Machine learning insights into predicting biogas separation in metal-organic frameworks

Effective purification of biogas, primarily a CH₄/CO₂ mixture with trace contaminants, is crucial for producing high-purity biomethane, a sustainable alternative to fossil fuels. Current CO₂ removal technologies can be expensive and energy-intensive. Adsorptive and membrane separations using porous materials offer a promising alternative, but require materials with high CO₂ uptake and selectivity over CH₄. A common trade-off exists between selectivity and uptake, complicating the search for optimal materials. Metal-organic frameworks (MOFs), with their high surface area and structural diversity, are attractive candidates. However, the vast chemical space of MOFs makes experimental screening impractical. High-throughput computational methods, such as force-field calculations, can predict properties, but remain computationally expensive. Machine learning (ML) offers a potential solution by predicting gas sorption properties from easily calculated features, enabling high-throughput screening of large databases at reduced computational cost. While ML has seen success in materials science and chemistry, previous MOF studies often relied on large, uncurated databases containing potentially unviable structures. This work addresses this limitation by developing an ML model trained on a carefully curated dataset of experimental MOFs to predict their biogas upgrading performance, focusing on established descriptors that offer chemical insight.

Several studies have explored the application of machine learning to predict gas sorption properties of MOFs, with varying degrees of success. Some studies reported higher accuracy using nonlinear methods compared to linear models. Feature selection has also been a key focus, with structural descriptors being favored due to their ease of calculation. However, incorporating chemical information, such as Henry constants, binding energy, or Voronoi energy, can improve model quality. A common limitation of previous studies is the use of large databases composed mainly of hypothetical MOFs without adequate curation. This raises concerns about using unviable structures and potential data leakage. The importance of data curation has been increasingly recognized, with studies showing that well-curated datasets lead to more accurate and insightful models. This work emphasizes the need for a high-quality, curated dataset of experimentally viable MOFs to train the machine-learning model effectively.

This study employs a two-step approach: (1) data curation and preparation, and (2) machine learning model development and evaluation. The dataset was initially obtained from the Cambridge Structural Database (CSD) after an algorithmic stripping of solvents and filtering based on geometric criteria. However, significant issues (overlapping atoms, unrealistic oxidation states, duplicates) necessitated a rigorous curation workflow (detailed in Supplementary Note 1 and visualized in Figure S1). This workflow reduced the initial dataset of 6768 MOFs to a curated set of 1910 structures. Grand Canonical Monte Carlo (GCMC) simulations (Methods Section 4.2) were then performed for each curated MOF to calculate key biogas separation performance metrics at 10 bar and 298 K. These metrics included single-component (SC) and binary mixture (BM) uptakes of CO₂ and CH₄, and selectivity (S), calculated using Equation (1). A trade-off metric, TSN (Equation (2)), quantifying the balance between selectivity and uptake was also calculated. For machine learning, nine carefully selected descriptors (Table 2), combining structural and energetic information, were used as features. These descriptors were chosen for their relevance to the targets and low computational cost, avoiding computationally expensive features like diffusion coefficients and permeability that are specific to membrane separations. Log10 scaling was applied to some descriptors to address skewed distributions. The chosen machine learning methods were Random Forest (RF), Support Vector Machine (SVM), Multiple Linear Regression (MLR), and k-Nearest Neighbors (kNN). The models were trained using 10-fold cross-validation, and their performance was evaluated using metrics such as Mean Absolute Error (MAE), R², accuracy, AUC, precision, recall, and F1 score. The best-performing models were then retrained on the full training set and tested on an independent external dataset of 330 hypothetical MOFs from the Northwestern hypothetical database. The external test set was also subjected to the same rigorous curation process as the training dataset. This external testing allows for a more robust assessment of the model's generalizability and predictive capability.

The curated dataset of 1910 MOFs exhibited a wide range of uptake and selectivity values, illustrating the trade-off between these two properties (Figure 1). Analysis of the six highest-TSN MOFs revealed common structural features, such as prevalent Zn metal centers, sql topology, and approximately square channels (Table 1, Figure 2). Machine learning models, particularly Random Forest, showed excellent performance in predicting gas uptake, with R² values consistently above 0.9 for the validation set (Figure 3). However, predicting TSN proved more challenging due to skewed data distribution, leading to more accurate results from classification models that distinguished between high and low TSN MOFs (Figure 3). The most important features for regression models were void fraction and density, while for the TSN classification model, the heat of adsorption of water was crucial, indicating the importance of hydrophilicity/polarity for selectivity. The analysis of the best and worst predicted MOFs from both regression and classification model showed that void fraction was a dominant factor in prediction accuracy, suggesting that available pore space is a major influencer in the adsorption properties, particularly for CO2. Testing on the external dataset of hypothetical MOFs revealed more challenges, and showed underprediction of MOFs with very high void fractions. This underprediction is consistent in both the training and test sets, suggesting a need for improved data representation in the training phase, particularly for MOFs with high void fractions. The classification models retained good overall accuracy in classifying the hypothetical MOFs as high or low performing, effectively filtering out over 90% of the low-performing MOFs. The analysis of the top six high TSN MOFs predicted by the external test set (Table 3, Figure 5) showed prevalent interpenetrated frameworks based on the pcu (primitive cubic) lattice. Similarly, the top six high-loading MOFs showed high void fraction and generally had larger pore limiting diameter.

The high accuracy of the machine learning models in predicting gas uptake and classifying high-performing MOFs demonstrates the potential of this approach for accelerating MOF discovery for biogas upgrading. The identified key descriptors, particularly void fraction and heat of adsorption of water, provide valuable insights into the structural features that contribute to optimal performance. The success in predicting the external test set, despite some limitations, indicates the generalizability of the models. The identified high-performing MOFs and structural features are relevant for future MOF design and synthesis. The observed underprediction of high-void fraction MOFs in the external test set highlights the importance of data representation and the need for careful consideration of the feature space covered by the training and test sets. Future work could focus on expanding the training dataset to better represent the full range of MOF properties and improve model accuracy.

This study successfully developed and validated machine learning models for predicting biogas separation properties of MOFs. The Random Forest models showed the best performance, particularly in predicting CO₂ uptake and classifying MOFs based on the trade-off between selectivity and uptake. The study highlighted the importance of data curation and the challenges of extrapolating model performance to unseen data, especially from hypothetical MOF datasets. Future research could focus on expanding the training dataset, exploring other machine learning techniques, and further investigating the relationship between MOF structure and separation performance. This work presents a significant advancement in accelerating the discovery and design of high-performance MOFs for biogas upgrading.

The study's primary limitation is the inherent bias in the training dataset, which primarily comprises experimentally synthesized MOFs. This might limit the generalizability of the model to hypothetical MOFs with significantly different structural features. Additionally, the accuracy of the GCMC simulations used to generate the training data depends on the force field parameters used, and there is an inherent approximation in using the rigid framework approximation when simulating MOFs, which can show flexibility in response to guest adsorption. The underprediction observed for high-void fraction MOFs in the external test set also suggests that the training data may not adequately capture this region of the feature space.