Geostatistical Property Modeling

Abstract:

Heterogeneity is responsible for the departure of solute transport behavior from that predicted by a Gaussian ADE behavior. Salomon et al. (2007) showed that using a proper geostatistical model to describe the heterogeneity of the MADE site, spatial realizations of hydraulic conductivity could be generated, some of which will respond to solute transport in a manner similar to the responses observed at the site. The realizations had to be generated on the same support at which the data had been collected, what implied a very fine discretization, since the conditioning conductivity data had been derived from the dense sampling network of flowmeter data. Building the realizations at such small resolution allowed the representation of the local scale heterogeneity that could be partly responsible for the transport behavior observed at MADE. When models are to be built with a discretization much coarser than the support of the data, there is a need to account for the loss of heterogeneity implied by the use of coarse homogeneous blocks: Fernàndez-Garcia et al. (2009) showed that an advective-dispersion process on a heterogeneous media has to be modeled as an advection-dispersion-mass transfer process when upscaling onto a homogeneous block, implying that there is a need to include a fictitious mass transfer process to account for the loss of heterogeneity within the block being upscaled. Therefore there is a need to properly account for the heterogeneity of the parameters controlling the state equations, at the support at which these parameters are observed, and there is also a need to account for the proper upscaling rules when using those observed parameters in models discretized at supports much larger than those in which they were observed.