Estimation of macrodispersion in 2-D highly heterogeneous porous media using the Eulerian-Lagrangian localized adjoint method

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 sigma(2) <= 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 sigma(2) is an element of [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 (sigma(2) = 0.25). For higher heterogeneity (sigma(2) = 9.0 for local dispersion and sigma(2) >= 4.0 for local diffusion), the longitudinal macrodispersion decreases due to local transverse mixing. Citation: Ramasomanana F., A. Younes, and P. Ackerer (2013), Estimation of macrodispersion in 2-D highly heterogeneous porous media using the Eulerian-Lagrangian localized adjoint method, Water Resour. Res., 49, doi:10.1029/2012WR012228.