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Special Issue Research Papers

Harvesting Natural Salinity Gradient Energy for Hydrogen Production Through Reverse Electrodialysis Power Generation OPEN ACCESS

[+] Author and Article Information
Mohammadreza Nazemi

Department of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405
e-mail: mrnazemi@gatech.edu

Jiankai Zhang

Department of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405
e-mail: jzhang794@gatech.edu

Marta C. Hatzell

Mem. ASME
Department of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405
e-mail: marta.hatzell@me.gatech.edu

1Corresponding author.

Manuscript received November 17, 2016; final manuscript received January 15, 2017; published online May 2, 2017. Assoc. Editor: Dirk Henkensmeier.

J. Electrochem. En. Conv. Stor. 14(2), 020702 (May 02, 2017) (6 pages) Paper No: JEECS-16-1152; doi: 10.1115/1.4035835 History: Received November 17, 2016; Revised January 15, 2017

There is an enormous potential for energy generation from the mixing of sea and river water at global estuaries. Here, we model a novel approach to convert this source of energy directly into hydrogen and electricity using reverse electrodialysis (RED). RED relies on converting ionic current to electric current using multiple membranes and redox-based electrodes. A thermodynamic model for RED is created to evaluate the electricity and hydrogen which can be extracted from natural mixing processes. With equal volume of high and low concentration solutions (1 L), the maximum energy extracted per volume of solution mixed occurred when the number of membranes is reduced, with the lowest number tested here being five membrane pairs. At this operating point, 0.32 kWh/m3 is extracted as electrical energy and 0.95 kWh/m3 as hydrogen energy. This corresponded to an electrical energy conversion efficiency of 15%, a hydrogen energy efficiency of 35%, and therefore, a total mixing energy efficiency of nearly 50%. As the number of membrane pairs increases from 5 to 20, the hydrogen power density decreases from 13.6 W/m2 to 2.4 W/m2 at optimum external load. In contrast, the electrical power density increases from 0.84 W/m2 to 2.2 W/m2. Optimum operation of RED depends significantly on the external load (external device). A small load will increase hydrogen energy while decreasing electrical energy. This trade-off is critical in order to optimally operate an RED cell for both hydrogen and electricity generation.

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The global energy demand is increasing and mainly dependent on fossil fuels. Presently, fossil fuels such as oil, gas, and coal satisfy 80% of the global energy demand. This results in more than 30 billion metric tons of carbon dioxide (CO2) annually [1]. The development of new methods to extract energy from clean (i.e., no emissions) energy sources is a viable alternative to meet energy demands and reduce emissions. Common approaches for extracting renewable energy have focused on wind, solar, biomass, and hydroelectric power. Another untapped source of renewable energy exists at estuaries where sea and river water mix. This energy termed salinity gradient energy (SGE) has been estimated to be between 1.7 and 2.6 TW, which is approximately 15–20% of the worldwide energy demand (global electricity consumption is 2 TW) [13].

Pressure retarded osmosis (PRO), capacitive mixing (CapMix), and reverse electrodialysis (RED) are currently the three main technologies being investigated to capture energy from salinity gradients. These technologies can convert the Gibbs free energy of mixing associated with high concentration (HC) and low concentration (LC) solutions, into usable forms of energy (e.g., electricity or fuels). PRO [46] uses the flow of water through the membranes to produce pressurized water which drives a shaft and generates electricity. Capacitive mixing [79] generates energy by modulating an electric double layer in high and low concentration solutions.

Experimental studies have investigated the production of hydrogen gas through RED power generation [10,11]. The results showed that RED can produce 50% more energy if the generated hydrogen gas is recovered using ammonium bicarbonate (AmB) solutions [10].

Experimental [1214] and modeling [1517] of RED mainly have investigated the effect stack design parameters (e.g., intermembrane distance and number of membrane pairs) have on electrical energy efficiency and power density. However, hydrogen gas production may also be a possible energy carrier for RED systems (Fig. 1). Hydrogen generation can be a viable solution to improve energy recovery in RED (50% energy recovery [17]) compared to PRO (65% energy recovery [5]). Furthermore, total global hydrogen production is increasing by approximately 6% each year.

There is no theoretical analysis which investigates the feasibility for hydrogen gas production using RED. RED [1820] uses a series of selective ion exchange membranes (IEM) to mix seawater and freshwater. An RED stack is comprised of a series of alternating anion membranes (AEM) and cation exchange membranes (CEM). The AEM and CEM aid in separating alternating flow channels with HC and LC solutions (Fig. 1). A Donnan potential or voltage created at the membrane interface due to this concentration gradient drives redox reactions creating electric current. Here, a thermodynamic model for RED is presented which evaluates the portion of mixing energy converted to not only electrical energy but also hydrogen energy at the redox electrodes. Performance metrics of RED (i.e., power density and energy density) for both hydrogen and electricity with various number of membrane pairs are examined. The relationship between power density, RED stack voltage, and total RED resistance with the number of membrane pairs is explored. Furthermore, the dependence of electrical energy and hydrogen energy on voltage and current density is evaluated.

In this section, a thermodynamic model for RED systems with a varying number of membrane pairs is outlined. For a fixed volume of water (irrespective of the number of membrane pairs), we evaluate the portion of free energy of mixing that can be harvested to generate electricity and hydrogen during a complete mixing process (closed loop). Equations to calculate Gibbs free energy (ideal work), electrical energy, hydrogen energy, and electrical and hydrogen power density of the RED are presented. In this model, a 1 L HC (600 mM or 35 g/L NaCl) and LC (1.5 mM or 88 mg/L NaCl) solutions are fixed to simulate seawater and river water. The operating temperature of the RED is 298 K and held constant during each analysis.

Thermodynamic Model of the RED Cell.

The RED stack components are not ideally electrically or ionically conductive, and a range of ohmic-based resistances impede ions movement through the solution and IEMs. The total ohmic resistance of the RED stack consisting of N membrane pairs is obtained by the following equation: Display Formula

(1)ASRstack=N(ASRAEM+ASRCEM+dHCκHC+dLCκLC)

where the area-specific resistance of the stack, ASRstack, is the product of the stack resistance (rstack) and the membrane area (A), d is the intermembrane distance, and κ is the solution conductivity. Here, ASR of the CEM and AEMs is fixed based on experimentally verified values, 3 Ω cm2, d is 150 μm, and HC and LC solutions' conductivities are 52.79 mS/cm and 0.132 mS/cm at the start of the controlled mixing process [21]. The reaction-based resistance is neglected in this work, making the IEMs the dominant resistance. However, in reality it is known that as the number of membrane pairs decreases, the electrodes limit system performance.

The Donnan potential of the stack, ξstack, is the sum of the voltage over each perfectly selective membrane (CEM + AEM) due to the salt concentration gradient between HC and LC solutions, which is calculated by the following equation: Display Formula

(2)ξstack=N(2αRgTzFlnγHCCHCγLCCLC)

where α is the permselectivity of the ion exchange membrane, Rg is the gas constant, T is the absolute temperature, z is the ion valence, F is the Faraday constant (96,485 C/eq), and γ is the activity coefficient of the salt ions (i.e., Na+ and Cl) in the HC and LC solutions.

The effect of activity coefficient (γ) is relatively small (∼5%) for the salt concentrations considered here. Therefore, the activity coefficient was assumed to be one. Furthermore, α is 1 for the membrane with perfect selectivity. Selectivity imperfections (α < 1, e.g., α = 0.9) such as co-ion transport across the membrane and diffusion of water from LC to HC due to osmotic force result in decreased stack voltage achieved using Eq. (2). In reality, the effect of osmosis during the batch cycle testing is less pronounced compared to the single pass as the concentration gradient between LC and HC diminishes over the course of experiment. Here, ideal ion exchange membrane with perfect selectivity is assumed.

In order to calculate the actual work of the system, an external load with constant ohmic resistance, RL, is connected in series with the RED stack. The potential difference across the load, ξL, is obtained by the following relation: Display Formula

(3)ξL=RLξstack(RL+ASRstack)

It is assumed that the ionic current from the RED stack is completely converted to electric current. This assumption is valid if the charge transfer resistance is negligible compared to ionic and electric resistance (∼3% of the ohmic-based resistances [22]). Therefore, the electric current density (i) based on ohm's law is calculated as Display Formula

(4)iIAe=ξstack(RL+ASRstack)=ξLRL

where I is the electric current and it is equal to the ionic current, and Ae is the electrode area which equals to a single membrane area (Ae = Am).

The theoretical moles of hydrogen produced in the RED stack are [10] Display Formula

(5)nH2=i×3600zFη

where nH2 is the moles of hydrogen gas, z is the ion valence (z = 2 per mole of hydrogen gas), and η is a electrolysis conversion efficiency factor which considers hydrogen gas losses (η = 0.8) [10]. This factor signifies that the current density generated is not fully converted to hydrogen gas due to various system related losses. The stack voltage should exceed the minimum required voltage for water splitting (1.23 V) to generate hydrogen. In this analysis, anode and cathode activation overpotentials and concentration losses which decrease the useful voltage and therefore hydrogen gas production are neglected. Sufficient mixing can decrease or mitigate the effects of concentration polarization at the membrane–solution interface. The oxygen evolution reaction (OER) overpotential acts as a major loss to decrease the usable voltage (e.g., ∼5% of the stack voltage prior to mixing for 20 membrane pairs). The hydrogen evolution reaction (HER) or cathode overpotential is almost negligible for various number of membrane pairs (<0.2% of the stack voltage prior to mixing). Future work will investigate incorporating these losses into the thermochemical model. Furthermore, the spacer shadow effect (i.e., reduction of effective membrane area by nonconductive spacers) is neglected.

The hydrogen power density (PDH2) is calculated using the higher heating value (HHV) of hydrogen Display Formula

(6)PDH2=nH2×ΔHH2(0.277)

where ΔHH2 is the HHV of hydrogen (286 kJ/mol), and 0.277 is a conversion factor from kilojoules to watt-hour. The overall power density of hydrogen is normalized by the total membrane area.

The entire duration of the controlled mixing process (t) required for LC and HC solutions to reach an equilibrium condition is Display Formula

(7)t=0Δnsf(νzFVRLξL)Δns

where ν is the number of ions each salt molecule decomposes into (e.g., ν is 2 for NaCl), z is the ion valence (e.g., z = ±1 for Na+ and Cl), V is the total volume of HC and LC solutions, Δns is the moles of salt transported across the IEMs, and Δnsf is the moles of salt finally permeated across the IEMs. Normalized time area is defined as the time calculated in Eq. (7) per unit total volume of the LC and HC solutions (2 L).

The total energy of hydrogen generated through the RED stack is calculated as the integral of hydrogen power density across the controlled mixing process duration Display Formula

(8)EH2=0tPDH2dt

The electrical energy produced in the RED stack is calculated as the integral of ξL across the charges transported [17] by the combination of Eqs. (2), (3), and (10)Display Formula

(9)Eelectrical=ξLdq=NνRgT0ΔnsfRLRL+ASRstacklncHCcLCdΔns

where the total number of charges transported over the controlled mixing process is obtained by Display Formula

(10)Δq=νzFΔns

the term νzΔns determines the total number of charge equivalents (eq) transported across the membrane.

In case of a very large external resistance (i.e., approximately zero current), the ratio RL/(RL+ASRstack) in Eq. (9) approaches unity. Therefore, maximum extractable energy or ideal work which is equal to the Gibbs free energy of the system in a reversible thermodynamic process is calculated by Display Formula

(11)Eideal=NνRgT0ΔnsflncHCcLCdΔns

The electrical power density (PDelectrical) of the RED stack with N membrane pairs is obtained as the electrical power generated over the total IEM area (A) Display Formula

(12)PDelectrical=PLA=12N(ξLRL)2(RL)

where PL is the electrical power generated (W).

The optimum RL that maximizes the overall hydrogen and electrical power density is obtained by solving for d(PDelectrical+PDH2)/dRL equals to zero. The optimum RL is calculated by the following relation: Display Formula

(13)RL=ASRstack(ξstack3600ηΔHH2·(0.277)zF)ξstack+3600ηΔHH2·(0.277)zF

This results in 6.35, 42.89, and 130.18 Ω cm2 constant optimum load for 5, 10, and 20 membrane pairs.

Energy conversion efficiency of the RED stack is the sum of electrical and hydrogen energy extracted over the maximum extractable energy (ideal work) Display Formula

(14)η=EH2+EelectricalEideal

In the developed model, the highest resistance corresponded to the start of the mixing process, where the LC solution accounted for 95% of the total RED resistance (Fig. 2). This trend is because membranes were assumed to be perfect (e.g., low resistance and high permselectivity). Practically, high membrane resistance in low concentration solutions also accounts for a significance portion of the stack resistance. As salt ions are transported from HC to LC solution, the salt concentration in the LC solution increases, decreasing the LC resistance (Eq. (1)). This also results in a decrease in the total RED stack resistance (e.g., from ASRstack = 600 Ω cm2 to ASRstack = 35.7 Ω cm2 for five membrane pairs in Fig. 2(a)). Here, the membrane resistances begin to dominate the whole cell after ∼1/3 of the ion mixing is completed (Fig. 3).

The total resistance of the stack increases linearly by increasing the number of membrane pairs (N) based on Eq. (1). The overall RED stack resistance increases from approximately 600 Ω m2 for five pairs to 2400 Ω m2 for 20 pairs at the start of the mixing process (Figs. 2(a)2(c)).

The moles of hydrogen produced in the RED stack are directly proportional to the current generated (Eq. (5)). By increasing the number of membrane pairs from 5 to 20, the maximum current density decreases from 11.5 mA/cm2 to 8.2 mA/cm2 (optimum load operation, RL = 6.35 Ω cm2 for five membrane pairs and RL = 130.18 Ω cm2 for 20 membrane pairs). This corresponds to a decrease in hydrogen produced from 1.72 × 10−4 mol/h cm2 to 1.23 × 10−4 mol/h cm2 (Fig. 3(a)). Maximizing the current density is heavily dependent on the external resistance and salt concentration of solutions used (Eqs. (3) and (4)). Decreasing RL can increase the current density and moles of hydrogen produced (Eqs. (4) and (5)). Furthermore, efforts to increase the concentration gradient of the input systems could lead to greater current generated; however, this can only be accomplished if synthetic (not natural) solutions, concentrated brine [23], or thermally regenerative salts are used.

Hydrogen power density is proportional to the moles of hydrogen produced (Eq. (6)). The trend for PDH2 as a function of Δns mimics that of nH2 and i. Maximum PDH2 with five membrane pairs approaches 13.6 W/m2. The minimum PDH2 (2.4 W/m2) is achieved using 20 membrane pairs (Fig. 3(b)) (RL = 6.35 Ω cm2 for five membrane pairs and RL = 130.18 Ω cm2 for 20 membrane pairs). Proper selection of external load can mimic operating near the limiting current density which corresponds to maximum hydrogen power density.

As salt ions permeated across IEMs, cHC decreases and cLC increases. Therefore, ξstack decreases and approaches zero when the equilibrium concentration is reached (Eq. (2)). The ξstack increases by the factor of N as increasing the number of membrane pairs (Fig. 4(a)). The ξL does not increase by the factor of N because of the increased overall RED resistance. With the optimum external resistance (RL = 6.35 Ω cm2 for five membrane pairs and RL = 130.18 Ω cm2 for 20 membrane pairs), the peak voltage across the load increases from 73.0 mV for five membrane pairs to 1067.8 mV for 20 membrane pairs (Fig. 4(a)).

The low value of ξL at the beginning of the mixing process is due to the high total RED resistance. By choosing an extremely high external resistance, greater load potential and electrical energy can be obtained based on Eqs. (3) and (9), yet this is at the expense of the hydrogen power and energy density as current density decreases. Here, optimum load was chosen to maximize the total electrical and hydrogen power density for various number of membrane pairs (Eq. (13)).

In the ideal case with no losses in the system, Eideal increases proportionally by increasing the number of membrane pairs where the maximum Eideal (11.2 kWh/m3) is achieved using 20 membrane pairs (Fig. 4(b)). In the actual case, Eelectrical increases from 0.32 kW h/m3 for five membrane pairs to 4.29 kWh/m3 for 20 membrane pairs (Fig. 4(b)).

The PDH2 is considerably greater than the PDelectrical (Fig. 5(a)). The maximum PDH2 (13.6 W/m2) is achieved using five membrane pairs, while ∼2.2 W/m2 maximum PDelectrical is obtained with 20 membrane pairs at the fixed optimum external resistance (RL = 6.35 Ω cm2 for five membrane pairs and RL = 130.18 Ω cm2 for 20 membrane pairs). Opposite trend of PDelectrical and PDH2 signifies the importance of choosing an appropriate load to optimize RED. Lower load resistance contributes to more hydrogen power density, while higher load resistance results in greater electrical power density.

By extracting hydrogen energy in RED, the portion of mixing energy (Gibbs free energy) converted into useful energy is increased (Figs. 5(b) and 5(c)). Although, by increasing the number of membrane pairs from 5 to 20, Eelectrical rises from 0.32 kWh/m3 to 4.29 kWh/m3, EH2 drops from 0.95 kWh/m3 to 0.24 kWh/m3 (Figs. 5(b) and 5(c)).

A thermodynamic model of the RED stack was developed to investigate the hydrogen gas and electricity generation. Maximum current density (11.5 mA/cm2) and moles of hydrogen gas produced (1.72 × 10−4 mol/h cm2) were obtained at five membrane pairs. The optimum fixed load (6.35, 42.89, and 130.18 Ω cm2 for 5, 10, and 20 membrane pairs) was chosen to maximize the overall hydrogen and electrical power density. By increasing external resistance, higher PDelectrical can be obtained, yet this is at the expense of hydrogen power and total energy density for various number of membrane pairs. Maximum PDH2 (13.6 W/m2) was obtained with five membrane pairs, while ∼2.2 W/m2 maximum PDelectrical was achieved with 20 membrane pairs. This compromise in selecting an appropriate load should be considered in future RED analysis. Changing the salt concentration of the HC and LC solutions or using the concentrated brine can improve the load potential and current density. This results in higher PDH2 and EH2, but requires the use of synthetic salt solutions rather than natural solutions. An increase in ξL (∼1 V) causes an improvement in Eelectrical (4 kW h/m3) from 5 to 20 membrane pairs. Overall, the total energy extracted (hydrogen and electrical) was 4.53 kW h/m3 which occurred with 20 number of membrane pairs.

The authors gratefully acknowledge Georgia Institute of Technology for supporting this work.

  • A =

    total membrane area (cm2)

  • Ae =

    electrode area (cm2)

  • Am =

    area of one membrane (cm2)

  • ASRAEM =

    area-specific resistance of the AEM (Ω cm2)

  • ASRCEM =

    area-specific resistance of the CEM (Ω cm2)

  • ASRstack =

    area-specific resistance of the RED stack (Ω cm2)

  • CHC =

    concentration of HC solution (mM)

  • CLC =

    concentration of LC solution (mM)

  • dHC =

    intermembrane distance of HC channel (μm)

  • dLC =

    intermembrane distance of LC channel (μm)

  • Eelectrical =

    electrical energy (kWh/m3)

  • Eideal =

    ideal energy (kWh/m3)

  • EH2 =

    hydrogen energy (kWh/m3)

  • F =

    Faraday's constant (C/eq)

  • i =

    current density (mA/cm2)

  • I =

    electric current (mA)

  • N =

    number of membrane pairs

  • nH2 =

    moles of hydrogen (mol/h cm2)

  • PL =

    electrical power (W)

  • PDelectrical =

    electrical power density (W/m2)

  • PDH2 =

    hydrogen power density (W/m2)

  • Rg =

    gas constant (J/mol K)

  • RL =

    external resistance (load) (Ω cm2)

  • rstack =

    stack resistance (Ω)

  • t =

    controlled mixing process duration (min m2/L)

  • T =

    absolute temperature (K)

  • z =

    ion valence (eq/mol)

  • γ =

    activity coefficient of the salt ions

  • ΔGmix =

    Gibbs free energy of mixing (kWh/m3)

  • ΔHH2 =

    HHV of hydrogen (kJ/mol)

  • Δns =

    moles of salt permeated across IEMs (mol)

  • Δnsf =

    moles of salt finally permeated across IEMs (mol)

  • η =

    electrolysis conversion efficiency factor

  • κHC =

    conductivity of the HC solution (mS/cm)

  • κLC =

    conductivity of the LC solution (mS/cm)

  • ν =

    number of ions each salt molecules dissociate into

  • ξL =

    potential difference across the load (mV)

  • ξstack =

    stack potential (V)

Nijmeijer, K. , and Metz, S. , 2010, “ Salinity Gradient Energy,” Sustainability Sci. Eng., 2, pp. 95–139.
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Brogioli, D. , 2009, “ Extracting Renewable Energy From a Salinity Difference Using a Capacitor,” Phys. Rev. Lett., 103(5), p. 058501. [CrossRef] [PubMed]
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References

Nijmeijer, K. , and Metz, S. , 2010, “ Salinity Gradient Energy,” Sustainability Sci. Eng., 2, pp. 95–139.
Alvarez-Silva, O. , Osorio, A. , and Winter, C. , 2016, “ Practical Global Salinity Gradient Energy Potential,” Renewable Sustainable Energy Rev., 60, pp. 1387–1395. [CrossRef]
Logan, B. E. , and Elimelech, M. , 2012, “ Membrane-Based Processes for Sustainable Power Generation Using Water,” Nature, 488(7411), pp. 313–319. [CrossRef] [PubMed]
Lee, K. P. , Arnot, T. C. , and Mattia, D. , 2011, “ A Review of Reverse Osmosis Membrane Materials for Desalination-Development to Date and Future Potential,” J. Membr. Sci., 370(1), pp. 1–22. [CrossRef]
Yip, N. Y. , and Elimelech, M. , 2012, “ Thermodynamic and Energy Efficiency Analysis of Power Generation From Natural Salinity Gradients by Pressure Retarded Osmosis,” Environ. Sci. Technol., 46(9), pp. 5230–5239. [CrossRef] [PubMed]
Straub, A. P. , Deshmukh, A. , and Elimelech, M. , 2016, “ Pressure-Retarded Osmosis for Power Generation From Salinity Gradients: Is It Viable?” Energy Environ. Sci., 9(1), pp. 31–48. [CrossRef]
Brogioli, D. , 2009, “ Extracting Renewable Energy From a Salinity Difference Using a Capacitor,” Phys. Rev. Lett., 103(5), p. 058501. [CrossRef] [PubMed]
Sales, B. , Saakes, M. , Post, J. , Buisman, C. , Biesheuvel, P. , and Hamelers, H. , 2010, “ Direct Power Production From a Water Salinity Difference in a Membrane-Modified Supercapacitor Flow Cell,” Environ. Sci. Technol., 44(14), pp. 5661–5665. [CrossRef] [PubMed]
Brogioli, D. , Ziano, R. , Rica, R. , Salerno, D. , and Mantegazza, F. , 2013, “ Capacitive Mixing for the Extraction of Energy From Salinity Differences: Survey of Experimental Results and Electrochemical Models,” J. Colloid Interface Sci., 407, pp. 457–466. [CrossRef] [PubMed]
Hatzell, M. C. , Ivanov, I. , Cusick, R. D. , Zhu, X. , and Logan, B. E. , 2014, “ Comparison of Hydrogen Production and Electrical Power Generation for Energy Capture in Closed-Loop Ammonium Bicarbonate Reverse Electrodialysis Systems,” Phys. Chem. Chem. Phys., 16(4), pp. 1632–1638. [CrossRef] [PubMed]
Hatzell, M. C. , and Zhu, X. , 2014, “ Simultaneous Hydrogen Generation and Waste Acid Neutralization in a Reverse Electrodialysis System,” ACS Sustainable Chem. Eng., 2(9), pp. 2211–2216. [CrossRef]
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Figures

Grahic Jump Location
Fig. 1

Reverse electrodialysis system for electricity and hydrogen gas generation. Hydrogen is produced at the cathode through a proton reduction reaction.

Grahic Jump Location
Fig. 2

Area-specific resistance (ASR) of the RED stack and its components (i.e., CEM, AEM, LC solution, and HC solution) and load as a function of moles of salt permeated across IEMs: (a) five membrane pairs, (b) 10 membrane pairs, and (c) 20 membrane pairs. IEMs include CEMs and AEMs. The total indicates overall RED stack resistance. Load is held constant during each analysis (6.35, 42.89, and 130.18 Ω cm2 for 5, 10, and 20 membrane pairs).

Grahic Jump Location
Fig. 3

(a) Moles of hydrogen, nH2, produced through RED stack and current density, i, and (b) hydrogen power density, PDH2, as a function of moles of salt permeated across IEMs for 5, 10, and 20 membrane pairs

Grahic Jump Location
Fig. 4

(a) Stack voltage, ξstack, and potential difference across the external load, ξL, and (b) maximum extractable energy (Gibbs free energy), Eideal, and electrical energy, Eelectrical, as a function of moles of salt permeated across IEMs for 5, 10, and 20 membrane pairs

Grahic Jump Location
Fig. 5

(a) Hydrogen and electrical power density, PD, (b) ideal energy (Gibbs free energy), Eideal, and (c) electrical and hydrogen energy extracted through RED stack as a function of normalized time area, t, for 5, 10, and 20 membrane pairs

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