Impact of helicity on mixing in heterogeneous porous media

Mixing is the process that homogenizes initially segregated miscible constituents, increases the volume occupied by a solute, and decreases concentration peaks. It is important for the assessment of contamination levels and biogeochemical reactions in groundwater and soils. Mixing processes are governed by the interplay of fluid advection, molecular diffusion and local-scale dispersion at Darcy scale. Here we study the mechanisms of mixing in three-dimensional Darcy scale porous media with different heterogeneity structure. We analyze the role of medium and flow topology on the mixing and dispersion behavior. To this end, we perform Darcy-scale numerical simulations of incompressible flow and transport in heterogeneous three-dimensional porous media. Hydraulic conductivity is represented as a multi-Gaussian random field with lognormal marginal distribution. We consider isotropic and anisotropic correlation structures and scalar and tensorial conductivity. Flow is solved using a finite volume two-point method and transport using a Lagrangian approach. The flow topology is quantified by the helicity of the velocity field. We consider a planar injection of particles. Dispersion is quantified by the longitudinal and transverse dispersion coefficient, which are determined by the evolution along time of the position’s variance in the respective direction divide by two. It is also quantified by the breakthrough curves, which measure the distribution of arrival times at a given position from the initial one. Mixing is quantified by the ability of the flow to stretch and elongate a fluid strip which enhances diffusion through the creation and sustaining of concentration gradients. Results show that for a helical flow, a finite transverse dispersion coefficient is observed at long times and that the elongation of elemental strips follow an exponential stretching  (for large logK variances). On the contrary, on non-helical flows, transverse dispersion tends asymptotically to zero and the stretching rate is algebraic. The longitudinal dispersion coefficient seems unaffected by the helicity of the flow. These results shed light on the relation between medium structure and flow topology on mixing, making an important step towards the control, upscaling and large scale representation of mixing in porous media

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