Prediction of Permeate Flux in Ultrafiltration Processes: A Review of Modeling Approaches.
18 May 2021-Vol. 11, Iss: 5, pp 368
TL;DR: In this paper, a review of different phenomenological and non-phenomenological models for permeate flux prediction in UF, and a comparison, between selected models, of the predictive capacity.
Abstract: 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.
Citations
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TL;DR: In this paper , a fouling resistant biopolymer N-phthaloylchitosan (CS)-based polythersulfone (PES) mixed matrix membranes (MMMs) incorporated with nanocrystalline cellulose (NCC) was fabricated via phase inversion method and applied for produced water (PW) treatment.
12 citations
TL;DR: In this paper, a nonlinear ordinary differential equation is developed, which accounts for the acceleration of the fluid and the contrasts of viscosity and density of the two fluids in capillaries.
Abstract: In imbibition or drainage processes, a fluid displaces another immiscible one. If the displacing fluid is wetting, this is an imbibition process and is drainage if otherwise. While imbibition can proceed without the action of external force (e.g., pressure), drainage cannot unless sufficient external force is applied. One of the most important phenomena in this regard is related to the estimation of the location of the meniscus inside the tube and its velocity with time. This has been the topic of extensive research works for which analytical expressions exist for some special cases including the case in which the displaced fluid is air. Recently, a generalization to this approach has been developed, which accounts for the more general scenario in which the displaced fluid assumes considerable viscosity and density contrasts compared with the displacing one. However, in this recently developed model, and even in most of the previously studied special cases, an inherent assumption was made to ignore inertial effects. While this assumption is reasonable given the relatively slow advancement of the meniscus in capillaries, it results in the velocity to jump at the start of the imbibition process to a relatively higher value before declining as the meniscus advances. In fact, in actual imbibition experiments, velocity develops from zero to a maximum value in a short period of time before it declines as the meniscus continues to advance. In this work, a generalized model is developed, which accounts for the inertia of the fluids inside the tube. A nonlinear ordinary differential equation is developed, which accounts for the acceleration of the fluid and the contrasts of viscosity and density of the two fluids in capillaries. A numerical algorithm is also developed where the differential equation is linearized to facilitate the numerical solution. Verifications of the numerical algorithm are conducted to build confidence in the computational approach.
8 citations
TL;DR: There are two paradigmatic approaches for modelling flux, one uses the overall driving force (in which case allowance for osmotic effects are expressed as additional resistances) and the other uses the net driving force across the separating layer or fouled separating layer, although often the two are unfortunately comingled as discussed by the authors .
Abstract: Concentration polarization refers to the rapid emergence of concentration gradients at a membrane/solution interface resulting from selective transfer through the membrane. It is distinguishable from fouling in at least two ways: (1) the state of the molecules involved (in solution for concentration polarization, although no longer in solution for fouling); and (2) by the timescale, normally less than a minute for concentration polarization, although generally at least two or more orders of magnitude more for fouling. Thus the phenomenon of flux decline occurring over a timescale of tens of minutes should not be attributed to concentration polarization establishing itself. This distinction and a number of questions surrounding modelling are addressed and clarified. There are two paradigmatic approaches for modelling flux, one uses the overall driving force (in which case allowance for osmotic effects are expressed as additional resistances) and the other uses the net driving force across the separating layer or fouled separating layer, although often the two are unfortunately comingled. In the discussion of flux decline models’ robust approaches for the determination of flux-time relationships, including the integral method of fouling analysis, are discussed and various concepts clarified. The final section emphases that for design purposes, pilot plant data are vital.
7 citations
TL;DR: In this article , a low-cost polyethylene (PE) lithium-ion battery separator was explored as a potential solution to tackle the intrinsic hydrophobic character which incurs severe fouling.
7 citations
TL;DR: In this article , the effect of process variables (transmembrane pressure (TMP), pH and concentration of feed solution) on lignocellulosic flux was analyzed using pore blocking model.
4 citations
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TL;DR: The equations derived here have been applied to various permeability measurements found in the literature, such as the penetration of heavy water into animal cells, permeability of blood vessels, threshold concentration of plasmolysis and relaxation experiments with artificial membranes.
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