Abstract
For ultrafiltration, and membrane filtration more generally, the quantitative determination of the modes of fouling remains a subject of great interest. Herein an integral method for determining the modes from a time series of volumetric flux Jleft(tright) is given and illustrated with previously published filtration data of bergamot juice (Ruby-Figueroa et al (J Membr Sci 524:108-116, 2017)). The integral method of fouling analysis has the potential to become the cornerstone of a robust empirical process. In addition to determining, in a clear-cut manner, the point at which there is a switch from one mode to another, the robust methodology yields characteristic Jleft(tright) equation for each mode that are an excellent fit to the data. The emphasis is upon the creation of a robust methodology which is best viewed as being a semi-empirical method that is indicative of the modes of fouling. For the example chosen, the initial 4 L/m2 generates some pore blocking after which the main mode of fouling is cake build-up. The variation of overall resistance with time is also informative and analysis of this series was used to check the result for the initial phase of fouling as determined from the time series of volumetric flux. A comparison against the ARIMA (Autoregressive integrated moving average) method, which has never been previously undertaken, is given herein. The integral method of fouling analysis was found to be superior, in part because of the quality of fit to the data and in part because it enables one to establish whether the initial fouling is different in character from the subsequent fouling. Having this information can improve membrane selection and overall membrane filtration performance.
Highlights
Over the past four decades numerous sets of membrane filtration data have been assessed to determine the modes of fouling
The primary aim of this paper has been the exposition of a robust methodology for the quantitative determination of the modes of fouling and the associated J(t) relationships
As information on the osmotic difference across the membrane is an unknown it has not been included and the methodology is best viewed as being semi-empirical; there is a theoretically inspired basis with the final relationships being empirically determined from the data
Summary
Over the past four decades numerous sets of membrane filtration data have been assessed to determine the modes of fouling. Whilst the hydrodynamic dependency of the removal term is still worth of further investigation, it is important to be able to differentiate between the various phases of fouling and this differentiation might be considered a prerequisite This contribution is focussed almost exclusively upon the third area, namely use of the integral method of fouling analysis to make this differentiation. The previous work mentioned above [1] dissipated its efforts across the aforementioned three areas which is probably why the authors of a recent paper [4] did not compare their approach with the integral method of analysis They used fruit juice ultrafiltration to explore the applicability of using ARIMA (Autoregressive integrated moving average) models and other models. Relating process-scale output of membranes to their surface architecture and physico-chemical properties is important as the advances in molecular engineering will permit the tailoring of membranes to specific applications
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