Delineation of Paths of the Smallest Hydraulic Resistance and Their Influence on Flow and Transport.

Abstract:

Heterogeneity of the hydraulic conductivity field causes channeling of the flow field. Flux concentrates along the paths of the smallest resistance and organizes a network of channels. These channels govern the effective flux through the domain and the fastest Darcy velocities that manages the first arrival times of the contamination. The smallest resistance of such paths is a crucial property for estimation of the flow and transport effective parameters.

We developed a methodology to delineate a backbone – a connected set of paths of the smallest resistance – from hydraulic conductivity field only with no flow and transport simulation. From the backbone delineation procedure it is also possible to derive the smallest resistance and number of channels with comparable resistances or evaluate the network structure that can be topologically complex because the channels may split or merge. The thickness of the channels is usually related to the correlation length of the hydraulic conductivity field. These parameters provide an effective estimation of the effective hydraulic conductivity for highly heterogeneous fields where the flow channeling is significant. The path of the smallest resistance also provides the fastest flux and thus is responsible for the first arrival of the contamination.

In the current work we present a methodology of backbone delineation, calculation of the smallest resistance and evaluation of the effective parameters and compare the results with effective parameters obtained from direct flow and transport simulation within highly heterogeneous fields with different connectivity. The approach proposed demonstrated a sufficient accuracy of prediction and may be used for a block up-scaling of flow and some parameters of transport in highly heterogeneous media.