On the Influence of Weak Heterogeneity of Porous Medium on Rayleigh–Taylor Convection of Miscible Fluids

Abstract

Experimental, analytical, and numerical investigations, addressing the onset and development of Rayleigh–Taylor convection in porous media, often give results, which do not agree with each other quantitatively. The reason of this discrepancy can be related to different fields of small perturbations, which always present in a system as a “hidden parameter”. Computational methods provide an opportunity to introduce small perturbations explicitly and investigate the response of fluid system to them. In the present work, numerical study of Rayleigh–Taylor convection of miscible fluids in a weak heterogeneous porous medium is conducted. Small random perturbations of porosity and permeability are considered. It was found that parameters of the convection onset and long-time evolution, which are analyzed statistically, depend on the amplitude of perturbations significantly. Particularly, the convection onset time increases by a factor of 15, if the amplitude of porosity perturbations, normalized by the average porosity, decreases from \(\mathtt{10^{-2}}\) to \(\mathtt{10^{-10}}\). To do conditions for the convection development identical, a periodic impact on the fluid system at the initial time is added. As obtained, the convection onset time under the periodic impact may become independent of the field of random perturbations. This finding may be employed to improve compatibility between different investigations. In addition, the periodic impact changes dramatically the long-time fluid behavior, which is studied in detail. We conduct in our work a representative statistical analysis, find the ensemble averages, and estimate standard deviations about the averages.