Permeate flux prediction in the ultrafiltration of fruit juices by ARIMA models

The quantitative prediction of phenomena responsible of flux decline is of great interest in membrane operations. In this work the application of ARIMA models was investigated to predict the permeate flux in the ultrafiltration (UF) of fruit juices during 6 h of continuous operation. Models were constructed with the filtration data of fruit juices (bergamot, kiwifruit and pomegranate) clarified with different membranes. The ARIMA 211 model showed the lowest value of root mean squared error (RMSE) (0.3891) and a mean absolute percentage error (MAPE) of 4.9476; the model was found to be very successful in predicting the flux decline over time with a prediction of 99.96% (R²_adj, R-squared adjusted by degree of freedom) in the clarification of bergamot juice. The ARIMA 111 model predicted 99.61% of experimental values (R²_adj) with the lowest values of RMSE (0.2516) and MAPE (1.9566) in the clarification of kiwifruit juice. The ARIMA 212 model fitted 99.14% of experimental data (R²_adj) in the clarification of pomegranate juice with lower values of RMSE (0.2768) and MAPE (2.2613). The proposed approach offers a simple alternative for the prediction of the permeate flux since modeling does not require information on feed solution, membrane material, membrane configuration and operating conditions.