Modelling the separation by nanofiltration of a multi-ionic solution relevant to an industrial process

Removal of Sulfadiazine by Polyamide Nanofiltration Membranes: Measurement, Modeling, and Mechanisms

In this study, a complete steric, electrostatic, and dielectric mass transfer model is applied to investigate the separation mechanism of typical antibiotic sulfadiazine by NF90, NF270, VNF-8040 and TMN20H-400 nanofiltration membranes. FTIR and XPS analysis clearly indicate that the membranes we used possess skin layers containing both amine and carboxylic acid groups that can be distributed in an inhomogeneous fashion, leading to a bipolar fixed charge distribution. We compare the theoretical and experimental rejection rate of the sulfadiazine as a function of the pressure difference across the nanopore for the four polyamide membranes of inhomogeneously charged nanopores. It is shown that the rejection rate of sulfadiazine obtained by the solute transport model has similar qualitative results with that of experiments and follows the sequence: RNF90>RVNF2−8040>RNF270>RTMN20H−400. The physical explanation can be attributed to the influence of the inhomogeneous charge distribution on the electric field that arises spontaneously so as to maintain the electroneutrality within the nanopore.

Retention of atenolol from single and binary aqueous solutions by thin film composite nanofiltration membrane: Transport modeling and pore radius estimation

The performance of a polyamide-based thin-film composite nanofiltration (NF) membrane (NF33) was investigated for the retention of atenolol, a pharmaceutical pollutant, from the single and binary aqueous solutions. The effect of pH, applied pressure, feed flux, initial atenolol (ATN) concentration, and different co-existing salts with varying concentrations were studied to test the performance of the membrane. The removal efficiency of ATN increased with increasing solution pH giving the highest retention (70.9 ± 3.1) at pH 9, which was slightly decreased with the increasing initial ATN concentration but increased with increasing applied pressure and feed flux. As per the uncharged solutes rejection concept, the average pore radius of NF membrane for slit-like and cylindrical pore geometries were, respectively 0.169 ± 0.003 and 0.264 ± 0.009 nm. The Spiegler-Kedem model could predict the performance of NF membrane by retaining ATN over the investigated range of feed flux. The calculated reflection coefficient (σ) was close to unity, demonstrating the convective transport. Addition of CaCl₂ as a co-existing salt into the feed showed promoting effect on ATN retention, and its efficiency was lowered by the addition of NaCl and Na₂SO₄ salts. As per the cost analysis, the total annualized cost of treatment by the NF was found to be 0.53 $/m³.

Modelling nanofiltration of electrolyte solutions

This review critically examines current models for nanofiltration (NF) of electrolyte solutions. We start from linear irreversible thermodynamics, we derive a basic equation set for ion transfer in terms of gradients of ion electrochemical potentials and transmembrane volume flux. These equations are extended to the case of significant differences of thermodynamic forces across the membrane (continuous version of irreversible thermodynamics) and solved in quadratures for single salts and trace ions added to single salts in the case of macroscopically-homogeneous membranes. These solutions reduce to (quasi)analytical expressions in the popular Spiegler-Kedem approximation (composition-independent phenomenological coefficients), which we extend to the case of trace ions. This enables us to identify membrane properties (e.g. ion permeances, ion reflection coefficients, electrokinetic charge density) that control its performance in NF of multi-ion solutions. Further, we specify the phenomenological coefficients of irreversible thermodynamics in terms of ion partitioning, hindrance and diffusion coefficients for the model of straight cylindrical capillaries. The corresponding expressions enable assessment of the applicability of the popular nanopore model of NF. This model (based on the use of macroscopic approaches at nanoscale) leads to a number of trends that have never been observed experimentally. We also show that the use of the Born formula (frequently employed for the description of dielectric exclusion) hardly leads to meaningful values of solvent dielectric constant in membrane pores because this formula disregards the very solvent structure whose changes are supposed to bring about the reduction of dielectric permittivity in nanopores. We conclude that the effect should better be quantified in terms of ion excess solvation energies in the membrane phase. As an alternative to the nanopore description of NF, we review recent work on the development of an advanced engineering model for NF of multi-ion solutions in terms of a solution-diffusion-electromigration mechanism. This model (taking into account spontaneously arising transmembrane electric fields) captures several trends observed experimentally, and the use of trace ions can provide model parameters (ion permeances in the membrane) from experiment. We also consider a recent model (ultrathin barrier layers with deviations from local electroneutrality) that may reproduce observed feed-salt concentration dependences of membrane performance in terms of concentration-independent properties like excess ion solvation energies. Due to its complexity, practical modelling of nanofiltration will probably be performed with advanced engineering models for the foreseeable future. Although mechanistic studies are vital for understanding transport and developing membranes, future simulations in this area will likely need to depart from typical continuum models to provide physical insight. For enhancing the quality of modelling input, it is essential to improve the control of concentration polarization in membrane test cells.

Application of a new dynamic transport model to predict the evolution of performances throughout the nanofiltration of single salt solutions in concentration and diafiltration modes

Although many knowledge models describing the rejection of ionic compounds by nanofiltration membranes are available in literature, they are all used in full recycling mode. Indeed, both permeate and retentate streams are recycled in order to maintain constant concentrations in the feed solution. However, nanofiltration of real effluents is implemented either in concentration or diafiltration modes, for which the permeate stream is collected. In these conditions, concentrations progressively evolve during filtration and classical models fail to predict performances. In this paper, an improvement of the so called "Donnan Steric Pore Model", which includes both volume and concentration variations over time is proposed. This dynamic model is used here to predict the evolution of volumes and concentrations in both permeate and retentate streams during the filtration of salt solutions. This model was found to predict accurately the filtration performances with various salts whether the filtration is performed in concentration or diafiltration modes. The parameters of the usual model can be easily assessed from full batch experiments before being used in the dynamic version. Nevertheless, it is also highlighted that the variation of the membrane charge due to the evolution of feed concentration over time has to be taken into account in the model through the use of adsorption isotherms.

High Total Dissolved Solids Water Treatment by Charged Nanofiltration Membranes Relating to Power Plant Applications

Selective desalination through nanofiltration (NF) is of great interest for many industrial applications including reuse of power plant scrubber wastewater and treatment of water containing high concentrations of TDS (total dissolved solids). This work seeks to understand the effect ion interactions at the membrane interface have on rejection and flux performance of charged NF membranes. NF membranes were also effective for low energy desalination of scrubber wastewater from Georgia Power Plant Bowen, composed primarily of Ca²⁺, Mg²⁺, Cl^-, and SO₄ ^2-. As NF membranes have the capability for selective separations, 80% water recovery was achieved experimentally while maintaining an overall rejection of over 60% for Ca²⁺ and Cl^-. The occurrence of CaSO₄ precipitation at high water recovery was observed. The effect of precipitation on osmotic pressure and the effect of Cl^- counterions on increasing gypsum solubility were explored for water recovery operation. This work expands on a previous work on the topics of desalination of multi-ionic solutions by incorporating the use of large scale membrane modules (0.59 m²) with several synthetic solutions as well as actual scrubber water containing precipitating elements, Ca²⁺ and SO₄ ^2-. It was observed that the spiral wound membrane modules maintained a stable water permeability over the 144 day course of tests.

Predicting the Rejection of Major Seawater Ions by Spiral-Wound Nanofiltration Membranes

Seawater nanofiltration (SWNF) generates a softened permeate stream and a retentate stream in which the multivalent ions accumulate, offering opportunities for practical utilization of both streams. This study presents an approach to simulation of SWNF including all major seawater ions (Na(+), Cl(-), Ca(2+), Mg(2+), and SO4(2-)) based on the Nernst-Planck equation, and uses it for permeate and retentate streams composition prediction. The number of degrees of freedom in the system was reduced by assuming a very high ionic permeability for Na(+), which only weakly affected the other parameters in the system. Two alternatives were examined to analyze the importance of concentration dependence of ion permeabilities: The assumption of constant ion permeabilities resulted in a reasonable fit with experimental data. However, for the permeate composition the overall fit was significantly improved (P < 0.0001) when the permeabilities of Ca(2+) and Mg(2+) were allowed to depend on the ratio of their total concentration to Na(+). This type of dependence emphasizes the strong interaction of divalent ions with the membrane and its effect on the membrane fixed charge through screening or charge reversal. When this effect was included, model predictions closely matched the experimental results obtained, corroborating the phenomenological approach proposed in this study.

Theoretical investigation of the ionic selectivity of polyelectrolyte multilayer membranes in nanofiltration

Polyelectrolyte multilayer membranes have proven to be promising materials for ion nanofiltration. In this work, we implement a continuum mesoscopic transport model developed in previous works (Szymczyk, A.; Zhu, H.; Balannec, B. Langmuir 2010, 26, 1214; Szymczyk, A.; Zhu, H.; Balannec, B. J. Phys. Chem. B 2010, 114, 10143) to investigate the pressure-driven transport of electrolyte mixtures through this kind of membrane. The model accounts for an inhomogeneous distribution of the fixed charge through an arbitrary number of polyelectrolyte bilayers. We show that accounting for the multiple bipolar charge distribution resulting from the layer-by-layer assembly of polyelectrolytes with opposite charge is responsible for the increase in the Na(+)/Mg(2+) selectivity reported experimentally with respect to conventional nanofiltration membranes. The model also allows the rationalizing of the seemingly contradictory experimental results reported in the literature (i.e., the increase or decrease in the selectivity with the number of bilayers or the existence of an optimum number of bilayers). It is shown, however, that the nonmonotonous variation of the ionic selectivity does not originate from the multibipolar distribution of the fixed charge through polyelectrolyte multilayer membranes but from the existence of an optimum skin layer thickness.

Determining the dielectric constant inside pores of nanofiltration membranes from membrane potential measurements

The membrane potential technique was applied to a nanofiltration polyamide membrane to determine its mean pore radius and the dielectric constant of electrolyte solutions inside pores. To our knowledge, this is the first attempt to assess these features from membrane potential measurements. Membrane potential data were analyzed by means of the SEDE (steric electric and dielectric exclusion) transport model. Experiments were conducted with single-salt solutions of NaCl and CaCl(2) and mixed-salt solutions of NaCl and CaCl(2) at various concentrations. It was shown that the pore-size values deduced from the high-concentration limit of the membrane potential measured with the two single-salt solutions are in good agreement. With this parameter being known, the membrane potential measured at high salt concentration with electrolyte mixtures was further used to compute the dielectric constant inside pores. The latter was found to be smaller than its bulk value and to decrease when sodium ions were replaced by calcium ions.

Interpretation of electrokinetic measurements with porous films: role of electric conductance and streaming current within porous structure

It is shown that in tangential electrokinetic measurements with porous films the porous structure makes contribution not only to the cell electric conductance (as demonstrated previously) but also to the observed streaming current. Both of these contributions give rise to dependences of streaming-potential and streaming-current coefficients on the channel height. However, due to the combined contribution of two phenomena, the dependence of streaming-potential coefficient on the channel height may be rather complicated and not allow for simple extrapolation. At the same time, the dependences of streaming-current coefficient and cell electric conductance on the channel height turn out linear and can be easily extrapolated to zero channel heights. This enables one to determine separately the contributions of external surface of porous film and of its porous structure to the streaming current and of the channel and porous structure to the cell electric conductance. This procedure is illustrated by the measurements of tangential electrokinetic phenomena and electric conductance with Millipore mixed-cellulose membrane filters of various average pore sizes (from 0.025 to 5 mum) in the so-called adjustable-gap cell of SurPASS electrokinetic instrument (Anton Paar GmbH). The design of this cell allows for easy and quasi-continuous variation of channel height as well as accurate determination of cell electric conductance, streaming-current coefficient, and channel height (from the cell hydraulic permeability). The quality of linear fits of experimental data has been found to be very good, and thus, the extrapolation procedures were quite reliable and accurate. Zeta-potentials could be determined of both external film and internal pore surfaces. It is demonstrated that the porous structures make considerable contributions to both streaming-current coefficient and cell electric conductance especially in the case of filters with larger pores. It is also found that, rather surprisingly, in filters with smaller pores the reduction in the filter electric conductivity turns out essentially stronger than could be expected proceeding from the filter porosity.