Assessment of mathematical models for ultrafiltration of multi-solute continuous cross-flow process
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In recent years, ultrafiltration membrane-based technology has received increasing attention and great importance for water and waste water treatment. Different mathematical models are proposed to analyze and predict the permeate quality and flux during ultrafiltration of multi-solute solutions. These models are obtained from the literature and are classified into two broad categories: (i) simplified models developed from the assumption that the flux decline is controlled by a single mechanism only such as (a) osmotic pressure controlled, (b) gel layer controlled and (c) resistance in series models, (ii) advanced models that describe the flux decline and permeate quality during UF as a cumulative effect of several mechanisms. Therefore, the models range from simple analytical closed-form solutions (with the fewest parameters) to complex systems of ordinary equations (ODEs) that require the use of a numerical solver. The main purpose of this study is to conduct a thorough assessment of important flux decline models that can be found in literature. The ultimate goal of this analysis is to choose the model that is both easy and reliable. Such analysis is well supported by the experimental data of permeate quality and flux from literature where the separation of POME (carbohydrate constituents, crude protein and ammonia) in continuous cross-flow ultrafiltration process is used as an example for this study. Preliminary results demonstrate that ultrafiltration models that don’t explicitly account for multiple solutes system seem to give accurate prediction of flux decline during the early stages of ultrafiltration. However, the discrepancy between experimental data and the simulation becomes larger as flux approaches steady-state level.