Hybrid modelling for enhancing the prediction of CO2 gas separation in biopolymer-based mixed-matrix membranes

To advance the progress of membrane materials and process development, accurate prediction of membrane performance has to be efficiently optimized. Such optimization is challenging when sustainable materials such as hydrophilic biopolymers from renewable resources are used on mixed matrix-membrane (MMM) fabrication. In this work, we systematically developed a hybrid model architecture using a delta model design pattern to enhance the prediction of the permeability of chitosan-based MMM for CO 2 /N 2 separation and gain insight in the design of new sustainable membrane separation processes. The parametric model baseline is focused on the modified Maxwell equation including temperature dependence, involving the estimation of two interpretable parameters: void thickness (i.e. the interaction between the components of the membrane matrix) and the rigidification of the dispersed phase in the continuous matrix, with increasing level of complexity. The predictions of MMM using phenomenological modified Maxwell models are confirmed locally dependent with high uncertainty levels, meaning a high correlation between the optimized parameters. A sequential combination of global and local optimization methods, yielded the best parametric model performance, reducing error by up to an order of magnitude. Then, a multilayer perceptron neural network (MLPNN) is trained using the output error of the parametric model and the introduction of additional experimental input variables. The hybrid model significantly improves the accuracy of gas permeability prediction and the empirical interpretability agrees with the Mutual Information (MI) predictions. This way, this approach can be used to direct the development of phenomenological models to describe the transport through novel MMM.