Flow Path Resistance in Heterogeneous Porous Media Recast into a Graph-Theory Problem

Abstract

This 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 Highlights A 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.

A DuMux Framework for Data-Driven Multi-Scale Parametrizations

“…Three primary metrics can be identified using graph representations: General pore-space connectivity, a shortest path analysis to describe the geometrical tortuosity, and a maximum flow analysis. Examples of other works using graphical representations of pore geometries are as follows: [21] where flow path resistance is investigated, [33] where preferential pathways are evaluated, and [11] where an affinity between rock core permeability and graph's Maximum Flow is demonstrated. In addition, the development of pore-network models is a similar method, where collections of highly connected nodes form pore bodies connected by throats [3].…”

Machine Learning to Predict Effective Reaction Rates in 3D Porous Media From Pore Structural Features

“…The discrepancies between well-mixed reaction rates and effective reaction rates are known to be caused by both geochemical and physical heterogeneities of porous media systems 19,[21][22][23][24] . Geochemical heterogeneity originates from the variety of minerals and complexity in chemical reactions [25][26][27][28][29][30][31] , while physical heterogeneity is caused by the structural heterogeneity of porous media, which controls fluid flow and mass transfer 22,[32][33][34][35][36][37][38][39][40][41] . In particular, pore structural heterogeneity is shown to exert dominant control over fluid mixing and homogeneous reaction rates [42][43][44] , and also shown to control porosity and permeability evolution induced by heterogeneous reactions (i.e., dissolution and precipitation) 17,34,[45][46][47][48][49][50] .…”