Lattice Boltzmann heat transfer model for permeable voxels

Area of Science:

• Computational physics
• Geophysics
• Fluid dynamics

Background:

• Heat transfer in rocks influences fluid flow and permeability due to thermal expansion.
• Accurate simulation of coupled fluid flow and heat transfer is crucial for understanding subsurface processes.

Purpose of the Study:

• To develop and validate a gray-scale lattice Boltzmann (LB) model for simulating fluid flow and heat transfer in porous media.
• To investigate the impact of thermal effects on fluid flow and permeability in realistic rock samples.

Main Methods:

• Development of a gray-scale lattice Boltzmann model capable of handling partially solid/void voxels.
• Validation of the LB temperature field against finite difference solutions for channel flow (Poiseuille and Brinkman).
• Application of the LB model to packed beds and sandstone samples to study convective and diffusive heat transfer regimes.

Main Results:

• The LB model demonstrated excellent quantitative agreement with analytical solutions for channel flow.
• The model successfully recovered both convective and diffusive heat transfer regimes in porous media.
• Significant temperature variations were observed even for low-permeability rocks (milli-Darcy range) due to thermal convection.

Conclusions:

• The gray-scale LB model is a robust and efficient tool for simulating coupled fluid flow and heat transfer in complex porous media.
• The LB method offers significant advantages over traditional numerical methods for irregular pore structures.
• The study highlights the importance of considering thermal effects in fluid flow analysis within geological formations.