Inquiry Regarding Multiphase Flow Simulation in Porous Media with High Density/Viscosity Ratios using the Lattice Boltzmann Method

[EnochMayor]

Hello LBPM community,

I am currently involved in researching hydrogen storage and migration within geological media. and I'm particularly interested in utilizing the lattice Boltzmann method to simulate multiphase flow within porous media formations. While exploring this field, I've come across several implemented LBM models. However, I'm unsure about which model would be most suitable for my specific case, which involves high viscosity ratio and density ratio due to simulating brine and hydrogen.

I discovered that most of the example simulations are done with a density and viscosity ratio of one and wondered if it's possible to simulate multiphase flow with high density/viscosity ratios using the color gradient approach.

Additionally, if anyone has any information about how I might achieve this with the lattice Boltzmann method, I would greatly appreciate your input.

[JamesEMcClure]

See the parameter ranges listed at the color documentation linked below

https://lbpm-sim.org/userGuide/models/color/index.html#model-parameters

The relaxation time tau controls the kinematic viscosity, and based on these numbers you can reliably achieve a kinematic viscosity ratio of about 5. Often the relevant viscosity ratio is the dynamic viscosity, which includes the effects of density. The LBPM color model tends to be pretty stable for density ratio up to 20 (also listed as that page), and you may be able to push it up to 100 (depending on the flow geometry and boundary conditions). You should be able to run simulations with dynamic viscosity ratio somewhere between 100 and 500, but will need to run some experiments with your particular case to figure out what makes the most sense.

There are other LBM schemes that can achieve very high density and viscosity ratio, but this can create challenges if you want to run real flow simulations.

[EnochMayor]

Thank you for the feedback and insight into how this can be implemented.
I will adjust these parameters to see if I can achieve this

I have two questions as I hope to utilize the colour gradient model. Permit me as my question might seem random but I am trying to understand the best way to achieve this objective (simulate multiphase flow and obtain relative permeability within micro-CT images).

Firstly, what protocol or workflow would you recommend I adopt from the LBPM model that would enable me to achieve my objective for the hydrogen/brine fluid system?

Secondly, this recent paper https://www.sciencedirect.com/science/article/pii/S0016236124005623
using the color gradient model for H2/brine flow which is very similar to what I am trying to achieve considering a density ratio of 1.
Does this not impact the relative permeability at the end of the simulation since H2/brine densities are not equal?

[haghanire]

Hello,

Although this response is delayed, I hope it will still be helpful for future reference.
Among the various CFD and LBM models, the color-gradient method is often regarded as the most reliable in terms of mass conservation and full control over parameters. There are also variations of this method that incorporate modified hydrodynamic equations to better handle high-density and viscosity ratios (a recent study Color-gradient-based phase-field equation for multiphase flow). In contrast, methods such as the Cahn–Hilliard approach tend to exhibit significant bubble or droplet shrinkage, making them less suitable for certain applications. The model you are referring to is likely the lbpm_color_simulator.

Regarding your second question: in methods like the color-gradient model, the interface-capturing equations are generally not directly affected by the density ratio. However, the hydrodynamic equations—and consequently the relative permeability—are influenced. Therefore, when using the full Navier–Stokes equations, it is important to first identify the relevant flow regime in order to make appropriate simplifications by neglecting certain terms where justified.