Abstract
Membrane-based separations are proven and useful industrial-scale technologies, suitable for automation. Digital twins are models of physical dynamical systems which continuously couple with data from a real world system to help understand and control performance. However, ultrafiltration and microfiltration membrane separation techniques lack a rigorous theoretical description due to the complex interactions and associated uncertainties. Here we report a digital-twin methodology called the Stochastic Greybox Modelling and Control (SGMC) that can account for random changes that occur during the separation processes and apply it to water ultrafiltration. In contrast to recent probabilistic approaches to digital twins, we use a physically intuitive formalism of stochastic differential equations to assess uncertainties and implement updates. We demonstrate the application of our digital twin model to control the filtration process and minimize the energy use under a fixed water volume in a membrane ultrafiltration of artificially simulated lakewater. The explicit modelling of uncertainties and the adaptable real-time control of stochastic physical states are particular strengths of SGMC, which makes it suited to real-world problems with inherent unknowns.