Fractal model for permeability estimation in low-permeable porous media with variable pore sizes and unevenly adsorbed water lay

Permeability can effectively represent the ability of fluids to flow in porous media, and is a crucial physical parameter for the exploration of unconventional oil reservoirs. In low-permeable porous media, such as tight rocks, not all pores function as fluid flow channels; meanwhile, the pore surface tends to form unevenly adsorbed water lay. To date, the two phenomena above have not been considered in previous studies on permeability estimation models. In this study, a new fractal permeability model with variable pore sizes was proposed resulting in two advancements: (1) unevenly adsorbed water lay attached to pore surfaces was considered; and (2) instead of the total pore space, the movable fluid space obtained from nuclear magnetic resonance (NMR) experiments was used as the fluid flow channels in the porous media. Helium permeability data of 26 mixed rock samples from tight oil reservoirs were used to establish the accuracy of the proposed permeability model. The results of a sensitivity analysis show that high porosity and large pore diameters play a positive role in generating high permeability in porous media. The permeability decreased with an increase in the fractal dimension of the total pore space and the tortuosity fractal dimension of the total pore space and movable fluid space, whereas it first decreased and then increased as the fractal dimension of the movable fluid space increased. Furthermore, the proposed model indicates that the movable fluid space and unevenly adsorbed water lay greatly influence the fluid flow, specifically at lower permeabilities (K<0.1 mD), while the influence of the unevenness of the adsorbed water lay on fluid flow is negligible at high permeabilities. Overall, the accuracy of the permeability estimation of the proposed model is reliable both in low-permeable and conventional porous media, and can be effectively applied to unconventional oil reservoirs.