Study On Filtration Model Of Dead-End Hollow Fiber Membrane System

Hollow fiber membrane has drawn increasing attention in wastewater and drinking water treatment due to its distinct advantages such as simple construction,high separation efficiency,small packing density,low fabrication cost,low energy consumption and flexible application.However,the performance of hollow fiber membrane can be greatly deteriorated by membrane fouling,which has become the major factor inhibiting the development of hollow fiber membrane separation technology.Mathematical models can be powerful tools to predict hollow fiber membrane fouling and optimize the operation performance of hollow fiber membrane system.The development of most hollow fiber membrane filtration models in literature was based upon the Hagen-Poiseuille theory.The influence of kinetic pressure drop in fiber bundle on flow resistance was ignored,which is caused by flow acceleration as it flows from the dead end to the open end,leading to the drop of model accuracy.Besides,commercial or open-source computational fluid dynamics(CFD)software was currently adopted for numerical solution of these models.The process of CFD is complex and needs a lot of boundary conditions which are usually unknown.Therefore it is not convenient to use or the obtained solutions might have a big error.Based on hydromechanics and membrane filtration theory,a mathematical model which describes the filtration process of dead-end hollow fiber membrane was developed by considering both frictional and kinetic pressure drops along the fiber.The spatial and temporal variations of membrane fouling and filtration parameters were investigated and the key factors affecting the filtration performance were determined,to provide scientific justifications for optimization of hollow fiber membrane system.The study results show that the model simulations were well calibrated and verified with the experimental data.By considering the kinetic pressure drops along the fiber,the accuracy of model was improved obviously.To solve the model,a critical step is to determine the transmembrane pressure at the dead end of the fiber,which could be conveniently and efficiently obtained with the inverse iteration bisection method.This method is well applicable,which can be used for numerical solution of models with various membrane fouling mechanisms under both constant imposed flux and applied pressure modes.Based on the proposed filtration model and numerical solution procedure,the spatial and temporal variations of membrane fouling and filtration parameters of dead-end hollow fiber membrane system were simulated and discussed.The simulations show that membrane fouling at different locations of fiber length increases with time.Besides,except for the clean membrane at the start,the filtration resistance is the largest at the open end and decreases along the fiber length.The distribution of transmembrane pressure,local flux and axial flow velocity along the fiber shows a gradual increasing trend from the dead end to the open end.With the increase of time,local flux of the points nearby open end decreases,those nearby dead end increases,and there exist some parts where local flux shows peak first and then gradually declines.Transmembrane pressure at all different locations of fiber length increases with time.The axial flow velocity of dead end and open end remains the same during the whole filtration process,while of other locations gradually increases.In dead-end hollow fiber membrane system,the applied pressure increases gradually with time.With the decrease of fiber length,imposed flux and foulant concentration,the increase of fiber inner diameter,the applied pressure decreases,which contributes to the drop of energy consumption.Besides,with the increase of time,the effect of fiber inner diameter,imposed flux and foulant concentration on applied pressure is in a gradual increase,while the influence of fiber length and membrane intrinsic resistance seems to keep constant.Besides,the uniformity of local flux distribution along the fiber gradually increases with time.With the decrease of fiber length,the increase of fiber inner diameter,imposed flux and foulant concentration,the uniformity of local flux distribution along the fiber increases,leading to a drop of membrane fouling trend.In addition,with the increase of time,the effect of fiber inner diameter,imposed flux and foulant concentration on the uniformity of local flux distribution along the fiber shows a trend of decrease after the first increase,while the influence of fiber length gradually decreases.The effect of membrane intrinsic resistance on the uniformity of local flux distribution along the fiber includes two stages:in the early stage,the more intrinsic membrane resistance,the higher uniformity of local flux distribution along the fiber,while it shows opposite trend in the later stage.It needs to point here that fiber inner diameter has important influence on filtration performance of hollow fiber membrane system.When the fiber inner diameter is less than a certain value,the applied pressure increases significantly and the uniformity of local flux distribution along the fiber reduces noticeably at the same time,the filtration performance of hollow fiber membrane therefore is greatly deteriorated.So in the practical application of hollow fiber membrane system,more attention should be paid to the optimization of fiber inner diameter.