<p>Digital rock physics provides new insights into the mechanisms of fluid displacement in porous media at the pore-scale, with potential applications for environmental sustainability purposes. In this study, the relative permeability curves of two-phase flows in a heterogeneous porous medium are characterized using a modified lattice Boltzmann method (MLBM). Comparison with the original model shows that, even under high viscosity ratios, parasitic velocities are significantly reduced in the MLBM. For instance, when the relaxation time is 1.5, the spurious velocities are reduced by about 98.2%, while at 0.7 the reduction is nearly 34.6%. These results demonstrate that the proposed MLBM consistently produces much smaller spurious velocities and becomes more reliable at higher viscosity ratios, where maintaining numerical stability is critical. Since spurious velocities can distort local flow fields, reducing them leads to more reliable simulations. After validating the adopted model with benchmark tests, including the Laplace test and the viscous coupling effect in the co-current flow test, its accuracy and reliability are confirmed. Subsequently, the effects of parameters such as capillary number, viscosity ratio, and wetting conditions on relative permeability curves are discussed. The capillary number is considered at three values: 1.42E − 3, 7.14E − 3, and 1.42E − 2, while the viscosity ratio is examined at 0.1, 1, and 10. Results show that increasing the capillary number shifts relative permeability curves toward higher values. However, the non-wetting/wetting phase permeability increases/decreases as the viscosity ratio and wettability increase. The effect of wetting strength on the wetting phase permeability is found to be marginal.</p>