Fenómenos de transporte

 

Numerical simulation of the water saturation at the interface between homogeneous porous medium

 

Simulación numérica de la saturación del agua sobre la interface entre medios porosos homogéneos

 

E. Cariaga¹, A. Vergara-Fernández²*, M. Lévano³ y N. Vergaray³

 

¹ Department of Mathematical and Physical Sciences-Universidad Católica de Temuco Casilla 15D-Temuco-Chile.

² Núcleo de Investigación en Energías Renovables-Universidad Católica de Temuco Casilla 15D- Temuco-Chile. * Corresponding author. E-mail: avergara@uctemuco.cl Tel.: +56 45 20 56 84, Fax +56 45 20 56 30.

³ School of Informatic Engineering- Universidad Católica de Temuco Casilla 15D- Temuco-Chile.

 

Received December 3, 2012
Accepted October 20, 2013

 

Abstract

The oil-water flow in a heterogeneous porous medium was studied numerically, with special emphasis on the interface between two homogeneous layers of the porous matrix. The heterogeneity considered consists of a discontinuous capillary pressure on the interface. The differential equation was solved using a fully implicit scheme based on the upwind finite volume method. The unknown was the water saturation. This study evaluated the impact of changes in: the porosity of trie entire domain, the initial water saturation, the water injection rate, the gravitational force, and the material grain size, on the water saturation at the interface. Experiments have improved the understanding of hydrodynamics on the interface. A full characterization of the porous matrix is an essential condition before defining conditions of oil extraction. The studied algorithm has great potential for use in earlier stages of design and planning for oil extraction.

Keywords: discontinuous capillary, porous medium, interface, finite volume, oil-water flow.

 

Resumen

En este trabajo se estudió numéricamente el flujo agua-petróleo en una medio poroso heterogeneo, con énfasis en la interface entre dos capas homogeneas de la matriz porosa. La heterogeneidad considerada consistió en una función discontinua de capilaridad sobre la interface. La ecuación diferencial fue resuelta utilizando un esquema tipo upwind completamente implícito basado en el método de volúmenes finitos. La incognita principal fue la saturación del agua. Se evaluó el impacto sobre la saturación de la interface de diversos parámetros tales como: la porosidad, la saturación inicial de agua, la razón de inyección de agua, la fuerza gravitacional, y el tamaño del grano del material. Se concluye que una completa caracterización de la matriz porosa, junto con una adecuada combinación de parámetros de control y modelado, son condiciones fundamentales para definir condiciones de extraccioín adecuadas. El algoritmo estudiado posee un gran potencial para ser utilizado en etapas tempranas de diseño y planeación para la extracción del petróleo.

Palabras clave: capilaridad discontinua, medio poroso, interface, volúmenes finitos, flujo agua-petróleo.

 

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Acknowledgements

EC has been supported by Fondecyt project 11100358.

 

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