Application of a* Algorithm for Tortuosity and Effective Porosity Estimation of 2D Rock Images

Characterization and understanding of fluid flow phenomena in underground porous media at the micro and macro scales is fundamental in reservoir engineering for the definition of the optimal reservoir exploitation strategy. Laboratory analyses on rock cores provide fundamental macroscale parameters such as porosity, absolute and relative permeability and capillary pressure curves. In turn, macroscale parameters as well as flow behavior, are strongly affected by the micro geometrical features of the rock, such as pore structure, tortuosity and pore size distribution. Therefore, a thorough comprehension of single and multiphase flow phenomena requires analyses, observations and characterization at the micro scale. In this paper we focus on the analysis of a 2D binary image of a real rock thin section to characterize the pore network geometry and to estimate tortuosity, effective porosity and pore size distribution. To this end, a geometrical analysis of the pore structure, based on the identification and characterization of the set of the shortest geometrical pathways between inlets and outlets pairs, is implemented. The geometrical analysis is based on the A* path-finding algorithm derived from graph theory. The results provided by the geometrical analysis are validated against hydrodynamic numerical simulation via the Lattice Boltzmann Method (LBM), which is well suited for simulating fluid flow at the pore-scale in complex geometries. The selected rock for this analysis is Berea sandstone, which is recognized as a standard rock for various applications such as core analysis and flooding experiment. Results show that the path-finding approach provides reasonable and reliable estimates of tortuosity and can be successfully applied for analyzing the distribution of effective pore radius, as well as for estimating the effective porosity.