Random generation of irregular natural flow or pore networks

Daniel W Meyer

doi:10.1016/j.advwatres.2021.103936

Abstract

Over the past years, tomographic scanning techniques like micro-CT have become popular for the acquisition of high-fidelity void-space geometries of natural porous media (e.g., Bultreys et al., 2016; Raeini et al., 2017). Limitations both in computing time and memory prohibit, however, direct numerical simulations of flow and transport in large resp. detailed sample geometries. Flow or pore networks derived from scans alleviate this limitation, but still necessitate a methodology to extrapolate to larger samples. In this work, we present a network generation algorithm that is particularly suited for heterogeneous irregular networks. While emulating from an existing base network new networks of equal or larger sizes, the outlined algorithm scales approximately linearly with the network node or pore count and maintains (1) node connectivity resp. pore coordination-number statistics, (2) geometrical pore/throat properties, as well as (3) the potentially inhomogeneous spatial clustering of pores. While existing methods address the first two properties, the third point is crucial especially in heterogeneous media to match flow/transport properties like the permeability that have a strong dependence on the spatial distance between connected pores. Moreover, the cubical networks generated by our algorithm are periodic in all spatial directions, thus eliminating topological boundary effects, which are not present in natural media. Bounded networks of arbitrary sizes can then be recovered by cutting the generated networks and thus flow/transport processes at larger scales can be studied while incorporating physically-based descriptions of pore-scale processes.

Highlights

Flow networks arise in diverse disciplines such as information transmission (Lambiotte et al, 2019) or transport in fractured subsurface formations (Jiang et al, 2017; Viswanathan et al, 2018)
Pore networks are a valuable idealization of natural porous media that can account for the spatial heterogeneities in pore arrangement and pore connectivity
Given the impact of node clustering on the flow properties of a network, the generator outlined in this work randomly perturbs the base network in a way that essentially preserves the dendrogram

Summary

Introduction

Flow networks arise in diverse disciplines such as information transmission (Lambiotte et al, 2019) or transport in fractured subsurface formations (Jiang et al, 2017; Viswanathan et al, 2018). Each voxel represents a cube occupied by either void or solid To translate these memoryintense 3d images into more compact networks, geometric methods such as the maximal ball algorithm (Silin and Patzek, 2006, figure 6) are applied (Bultreys et al, 2016, section 4.2). In this algorithm, the largest spheres inscribed in the void space and centered at each voxel are determined. Pore bodies are identified based on the largest spheres that contain the centers of smaller spheres Connections between these pore bodies or pores are represented through tubes or throats leading to a simplified network-based representation of the void-space geometry. Pore networks are a valuable idealization of natural porous media that can account for the spatial heterogeneities in pore arrangement and pore connectivity

Methods

Results

Conclusion