Optimization of Material Permeability Analysis Algorithm for 3D Raster Structures Using Graph-Based and Morphological Approaches

Quantitative characterization of permeability in porous media represents a central problem in filtration theory, geosciences, and materials engineering. Standard numerical approaches, including finite element methods and Lattice Boltzmann simulations, typically require extensive domain-specific expertise together with specialized computational software. This motivates the development of computationally simpler and more accessible geometric approaches applicable directly to binary volumetric data. We introduce a novel algorithmic framework for the analysis of porous structures that reformulates permeability-related characterization in terms of discrete geometry and graph-based computation. The method combines parallel raster-grid and graph representations of a binarized three-dimensional CT image. The principal transport-limiting feature of the pore network, interpreted as the minimal constriction governing connectivity, is identified through iterative morphological dilation coupled with a three-dimensional scanline seed-fill procedure. In addition, a dichotomous bisection strategy is proposed to accelerate the determination of the critical bottleneck scale. The proposed methodology was evaluated on five volumetric datasets of size 100 × 100 × 100 voxels obtained from CT-derived porous structures. Experimental results demonstrate that dilation- and erosion-based formulations yield equivalent estimates of the bottleneck parameter in four of the five investigated samples. Furthermore, incorporation of the bisection optimization reduces computational time in three-dimensional experiments by approximately 50% relative to sequential iteration. The presented approach provides a computationally efficient and fully open-source alternative to conventional physics-based permeability solvers for binary porous media. The resulting bottleneck parameter b should be interpreted as a discrete geometric invariant characterizing the pore-network connectivity and minimal transport cross-section. It is not intended to replace the absolute permeability coefficient K appearing in Darcy’s law, but rather to serve as an independent structural descriptor suitable for comparative and topological analysis of porous systems.