(372r) Barriers to Electrodialysis Implementation: Maldistribution and Its Impact on Resistance and Limiting Current Density

Electrodialysis (ED) is an emerging electromembrane technology with broad applications in electrochemical separations such as desalination, resource recovery and wastewater treatment. As the global water crisis worsens, it is more important than ever that natural freshwater resources are conserved, and new sources are established. To achieve this, significant research and development of separation technologies is required, and ED is uniquely positioned to achieve this. In ED, an electric field is applied tangentially to saline streams flowing between ion exchange membranes in a geometry analogous to that of a plate-and-frame heat exchanger (PFHEX) (Fig. 1). The electric field drives the transport of ions from one stream, through ion exchange membranes (IEMs), and into another. The membranes exist as semi-permeable barriers, theoretically allowing the transport of anions or cations only. As opposed to competing technologies such as reverse osmosis and thermal separations, in ED it is the solute, which is transported, rather than thesolvent. This presents several inherent benefits such as a higher rate of separation, greater controllability, a lower susceptibility to fouling, a greater membrane lifespan, and a higher recovery ratio.

Recent developments in IEM performance and manufacturing techniques have meant that ED is, for the first time, commercially viable. However, there are several technological challenges which remain as a result of limited fundamental understanding of ED. A salient example of this is the limiting current density (LCD). Concentration gradients form adjacent to membranes as a result of concentration polarization, the magnitude of which increases as the ion flux, and thus the current density, increases. The membrane-solution interfacial concentration decreases until it vanishes, at which point the LCD has been reached. A substantial increase in electrical resistance and unwanted pH changes then occur due to the onset of water splitting. The LCD represents the highest possible ion flux and so has important consequences for process intensification. Complex phenomenological interactions drive the use of highly empirical power-law models as theoretical models are inadequate and over-predict the LCD. This makes models highly specific to the system they were initially built for and obscures fundamental interactions, making it difficult to identify methods to improve the LCD.

Several other prevalent assumptions about ED behavior add to the obfuscation of underlying phenomena, again inhibiting fundamental understanding. One ubiquitous assumption in ED modelling and experimental analysis is that of channel uniformity, an assumption which has never been validated. The distribution of flow within an ED stack has been given virtually no attention across published literature despite it having significant consequences for ED operation. Herein, we evaluate this assumption to its breaking point and aim to quantify the extent of maldistribution within an ED stack. Crucially, we go further to investigate what design elements affect maldistribution, as well as the effect it has on performance metrics such as the electrical resistance and the LCD.

Methodology

In this work, 3D computational fluid dynamics (CFD) simulations are used for the first time to generate realistic flow fields of entire lab-scale ED stacks (Fig. 2). This is a significant step forward from previous maldistribution studies which have used 2D simulations or focused on only one part of the geometry. Further, an analytical maldistribution model, originally derived for a PFHEX, was applied to the results of the CFD simulations. Two important benefits arose from the use of this model: laborious CFD simulations can be avoided, and a dimensionless maldistribution number is provided as a suitable metric for the degree of maldistribution. The effect stack design and operation have on maldistribution was investigated by modifying the geometry and velocity boundary conditions and computing the associated maldistribution number. The specific design aspects varied were the inlet flowrate, channel width, distributor angle, number of manifolds, number of cell pairs, and the length-to-width ratio of the flow channels (Fig. 2). To determine the effect that maldistribution has on operation, a simplified 1D circuit-based model was developed and used to predict the LCD and stack resistance.

Experimental validation of the results was conducted in two ways. To validate the CFD flow fields, particle image velocimetry (PIV) experiments were conducted on a 3D printed flow cell with the geometry used in the simulations. Experiments on a recirculating batch ED system (PC Cell BED 1-4) in steady state were then conducted to validate the effect maldistribution has on the LCD. An increase in either the salt concentration or solution flowrate will increase the LCD. These effects were balanced out to achieve a constant salt molar flowrate while increasing the volumetric solution flowrate. Since the LCD is bound by the salt molar flowrate of the slowest channel, if no maldistribution is present then the LCD will be constant. However, if maldistribution is present and is affected by the volumetric flow rate, the LCD will change in accordance with model predictions.

Results and Discussion

Initial CFD simulations on a standard lab-scale stack geometry revealed maldistribution to be significant (Fig. 3). The fastest channel, adjacent to the entrance and exit, was found to have twice the flowrate of the slowest, and thus half the residence time. These results were confirmed by the PIV experiments. It can therefore reasonably be concluded that maldistribution exists in lab-scale electrodialysis stacks and must affect electrodialysis experiments conducted on similar geometries. Since this geometry is commonplace to find in published research, these results are of great significance.

The analytical maldistribution model was found to fit the flow distributions very accurately with a root-mean-square error of only 0.4%. Further, the model reasonably predicted the flow distribution using common friction factor correlations. This shows the model is an invaluable tool for studying maldistribution in ED without requiring computationally demanding CFD simulations. The use of a single dimensionless number to quantify maldistribution facilitates the comparison of maldistribution between different units and is useful as a simple but objective input into phenomenological models.

The stack design was found to have a significant effect on the maldistribution. In general, design choices which increased the channel pressure drop or reduced the channel flow rate were found to reduce maldistribution. For example, increasing the stack inlet velocity was found to increase the maldistribution (Fig 4). Additionally, the number of channels had the greatest effect on maldistribution and was found to be proportional to the maldistribution number. Industrial ED stacks tend to have between 50 and 200 cell pairs, and so maldistribution will likely be worse at industrial scale.

It was suggested by the 1D-modelling results that maldistribution has a detrimental effect to both LCD and electrical resistance, but that the effect on the LCD is much greater. The degree of maldistribution present in the standard lab scale stack was found to reduce the LCD by 23% but increase the resistance by only 2%. This may go some way to explain why there has been a distinct lack of maldistribution research present in literature. While a large and unexplained increase in resistance would be difficult to ignore, the uncertainty surrounding what affects the LCD and highly empirical nature of its modelling could easily obfuscate the impact of maldistribution.

The ED stack experiments were successful in validating the modelling results. The LCD decreased when the volumetric flowrate increased, in line with what would be expected given the predicted degree of maldistribution (Fig. 5). The measured values of the LCD were consistently 30% lower than what was predicted, indicating the presence of other limiting phenomena beyond maldistribution which were not accounted for in the simplified 1D model. However, the constant ratio between prediction and measurement gives confidence to the conclusions drawn about the effect of maldistribution on LCD.

Conclusion and Significance

This work has shown, for the first time, that maldistribution is prevalent in ED stacks and has a significant and detrimental impact on performance. The use of robust CFD techniques on realistic 3D geometries and experimental validation gives a high degree of confidence to these conclusions. Since maldistribution has not been considered historically, it has been unknowingly reducing performance of both industrial applications and lab experiments. This is impeding the decision-making process of industry as well as the depth of analysis that is achievable at all scales. It further highlights that our understanding of the engineering challenges of ED is far from complete and that performance may be significantly improved through fundamental research and mathematical modelling. The modelling techniques established herein can be used to develop methods to reduce or eliminate maldistribution by artificially increasing the pressure drop of channels nearer to the entrance. Subsequently, the LCD can be increased by as much as 50% for a lab-scale unit and potentially even more at industrial scale.

The fundamental and impactful nature of this research ensures that the conclusions are significant to applications beyond conventional electrodialysis. This includes bipolar membrane electrodialysis for chemical-free pH manipulation, flow batteries and reverse electrodialysis for power generation. This research can therefore aid the development and commercialization of many industrial processes which have been hampered by a less than ideal performance.

This work is an extension of our recent publication: https://doi.org/10.1016/j.desal.2022.115691