Modeling Mixing in Stratified Heterogeneous Media: The Role of Water Velocity Discretization in Phase Space Formulation

Modeling solute transport in heterogeneous porous media faces two challenges: scale dependence of dispersion and reproducing mixing separately from spreading. Both are crucial since real applications may require km scales whereas reactions, often controlled by mixing, may occur at the pore scale. Methods have been developed in response to these challenges, but none has satisfactorily characterized both processes. In this paper, we propose a formulation based on the Water Mixing Approach extended to account for velocity variability. Velocity is taken as an independent variable, so that concentration depends on time, space and velocity. Therefore, we term the formulation the Multi-Advective Water Mixing Approach. A new mixing term between velocity classes emerges in this formulation. We test it on Poiseuille's stratified flow using the Water Parcel method. Results show high accuracy of the formulation in both dispersion and mixing. Moreover, the mixing process exhibits Markovianity in space even though it is modeled in time.

Automated summary

This paper proposes a formulation based on the Water Mixing Approach to model solute transport in heterogeneous porous media. The formulation takes into account the scale dependence of dispersion and the separation of mixing from spreading. It introduces velocity as an independent variable, allowing concentration to depend on time, space, and velocity. The formulation, termed the Multi-Advective Water Mixing Approach, incorporates a new mixing term between velocity classes. Experimental results demonstrate the high accuracy of the formulation in both dispersion and mixing, with the mixing process exhibiting Markovianity in space despite being modeled in time.