INSTABILITY OF FLUID AND THERMAL FRONTS IN NON-ISOTHERMAL FLOWS IN HOMOGENEOUS POROUS MEDIA

摘要

The viscous fingering of miscible flow displacements in a homogeneous porous media is examined in the case involving heat transfer between the fluids. The problem is formulated using continuity equation, Darcy's law, and volume-averaged forms of convection-diffusion equation for mass and energy balance. Full nonlinear simulations, using a pseudo-spectral method, allowed to analyze the mechanisms of fingering instability that result from the dependence of the fluids viscosities on both temperature and concentration. This dependence is represented by two dimensionless parameters; the solutal viscosity ratio; β_C and the thermal viscosity ratio; β_T. In particular, the study examined the effects of varying important parameters such as the Lewis number, the thermal lag coefficient and the thermal mobility ratio on the dynamics of the flow. The development of the new finger structures is analyzed by examining contours of the concentration and characterizing them qualitatively through a spectral analysis of the average concentration and an analysis of the variations of the mixing length and the relative contact area. It is found that diffusion of heat and its redistribution between the fluid and solid phases have a strong effect on the growth of the fingers. Furthermore, close and intricate interactions between the fluid and thermal fronts affect the subsequent development of the instability even in case where the two fronts are separated, with the thermal front lagging behind the fluid one.