Pore Network Model Extraction and the Influence on Relative Permeability: A Comparison with Percolation Theory

Abstract

This study introduces a new pore network structure model, based on the fundamentals of medial axis thinning and the maximal ball algorithm. Combining both methods provides great potential in preserving both topology and geometry, two key aspects to accurately mimic the respective pore space. To increase the accuracy of the pore network model even further, several characteristic improvements have been applied regarding the merging algorithm and the partitioning of the geometrical features. All alterations are physically viable and enhance the amount of detail, increasing the realism and robustness compared to other models. Ultimately, the model combines proven concepts and correct alteration to improve estimations related to fluid flow properties in porous media.

The model is tested on twelve different samples, incorporating two carbonates and ten sandstones. Results regarding the pore network properties and absolute permeability are directly compared to the medial axis algorithm (Lindquist et al., 1996) and maximal ball algorithm (Dong and Blunt, 2009). The flow properties, including the relative permeability, are extracted using PoreFlow (Raoof et al., 2013). Percolation theory is also introduced to derive the relative permeability, combining critical path analysis and universal scaling. The results generated by this analytical framework are compared to the results generated by PoreFlow, giving new insights into the predictive capabilities of percolation theory. Overall, percolation theory shows great potential, however, accurately estimating the fractal dimensionality is crucial to guarantee accurate predictions.