The modelling of instabilities in liquid-liquid miscible displacement processes by the Galerkin-based finite element method

Abstract

The Galerkin-based finite element method has been used to successfully simulate the propagation of instabilities in the liquid-liquid miscible displacement process. The convective-dispersion equation is sufficient to model the liquid-liquid miscible displacement process under unstable conditions. The investigations reveal:

i. An unconditional instability which will not disappear with time, ii. The rate of growth of the instabilities, tended to increased proportionally to a number to the M power, where M is the mobility ratio, iii. The propagation of instabilities can be achieved through the actions of viscous, gravity and heterogeneous forces, and iv. Heterogeneity in permeability introduces a macroscopic dispersion effect that attempts to stabilize the instabilities.



Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 173-176