EVALUATION OF THE DISPERSION PROCESSES IN CONDITIONEDTRANSMISSIVITY FIELD

Conditioning on available measures makes the mathematical description of the hydraulic transmissivity field as inhomogeneous even if the original one isn't. Clear examples about multigaussian conditioning shows as, starting from a field that is stationary in the strict sense, the conditioned random function is no more statistically homogeneous being conditioned mean, covariance and variance depending on the spatial position. Obviously velocity fields deduced from the latter are inhomogeneous too, as shown in papers dealing with nonlocal formalism and non-Darcian flux. Among various aspects of conditioning widely discussed in the literature, we focus the attention on the effects related to the effective dispersion8 in conditioned log transmissivity fields. This topic has been tackled in the past in a hydraulic transmissivity field of finite correlation length and in self-similar porous formations with a large scale cutoff. While the former describes the impact of an uniform recharge on the conditioning process, in the latter it is shown as a single measurement reduces the difference between ensemble and effective solute moments, depending the effectiveness in reducing uncertainty on the position of the measurement respect the plume mean trajectory. Respect to these papers, we stress here the role of the flow field inhomogeneity to analyze its impact on the effective dispersion prevision in conditioned transmissivity fields. This goal is reached by use of the stochastic finite element method (SFEM) to handle nonstationarity stemming from the transmissivity conditioning in a finite 2-D domain, and by taking into account the mutual relevance of the initial plume finite size and of the inhomogeneity of the flow field in the nonergodic dispersion process. From the analysis of the developed numerical examples, it is shown as the effective dispersion may lead to a reductive forecast of the real plume spreading when, as in conditioned hydraulic transmissivity fields, the spatial stationarity of the flow field is not obeyed.