PNNL

Abstract

A meso-scale stochastic Lagrangian particle model is presented and used to simulate conservative and reactive transport in porous media. In the stochastic model, the fluid flow in a porous continuum is governed by a combination of a Langevin equation and continuity equation. Pore-scale velocity fluctuations, the source of mechanical dispersion, are represented by the white noise. Molecular diffusion and sub-pore-scale Taylor-type dispersion is modeled by effective stochastic advection-diffusion equation.In the meso-scale stochastic model the molecular and sub-pore-scale Taylor type dispersion is modeled by stochastic advection-diffusion equation. The advective velocity (the solution of langevin flow equation) causes the mechanical dispersion of a solute. A smoothed particle hydrodynamics method was used to solve the meso-scale transport equations. The comparison of the meso-scale model with pore-scale and Darcy-scale models shows that: 1) for a wide range of Peclet numbers the meso-scale model predicts the mass of reaction product more accurately than the macro-scale model; 2) for small Peclet numbers predictions of both the meso-scale and the macro-scale models agree well with a prediction of the pore-scale model; 3)the accuracy of the meso-scale model deteriorates with the increasing Peclet number but more slowly than the accuracy of the macro-scale model. These results show that the separate treatment of advective and diffusive mixing in the stochastic transport model is more accurate than the classical advection-dispersion theory, which uses a single effective diffusion coefficient (the dispersion coefficient) to describe both types of mixing.