Negative capillary pressure instability on the saturation front in the caprock during CO2 storage

[tjlyh777]

Hi all, I have been simulating CO2 flow in a model with two layers, i.e., capock and aquifer, trying to model the CO2 invasion into the caprock. The size of the model is 50 x 7 m. The thickness of caprock is 1m and the thickness of aquifer is 6 m. The injection is located in the center of aquifer which is a line source term. The injection rate is 0.003 kg * m2 / s. The saturation model of the caprock and aquifer is Van Genuchten model and relative permeability model is Udell model which have been implemented in OGS6. The initial gas pressure on the top boundary is 10 MPa and distribution in the domain is hydrostatic. The initial capillary pressure is 5000 Pa and the distribution in the domain is constant. Top boundaries are Dirichlet for both gas pressure and capillary pressure. Other three boundaries are no-flow. I only consider hydraulic process so that the displacment and temeprature are fixed not to change during the simulation. The parameters properties in aquifer and caporck are listed in the following figure.

After the equilibrium the injection of CO2 is 14 days. In the figures below the injected CO2 has floated up due to the gravity and invaded into the caprock. A high capillary is seen around the interface. However, in the caprock the saturation front meets a very large negative capillary pressure, but the saturation looks smooth in the caprock. I think the high capillary pressure in the caprock is good to see because the entry pressure is higher. However, The negative capillary pressure on the front looks strange. A slight oscillation is normal but such a large value (-2e5 Pa) is problematic to me. Decreasing the entry pressure of the caprock to the same value as that in the aquifer could help but I think this is not realistic. The capillary pressure and sarturation curves across the interface have also been uploaded. In the curves, the large negative capillary pressure exists where the saturation has just a little bit oscillation (around x = 0.12 m in the curves).

For the current results, I wonder if there are some numerical stabilization terms in OGS which can help this oscillation? Or there are some other problematic parameters in my model with these aquifer and caprock layers?

Thank you very much for the time.

Best,
Yuhao

[jtecklenburg]

Hi Yuhao,

The negative capillary pressures could result from a numerical issue or gravity. What happens if you set gravity to zero? The oscillations at x=0.12 look to me like the simulation isn’t really converging. How did you set the time step size?

Do you know Fucik’s analytical solution [1]? It’s without gravity. The interesting part is that for some parameter sets you can’t actually get an analytical solution. Maybe you could try your parameters with that solution. Your simulations should show similar behavior.

Best regards,
Jan

[1] https://mmg.fjfi.cvut.cz/~fucik/index.php?page=exacthetero

[tjlyh777]

Hi Jan,

thanks a lot for your advice. I don’t try zero gravity since I want the injected CO2 float up to the interface. But I can have a test, thanks. For hydraulic process simulation I use mumps solver so the it is easier to get the output but yes, also with divergence sometimes. My timestep after the CO2 has invaded into the caprock is 5 seconds, which is very small. Now I have tried a small residual relative permeability for both phases and the large negative capiilary pressure has been improved a lot, from -2e5 Pa to -1e4Pa, but still negative. I feel that the root cause is the large dPc/dSe when effective saturation is close to 1. Since we get saturation inversely from the capillary pressure, the derivative dPc/dSe is very steep at the Se→0 and Se→1. I may also try a maximum effective saturation minimum effective saturation to resist the effective saturation before get water saturation to see if things will get better. Fucik’s analytical solution is a good case for me. I will try. Thanks for providing the information.

Best,
Yuhao