A new model for determining the effective permeability of tight reservoirs based on Fractal-Monte Carlo method

In contrast to conventional reservoirs, tight formations have more complex pore structures and significant boundary layer effect, making it difficult to determine the effective permeability. To address this, this paper first proposes a semi-empirical model for calculating boundary layer thickness based on dimensional analysis, using published experimental data on microcapillary flow. Furthermore, considering the non-uniform distribution of fluid viscosity in the flow channels of tight reservoirs, a theoretical model for boundary layer thickness is established based on fractal theory, and permeability predictions are conducted through Monte Carlo simulations. Finally, sensitivity analyses of various influencing parameters are performed. The results show that, compared to other fractal-based analytical models, the proposed permeability probabilistic model integrates parameters affecting fluid flow with random numbers, reflecting both the fractal and randomness characteristics of capillary size distribution. The computational results exhibit the highest consistency with experimental data. Among the factors affecting the boundary layer, in addition to certain conventional physical and mechanical parameters, different microstructure parameters significantly influence the boundary layer as well. A higher tortuosity fractal dimension results in a thicker boundary layer, while increases in pore fractal dimension, porosity, and maximum capillary size help mitigate the boundary layer effect. It is also observed that the permeability of large pores exhibits greater sensitivity to changes in various influencing parameters. Considering micro-scale flow effects, the proposed model enhances the understanding of the physical mechanisms of fluid transport in dense porous media.