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Description
The study of immiscible two-phase flow in porous media remains a topic of major scientific and technological relevance, with applications in reservoir engineering, hydrogeology, and enhanced oil recovery. Since the 1930s, several models have been proposed to describe this phenomenon at the pore scale, yet significant challenges persist due to the complexity introduced by mobile interfaces and their coupled physical interactions.
This work presents a numerical methodology to estimate permeability and viscous drag tensors in water/oil systems under drainage and imbibition scenarios, based on the theoretical framework developed by Whitaker (1986, 1994). The model consists of four governing equations: two for the mass balance of the mobile phases and two for the momentum, coupled through four tensors. Two tensors represent the effective permeability of each phase, while the other two correspond to viscous drag tensors, which capture cross-phase interactions.
The methodology employs a representative unit cell mimicking pore and throat geometry, with dimensions derived from a standard sandstone sample. Fluid dynamics and interface motion are simulated using the Phase-Field method implemented in Comsol Multiphysics. Solving the associated closure problems in these representative geometries allows the estimation of transport coefficients.
Results indicate that the qualitative permeability predictions are consistent with values reported in the literature and align with Whitaker’s analytical predictions, while also partially agreeing with empirical correlations. These findings validate the proposed approach and highlight its potential to address problems that historically remained unsolved due to computational limitations.
In conclusion, this study provides a modern computational framework that bridges rigorous theoretical formulations with advanced numerical simulations. It represents a significant step toward the accurate characterization of transport tensors in immiscible two-phase porous media, paving the way for extensions to more complex geometries and flow conditions representative of natural and industrial systems.
| References | Whitaker, S. (1986), Flow in porous media II: The governing equations for immiscible two-phase flow, Transport in Porous Media, 1, 105-125.Whitaker, S. (1994), The closure problem for two-phase flow in homogenous porous media, Chemical Engineering Science, 49(5), 765-780. |
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| Country | México |
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