Nonlinear convection regimes of a ternary mixture in a two-layer porous medium

Abstract

Numerical experiments have been performed to study the onset and nonlinear regimes of convection of a ternary mixture of methane (35%), ethane (35%), and butane (30%) in a horizontally elongated rectangular region of a porous medium under the action of a geothermal gradient. The region has rigid, impermeable boundaries and is divided into two horizontal layers with equal porosity but different permeability and having the heights in ratio 1:3. The values of medium porosity and permeability are chosen close to those of real media, such as sands, sandstones or limestones. The components of the mixture belong to the main groups of chemical compounds present in oil and gas fields. The configuration under study is a model of hydrocarbon field. The calculations are carried out for the cases when the value of permeability of the upper layer is higher than that of the lower one and, conversely, when the lower layer is more permeable than the upper one. The rest of the parameters of the porous medium are considered to be the same in the entire computational domain. The problem is solved within the framework of the Darcy-Boussinesq model taking into account the effect of thermal diffusion. The temporal evolution of the local characteristics of the flow, the structure of the forming flow, and the distribution of the mixture components is evaluated. Analysis of the data shows that in the case of a more permeable narrow layer, the onset of convection has a local character. The flow arises in a more permeable layer and, as soon as convection develops, it begins to penetrate into a less permeable layer. However, the centers of the forming vortices are noticeably shifted towards the more permeable layer. Similar vortex displacements are observed in a thick layer with higher permeability, yet convection, in this case, is of the "large-scale" character.