Stochastic Analysis of Flow in Heterogeneous Porous Media

It is becoming widely recognized that natural earth materials are rather heterogeneous in terms of their hydrologic properties. Figure 1 shows observations of permeability and porosity in a sandstone aquifer in Illinois. These data are based on laboratory analysis of cores collected from deep boreholes in the Mt. Simon aquifer in central Illinois. The variation of permeability is seen to be rather large; the values range over four orders of magnitude. Porosity on the other hand shows a somewhat smaller degree of variability but still a significant percentagewise change. Figure 2 is the second example of the variability of permeability in earth materials. These data show observed infiltration rates of surface soils along a transect some 700 m long in an irrigated area near Socorro, New Mexico. Here the saturated hydraulic conductivity is seen to vary over two orders of magnitude. The observations in Figure 1 and 2 also illustrate that the variation of hydraulic conductivity or permeability is not completely disordered in space. There is some spatial structure which should be taken into account when considering the effects of such heterogeneity. Many other observations from different geologic environments show similar kinds of natural variability of permeability and other properties.

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