The Eulerian-Lagrangian localized adjoint method (ELLAM) formulation of Younes et al. (2006) is applied to solve the advection-dispersion equation used to describe conservative solute transport in highly heterogeneous porous media. Heterogeneity is described by a correlated random field with an exponential covariance. Macrodispersion coefficients are calculated for a broad range of heterogeneities using Monte Carlo (MC) simulations on large size domains. ELLAM circumvents some drawbacks of usual particle-tracking and Eulerian-Lagrangian methods when local dispersion/diffusion is added. ELLAM is also highly efficient and well adapted for advective dominant transport and for MC simulations. For pure advection, first-order approximation provides good estimates of the duration of the preasymptotic regime and of the longitudinal macrodispersion coefficient for a variance of the log conductivity σ2 ≤ 2.25. Higher-order theories overestimated this coefficient for higher variances. Computed transverse macrodispersion is equal to 0 for each studied variance of log conductivity σ2 ∈ [0.25;1.0;2.25;4.0; 6.25; 9.0]. Local dispersion/diffusion affects the macrodispersion for quite low Peclet number (< 100) compared to previous work. For a Peclet number of 10, it leads to an increase of the longitudinal and transverse macrodispersion for low variances (σ2 = 0.25). For higher heterogeneity (σ2 = 9.0 for local dispersion and σ2 ≥ 4.0 for local diffusion), the longitudinal macrodispersion decreases due to local transverse mixing.
ASJC Scopus subject areas
- Water Science and Technology