Machine-learning-Based modelling of multicomponent forward osmosis processes using novel ternary organic draw solutions

Abstract

Predicting water flux in forward osmosis (FO) systems that use multicomponent organic draw solutions remains a difficult problem This study evaluates whether data-driven models can predict flux for binary mono propylene glycol propyl ether (PGPE) and ternary hydroxypropyl cellulose-PGPE (HPC-PGPE) and sodium carboxymethyl cellulose-PGPE (NaCMC-PGPE) draw solutions, using 312 flux measurements from 26 independent bench-scale FO runs. As the 12 measurements within each 120-min run lie on a single flux-decay trajectory, five partitioning schemes of increasing strictness were compared: point-wise random, run-wise random, leave-one-run-out (LORO), leave-one-operating-condition-out (LOCO), and leave-one-draw-solution-out (LODO) cross-validation. Point-wise partitioning overstated accuracy relative to run-wise partitioning, confirming leakage from within-run autocorrelation. Under LORO, the best network (one hidden layer, 16 neurons, 161 parameters) achieved R² = 0.56, RMSE = 2.92 LMH, against a measured experimental repeatability of 1.42 LMH (11.4% RSD); a nine-parameter ridge regression performed better still (R² = 0.803, RMSE = 1.95 LMH), indicating a neural architecture is not justified here. Withholding an entire operating condition (LOCO) or draw-solution formulation (LODO) eliminated this advantage: both models underperformed the trivial mean-flux baseline (R² = −0.04–−1.09; RMSE of 5.0–7.7 LMH), most severely when the withheld formulation's molecular weight fell outside the training range.