Nanofiltration Model Research Articles

Charge and dielectric characterization of nanofiltration membranes by impedance spectroscopy

The conductance and capacitance of a nanofiltration membrane have been obtained by impedance spectroscopy analysis in a wide range of concentrations of KCl aqueous solutions. The permittivity and conductivity of the electrolyte–membrane system have been determined by means of dielectric analysis and modeling the system with an equivalent circuit that corresponds to the relaxation times experimentally observed.The volumetric charge in the membrane has been assessed by solving the equilibrium partitioning equations in the membrane that include Donnan, steric and dielectric effects. The mean transport number has been evaluated by the membrane potential method.It has been proved that the effects of confinement within the narrow pores of nanofiltration pores on the dielectric phenomena arising in such narrow pores are substantial and have to be taken into account in transport models.In summary by using impedance spectroscopy and membrane potential measurements it has been possible to get the electric and dielectric parameters that should allow the available nanofiltration models to be used as predictive tools.

Mathematical modeling of nanofiltration for concentrated electrolyte solutions

As one of the most newly developed liquid-phase membrane separation processes, nanofiltration (NF) is used in several industrial and environmental applications due to low energy consumption and elevated flux rates. In spite of several attempts for modeling NF separation ranging from rigorous space-charge approaches to simpler irreversible thermodynamics, neither have been totally sufficient either due to extensive computational requirements limiting their application in multi-component systems or oversimplifying assumptions leading to loss of generality. A promising model as a compromise between simplicity and accuracy can then be very helpful in this regard.This paper is an effort for modeling the nanofiltration separation process based on the modified extended Nernst–Planck equation (MENP) for solute transport through membrane active layer which is improved for concentrated electrolyte solutions. Based on simulation results, the effect of high ionic concentrations on the rejection of chloride ion is investigated, in case of pure NaCl solutions. The modified version of ENP, takes into account the variations of activity coefficient and the resulting influence on the retention behavior by increasing the ionic strength. The results show significant reduction of the predicted rejection by increasing the ionic strength.

Crossed mixture–process design approach to model nanofiltration rejection for non-dilute multi-ionic solutions in a given range of solution compositions

The goal of the present work is to illustrate the applicability of crossed mixture–process design to predict the rejection of the nanofiltration membranes when treating non-dilute solutions. The method used in this work is based on the use of mixture factors derived from the fractions of equivalents of the major ions present in solution combined with the total concentration as a process variable. In this way, polynomial models for permselectivity properties can be obtained. Model accuracy is improved by using pseudo-components to restrict the range of the composition variables to that expected for the feed water compositions. The experimental plan uses the D-optimal criterion. As an application example, the procedure was used to model the performance of the nanofiltration membrane NF270 (Dow-Filmtec) with ionic mixtures containing chloride, nitrate, sulfate, sodium and calcium. The experiments were carried out in a pilot plant with solutions of total concentration ranging from 2480 to 4050mg/L. The obtained polynomial models could satisfactorily describe individual ion rejection despite the solutions not being dilute. The polynomial models can be useful for design and operation purposes as an alternative to physical-based nanofiltration models.

Arsenic Separation by a Membrane-Integrated Hybrid Treatment System: Modeling, Simulation, and Techno-Economic Evaluation

A modeling and simulation study along with economic analysis was carried out for arsenic separation by a membrane-integrated hybrid treatment system that consisted of an oxidation unit integrated with a cross flow nanofiltration membrane module. About 96–98% arsenic removal efficiency was achieved in the membrane module after pre-oxidation. When pH was increased from 3 to 10, arsenic rejections reached as high as 98.5%. The dynamic mathematical model developed for the system used Extended Nernst-Plank equation as the basis for the nanofiltration model. A linearized approach in modeling was adopted that reduced the computation time significantly. Model predictions were found to corroborate very well with the experimental findings as indicated in the small relative errors of the order of only 0.003 and Willmott d-index of 0.993 reflecting very good model performance. Thus the developed model is expected to be very useful in scale-up, design and optimization of the membrane-integrated hybrid treatment system for removal of arsenic from contaminated groundwater.

Modeling of ammonium lactate recovery and impurity removal from simulated fermentation broth by nanofiltration

A multistage version of nanofiltration (NF) model has been developed, which can predict the transient and steady-state behaviors of the process for lactate recovery from fermentation broth. The model parameters were estimated based on experimental data at various lactate concentrations and operating pressures with simulated fermentation broth containing impurities as well as lactate by using Spiegler–Kedem model and Teorell–Meyer–Sievers model. Continuous NF operations were carried out for various bleed ratios to investigate the effects of bleed on the lactate recovery and level of impurity represented by sulfate in this study. Time profiles of lactate and sulfate concentrations in the system and permeate predicted by the proposed model were in a good agreement with the experimental data. Also, the accuracy of the steady-state prediction by the model was experimentally proved. It was demonstrated that impurity concentration decreased as the bleed ratio was increased, while the lactate recovery decreased proportional to the bleed ratio as expected. The proposed model can be used for predicting the process behaviors during a start up period and at the steady state, providing a useful tool in process design and optimization.

Separation of potassium clavulanate and potassium chloride by nanofiltration: Transport and evaluation of membranes

In this work, four commercial nanoporous membranes (NF and NF90 from Filmtec TM, and NP010 and NP030 from Microdyn Nadir) have been characterized and evaluated in order to use them to separate potassium clavulanate and potassium chloride. Their charge density has been investigated by Tangential Streaming Potential measurements for several concentrations of KCl and pH. The isoelectric point of the membranes has been found to be between pH 5.0 and 6.0. Their rejection for KCl has also been measured and the corresponding concentration polarization effect has been taken into account. Nanofiltration modeling, that considers the steric, electric and dielectric exclusion and the charge variation along the pores (SEDE-VCh model), satisfactorily describes the retention of KCl by using the dielectric constant inside the pores, ε p , as the only fitting parameter. Although all the studied membranes are highly retentive for the potassium clavulanate, KCA, the most suitable membranes for KCA purification, attending to the KCl/KCA selectivity are NF or NF90 membranes at all pH. Lower pH values give higher selectivity for all the membranes.

MODELING OF DIAFILTRATION PROCESSES FOR DEMINERALIZATION OF ACID WHEY: AN EMPIRICAL APPROACH

ABSTRACTIn this paper, a mathematical model is provided to describe the dynamics of membrane diafiltration processes for desalting acid whey. A rich representation of the separation process is given due to the employment of concentration‐dependent solute rejections in the design equations. We propose an experimental design and a suitable empirical method for parameter estimation. This technique supports the disciplined use of experimental data and reduces the number of necessary a‐priori experiments. With the help of experimental data we demonstrate the power of the presented modeling method.PRACTICAL APPLICATIONSThe annual volume of dairy whey produced globally exceeds 160 million tons. Demineralized whey is of large importance for the food industry. A suitable degree of demineralization can be achieved by diafiltration. Whey represents a complex multi‐component system. Modeling of nanofiltration of such complex systems is a difficult task. We provide a rigorous mathematical model to predict the dynamics of whey diafiltration. The presented robust simulation technique is able to predict the experimentally observed behavior. We propose a minimal experimental design and a suitable mathematical tool to convert the raw experimental data into useful information. The provided methodology might be particularly applicable for decision makers to choose an appropriate diafiltration technique for a given separation design problem.

Multicomponent Steady State Modeling of Concentration Polarization Including Adsorption during Nanofiltration of a Textile Effluent

Steady state modeling of nanofiltration of a textile effluent was carried out. The model comprised of three distinct parts. Film theory was used to account for the solute transport outside the membrane surface within the mass transfer boundary layer. An osmotic pressure model and a solution-diffusion model were used to quantify the solvent and solute flux through the porous membrane. The osmotic pressure model was modified by incorporating adsorption of dyes onto the membrane surface. The system had three components, namely, Cibacron Black and Cibacron Red and the salt as sodium chloride. The model had three parameters, namely, solute permeability of two dyes and sodium chloride through the membrane. These parameters were estimated by comparing the calculated and experimental data of permeate flux and permeate concentration. It was observed that membrane hydraulic resistance and the resistance due to concentration boundary layer were more significant. The calculated permeate flux was within ±20% of the experimental data. Values of resistance due to adsorption of dyes onto the membrane surface were calculated to be about 2 to 3% of total resistance and of those due to concentration boundary layer were about 47%.

A combined pore blockage, osmotic pressure, and cake filtration model for crossflow nanofiltration of natural organic matter and inorganic salts

The performance of nanofiltration (NF) process for water treatment is affected by flux decline due to membrane fouling. Many models have been applied to explain fouling mechanisms. In this work, a combined pore blockage, osmotic pressure, and cake filtration model was developed and successfully used to determine NF performance and model parameters for crossflow NF. NOM solutions containing sparingly soluble inorganic salts (i.e. CaCO 3, CaSO 4, and Ca 3(PO 4) 2), showed higher normalized flux decline than those containing soluble inorganic salts (i.e. NaCl and CaCl 2). The α blocked and R m,s parameters for sparingly soluble inorganic salts exhibited higher values than those for soluble inorganic salts, while the R m,s and α cake parameters were found to be significant for soluble inorganic salts due to increased salt concentration and NOM cake accumulation at the membrane surface. Increased ionic strengths from 0.01 M to 0.11 M resulted in more pronounced flux decline, thus increased model parameters (i.e. α blocked and R m,s ). The membrane surface characteristics examined by the scanning electron microscopy (SEM) images evidently supported the precipitation of sparingly soluble inorganic salts. The flux decline was the most pronounced for phosphate species, corresponding to the lowest water flux recovery, thus increased non-recoverable resistance ( R non-rec ) due to pore plugging from phosphate salt precipitation.

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.

Infl uence of an inhomogeneous membrane charge density on the rejection of electrolytes by nanofiltration membranes

The salt rejection of membranes with inhomogeneous fixed charge densities including both symmetric and asymmetric distributions has been investigated theoretically. The rejection rates for the different fixed charge distributions, have been calculated by using a standard nanofiltration (NF) model based on the extended Nernst-Planck equation, the local electroneutrality condition and a modified Donnan equation including both steric and electrostatic effects and have been compared with the rejection rate obtained for a homogeneous distribution with the same average fixed charge concentration. The effects of the ion diffusion coefficients and the pore radius on the membrane rejection have also been investigated for the various fixed charge distributions. It has been shown that inhomogeneous fixed charge distributions may significantly affect the rejection properties of NF membranes. The value of the fixed charge concentration at the pore inlet plays a major role and high charge densities at the pore inlet tend to increase the salt rejection. Nonetheless, it has also been shown that strong axial gradients of the fixed charge concentration can affect significantly the ion transport within pores.

Coupled concentration polarization and pore flow modeling of nanofiltration of an industrial textile effluent

A coupled model of concentration polarization and transport of solutes through the pores was used to study the nanofiltration of two dye system and salt (NaCl) in a textile effluent. The transport coefficients, namely, hindered coefficient for diffusion and convection as well as steric hindrance factor of the dyes were estimated by minimizing the error involved between experimental and calculated permeate flux and permeate concentration under various operating conditions. Although the removal of dyes through the membrane was significant (more than 90%), the salt retention was less than 4% due to its very high concentration in the textile effluent. The contributions of electrical migration, convection and diffusion towards the flux of dyes through the pores were quantified. It was found that in case of bulkier dye molecules, diffusive flux was predominant mechanism, which was an order of magnitude higher than the flux due to convection and electrical migration. For smaller salt species, the convective flux was more dominant.

Performance evaluation of nanofiltration membranes for diafiltration of dye/salt mixtures: Experimental observations and model verification

The process of desalination of aqueous dye-salt solutions by polymeric nanofi ltration membranes using commercially available modules were studied. The experimental part was focused on determination of basic characteristics of tested membranes (Esna 1, Desal 5DK, NF 70, NF 90, NF 270 and TR 60), which above all, means determination of the dependence of permeate fl ow intensity or rejection on pressure difference used. The demineralised water and water solution of NaCl are used to characterize all of the tested membranes. Great interest is also attached to the mathematical modelling of nanofi ltration and description of discontinuous diafi ltration by periodically adding solvent at constant pressure difference.

Nanofiltration in the manufacture of liquid dyes production

In the manufacture of liquid dyes, almost complete desalting, which helps to improve the stability of the product, enhances the solubility of the dye. Diafiltration is used to allow a high level of desalting to be achieved. The process of desalination of aqueous dye-salt solutions by polymeric nanofiltration membranes using commercially available modules was studied. The influence of dye and salt concentration on the salt rejection and pressure applied on the flux as well as comparison of individual NF membranes for desalting purposes is presented. The great interest is also devoted to the mathematical modelling of nanofiltration and description of discontinuous diafiltration by periodically adding solvent at constant pressure difference.

Application of nanofiltration models for the prediction of lactose retention using three modes of operation

The desal 5 DL membrane (Dow Chemical, USA) was used to recover lactose from whey ultrafiltration permeate. Lactose and ions rejection and permeate flux were measured using ultrafiltered sweet whey as feed solution. Three different operation modes (total recycle mode, concentration mode and continuous diafiltration mode) were considered. Lactose retention was predicted by means of the Donnan Steric Partioning model (DSPM) and the Kedem–Spiegler model (KSM). The best fit for the total recycle and concentration modes was obtained with the KSM. Moreover, the KSM predictions were worse for the CDM. These models contribute to a better understanding of the transport mechanisms involved in nanofiltration processes and to optimize the process at industrial scale. The two models can be considered as a useful tool to improve the recovery, demineralization and concentration of lactose.

Response surface modeling and optimization of composite nanofiltration modified membranes

The experimental design and response surface methodology (RSM) have been used to develop predictive models for simulation and optimization of nanofiltration modified membranes by UV-initiated graft polymerization technique. The objective is to prepare optimum membrane with high nanofiltration performance and low fouling. The factors considered for experimental design were the UV-irradiation time, UV-intensity and the concentration of the monomer N-vinyl-2-pyrrolidone (NVP) in aqueous grafting solution. The dip method has been followed for membrane grafting employing 365 nm wavelength UV-lamp. The significant factors were optimized using a central composite design of orthogonal type. The nanofiltration membrane performance has been studied using humic acid model solution 15 mg/L at a pH value 7. Pure water permeation flux, permeate flux when using humic acid feed solution, rejection factor and irreversible membrane fouling parameters have been determined. The nanofiltration performance index and the recoverable flux ratio have been considered as responses. The quadratic models between each response and the independent parameters were developed and the response surface models were tested with analysis of variance (ANOVA). By applying the desirability function approach maximal output responses have been predicted and confirmed experimentally. The obtained optimal point was located in the valid region and the experimental confirmation tests were conducted showing a good accordance between the predicted optimal points and the experimental ones. The optimum operating conditions determined were a monomer concentration of 5.13 g/L, UV-intensity of 16.57 × 10 4 mW/m 2 and UV-irradiation time of 37.9 s. Under these optimal conditions maximum nanofiltration performance index, 84.88 L/m 2 h and recoverable flux ratio 88.14% have been achieved. These values are the highest compared to all experimental data carried out within the overall region of experimentation. The optimum NVP UV-grafted membrane exhibits low humic acid fouling tendency than the unmodified membrane.

Steady state modeling of concentration polarization including adsorption during nanofiltration of dye solution

Steady state modeling of nanofiltration of a dye (eosin as model dye) solution was carried out. The model was based on simultaneous solution of solution-diffusion model, film theory and osmotic pressure model. The osmotic pressure model was modified by incorporating adsorption of dyes onto the membrane surface. The model parameters were estimated by comparing the calculated and experimental data of permeate flux and permeate concentration. It was observed that although membrane hydraulic resistance was the dominant one, adsorption resistance becomes more significant with increase in feed dye concentration and transmembrane pressure drop and decrease in crossflow velocity. For example, for eosin feed concentration of 0.2 kg/m 3 and crossflow velocity of 0.46 m/s and transmembrane pressure of 828 kPa, the resistance offered by adsorbed solutes was found to be as high as 21% of the total resistance. The combined model successfully simulates the system performance in terms of permeate flux and permeate concentration.

Implementation of the DSPM model using a commercial finite element system

A solution procedure based on the use of the finite element method (FEM) was developed to solve the Donnan steric-partioning pore model (DSPM) for a nanofiltration membrane coupled with a boundary layer. The numerical solution of nanofiltration models like DSPM is usually carried out by combining an integration method like Runge-Kutta with an iterative procedure that starts from guessed permeate concentrations values. However, this approach may have problems of lack of convergence. As an alternative procedure, a finite element system is used to easily implement the transport equation for the membrane and the boundary layer with Donnan-steric conditions in both membrane sides. To test the solution method, an analytical solution was developed for the transport of an uncharged solute across a membrane with boundary layer. Afterwards, the method was applied to the calculation of binary and ternary ionic systems and its performance was compared with that obtained with the classical iterative method. The developed methodology benefits from the accuracy of FEM and the representation and analysis capabilities of the software used.

Process modeling of brackish and seawater nanofiltration

We demonstrate that the multi-scale nanofiltration (NF) process software, NanoFlux, that we are developing can be used to perform reliable desalination plant modeling for highly concentrated brine and seawater feeds in real-world situations.

Removal of potassium chloride from ion-exchanged solution containing potassium clavulanate by diafiltration with nanomembrane and its modeling

When an ion-exchange chromatography process is employed for the recovery of potassium clavulanate (KCA) from fermentation broth, the resulting KCA solution usually contains a large amount of KCl due to the use of a concentrated elution buffer. In this study, nanofiltration (NF) with NF200 membrane has been carried out in a diafiltration (DF) mode to remove KCl from the ion-exchanged KCA solution, and a multistage version NF model has been proposed to represent this process. In this model, the effect of temperature on clavulanate degradation during the filtration has been incorporated. For the determination of model parameters associated with NF and clavulanate degradation, separate series of experiments at different concentrations, pressures and temperatures were performed. The clavulanate rejection could be assumed to be constant with no loss of modeling accuracy based on the experimental data. The chloride rejection was represented as a function of its concentration simply by nonlinear fitting. For the estimation of solution flux, the reflection coefficient and effective volume charge density were calculated by using the Speigler–Kedem model together with the Teorell–Meyer–Sievers model. Model prediction of clavulanate and chloride concentration profiles was in good agreement with the experimental data. It was also demonstrated that KCl could be removed effectively by NF in a DF mode.