Binary interaction parameters of a million mixtures for PCP-SAFT using deep learning

Vapor-liquid equilibria of mixtures are essential for designing processes in the chemical, pharmaceutical, and energy industries. In the absence of experimental data, early conceptual process design relies on prediction methods such as molecular equations of state. Among these, PCP-SAFT has proven to be a robust theory for modeling phase behavior. Recent regression efforts yielded high-quality PCP-SAFT parameters for 1842 pure substances and 7861 of their binary mixtures. However, the mixtures with regressed binary interaction parameters only cover a minor part of the binary mixture space spanned by the 1842 pure substances that comprises nearly 1.7 million mixtures. To fill this data gap, we propose a deep learning model that predicts binary interaction parameters of non-cross-associating mixtures. We employ a multi-layer perceptron and compare its performance for different mixture representations. Our findings indicate that a combination of PCP-SAFT parameters and structural information predicts binary interaction parameters most accurately. Introducing physical hard constraints into the model provides additional soundness without affecting its generalization performance. The resulting hard-constrained, transformer-based model is evaluated on a hold-out test set of 841 mixtures. We demonstrate that the predicted binary interaction parameters halve the median deviation in bubble/dew point and relative volatility predictions compared to the benchmark of not using the binary interaction parameter. Substantial improvements are observed across almost all combinations of chemical families in the test set. As a final result, the proposed model predicts binary interaction parameters of 1 026 523 mixtures, vastly extending the existing database.