Spontaneous imbibition in a porous medium under longitudinal temperature gradients

M. Sánchez^a and A. Medina^a, A. Rojano^b

^a Grupo de Medios Porosos y Granulados, Programa de Matemáticas Aplicadas y Computación, IMP Eje Central Lázaro Cárdenas #152, 07730 México D.F., México.

^b Programa Universitario de Investigación en Matemáticas, Estadística y Computación Inteligente, Universidad Autónoma Chapingo, 56230 Chapingo, México.

Abstract

In this work, the influence of a longitudinal temperature gradient on the spontaneous imbibition into a homogeneous porous medium has been analyzed. Theory and experiments done on a permeable rock (Berea sandstone) allow us to show how this gradient modifies the temporal evolution of the averaged imbibition front h(t). Despite the existence of a thermal boundary layer outside the rock, experimental data are in good agreement with the theoretical profiles of h(t).

Keywords: Imbibition; Flow through porous media; Heat flow in porous media; Surface-tension-driven instability.

Resumen

En este trabajo se analiza la influencia de un gradiente de temperatura longitudinal sobre la imbibición espontanea en un medio poroso homogéneo. La teoría y los experimentos hechos en una roca permeable (arenisca Berea) permiten mostrar cómo este gradiente modifica la evolución temporal del frente promedio de imbibición h(t). A pesar de la existencia de una capa límite térmica fuera de la roca, los datos experimentales muestran un buen acuerdo con los perfiles teóricos de h(t).

Descriptores: Imbibición; Flujo en medios porosos; Flujo de calor en medios porosos; Inestabilidades inducidas por tensión superficial.

PACS: 47.55.Mh; 44.30.+v; 47.20.Dr

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Acknowledgments

The authors acknowledge the careful revision given to this work by the anonymous reviewer. This work has been supported by PIMAC-IMP under project D.0330.

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