PNNL

Abstract

A meso-scale stochastic Lagrangian particle model was developed 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 hydrodynamic dispersion, are represented by the white noise. A smoothed particle hydrodynamics method was used to solve the governing equations. Changes in the properties of the fluid particles (e.g., the solute concentration) are governed by the advection-diffusion equation. The separate treatment of advective and diffusive mixing in the stochastic transport model is more realistic than the classical advection-dispersion theory, which uses a single effective diffusion coefficient (the dispersion coefficient) to describe both types of mixing leading to over-prediction of mixing induced effective reaction rates. The stochastic model predicts much lower reaction product concentrations in mixing induced reactions. In addition, the dispersion theory predicts more stable fronts (with a higher effective fractal dimension) than the stochastic model during the growth of Rayleigh-Taylor instabilities.