Recently, I came across Pore Network Modelling. Well, I am curious about how LBM is more benefit than the PNM?
The LBM generally describes flow in a small region but with high fidelity (actual pores/pore sizes). The Pore Network model generally describes flow through a larger region but without resolving individual pore behavior. The following recent comparison may be useful for you. Kohanpur, A. H.; Chen, Y.; Valocchi, A. J.; Tudek, J.; Crandall, D. "Comparison of Pore-Network and Lattice Boltzmann Models for Pore-Scale Modeling of Geological Storage of CO2 in Natural Reservoir Rocks"
https://www.sciencedirect.com/search?qs=Lattice%20Boltzmann%20Methods%20hold%20above%20Pore%20Network%20modelling&show=25&sortBy=relevance
The answer is, how is a typical FVM or FDM simulation of flow in porous media more beneficial than a pore network simulation? The former (also refered to as Direct Numrical Simulations, and the bare LB method is a DNS solver) provides flow information at the pore scale (because you are actually solving NS and/or species transport equations without subgrid models) while the latter is a macroscopic simulation (with so-called subgrid models) not providing flow information at the pore-scale (obviously because you are not solving the previously mentionned PDEs).
I think scale is not the different between LBM and PNM.
LBM can be extend from macroscale to nanoscale via setting boundary conditions (see, International Journal of Heat and Mass Transfer 111, 1172-1180 ) and the scale of PNM is determined by the flow equation describing each single pore of networks (see, Multiscale simulations of shale gas transport in micro/nano-porous shale matrix considering pore structure influence ).
In a word, the accuracy of PNM dependents on the extraction algorithm from digital core of porous media and LBM needs accurate boundary conditions to depict the fluids transport in porous media.
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