Fast direct flow simulation in porous media by coupling with pore network and Laplace models

Permeability characterises flow in porous rocks/media for upscaling, while steady-state flow fields allow analysis of reactive transport, fines migration, and tight unconventional rocks. Fast calculation of permeability and flow fields obtained from Pore Network Models (PNM) and Laplace Semi-Analytical Solvers (SAS) deviate from computationally demanding simulation of Navier Stokes Equations (NSE) due to flow and geometry simplifications. Coupling PNM/SAS with direct simulation via Lattice Boltzmann Method (LBM) provides 5-150x speed-up without accuracy loss over 100 samples from 0.7mD to 3.5D. Permeability errors in PNM/SAS show 10-20% (up to 50-70%) error. PNM shows higher variance from geometric simplifications compared to SAS which only makes flow-based assumptions. PNM/SAS errors are eliminated by coupling with LBM at a fraction of LBM-only compute cost. Steady-state conditions with PNM/SAS-LBM are reached in 2 , 000 timesteps, compared to LBM-only which can require > 10(5) timesteps in tight domains such as cemented sandstone, carbonate, coal, and shale.

Automated summary

Permeability and flow fields are analyzed using PNM and SAS, with a faster and more accurate solution achieved by coupling with LBM. The errors in PNM/SAS can be eliminated with LBM coupling, reaching steady-state conditions in significantly fewer timesteps than LBM-only simulations in tight domains.