### Abstract

Scaling laws for the macrodispersivity of flow through porous media are derived from the assumed scaling properties of geological heterogeneity. If γ is the exponent characterizing fluid scaling and β is the exponent which characterizes geological heterogeneity, then a simple scaling relation is γ = max{ 1/2 , 1-β/2}. Typically, 0<β<1, and 1/2 <γ<1, leading to an anomalous, or scale dependent, diffusion process. These results are based on primitive and renormalized perturbation theory. The derivations are confirmed and limits placed on their validity by numerical simulation and by the exact mathematical solution and analysis of simplified model problems. Macrodispersivity is known from field data to depend in an essential fashion on length scale. Longitudinal dispersivity is a significant flow parameter. Geological features to characterize multilength scale and multifractal heterogeneity are proposed, as well as numerical parameters to quantify these features.

Original language | English |
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Pages | 35-49 |

Number of pages | 15 |

State | Published - Jan 1 1992 |

Event | Proceedings of the 9th International Conference on Computational Methods in Water Resources - Denver, CO, USA Duration: Jun 1 1992 → Jun 1 1992 |

### Conference

Conference | Proceedings of the 9th International Conference on Computational Methods in Water Resources |
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City | Denver, CO, USA |

Period | 06/1/92 → 06/1/92 |

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### Cite this

*Scaling laws for macrodispersion*. 35-49. Paper presented at Proceedings of the 9th International Conference on Computational Methods in Water Resources, Denver, CO, USA, .