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This study introduces a stochastic model based on cellular automata (CA) to simulate particle transport in two-dimensional porous media. The model is applied to microstructures obtained from digital micrographs of shales from the La Peña and Eagle Ford formations in the Sabinas Basin, Coahuila. The displacement dynamics combine a directional trend driven by a pressure gradient with a random component, representing fluid movement as a biased random walker. This approach enables the characterization of fluid–rock interactions within complex microstructures, quantifying key petrophysical parameters such as tortuosity, effective porosity, and specific surface area.
Image preprocessing, including binarization and segmentation, was performed using open-source software (GIMP, Inkscape, Fiji). Simulation results were integrated into the Carman-Kozeny equation to estimate absolute permeability and analyze pore-scale flow behavior. The findings indicate that the model effectively captures the impact of structural heterogeneity on transport, showing consistent correlation with theoretical predictions.
The proposed methodology provides a robust tool for petrophysical characterization from digital images, with potential applications in unconventional reservoir evaluation and production optimization. Its stochastic nature and computational efficiency make it an attractive alternative to traditional deterministic approaches.
Keywords: porous media, shales, cellular automata, Carman-Kozeny, particle transport, stochastic modeling.
| References | C.G. Aguilar-Madera, J.V. Flores-Cano, V. Matías-Pérez, J.A. Briones-Carrillo, F. Velasco-Tapia, Computing the permeability and Forchheimer tensor of porous rocks via closure problems and digital images, Advances in Water Resources, Volume 142, 2020,103616,ISSN 0309-1708, https://doi.org/10.1016/j.advwatres.2020.103616. Carrillo, J. A. B., Villalobos, R. S., Madera, C. G. A., & Ramos, A. (2016). Estimación de porosidad en areniscas a partir de micrografías digitales utilizando R-Studio. |
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| Country | Nuevo León, México. |
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