Impact of the choice of the variogram model on flow and travel time predictors in radial flows

Prediction of hydraulic head, flux and contaminant travel time/trajectories in natural aquifers is uncertain due to the geologic media complexity and lack of information. Hence it is appropriate to cast the equations that govern groundwater flow and contaminant transport within a stochastic framework. The latter is oriented towards rendering ensemble moments of the analyzed quantities. In this view the spatial variable transmissivity is usually modeled as a Stochastic Continuum, characterized by a set of parameters (covariance shape, geometric mean, variance and correlation length). These are generally assumed to be known with certainty even though they are usually derived using a limited amount of experimental data, which are often not enough for a complete characterization. Full-Bayesian approaches (e.g. Woodbury and Rubin 2000; Woodbury and Ulrych 2000) take into account the uncertainty in the knowledge of the variogram parameters (geometric mean, variance and correlation length). Feyen et al. (2002) illustrate an application of these methodologies to determine the uncertainty asso-ciated with the delineation of well capture zones. Hendricks Franssen et al. (2002) investigate the impact of the uncertainty of variogram parameters on the same topic using sequential Gaussian simulation (Gómez-Hernández and Journel 1993) to generate transmissivity fields and the sequential self-calibrated method for in-verse conditioning. In all these works the shape of the correlation structure of the natural logarithm of transmissivity is fixed and assumed known without uncertainty. Salandin and Rinaldo (1989) analyze the influence of the form of the log-conductivity covariance on dispersion coefficients in random permeability fields under mean uniform flow conditions. Here, we focus on the impact of the choice of the functional form for the log-transmissivity variogram on (ensemble) moments of hydraulic head and contami-nant residence time under convergent flow conditions, such as those created by a single pumping well. Although of high relevance in practical applications, problems associated to contaminant transport in the vicinity of extraction wells in heterogeneous media have been tackled only recently (e.g. Guadagnini and Franzetti 1999, Riva et al. 1999, Dagan and Indelman 1999, van Leeuwen et al. 2000, Feyen et al. 2002). We perform a numerical Monte Carlo analysis of (a) the predictors of hydraulic head and residence time (rendered by their means) for conservative solute particles injected at various radial distances from the well, and (b) the associated prediction errors (rendered by the variance of the state variables investigated). The natural logarithm of aquifer transmissivity, Y, is modeled as a statistically homogeneous Gaussian random field. Three functional forms of the variogram (namely Exponential, Gaussian and Spherical), chosen amongst the most common models used in the literature, are considered. The impact of the choice of the variogram model on flow and travel time predictors is analyzed for different domain sizes in terms of correlation scale of Y (i.e. extent of the aquifer within which the effects of pumping are not negligible) and degrees of heterogeneity (in terms of the variance of Y ).