Hydrodynamic dispersion in porous media
 

Hi

I'm currently working on a mass induced natural convection 2D problem in porous media (single phase miscible displacement).

System description:

At the initial condition, component 1 fills a rectangular domain. On top, a Dirichlet BC is set with mass fraction(component 2)=1. A non-monotonic density-mass fraction function is implemented, such that when component 1 is pure, it is lighter than component 2. However, when they mix due to diffusion, the mixture becomes heavier forming instabilities which lead to the classical fingering patterns.

In order to do so i'm solving the two components mass conservation. The conservation of momentum in done via the Darcy law for porous media. Hydrodynamic dispersion is represented by the scheidegger model which states linear dependency between the mechanical dispersion and velocity (multiplied by the dispersivity coefficient). Finally, a linear viscosity-mass fraction function is implemented.

So far so good. I currently use Comsol (finite element and implicit scheme) to do so, and manage to solve the system to get reasonable results (compared to experimental results).

The conundrum:

Problem starts when i increase the dispersivity coefficient. For some reason, which is counter intuitive to me, when i increase dispersivity, for the same element size, convergence becomes worse up to a point where it doesn't converge at all. I assumed that increasing dispersivity would play a stabilizing factor (decreasing the elemental Peclet number), but for some reason it is not.

Any insights?

Thanks!