Determination of permeability in tight sandstone reservoirs using Gaussian process regression and high-pressure porosimetry: A case study of the Member-7 of Yanchang Formation in the Jiyuan area of the Ordos Basin

Abstract

Because of the Klinkenberge effect in tight sandstones, errors exist forusing air permeability to reflect its reality, and it is thus important to determine the absolute permeability of tight sandstone.The Gaussian process regression (GPR), a state-of-the-art machine learning algorithm, has advantages in dealing with nonlinear and multidimensional complex problems in the petroleum industry. In this paper, the tight sandstone of the Member-7 of Yanchang Formation in the Jiyuan area of the Ordos Basin was taken as a sample to adopt the GPR model. In the model, the squared exponential and Matern covariance functions were taken as two covariance functions. The absolute permeability of tight sandstone was predicted by parameters including the porosity, volume ratio of unsaturated mercury, displacement pressure and fractal dimension measured by high-pressure porosimetry experiments, and the precision of different GPR models in predicting permeability were studied in combination with error analysis. The results indicate that GPR with Matern gives high precision with a mean magnitude relative error (MMRE), root mean square error (RMSE) and standard deviation (STD) equal to 32%, 0.16 and 0.57, respectively. Particularly, if the permeability is less than 0.1×10-3 μm2, the precision of the Matern model is obviously better than that of the squared exponential model and Winland model, so the Matern model has higher precision for permeability prediction of tight sandstones. In addition, sensitivity analysis reveals that porosity and displacement pressure have the highest and lowest absolute impact values on permeability estimation. The applicability and effectiveness of the GPR model are also demonstrated by means of leverage values and standardized residuals. Therefore, the Matern model can better predict tight sandstone reservoirs with permeabilities less than 0.1×10-3 μm2, and this model plays an important role in the exploration and evaluation for tight sandstone reservoirs.

Keywords

• permeability determination
• tight sandstone
• gaussian process regression
• high-pressure porosimetry
• fractal dimension
• ordos basin