Frequency analysis and resonant operation for efficient capacitive deionization

Abstract

Capacitive deionization (CDI) performance metrics can vary widely with operating methods. Conventional CDI operating methods such as constant current and constant voltage show advantages in either energy or salt removal performance, but not both. We here develop a theory around and experimentally demonstrate a new operation for CDI that uses sinusoidal forcing voltage (or sinusoidal current). We use a dynamic system modeling approach, and quantify the frequency response (amplitude and phase) of CDI effluent concentration. Using a wide range of operating conditions, we demonstrate that CDI can be modeled as a linear time invariant system. We validate this model with experiments, and show that a sinusoid voltage operation can simultaneously achieve high salt removal and strong energy performance, thus very likely making it superior to other conventional operating methods. Based on the underlying coupled phenomena of electrical charge (and ionic) transfer with bulk advection in CDI, we derive and validate experimentally the concept of using sinusoidal voltage forcing functions to achieve resonance-type operation for CDI. Despite the complexities of the system, we find a simple relation for the resonant time scale: the resonant time period (frequency) is proportional (inversely proportional) to the geometric mean of the flow residence time and the electrical (RC) charging time. Operation at resonance implies the optimal balance between absolute amount of salt removed (in moles) and dilution (depending on the feed volume processed), thus resulting in the maximum average concentration reduction for the desalinated water. We further develop our model to generalize the resonant time-scale operation, and provide responses for square and triangular voltage waveforms as two examples. To this end, we develop a general tool that uses Fourier analysis to construct CDI effluent dynamics for arbitrary input waveforms. Using this tool, we show that most of the salt removal (∼95%) for square and triangular voltage forcing waveforms is achieved by the fundamental Fourier (sinusoidal) mode. The frequency of higher Fourier modes precludes high flow efficiency for these modes, so these modes consume additional energy for minimal additional salt removed. This deficiency of higher frequency modes further highlights the advantage of DC-offset sinusoidal forcing for CDI operation.

Electrochemical Methods for Water Purification, Ion Separations, and Energy Conversion

“…With these general guidelines established, researchers have sought to develop efficient electrochemical processes by engineering improved systems, materials, and operating conditions. Systems to improve energy efficiency were designed, such as cyclic recovery of stored energy, reduction of series resistances, , and use of membranes in electrosorption methods. , Materials to suppress parasitic reactions were developed, including redox-active electrodes and intercalation materials, ,, and operating parameters were tuned, like flow rate, current, and voltage. ,− ,,, The use of IEMs directly adjacent to the electrodes in electrosorption was first reported by Andelman and Walker, and this approach was since pursued by many researchers. ,,,, The selectivity introduced by these membranes increases charge efficiency by allowing for voltage reversal and increasing the capacity of adsorption . One disadvantage of using IEMs, however, is that they can incur additional capital costs that exceed those of all other components in an electrochemical device …”

“…These high efficiencies were achieved by operating the system at constant current, recovering energy during discharging, balancing the rates of charge transfer and fluid transport (which represent the rates of adsorption and ion advection, respectively), limiting the window of voltages to between 0.4 and 1 V (higher voltages trigger side reactions and smaller ones diminish charge efficiency), and lowering series resistances by using current collectors made of titanium mesh separated by thin (30 μm) spacers. In another study, Ramachandran et al proposed the use of alternating electrical current and successfully removed much of the salt fed without compromising energy efficiency . The alternating current was sustained at the intrinsic resonant frequency of the system (equivalent to the time constant of an RC circuit), which was shown to be inversely proportional to the geometric mean of residence time and charging time.…”

“…753,1183 Materials to suppress parasitic reactions were developed, including redox-active electrodes 96 and intercalation materials, 116,127,944 and operating parameters were tuned, like flow rate, current, and voltage. 753,[758][759][760]763,1184,1185 The use of IEMs directly adjacent to the electrodes in electrosorption was first reported by Andelman and Walker, 1186 and this approach was since pursued by many researchers. 637,753,1183,1187,1188 The selectivity introduced by these membranes increases charge efficiency by allowing for voltage reversal and increasing the capacity of adsorption.…”

“…In another study, Ramachandran et al proposed the use of alternating electrical current and successfully removed much of the salt fed without compromising energy efficiency. 1185 The alternating current was sustained at the intrinsic resonant frequency of the system (equivalent to the time constant of an RC circuit), which was shown to be inversely proportional to the geometric mean of residence time and charging time. In a similar way to electrical current, the flow profile can be better controlled to improve performance, particularly in systems that are cyclic like CDI and Faradaic electrosorption.…”

Using Ultramicroporous Carbon for the Selective Removal of Nitrate with Capacitive Deionization

“…Capacitive deionization (CDI) is a water treatment technology of emergent interest for use in treating low salinity brackish waters. − In addition to general salinity reduction, − a particular area of interest in CDI research is the selective removal of specific ionic contaminants. − One of the major contaminants of interest in CDI research is nitrate, − which is regulated by the US Environmental Protection Agency to a maximum contaminant level in drinking water of 10 mg/L as N or 0.7 mM of NO 3 – . Unfortunately, the concentration of nitrate in groundwater is increasing by a reported 1–3 mg/L/y due to a number of factors, making the development of effective treatment methods increasingly important.…”