Mercury injection capillary pressure analysis is a methodology for determining different petrophysical properties, including bulk density, porosity, and pore throat distribution. In this work, distinct parameters derived from mercury injection capillary pressure tests was considered for the prediction of permeability by coupling machine learning and theoretical approaches in a dataset composed of 246 tight sandstone samples. After quality checking the dataset, the feature selection was carried out by correlation analysis of different theoretical permeability models and statistical parameters with the measured permeability. Finally, porosity, median capillary pressure, Winland model, and mean pore-throat radius (corresponding to the saturation range 0.4-0.8) were chosen as the input features of the machine learning model. As the machine learning approach, a support vector machine (SVM) model with a radial basis function kernel was proposed. Furthermore, the model and its metaparameters were trained with a particle swarm optimization (PSO) algorithm to avoid over-fitting or under-fitting. In contradiction to the theoretical models, the implemented SVM-PSO model could acceptably predict the experimentally measured permeability values with an R ${}^2$ rate of over 0.88 for training and testing datasets. The introduced approach could reduce the mean relative errors from about 10 to values less than 0.45. The improvements were more significant for low permeability samples. This successful implementation shows the potential of coupled usage of theoretical and machine learning methodologies for improved prediction of permeability of tight sandstone rocks.

The characterization of two-phase flow has been commonly based on homogeneous wet capillary models, which are limited to heterogeneous wet porous media. In this work, capillary pressure and relative permeability models for three heterogeneous wet systems are derived, which enable the analysis of the effect of oil-wet ratio on the two-phase flow mechanism. The capillary pressures, relative permeabilities and water cut curves of three systems are simulated at the primary drainage stage. The results show that water-wet and oil-wet systems exhibit drainage and imbibition characteristics, respectively, while heterogeneous wet systems show both of these characteristics, and a large oil-wet ratio is favourable to oil imbibition. Mixed-wet large and mixed-wet small systems have water-wet and oil-wet characteristics, respectively, at the end and the beginning of oil displacement. At the drainage stage, the oil-wet ratio can significantly decrease oil conductivity, while water conductivity is enhanced. The conductivity difference between oil and water firstly decreases and then increases with rising water saturation, and the difference diminishes with the increase in oil-wet ratio. The oil-wet ratio can reduce water displacement efficiency, and its effects on the water cut curves vary between the three systems due to wettability distribution and pore-size mutation. The mixed-wet small system has the strongest oil imbibition ability caused by the largest capillary pressure in oil-wet pores and the smallest drainage pressure in water-wet pores, and high water conductivity causes the greatest water cut. The trend of variations in the mixed-wet large system is opposite to that in the mixed-wet small system, and the fractional-wet system is located between the other two systems.