Ergodic transport through aquifers of non‐Gaussian log conductivity distribution and occurrence of anomalous behavior

Abstract

Three‐dimensional advective transport of passive solutes through isotropic porous formations of stationary non‐Gaussian log conductivity distributions is investigated by using an approximate semianalytical model, which is compared with accurate numerical simulations. The study is a continuation of our previous works in which formation heterogeneity is modeled using spherical nonoverlapping inclusions and an approximate analytical model was developed. Flow is solved for average uniform velocity, and transport of an ergodic plume is quantified by mass flux (traveltime distribution) at a control plane. The analytical model uses a self‐consistent argument, and it is based on the solution for an isolated inclusion submerged in homogeneous background matrix of effective conductivity. As demonstrated in the past, this analytical model accurately predicted the entire distributions of traveltimes in formations of Gaussian log conductivity distributions, as validated by numerical simulations. The present study (1) extends the results to formations of non‐Gaussian log conductivity structures (the subordination model), (2) extends the approximate analytical model to cubical blocks that tessellate the entire domain, (3) identifies a condition in conductivity distribution, at the tail of low values, that renders transport anomalous with macrodispersivity growing without bounds, and (4) provides links of our work to continuous time random walk (CTRW) methodology, as applied to subsurface transport. It is found that a class of CTRW solutions proposed in the past cannot be based on solution of flow in formations with conductivity distribution of finite integral scale.