Estimating geometric tortuosity of saturated rocks from micro-CT images using percolation theory

Abstract

Tortuosity (\(\tau\)) is one of the key parameters controlling flow and transport in porous media. Although the concept of tortuosity is straightforward, its estimation in porous media has yet been challenging. Most models proposed in the literature are either empirical or semiempirical including some parameters whose values and their estimations are in prior unknown. In this study, we modified a previously presented geometric tortuosity (\({\tau }_{g}\)) model based on percolation theory and validated it against a methodology based on the pathfinding A* algorithm. For this purpose, we selected 12 different porous materials including four sandstones, three carbonates, one salt, and four synthetic media. For all samples, five sub-volumes at different lengths with fifty iterations were randomly selected except one carbonate sample for which three sub-volumes were extracted. Pore space properties, such as pore radius, throat radius, throat length, and coordination number distributions were determined by extracting the pore network of each sub-volume. The average and maximum coordination numbers and minimum throat length were used to estimate the \({\tau }_{g}\). Comparison with the A* algorithm results showed that the modified model estimated the \({\tau }_{g}\) accurately with absolute relative errors less than 28%. We also estimated the \({\tau }_{g}\) using two other models presented in the literature as well as the original percolation-based tortuosity model. We found that our proposed model showed a significantly higher accuracy. Results also indicated more precise estimations at the larger length scales demonstrating the effect of uncertainties at the smaller scales.