Permeability and relative permeability from digital rocks: Issues on grid resolution and representative elementary volume

The Lattice‐Boltzmann (LB) method has been recognized as a very powerful tool for computational fluid dynamics, especially with complex pore structures. Although the LB methods can simulate realistic fluid flow in complex digital pore structure, we cannot predict accurate permeability and relative permeability without good input data — digital rocks. The parameters that make the digital rocks good or bad, is two length scales — grid spacing and the size of digital rock (representative elementary volume). To have fair comparison of these two length scales among many digital rocks with different grain/pore sizes, we first define the characteristic length scale (a) of pore geometry. Absolute permeability and relative permeability shows very similar behaviors with the grid spacing (d). When the grid spacing is reasonably small (d≤a/10), permeability stays within reasonable error range. We also found that permeability is consistently overestimated with the increase of grid spacing. Permeability is reasonable determined when the size the digital rock (L) is greater than 10 autocorrelation lengths (L≥10a). Relative permeability requires bigger digital rocks to be determined accurately. We recommend L≥20a for accurate prediction of relative permeability.