Multifractal analysis of the heterogeneity of nanopores in tight reservoirs based on boosting machine learning algorithms

Exploring the geological factors that affect fluid flow has always been a hot topic. For tight reservoirs, the pore structure and characteristics of different lithofacies reveal the storage status of fluids in different reservoir environments. The size, connectivity, and distribution of fillers in different sedimentary environments have always posed a challenge in studying the microscopic heterogeneity. In this paper, six logging curves (gamma-ray, density, acoustic, compensated neutron, shallow resistivity, and deep resistivity) in two marker wells, namely, J1 and J2, of the Permian Lucaogou Formation in the Jimsar Basin are tested by using four reinforcement learning algorithms: LogitBoost, GBM, XGBoost, and KNN. The total percent correct of training well J2 is 96%, 96%, 96%, and 96%, and the total percent correct of validation well J1 is 75%, 68%, 72%, and 75%, respectively. Based on the lithofacies classification obtained by using reinforcement learning algorithm, micropores, mesopores, and macropores are comprehensively described by high-pressure mercury injection and low-pressure nitrogen gas adsorption tests. The multifractal theory servers for the quantitative characterization of the pore distribution heterogeneity regarding different lithofacies samples, and as observed, the higher probability measure area of the generalized fractal spectrum affects the heterogeneity of the local interval of mesopores and macropores of the estuary dam. In the micropore and mesopore, the heterogeneity of the evaporation lake showed a large variation due to the influence of the higher probability measure area, and in the mesopore and macropore, the heterogeneity of the evaporation lake was controlled by the lower probability measure area. According to the correlation analysis, the single-fractal dimension is well related to the multifractal parameters, and the individual fitting degree reaches up to 99%, which can serve for characterizing the pore size distribution uniformity. The combination of boosting machine learning and multifractal can help to better characterize the micro-heterogeneity under different sedimentary environments and different pore size distribution ranges, which is helpful in the exploration and development of oil fields.