Colloidal fouling in electrodialysis: a neural differential equations model

Abstract The attachment of colloids to the ion-exchange membranes in electrodialysis is an important hurdle when processing bio-based process streams. Previous research showed that fouling strongly depends on the crossflow velocity, the current and the salt concentration of the medium. Predicting the influence of these variables on the fouling rate is challenging due to the complex physics at play and optimising the process conditions to reduce fouling remains a challenge. The objective of this study is the development of a model to predict the dynamic behaviour of electrodialysis fouling under varying process settings to facilitate this optimisation. A neural differential equation is fit to experimental data of an electrodialysis pilot undergoing humic acid fouling. We show that this model can predict the fouling rate even when using a limited set of experimental data. The robustness of the model is demonstrated by a simulation study and a sensitivity analysis indicates that the crossflow velocity is the most important variable influencing the fouling rate ( ≈ 40 % ). Both the effect of the current ( ≈ 20 % ), the salt concentration ( ≈ 13 % ) and their interaction effects are considerable. With the model, the evolution of the stack resistance as a result of membrane fouling can be simulated, facilitating process control or decision-making.