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Hemodialysis is a membrane-based process in which solute transport from the patient’s blood to a rinsing solution (dialysate) occurs by diffusion and ultrafiltration. Devices used in hemodialysis are cylindrical modules filled with hollow-fiber membranes which allow the removal of toxic substances and metabolic wastes from the blood, but inhibit the passage of proteins and cells to the dialysate. A predictive porous-media model of hemodialysis was developed and validated against experimental data. Unlike previous literature models, it requires only basic membrane properties (hydraulic and diffusive permeabilities and reflection coefficients) instead of relying on empirically adjusted global mass transfer coefficients. The necessary porous-media characteristics, notably Darcy permeabilities and shell-side mass transfer coefficients, were obtained by combining theoretical results, CFD predictions for regular fiber arrays and experimental data for commercial modules. A parametric analysis was conducted to assess the influence of different physical quantities and operating conditions. Simulation results for different solutes showed that clearance is affected, in decreasing order of significance, by the membrane’s diffusive permeability (kM), the dialysate flow rate (QD) and the ultrafiltration flow rate (QUF). Doubling kM yields an enhancement in clearance of ~7% for urea and ~20% for B12 vitamin, while halving kM yields a decrease of ~14% for urea and ~32% for B12 vitamin. Changes in the flow rates affect clearance to a lesser extent: a 50% increase of QD yields a clearance increase of ~4−5%, while a ±10 mL/min variation of QUF with respect to the reference value of 10 mL/min leads to a clearance change of ±1.3% for urea and ±3.2% for B12 vitamin. The oncotic pressure in blood has almost no influence. Therefore, possible performance improvements, at least in terms of clearance, strictly rely on the development of a novel generation of membranes characterized by a significantly higher solute diffusive permeability.

Background Electro-membrane processes are gaining great interest in the field of desalination and brine valorisation. However, limiting current phenomena can be a bottleneck for their techno-economic performances. In the present work, the in-out distribution of current density is measured to elucidate the achievement of limiting conditions in real stacks. Materials and Methods A 10-cell pairs Electrodialysis stack (10×40 cm2 active area), equipped with four-segmented electrodes, was tested. NaCl solutions at an inlet concentration ranging from 0.5 to 60 g/l were fed at velocities of either 2 or 4 cm/s in parallel flow. Current density-voltage curves were built by applying equal increasing steps of voltage to each electrode. Outlet concentrations and current efficiency were investigated [1]. Results Figure 1 shows the current density-voltage curves for two couples of inlet concentration. Between the final tract of the ohmic region and the plateau region of the overall stack curve, the current density distribution at the four segments changes markedly. In fact, while at the first electrode the current density continues to increase, at the other three it reaches a maximum and decreases. Thus, as the voltage increases, the current concentrates in a shorter tract of the channel, while it reduces in the remaining part, becoming ineffective for desalination, due to its high resistance. This is caused by the high desalination rate in the first few centimetres, making the dilute conductivity much lower. Moreover, the longer tract of channels at high salinity gradient in the final part of the stack promotes larger diffusion, lowering the current efficiency [2]. Figure 1. Current density-voltage curves for tests at a) Cdil,IN=0.5 g/l and Cconc,IN=30 g/l and b) Cdil,IN=Cconc,IN=1 g/l. Conclusions The attainment of limiting conditions in electrodialysis stacks is strongly related to ohmic phenomena and to the distribution of current density, highlighting its importance in the design of efficient electro-membrane systems. Acknowledgments This work was supported by the SEARcularMINE (Circular Processing of Seawater Brines from Saltworks for Recovery of Valuable Raw Materials) project – Horizon 2020 programme, Grant Agreement no. 869467. The authors are grateful to REDstack B.V. and Fujifilm Manufacturing Europe B.V. for supplying stack and membranes, respectively.

Objectives The study aims to predict 3-D flow and solute concentrations fields both for blood and dialysate and overall performance parameters (such as dialysate pressure drop and clearance) for different hollow-fibre haemodialysis modules. Methods A multiscale approach was used. At small (unit cell)-scale, dialysate flow and mass transfer around straight cylindrical fibres arranged in regular lattices were simulated. At module-scale, hydraulic permeabilities and mass transfer coefficients derived from small-scale simulations were used to define two different porous media representative of blood and dialysate, sharing the same volume and exchanging solute. Simulations involved different module configurations, sharing the same membrane area but differing in geometry and inlet-outlet arrangement. Literature values of solute diffusive permeability for commercial PES membranes were used. Results and discussions For given blood and dialysate flow rates (300 and 450 mL/min, respectively), different module configurations yielded very different dialysate-side flow patterns and pressure drops, moderately different Sherwood numbers but similar values of the clearance. For urea, this ranged between 209 and 235 mL/min in most configurations, indicating that almost all the membrane area was active in most configurations. For a typical commercial geometry, the predicted clearances at different blood flow rates exhibited a satisfactory agreement with experimental measurements (maximum discrepancy ˂2%). Conclusions Using commercial membranes properties, dialysate-side mass transfer resistance is small compared with blood-side and membrane contributions. As membranes with higher diffusive permeability will be developed, the influence of dialysate-side resistance will become larger and an accurate prediction of the dialysate flow field will become more important.

Reverse osmosis (RO) is the most widespread technology to produce drinking water from seawater (SW). However, the integration of different membrane processes offers interesting alternatives. In this work, electromembrane processes were integrated with RO to desalinate real seawater in a pilot plant with 25 m3/day capacity. Electrodialysis (ED, either two-stage or single stage), shortcut reverse electrodialysis (scRED) and assisted reverse electrodialysis (ARED) pre-desalinated seawater before RO with the ED-ED-RO, ED-RO, and scRED-ARED-RO process schemes. Treated wastewater was used as salt sink in the scRED-ARED tests. The performance of the pilot plant can be summarized as follows: water recovery of ~27–51%, productivity of ~7–14 L/(m2 h) in the electromembrane processes and of ⁓19–31 L/(m2 h) in the RO process, energy consumption of 3.5–8.4 kWh/m3. The ED-RO configuration yielded the maximum productivity of the electromembrane step, while the scRED-ARED-RO integration reached the minimum energy consumption. Overall, the energy performance of the pilot plant (especially in the ED-RO and scRED-ARED-RO schemes) was comparable to that of a standalone SWRO system. The field tests demonstrated that the coupling of electromembrane processes with RO is feasible and suggest the possibility to develop alternative and competitive industrial pants for seawater desalination.

Bipolar membrane electrodialysis (BMED) is a technology combining solute and solvent dissociation to produce chemicals. In the recent decades, it has been typically studied for the production of valuable acid and base solutions from salt streams. Although many works have been devoted to the experimental investigation of BMED, only a few efforts have focused on its mathematical modelling. In the present work, a comprehensive process model based on a multi-scale approach with distributed parameters is presented for the first time. Five models related to four different dimensional scales were fully integrated to form a comprehensive tool. The integrated model was developed by using the process simulator gPROMS Model builder and was based on a semi-empirical approach combining high prediction accuracy and low computational demand. Once validated through a wide range of experimental data, the model capability was shown by carrying out a broad sensitivity analysis assessing the performance of the BMED technology for industrial-scale applications. Results showed how the performance of a BMED unit changes with both varying process conditions and the installed membrane area. Particularly, the non-ideal phenomena that reduce the produced NaOH concentration and increase the energy consumption were thoroughly investigated. Finally, this study demonstrated that a Levelized Cost Of Caustic Soda of about 280 € ton-1NaOH can be obtained, thus making this technology a possible candidate for the industrial production of caustic soda from brines in the future.

In the context of renewable energy sources, storage systems have been proposed as a solution to the issues related to fluctuations in the production and consumption of electric power. The EU funded BAoBaB project is aimed at developing the Acid/Base Flow battery (AB-FB), an environment-friendly, cost-competitive, grid-scale battery storage system based on the cyclic coupling of Bipolar Membrane ElectroDialysis (BMED) and its reverse, the Bipolar Membrane Reverse ElectroDialysis (BMRED) (Pärnamäe et al., 2020). Bipolar membranes promote catalytically water dissociation, thus allowing the storage of electric power in the form of acidic and alkaline solutions (pH gradient), obtained from their corresponding salt (charging mode – BMED), which are then recombined to provide electrical power (discharging mode – BMRED). The membranes are key elements for the process performance; however, the energy conversion efficiency is also affected by the operating parameters of the process and the design features of the stack. In this work, we performed a sensitivity analysis by a mathematical multi-scale model previously developed (Culcasi et al., 2020a). The performance of AB-FB systems was predicted, focusing on the Round Trip Efficiency. Results showed that proper design features made the effect of parasitic currents negligible. Moreover, proper operating conditions maximized the RTE up to 66%.

The increasing share of renewables in electric grids nowadays causes a growing daily and seasonal mismatch between electricity generation and demand. In this regard, novel energy storage systems need to be developed, to allow large-scale storage of the excess electricity during low-demand time, and its distribution during peak demand time. Acid–base flow battery (ABFB) is a novel and environmentally friendly technology based on the reversible water dissociation by bipolar membranes, and it stores electricity in the form of chemical energy in acid and base solutions. The technology has already been demonstrated at the laboratory scale, and the experimental testing of the first 1 kW pilot plant is currently ongoing. This work aims to describe the current development and the perspectives of the ABFB technology. In particular, we discuss the main technical challenges related to the development of battery components (membranes, electrolyte solutions, and stack design), as well as simulated scenarios, to demonstrate the technology at the kW–MW scale. Finally, we present an economic analysis for a first 100 kW commercial unit and suggest future directions for further technology scale-up and commercial deployment.

Reverse Electrodialysis (RED) extracts electrical energy from the salinity difference between two solutions using selective ion exchange membranes. In RED, conditions yielding a large net power density (NPD) are generally desired, due to the still large cost of the membranes. NPD depends on a large number of physical and geometric parameters. Some of these, for example the inlet concentrations of concentrate and diluate, can be regarded as “scenario” variables, imposed by external constraints (e.g., availability) or chosen by different criteria than NPD maximization. Others, namely the thicknesses HCONC, HDIL and the velocities UCONC, UDIL in the concentrate and diluate channels, can be regarded as free design parameters and can be chosen so as to maximize NPD. In the present study, a simplified model of a RED stack was coupled with an optimization algorithm in order to determine the conditions of maximum NPD in the space of the variables HCONC, HDIL,UCONC, UDIL for different sets of “scenario” variables. The study shows that an optimal choice of the free design parameters for any given scenario, as opposed to the adoption of standard fixed values for the same parameters, may provide significant improvements in NPD.

The problem of mass transfer in ducts with transpiring walls is analysed: the concepts of “solvent” and “solute” fluxes are introduced, all possible sign combinations for these fluxes are considered, and relevant examples from membrane processes such as electrodialysis, reverse osmosis and filtration are identified. Besides the dimensionless numbers commonly defined in studying flow and mass transfer problems, new dimensionless quantities appropriate to transpiration problems are introduced, and their limiting values, associated with “drying”, “desalting” and “saturation” conditions, are identified. A simple model predicting the Sherwood number Sh under all possible flux sign combinations is derived from the single simplifying assumption that concentration profiles remain self-similar (so that the Sherwood number based on diffusion only remains unchanged) also under transpiration conditions. The simple model provides not only local values of Sh, but also its axial profiles. Predictions are validated against fully predictive CFD results, not based on the above simplifying assumption, and a good agreement is demonstrated provided the transpiration rate complies with certain limitations, depending on the Schmidt number.

This Special Issue of Membranes journal focuses on electromembrane processes and is motivated by the increasing interest of the scientific community towards their characterization by experiments and modelling for several applications [...]

Flow and heat or mass transfer in channels provided with woven spacers made up of mutually orthogonal filaments were studied by Computational Fluid Dynamics. The problem addressed was the combined effect of the parameters that characterize the process: pitch to height ratio P/H (2, 3 and 4), flow attack angle θ (0, 7, 15, 20, 30, 40 and 45°) and Reynolds number Re (from ~1 to ~4000). The Prandtl number was 4.33, representative of water at ~40°C, while the Schmidt number was 600, representative of NaCl solutions. Simulations were performed by the finite volume code Ansys CFX™ 18.1 using very fine grids of ~6 to ~14 million volumes. For Re > ~400, the SST turbulence model was used to predict flow and heat transfer; no simulations of mass transfer were performed in the turbulent regime because the resolution of the diffusive sublayer would have required a prohibitive number of grid points. Results were validated against experimental data, including results obtained by Liquid Crystal Thermography and Digital Image Processing. The flow attack angle θ = 45° was the most effective for mixing (higher Nusselt number, Nu, and Sherwood number, Sh) and caused lower values of friction coefficient (f). In the range investigated, increasing the pitch to height ratio P/H caused Nu, Sh and f all to decrease. Therefore, the highest values of Sh and Nu were provided by the configuration P/H = 2, θ = 45°. Compared with non-woven spacers, woven spacers provided a better mixing, especially at intermediate values of Re, but at the expenses of higher pressure drops.

Numerical simulations were conducted for fully developed, steady-state flow with mass transfer in fiber bundles arranged in regular lattices. The porosity was 0.5 and the Schmidt number 500. Several combinations of axial flow, transverse flow and flow attack angles in the cross-section plane were considered. The axial and transverse Reynolds numbers Rez , ReT were made to vary from 10(^−4) to 10(^2). Concentration boundary conditions, and the definition of an average Sherwood number, were addressed. Results for the hydraulic permeability were compared with the literature. Both hexagonal and square lattices were found to be hydraulically almost isotropic up to transverse flow Reynolds numbers ReT of ~10, while they behaved anisotropically in regard to mass transfer even at ReT as low as 0.1. A larger anisotropy was exhibited by the square lattice. In mixed (axial + transverse) flow, the transverse friction coefficient was almost completely unaffected by the simultaneous presence of axial flow, while the axial friction coefficient (and thus the axial pressure loss) increased with the transverse Reynolds number for ReT > ~5-10. In regard to mass transfer, the Sherwood number settled in all cases to the higher between the Sherwood number in purely transverse flow and that in purely axial flow.

This paper presents a comprehensive review of studies on electrodialysis (ED) applications in wastewater treatment, outlining the current status and the future prospect. ED is a membrane process of separation under the action of an electric field, where ions are selectively transported across ion-exchange membranes. ED of both conventional or unconventional fashion has been tested to treat several waste or spent aqueous solutions, including effluents from various industrial processes, municipal wastewater or salt water treatment plants, and animal farms. Properties such as selectivity, high separation efficiency, and chemical-free treatment make ED methods adequate for desalination and other treatments with significant environmental benefits. ED technologies can be used in operations of concentration, dilution, desalination, regeneration, and valorisation to reclaim wastewater and recover water and/or other products, e.g., heavy metal ions, salts, acids/bases, nutrients, and organics, or electrical energy. Intense research activity has been directed towards developing enhanced or novel systems, showing that zero or minimal liquid discharge approaches can be techno-economically affordable and competitive. Despite few real plants having been installed, recent developments are opening new routes for the large-scale use of ED techniques in a plethora of treatment processes for wastewater.

The theoretical energy density extractable from acidic and alkaline solutions is higher than 20 kWh m−3 of single solution when mixing 1 M concentrated streams. Therefore, acidic and alkaline industrial wastewater have a huge potential for the recovery of energy. To this purpose, bipolar membrane reverse electrodialysis (BMRED) is an interesting, yet poorly studied technology for the conversion of the mixing entropy of solutions at different pH into electricity. Although it shows promising performance, only few works have been presented in the literature so far, and no comprehensive models have been developed yet. This work presents a mathematical multi-scale model based on a semi-empirical approach. The model was validated against experimental data and was applied over a variety of operating conditions, showing that it may represent an effective tool for the prediction of the BMRED performance. A sensitivity analysis was performed in two different scenarios, i.e. (i) a reference case and (ii) an improved case with high-performance membrane properties. A Net Power Density of ~15 W m−2 was predicted in the reference scenario with 1 M HCl and NaOH solutions, but it increased significantly by simulating high-performance membranes. A simulated scheme for an industrial application yielded an energy density of ~50 kWh m−3 (of acid solution) with an energy efficiency of ~80–90% in the improved scenario.

Commercial hemodialyzers are hollow-fiber cylindrical modules with dimensions and inlet–outlet configurations dictated mostly by practice. However, alternative configurations are possible, and one may ask how they would behave in terms of performance. In principle, it would be possible to depart from the standard counter-flow design, while still keeping high clearance values, thanks to the increase in the shell-side Sherwood number (Sh) due to the cross-flow. To elucidate these aspects, a previously developed computational model was used in which blood and dialysate are treated as flowing through two interpenetrating porous media. Measured Darcy permeabilities and mass transfer coefficients derived from theoretical arguments and CFD simulations conducted at unit-cell scale were used. Blood and dialysate were alternately simulated via an iterative strategy, while appropriate source terms accounted for water and solute exchanges. Several module configurations sharing the same membrane area, but differing in overall geometry and inlet–outlet arrangement, were simulated, including a commercial unit. Although the shell-side Sherwood number increased in almost all the alternative configurations (from 14 to 25 in the best case), none of them outperformed in terms of clearance the commercial one, approaching the latter (257 vs. 255 mL/min) only in the best case. These findings confirmed the effectiveness of the established commercial module design for the currently available membrane properties.

This work presents computational fluid dynamics simulations aimed at characterizing flow and mass/heat transport mechanisms in spacer-filled channels for membrane processes, with particular reference to (reverse) electrodyalisis and membrane distillation.

La Acid/Base Flow Battery (AB-FB) è una batteria innovativa che rappresenta un metodo sostenibile di immagazzinare energia elettrica. Questa batteria può, in linea teorica, garantire una densità di energia pari a 11 kWh/m3 che è un valore maggiore rispetto a quello fornito dalle tecnologie attualmente più utilizzate nel mondo quali quelle che sfruttano l’energia idroelettrica, l’energia osmotica o ancora l’aria compressa. La batteria AB-FB accumula energia sottoforma di gradienti di salinità e di pH. In particolare, essa funziona grazie ad una unità chiamata “stack” al cui interno ospita una serie di canali che permettono il passaggio di soluzioni elettrolitiche a diversi pH e concentrazioni delle specie chimiche. Questi canali sono separati da membrane monopolari e bipolari a scambio ionico. Nello stack sono coinvolti due processi a membrana: l’elettrodialisi con membrane bipolari (ED-BM) e il suo processo inverso ovvero la elettrodialisi inversa con membrane bipolari (RED-BM). Il primo avviene durante la carica e il secondo durante la scarica della batteria. Questo lavoro di ricerca mira a predire le performance di questo dispositivo attraverso la messa a punto di un modello matematico basato su un approccio di tipo multi-scala. Nello specifico, il singolo canale dello stack rappresenta la scala più bassa del modello, nel quale simulazioni di fluidodinamica computazionale permettono di predire le perdite di carico e il fenomeno della polarizzazione di concentrazione lungo il canale. Il livello medio-basso del modello riguarda il cosiddetto “triplet” ossia l’unità ripetitiva dello stack. A questa scala dimensionale vengono calcolati tutti i flussi attraverso la membrana cioè quello migrativo, diffusivo, osmotico ed elettro-osmotico. Alla scala medio-alta, questo modello consente di predire le perdite di carico e le correnti parassite nei collettori e nei distributori dello stack. In particolare viene calcolata l’incidenza delle correnti di corto-circuito ionico (correnti parassite). Infine, la scala più alta del modello include il calcolo delle equazioni di bilancio di materia all’interno dei recipienti esterni e le perdite di carico nei tubi di collegamento dello stack ai recipienti stessi. Tutte le scale del modello sono completamente integrate l’un l’altra in un unico e originale strumento di simulazione che è in grado di predire parametri di performance della batteria come la densità di potenza prodotta oppure il valore di Round Trip Efficiency. Un’analisi di sensitività è stata effettuata variando caratteristiche geometriche come il diametro del distributore e del collettore e condizioni operative come la densità di corrente durante la carica e la scarica in un ampio range di valori. I risultati ottenuti mostrano che le correnti ioniche parassite attraverso i collettori e i distributori possono rappresentare il limite più importante per questa tecnologia. La progettazione della batteria con geometrie e condizioni operative ottimali possono portare alla riduzione dei fenomeni parassiti e a valori di Round Trip Efficiency anche maggiori del 65% rendendo così questa batteria competitiva rispetto alle tecnologie attualmente più utilizzate.

The Acid/Base Flow Battery (AB-FB) is an innovative and sustainable way to store electric energy. It can theoretically guarantee an energy density of about 11 kWh/m3, which is higher than that provided by pumped hydropower, osmotic energy storage and compressed air. The AB-FB stores energy as pH and salinity gradients by employing a stack provided with (i) channels, hosting the solutions at difference pH and concentrations, separated by (ii) monopolar and bipolar ion exchange membranes. Two different membrane processes are involved: the Bipolar Membrane Electrodialysis (ED-BM) as charging step and its opposite, Bipolar Membrane Reverse Electrodialysis (RED-BM) as discharging step. The present work aims at predicting the performance of this AB-FB energy storage device via the development of a mathematical model based on a multi-scale approach. The channel represents the lowest scale of the model where Computational Fluid Dynamic Simulations are adopted to predict pressure drops and polarization phenomena. The middle-low-scale model concerns the triplet (which is the repeating unit of the stack) where all membrane fluxes (i.e. ohmic, diffusive, osmotic, etc.) are calculated. The middle-high-scale is devoted to predicting the pressure losses and the ionic losses (due to ionic short-circuit currents) in the manifolds. The highest scale includes all equations relevant to the connections of the stack with the tanks used to store the solutions. All model-scales are fully integrated, thus representing an original tool able to predict the flow battery performance parameters such as the power density produced and the overall battery round trip efficiency. A sensitivity analysis is performed by letting geometrical features (e.g. manifold size) and operating conditions (e.g. charge and discharge current density) to vary in a wide range of values. Main results show that the parasitic currents in the manifolds may represent the main limit to the present technology among all the detrimental phenomena. Suitable geometries and operating conditions can be adopted to reduce their effect thus leading to round-trip efficiencies higher than 65%.

In the present work, we experimenrtally investigated the effect of different membrane profiles on the LCD, testing also different operating conditions.

L’elettrodialisi (ED) è una promettente tecnologia a membrana utilizzata in diversi campi, ad esempio nella dissalazione delle acque e nell’industria alimentare. L’ED usa un potenziale elettrico per indurre una migrazione selettiva di cationi ed anioni da una soluzione elettrolitica ad un’altra, sfruttando membrane a scambio ionico. Membrane anioniche e cationiche sono alternativamente collocate all’interno di una unità ED. A queste sono solitamente interposti spaziatori che prevengono il contatto tra le membrane e delineano i canali in cui scorrono le soluzioni. L’utilizzo di membrane profilate consente di costruire unità prive di tradizionali spaziatori a rete non conduttivi. In genere, la differenza di pressione tra le due soluzioni (trans-membrane pressure, TMP) in unità ED assume valori modesti o trascurabili (TMP

Reverse electrodialysis (RED) is a blue energy technology for clean and sustainable electricity harvesting from the mixing entropy of salinity gradients. Recently, many efforts have been devoted to improving the performance of RED units by developing new ion-exchange membranes and by reducing the detrimental phenomena affecting the process. Among these sources of “irreversibility”, the shortcut currents (or parasitic currents) flowing through alternative pathways may affect the process efficiency. Although such phenomena occur in several electrochemical processes (e.g. fuel cells, bipolar plate cells and vanadium redox flow batteries), they have received a poor attention in RED units. In this work, a process simulator with distributed parameters was developed and experimentally validated to characterize the shortcut currents and to assess their impact in RED stack performance under different designs and operating conditions. Results showed that shortcut currents can play a crucial role in stacks with a large number of cell pairs when the electrical resistance of the parasitic pathways is relatively low, e.g. configurations with concentrated brines, high resistance membranes, short channels or large manifolds. Future designs of efficient industrial-scale units cannot ignore these aspects. Finally, the model can be easily adapted for the simulation of electrodialysis and other electromembrane processes.

Selectivity, high recovery, and chemical-free operation are strengths of electrodialysis. Different configurations have been proposed for several applications. Effluents from municipal wastewater treatment plants (including sludge and supernatants), desalination plants, and animal farms can be treated for recovering water, nutrients, salts, and acids/bases. Although many applications are technoeconomically feasible and competitive with other zero liquid discharge systems, only a few real plants have been installed. However, the research is currently very active, thus paving the way for a widespread use at large scale in the next future.

Electrodialysis and related processes have huge potential in the treatment of effluents from a variety of industrial processes. They can recover water and other valuable products, including heavy metal ions, acids and bases, nutrients, and organics. In recent years, novel and improved systems have been continuously developed as a result of research in the field, showing that the (near) zero liquid discharge approach can be affordable in several industrial applications. A larger market share is expected in the near future.

Bipolar Membrane Reverse Electrodialysis (BMRED) can be used to produce electricity exploiting acid-base neutralization, thus representing a valuable route in reusing waste streams. The present work investigates the performance of a lab-scale BMRED module under several operating conditions. By feeding the stack with 1 M HCl and NaOH streams, a maximum power density of ~17 W m−2 was obtained at 100 A m−2 with a 10-triplet stack with a flow velocity of 1 cm s−1, while an energy density of ~10 kWh m−3 acid could be extracted by a complete neutralization. Parasitic currents along feed and drain manifolds significantly affected the performance of the stack when equipped with a higher number of triplets. The apparent permselectivity at 1 M acid and base decreased from 93% with the five-triplet stack to 54% with the 38-triplet stack, which exhibited lower values (~35% less) of power density. An important role may be played also by the presence of NaCl in the acidic and alkaline solutions. With a low number of triplets, the added salt had almost negligible effects. However, with a higher number of triplets it led to a reduction of 23.4–45.7% in power density. The risk of membrane delamination is another aspect that can limit the process performance. However, overall, the present results highlight the high potential of BMRED systems as a productive way of neutralizing waste solutions for energy harvesting.

Electrodialysis (ED) has recently gained much attention in the wide field of desalination and water treatment. However, energy consumption and capital costs may impair the process competitiveness. In this regard, limiting current density (LCD) and current efficiency (η) are key performance parameters for optimized ED systems. In this work, an experimental campaign was carried out characterizing the performance of ED stacks when adopting asymmetrically profiled membranes. Current–voltage curves were recorded under different operating conditions mimicking the operation of brackish water or seawater desalination units. Results showed that there was a preferable direction of the electric current relative to the membrane profiles, which provided higher values of LCD and of maximum η. Stacks with Overlapped Crossed Filaments profiled membranes performed better than conventional ED stacks with flat membranes and spacers by increasing the LCD (by ~20% under various operating conditions) and the maximum η (e.g., from ~55–65% to ~70–73% at 0.5 – 60 g/l inlet concentrations of diluate and brine, respectively). The specific energy consumption was significantly reduced (even more than 50%). On the contrary, the investigated pillar-profiled membranes exhibited the worst performances. The present results suggest that well-designed profiled membranes can reduce the costs of desalination via ED.

Membrane-based processes have gained a relevant role in many engineering applications. Much effort has been devoted to thoroughly understand the fundamental phenomena behind them. However, membrane deformation has been taken into consideration only recently, although much evidence has shown its impacts in many applications. This work presents a novel 2-D, multi-scale, semi-empirical process model able to predict the behavior and the performance of Electrodialysis (ED) systems in cross-flow configurations in the presence and absence of local membrane deformations. The model exploits the results and the simulation approaches of previous fluid-structure investigations performed by the authors. Low-scale numerical simulations are coupled with a high-scale model to predict the redistribution of channel height, flow rate, friction coefficient and Sherwood number in ED stacks caused by local membrane deformations. Finally, salt and water fluxes, mass balances and electrochemical quantities are computed to assess the performances of cross-flow ED stacks. Different test cases have been simulated for the desalination of seawater by two-stage ED. Interestingly, membrane deformation is found to reduce, albeit slightly, the energy consumption. More pronounced effects are expected if thinner or less stiff membranes are used.

In the present work, in order to explore such issues on the LCD identification, we performed in-situ measurements with ED units, assessing the influence of operating conditions and validating a purposely implemented process simulator, which was then used for further investigation

The present work describes the development of the first dynamic model for CED

In this work, we developed an advanced model useful for the design of profiled IEMs, based on the coupled simulation of local mechanical deformations and of fluid dynamics and associated mass transport phenomena within deformed channels

The need to reduce energy consumption in seawater reverse osmosis processes has pushed research towards the development of new hybrid systems in which, for example, other membrane processes can be used to pre-treat seawater. Electrodialysis and reverse electrodialysis can act as a dilution step before seawater enters the RO unit, thus leading to an important energy saving in RO. In this work, two coupled models are proposed for the RED-RO and ED-RO system. Each process model was validated before being used for a sensitivity analysis in which the effect of the integration on the cost saving in the overall process was assessed. The analysis was performed by changing (R)ED voltage and RO pressure and considering three different scenarios: a standard scenario, an optimist scenario with a lower membrane cost and a pessimistic scenario with a lower electricity cost and comparing the result with the a standalone RO process. Negative values of “Cost Saving” were found when an excessive dilution step was performed before the RO, while competitive scenarios were found by optimizing the dilution extent, especially for the RED-RO case.

In recent years, water and energy supply issues have boosted a noticeable interest in the scientific community on electromembrane processes such as electrodialysis and reverse electrodialysis. In order to gain an important place in the industrial market, technological challenges on various aspects are involved for the optimization of these processes. In this context, profiled membranes exhibit interesting performances and offer countless geometric alternatives. However, the mechanical behavior of the membranes and its interaction with fluid dynamics has been poorly investigated so far. In membrane-based processes, a trans-membrane pressure (Ptm) between the different solutions flowing through a module may be a design feature or may arise for various reasons, including flow arrangement and differences in physical properties, flow rate or friction coefficient. This leads to local deformations of membranes and channels, affecting flow and mass transfer characteristics, thus causing uneven distributions of flow and mass fluxes, which worsen the process performance. In this work, we developed an integrated model for the numerical simulation of local mechanical deformations and of fluid dynamics and associated mass transport phenomena inside deformed channels. Two diverse profiled membrane types (“overlapped cross filaments”, OCF, and “round pillars”, RP) were simulated under conditions representative of (reverse) electrodialysis and under the assumption of perfectly elastic behaviour. 3-D simulations of a couple of membranes and of the interposed fluid were conducted by the unit cell approach (periodic domain). The Ansys Mechanical 18 (Workbench) and the Ansys CFX 18 software was used. The selected geometries were simulated under Ptm ranging from -0.4 to +0.4 bar, computing expanded and compressed configurations. Then, CFD simulations of the deformed channels were performed, showing significant effects of the deformation on fluid flow and mass transfer. The influence of Ptm was to increase friction under compression conditions (up to ∼2.2-2.5 times) and to reduce it under expansion conditions (but to a lesser extent, i.e. up to ∼50-60%). Overall, compression enhanced mass transfer and expansion reduced it, but with smaller and more complex effects than on friction. The influence of the flow attack angle was negligible for friction, but more significant for mass transfer. In future works the same simulation approach will be adopted in order to compute also the Ohmic resistance in deformed configurations. The simulation results will be implemented in the form of correlations into higher-scale models, in order to study distributions of flow, mass transfer and Ohmic resistance in whole channels. The method proposed can be extended to other membrane applications with minor modifications.

The future energetic supply based on the massive use of renewable sources poses issues linked to fluctuations of power produced and consumed, thus requiring the use of energy storage systems.

Reverse Electrodialysis (RED) harvests electrical energy from a salinity gradient. The maximum obtainable net power density (NPD) depends on many physical and geometric variables. Some have a monotonic (beneficial or detrimental) influence on NPD, and can be regarded as “scenario” variables chosen by criteria other than NPD maximization. Others, namely the thicknesses HCONC, HDIL and the velocities UCONC, UDIL in the concentrate and diluate channels, have contrasting effects, so that the NPD maximum is obtained for some intermediate values of these parameters. A 1-D model of a RED stack was coupled here with an optimization algorithm to determine the conditions of maximum NPD in the space of the variables HCONC, HDIL,UCONC, UDIL for different combinations of the “scenario” variables. The model accounts for entrance effects, property variation, concentration polarization, axial concentration changes, osmotic, electro-osmotic and diffusive fluxes, and can deal with complex channel geometries using Ohmic resistances, friction factors and mass transfer coefficients computed by 3-D simulations.

A new hierarchical model for the electrodialysis (ED) process is presented. The model has been implemented into gPROMs Modelbuilder (PSE), allowing the development of a distributed-parameters simulation tool that combines the effectiveness of a semi-empirical modelling approach to the flexibility of a layered arrangement of modelling scales. Thanks to its structure, the tool makes possible the simulation of many different and complex layouts, requiring only membrane properties as input parameters (e.g. membrane resistance or salt and water permeability). The model has been validated against original experimental data obtained from a lab scale ED test rig. Simulation results concerning a 4-stage treatment of seawater and dynamic batch operations of brackish water desalination are presented, showing how the model can be effectively used for predictive purposes and for providing useful insights on design and optimisation.

In the membrane processes, a trans-membrane pressure (TMP) may arise due to design features or operating conditions. In most applications, stacks for electrodialysis (ED) or reverse electrodialysis (RED) operate at low TMP (&lt, 0.1 bar), however, large stacks with non-parallel flow patterns and/or asymmetric configurations can exhibit higher TMP values, causing membrane deformations and changes in fluid dynamics and transport phenomena. In this work, integrated mechanical and fluid dynamics simulations were performed to investigate the TMP effects on deformation, flow and mass transfer for a profiled membrane-fluid channel system with geometrical and mechanical features and fluid velocities representative of ED/RED conditions. First, a conservatively high value of TMP was assumed, and mechanical simulations were conducted to identify the geometry with the largest pitch to height ratio still able to bear this load without exhibiting a contact between opposite membranes. The selected geometry was then investigated under expansion and compression conditions in a TMP range encompassing most practical applications. Finally, friction and mass transfer coefficients in the deformed channel were predicted by computational fluid dynamics. Significant effects of membrane deformation were observed: friction and mass transfer coefficients increased in the compressed channel, while they decreased (though to a lesser extent) in the expanded channel.

The need for unconventional sources of fresh water is pushing a fast development of desalination technologies, which proved to be able to face and solve the problem of water scarcity in many dry areas of the planet. Membrane desalination technologies are nowadays leading the market and, among these, electrodialysis (ED) plays an important role, especially for brackish water desalination, thanks to its robustness, extreme flexibility and broad range of applications. In fact, many ED-related processes have been presented, based on the use of Ion Exchange Membranes (IEMs), which are significantly boosting the development of ED-related technologies. This paper presents the fundamentals of the ED process and its main developments. An important outlook is given to operational aspects, hydrodynamics and mass transport phenomena, with an extensive review of literature studies focusing on theoretical or experimental characterization of the complex phenomena occurring in electromembrane processes and of proposed strategies for process performance enhancement. An overview of process modelling tools is provided, pointing out capabilities and limitations of the different approaches and their possible application to optimisation analysis and perspective developments of ED technology. Finally, the most recent applications of ED-related processes are presented, highlighting limitations and potentialities in the water and energy industry.

Reverse electrodialysis (RE) is a promising technology for electric power generation from controlled mixing of two differently concentrated salt solutions, where ion-exchange membranes are adopted for the generation of ionic currents within the system. Channel geometry strongly influences fluid flow and thus crucial phenomena such as pressure drop and concentration polarization. Profiled membranes are an alternative to the more commonly adopted net spacers and offer a number of advantages: avoiding the use of non-conductive and relatively expensive materials, reducing hydraulic losses and increasing the active membrane area. In this work, Computational Fluid Dynamic simulations were performed to predict the fluid flow and mass transfer behaviour in channels with profiled membranes for RE applications. In particular, channels equipped with pillars were simulated. The influence of channel geometry on fluid flow and concentration polarization was assessed by means of a parametric analysis for different profile geometries. The unit cell approach along with periodic boundary conditions was adopted to simulate fully developed boundary conditions. Transport equations, valid also for concentrated solutions, were obtained from the rigorous Stefan–Maxwell equation along with the assumptions of binary electrolyte and local electroneutrality. Simulation results show that, in the geometries investigated here, the pumping power consumption is much lower than in a conventional net spacer and very close to that of the empty channel, while calm zones are generated by the profiles, which may accentuate polarization phenomena.

In electro-membrane processes, a pressure difference may arise between solutions flowing in alternate channels. This transmembrane pressure (TMP) causes a deformation of the membranes and of the fluid compartments. This, in turn, affects pressure losses and mass transfer rates with respect to undeformed conditions and may result in uneven flow rate and mass flux distributions. These phenomena were analyzed here for round pillar-type profiled membranes by integrated mechanical and fluid dynamics simulations. The analysis involved three steps: (1) A conservatively large value of TMP was imposed, and mechanical simulations were performed to identify the geometry with the minimum pillar density still able to withstand this TMP without collapsing (i.e., without exhibiting contacts between opposite membranes), (2) the geometry thus identified was subject to expansion and compression conditions in a TMP interval including the values expected in practical applications, and for each TMP, the corresponding deformed configuration was predicted, and (3) for each computed deformed configuration, flow and mass transfer were predicted by computational fluid dynamics. Membrane deformation was found to have important effects, friction and mass transfer coefficients generally increased in compressed channels and decreased in expanded channels, while a more complex behavior was obtained for mass transfer coefficients.

The sustainable production of freshwater from seawater desalination is receiving increasing attention. Recently, some desalination technologies are taking advantage from the coupling with renewable resources; among them, membrane distillation (MD) is one of the most promising since it can be easily powered by low-grade thermal energy. MD being an emerging technology, efforts are required to optimize geometry and operating conditions of real units in order to reduce the unitary freshwater production cost. In particular, temperature polarization is a well-known detrimental effect for the process driving force; spacers are traditionally used to enhance mixing and make temperature boundary layers thinner, at the cost of higher pressure losses. The present work is devoted to testing and comparing the performance of two different two-layer net spacers: overlapped and woven. Investigations were carried out both by experiments and by computational fluid dynamics (CFD) at different Reynolds numbers, ranging from creeping flow to turbulent flow regimes. Experiments (for intermediate to high Re) made use of thermochromic liquid crystals along with digital image processing. Computational results (for low to intermediate Re) were obtained via steady state (low Re) or direct numerical simulations (intermediate Re) along with the unit cell approach. A good agreement between experiments and CFD results was obtained in the range of superposition. Results showed that woven spacers guarantee a better mixing than overlapped ones, especially in the low to intermediate Re range, thus resulting in Nusselt numbers 2.5–3 times higher. On the other hand, the less disturbed flow field induced by overlapped spacers was found to yield friction coefficients up to 4 times lower, thus allowing lower pumping costs. The choice between the two configurations depends crucially on the relative importance attributed to savings in membrane surface area and in pumping energy for any specific application.

Different computer-based simulation models, able to predict the performance of Reverse ElectroDialysis (RED) systems, are currently used to investigate the potentials of alternative designs, to orient experimental activities and to design/optimize prototypes. The simulation approach described here combines a one-dimensional modelling of a RED stack with a fully three-dimensional finite volume modelling of the electrolyte channels, either planar or equipped with different spacers or profiled membranes. An advanced three-dimensional code was used to provide correlations for the friction coefficient (based on 3-D solutions of the continuity and Navier-Stokes equations) and the Sherwood numbers (based on 3-D solutions of a scalar transport equation), as well as to test simple models for the Ohmic resistances (based on 3-D solutions of a Laplace equation for the electrical potential). These results were integrated with empirical correlations for the transport properties of electrolytes and membranes, and were used as the input for the higher scale model. The overall model was validated by comparison with experimental data obtained in laboratory-scale RED stacks under controlled conditions. This combined approach constitutes a fully predictive, potentially very accurate, and still extremely fast-running, tool for the approximate simulation of all the main variables, suitable for performance prediction and optimization studies.

Reverse electrodialysis (RED) is an electrochemical membrane process that directly converts the energy associated with the concentration difference between two salt solutions into electrical energy by means of a selective controlled mixing. The physics of RED involves the interaction of several phenomena of different nature and space-time scales. Therefore, mathematical modelling and numerical simulation tools are crucial for performance prediction. In this work, a multi-physical modelling approach for the simulation of RED units was developed. A periodic portion of a single cell pair was simulated in two dimensions. Fluid dynamics was simulated by the Navier-Stokes and continuity equations, and ion transfer by the Nernst–Planck approach along with the local electroneutrality condition. The Donnan exclusion theory was implemented in order to simulate interfacial phenomena. A sensitivity analysis of the process performance was carried out. Different membrane/channel geometrical configurations were investigated, including flat membranes, either with or without non-conductive spacers, and profiled membranes. The influence of feeds concentration/velocity was also evaluated. Results confirmed that, with respect to the ideal case of plane (empty) channels and planar membranes, non-conductive spacers always reduce the power produced, while profiled membranes may or may not perform better, depending on stack features and operating conditions.

This study addresses issues which arise in the computational and experimental modelling of flow and heat/mass transfer in membrane distillation and other processes adopting spacer-filled channels (either planar or spiral wound), but have not been sufficiently clarified in the literature so far. Most of the argumentations presented are based on original computational results obtained by the authors by finite volume simulations; some literature results are also considered. The questions addressed regard the choice of scales for the reduction of data and the definition of dimensionless numbers ( Re , f , Nu , Sh ); the definition of average heat or mass transfer coefficients; the combined effects of the parameters that characterize the process (spacer pitch to channel height ratio l / H , flow attack angle γ and Reynolds number Re ) and the applicability of simple correlations; the influence of the spacer's thermal conductivity. In regard to the influence of the parameters, Re, l / H and γ were found to interact heavily, making a separate-effect analysis impossible and power-law friction or heat/mass transfer correlations of little use. Thermal conduction in the spacer, even for low-conductivity polymeric spacers ( λ ≈ 0.15 Wm − 1 K − 1 ), was found to be responsible for up to 10% of the total heat transfer.

Salinity Gradient Power by Reverse Electrodialysis (SGP-RE) technology allows the production of electricity from the different chemical potentials of two differently concentrated salty solutions flowing in alternate channels suitably separated by selective ion exchange membranes. In SGP-RE, as well as in conventional ElectroDialysis (ED) technology, the process performance dramatically depends on the stack geometry and the internal fluid dynamics conditions: optimizing the system geometry in order to guarantee lower pressure drops (DP) and uniform flow rates distribution within the channels is a topic of primary importance. Although literature studies on Computational Fluid Dynamics (CFD) analysis and optimization of spacer-filled channels have been recently increasing in number and range of applications, only a few efforts have been focused on the analysis of the overall performance of the process. In particular, the proper attention should be devoted to verify whether the spacer geometry optimization really represents the main factor affecting the overall process performance. In the present work, realized within the EU-FP7 funded REAPower project, CFD simulations were carried out in order to assess the effects of different parameters on the global process efficiency, such as the choice of spacer material and morphology, and the optimization of feed and blowdown distribution systems. Spacer material and morphology can affect the fluid dynamics inside each channel. In particular, the appropriate choice of net spacer material can influence the slip/no-slip condition of the flow on the spacer wires, thus significantly affecting the channel fluid dynamics in terms of pressure drops. A Unit Cell approach was adopted to investigate the effect of the different choices on the fluid flow along the channel. Also, the possibility of choosing a porous medium to substitute the net spacer was theoretically addressed. Such investigation focused on the porosity and the fiber radius required to respect the process constrains of pressure drops and mechanical stability. On the other hand, the overall pressure drops of a SGP-RE or ED stack can be considered as resulting from different contributions: the pressure drop relevant to the feed distributor, the pressure drop inside the channel, and the pressure drop in the discharging collector. The choice of the optimal stack geometry is, therefore, strongly related to the need of both minimizing each of the above terms and obtaining the most uniform feed streams distribution among the stack channels. In order to investigate such aspects, simulations were performed on a simplified ideal planar stack with either 50 spacer-less or 50 spacer-filled channels. The effect of the distribution/collector channel thickness and geometry on single-channel flow rates and overall pressure drops in the system was analyzed and a significant influence of distributor layout and size on the overall process performance was found.

In reverse electrodialysis (RED) concentration polarization phenomena and pressure drop affect strongly the power output obtainable; therefore the channel geometry has a crucial impact on the system optimization. Both overlapped and woven spacers are commonly commercialised and adopted for RED experiments; the latter exhibit some potential advantages, such as better mixing and lower shadow effect, but they have been poorly investigated in the literature so far. In this work, computational fluid dynamics was used to predict fluid flow and mass transfer in spacer-filled channels for RED applications. A parametric analysis for different spacer geometries was carried out: woven (w) and overlapped (o) spacers with filaments at 90° were simulated, and Reynolds number, pitch to height ratio (l/h) and orientation with respect to the main flow (α=0° and α=45°) were made to vary. The filament arrangement was found to be a crucial feature; for any given pumping power, higher Sherwood numbers were provided by the w-arrangement. The influence of flow attack angle and filament spacing depends on Reynolds number and filament arrangement. Only the configuration w-α45 avoids the presence of poorly mixed zones near the wires. Among the cases investigated here, the configuration that provided the best mixing conditions was w, l/h=2, α=45°.

The measurement of local temperature distributions within a membrane distillation (MD) channel is a crucial step for the optimization of the channel and spacer geometry. This information allows the estimation of temperature polarization phenomena, which can dramatically influence the thermal efficiency of the process and the optimal choice of the geometric configuration (net spacer features, channel size, etc.). In the present work, a recently presented experimental technique, based on the use of thermochromic liquid crystals and digital image analysis, has been employed in order to assess the temperature polarization phenomena. The local heat transfer coefficient distribution on the membrane surface in a MD spacer-filled channel was thus assessed. The membrane has been modelled by a heat transfer polycarbonate layer. Different diamond spacer geometries were investigated, in order to highlight how the geometrical features affect both pressure drop and heat transfer in spacer-filled channels.

Salinity Gradient Power generation through Reverse Electrodialysis (SGP-RE) is a promising technology to convert the chemical potential difference of a salinity gradient into electric energy. In SGP-RE systems, as in most membrane processes, concentration polarization phenomena may affect the theoretical driving force and thus the performance of the process. Operating conditions, including the feed solution flow rate and concentration and the channels׳ geometrical configuration, may greatly influence both the polarization effect and the pumping energy consumption. The present work uses CFD to investigate the dependence of concentration polarization and pressure drop on flow rate, feeds concentration, current density and spacer features. Concentration polarization effects were found to be significant at low feed solution concentration (river water), but only secondary at higher concentrations (seawater and brine), thus suggesting that different optimization strategies should be employed depending on the feeds concentration. The features that a spacer-filled channel should possess for high efficiency and high current density SGP-RE applications were identified.

A crucial parameter for the design and operation of electrodialysis (ED) units is the limiting current density (LCD). This is often identified with the diffusion-limited current density, which corresponds to the complete solute depletion in the layer adjacent to the membrane. Current-voltage curves obtained from measurements with electrodes in contact with the solution (i.e. without membranes) are consistent with this interpretation and exhibit a horizontal plateau identifying LCD. However, real ED systems show more complex behaviours, with a reduced-slope tract instead of a plateau and a third region in which the current increases more markedly (overlimiting current). The phenomena involved in the limiting region are not yet totally characterized and the determination of LCD in ED units is still ambiguous. In the present work, we explore the issues related to the identification of LCD, by measurements on ED units, assessing the influence of operating conditions and validating a simplified process simulator. A new method to determine LCD, based on the current efficiency, is proposed and compared with other methods presented in the literature. A second limiting quantity is also identified, i.e. the critical current density, below which diffusion phenomena prevail on migration and a method for its assessment is proposed.

The need to reduce energy consumption in seawater Reverse Osmosis (RO) process has pushed research towards the development of new hybrid systems in which, for example, other membrane processes can be used to pre-treat seawater. Electrodialysis (ED) and Reverse Electrodialysis (RED) can act as a pre-desalting step before seawater enters the RO unit, thus leading to an important energy saving in RO. In this work, two coupled models are proposed for the RED-RO and ED-RO systems. Each process model was validated. Then a sensitivity analysis was performed to assess the effect of the integration on the overall process cost saving. The analysis was performed by changing ED or RED voltage and RO pressure and considering eight different cost scenarios. The performance of the hybrid system was compared with the stand-alone seawater RO process. Competitive scenarios were found especially for the RED-RO case, by optimizing the pre-desalting extent, with significant cost saving and promising potentials for future industrial implementation.

Membrane Distillation (MD) is a thermal process that separates water from aqueous solutions containing non-volatile components such as salt. Water vapor from the hot feed channel permeates through a hydrophobic membrane thanks to a partial pressure gradient, and condenses in the cool channel. One of the main advantages of MD is the easy coupling with renewable resources, as the solar thermal energy. In the various MD configurations developed, net spacers are used in order to support the membrane, thus creating the channels; moreover, they can counteract the side effects of temperature polarization by promoting mixing. However, the presence of the spacer involves an increase of pressure drops and thus of pumping costs. In the design of MD modules, therefore, the choice of the spacer is crucial for the process efficiency. In this work, flow and heat transfer in spacer-filled channels were predicted by computational fluid dynamics simulation. A parametrical study of net spacers made of two layers of overlapped filaments at 90° was performed; several values of (i) pitch to channel height ratio p/h (1-6), (ii) flow attack angle (0°-45°) and Reynolds numbers (20-350) were examined. The periodic domain of the hot channel was simulated under the hypothesis of fully developed conditions (Unit Cell approach). A very complex influence of the parameters on the heat transfer and pressure drop was found; nevertheless, better compromises between high Nusselt numbers and low friction factors were reached for p/h larger than 3. Simulation results provided directions for an optimal spacer features and are part of a large database that can be used for the process design and optimization.