Radial propagation of two-layer gravity currents in porous media

Gravity currents have been the subject of research for many decades, but there are still many unanswered questions that require further investigation. Understanding the dynamics of this phenomenon in different media and under varying circumstances and parameters, particularly in porous media, is essential for clarifying these questions. Studying the dynamics of two-layer gravity currents involving fluids with different viscosities and densities as it traverses a simulated porous layer is an essential aspect when examining the flow of gravity currents between two layers in permeable rocks. This phenomenon can be studied in the plane and the radial propagation for finding the shape of currents in real phenomenon. In one scenario, where each layer of the current has a finite volume (α=0), the motion of the fluids is described using a similarity solution to analyze in plane and radial propagation. By applying this approach, a partial differential equation (PDE) is derived and solved to determine the shape of the advancing gravity current and illustrate the interaction between the fluids in porous media. To visualize and analyze the derived equations, mathematical models are developed using MATLAB software. The results demonstrate how the morphology of the interface between the two layers is influenced by dimensionless factors such as the density ( R=ρ_l/ρ_u ), volume (F=Q_l/Q_u ), and viscosity ratio (V=μ_u/μ_l ) of the two currents.