Probabilistic estimation of well catchments in heterogeneous aquifers

The estimation of well catchments in uniform background flow is usually made by means of models that rely on the assumption of homogeneous and isotropic conductivity fields. Properties of natural systems may vary significantly and in a very complex manner in space. One conceptualisation that takes into account this variability in hydraulic conductivity is based on the theory of random space functions. The effect of this randomness is that the influence of a discharge well cannot be delineated without some degree of uncertainty. This uncertainty needs to be considered when areas of contribution to wells under field conditions are to be defined. In this work, the problem is tackled by dimensional analysis and the solution is numerically treated within a stochastic approach. A steady 2-D non-uniform groundwater flow is considered in a statistically isotropic field of hydraulic conductivity K(x), with a single production well and a uniform base gradient. The analysis is performed via a Monte Carlo procedure that involves the generation of a great number of realisations of a given Y′ = ln(KKG) field, normally distributed, with zero mean, σY2 variance and simple expotential correlation. Various degrees of domain heterogeneity, i.e. σY2, are considered. The probability P1 that an ideal solute pulse released in a given location in the aquifer reaches the well is identified, and conceptually consistent equations of practical use for engineering purposes are proposed.