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Prediction of Permeate Flux in Ultrafiltration Processes: A Review of Modeling Approaches

Programa Institucional de Fomento a la Investigación, Desarrollo e Innovación (PIDi), Universidad Tecnológica Metropolitana, Santiago 8940577, Chile
Programa de Doctorado en Ciencia de Materiales e Ingeniería de Procesos (Doctoral Program in Materials Science and Process Engineering), Universidad Tecnológica Metropolitana, Santiago 8940577, Chile
Advanced Mining Technology Center (AMTC), University of Chile, Av. Tupper 2007 (AMTC Building), Santiago 8370451, Chile
Institute on Membrane Technology, ITM-CNR, via P. Bucci, 17/C, I-87030 Rende, Italy
Authors to whom correspondence should be addressed.
Academic Editors: Patrick Dutournié and Sébastien Déon
Membranes 2021, 11(5), 368;
Received: 8 March 2021 / Revised: 27 March 2021 / Accepted: 12 May 2021 / Published: 18 May 2021
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
In any membrane filtration, the prediction of permeate flux is critical to calculate the membrane surface required, which is an essential parameter for scaling-up, equipment sizing, and cost determination. For this reason, several models based on phenomenological or theoretical derivation (such as gel-polarization, osmotic pressure, resistance-in-series, and fouling models) and non-phenomenological models have been developed and widely used to describe the limiting phenomena as well as to predict the permeate flux. In general, the development of models or their modifications is done for a particular synthetic model solution and membrane system that shows a good capacity of prediction. However, in more complex matrices, such as fruit juices, those models might not have the same performance. In this context, the present work shows a review of different phenomenological and non-phenomenological models for permeate flux prediction in UF, and a comparison, between selected models, of the permeate flux predictive capacity. Selected models were tested with data from our previous work reported for three fruit juices (bergamot, kiwi, and pomegranate) processed in a cross-flow system for 10 h. The validation of each selected model’s capacity of prediction was performed through a robust statistical examination, including a residual analysis. The results obtained, within the statistically validated models, showed that phenomenological models present a high variability of prediction (values of R-square in the range of 75.91–99.78%), Mean Absolute Percentage Error (MAPE) in the range of 3.14–51.69, and Root Mean Square Error (RMSE) in the range of 0.22–2.01 among the investigated juices. The non-phenomenological models showed a great capacity to predict permeate flux with R-squares higher than 97% and lower MAPE (0.25–2.03) and RMSE (3.74–28.91). Even though the estimated parameters have no physical meaning and do not shed light into the fundamental mechanistic principles that govern these processes, these results suggest that non-phenomenological models are a useful tool from a practical point of view to predict the permeate flux, under defined operating conditions, in membrane separation processes. However, the phenomenological models are still a proper tool for scaling-up and for an understanding the UF process. View Full-Text
Keywords: ultrafiltration; phenomenological models; non-phenomenological models; permeate flux prediction ultrafiltration; phenomenological models; non-phenomenological models; permeate flux prediction
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MDPI and ACS Style

Quezada, C.; Estay, H.; Cassano, A.; Troncoso, E.; Ruby-Figueroa, R. Prediction of Permeate Flux in Ultrafiltration Processes: A Review of Modeling Approaches. Membranes 2021, 11, 368.

AMA Style

Quezada C, Estay H, Cassano A, Troncoso E, Ruby-Figueroa R. Prediction of Permeate Flux in Ultrafiltration Processes: A Review of Modeling Approaches. Membranes. 2021; 11(5):368.

Chicago/Turabian Style

Quezada, Carolina, Humberto Estay, Alfredo Cassano, Elizabeth Troncoso, and René Ruby-Figueroa. 2021. "Prediction of Permeate Flux in Ultrafiltration Processes: A Review of Modeling Approaches" Membranes 11, no. 5: 368.

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