A mass transfer model for the prediction of rejection and flux during ultrafiltration of PEG-6000

A mass transfer model in case of ultrafiltration is proposed in the present study which is capable of predicting the permeate volumetric flux and rejection at different pressure, concentration and stirrer speed. The model is based on the steady state mass balance over the boundary layer, coupled with the results from irreversible thermodynamics. It first predicts the membrane surface and permeate concentrations — which are then utilized to calculate rejection. Permeate flux is then predicted using the result obtained from filtration theory. The model utilizes four parameters, namely, solvent permeability, solute permeability, reflection coefficient and specific cake resistance. These parameters along with the known values of the operating conditions and solution properties enable one to predict the flux as a function of time and rejection. The computed results are found to be in good agreement with the previously published data of Bhattacharjee and Bhattacharya during ultrafiltration of PEG-6000 by cellulose acetate membrane.     

Prediction of permeate flux during osmotic pressure-controlled electric field-enhanced cross-flow ultrafiltration

Electric field-enhanced cross-flow ultrafiltration has been carried out to separate protein, bovine serum albumin, from aqueous solution using a 30,000 molecular weight cutoff membrane. A theoretical model is developed to predict permeate flux under a laminar flow regime including the effects of external d.c. electric field and suction through the membrane for osmotic pressure-controlled ultrafiltration. The governing equations of the concentration profile in the developing mass transfer boundary layer in a rectangular channel are solved using a similarity solution method. The effect of d.c. electric field on the variation of membrane surface concentration and permeate flux along the length of the channel is quantified using this model. The expression of Sherwood number relation for estimation of mass transfer coefficient is derived. The analysis revealed that there is a significant effect of electric field on the mass transfer coefficient. A detailed parametric study has been carried out to observe the effect of feed concentration, electric field, cross-flow velocity, and pressure on the permeate flux. For 1 kg/m3 BSA solution, by applying a d.c. electric field of 1000 V/m, the permeate flux increases from 42 to 98 L/m2 h compared to that with zero electric field. The experimental results are successfully compared with the model predicted results.     

Prediction of mass transfer coefficient with suction for turbulent flow in cross flow ultrafiltration

Sherwood number relations for the prediction of the mass transfer coefficient for developing concentration boundary layer have been obtained for turbulent flow regime from first principles. The common flow modules, namely, rectangular channel, tubular and radial cross flow are considered. The relationships developed include the effect of suction through the membrane. Relevant relations for the estimation of mass transfer coefficient for cross flow ultrafiltration are formulated. The proposed Sherwood relations are used in conjunction with the osmotic pressure model to predict the permeate flux in osmotic pressure governed ultrafiltration. The simulated results are compared with the experimental data obtained from the literature. A detailed parametric study has been performed to observe the effects of the operating conditions on the filtration performance in terms of the permeate quantity and quality.     

Concentration Polarization of Interacting Solute Particles in Cross-Flow Membrane Filtration

A theoretical approach for predicting the influence of interparticle interactions on concentration polarization and the ensuing permeate flux decline during cross-flow membrane filtration of charged solute particles is presented. The Ornstein-Zernike integral equation is solved using appropriate closures corresponding to hard-spherical and long-range solute-solute interactions to predict the radial distribution function of the solute particles in a concentrated solution (dispersion). Two properties of the solution, namely the osmotic pressure and the diffusion coefficient, are determined on the basis of the radial distribution function at different solute concentrations. Incorporation of the concentration dependence of these two properties in the concentration polarization model comprising the convective-diffusion equation and the osmotic-pressure governed permeate flux equation leads to the coupled prediction of the solute concentration profile and the local permeate flux. The approach leads to a direct quantitative incorporation of solute-solute interactions in the framework of a standard theory of concentration polarization. The developed model is used to study the effects of ionic strength and electrostatic potential on the variations of solute diffusivity and osmotic pressure. Finally, the combined influence of these two properties on the permeate flux decline behavior during cross-flow membrane filtration of charged solute particles is predicted. Copyright 1999 Academic Press.     

A constant flux based mathematical model for predicting permeate flux decline in constant pressure protein ultrafiltration

This paper discusses a novel approach for predicting permeate flux decline in constant pressure ultrafiltration of protein solutions. A constant pressure process is assumed to be made up of a large number of small, sequential, constant flux ultrafiltration steps: the flux decreasing due to fouling and other related factors at the end of each step. The advantage of this approach is that constant flux ultrafiltration is easier to study, characterize, and model than constant pressure ultrafiltration. Consequently model parameters can be obtained in reliable and reproducible manner. Constant pressure ultrafiltration is dynamic in nature since both the magnitude of osmotic back-pressure and the extent of membrane fouling decrease as the permeate flux decreases with time. The proposed model takes into consideration the interplay between permeate flux, concentration polarization, and membrane fouling. The model demonstrates that the initial rapid flux decline is due to a combination of concentration polarization and membrane fouling while during the remaining part of the process, the effect of concentration polarization becomes negligible. The model also shows that concentration polarization affects the initial flux decline only at higher transmembrane pressures. This model which was validated using experimental data is conceptually simpler than other available models and easy to use. In addition to its value as a predictive tool it would particularly be useful for deciding appropriate start-up conditions in ultrafiltration processes.     

Modeling of flux decline during crossflow ultrafiltration of colloidal suspensions

Mass transfer during crossflow ultrafiltration is mathematically expressed using the two-dimensional convective–diffusion equation. Numerical simulations showed that mass transfer in crossflow filtration quickly reaches a steady-state for constant boundary conditions. Hence, the unsteady nature of the permeate flux decline must be caused by changes in the hydraulic boundary condition at the membrane surface due to cake formation during filtration. A step-wise pseudo steady-state model was developed to predict the flux decline due to concentration polarization during crossflow ultrafiltration. An iterative algorithm was employed to predict the amount of flux decline for each finite time interval until the true steady-state permeate flux is established. For model verification, crossflow filtration of monodisperse polystyrene latex suspensions ranging from 0.064 to 2.16 μm in diameter was studied under constant transmembrane pressure mode. Besides the crossflow filtration tests, dead-end filtration tests were also carried out to independently determine a model parameter, the specific cake resistance. Another model parameter, the effective diffusion coefficient, is defined as the sum of molecular and shear-induced hydrodynamic diffusion coefficients. The step-wise pseudo steady-state model predictions are in good agreement with experimental results of flux decline during crossflow ultrafiltration of colloidal suspensions. Experimental variations in particle size, feed concentration, and crossflow velocity were also effectively modeled.     

Generalized integral and similarity solutions of the concentration profiles for osmotic pressure controlled ultrafiltration

A mathematical model describing the concentration polarization phenomenon during osmotic pressure controlled ultrafiltration is presented. Generalized integral and similarity solutions of the concentration profile in the mass transfer boundary layer are obtained. The parameters governing the shape of the concentration profile vary with time in case of a batch cell and axial distance in a cross flow cell. The model is used to predict the permeate flux and the solute rejection simultaneously during unstirred batch cell and cross flow UF. The results obtained by integral and similarity solutions are compared with the results of detailed numerical solution of the governing equations for both the systems. The predictions of permeate flux from the generalized integral method are also compared with some approximate solutions in order to assess the limitations of the various approximations. UF experiments were performed with Dextran (T-20) in cross flow system and with PEG-6000 and Dextran (T-40 and T-20) in unstirred batch cell. Predictions of the model are in remarkably good agreement with detailed simulation as well as experimental results. Moreover, the integral solution can also account for the variation of diffusivity with solute concentration. Comparisons show that (a) while the generalized integral method is much simpler than the detailed numerical solutions, it is much more general and accurate than other analytical and semi-analytical solutions, and, (b) the proposed solution predicts the osmotic pressure controlled flux decline accurately over a wide range of operating conditions. The expression for gel layer governed UF (constant membrane surface concentration) is found to be an asymptotic case of the present solution.     

Factors affecting flux and ethanol separation performance in vacuum membrane distillation (VMD)

Membrane distillation (MD) has a great potential as a concentration process for temperature labile liquids such as fruit juices, etc. Besides water, also aroma compounds will permeate through the membrane depending on their volatility and how the MD process is operated on the permeate side.In this paper, an experimental and theoretical investigation of the influence of concentration polarisation and temperature polarisation on the flux and selectivity of binary aqueous mixtures of ethanol is presented for vacuum membrane distillation (VMD) processes. Experimental results include changes of the following parameters: nature of solutions, membrane material and pore size, feed temperature, recirculation flow rate. One method was proposed in order to evaluate the concentration polarisation effects from the fit of the experimental data. General models taking into account Knudsen and viscous flows were proposed, but viscous contribution resulted to be negligible under our operating conditions. Therefore, theoretical fluxes were estimated using Knudsen model and a good agreement between them and the experimental ones was found.     

A novel approach for modeling concentration polarization in crossflow membrane filtration based on the equivalence of osmotic pressure model and filtration theory

A theoretical model for prediction of permeate flux during crossflow membrane filtration of rigid hard spherical solute particles is developed. The model utilizes the equivalence of the hydrodynamic and thermodynamic principles governing the equilibrium in a concentration polarization layer. A combination of the two approaches yields an analytical expression for the permeate flux. The model predicts the local variation of permeate flux in a filtration channel, as well as provides a simple expression for the channel-averaged flux. A criterion for the formation of a filter cake is presented and is used to predict the downstream position in the filtration channel where cake layer build-up initiates. The predictions of permeate flux using the model compare remarkably well with a detailed numerical solution of the convective diffusion equation coupled with the osmotic pressure model. Based on the model, a novel graphical technique for prediction of the local permeate flux in a crossflow filtration channel has also been presented.     

Modeling and analytical simulation of rotating disk ultrafiltration module

An unsteady state mass transfer model has been developed for rotating disk ultrafiltration module. Starting from the basic physics of the system, analytical expression of back transport flux generated due to rotation-induced shear field is determined, which is subsequently incorporated in the fundamental material balance equation. In order to get an analytical solution of governing partial differential equation via Laplace transformation, pseudo steady state consideration is imposed both on permeate as well as back transport flux. Once the analytical form of concentration field is obtained using the expression permeate flux, membrane surface concentration are evaluated using polymer solution theory and irreversible thermodynamics. Finally an iterative scheme is designed to simulate the permeate flux and membrane surface concentration under specified set of operating parameters. The prediction from this model is found to be in good agreement with experimental data obtained from PEG-6000/water system using cellulose acetate membrane of 5000 Da molecular weight cut-off.     

Effect of electric field during gel-layer controlled ultrafiltration of synthetic and fruit juice

Electric field enhanced ultrafiltration of pectin–sucrose mixture (synthetic juice) and mosambi (Citrus sinensis (L.) Osbeck) fruit juice using 50,000 (MWCO) polyerthersulfon membrane is studied in a cross-flow cell. Pectin, completely rejected by the membrane, forms a gel type layer over the membrane surface. Under the application of an external dc electric field across the membrane, gel-layer formation is restricted leading to an enhancement of permeate flux. During ultrafiltration of synthetic juice, application of dc electric field (800 V/m) increases the permeate flux to almost threefold compared to that with zero electric field. A theoretical model based on integral method assuming suitable concentration profile in the boundary layer is developed. The proposed model is used to predict the permeate flux in gel-layer governed electric field enhanced ultrafiltration. Predictions of the model are successfully compared with the experimental results under a wide range of operating conditions. Experiments with fruit juice also demonstrated significant increase in flux with the application of a suitable electric field.     

Response surface modelling and optimization in pervaporation

Both the conventional method of experimentation, in which one of factors is varied maintaining the other factors fixed at constant levels and the statistically designed experimental method, in which all factors are varied simultaneously are carried out for organic removal from water by pervaporation. Binary acetonitrile–water mixtures are considered. The effects of the operating parameters on the pervaporation performance of the membrane system have been investigated. The overall mass transfer coefficients have been determined for different conditions of feed temperature and initial organic concentration. In addition, the activation energy associated to the permeation process has been determined and discussed for each feed organic mixture. Statistical experimental design and response surface methodology, RSM, have been applied to optimize the operational conditions of pervaporation process in order to maximize the output responses, which are permeate flux ratio and concentration of organic in permeate. The input variables employed for experimental design were the feed temperature, initial concentration of organic in feed and operational downstream pressure. Based on the design of experiment the quadratic response surface models have been developed to link the output responses with the input variables via mathematical relationships. The constructed response models have been tested using the analysis of variance and the canonical analysis. The obtained optimal point by means of Monte Carlo simulation method and desirability function corresponds to a feed temperature of 57.69 °C, a feed acetonitrile concentration of 6.96 wt% and a downstream pressure of 28.95 kPa. The maximal values of the permeate flux ratio and the concentration of organic in permeate obtained under optimal process conditions have been confirmed experimentally.     

Radial Basis Function Neural Networks-Based Modeling of the Membrane Separation Process： Hydrogen Recovery from Refinery Gases

Membrane technology has found wide applications in the petrochemical industry, mainly in the purification and recovery of the hydrogen resources. Accurate prediction of the membrane separation performance plays an important role in carrying out advanced process control (APC). For the first time, a soft-sensor model for the membrane separation process has been established based on the radial basis function (RBF) neural networks. The main performance parameters, i.e, permeate hydrogen concentration, permeate gas flux, and residue hydrogen concentration, are estimated quantitatively by measuring the operating temperature, feed-side pressure, permeate-side pressure, residue-side pressure, feed-gas flux, and feed-hydrogen concentration excluding flow structure, membrane parameters, and other compositions. The predicted results can gain the desired effects. The effectiveness of this novel approach lays a foundation for integrating control technology and optimizing the operation of the gas membrane separation process.     

Modeling of the Permeate Flux during Microfiltration of BSA-Adsorbed Microspheres in a Stirred Cell

A study on the variation of the permeate flux was performed in a stirred cell charged with microspheres, to investigate the effects of the stirrer speeds (300, 400, and 600 rpm) and the BSA concentration (0.1, 0.2, 0.4, and 0.8 g/L) under constant pressure. The permeate flux increased over time before the saturation point, but it began to decrease after that point. An increase of the BSA concentration and the stirrer speed resulted in the rapid increase of the permeate flux. This is contrary to the observation of the conventional filtration experiments using a stirred cell. A resistance-in-series model was employed for the modeling of the permeate flux. The cake resistance (R(c), induced by the concentration polarization of microspheres) and the fouling resistance (R(f), induced by the adsorption of BSA inside the membrane pore) must be considered simultaneously for the modeling. These modeling results were in good agreement with the experimental data. These can be applied to the special system considering both R(c) and R(f) as well as the general filtration systems using a stirred cell. Copyright 2000 Academic Press.     

A new generator of unsteady-state flow regime in tubular membranes as an anti-fouling technique: A hydrodynamic approach

A new generator of pulsatile flow has been developed. It consists of a rotating distributor disc judiciously perforated and placed in front of the entrance plane of a tubular membrane bundle. A laboratory-scale apparatus was built with a five membrane bundle. Two configurations were studied: upstream-disc-position (UDP) and downstream-disc-position (DDP). The main new feature is that the pulsatile flow is generated only in the membranes whereas no variation of flow or pressure occurs elsewhere in the equipment. The hydrodynamic behaviour was successfully modelled; experimental and calculated data are in good agreement. Filtration tests with an aqueous suspension of bentonite showed a close relation between the permeate flux and the pulsatile crossflow velocity. First results are encouraging: a reduction in crossflow velocity of 50% with the same power consumption per unit permeate flux as required for steady crossflow filtration.     

Experimental contribution to the understanding of transport through polydimethylsiloxanenanofiltration membranes: Influence of swelling,compaction and solvent on permeation properties

This study aims to better understand the permeation properties of polydimethylsiloxane (PDMS) membranes. The compressibility and nanofiltration fluxes were measured for swollen PDMS films using several solvents at applied pressures ranging from 5 to 50 bar. The degree of swelling varied according to the solvent and the pressure applied. To show the correlation between the behaviour of the swollen PDMS under pressure and its permeation performance, the thickness reduction of the membrane was mimicked using uniaxial compression tests. The evolution of the nanofiltration flux as a function of the transmembrane pressure proved to be non-linear. Linearization was achieved by taking into account both the swelling and the thickness reduction previously measured, confirming that these phenomena may have occurred during the nanofiltration experiments. Moreover, the solvents' viscosity and affinity for the polymer were confirmed to have a great influence on their ability to permeate the membrane. Finally, employing the most commonly used models, a study of transport through the membrane led to the conclusion that the experimental results were in agreement with the hydraulic theory of transport.     

A concentration polarization model for the ultrafiltration of nonionic surfactants

A theoretical model has been developed that describes ultrafiltration of nonionic surfactants. The model takes into account the fact that surfactants start to aggregate and form micelles at the critical micelle concentration. The model can be used to predict the performance of the membrane if the transport properties inside and at the membrane surface as well as the surfactant association behavior, are known. Three hydrophilic ultrafiltration membranes, made of regenerated cellulose, were used in the investigation. The cut-offs of the membranes were 10,000, 20,000, and 30,000 Da. The surfactant used in the investigation was the nonionic surfactant Triton X-100. The influence of the concentration of surfactant, transmembrane pressure and pure water flux were studied theoretically and experimentally. From the results presented in this work it can be concluded that the calculated values are in good agreement with experimental data.     

Predicting limiting flux of skim milk in crossflow microfiltration

Four models for back-transport mechanisms in crossflow microfiltration have been investigated concerning their ability to predict the limiting permeate flux for skim milk. A tubular, ceramic membrane was used to measure the limiting fluxes for a series of crossflow velocities at two temperatures. One of the models — the shear-induced diffusion model — predicts values of the limiting flux close to our experimental values both at 55 and 15°C. The best prediction of the limiting flux is obtained by the empirical relation: flux=Re · 6.94×10⁻¹⁰ m/s.     

Treatment of textile desizing wastewater by pilot scale nanofiltration membrane separation

Desizing wastewaters from the bleaching and dyeing industry of Hong Kong were treated by nanofiltration (NF) membrane separation on a pilot scale in the pressure controlled region. The two brown colored wastewaters had chemical oxygen demand (COD) of 14,000 mg l⁻¹ and 5430 mg l⁻¹, respectively. Permeate flux and COD retention were investigated in relation to transmembrane pressure drop, temperature, and feed-solution concentration. The permeate flux was found to increase significantly with transmembrane pressure drop and to decrease with feed concentration. Higher permeate flux was found for wastewater with higher pH. A minor increase in COD retention was found for the increase in transmembrane pressure drop as well as operating temperature. The COD retention was about 95% for wastewater with pH 10.2, and 80–85% for wastewater with pH 5.5. The difference in the results obtained for the two kinds of wastewater was attributed to their compositional difference that resulted from the desizing operation. Fouling of membrane is not a big concern for the NF membrane tested in treating this type of wastewater. The quality of the permeate is all above the discharge standard for foul sewer in Hong Kong. The experimental results are consistent with the theoretical analysis.