On the multiscale characterization of effective hydraulic conductivity in random heterogeneous media: A historical survey and some new perspectives

COLECCHIO, IVÁN; BOSCHAN, ALEJANDRO; OTERO, ALEJANDRO D.; NOETINGER, BENOÎT

ADVANCES IN WATER RESOURCES

ELSEVIER SCI LTD

Año: 2020 vol. 140

0309-1708

   In large scale heterogeneous aquifer simulations, determining the appropriate coarsening scale $lambda$ to define an effective hydraulic conductivity $K_{eff}$ is a challenging task, that involves a trade-off between accuracy and cost. Efficiently adjusting the scale $lambda$ is then key, in particular for uncertainty quantification.    In this paper, we obtain improved analytical results for the variance of $K_{eff}$, valid at any scale, in the context of energy dissipation formulation. Using this formulation, we then derive an efficient $K_{eff}$ numerical estimator, and compare it with those of the potential-flow average and permeameter formulations in 2D, for lognormal and binary media, over a wide range of $lambda$ and of heterogeneity. We analyze the probability density function (pdf), mean, and variance, of these estimators, comparing them with the analytical results.    In the lognormal case, the pdf´s are rather similar for the three estimators, and remain lognormal at all scales. In the binary case, slow convergence to an asymptotic regime is observed close to the percolation threshold.