Mixing-Scale Dependent Effective Dispersion for Solute Transport in Spatially Heterogeneous Flows

Abstract:

Dispersion quantifies the impact of micro-scale velocity fluctuations on the effective movement of particles and the evolution of scalar distributions in heterogeneous flows. Dispersion coefficients depend on the interaction between the velocity fluctuation scales and the scale on which the scalar is homogenized. The mixing, or coarse grained scale is the characteristic length below which the scalar is well mixed. The mixing scale evolves in time as a result of dispersion and deformation of material fluid elements in the heterogeneous flow. We propose to use the mixing scale as a natural coarse graining scale for dispersion in heterogeneous flows. Using a stochastic modeling framework, we derive explicit expressions for the mixing-scale dependent dispersion tensor and its variance for a spatially heterogeneous steady-state flow field within a porous formation. The fundamental mechanisms of local scale dispersion and compression of material fluid elements on evolving velocity scales determine the evolution of mixing-scale dependent dispersion and its self-averaging behavior.