Langevin Model for Reactive Transport in Porous Media

Journal Article · Thu Aug 05 04:00:00 EDT 2010 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 82(2 PT 2):Art. No. 026302

DOI:https://doi.org/10.1103/PhysRevE.82.026302· OSTI ID:988648

Tartakovsky, Alexandre M

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.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (US), Environmental Molecular Sciences Laboratory (EMSL)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 988648
• Report Number(s): PNNL-SA-67811; 32297; KJ0401000
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 82(2 PT 2):Art. No. 026302, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 82(2 PT 2):Art. No. 026302 Journal Issue: 2 PT 2 Vol. 82; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACCURACY
CONTINUITY EQUATIONS
DIFFUSION
Environmental Molecular Sciences Laboratory
FLUCTUATIONS
FLUID FLOW
FORECASTING
HYDRODYNAMICS
LAGRANGIAN FUNCTION
LANGEVIN EQUATION
PARTICLE MODELS
TRANSPORT
VELOCITY
langevin model
transport
reactions