Fast computation of head and velocity covariances in three-dimensional statistically axisymmetric heterogeneous porous media

Abstract

Modeling of flow and transport through axisymmetric porous media conditional to log conductivity and hydraulic head measurements is reviewed using stochastic Lagrangian framework. This approach necessitates expression of the covariances of the velocities, the hydraulic head, and the log conductivity, on one hand, and cross covariances between the velocities and hydraulic head and log conductivity. It is recognized that conditional modeling becomes very computationally burdensome for even conditioning on a small number of measurements, particularly for three-dimensional modeling. The present manuscript provides an integration scheme [Anderson, 1979] that simplifies considerably the computations of the velocity covariances [Rubin and Dagan, 1992] and thereby opens the possibility for a wider range of applications of the stochastic analytical models for solute transport by groundwater.