Influence of Thermal Dispersion on Spontaneous Imbibition Process in a Homogeneous Porous Medium

In this work we analyze the effect of thermal dispersion on spontaneous imbibition process of a fluid in a homogeneous porous medium, considering that it is subject to the presence of a temperature gradient. We assume that the porous medium is found initially at temperature T-0 and pressure P-0; suddenly the lower part touches a liquid reservoir with temperature T-1 and pressure P-0 and begins the spontaneous imbibition process into de porous medium. The physical influence of three nondimensional parameters such as the ratio of the characteristic thermal time to the characteristic imbibition time, beta, the ratio of the hydrostatic head of the imbibided fluid to the characteristic pressure difference between the imbibition front and the dry zone of the porous medium, alpha, and Omega defined as the ratio of thermal dispersion effect to thermal diffusivity of the medium, serve us to evaluate the position and velocity of the imbibition front as well as the temperature profiles and the corresponding Nusselt number in the wetting zone. In particular for small values of time, we recover the well known Washburn law. The numerical predictions show that the imbibition and temperature profiles depend strongly on the above nondimensional parameters, revealing a clear deviation from the simple Washburn law.