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Performance Metrics for the Objective Assessment of Capacitive Deionization Systems

Steven A. Hawks, Ashwin Ramachandran, Slawomir Porada, Patrick G. Campbell, Matthew E. Suss, P. M. Biesheuvel, Juan G. Santiago, Michael Stadermann

arXiv:1805.03247v2physics.chem-ph

TL;DR

CDI performance comparisons are hindered by unspecified or unequal separation conditions and by metrics that can improve as removal decreases. The paper proposes standardized, volume-based energy and throughput metrics for equivalent separations, demonstrates them on fte-CDI and fb-MCDI, and identifies operational assumptions and cell indicators needed to interpret results.

  • Problem

    CDI studies often report performance without consistently specifying separation conditions, limiting comparability across devices, materials, and operation modes.

  • Method

    The paper develops a framework using volumetric energy consumption and throughput productivity at defined feed salinity, concentration reduction, and water recovery, alongside supporting performance indicators.

  • Results

    Under a 5 mM removal from 20 mM NaCl at 50% recovery, fb-MCDI consumes ∼69% of the energy at 1.38× the productivity of fte-CDI.

  • Takeaways & Limitations

    Meaningful CDI comparisons require equivalent separations and joint consideration of energy consumption and throughput rather than optimizing a single metric.

  • Takeaways & Limitations

    Energy consumption values should distinguish perfect from absent energy recovery because laboratory measurements commonly quantify recoverable energy without actually reusing it.

Abstract

from arXiv · show

In the growing field of capacitive deionization (CDI), a number of performance metrics have emerged to describe the desalination process. Unfortunately, the separation conditions under which these metrics are measured are often not specified, resulting in optimal performance at minimal removal. Here we outline a system of performance metrics and reporting conditions that resolves this issue. Our proposed system is based on volumetric energy consumption (Wh/m$^3$) and throughput productivity (L/h/m$^2$) reported for a specific average concentration reduction, water recovery, and feed salinity. To facilitate and rationalize comparisons between devices, materials, and operation modes, we propose a nominal standard testing condition of removing 5 mM from a 20 mM NaCl feed solution at 50% water recovery for CDI research. Using this separation, we compare the desalination performance of a flow-through electrode (fte-CDI) cell and a flow between membrane (fb-MCDI) device, showing how significantly different systems can be compared in terms of generally desirable desalination characteristics. In general, we find that performance analysis must be considered carefully so to not allow for ambiguous separation conditions or the maximization of one metric at the expense of another. Additionally, for context we discuss a number of important underlying performance indicators and cell characteristics that are not performance measures in and of themselves but can be examined to better understand differences in performance.

1 Introduction

CDI studies often report performance under different or incompletely specified separations, making comparisons unreliable. The paper proposes comparing volumetric energy consumption and throughput for identical feed salinity, concentration reduction, and water recovery, while examining their tradeoff.

  • CDI studies are difficult to compare because critical performance parameters or desalination conditions are often missing or substantially different.
  • Energy consumption and throughput define performance only when water recovery, feed salinity, and total concentration reduction are equivalent.
  • The framework uses volumetric energy consumption, Ev, and throughput productivity, P, as primary metrics because treated-water volume is the practical output.
  • Lower water recovery or concentration reduction can improve several CDI metrics, producing apparently optimal values at negligible removal.
  • Energy and throughput exhibit an inherent tradeoff, so both metrics must be reported for the same separation.
  • For an identical 5 mM removal from 20 mM NaCl at 50% recovery, fb-MCDI consumes ∼69% of the energy at 1.38× the productivity of fte-CDI.

3 Definitions

The paper defines volumetric energy consumption, water recovery, concentration reduction, and productivity from full dynamic-steady-state cycle data. These definitions can be adapted across cyclic, flowable-electrode, and batch operation modes, while traditional metrics remain mathematically convertible when average concentration reduction is specified.

  • General calculation basis: Analyses use complete dynamic-steady-state charge/discharge cycles and should include raw effluent concentration or conductivity and current/voltage time series.Dynamic steady state is typically reached by the third or fourth identical cycle.
  • Water recovery: Water recovery is the diluate volume divided by total diluate plus concentrate volume over a cycle.Diluate is lower-salinity collected water, while concentrate is enriched relative to the feed; the diluate collection interval may be chosen arbitrarily if its final average salinity is below feed salinity.
  • Concentration reduction: Average concentration reduction is calculated from salt removed relative to feed concentration and the collected diluate volume.Salt removal depends on the selected collection interval: using c_thresh = c_feed maximizes ΔN_d, whereas retaining only more strongly desalinated water increases concentration reduction but reduces salt removed.
  • Energy consumption: Volumetric energy consumption accounts for energy input, recoverable discharge energy, recovery efficiency η, cycle time, and diluate volume.The framework recommends reporting at least η = 0 and η = 1 because real energy-transfer circuits recover only part of the recoverable energy.
  • Productivity: Productivity is the diluate volume produced per cycle time and projected device face area, with P reported in L/h/m2.Because separation conditions already specify average removal, water recovery, and feed concentration, productivity replaces the need for an average removal-rate metric such as ASAR.
  • Metric relationships and operating modes: With average concentration reduction specified, volumetric metrics can be converted to traditional molar parameters, but metric relationships may provide no insight beyond definitions.The paper advocates Ev and P as primary metrics because deionization produces treated-water volume; normalized metrics require caution when low removal produces apparently optimal values.
  • Metric relationships and operating modes: The framework applies across operation modes: flowable-electrode systems replace specified integration time with total experiment time, while batch quantities can be used directly.The authors state that DSS equations can be adapted straightforwardly to reflect flowable-electrode and batch operation.

4 Performance Indicators

The paper distinguishes operational performance metrics from supporting indicators that explain CDI cell behavior and material limitations. These indicators include capacity, capacitance, efficiency, and resistance measures.

  • 4 Performance Indicators: Performance indicators help explain why particular CDI materials, architectures, and operation modes perform differently, but are not performance metrics themselves.They should be interpreted alongside reported operational performance metrics.
  • 4.1 Salt Adsorption Capacity: Eq-SAC estimates the upper limit of desalination capacity over a voltage window, but cannot substitute for energy consumption and throughput.Higher Eq-SAC values typically correspond to larger obtainable concentration reductions and water recoveries.
  • 4.2 Capacitance: Volumetric capacitance is more relevant to CDI operation, whereas gravimetric capacitance is more comparable with electrochemical capacitors; both normalizations are useful.Reported electrode density allows conversion between volumetric and gravimetric values.
  • 4.2 Capacitance: Capacitance assessment should use CDI-relevant low electrolyte concentrations and sufficiently many cycles to reach dynamic steady state.Low ionic strength can introduce PZC, depletion, resistive, and Faradaic effects, while double-layer capacitance scales nonlinearly with concentration.
  • 4.3 Charge and Coulombic Efficiencies: Flow efficiency relates salt removed from the effluent to salt adsorbed by electrodes, while Coulombic efficiency measures charge loss associated with Faradaic processes.Total cycle charge efficiency is influenced by flow efficiency, double-layer effects, and Faradaic effects.
  • 4.4 Series Resistance: Series resistance captures external electronic and separator resistance, while energy dissipation also occurs through Joule heating and unwanted Faradaic reactions.The electrode porous-material resistance is excluded from the defined total series resistance.

5 Parameter Summary

The parameter summary combines separation conditions, performance metrics, indicators, and cell characteristics needed to interpret CDI desalination results. Supporting characteristics include material density, membrane count, and device geometry.

  • 5 Parameter Summary: Table 1 summarizes essential separation conditions, performance metrics, and performance indicators discussed in the paper.The supporting information defines the parameters used in the summary.
  • 5 Parameter Summary: Dry electrode material density enables conversion between gravimetric and volumetric parameters.This property is therefore important for comparing reported quantities using different normalizations.
  • 5 Parameter Summary: The number of membranes helps estimate device cost, while electrode and separator thickness influence many reported parameters.These are cell characteristics rather than performance metrics themselves.
  • 5 Parameter Summary: A separation-report format and calculation spreadsheet are provided to facilitate consistent reporting and reuse across studies.The spreadsheet is implemented in generally available commercial software.

6 Conclusions

The paper concludes that CDI performance should be quantified with volume-based metrics under explicitly equivalent separation conditions. It proposes a nominal standard separation for comparing materials, devices, and operation modes.

  • 6 Conclusions: The framework quantifies CDI performance using volumetric energy consumption in Wh/m^3 and throughput productivity in L/h/m^2.These metrics are intended to describe desalination performance for a defined separation.
  • 6 Conclusions: 5 mM removal from a 20 mM NaCl feed at 50% water recovery is proposed as a nominal standard testing condition for CDI research.The condition is intended for comparisons among new materials, devices, and operation modes.
  • 6 Conclusions: Equivalent separation conditions are essential for obtaining comparable and practically meaningful CDI performance values.The framework addresses prior reporting that omitted concentration reduction, feed concentration, or water recovery.
  • 6 Conclusions: The framework demonstrates comparison of a flow-through electrode CDI cell and a flow-between-membrane CDI cell using the same separation.The comparison is framed in terms of generic desalination performance.

Supporting Information for: Performance Metrics for

The supporting information accompanies the paper’s title and author-affiliation material. The supplied passages contain bibliographic and institutional details rather than scientific findings.

  • Supporting Information for: Performance Metrics for: The supporting-information material identifies the work as concerning objective assessment of capacitive deionization.The supplied passages provide the title fragment and author affiliations.
  • Supporting Information for: Performance Metrics for: The authors are affiliated with Lawrence Livermore National Laboratory, Stanford University, Wetsus, and the Technion-Israel Institute of Technology.The passages list institutional affiliations in the United States, the Netherlands, and Israel.
  • Supporting Information for: Performance Metrics for: The listed affiliations include departments spanning engineering, science and technology, and water technology research.Specific affiliations include mechanical engineering, aeronautics and astronautics, and a European water-technology center.

1 Parameter Definitions

Table S1 defines the parameters and symbols used throughout the main text and supplementary analysis, together with their typical units.

  • Table S1 lists cell-level quantities including maximum salt adsorption capacity, feed-stream molar mass, electrode mass, electrode-pair number, and membrane count.
  • Cycle and efficiency parameters include total charging and discharging charge, cycle charge efficiency, and measured round-trip Coulombic efficiency.
  • Electrode and separator descriptors include electrical conductivity, macro- and microporosity, skeleton-material fraction, porosity, and tortuosity.
  • The table also defines the van’t Hoff factor, absolute temperature, and ideal gas constant, with units of dimensionless, kelvin, and joules per mole per kelvin, respectively.

2 Cell Data for Figs. 1 and 2

The supplementary data document the designs, operating conditions, and raw measurements used to evaluate fte-CDI and fb-MCDI performance. They provide cell geometry, flow conditions, concentration and voltage data, and charge-cycle information underlying the reported figures.

  • fte-CDI Cell Design and Testing: Figure S1 reports CV and EIS data for the device used in Figs. 3 and 4a,b, measured at 3.9 ml/min to avoid depletion effects.
  • fte-CDI Cell Design and Testing: The fte-CDI cell is documented with an exploded schematic showing projected face area as width multiplied by height and dimensions relevant to the device.
  • fte-CDI Cell Design and Testing: Raw fte-CDI data include DSS concentration and voltage versus time, collected using closed-loop circulation with a 2 L reservoir and specified conductivity-measurement and gas-equilibration conditions.
  • fb-MCDI Cell Design and Testing: Experimental fb-MCDI results covered cycle times of 2 and 6 min and total flow rates of 7.5, 3.75, 2.5, and 1.875 mL/min per cell.

3 Thermodynamic Energy Consumption for a Separation

The supplementary analysis derives thermodynamic minimum volumetric energy consumption for the specified separation and compares it with measured energy use. The resulting ratio gives thermodynamic separation efficiency, with supporting values shown for the main-text figures.

  • The analysis uses specific Gibbs free energy of separation to calculate the thermodynamic minimum volumetric energy consumption, Ev,th, for a removal.
  • The calculation assumes a van’t Hoff factor of 2, an ideal gas constant of 8.3145 J/mol/K, and an absolute temperature of 294.15 K.
  • Thermodynamic separation efficiency is obtained by dividing the thermodynamic minimum energy by experimentally measured Ev for the separations in Fig. 4b.
  • At the 5 mM removal point, the reported productivity is 24 L/h/m2.
  • The supplementary figures provide thermodynamic-efficiency analyses for the energy-consumption data in Figs. 4b and 5b.

4 Numerical Analysis of Experimental Cycle Data

The numerical analysis computes areas of a function above and below a reference value over an experimental interval. This approach supplies cycle-level quantities used to calculate CDI performance indicators from experimental data.

  • The method determines the areas of f(t) above and below a reference value f0 between t0 and tf.
  • The resulting areas can be applied to compute Nout, Ein, Eout, Vd, Vc, qin, and qout used in the main-text analysis.
  • Only integrals over the entire DSS cycle are needed in the formulation, with sign manipulation producing the areas of interest.
  • An accompanying spreadsheet includes a cycle calculator implementing the area analysis and a procedure for converting conductivity data to salt concentration.

5 Measuring Capacitance and PZC with CV

CV analysis measures capacitance and the potential of zero charge (PZC) under CDI-relevant conditions. For HCAM, capacitance at the PZC decreases substantially at low ionic strength, and measurement location affects comparisons.

  • CV analysis examines material properties relevant to CDI, including capacitance and PZC.
  • The electrodes were 2×2.5 cm, 365 µm thick, and 0.098 g each, with density 0.54 g/cm3 and total porosity 72.5%.
  • A 2-electrode HCAM cell was measured across NaCl concentrations from 20 mM to 2 M using stirred-beaker CV.The electrodes were separated by polyester mesh and contacted with a 4-wire point-probe clamp.
  • Capacitance differs between zero applied voltage and the PZC, so the evaluation point must be considered when comparing materials.
  • 67%: PZC capacitance at 20 mM NaCl relative to 2 M, showing strong dependence on ionic strength.The reported PZC was approximately symmetric at ±0.48 V.

6 Measuring Series Resistance with EIS

EIS separates and quantifies series-resistance contributions in assembled CDI cells. Nyquist intercepts identify Rs, while controlled separator and concentration series reveal separator and solution-resistivity effects.

  • Rs is defined by the high-frequency Re(Z) intercept where -Im(Z) tends to zero in an EIS Nyquist plot.
  • Increasing separator thickness shifts the Nyquist plot to higher Re(Z) without changing its overall shape.
  • A simple EIS concentration series can expose underlying series-resistance components in fully assembled cells.
  • 3.82 Ω/separator: slope of Rs versus stacked 125 µm coffee-filter separators in the tested HCAM assembly.
  • Rs scales linearly with solution resistivity, with tested Rs-intercept frequencies ranging from approximately 500 Hz to 125 kHz across 2 M to 20 mM NaCl.

7 Separation Report

The separation report records cell dimensions, material characteristics, and operating information needed to interpret CDI performance and resistance. Even partially completed reports remain valuable for reproducibility and comparison.

  • The proposed SI separation report is intended to ensure that critical characteristics are reported alongside CDI data.
  • Cell face area and electrode thickness support normalization of capacitance and productivity.Electrode volume is normalized as A·le, while productivity uses cell face area.
  • Membrane face area and membrane count are important for estimating device cost, with membranes typically costing $200/m2 or more.
  • Electrode mass, density, and separator and electrode porosities help categorize material performance and characterize the cell.
  • A partially filled report is still highly valuable when some measurements or information are unavailable.
  • Tables S2 and S3 provide separation reports for the fte-CDI and fb-MCDI cells at 5 mM removal.
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