Miscible Thermo-Viscous Fingering Instability in Porous Media. Part 1: Linear Stability Analysis

The development of the thermo-viscous fingering instability of miscible displacements in homogeneous porous media is examined. In this first part of the study dealing with stability analysis, the basic equations and the parameters governing the problem in a rectilinear geometry are developed. An exponential dependence of viscosity on temperature and concentration is represented by two parameters, thermal mobility ratio beta (T) and a solutal mobility ratio beta (C) , respectively. Other parameters involved are the Lewis number Le and a thermal-lag coefficient lambda. The governing equations are linearized and solved to obtain instability characteristics using either a quasi-steady-state approximation (QSSA) or initial value calculations (IVC). Exact analytical solutions are also obtained for very weakly diffusing systems. Using the QSSA approach, it was found that an increase in thermal mobility ratio beta (T) is seen to enhance the instability for fixed beta (C) , Le and lambda. For fixed beta (C) and beta (T) , a decrease in the thermal-lag coefficient and/or an increase in the Lewis number always decrease the instability. Moreover, strong thermal diffusion at large Le as well as enhanced redistribution of heat between the solid and fluid phases at small lambda is seen to alleviate the destabilizing effects of positive beta (T) . Consequently, the instability gets strictly dominated by the solutal front. The linear stability analysis using IVC approach leads to conclusions similar to the QSSA approach except for the case of large Le and unity lambda flow where the instability is seen to get even less pronounced than in the case of a reference isothermal flow of the same beta (C) , but beta (T) = 0. At practically, small value of lambda, however, the instability ultimately approaches that due to beta (C) only.