: Lester, D.R., Trefry, M.G., Metcalfe, G.
• Format: Article
• Language: English
• Subjects: Advection; Architecture; Chaos; Chaos theory; Chaotic advection; Computational fluid dynamics; Conditioning; Deformation; Deformation mechanisms; Diffusion; Dilution; Dispersal; Dispersion; Dye dispersion; Fluid flow; Fluid mechanics; Fluids; Frameworks; Hydrodynamics; Kinematics; Mathematical models; Media; Mixing; Mixing processes; Molecular diffusion; Plumes; Porous materials; Porous media; Random walk; Solutes; Spreading; Stochastic models; Three dimensional flow; Transit time; Two dimensional flow; Upscaling
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2016.09.007

•The mechanisms and impacts of pore-scale chaotic advection in porous media are studied via a model 3D porous network.•Pore-scale chaotic advection results in exponential decay of concentration variance with longitudinal distance.•Longitudinal dispersion is retarded by chaotic advection and predictions agree well with computational studies on natural media.•These theoretical predictions can be extended natural systems via a continuous time walk model of fluid deformation. The macroscopic spreading and mixing of solute plumes in saturated porous media is ultimately controlled by processes operating at the pore scale. Whilst the conventional picture of pore-scale mechanical dispersion and molecular diffusion leading to persistent hydrodynamic dispersion is well accepted, this paradigm is inherently two-dimensional (2D) in nature and neglects important three-dimensional (3D) phenomena. We discuss how the kinematics of steady 3D flow at the pore scale generate chaotic advection—involving exponential stretching and folding of fluid elements—the mechanisms by which it arises and implications of microscopic chaos for macroscopic dispersion and mixing. Prohibited in steady 2D flow due to topological constraints, these phenomena are ubiquitous due to the topological complexity inherent to all 3D porous media. Consequently 3D porous media flows generate profoundly different fluid deformation and mixing processes to those of 2D flow. The interplay of chaotic advection and broad transit time distributions can be incorporated into a continuous-time random walk (CTRW) framework to predict macroscopic solute mixing and spreading. We show how these results may be generalised to real porous architectures via a CTRW model of fluid deformation, leading to stochastic models of macroscopic dispersion and mixing which both honour the pore-scale kinematics and are directly conditioned on the pore-scale architecture.