Solution-diffusion Model Research Articles

Modeling, control, and dynamic performance analysis of a reverse osmosis desalination plant integrated within hybrid energy systems

An RO (reverse osmosis) desalination plant is proposed as an effective, FLR (flexible load resource) to be integrated into HES (hybrid energy systems) to support various types of ancillary services to the electric grid, under variable operating conditions. To study the dynamic analysis of such system, special attention is given here to the detailed dynamic modeling and control design of RO desalination process that employs a spiral-wound membrane module. In particular, the solution-diffusion model modified with the concentration polarization theory is applied to predict RO performance over a large range of operating conditions. Simulation results involving several case studies suggest that an RO desalination plant can provide operational flexibility to participate in energy management at the utility scale by dynamically optimizing the use of excess electrical energy. The incorporation of additional commodity (fresh water) produced from a FLR allows a broader range of HES operations for maximizing overall system performance and profitability.

Steady three dimensional flow and mass transfer analyses for brackish water desalination by reverse osmosis membranes

Reverse osmosis has been emerged as one of the most used technologies to desalinate water. Present study investigates steady three dimensional flows and mass transfer in the feed channel for a brackish water desalination process by using reverse osmosis membranes. Flow and the mass transfer in the feed channel are governed by Navier–Stokes and mass transport equations. The channel containing cylindrical shaped spacers is bounded by membranes. Computational fluid dynamics simulations are conducted for the range of the Reynolds number 100⩽Re⩽800. The laminar flow model is employed when Re=100 while SST k–ω turbulence model is employed when Re⩾400. Membranes are treated as a functional surface where water flux is determined from local concentration and pressure by employing the solution-diffusion model of the reverse osmosis. The influence of three dimensional flow structures on the concentration polarization and the potential fouling over the membrane surface is discussed. It is shown that high water flux regions and low concentration regions coincide with low wall shear regions. The high intensity concentration polarization sites correlates directly with the high potential fouling sites. Spacers enhance the membrane performance and they help to alleviate concentration polarization.

Air-jet atomization for preparation of lipid nanoparticles: Dependence of size on solute concentration

Engineering nanoparticles for applications such as drug delivery, needs understanding of dependence of particle size on process and precursor parameters. The size of nanoparticles prepared through the aerosol route using solution droplet drying technique is traditionally governed by a 1/3rd scaling law between dry particle diameter and precursor solute concentration. Here, we experimentally investigate this relationship, for precursor solutions of lipids in organic solvents. Nanoparticles were prepared using air-jet atomization of precursor solutions of stearic acid in organic solvents (acetone, chloroform, methanol and ethanol), in a pulse heat aerosol reactor, at a process temperature of 50°C. The relationship between median mobility diameter of prepared nanoparticles (40–155nm) and solute concentration was governed by a scaling law exponent (SLE) in the range 0.104–0.182. The observed exponents showed significant deviations from the classical 1/3rd law. The experimental investigation indicated an unexpected increase in particle number concentration with increasing solute concentration for all solvents studied. Simulations with a critical super saturation based solute diffusion model and theoretical calculations of size dependent external factors such as coagulation and wall losses during transit, could not explain the deviation in SLE, nor the increased number concentrations. These considerations point to possible effects of solute concentration on the mechanism of droplet formation during the atomization process. A preliminary model based on an area conservation law has been proposed to explain the twin effects of deviation in SLE and increased droplet number concentration with increasing solute concentration. The present study provides empirical data on the relationship between dry particle diameter and solute concentration in the selected lipid-organic solvent systems. Also, it opens avenues for further understanding nanoparticle formation by air-jet atomization.

Monitoring oxygen permeation through polymeric packaging films using a ratiometric luminescent sensor

An optical sensor for oxygen detection based on the immobilization of tris 1,10-phenanthroline ruthenium (Ru(phen)3) into polystyrene (PS) films was employed for monitoring the oxygen permeation through polymeric packaging films.7-Methoxy-4-methylcoumarin was selected as non-sensitive reference to oxygen and dispersed with the Ruthenium complex in order to develop a ratiometric sensor correcting the artifacts induced by operating conditions and improving the robustness of the sensor. The developed ratiometric sensor was successfully employed for the measurement of the oxygen permeation rate in an enclosed atmosphere (package) using polymeric films made of biaxially oriented polypropylene (BOPP) and polydimethyl siloxane (PDMS). It was observed that the oxygen concentration in the enclosed atmosphere increased from 0% to 21% in 3 h in the case of PDMS and from 0% to 3.6% in 24 h for BOPP. The concentration evolvement with time was well predicted by a solution-diffusion model and the final oxygen concentration in the packed atmosphere was confirmed by chromatographic measurements. According to these results, the ratiometric luminescent sensor is suitable for the development of smart packaging films allowing for continuous monitoring of oxygen concentration in-situ.

Experimental determination of nanofiltration models: application to nitrate removal

Nowadays, nitrate contamination of groundwater is a growing problem both in developed and developing countries. Such contamination comes mainly from the intensive use of nitrogen fertilizers in agriculture. Other possible sources of water contamination by nitrates are improper discharges of industrial effluents, the inadequate management of leachate from landfill of municipal solid waste and effluents from intensive farming. The maximum permissible concentration of nitrates in the water for public consumption in the EU countries is 50 mg/L, although the World Health Organization established a value of 25 mg/L to be considered a quality water. This problem of nitrate contamination, widespread in countries of the European Union, is very important in Spain, where there are some regions with a high presence of aquifers with nitrate concentrations significantly higher than the established limits. Among the possible treatments for nitrate removal from contaminated waters, nanofiltration (NF) is a technically proven process that eliminates nitrates without causing a significant imbalance in the rest of dissolved salts. In this work, the removal of nitrates from water using a commercial NF membrane is studied. Synthetic feeds with levels of nitrate concentration higher than the ones usually found in contaminated aquifers have been considered. On the other hand, the experimental results have been fitted to the solution-diffusion model, having found mathematical expressions that can be used to predict membrane performance for feed concentrations higher than 100 mg/L. The model considers the concentration on the surface of the membrane, estimated by the film theory model. It has been proved that concentration polarization cannot be neglected for this application. The tested membrane allows nitrate decontamination of water (concentration below the legal limit) in one pass for values of feed concentration up to 100 mg/L, with a transmembrane pressure of 5 bar.

Steady state and dynamic modeling of spiral wound wastewater reverse osmosis process

Reverse osmosis (RO) is one of the most important technologies used in wastewater treatment plants due to high contaminant rejection and low utilization of energy in comparison to other treatment procedures. For single-component spiral-wound reverse osmosis membrane process, one dimensional steady state and dynamic mathematical models have been developed based on the solution-diffusion model coupled with the concentration polarization mechanism. The model has been validated against reported data for wastewater treatment from literature at steady state conditions. Detailed simulation using the dynamic model has been carried out in order to gain deeper insight of the process. The effect of feed flow rate, pressure, temperature and concentration of pollutants on the performance of the process measured in terms of salt rejection, recovery ratio and permeate flux has been investigated.

Mass transfer and transient response time of a split-feed nanofiltration pilot unit

The transient response of a center-port nanofiltration membrane process was evaluated using a step-input dose of a sodium chloride solution. The pilot was configured as a two-stage, split-feed, center-port, 7:2 pressure vessel array process, where the feed water is fed to both ends of six-element pressure vessels, and permeate and concentrate streams are collected after only three membrane elements. The transient response was described as a log-logistic system with a maximum delay time of 285 s for an 85% water recovery and 267 gallon per minute feed flowrate. The log-logistic model was shown to be >98% accurate in predicting the transient response of the permeate streams. When compared with a first-order nonlinear regression model, there was no difference in the predictability of transient response when using the log-logistic model in first-stage and second-stage membrane processes. However, the log-logistic model was found to be more predictive in describing third-stage transient response by a factor of 236 over a first-order method. Furthermore, the homogeneous solution diffusion model was shown to effectively predict the permeate concentration for any transient permeate perturbation.

Charged Polymer Membranes for Environmental/Energy Applications.

Ion exchange membranes are used in various membrane-based processes (e.g., electrodialysis, fuel cells). Charged solute transport is largely governed by the charged groups on the polymer backbone. In this review, fundamental relationships describing salt permeability and ionic conductivity, as well as water permeability, in charged polymers are developed within the framework of the Nernst-Planck and solution-diffusion models. The influence of fixed charge groups and polymer structure on water sorption and diffusion is discussed. Current understanding of ion partitioning in charged polymers, focusing on the use of thermodynamic models (i.e., Donnan theory) to describe such phenomena, is summarized. Ion diffusivity data from the literature are interpreted using a model developed by Mackie and Meares to assess relative and absolute effects of the polymer and fixed charge groups on ion diffusivity. Furthermore, membrane requirements for several important technologies are listed. Knowledge gaps and opportunities for fundamental research are also discussed.

Deviations from Electroneutrality in Membrane Barrier Layers: A Possible Mechanism Underlying High Salt Rejections.

Reverse osmosis and nanofiltration (NF) employ composite membranes whose ultrathin barrier layers are significantly more permeable to water than to salts. Although solution-diffusion models of salt transport through barrier layers typically assume ubiquitous electroneutrality, in the case of ultrathin selective skins and low ion partition coefficients, space-charge regions may occupy a significant fraction of the membrane barrier layer. This work investigates the implications of these deviations from electroneutrality on salt transport. Both immobile external surface charge and unequal cation and anion solvation energies in the barrier layer lead to regions with excess mobile charge, and the size of these regions increases with decreasing values of either feed concentrations or ion partition coefficients. Moreover, the low concentration of the more excluded ion in the space-charge region can greatly increase resistance to salt transport to enhance salt rejection during NF. These effects are especially pronounced for membranes with a fixed external surface charge density whose sign is the same as that of the more excluded ion in a salt. Because of the space-charge regions, the barrier-layer resistance to salt transport initially rises rapidly with increasing barrier thickness and then plateaus or even declines within a certain thickness range. This trend in resistance implies that thin, defect-free barrier layers will exhibit higher salt rejections than thicker layers during NF at a fixed transmembrane pressure. Deviations from electroneutrality are consistent with both changes in NF salt rejections that occur upon changing the sign of the membrane fixed external surface charge, and CaCl2 rejections that in some cases may first decrease, then increase and then decrease again with increasing CaCl2 concentrations in NF feed solutions.

Hollow fiber type PRO module and its characteristics

Seawater desalination reverse osmosis, SWRO, is expected to be a promising process to solve the problem of water scarcity. However, higher cost-effectiveness and less energy consumption are required for SWRO plants. Forward osmosis, FO processes using the comparable permselective membranes same as RO have gained renewed interest in recent years, and they might become a solution for the most challenging problem of water and energy scarcity. This FO process is expected to have capability of applying energy-saving seawater desalination and power generation by Pressure Retarded Osmosis, PRO. Especially, the PRO technology has drawn attention as a process that could recover energy from the salinity difference between the concentrated brine from SWRO plant and pure water and reduce energy consumption of SWRO plant.A Cellulose triacetate (CTA) hollow fiber type PRO module has been developed and PRO probabilities have been investigated by operating at a prototype PRO plant. The PRO module has characteristics similar to RO module such as high selectivity, chlorine resistance and sufficient pressure resistance. A CTA hollow fiber type PRO membrane module can be expected to have superior fouling resistance compared to a polyamide PRO membrane module from the viewpoint of chemical property such as chlorine resistance.The performance of the PRO module was investigated and analyzed by a hollow fiber type FO module analytical model. The investigation has found that this analytical model based on solution–diffusion model was applicable to the CTA hollow fiber type PRO module.The PRO module configuration and operating condition are expected to be optimized more effectively by this analytical model in the future.

Separation of Peptides and Interaction with Forward Osmosis Biomimetic Membranes: A Solution Diffusion Model

Recently, a membrane based technique, forward osmosis (FO), has gained interest with respect to the separation and purification of biomolecules. Forward osmosis relies on concentration gradients to draw water across the membrane and is as such a gentle technique compared to the traditional pressure driven membrane processes. The challenge within FO is to operate at a high water flux while maintaining a high rejection and low reverse flux of salt that may otherwise interfere with the biomolecules. By adding water-transporting aquaporin protein channels to the membrane matrix to create biomimetic membranes, selective transport of water is possible. These kinds of membranes could as such be ideal for separation of biomolecules.In this study, a biomimetic forward osmosis membrane was tested for the separation of two peptides (416.48 Da and 691.71 Da). The membrane was found to exhibit high, but not complete, rejection rates of both peptides (>98%). It is interesting that even relatively large molecules are able to pass the otherwise dense active layer of the forward osmosis membrane. Therefore, to further understand the transport mechanisms underlying the filtration process, a custom made cell was constructed and used to model the process with filtration models. It was found that the filtration process could be modeled using the solution diffusion approach, with the diffusion coefficient being related to the radius of gyration of the peptides.

Process engineering optimization of nanofiltration unit for the treatment of textile plant effluent in view of solution diffusion model

A nanofiltration (NF) based separation process is used to treat the effluent from a textile plant to allow for water reuse and fulfill environmental standards. The wastewater effluent contains reactive black (RB5)- and disperse (DR60) dyes. A NF-unit model E2 series with HL 2521 TF spiral wound module was used to carry out experiments. 90 & 93% color removal and COD reduction for RB5 and 98 & 95% for DR60 were achieved. A parametric study of the separation process is undertaken to characterize the effects of the operating variables, e.g., trans-membrane pressure, dye/salt concentration in the feed, temperature, and cross flow velocity. The solution diffusion model was used to develop power correlations to calculate the permeate side solute mass transfer coefficient as a function of effective cross-flow Reynolds number. In contrast to the commonly assumed constant hydraulic solvent permeability, a non-linear relationship was developed over the applied trans-membrane net driving pressure. The latter correlates exponentially with salt permeability for both dyes. The effects of feed salt-content on solute mass transfer coefficient, water and salt permeability, concentration polarization, dye hydrophobicity and ionic strength were studied. Results were used to assess engineering specifications of a commercial size NF-plant (500m3/d capacity).

Designing Better Membrane Modules Using CFD

Abstract In the last decades, a large number of studies have been carried out on the utilization of membranes in separation processes. However, most of these studies deal with material properties, experimental investigations and process modeling. Only quite a few authors utilized computational fluid dynamics (CFD) to analyze the flow and mass transfer in membrane modules. Using CFD it is possible to obtain spatially resolved information on the behavior of membrane modules, allowing for the investigation of geometric effects on the performance of the module. This includes e. g. the positioning of the permeate outlets, the flow alignment (co- and/or counter-current), the use of spacers and other mixing promoters and also the subject of concentration polarization close to the membrane surface. In our present study we made use of OpenFOAM®, which is a free open sourced CFD toolbox. The toolbox enables for introducing new solver code, membraneFoam, based on the standard multicomponent solver reactingFoam. In membraneFoam suitable source and sink terms have been added to account for trans-membrane flux – in this case based on the solution-diffusion model for glassy polymer gas permeation membranes. The solver has been preliminary validated using literature data obtained from a process simulation code. In a first stage of the research work the positioning of the permeate outlet and the flow alignment have been investigated for a hollow fiber gas permeation module. By adjusting the position of the permeate outlet the shell side flow can be co-current, counter-current or mixed type relative to the retentate flow inside the fibers. Since this influences the driving force for the trans-membrane flux, effects on the module performance are expected which have been analyzed using the described membraneFoam CFD approach.

Concentration of Polyphenolic Compounds in Blackberry (Rubus AdenotrichosSchltdl.) Juice by Nanofiltration

Nanofiltration membranes with molecular weight cut-off around 200 Da were evaluated to concentrate anthocyanins and ellagitannins in a blackberry juice. Temperature was 30°C and cross-flow velocity 0.3 m/s. Transmembrane pressures varied from 0.5 to 3 MPa. At volumetric reduction ratio (VRR) of 1, higher transmembrane pressures caused an increase of permeate flux and of retention of total anthocyanins (>94%) and total soluble solids (44–97%). Every membrane presented 100% of total ellagitannin retention. Results were represented using the solution-diffusion model. NF270 membrane at 3 MPa showed the highest potential for concentration of blackberry's main polyphenolic compounds (highest permeate flux and solute retention). Nevertheless, a simulated increase of VRR showed that permeate flux declined as the concentration of the feed solution increased. NF270 membrane may also be of interest to deacidify the juice, since at high pressures, sugars were completely retained and retention of acids was under 90%. (Resume d'auteur)

Removal of Dilute Benzene in Water through Ionic Liquid/Poly(Vinyl Chloride) Membranes by Pervaporation

This paper focuses on the effects of the addition of an ionic liquid, 1-Allyl-3-butylimidazilium bis(trifluoromethane sulfonyl)imide ([ABIM]TFSI), which has a high affinity for benzene, into the poly(vinyl chloride) (PVC) membrane on the pervaporation characteristics of the removal of benzene from aqueous solutions of dilute benzene. When aqueous solutions of 100～500 ppm benzene were permeated through the [ABIM]TFSI)/PVC membranes, they showed a high benzene/water selectivity and permeability of these membranes was enhanced with increasing [ABIM]TFSI content significantly. These pervaporation characteristics are discussed from the viewpoint of chemical and physical structure of [ABIM]TFSI)/PVC membranes in detail. The mechanism of permeation and separation was analyzed by the solution-diffusion model.

Economic Evaluation of a Hybrid Desalination System Combining Forward and Reverse Osmosis

This study seeks to evaluate the performance and economic feasibility of the forward osmosis (FO)–reverse osmosis (RO) hybrid process; to propose a guideline by which this hybrid process might be more price-competitive in the field. A solution-diffusion model modified with film theory was applied to analyze the effects of concentration polarization, water, and salt transport coefficient on flux, recovery, seawater concentration, and treated wastewater of the FO process of an FO-RO hybrid system. A simple cost model was applied to analyze the effects of flux; recovery of the FO process; energy; and membrane cost on the FO-RO hybrid process. The simulation results showed that the water transport coefficient and internal concentration polarization resistance are very important factors that affect performance in the FO process; however; the effect of the salt transport coefficient does not seem to be large. It was also found that the flux and recovery of the FO process, the FO membrane, and the electricity cost are very important factors that influence the water cost of an FO-RO hybrid system. This hybrid system can be price-competitive with RO systems when its recovery rate is very high, the flux and the membrane cost of the FO are similar to those of the RO, and the electricity cost is expensive. The most important thing in commercializing the FO process is enhancing performance (e.g.; flux and the recovery of FO membranes).

Effective permeability of binary mixture of carbon dioxide and methane and pre-dried raw biogas in supported ionic liquid membranes

Abstract The influence of the temperature and stage cut on permeation of CO 2 and CH 4 through two different supported ionic liquid membranes were studied. The measurements were performed with binary mixture of CH 4 and CO 2 and with real pre-dried biogas collected in sewage plant. The influence of temperature on permeability followed the Arrhenius behavior in agreement with solution diffusion model of transport. The influence of stage cut was also very small, what helped to confirm that the membrane was operated under optimal conditions. The results obtained with real pre-dried biogas were very close to those obtained with the binary mixture. This was caused by the fact that the amount of trace compounds present in real pre-dried biogas was very small (less than 1 vol.%). The results showed that supported ionic liquid membranes (SILMs) can be used for biogas upgrading. It can be also concluded that the use of model mixture instead of real biogas for measurements brings relevant results.

Nanoconfinement and Chemical Structure Effects on Permeation Selectivity of Self-Assembling Graft Copolymers.

Permeation of small molecule solutes through thin films is typically described by the solution-diffusion model, but this model cannot predict the effects of nanostructure due to self-assembly or additives. Other models focusing on diffusion through isolated nanopores indicate that confining permeation to channels slightly larger than the size of the solute can lead to an increased influence of solute-pore wall interactions on permeation rate. In this study, we analyze how differences in polymer nanostructure affect the relative contributions of solute size and polymer-solute interactions on transport rate. We compared the diffusion rates of several small molecules through two polymer thin films: A cross-linked, homogeneous film of poly(ethylene glycol phenyl ether acrylate) (PEGPEA) and a graft copolymer with a poly(vinylidene fluoride-co-chlorotrifluoroethylene) (P(VDF-co-CTFE)) backbone and PEGPEA side chains that self-assemble into continuous ∼1-3 nm PEGPEA domains through which transport occurs. We correlated these rates with the size of each solute and its chemical affinity to PEGPEA, as measured by the difference between their solubility parameters. Diffusion rate through the homogeneous polymer film was controlled by solute size, whereas diffusion rate through the copolymer was strongly controlled by the difference between the solubility parameters. Furthermore, permeation selectivity between two selected molecules was 2.5× higher for the nanostructured copolymer, likely enhanced by the nanoconfinement effects. These initial results indicate that polymer self-assembly is a promising tool for designing polymeric membranes that can differentiate between solutes of similar size but differing chemical structures.

Numerical analysis of dialysis with chemical reaction at steady state. Irreversible second-order reaction

In the present work, the effect of chemical reaction on the rate of dialysis is analysed. The attention is paid to an irreversible second-order chemical reaction at steady state. A simple scheme, in which component A is transported through the membrane by diffusion and reacts with component B diffusing in the opposite direction, is considered. The analogy between the solution-diffusion model in the membrane transport and mass transfer in gas-liquid systems described by the film theory, both accompanied by chemical reactions, is taken into consideration. A numerical solution scheme is presented and the effect of chemical reaction is evaluated in terms of the enhancement factor for a wide range of parameters. The analysis of limiting cases is carried out and the applicability of the existing approximate solutions for the mass transfer accompanied by chemical reaction is examined. An effort was made to develop new correlations for the enhancement factor in the case that no approximate solution is available in literature.

Aroma scalping characteristics of polybutylene succinate based films

The removal of aroma compounds from packaged food items - aroma scalping – can be primarily controlled by the choice of packaging materials. Although the utilization of biodegradable polymers as packaging materials can greatly contribute to the sustainability of the packaging industry, only limited data on their aroma scalping properties are available. In this work, the aroma scalping characteristics of a series of films made from biodegradable polybutylene succinate (PBS) and polybutylene succinate-co-addipate (PBSA) for common aroma compounds in foods (ethyl acetate, ethyl butyrate, ethyl hexanoate, hexan-1-ol, heptanal and (R)-(+)-limonene) are reported. The aroma scalping characteristics of a film made from poorly biodegradable low density polyethylene (LDPE) are reported for comparison.The aroma scalping characteristics, namely sorption and diffusion coefficients, of the tested aroma compounds were determined at 23 °C by means of sorption microgravimetry, and the permeability coefficients were estimated using the solution-diffusion model. The permeability coefficients for the films made from PBS, PBSA and LDPE were comparable for the more polar compounds: hexan-1-ol, ethyl acetate and ethyl butyrate. Conversely, the permeability coefficients of the less polar aroma compounds (ethyl hexanoate, heptanal and (R)-(+)-limonene) in PBS and PBSA-based films were by one to two orders of magnitude lower than those of the LDPE. In addition, a new mathematical model was proposed for the kinetics of the transient sorption of aroma compounds of low volatility (psat < 1 kPa).