Time-related capture zones for contaminants in randomly heterogeneous formations

Prediction of solute travel distance based on homogeneous, and isotropic hydraulic conductivity may lead to substantial differences in terms of the actual travel distance in a heterogeneous system. The effect of randomly varying hydraulic conductivity on the spatial location of time-related well capture zones for a non-reactive tracer in a confined aquifer with uniform base flow is considered. A numerical Monte Carlo procedure is used in conjunction with Fast Fourier Transform-based spectral methods. The log hydraulic conductivity field is assumed to be Gaussian and stationary, with isotropic exponential autocovariance. Various degrees of domain heterogeneity are considered and stability and accuracy of the numerical procedure are examined. The total probability that a particle injected at a point in the aquifer is extracted by the well within a given time is identified. The concept of probabilistic isochrone, which is the boundary of a given time-related capture zone, is introduced. A simple analytical model that extends the deterministic capture-zone model for uniform media is derived, by taking into account the effect of random variations of hydraulic conductivity. Knowledge of the spatial pattern of probabilistic isochrones allows reconstructing the breakthrough curve at the well for solute injections at selected locations in the aquifer.