ABSTRACT
Scaling is the process of relating a property’s value at one scale to its value at another scale. A complete solution gives the dependence of the property on scale over a continuous and (hopefully) wide range of scales. Scaling, as a theoretical tool, is usually based on physical arguments. Dimensional arguments can be used to generate dimensionless constants, helping to identify the relative importance of various forces relevant to uid motion in the subsurface (capillary, gravity, viscous, etc.) or of transport processes such as diusion and advection. Except for the Peclet number, which measures the scale-dependent relevance of diusion and advection, this kind of argument is not a focus here. Rather, our approach to scaling
is inuenced by the concept of renormalization, which is itself based on perspective and information: How does the appearance of an object change when an observer moves closer or farther? Does it look the same at all scales (called scale invariant)? If so, the object may t a fractal description. How does such a description relate to the hydraulic and transport properties of porous media? Interestingly, the scaling properties of the medium, important as they may be, are of secondary consequence to the scaling properties of the dominant ow paths through the medium (Sahimi, 1994), and in many respects, these paths are independent of most specics of the medium (although sometimes correlations in the medium may inuence ow and transport; Sahimi and Mukhopadhyay, 1996).
