Interpretable white-box modeling for nitrogen storage in metal-organic frameworks

The efficient removal of low-concentration nitrogen (N₂) is a critical and challenging task in the industrial production of high-purity oxygen (O₂), particularly in air separation processes and in natural gas purification for generating high-purity methane (CH₄). In this work, three advanced modeling techniques, namely the group method of data handling (GMDH), gene expression programming (GEP), and genetic programming (GP) were applied to develop user-friendly mathematical correlations for predicting nitrogen storage capacity of MOFs. A broad dataset of 3073 laboratory measurements was employed. The developed models were further evaluated for their accuracy and reliability using various statistical and graphical methods. Among the models, the GEP correlation provided the most reliable outcomes with superior statistical metrics, yielding mean absolute error (MAE) values of 0.9924, 1.0101 and 0.9959 for the training, testing, and overall datasets, and R² values of 0.9703, 0.9750, and 0.9714, respectively. All the models closely followed the expected trend of N₂ storage under varying pressure. Additionally, the Pearson, Spearman, and Kendall correlation analyses were employed to examine the influence of individual input factors on the model outputs. The findings revealed that temperature has the most substantial impact on storage capacity across both linear and non-linear dimensions, whereas pressure primarily affects it through nonlinear interactions. At last, the credibility of the collected databank and the applicability of the recommended correlations were confirmed using the leverage method, demonstrating more than 95% of the collected data fell within the acceptable range of the Williams plot.