One way to incorporate the uncertainty of field data and the spatial variability in the hydraulic properties of aquifers is to prescribe probability distributions to the material properties of the medium. The statistical properties of the hydraulic potential are then determined by the numerical solution of stochastic differential equations governing the flow in the aquifer. For this purpose we consider two stochastic finite element methods, Monte Carlo and stochastic Collocation, to estimate the mean and variance of the potential for saturated flow in statistically heterogeneous media, assuming that the coefficient of hydraulic transmissibility follows a lognormal distribution. One of the crucial issues in the accuracy of numerical methods is the spatial correlation length associated with the transmissibility. We also discuss some configurations of plant extraction that were recently proposed for a rational exploration of the Recôncavo aquifer in the Capivara river basin (Bahia, Brazil), by comparing two classical models and by introducing the randomness of transmissibility in one of these configurations.
Karhunen-Loève expansion; stochastic finite element methods; free aquifer
