Nonlinear regimes of binary mixture convection in a two-layer porous medium of different configurations

Abstract

The results of modeling the convection of a binary mixture of liquid hydrocarbons in a two-layer porous medium are presented. The simulation area is a horizontally elongated rectangular cavity divided into two layers. In one of the considered cases, these sublayers are of equal height, and in the other case, the interface between the layers has the shape of a convex downward circular arc, which imitates a synclinal geological fold. The layers have different permeability. In the cavity, there is a geothermal temperature gradient with an average temperature characteristic of a depth of 2000 m, which corresponds to the average oil depth. The composition of the mixture, the thermal conditions and the geometry used make up the reservoir model of the hydrocarbon deposit. The problem is solved in terms of the Darcy–Boussinesq model with allowance for the effect of thermal diffusion. The emergence and establishment of nonlinear convection regimes, as well as the distribution of the concentration of mixture components for different values of the permeability of the layers and their dependence on which of these layers is more permeable, are considered in simulations. It is found that in the case of a small difference in the permeabilities of the layers, a stationary regime is established in the cavity of any of the considered configurations. With a significant difference in permeability of the layers in the cavity, either quasi-periodic oscillations of a complex shape or irregular oscillations can be observed. A "local" occurrence of convection is shown for a large permeability difference, followed by a weak penetration of the flow into a less permeable layer, as well as a "large-scale" occurrence of convection in the case of an insignificant permeability difference.