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Abstract The presence of well‐connected paths is commonly observed in spatially heterogeneous porous formations. Channels consisting of high hydraulic conductivity (K) values strongly affect fate and transport of dissolved species in the subsurface environment. Several studies have established a correlation between connectivity properties of the spatially variableK‐field and solute first arrival times. However, due to limited knowledge of the spatial structure of theK‐field, connectivity metrics are subject to uncertainty. In this work, we utilize the concept of the minimum hydraulic resistance and least resistance path to evaluate the connectivity of aK‐field in a stochastic framework. We employ a fast graph theory‐based algorithm to alleviate the computational burden associated with stochastic computations in order to investigate both the impact of the hydrogeological structural conceptualization and domain dimensionality (2‐D vs. 3‐D) on the uncertainty of the minimum hydraulic resistance. Finally, we propose an iterative data acquisition strategy that can be utilized to identify the least resistance path (which is linked to preferential flow channels) in real sites. A synthetic benchmark test is presented, showing the advantages of the proposed sampling strategy when compared to a regular sampling strategy. By using the iterative data sampling strategy, we were able to reduce first arrival time uncertainty by 47% (when compared to the regular sampling strategy), while maintaining site characterization efforts constant.
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Flow Path Resistance in Heterogeneous Porous Media Recast into a Graph-Theory Problem
AbstractThis work aims to describe the spatial distribution of flow from characteristics of the underlying pore structure in heterogeneous porous media. Thousands of two-dimensional samples of polydispersed granular media are used to (1) obtain the velocity field via direct numerical simulations, and (2) conceptualize the pore network as a graph in each sample. Analysis of the flow field allows us to distinguish preferential from stagnant flow regions and to quantify how channelized the flow is. Then, the graph’s edges are weighted by geometric attributes of their corresponding pores to find the path of minimum resistance of each sample. Overlap between the preferential flow paths and the predicted minimum resistance path determines the accuracy in individual samples. An evolutionary algorithm is employed to determine the “fittest” weighting scheme (here, the channel’s arc length to pore throat ratio) that maximizes accuracy across the entire dataset while minimizing over-parameterization. Finally, the structural similarity of neighboring edges is analyzed to explain the spatial arrangement of preferential flow within the pore network. We find that connected edges within the preferential flow subnetwork are highly similar, while those within the stagnant flow subnetwork are dissimilar. The contrast in similarity between these regions increases with flow channelization, explaining the structural constraints to local flow. The proposed framework may be used for fast characterization of porous media heterogeneity relative to computationally expensive direct numerical simulations. Article HighlightsA quantitative assessment of flow channeling is proposed that distinguishes pore-scale flow fields into preferential and stagnant flow regions.Geometry and topology of the pore network are used to predict the spatial distribution of fast flow paths from structural data alone.Local disorder of pore networks provides structural constraints for flow separation into preferential v stagnant regions and informs on their velocity contrast.
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- Award ID(s):
- 1847689
- PAR ID:
- 10391886
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Transport in Porous Media
- Volume:
- 146
- Issue:
- 1-2
- ISSN:
- 0169-3913
- Page Range / eLocation ID:
- p. 267-282
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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