modeling steady state gas concentration for dense gases

I was wondering how to correctly model a tank full of gas that has a higher density than air:  I've got a below-ground tank full of hydrogen sulfide gas, and air up above.  If I set up a steady-state simulation, eventually the entire system reaches equilibrium with a mixture of H2S and air filling the entire computational domain.  I was expecting the heavier gas to settle to the bottom of the tank over time - can flow simulation model this?  I tried changing the temperature of the H2S gas to 55F (local initial condition) while keeping the rest of the computational domain at 68F, and it seemed to help a little bit at the beginning, but overall it still doesn't behave like I was expecting.  I've tried with and without pressure potential checked, and gravity is turned on.  Are the densities of the two gases too similar for this type of settling to occur?

SolidworksFlow Simulation