Objective: The objective of this study is to investigate a machine learning methodology based on the physics of dynamic fluid flow, with the aim of incorporating the knowledge of physical laws into learning algorithms to estimate precise results with lower computational cost. Theoretical Framework: This section presents the main concepts and theories that underpin the research. Key theories include nonlinear partial differential equations (PDEs), Darcy's Law, and the conservation of mass and energy, providing a solid foundation for understanding the research context. Method: The methodology adopted for this research involves modeling a one-dimensional two-phase fluid flow problem in a porous medium, governed by a first-order hyperbolic nonlinear equation. Data collection was conducted through numerical simulations, using micro and macro grids to evaluate permeability and boundary conditions. Results and Discussion: The results revealed that considering learning only in absolute permeability yielded good estimates of reservoir pressures. However, small discrepancies were observed in the estimation of saturations. The discussion contextualizes these results in light of the theoretical framework, highlighting the identified implications and relationships, as well as the study's limitations. Research Implications: The practical and theoretical implications of this research are discussed, providing insights into how the results can be applied or influence practices in the field of reservoir modeling and fluid flow simulations. These implications may include optimizing oil extraction processes and improving predictive models in reservoir engineering. Originality/Value: This study contributes to literature by presenting an innovative approach that integrates physical laws into machine learning algorithms, resulting in more accurate and efficient estimates. The relevance and value of this research are evidenced by the potential application of the results in optimizing industrial processes and improving computational simulations.
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