Flow pattern effect on the pressure drop of biphasic flow through porous media from a fractal dimension perspective

• Published in: CienciaUAT 2020-01, Vol.14 (2), p.146
• Main Authors: Suárez-Domínguez, Edgardo Jonathan, Palacio-Pérez, Arturo, Pérez-Sánchez, Josúe Francisco, Izquierdo-Kulich, Elena
• Format: Article
• Language: Spanish
• Subjects: Channel pores; Differential calculus; Differential geometry; Flow pattern; Fractal geometry; Fractals; Friction; Function words; Gravitational effects; Gravity; Gravity effects; Morphology; Porous media; Pressure; Pressure drop; Pressure effects; Pressure loss; Single-phase flow; Surface tension; Transport phenomena
• ISSN: 2007-7521; 2007-7858
• DOI: 10.29059/cienciauat.v14i2.1308

The description of the behavior of a biphasic flow through porous beds by means of models based on the equations of transport phenomena is made difficult due to the geometric irregularity of the channels that are formed between the solid particles that make up the bed. Deterministic models developed for single-phase flows require the adjustment of empirical constants and cannot be extrapolated to biphasic flows, where the flow pattern generated in the system significantly influences the behavior of the total flow and the frictional pressure losses. Therefore, in this paper, we present a model to describe the behavior of the biphasic flow in relation to the flow pattern and the morphology, dimensions, and operating conditions of the porous bed, whose obtainment was based on a hierarchy that used the equa tions for conservation of momentum, fractal geometry and fractional differential calculus jointly. The model predicts that, for the same composition of the biphasic flow, the flow pattern significantly influences friction pressure losses, with an increase when one of the phases is dispersed within the other. On the other hand, the increase in the fractal dimension of the pores, in turn, causes an increase in pressure loss due to friction. The model has limitations associated with the considerations established during its collection, since it is only valid when the effects of surface tension are more significant than the gravitational effects, the effects of the latter being disregarded on the flow pattern, as well as for the stationary state. La descripción del comportamiento de un flujo bifásico, a través de lechos porosos, por medio de modelos, basados en las ecuaciones de fenómenos de transporte, se dificulta debido a la irregularidad geométrica de los canales que se forman entre las partículas sólidas que constituyen el lecho. Los modelos deterministas desarrollados para flujos monofásicos requieren del ajuste de constantes empíricas y no pueden extrapolarse a flujos bifásicos, donde el patrón de flujo generado en el sistema influye significativamente sobre el comportamiento del flujo total y las pérdidas de pre sión por fricción. Por lo anterior, en este trabajo se presenta un modelo para describir el comportamiento del flujo bifásico en función del patrón de flujo y de la morfología, las dimensiones y las condiciones de operación del lecho poroso, cuya obtención se basó en un formalismo, empleando conjuntamente las ecua ciones de conservación de la ca