Efficient and accurate simulation of two-phase relative permeability curves using the lattice Boltzmann method

The steady-state method, commonly utilizing periodic boundary conditions and constant volume force, has long been employed to measure two-phase relative permeability using the lattice Boltzmann method (LBM). This study introduces the first application of LBM for unsteady-state measurement of two-phase relative permeability curves, removing the restrictions imposed by periodic boundaries. By comparing the results with steady-state measurements, we demonstrate that the proposed unsteady-state methods yield accurate relative permeability curves while significantly enhancing computational efficiency. We detail the process of determining the driving pressure (Δp) and initial flow rates (q) in unsteady simulations and analyze the characteristics of Kro in these simulations. Our study suggests that, while Kro should ideally be plotted as a function of saturation within the porous media (Sw), Krw, calculated based on the flow at the exit, should be expressed as a function of Swe rather than Sw. To obtain an accurate Krw curve, it is essential to discard spurious data from unsteady LBM simulations, particularly at higher Sw values approaching unity. Our findings show that both “constant-Δp” and “constant-q” unsteady simulations can produce satisfactory relative permeability curves. However, the constant-q method is more predictable, with the measured flow flux closely aligning with the specified value, making it more reliable and easier to manage. Overall, the unsteady-state method offers a robust and efficient framework for future numerical research on relative permeability measurement in porous media.