Scaling Laws For Macrodispersion
نویسندگان
چکیده
Scaling laws for the macrodispersivity of ow through porous media are derived from the assumed scaling properties of geological heterogeneity. If is the exponent characterizing uid scaling and is the exponent which characterizes geological heterogeneity, then a simple scaling relation is = maxfa2 ; 1 a2 g. Typically, 0 < < 1, and 12 < < 1, leading to an anomalous, or scale dependent, di usion process. These results are based on primitive and renormalized perturbation theory. The derivations are con rmed and limits placed on their validity by numerical simulation and by the exact mathematical solution and analysis of simpli ed model problems. Macrodispersivity is known from eld data to depend in an essential fashion on length scale. Longitudinal dispersivity is a signi cant ow parameter. Geological features to characterize multilength scale and multi{ fractal heterogeneity are proposed, as well as numerical parameters to quantify these features.
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