A hybrid modelling approach for reverse osmosis processes including fouling

A novel hybrid modelling approach, combining the strengths of a mechanistic reverse osmosis (RO) model and a data-driven fouling model, is developed on a unique long-term dataset from a full-scale RO installation to predict its performance. The mechanistic solution-diffusion model describes well understood phenomena in RO such as concentration polarisation, osmotic pressure and solutes transport throughout the membrane. This solution-diffusion model is combined with a data-driven model to cover the gaps in knowledge related to fouling phenomena. Several fouling models are tested to predict the membrane resistance over time and a thorough analysis of important input features was performed. A non-linear recurrent neural network with long short-term memory (RNN-LSTM) clearly outperformed (RMSE = 1.01e13) a linear autoregressive integrated moving average with exogenous variables (ARIMAX) model (RMSE = 1.97e13) for an 8 month testing period. The best performance was achieved when including membrane cleaning as two separate features representing short and long CIPs. Moreover, recovery setpoint, concentrate flow rate, feed temperature, feed conductivity and feed calcium concentration were shown to be important model input features. Fouling sensitive parameters of the solution-diffusion model (the water permeability, the feed spacer channel height and the solute permeability - determined by a global sensitivity analysis) were made function of the output (membrane resistance) of the RNN-LSTM thus leading to a serial hybrid model. The predictions of the hybrid model showed a clear improvement for all output variables when compared to a solution-diffusion model including temperature correction. The model was developed, calibrated and trained on measurements of standard sensors and can thus be used for real-time applications such as advanced control and predictive scenario analysis in a digital twin context. [Display omitted] •An RNN-LSTM model was developed to predict fouling in a full-scale RO installation.•The RNN-LSTM includes feed properties, recovery setpoint and CIPs as input features.•The fouling model is coupled to a solution-diffusion model resulting in a hybrid model.•Water and solute permeability and feed spacer channel height were made function of fouling.•The hybrid model outperformed the solution-diffusion model on a prediction horizon of 2.5 months.