A Study on Concentration Polarization in Ultrafiltration

Abstract

A finite-difference solution of coupled transport equations for momentum and solute continuity is presented to model the concentration polarization in a tubular ultrafiltration (UF) system. The model includes the effects of solute osmotic pressure and solute rejection at the membrane surface, axial pressure drop and resistance of the gel layer. This provides a fundamental understanding of the dynamics of various operating parameters on concentration polarization and transmembrane flux. Simulation results are presented for a wide range of operating variables to show their effects on local variation of solute concentration and transmembrane flux. The numerical results were also compared with previously published experimental data, which shows that a concentration polarization model based on constant membrane permeability (usually obtained from pure water flux data) grossly overestimates the flux behavior. If the effect of gel polarization is included, the model can predict the actual permeate flux very closely. Thus, in modeling ultrafiltration, one needs to be careful in using the appropriate membrane permeability terms. The commonly used intrinsic membrane permeability which is usually a constant, may not describe the true flux behavior in ultrafiltration. Actually the nature of the feed, solute-surface interaction and gel layer formation control the effective permeability, which varies axially along the membrane length.     

Transient solute adsorption incorporated modeling and simulation of unstirred dead-end ultrafiltration of macromolecules: An approach based on self-consistent field theory

An unsteady state mass transfer model of unstirred dead-end ultrafiltration module has been developed in the present study. The dynamic membrane surface concentration is evaluated using a modified self-consistent field theory, which enables the development of an algorithm to incorporate the contribution of solute adsorption in the membrane surface concentration dynamics. Knowing the corrected membrane surface concentration, permeate flux and permeate side concentration is determined using osmotic pressure model and flux–rejection relation as predicted by irreversible thermodynamics. The time evolution of all the different process variables is achieved by solving two component balance equations developed at the membrane surface and in the solution phase respectively. The basic feature of the model is the incorporation of adsorbed fraction in the unsteady state membrane surface concentration. For the validation of the proposed model, experiments were conducted with Bovine Serum Albumin (BSA)/water as feed in a standard unstirred batch ultrafiltration module fitted with Polyethersulfone (PES) membrane of 30 kDa molecular weight cut-off (MWCO). The model predicted flux and the permeate concentration were found to be in good agreement with the experimental data.     

Sugars and Fructans Separation by Nanofiltration from Model Sugar Solution and Comparative Study with Natural Agave Juice

The fructan separation from a model sugar solution and natural agave juice was studied using a stirred-cell nanofiltration unit operated in concentration mode. Hydrophilic cellulose membrane with MWCO of 1000 Da was used. The experimental conditions were varied to predict the influence of pressure (0.14–0.350 MPa) and feed concentration (0.15–0.25 g/mL) on the initial permeate flux and solute retained fraction (SRF) values of the process. Response surface plots (p < 0.05) showed that the permeate flux and SRF increased significantly with the pressure and decreased with feed concentration. The permeate flux varied from 0.5 to 4.1 L · h^?1 · m^?2. The fructan retained fraction in model sugar solution varied from 0.85 to 0.97 whereas fructose, glucose and sucrose presented similar SRF values ranging from 0.38 to 0.65. Promising results were obtained when natural agave juice was used.     

COMPARATIVE LIMITING FLUX ANALYSIS OF BLACK LIQUOR AND POLYETHYLENE GLYCOL IN ULTRAFILTRATION

Ultrafiltration of black liquor was carried out using an asymmetric membrane and the results were compared with that of polyethylene glycol, a standard macromolecule, in a stirred batch cell. The effects of system parameters, e.g., pressure, concentration and stirrer speed on permeate flux and solute rejection were studied extensively for both the solutes.

An osmotic pressure model was used to analyze experimental results. To take into account the phenomena of concentration polarization, an extra resistance term, called the polarization layer resistance (R_p), was incorporated into the model. The polarization layer resistance was found to be a function of flow regime and concentration at the membrane. To correlate these, the following two types of relationship were examined and tested with the experimental results,

and

where a, b, c, a₁, b₁, are constants.     

Modeling of Nanofiltration of Dye Using a Coupled Concentration Polarization and Pore Flow Model

Concentration polarization and transport through pores are used to explain the permeation of eosin dye through a nanofiltration membrane. Due to the ionic character of the dye, fixed charges in the membrane pores affect the permeation of the dye. Two transport coefficients, namely, hindered coefficients for diffusion and convection, steric hindrance factor of dye, and pore charge density are estimated by minimizing the error involved between the experimental and calculated permeate flux and concentration values. Contributions of electrical migration, convection, and diffusion towards the solute flux, have been quantified. It is found that more negative fixed charges on membrane pores leads to reduced dye concentration in the permeate.     

Modeling of the Ultrafiltration of a Dextran T500 Solution in a Tubular Membrane Module

Mathematical modeling of an ultrafiltration membrane separation process, based mainly on the transmembrane pressure (TMP), is undertaken in the present work. The main objective is the prediction of the permeate flux of a solution containing Dextran T500 through a cylindrical module. The proposed model incorporates the resistance‐in‐series model coupled with the equation describing the solute (Dextran T500) transport, as well as the continuity and Navier‐Stokes equations for solution flow modeling. The model equations are solved using finite‐volume numerical methods, with appropriate initial and boundary conditions. The effects of the TMP and the length of the membrane on the mean permeate flux were also investigated. The influence of the membrane dimensions (aspect ratio) on the relative dimensionless mean permeate flux, at different inlet TMPs and different solution concentrations, respectively, have also been considered. The variations of the TMP with the membrane length as well as the influence of the Peclet number on the solute surface concentration were also examined. The numerical results obtained are compared with experimental values reported in the literature, and in general, the agreement is satisfactory enough to encourage further refinement of the model.     

Effect of solution chemistry on membrane resistance and flux decline

Variations in the membrane resistance due to the adsorption of cakes of Glutamicum onto polysulphone membrane surface were evaluated by measuring the change in the permeation of pure water at constant pressure. Relations giving the membrane resistance as a function of contact time at varying bulk concentration, pH and ionic strength were obtained, by analogy with adsorption laws. Static (zero pressure) and dynamic (crossflow) experiments were then compared in order to determine the effect of convective flow and electrostatic interactions on cell adsorption, irreversible resistance and flux decline. Although convective forces tended to increase the amount of material accumulated near the membrane surface, it was electrostatic interactions that strongly affected cell adsorption and irreversible resistance, as evident in the irreversible adsorption and resistance results from the static and dynamic cases. Cell-cell interactions affect the porosity of the cake layer on the membrane, while cell-membrane interactions affect irreversible adsorption onto the membrane. Solution chemistry affects both types of interactions, as evident in the increased irreversible resistance of the cake layer and irreversibly adsorbed cells at the isoelectric point of cells (IEP). Additionally, the irreversible resistance of the fouled layer is dependent on its compactness, which is directly affected by solution chemistry. The flux decline rapidly decreased after the first 10 minutes of filtration. Flux decline is more pronounced at the IEP of the cell, also indicating that fouling and adsorption are strongly dependent on cell-cell and cell-membrane interactions.     

Analysis of transient permeation fluxes into and out of membranes for adsorption measurements

A relationship between the integrated fluxes into and out of a membrane following a positive or negative step change in feed concentration was derived. This analysis allows adsorption isotherms in the transport pathways through membranes to be determined from transient permeation responses to step concentration changes in the feed without measuring the retentate response. For Fickian diffusion through a membrane with Langmuir adsorption and zero coverage at the permeate boundary, the difference between the time-integrated flux into and flux out of the membrane is shown to be three times the time-integrated difference between the steady-state flux and the flux out. For Maxwell-Stefan diffusion, this ratio of integrated flux differences is 3 at low coverages and decreases towards 2 at saturation coverage. Mass transfer resistance at the permeate boundary increases the Fickian ratio above 3, and the ratio increases with decreasing Sherwood number. The ratio of integrated flux differences is shown to be identical to the steady-state replenishment time divided by the time lag. Thus, the ratio can be calculated directly from the steady-state concentration profile and the concentration-dependent diffusion coefficient. Surface diffusion through zeolite membranes was analyzed to demonstrate the calculation of the flux relationship for specific adsorption and diffusion models, but the method developed can be applied to membrane permeation in general.     

Theoretical considerations of membrane fouling and its treatment with immobilized enzymes for protein ultrafiltration

The ultrafiltration process was modelled in three separate stages with distinctive time constants. It was shown that in the first stage lasting less than 5 s a quasi-steady-state concentration profile is reached on the membrane/solution interface. In the second stage of 1–10-min solute adsorption on the membrane surface including the pores controls the permeation rate. The third stage is governed by a reaction mechanism which produces a surface gel causing flux decline at a slower rate than in the previous adsorption step. This polymerization of the protein to a gel on the membrane was shown to be second order in the interface protein concentrations. A reproducible and inexpensive method has been developed to attach food-grade proteases onto UF membranes by producing a primary adsorbed layer of enzyme which then retards the rate of gel formation on the ultrafilter. This resulted in 25–78% improvement in cumulative permeate yield in a standard 22-h run when processing 0.5% albumin or hemoglobin. The enhanced fluxes with self-cleaning membranes were modelled by incorporating an enzyme activity term to counteract the deposition of gel on the membrane surface and altering the apparent order of the gelation reaction.     

Modeling and Simulation of Rotating Disk-Membrane Module in Ultrafiltration of Bovine Serum Albumin

A dynamic mass transfer model, coupled with transient back transport flux for a Rotating Disk-Membrane (RDM) module has been developed in the present study. The simulation algorithm is capable of predicting the permeate flux (J), membrane surface concentration (c _m ), and permeate concentration (c _p ) under different parametric conditions of transmembrane pressure (TMP), feed concentration (c ₀), stirrer speed (Ω₂), and membrane speed of rotation (Ω₁). The key feature of the proposed model is the analytical solution of the governing component balance equation. Additionally, the well-known osmotic pressure model and the Spiengler-Kedem black box model were used to describe the solvent transport through membrane. The proposed model was validated with the experimental results obtained in ultrafiltration of bovine serum albumin (BSA)/water solution conducted in a standard RDM module, fitted with polyethersulphone (PES) membrane of 30 kDa molecular weight cut-off (MWCO). The maximum absolute deviation of the model predictions with respect to the experimental results was observed to be well within 5%.     

Influence of feed concentration and transmembrane pressure on membrane fouling and effect of hydraulic flushing on the performance of ultrafiltration

Micellar-enhanced ultrafiltration (MEUF) is a promising technology developed for treating the wastewater containing metal ions or organic pollutants. One of the greatest problems in MEUF is membrane fouling which is mainly caused by concentration polarization, gel layer or cake formation caused by the deposition of surfactant micelles on the membrane surface and surfactant adsorption in the membrane interior. In this study, surfactant sodium dodecyl sulfate (SDS), which was used in membrane separation as colloidal particles, caused the flux decline. The transmembrane pressure (TMP) and feed concentration of SDS had significant influences on the flux. This paper presented that the lower TMP had a smaller effect on membrane fouling, and when SDS concentration was around the critical micelle concentration (CMC), lower permeate flux and higher additional membrane fouling resistance were obtained. The effects of three kinds of hydraulic flushing methods on membrane permeate flux were investigated, including periodic forward flushing, periodic backwashing and forward flushing followed by backwashing. It was found that when the periodic combined flushing interval was 10 min, forward flushing and backwashing phase times were 150 s and 90 s, respectively, and that combined flushing was more conductive to permeate flux recovery in this study.     

Reactive dye removal in dye/salt mixtures by nanofiltration membranes containing vinylsulphone dyes: effects of feed concentration and cross flow velocity

In this study, DS5 DK type nanofiltration membranes were tested to recycle the reactive dye bath effluents. Reactive black 5 (RB5), reactive orange 16 (RO16), reactive blue 19 (RB19) and NaCl were used in the experiments to prepare the synthetic dye and salt mixtures. Effects of feed concentration, pressure and cross flow velocity on the permeate flux and color removal were investigated. Permeate flux increased with increasing pressure for all NaCl solutions. Dye concentration had a significant effect on flux values. Under the fixed NaCl concentrations the flux decreased with increasing dye concentrations. Dye rejections greater than 99% were achieved. Permeate was almost colorless. A gel layer formed by the rejected dye on membrane surface operates as a resistance to the permeation of dyes due to complete rejection of high molecule weight dyes, especially for the low salt concentrations. The presence of salt concentration has an interesting effect on color removal. Color removal decreased with increasing salt concentration. Cross flow velocities had also a significant effect on flux values. The dye formed agglomerates at high NaCl concentrations. High cross flow velocities decreased this effect.     

腐殖酸聚集体对膜蒸馏过程膜污染的作用机理

膜污染是膜蒸馏过程应用于工业水处理中遇到的主要问题之一。选取水体中具有代表性的有机物（腐殖酸）、微溶无机盐（碳酸钙）作为典型污染物,研究有机腐殖酸聚集体对于膜蒸馏过程膜污染进程的影响规律,探讨天然有机物-无机微溶盐混合水体中腐殖酸聚集体对于无机盐结晶过程的控制机理。结果表明：膜蒸馏通量的衰减大致可分为由滤饼层的形成造成的不可恢复部分以及由浓差极化、膜孔“半润湿”而造成的可部分恢复的通量降低。Ca²⁺通过加速腐殖酸分子的聚集过程,使表面负电性降低的腐殖酸聚集体率先吸附在聚偏氟乙烯中空纤维膜内表面,形成有机基质污染层;碳酸钙在有机腐殖酸聚集体的诱导下在膜内表面异相成核,最终成长为稳定的晶体。腐殖酸聚集体为无机盐晶体在疏水性膜内表面的生长提供了异相成核的基础。可通过控制污染水体中有机物的含量控制微溶碳酸钙在膜内表面成核及生长,实现控制其在膜内表面附着进而诱发疏水膜发生亲水化的过程。     

Impact of osmotic agent on the transport of components using forward osmosis to separate ethanol from aqueous solutions

The separation of low molecular weight organic compounds such as the ethanol from aqueous solutions represents an important area to be investigated and increment the range of applications of forward osmosis. This investigation assesses the effects of using different draw solutes for ethanol separation from dilute aqueous solutions. The influence of glucose, sucrose, sodium chloride, and magnesium chloride was evaluated in terms of total permeate, reverse solute and ethanol fluxes. Inorganic solutes promoted higher total permeate and ethanol fluxes than the organic solutes (2.5 and 1.5 times higher in average, respectively) for the same molar concentration, while presenting only 1.1 times higher reverse solute fluxes. Despite the lower ethanol flux promoted by the organic draw solutes, these osmotic agents promoted higher concentration of ethanol in the total permeate flux, suggesting that they can also be alternatives for specific processes. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4499–4507, 2017     

Ultrafiltration on Sizing Agent Solution in Tubular-Membrane Module

Ultrafiltration of an aqueous solution of carboxymethyl cellulose (CMC) was carried out in a tubular-membrane model made of ZrO₂/carbon. Water was forced through the macroporous membrane as the permeate, while CMC was concentrated and recovered as the retentate. Correlation equations for calculating the permeate flux of membrane ultrafiltration were derived based on the resistance-in-series model. Correlation results were confirmed by the experimental data. Experimental results showed that the permeate flux increases as transmembrane pressure or fluid velocity increases, but decreases when feed concentration increases. Because membrane ultrafiltration is a pressure-driven process, high cross-flow velocity enhances the mass transfer coefficient of the solute and high solution concentration increases the thickness of the concentration polarization layer.     

SIZING AGENT RECOVERY BY MEMBRANE ULTRAFILTRATION IN HOLLOW-FIBER MODULES

Ultrafiltration of an aqueous solution of polyvinyl alcohol was carried out in an Amicon model H1P30-20 hollow-fiber cartridge made of polysuifone. Fresh water was forced through the macroporous membrane, as the permeate, while polyvinyl alcohol was concentrated and re covered as the retentate. Correlation equations for calculating the permeate flux of membrane ultrafiltration of the polyvinyl alcohol were derived based on the resistance-in-series and exponential models. Correlation results were confirmed by the experimental data, especially for the results obtained from the exponential model. It was found that the permeate flux increases as transmembrane pressure or fluid velocity increases, but decreases when feed concentration increases. Because membrane ultrafiltration is a pressure-driven process, high cross-flow velocity enhances the mass transfer coefficient of the solute and high solution concentration in creases the thickness of the concentration polarization layer.     

SIZING AGENT RECOVERY BY MEMBRANE ULTRAFILTRATION IN HOLLOW-FIBER MODULES

Ultrafiltration of an aqueous solution of polyvinyl alcohol was carried out in an Amicon model H1P30-20 hollow-fiber cartridge made of polysuifone. Fresh water was forced through the macroporous membrane, as the permeate, while polyvinyl alcohol was concentrated and re covered as the retentate. Correlation equations for calculating the permeate flux of membrane ultrafiltration of the polyvinyl alcohol were derived based on the resistance-in-series and exponential models. Correlation results were confirmed by the experimental data, especially for the results obtained from the exponential model. It was found that the permeate flux increases as transmembrane pressure or fluid velocity increases, but decreases when feed concentration increases. Because membrane ultrafiltration is a pressure-driven process, high cross-flow velocity enhances the mass transfer coefficient of the solute and high solution concentration in creases the thickness of the concentration polarization layer.     

白炭黑填充PDMS/PVDF复合膜的纳滤分离性能及传质特性

将纳米级白炭黑填充于PDMS制备了白炭黑填充PDMS/PVDF复合膜,采用红外(FT-IR)、热失重(TGA)和接触角(CA)等方法对填充复合膜进行了分析和表征,并采用纳滤的方法系统研究了复合膜对大豆油/己烷混合油的分离性能。结果表明,白炭黑填充能有效促进PDMS的交联,提高PDMS的疏水性、热失重温度以及对溶剂的稳定性;白炭黑填充量增加使复合膜渗透通量降低,但截留率从96%提高到98%;随溶液浓度增加,渗透通量和截留率同时降低;随温度的升高,渗透通量上升,截留率降低。大豆油和己烷在膜中的传质特性可用不完全的溶解-扩散模型描述,溶液渗透压实验值与计算值符合较好。     

Modeling of Aniline Removal by Reverse Osmosis Using Different Membranes

The behavior of different reverse osmosis membranes, namely, HR98PP, SEPA‐MS05, and DESAL‐3B, was compared with the one predicted by a solution‐diffusion model. This model assumes that the membrane has a homogeneous, nonporous surface layer and uses two main parameters, permeate concentration C_p and volumetric permeate flux Q_p, to characterize the membrane system. In order to calculate these parameters, the theoretical values of water and solute permeability constants, A_w and B_s, and the osmotic pressure coefficient, Ψ, were initially determined. Using the software Sigma Plot V 10.0, accurate values of Ψ, Q_p, and C_p were only obtained for the DESAL‐3B membrane, i.e., the selected solution‐diffusion model can be applied to this membrane.     

Effect of operating parameters on permeate flux decline caused by cake formation — a model study

A phenomenological model employing cake formation theory has been developed for describing permeate fluxdecline in cross-flow membrane filtration. In the model the physicochemical parameters, which are often difficult to estimate, were excluded. Instead, the flux decline due to cake formation caused by inorganic scaling/precipitation was related to the operating parameters for fouling prediction. The processes of solute deposition on membrane surface and its re-dissolution back to the bulk phase were modeled to estimate dynamic cake formation and permeate flux profiles. The modeled results show that the permeate flux declined rapidly at the early stage of cake formation, then gradually leveled off as time progressed, and eventually reached a steady-state “ultimate” flux when the rate of solid deposition was balanced by back dissolution. Sensitivity analyses show that an increase of cross-flow velocity from 0.06 to 0.14 m/s increased the ultimate flux from 0.016 m/h to 0.035 m/h. Membrane permeability and transmembrane pressure (400-750 kPa) affected the initial flux but not the ultimate flux. The flux decline pattern strongly depended on the specific cake resistance, which affects the time to reach steady state but not the ultimate flux. Verification of the model with data in the literature showed excellent agreement.