Adaptive model forecasting of the time-variant fouling rate in dynamic ultrafiltration for produced water reclaim

Oscar A. Prado-Rubio, Jakob K. Huusom

Research output: Contribution to journalJournal articleResearchpeer-review


The Gas and oil industry is water intensive and there is a need to develop strategies to mitigate its environmental impact. Dynamic ultrafiltration has shown remarkable performance for wastewater reclaim. However, the system complexity under uncertain input conditions limits aiming for an adaptive operation. Herein, a digital shadow tool is built for real-time adaptive model calibration and fouling rate forecasting to facilitate system operation. Previously obtained data from 18 pilot plant experiments in an oil recovery facility have been used. First, a signal preprocessing step allows the reconstruction of unrecorded backwash/backshock signals. Then, the multivariable Recursive Least Squared method with a forgetting factor using an autoregressive model (ARX) is investigated to decouple the effect of applied disturbances from the unknown input disturbances and process noise. Hyperparameters were determined through a sensitivity analysis. This approach allows accurate transmembrane pressure and membrane flux predictions (average r2> 0.98 and forecasting error <10%), matching machine learning and hybrid model prediction capabilities. Model analysis showed a correlation between model gains and the critical flux, particularly the flux setpoint. Besides, the forecasted fouling rate brought novel information regarding the onset of irreversible fouling formation. This investigation illustrates how this approach facilitates understanding the complex operation of dynamic ultrafiltration.
Original languageEnglish
Article number109736
JournalChemical Engineering and Processing - Process Intensification
Number of pages12
Publication statusPublished - 2024


  • Adaptive modelling
  • Online system identification
  • Dynamic ultrafiltration
  • Fouling rate prediction
  • Produced water treatment


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