Abstract
In this chapter we consider the diffusive and mixing properties of fluids moving in heterogeneous porous media by means of Eulerian velocity fields. We shall discuss here the basic principles of advection and dispersion in heterogeneous media from an Eulerian perspective. The common theme for the various methods we shall explore is the treatment of the concentration as an SRF. The first approach models the concentration through its statistical moments, such as the expected value and the variance, and computes them through a set of differential equations, an equation for each statistical moment. The second approach is MC based, and it computes an ensemble of physically plausible realizations of the concentration field, which can then be used for computing the statistics of the concentration, and from there the probability of events such as the concentration exceeding a threshold value at specified locations and times. Let us emphasize that stochastic modeling of contaminant transport is not just about the effects of media heterogeneity. There is also room for stochastic modeling in uniform media if there is uncertainty with regard to the media's parameters. Prediction with parameter error is discussed in chapter 13. Let us consider the case of passive solutes which are injected into a fluid body at rest.
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