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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 research needs clearer guidance for comparing performance when separation conditions are not consistently specified. This paper proposes reporting energy consumption and throughput productivity for defined separations, and shows that fb-MCDI consumes ∼69% of the energy at 1.38× the productivity of fte-CDI under the proposed comparison.

  • Problem

    CDI research needs guidelines for evaluating, reporting, and comparing device performance, including reporting metrics for equivalent separation conditions.

    Source: §1 · p. 1, §6 · p. 14

  • Method

    The paper proposes comparing CDI systems using volumetric energy consumption and throughput productivity reported for specified separations, with a nominal protocol of 5 mM removal from 20 mM NaCl at 50% water recovery.

    Source: §1 · p. 2, §6 · p. 14

  • Results

    ∼69% of the energy at 1.38× the productivity: fb-MCDI versus fte-CDI under the specified separation conditions.

    Source: §2.1 · p. 7

  • Takeaways & Limitations

    Reporting energy consumption and productivity for equivalent separation conditions is essential for comparable, practically meaningful CDI performance values.

    Source: §6 · p. 14

    The reported energy-consumption data assume perfect capacitive energy recovery and reuse, an idealized condition not achieved by real circuits.

    Source: §2.1 · p. 6

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

The introduction proposes a framework for comparing CDI desalination performance that reports both energy consumption and throughput for a defined separation. It argues that comparable conditions and separate performance indicators are needed to interpret device performance.

1 Introduction

  • Published CDI studies are often incomparable because critical performance parameters are missing or desalination conditions differ substantially.The field’s growth has increased the need for guidelines to evaluate, report, and compare device performance.Source: §1 · pp. 1–2
  • Energy and throughput values are comparable only at matched water recovery, feed salinity, and concentration reduction, conditions that are difficult to align in CDI.Because CDI often removes a smaller, variable fraction of ions, extrapolating performance across separation conditions is not straightforward.Source: §1 · p. 2
  • CDI studies use many energy, throughput, and materials metrics, but these can trade off, supporting a minimum set that reports energy and throughput separately.For example, adsorption rate can increase at the cost of higher energy consumption or lower salt adsorption capacity.Source: §1 · p. 2
  • The proposed framework reports energy consumption and throughput for a defined separation, while distinguishing generic performance metrics from indicators that help explain outcomes.The authors also propose a laboratory-scale protocol that does not prescribe flow rate, charging method, device size, electrode configuration, or removal mechanism.Source: §1 · p. 2

2 Framework for Comparing Deionization Performance

The framework compares CDI systems only at defined feed salinity, concentration reduction, and water recovery, using volumetric energy consumption and throughput productivity as primary metrics. A nominal 20 mM NaCl feed, 5 mM reduction, and 50% recovery supports standardized comparisons while exposing energy–throughput tradeoffs.

2 Framework for Comparing Deionization Performance

  • Defining feed concentration, average concentration reduction, and water recovery before comparing volumetric energy consumption and throughput productivity makes performance comparisons objective across materials, geometries, electrode configurations, and operating modes.Productivity and energy use serve as surrogates for capital and operational costs, respectively, while volume-based metrics align with treated-water applications.Source: §2 · pp. 2–3
  • Without specified separation conditions, metrics can appear better at lower removal or recovery, and results at different feed salinities are not equivalent; energy and throughput must both be reported because they trade off.Concentration reduction and recovery affect absolute removal, and there is no straightforward conversion between performance values measured under different separations.Source: §2 · pp. 3–4

2.1 Example Standardized Separation for CDI Research

  • The proposed nominal condition is 20 mM NaCl feed, 5 mM average concentration reduction, and 50% water recovery, with energy consumption and productivity reported for that separation.The authors describe this as an attainable compromise between research-lab feasibility and desalination relevance; a threshold concentration determines collected diluate and changes the resulting recovery and concentration reduction.Source: §2.1 · pp. 4–5
  • At 5 mM removal, fte-CDI consumed 150 Wh/m3 with no energy recovery, about 2.6× its perfect-recovery value of 58 Wh/m3; fb-MCDI's thermodynamic efficiency was 4.1%.The thermodynamic minimum for the fte-CDI separation was 2.8% of its measured energy consumption; productivity must also be considered when interpreting efficiency.Source: §2.1 · p. 6

2.2 Performance Tradeoffs

  • At η = 1, fb-MCDI delivered ∼3× more throughput than fte-CDI at ∼56 Wh/m3; at the 5 mM separation, it used ∼69% of the energy at 1.38× productivity.At equivalent energy consumption, the throughput gap suggests fte-CDI would need to be roughly ∼3× less expensive to compete.Source: Figure 4 · p. 6, Figure 5 · p. 7, §2.2 · p. 7
  • For constant-current operation, energy consumption and throughput show a linear tradeoff; the larger energy difference between η = 0 and η = 1 for fte-CDI suggests greater energy storage than in fb-MCDI, likely due to lower series resistance.Performance comparisons across operating variables should use identical separations and weigh membrane-associated performance gains against added cost.Source: Figure 5 · p. 7, §2.2 · p. 7

3 Definitions

The proposed metrics are calculated from full dynamic-steady-state cycles and describe desalination at specified separation conditions. The definitions also explain how to adapt the calculations to noncyclic operation and relate the proposed metrics to traditional ones.

3 Definitions

  • Analyses use a full dynamic-steady-state (DSS) cycle; matching effluent conductivity at cycle start and end is a simple check, and raw conductivity and current/voltage time series should be reported.DSS is typically reached by the third or fourth identical cycle.Source: §3 · p. 8

3.0.1 Water Recovery

  • Water recovery is defined from collected diluate and concentrate volumes over a DSS cycle, with the diluate collection interval selectable as long as its average salinity is below the feed.The typical interval includes times when effluent conductivity is below feed conductivity; total cycle volume is the sum of diluate and concentrate volumes.Source: §3.0.1 · p. 8

3.0.2 Concentration Reduction

  • Salt removed and average concentration reduction depend on the chosen collection intervals: maximizing salt removal uses cthresh = cfeed, while retaining more strongly desalinated water raises concentration reduction but lowers salt removal.Using some concentrate can increase water recovery.Source: §3.0.2 · p. 8

3.0.3 Energy Consumption

  • Volumetric energy consumption accounts for cycle energy input and the fraction of recoverable energy reused; report it for at least η = 0 and η = 1, and include pumping energy if significant.For the paper’s data, pumping energy was at least 4× lower than desalination energy (about 5 Wh/m^3), so it was considered negligible.Source: §3.0.3 · pp. 8–9

3.0.4 Productivity

  • Productivity is diluate volume produced per unit time per projected cell face area, a throughput measure suited to comparisons when separation conditions are specified.The authors argue that projected area relates more directly to cell resistance and cost when membranes are used, while volume throughput reflects general desalination performance.Source: §3.0.4 · p. 9

3.0.5 Performance Metric Relationships

  • At specified average concentration reduction, water recovery, and feed salinity, volumetric energy consumption and productivity describe treated-water performance; traditional molar metrics can be derived but require careful interpretation.The authors favor volume-normalized metrics because deionization produces treated water, and efficiency metrics such as ENAS may look best at impractically low concentration reduction.Source: §3.0.5 · p. 9

3.0.6 Non-DSS Operation

  • The framework extends beyond DSS cycling: flowable-electrode calculations use total experiment time, while batch-mode quantities can be used to compute the same performance metrics.The general approach is intended to hold across operation methods.Source: §3.0.6 · p. 10

4 Performance Indicators

The section presents indicators that complement operational performance metrics by helping explain why materials, device architectures, and operating modes perform differently; they are not performance metrics themselves.

4.1 Salt Adsorption Capacity

  • Eq-SAC indicates the upper limit of desalination capacity over a voltage window, but cannot substitute for energy consumption and throughput as a performance metric.It is influenced by equilibrium charge efficiency, charging and discharging voltages, point of zero charge (PZC), and material capacitance.Source: §4.1 · p. 10

4.2 Capacitance and PZC

  • Capacitance and PZC affect desalination capacity; evaluating capacitance at CDI-relevant low salinities requires care because depletion, resistive, PZC, and Faradaic effects can obscure measurements.Cyclic voltammetry should use relevant concentrations and sweep rates, avoid depletion, and continue until desalination steady state is reached; intercalation storage may be better characterized by electrode capacity and voltage window.Source: §4.2 · p. 11

4.3 Charge and Coulombic Efficiencies

  • Charge and Coulombic efficiencies reflect disparities between electrical charge transferred and salt removed; together they help identify operational performance losses.Flow efficiency captures the fraction of electrode-adsorbed salt removed from the effluent, while round-trip Coulombic efficiency measures Faradaic charge loss; co-ion expulsion, parasitic reactions, and unrecovered desalinated water can contribute to disparities.Source: §4.3 · p. 12

4.4 Series Resistance

  • Series resistance helps explain energy loss and operational performance in CDI’s high-current, low-voltage cells; it comprises external electronic resistance and separator resistance.High-frequency electrochemical impedance spectroscopy can measure total series resistance, but abrupt current or voltage steps may also capture electrode ionic resistance, and resistance changes during a cycle as electrolyte conductivity changes.Source: §4.4 · pp. 12–13

5 Parameter Summary

The section consolidates separation conditions, performance metrics, and indicators, alongside cell characteristics useful for interpreting desalination results. It also provides a separation-report format and a downloadable spreadsheet for reuse.

5 Parameter Summary

  • Table 1 summarizes essential separation conditions, performance metrics, and indicators, while the SI defines the parameters and adds cell characteristics in Tables S2 and S3.Source: §5 · p. 13
  • Dry electrode density enables conversion between gravimetric and volumetric parameters, membrane count informs device-cost estimates, and electrode and separator thickness influence many reported parameters.Source: §5 · pp. 13–14
  • The cell underlying Fig. 4 is documented in an SI Table S2 separation report, and a downloadable Excel spreadsheet provides the report format for other studies.Source: §5 · p. 14

6 Conclusions

The paper proposes a CDI performance framework based on volumetric energy consumption and throughput productivity reported under equivalent separation conditions. It recommends a nominal standard separation to make evaluations more comparable and practically meaningful.

6 Conclusions

  • The proposed framework quantifies CDI performance using volumetric energy consumption (Wh/m3) and throughput productivity (L/h/m2), reported for equivalent separation conditions.The authors argue that unspecified removal conditions can make comparisons ambiguous and allow evaluation at unspecified removal.Source: §6 · p. 14
  • For research comparisons, the proposed nominal standard is removing 5 mM from a 20 mM NaCl feed at 50% water recovery.The authors use this separation to compare an fte-CDI cell with an fb-MCDI cell in terms of generic desalination performance.Source: §6 · p. 14
  • The paper also discusses cell characteristics and performance indicators that help explain measured performance metrics, though they are not themselves the framework’s headline metrics.The framework is intended to align CDI reporting with desalination more generally and support more comparable, relevant performance evaluations.Source: §6 · p. 14

1 Parameter Definitions

This section inventories the symbols, definitions, and typical units used in the main text and SI, covering cell performance, operation, and material properties.

1 Parameter Definitions

  • The parameter inventory defines cell-level quantities including maximum salt adsorption capacity, feed-salt molar mass, electrode mass, electrode-pair and membrane counts, and cycle charge metrics.It also specifies the units for each quantity, including mg/g for maximum salt adsorption capacity and % for cycle charge efficiency.Source: Table S1 · p. 20, §1 · p. 21
  • Operating parameters include applied charging/discharging current and voltage, cell pressure drop, electrode and separator thicknesses, and electrode mass density.Their typical units include mA, V, psi, µm, and g/cm3, respectively.Source: Table S1 · p. 20, §1 · p. 21
  • Material and structural parameters cover electrode conductivity, macro- and microporosity, skeleton-material fraction, separator porosity, and electrode and separator tortuosity.The inventory also defines the van’t Hoff factor, absolute temperature, and ideal gas constant, with temperature in K and R = 8.3145 J/mol/K.Source: §1 · p. 21

2 Cell Data for Figs. 1 and 2

This section documents the fte-CDI and fb-MCDI cell designs, characterization data, and experimental operating conditions used for the reported performance measurements.

2.1 fte-CDI Cell Design and Testing

  • Supplementary data show CV and EIS for the fte-CDI cell in main-text Figs. 3 and 4a,b, with flow at 3.9 ml/min to avoid depletion; DSS concentration- and voltage-time data underlie Fig. 4a,b performance.Source: Figure S1 · p. 21, §2.1 · p. 22, Figure S3 · p. 23
  • The fte-CDI cell’s projected face area is its width multiplied by its height.Figure S2 provides an exploded-view schematic illustrating the relevant cell dimensions.Source: Figure S2 · p. 22, §2.1 · p. 22

2.2 fb-MCDI Cell Design and Testing

  • The fb-MCDI stack comprised four cells with 135 cm2 total projected area, each containing porous carbon electrodes, cation- and anion-selective membranes, and a woven-mesh separator.Each cell had a projected area of 33.75 cm2; electrodes were approximately 0.55 g and 250 µm thick, and the separator was approximately 150 µm thick.Source: §2.2 · p. 23
  • The MCDI experiments used a fixed feed-water concentration of approximately 20 mM, pumped from a 10 L vessel without nitrogen flushing to remove dissolved oxygen.fb-MCDI cycles held charging/discharging current equal and flow rate constant, used a preset 0 V discharge voltage, and varied current from 0.74–1.85 mA/cm2.Source: §2.2 · pp. 23–24
  • Experimental data were collected at cycle times of 2 and 6 min; Fig. 5 results used total flow rates of 7.5, 3.75, 2.5, and 1.875 mL/min.Figure S4 reports a 6-min cycle at 3.75 ml/min per cell; Figure S5 gives experimental charge and Coulombic-efficiency data underlying Fig. 4c,d.Source: §2.2 · p. 24, Figure S4 · p. 25, Figure S5 · p. 26

3 Thermodynamic Energy Consumption for a Separation

The section defines thermodynamic minimum volumetric energy consumption for a separation using specific Gibbs free energy, then compares that minimum with measured energy consumption to assess thermodynamic efficiency.

3 Thermodynamic Energy Consumption for a Separation

  • The thermodynamic minimum volumetric energy consumption (Ev,th) for a removal is calculated using the specific Gibbs free energy of separation defined in Wang et al.,6.The equation is expressed for the separation conditions discussed in this work.Source: §3 · p. 26
  • The calculation assumes a van’t Hoff factor of 2 and an absolute temperature of 294.15 K.The ideal gas constant is 8.3145 J/mol/K.Source: §3 · p. 26
  • The thermodynamic efficiency is the minimum energy divided by experimentally measured Ev for the Fig. 4b separations, with Fig. S6 noting 24 L/h/m2 productivity at 5 mM removal.The efficiency is shown in Fig. S6.Source: §3 · p. 26, Figure S6 · p. 27

4 Numerical Analysis of Experimental Cycle Data

The section describes a numerical approach for obtaining areas of a function above and below a reference value over a time interval. These areas support calculation of several cycle metrics using integrals over the full DSS cycle.

4 Numerical Analysis of Experimental Cycle Data

  • The method obtains areas of f(t) above and below f0 over [t0, tf] to calculate Nout, Ein, Eout, Vd, Vc, qin, and qout.The areas are denoted |A+| and |A−|, their magnitudes above and below f0, respectively.Source: §4 · p. 28, Figure S8 · p. 28
  • Only integrals over the entire DSS cycle need to be computed to obtain the areas of interest.Appropriate manipulation of the integrand’s sign yields the required areas.Source: §4 · p. 28

5 Measuring Capacitance and PZC with CV

CV analysis shows that capacitance depends on ionic strength and on how it is evaluated, so CDI-relevant material comparisons need specified measurement conditions.

5 Measuring Capacitance and PZC with CV

  • The example CV measurements span NaCl concentrations from CDI-relevant 20 mM to energy-storage-relevant 2 M using two identical activated-carbon electrodes in a stirred beaker.The electrodes were separated by polyester mesh and contacted with a four-wire probe.Source: §5 · p. 29
  • In the identical two-electrode cell, the PZC minimum appears on both the positive-voltage charging side and the discharge, negative-voltage half of the CV measurement.The PZC is approximately symmetric at ±0.48 V.Source: §5 · p. 29, Figure S9 · p. 30
  • Capacitance evaluated at zero applied voltage differs significantly from capacitance at the PZC, so the evaluation method matters in CDI-relevant comparisons.The reported values compare capacitance at V = 0 with the average discharge PZC local minimum.Source: §5 · p. 29
  • At 20 mM NaCl, PZC capacitance is 67% of its value at 2 M NaCl.The comparison uses capacitance evaluated at the PZC.Source: §5 · p. 29, Figure S9 · p. 30

6 Measuring Series Resistance with EIS

EIS identifies series resistance (Rs) from the high-frequency Nyquist intercept where -Im(Z) tends to zero. Separator-stacking and concentration-series tests show how Rs varies with separator number and solution resistivity, enabling resistance analysis in assembled cells.

6 Measuring Series Resistance with EIS

  • Rs is the high-frequency Re(Z) value where -Im(Z) tends to zero; the example spectra used a 2×2 cm stacked HCAM assembly in 20 mM NaCl at zero applied bias.The spectra covered 700 kHz to 40 mHz and used a 4-wire point-probe connection with 1 mm thick electrodes.Source: §6 · p. 30
  • The EIS method applies to fully assembled cells and can identify a significant portion of device resistance breakdown [5,11–13].The total Nyquist-plot shape provides information about all system resistances, while the -Im(Z)=0 intercept reveals Rs specifically.Source: §6 · p. 31
  • Stacking separators shifts the Nyquist plot to higher Re(Z) without changing its shape, while Rs versus separator count forms a straight line revealing REER and Rs.For the tested arrangement, the reported slope is 3.82 Ω/separator.Source: §6 · pp. 30–31, Figure S10 · p. 32
  • A concentration series reveals series-resistance components: Rs varies linearly with solution resistivity, and higher NaCl concentration shifts the Nyquist data to lower Re(Z).The reported slope for the tested arrangement is 0.521 m−1; EIS measurements were taken at zero applied bias.Source: §6 · p. 31, Figure S11 · p. 33

7 Separation Report

The section proposes a supplementary CDI separation report to ensure critical cell dimensions and material characteristics are reported. It explains which measurements aid performance normalization, cost estimation, and understanding cell resistance and fluid volume.

7 Separation Report

  • Cell face area A and electrode thickness le support performance normalization: electrode volume A·le normalizes capacitance, while face area normalizes productivity.The report also calls for the basic cell dimensions and material characteristics behind the separation.Source: §7 · p. 34
  • Membrane face area and number nm are important for estimating device cost, since membranes typically cost $200/m2 or more.Source: §7 · p. 34
  • Electrode mass m and density ρe help categorize material performance, while separator and electrode porosity estimates inform cell resistance and fluid volume [5,14] [2,12].Porosity examples include microporosity pmi, macroporosity pmA, and “skeleton” porosity psk.Source: §7 · p. 34
  • A supplementary separation report, accompanied by an SI spreadsheet, should capture critical cell characteristics; even a partially completed report is valuable.The proposed report corresponds to the data in Fig. 2 in the main text.Source: §7 · p. 34
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