Miscible Thermo-Viscous Fingering Instability in Porous Media. Part 2: Numerical Simulations

Abstract

In this second part of a two-part study, full nonlinear simulations of miscible thermo-viscous fingering are carried out using Hartley transform-based Pseudo-spectral method. Vorticity-streamfunction formulation is applied to the model equations developed in Part 1. Time evolutions of nonlinear fingers are examined qualitatively by plotting concentration and temperature iso-surfaces. The effect of increase in the thermal mobility ratio as well as decrease in the thermal lag coefficient is examined first for a hypothetical value of the Lewis number, Le = 1. For fixed solutal mobility ratio, an enhancement in instability is observed with the increase in the thermal mobility ratio for all values of the thermal lag coefficient. However, at large values of the Lewis number, the instability is seen to be strictly dominated by the solutal mobility ratio. At unity thermal lag coefficient, for the tested values of the other parameters, less complex finger structures are observed than in a reference isothermal case with the same solutal mobility ratio but zero thermal mobility ratio. As the thermal lag coefficient is decreased, a highly diffuse thermal front lags farther behind the fluid front, and the stabilizing effect of strong thermal diffusion gets alleviated. Consequently, the fluid front becomes as unstable as the reference isothermal case. The qualitative observations are further substantiated quantitatively using relative contact area (R.C.A.) and Sweep Efficiency as well as through identifying the relative contributions of solutal and thermal vorticity components in the development of the instability. The conclusions drawn from this study are in complete qualitative agreement with the ones obtained from Part 1, particularly using the initial value calculations (IVC) approach. Such agreement infers the superiority of (IVC) approach over the quasi-steady-state approximation (QSSA) approach in linear stability analysis of the problem under investigation.