###### Abstract
This study focuses on geometric tortuosity (Dijkstra) and flow tortuosity (Streamline), comparing both with tortuosity values obtained from mathematical formulations. Typically, Dijkstra is calculated using shortest-path algorithms applied to digital representations of the pore structure. These algorithms have proven effective in modeling pore networks in both two-dimensional (2D) and three-dimensional (3D) rock structures [21]. Since flow tortuosity represents the actual path traveled by the fluid through the porous medium, it is derived from the velocity field obtained via numerical flow simulations such as the Lattice Boltzmann Method (LBM), which is widely employed due to its advantages in handling complex boundaries and realistic porous media geometries [22; 23; 24; 25]. Flow tortuosity is calculated from the streamline visualizations derived from the velocity field and is the ratio between the total length of the traced streamline representing the actual fluid trajectory through the pore space and the straight line distance between the inlet and outlet boundaries of the sample domain [26; 27; 28]. Tortuosity can also be estimated using empirical or semi-theoretical equations involving petrophysical parameters such as effective porosity, coordination number, and throat length derived from segmentation and digital characterization of the pore structure [29]. Several classical models remain in use due to their ease of implementation and ability to provide reasonably representative initial estimates. However, their accuracy is highly influenced by the pore morphology complexity and the validity of the homogeneity assumptions inherent in these models [30; 31; 32]. Table 1 summarizes the approaches used by various authors to evaluate tortuosity. [PERSON] et al. [28] employed 2D synthetic data to evaluate flow tortuosity and compared it with several empirical models. In comparison, [PERSON] et al. [2] estimated geometric tortuosity from 3D images of carbonate and sandstone rocks and compared these values with those obtained from various empirical models. Meanwhile, [PERSON] et al. [26] calculated multiple petrophysical parameters, including tortuosity, from 2D images using  
the A* algorithm. Subsequently, the authors extended this approach to 3D data, focusing on streamline-based tortuosity estimation and analysis of other relevant physical parameters for porous media characterization [33]. A relevant precedent can also be found in the work by [PERSON] et al. [34], which proposed a Lagrangian particle-based finite element model to simulate Brownian motion within trabecular bone structures reconstructed from micro-CT imaging. Their study highlights the value of combining high-resolution microstructural data with numerical simulation to investigate transport phenomena in complex porous media. This approach shares conceptual similarities with the present work, which employs micro-CT-based reconstructions and numerical analysis to evaluate tortuosity in geological samples. The alignment between these studies underscores the broader applicability of image-based modeling frameworks across disciplines involving porous structures. While previous studies have investigated tortuosity using various methods and rock types, none have comprehensively combined geometric tortuosity, flow tortuosity, and empirical model estimations across a large 3D dataset of sandstone and carbonate rocks. This study integrated numerical modeling, digital image analysis, and empirical model evaluation to provide new insights into the complexity of pore structures and fluid flow in porous media, particularly within the highly heterogeneous pre-salt carbonate formations. The findings are expected to support improved data-driven decision-making in reservoir management and enhance the accuracy of fluid flow predictions in subsurface environments.