Probabilistic estimation of well catchments in heterogeneous aquifers

Evaluation of solute travel times to wells is an environmental problem of high relevance. It is usually accomplished by means of models that rely on the assumption of uniform and isotropic conductivity field and general rules can be derived only for simple cases. We study the travel time of an ideal tracer to a single, steady-state pumping well, fully penetrating a confined aquifer, with uniform background flow, to analyse the influence of natural heterogeneity on the spatial location of the isochrones, that are the boundaries of time-related well capture zones. In a uniform aquifer the location of the isochrones is deterministic while heterogeneity of the hydraulic conductivity is the main source of natural uncertainty in the estimate of their spatial distribution. Local dispersion is not considered and the problem is stated in terms of dimensionless variables. The analysis is performed via a Monte Carlo procedure in conjunction with FFT-based spectral methods. The log-conductivity field is assumed to be Gaussian and stationary, with variance SIGMA2_Y and isotropic exponential correlation. Various degrees of domain heterogeneity are considered and stability and accuracy of the MC procedure is examined. The total probability that a particle starting from a point in the acquifer is pumped within a given time is identified. It is demonstrated that due to heterogeneity the location of an isochrone becomes uncertain and it is strongly influenced by SIGMA2_Y. We postulate an expression for the probabilistic spatial distribution of the isochrones which is formally similar to that derived by Bear and Jacobs (1965) for a uniform medium and introduce an additional coefficient, numerically determined, to reproduce the effect of heterogeneity. Conceptually consistent equations of practical use for engineering purposes are proposed.