Nonlinear Simulation of Thermo-Viscous Fingering in Nonisothermal Miscible Displacements in Porous Media Available to Purchase

Full nonlinear simulation of the thermo-viscous flow is carried out to study the thermo-viscous fingering in non-isothermal miscible displacements in two-dimensional rectilinear porous media. The problem is formulated using momentum balance equation in the form of Darcy's law, and volume-averaged mass and energy balance equations in the form of convective-diffusion equations. Exponential dependence of viscosity on concentration and temperature is used. With the use of vorticity-streamfunction formulation and periodic boundary conditions, the coupled system of nonlinear equations is solved conveniently using highly accurate pseudo-spectral method. The transient development of thermo-viscous instability is studied for different values of solutal (Pe_C) and thermal (Pe_T) Peclet numbers, Lewis number (Le) and the parameters representing the concentration (β_C) and temperature (β_T) dependence of viscosity. In Hele-Shaw flow, the effects of β_C and β_T are found to be additive when Le is unity, while at smaller values of Le the frontal instability is further enhanced. At practically large values of Le, the fluid and the thermal fronts evolve differently, with the fluid front being more unstable. The reduction in instability on the thermal front is found to be due to the enhancement of the thermal dispersion in such flow. Finally, it has been noticed that at large values of Le, the instability in the thermo-viscous flow is dominated by the viscosity contrast due to the variation in concentration across the fluid front, which was also reported in earlier literature.