## 3 Results
### Pore Network Permeabilities
Comparison of the LBM permeabilities with those obtained with PoreNetwork models [39; 40] for group 1 shows very reasonable agreement and no clear trends. The largest difference is obtained for the 1_C1 sample, where the LBM estimate is twice as high. On the contrary, the permeability of the 1_S9 sandstone sample was 1.5 times lower than the PNM result. The discrepancies appear random, with no clear trend. We should say that our results show somewhat better agreement with the experiment, and at least the LBM calculations showed no large discrepancies. The PNM solver underestimates the permeability of the 1_C1 sample by the factor of 2 and overestimates the permeability of the 1_S9 sample by 70%, while the LBM estimates fall with 10% from the experimental result for both systems. However, in general, the discrepancies are by no means dramatic for both methods. The samples from group 2 are somewhat tighter. Since the experiments are not available, we can only compare them with the same simulation benchmark of the OpenFOAM finite volume solver [40]. Again, the agreement between the LBM and DNS calculations is reasonable and does not show any clear trend. Yet again, LB showed substantially higher permeability (compared to DNS) for the least permeable sample, 2_EC carbonate. The same tendency was noted above for the group 1 sample. At the same time, the permeability of the Bentheimer sandstone sample (2_BS) has a wide PVD with a high share of very narrow pores but higher share of wide pores (which contribute the most to the permeability); LBM underestimated the permeability by 20% compared to the ICL direct simulations [40]. We relate this difference to two important factors in the LBM modeling. First, at high pressure gradients applied in sandstone permeability measurements, the compressibility of the fluid becomes important for the overall flow. In most LBM simulations, including those reported here, the compressibility is ignored and, therefore, the permeability is somewhat overestimated. At the same time, an artificial and anisotropic slip caused by the bounce-back boundary condition applied in our LBM simulations effectively decreases the viscosity-dependent friction between the pore fluid and the wall. The tighter the pores, the more pronounced this distortion is, leading to an overall overestimation of the permeability of tight-pore samples by the LBM. Considering the tightest samples of this work, the Achimov sandstones of groups 3 and 4, we observe that the overprediction of the permeability by LBM becomes somewhat systematic. Unfortunately, the rigorous test against the experimental data is not available. However, LBM shows a higher permeability compared to both DHD and DiMP for all Achimov sandstone samples considered here, while DHD and DiMP results are reasonably close and show no clear trends when compared with each other (for example, DHD permeability is higher for the 3_B sample and lower for the 3_C sample compared to the DiMP permeability). Overall, the largest discrepancies between LBM and other methods are obtained for the tightest pore samples with the lowest permeabilities (3_C and 3_E). The exception is sample 3_B, which is poorly permeable, and yet, the results obtained by LBM and DHD are quite close. In fact, the larger discrepancy between DiMP and LBM permeabilities (sample 4_B) is no worse than the diescrepancy between the PNM results from [40] and the experiment for wide-pore sandstone 1_S2. In no case did we observe a dramatic disagreement that would certainly prohibit the practical application of LBM as the method for permeability prediction. It might have also been expected that the artificial effect of friction reduction in LB were more pronounced for physically large samples. The longer the path the fluid needs to take \"from start to finish\", the more important the friction forces become. Thus, for larger samples with larger geometry discretization error and more wall boundary voxels, higher deviations of LB calculations from the benchmark results were expected.