A fractal effective permeability model for dual-wet porous media

Recent studies have shown that the pores of some unconventional rocks can be categorized into hydrophilic pores that boarded by inorganic minerals such as quartz and hydrophobic pores that within the organic matter. The rock which consists of both hydrophilic and hydrophobic pores shows a dual-wettability behavior. The previously-proposed imbibition transient analysis technique has been applied in characterizing the pore size distribution of the dual-wet rocks by analyzing comparative oil and water imbibition data. On the basis of the determined pore size distribution, a fractal model for estimating effective permeability of the dual-wet rock was proposed. The proposed model, together with the imbibition transient analysis technique, is able to estimate effective permeability of the dual-wet rocks by using imbibition data. The proposed model can also estimate the effective permeability of hydrophilic pores and hydrophobic pores. The proposed model takes injection pressure, wettability behavior and pore size distribution of the dual-wet rock into the consideration. Our sensitivity analyses show that injection pressure affects effective permeability and hydrophobic permeability by controlling the water saturation within hydrophobic pores. The rock with higher volumetric fraction of hydrophilic pores tends to have higher hydrophilic permeability and lower hydrophobic permeability. By keeping the porosity constant, effective permeability decreases as the volumetric fraction of small pores increases.