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Otw ysn flow1/23/2024 Finally, various AI methods have been used to model (cross-flow) membrane filtrations 17, including hybrid systems combining neural networks and physical theory 18.ĭigital twins present the latest stage of the models of physical dynamical systems, featuring a continual coupling between the virtual (modelling) and the physical domains of an experimental set-up 19. The cross-flow transports away the accumulated particles or solutes at membrane’s surface thus increasing the permeate flux, Fig. Hydrodynamic boundary layer theory (based on partial differential equations, PDEs), both laminar and turbulent, describes the cross-flow versions of the above separation techniques, providing a spatial resolution 16. The flux’ decline is then usually modelled by an ordinary differential equation (ODE), expressing directly the flux’ differential change, with different power-law exponents of flux decay associated with different blocking mechanisms 12, 13, 14, 15. In current models of ultra- & microfiltration, Darcy’s linear phenomenological law (or its quadratic Darcy-Forchheimer extension for turbulent flows) is expanded by an extra resistance term to account for the filtrate 12, making the flux vs. The ultra- & microfiltration lack rigorous theoretical description because of complex interactions and associated uncertainties including variable pore size and geometries, unknown surface forces of membranes, and nature of filtrate 3, 4, 5, 6, 7, 8, 9, 10, 11. The systems are thus operated below a critical constant trans-membrane pressure to minimize the blockage and extend the lifetime of membranes 1, 2. The common problem to all is that permeate flux through membranes diminishes due to particles that accumulate at the membrane surface (in the form of solid filtrate, or as concentration polarization of built-up salts), or penetrate and block the pores, both reversibly and irreversibly (the latter called membrane fouling). water, milk, wine, blood, fruit juice etc., categorized by the size of membrane pores: reverse osmosis (<1 nm), nanofiltration (1–2 nm), ultrafiltration (2–100 nm) and microfiltration (100 nm–10 μm) 1. Membrane separation technologies are well established techniques of removal of unwanted particles from a solvent e.g. 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. 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. 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. 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. However, ultrafiltration and microfiltration membrane separation techniques lack a rigorous theoretical description due to the complex interactions and associated uncertainties. Digital twins are models of physical dynamical systems which continuously couple with data from a real world system to help understand and control performance. Membrane-based separations are proven and useful industrial-scale technologies, suitable for automation.
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