#
Heat to H_{2}: Using Waste Heat for Hydrogen Production through Reverse Electrodialysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### Scope of This Paper

## 2. Concepts

#### 2.1. Salt Extraction by Precipitation

#### 2.2. Water Extraction by Evaporation

#### 2.3. Temperature and Concentration Limitaitons

## 3. Theory

#### 3.1. Driving Voltage

#### 3.2. Losses

#### 3.3. Ionic Membrane Conductivity

#### 3.4. Electrochemical Impedance Spectrocopy

## 4. Experimental

#### 4.1. Membrane Preparation

#### 4.2. Ion Conductivity Measurement

#### 4.3. Power Density and Hydrogen Production

#### 4.4. Energy Used in Solution Separation

## 5. Results and Discussion

#### 5.1. Ion Conductivity Measurements

#### 5.2. Modeling of Hydrogen Production

#### 5.3. Energy Consumption and Cost

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- From Waste Heat to a Resource. Available online: https://www.sintef.no/en/projects/from-waste-heat-to-a-resource/ (accessed on 1 July 2019).
- Enova, S.F. Annual Report 2009—Results and Activities; Technical Report; Enova: Trondheim, Norway, 2009.
- Brueckner, S.; Miró, L.; Cabeza, L.F.; Pehnt, M.; Laevemann, E. Methods to estimate the industrial waste heat potential of regions–A categorization and literature review. Renew. Sustain. Energy Rev.
**2014**, 38, 164–171. [Google Scholar] [CrossRef] - Jalili, Z.; Krakhella, K.W.; Einarsrud, K.E.; Burheim, O.S. Energy generation and storage by salinity gradient power: A model-based assessment. J. Energy Storage
**2019**, 24, 100755. [Google Scholar] [CrossRef] - Pattle, R. Production of electric power by mixing fresh and salt water in the hydroelectric pile. Nature
**1954**, 174, 660. [Google Scholar] [CrossRef] - Wick, G.L. Power from salinity gradients. Energy
**1978**, 3, 95–100. [Google Scholar] [CrossRef] - Weinstein, J.; Leitz, F. Electric power from differences in salinity: The dialytic battery. Science
**1976**, 191, 557–559. [Google Scholar] [CrossRef] - Lacey, R. Energy by reverse electrodialysis. Ocean Eng.
**1980**, 7, 1–47. [Google Scholar] [CrossRef] - Tamburini, A.; Tedesco, M.; Cipollina, A.; Micale, G.; Ciofalo, M.; Papapetrou, M.; Van Baak, W.; Piacentino, A. Reverse electrodialysis heat engine for sustainable power production. Appl. Energy
**2017**, 206, 1334–1353. [Google Scholar] [CrossRef] - Raka, Y.D.; Karoliussen, H.; Lien, K.M.; Burheim, O.S. Opportunities and challenges for thermally driven hydrogen production using reverse electrodialysis system. Int. J. Hydrog. Energy
**2019**. [Google Scholar] [CrossRef] - Luo, X.; Cao, X.; Mo, Y.; Xiao, K.; Zhang, X.; Liang, P.; Huang, X. Power generation by coupling reverse electrodialysis and ammonium bicarbonate: Implication for recovery of waste heat. Electrochem. Commun.
**2012**, 19, 25–28. [Google Scholar] [CrossRef] - Zhu, X.; He, W.; Logan, B.E. Influence of solution concentration and salt types on the performance of reverse electrodialysis cells. J. Membr. Sci.
**2015**, 494, 154–160. [Google Scholar] [CrossRef][Green Version] - Long, R.; Li, B.; Liu, Z.; Liu, W. Hybrid membrane distillation-reverse electrodialysis electricity generation system to harvest low-grade thermal energy. J. Membr. Sci.
**2017**, 525, 107–115. [Google Scholar] [CrossRef] - Nam, J.Y.; Cusick, R.D.; Kim, Y.; Logan, B.E. Hydrogen generation in microbial reverse-electrodialysis electrolysis cells using a heat-regenerated salt solution. Environ. Sci. Technol.
**2012**, 46, 5240–5246. [Google Scholar] [CrossRef] - Luo, X.; Nam, J.Y.; Zhang, F.; Zhang, X.; Liang, P.; Huang, X.; Logan, B.E. Optimization of membrane stack configuration for efficient hydrogen production in microbial reverse-electrodialysis electrolysis cells coupled with thermolytic solutions. Bioresour. Technol.
**2013**, 140, 399–405. [Google Scholar] [CrossRef] - Hatzell, M.C.; Ivanov, I.; Cusick, R.D.; Zhu, X.; Logan, B.E. Comparison of hydrogen production and electrical power generation for energy capture in closed-loop ammonium bicarbonate reverse electrodialysis systems. Phys. Chem. Chem. Phys.
**2014**, 16, 1632–1638. [Google Scholar] [CrossRef] - Skilbred, E.S.; Krakhella, K.W.; Haga, I.J.M.; Pharoah, J.G.; Hillestad, M.; del Alamo Serrano, G.; Burheim, O.S. Heat to H2: Using Waste Heat to Set Up Concentration Differences for Reverse Electrodialysis Hydrogen Production. ECS Trans.
**2018**, 85, 147–161. [Google Scholar] [CrossRef] - FuelCellStore. Fumasep FAS-50; FuelCellStore: College Station, TX, USA, 2019. [Google Scholar]
- FuelCellStore. Fumasep FKS-50; FuelCellStore: College Station, TX, USA, 2019. [Google Scholar]
- Rumble, J.R. Aqueous solubility of inorganic compounds at various temperatures. In Handbook of Chemistry and Physics, 99th ed.; CRC: Boca Raton, FL, USA, 2018. [Google Scholar]
- Inorganic Salts. Available online: https://www.sigmaaldrich.com/chemistry/chemistry-products.html?TablePage=16281684 (accessed on 22 August 2019).
- Tufa, R.A.; Rugiero, E.; Chanda, D.; Hnàt, J.; van Baak, W.; Veerman, J.; Fontananova, E.; Di Profio, G.; Drioli, E.; Bouzek, K.; et al. Salinity gradient power-reverse electrodialysis and alkaline polymer electrolyte water electrolysis for hydrogen production. J. Membr. Sci.
**2016**, 514, 155–164. [Google Scholar] [CrossRef] - Kim, Y.; Logan, B.E. Hydrogen production from inexhaustible supplies of fresh and salt water using microbial reverse-electrodialysis electrolysis cells. Proc. Natl. Acad. Sci. USA
**2011**, 108, 16176–16181. [Google Scholar] [CrossRef][Green Version] - Burheim, O.S. Engineering Energy Storage; Academic Press: Cambridge, MA, USA, 2017. [Google Scholar]
- Stokes, R.H.; Robinson, R.A. Ionic hydration and activity in electrolyte solutions. J. Am. Chem. Soc.
**1948**, 70, 1870–1878. [Google Scholar] [CrossRef] - Glueckauf, E. The influence of ionic hydration on activity coefficients in concentrated electrolyte solutions. Trans. Faraday Soc.
**1955**, 51, 1235–1244. [Google Scholar] [CrossRef] - Dash, D.; Kumar, S.; Mallika, C.; Mudali, U.K. New data on activity coefficients of potassium, nitrate, and chloride ions in aqueous solutions of KNO
_{3}and KCl by ion selective electrodes. ISRN Chem. Eng.**2012**, 2012. [Google Scholar] [CrossRef] - Der Mar Marcos-Arroyo, M.; Khoshkbarchi, M.K.; Vera, J.H. Activity coefficients of sodium, potassium, and nitrate ions in aqueous solutions of NaNO
_{3}, KNO_{3}, and NaNO_{3}+KNO_{3}at 25 °C. J. Solut. Chem.**1996**, 25, 983–1000. [Google Scholar] [CrossRef] - Pitzer, K.S.; Pabalan, R.T. Thermodynamics of NaCl in steam. Geochim. Cosmochim. Acta
**1986**, 50, 1445–1454. [Google Scholar] [CrossRef] - Afanasiev, V.N.; Ustinov, A.N.; Vashurina, I.Y. State of Hydration Shells of Sodium Chloride in Aqueous Solutions in a Wide Concentration Range at 273.15–373.15 K. J. Phys. Chem. B
**2008**, 113, 212–223. [Google Scholar] [CrossRef] - Onori, G. Ionic hydration in sodium chloride solutions. J. Chem. Phys.
**1988**, 89, 510–516. [Google Scholar] [CrossRef] - Lu, G.W.; Li, C.X.; Wang, W.C.; Wang, Z.H. Structure of KNO
_{3}electrolyte solutions: A Monte Carlo study. Fluid Phase Equilibria**2004**, 225, 1–11. [Google Scholar] [CrossRef] - Ribeiro, A.C.; Lobo, V.M.; Burrows, H.D.; Valente, A.J.; Sobral, A.J.; Amado, A.M.; Santos, C.I.; Esteso, M.A. Mean distance of closest approach of potassium, cesium and rubidium ions in aqueous solutions: Experimental and theoretical calculations. J. Mol. Liq.
**2009**, 146, 69–73. [Google Scholar] [CrossRef] - Malmberg, C.G.; Maryott, A.A. Dielectric constant of water from 0 °C to 100 °C. J. Res. Natl. Bur. Stand.
**1956**, 56, 1–8. [Google Scholar] [CrossRef] - Sangster, J.; Teng, T.; Lenzi, F. A general method of calculating the water activity of supersaturated aqueous solutions from ternary data. Can. J. Chem.
**1973**, 51, 2626–2631. [Google Scholar] [CrossRef] - Zlotorowicz, A.; Strand, R.V.; Burheim, O.S.; Wilhelmsen, Ø.; Kjelstrup, S. The permselectivity and water transference number of ion exchange membranes in reverse electrodialysis. J. Membr. Sci.
**2017**, 523, 402–408. [Google Scholar] [CrossRef][Green Version] - Krakhella, K.W.; Seland, F.; Einarsrud, K.E.; Burheim, O.S. Electrodialytic Energy Storage System: IEM Permselectivity and Stack Measurements. Unpublished work.
- Ji, Y.; Geise, G.M. The Role of Experimental Factors in Membrane Permselectivity Measurements. Ind. Eng. Chem. Res.
**2017**, 56, 7559–7566. [Google Scholar] [CrossRef] - Długołȩcki, P.; Gambier, A.; Nijmeijer, K.; Wessling, M. Practical potential of reverse electrodialysis as process for sustainable energy generation. Environ. Sci. Technol.
**2009**, 43, 6888–6894. [Google Scholar] [CrossRef] - Van Egmond, W.; Starke, U.; Saakes, M.; Buisman, C.; Hamelers, H. Energy efficiency of a concentration gradient flow battery at elevated temperatures. J. Power Sources
**2017**, 340, 71–79. [Google Scholar] [CrossRef][Green Version] - Post, J.W.; Hamelers, H.V.M.; Buisman, C.J.N. Energy recovery from controlled mixing salt and fresh water with a reverse electrodialysis system. Environ. Sci. Technol.
**2008**, 42, 5785–5790. [Google Scholar] [CrossRef] - Isono, T. Density, viscosity, and electrolytic conductivity of concentrated aqueous electrolyte solutions at several temperatures. Alkaline-earth chlorides, lanthanum chloride, sodium chloride, sodium nitrate, sodium bromide, potassium nitrate, potassium bromide, and cadmium nitrate. J. Chem. Eng. Data
**1984**, 29, 45–52. [Google Scholar] - Hamann, C.; Hamnett, A.; Vielstich, W. Electrochemistry; Wiley-VCH: Weinheim, Germany, 2007. [Google Scholar]
- Vermaas, D.A.; Guler, E.; Saakes, M.; Nijmeijer, K. Theoretical power density from salinity gradients using reverse electrodialysis. Energy Procedia
**2012**, 20, 170–184. [Google Scholar] [CrossRef][Green Version] - Güler, E.; Elizen, R.; Vermaas, D.A.; Saakes, M.; Nijmeijer, K. Performance-determining membrane properties in reverse electrodialysis. J. Membr. Sci.
**2013**, 446, 266–276. [Google Scholar] [CrossRef] - Kamcev, J.; Paul, D.R.; Manning, G.S.; Freeman, B.D. Ion diffusion coefficients in ion exchange membranes: Significance of counterion condensation. Macromolecules
**2018**, 51, 5519–5529. [Google Scholar] [CrossRef] - Kamcev, J.; Doherty, C.M.; Lopez, K.P.; Hill, A.J.; Paul, D.R.; Freeman, B.D. Effect of fixed charge group concentration on salt permeability and diffusion coefficients in ion exchange membranes. J. Membr. Sci.
**2018**, 566, 307–316. [Google Scholar] [CrossRef] - Beers, K.M.; Hallinan, D.T., Jr.; Wang, X.; Pople, J.A.; Balsara, N.P. Counterion condensation in Nafion. Macromolecules
**2011**, 44, 8866–8870. [Google Scholar] [CrossRef] - Tansel, B.; Sager, J.; Rector, T.; Garland, J.; Strayer, R.F.; Levine, L.; Roberts, M.; Hummerick, M.; Bauer, J. Significance of hydrated radius and hydration shells on ionic permeability during nanofiltration in dead end and cross flow modes. Sep. Purif. Technol.
**2006**, 51, 40–47. [Google Scholar] [CrossRef] - Soboleva, T.; Xie, Z.; Shi, Z.; Tsang, E.; Navessin, T.; Holdcroft, S. Investigation of the through-plane impedance technique for evaluation of anisotropy of proton conducting polymer membranes. J. Electroanal. Chem.
**2008**, 622, 145–152. [Google Scholar] [CrossRef] - Barsoukov, E.; Macdonald, J.R. Impedance Spectroscopy: Theory, Experiment, and Applications; John Wiley & Sons: Hoboken, NJ, USA, 2005. [Google Scholar]
- Müller, F.; Ferreira, C.A.; Azambuja, D.S.; Alemán, C.; Armelin, E. Measuring the proton conductivity of ion-exchange membranes using electrochemical impedance spectroscopy and through-plane cell. J. Phys. Chem. B
**2014**, 118, 1102–1112. [Google Scholar] [CrossRef] - Datt, P. Latent heat of vaporization/condensation. In Encyclopedia of Snow, Ice and Glaciers; Springer: Berlin/Heidelberg, Germany, 2011; p. 703. [Google Scholar]
- Parker, V. Thermal Properties of Uni-Univalent Electrolytes; National Bureau of Standards: Washington, DC, USA, 1965; Volume 2, p. 66.
- Carmo, M.; Fritz, D.L.; Mergel, J.; Stolten, D. A comprehensive review on PEM water electrolysis. Int. J. Hydrog. Energy
**2013**, 38, 4901–4934. [Google Scholar] [CrossRef] - Barbir, F. PEM electrolysis for production of hydrogen from renewable energy sources. Sol. Energy
**2005**, 78, 661–669. [Google Scholar] [CrossRef] - Tsuchiya, H.; Kobayashi, O. Mass production cost of PEM fuel cell by learning curve. Int. J. Hydrog. Energy
**2004**, 29, 985–990. [Google Scholar] [CrossRef] - Rashid, M.M.; Al Mesfer, M.K.; Naseem, H.; Danish, M. Hydrogen production by water electrolysis: A review of alkaline water electrolysis, PEM water electrolysis and high temperature water electrolysis. Int. J. Eng. Adv. Technol.
**2015**, 4, 2249–8958. [Google Scholar] - Zeng, K.; Zhang, D. Recent progress in alkaline water electrolysis for hydrogen production and applications. Prog. Energy Combust. Sci.
**2010**, 36, 307–326. [Google Scholar] [CrossRef] - Proost, J. State-of-the art CAPEX data for water electrolysers, and their impact on renewable hydrogen price settings. Int. J. Hydrog. Energy
**2019**, 44, 4406–4413. [Google Scholar] [CrossRef] - National Academy of Sciences. Carbon Capture and Storage—The rationale of carbon capture and storage from hydrogen production. In The Hydrogen Economy: Opportunities, Costs, Barriers, and R&D Needs; The National Academies Press: Washington, DC, USA, 2019. [Google Scholar]

**Figure 2.**Illustration of the thermal separation unit (in Figure 1) using precipitation. Thermal energy is removed from the spent dilute solution (Q

_{C}), to precipitate salt. Thermal energy (Q

_{H}) is added to the spent concentrated solution after the salt slurry is added.

**Figure 3.**Illustration of the thermal separation unit (in Figure 1) using evaporation. The spent concentrated solution from RED, is decompressed to a lower evaporation temperature, before heat (Q) is added and water evaporated from the spent dilute solution. The vaporised water is heated (Q

_{H}) and compressed, before thermal energy is exchanged with the spent concentrated, and the vaporised water is condensed back to a liquid and added to the spent dilute solutions.

**Figure 8.**Nyquist plot of Equation (18), and where the ohmic resistance of the membrane is found.

**Figure 9.**Sketch of the measurement cell for membrane conductivity, with (1) membrane sample(s), (2) platinum plates, (3) heating wire, (4) end of the thermocouple emerging from the cell, (5) end of the platinum wire (attached to the platinum plate) emerging from the cell.

**Figure 11.**The mass flow in the precipitation system. ${\mathsf{\Phi}}_{\mathrm{w},1}$ is the water flow from the concentrated to the dilute solution, while ${\mathsf{\Phi}}_{\mathrm{w},2}$ is the water flow from dilute to concentrated solution. For no loss of water, ${\mathsf{\Phi}}_{\mathrm{w},1}\equiv {\mathsf{\Phi}}_{\mathrm{w},2}$.

**Figure 12.**The mass flow in the evaporation system. ${\mathsf{\Phi}}_{\mathrm{w},1}$ is the water flow from concentrated to the dilute solution, while ${\mathsf{\Phi}}_{\mathrm{w},2}$ is the water flow from the dilute to the concentrated solution. For no loss of water, ${\mathsf{\Phi}}_{\mathrm{w},1}\equiv {\mathsf{\Phi}}_{\mathrm{w},2}$.

**Figure 13.**Ion conductivity at 23 ${}^{\circ}$C in (

**a**) CEM and (

**b**) AEM, and at 40 ${}^{\circ}$C in (

**c**) CEM and (

**d**) AEM, with 95% confidence interval.

**Figure 14.**The change in the hydrogen production as a function of the dilute concentration in RED. The concentration of the concentrated inlet is set by the solubility limit at 25 and 40 ${}^{\circ}$C, 3.79 and 6.22 mol kg${}^{-1}$.

**Figure 15.**Driving force for RED using concentrations relevant for the separation techniques evaporation and precipitation.

**Figure 16.**The total ohmic resistance in a RED unit cell at 23 °C and 40 °C using concentrations relevant for (

**a**) evaporation and (

**b**) precipitation. The calculation of the four contributions can be seen in Equation (14).

**Figure 17.**Power density from one RED unit cell (no tafel or electrode losses) per cross-section area using concentrations relevant for the separation techniques evaporation and precipitation.

**Figure 18.**Hydrogen production per hour and unit cell area from RED using concentrations relevant for the separation techniques evaporation and precipitation.

**Table 1.**Coefficients for Equation (15) with 95% conf. interval.

Name | Value |
---|---|

${k}_{1,23\phantom{\rule{4.pt}{0ex}}{}^{\circ}\mathrm{C}}$ | $12.2\pm 0.3$ |

${k}_{2,23\phantom{\rule{4.pt}{0ex}}{}^{\circ}\mathrm{C}}$ | $3.4\pm 0.2$ |

${k}_{1,40\phantom{\rule{4.pt}{0ex}}{}^{\circ}\mathrm{C}}$ | $15.8\pm 0.4$ |

${k}_{2,40\phantom{\rule{4.pt}{0ex}}{}^{\circ}\mathrm{C}}$ | $4.5\pm 0.2$ |

**Table 2.**Crystal and hydrated radii of Na${}^{+}$, K${}^{+}$, Cl${}^{-}$ and NO${}_{3}^{-}$. Data obtained from [49].

Na${}^{+}$ | K${}^{+}$ | Cl${}^{-}$ | NO${}_{3}^{-}$ | |
---|---|---|---|---|

Crystal radius (nm) | 0.101–0.117 | 0.138–0.149 | 0.181–0.194 | 0.179–0.189 |

Hydrated radius (nm) | 0.178–0.358 | 0.201–0.331 | 0.195–0.332 | 0.340 |

**Table 3.**Galvanostatic EIS settings for the potentiostat. * rms = root mean square, ≈0.7× peak current.

Variable | Value |
---|---|

DC current [A] | 0 |

AC current [A rms] * | 0.001 |

Initial frequency [Hz] | 1 MHz |

Final frequency [Hz] | 5 |

Points/decade | 10 |

Name | Symbol | Value |
---|---|---|

Solutions | ||

Conc. dilute solution—evaporation | ${b}_{\mathrm{d}}^{\mathrm{eva}}$ | calc. from H${}_{2}^{\mathrm{max}}$ |

Conc. dilute solution—precipitation (T = 10 ${}^{\circ}$C) | ${b}_{\mathrm{d}}^{\mathrm{pre}}$ | 2.11 mol kg${}^{-1}$ * |

Conc. concentrated solution (T = [25 40] ${}^{\circ}$C) | ${b}_{\mathrm{c}}$ | [3.79 6.22] mol kg${}^{-1}$ * |

Temperature | T | [297 313] K |

Flow volume per unit cell | $\mathsf{\Phi}$ | $5.4\times 10$${}^{-5}$ kg s${}^{-1}$m${}^{-2}$ ** |

Membrane | ||

Mean permselectivity CEM and AEM | $\overline{\alpha}$ | 0.63–0.96 *** |

Conductivity AEM | ${\rho}_{\mathrm{AEM}}$ | measured |

Conductivity CEM | ${\rho}_{\mathrm{CEM}}$ | measured |

Thickness AEM | ${d}_{\mathrm{AEM}}$ | $50\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m |

Thickness CEM | ${d}_{\mathrm{CEM}}$ | $50\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m |

Cell geometry | ||

Thickness spacer | ${d}_{\mathrm{s}}$ | $155\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m [37] |

Spacer parameters | ||

Shadow factor | $\beta $ | 0.35 [37] |

Porosity | $\u03f5$ | 0.84 [37] |

Electrode | ||

Lumped electrode losses | ${E}_{\mathrm{L}}$ | 0.10 V [24] (p. 156) |

Constants | ||

Molar mass KNO${}_{3}$ | M | 0.101 kg mol${}^{-1}$ |

Molar mass H${}_{2}$ | M | 0.00202 kg mol${}^{-1}$ |

Faraday’s constant | F | 96,485 C mol${}^{-1}$ |

Universal gas constant | R | 8.314 J K${}^{-1}$mol${}^{-1}$ |

Name | Symbol | Value |
---|---|---|

Vaporizing water | $\Delta $H${}_{\mathrm{vap}.}$ | $11.3$ Wh mol${}^{-1}$ (628 Wh kg${}^{-1}$) [53] |

Heating water | $\Delta $H${}_{\mathrm{heating}}$ | 0.0209 Wh (mol K)${}^{-1}$ (1.16 Wh (K kg)${}^{-1}$) |

Disolving KNO${}_{3}$ in water | $\Delta $H${}_{\mathrm{dissolve}}$ | 9.69 Wh mol${}^{-1}$ (538 Wh kg${}^{-1}$) [54] |

**Table 6.**Measured membrane ion conductivity for the relevant mean concentration of KNO${}_{3}$ for the inlet to RED, 23 ${}^{\circ}$C and 40 ${}^{\circ}$C.

${\mathit{\kappa}}_{\mathbf{AEM}}$ | ${\mathit{\kappa}}_{\mathbf{CEM}}$ | |
---|---|---|

23 ${}^{\mathbf{\circ}}$C | 0.08 ± 0.01 S m${}^{-1}$ | 0.18 ± 0.07 S m${}^{-1}$ |

40 ${}^{\mathbf{\circ}}$C | 0.11 ± 0.09 S m${}^{-1}$ | 0.20 ± 0.11 S m${}^{-1}$ |

**Table 7.**The number of unit cells needed to have a total stack potential of 1.33 V and an operating current density at peak power.

25 ${}^{\circ}$C | 40 ${}^{\circ}$C | |
---|---|---|

Precipitation | 93$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}16$ | 43$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}8$ |

Evaporation | 18$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}3$ | 15$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}3$ |

**Table 8.**The operating current density of RED (see Equation (11)).

25 ${}^{\circ}$C | 40 ${}^{\circ}$C | |
---|---|---|

Precipitation | 10$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}2$ A m${}^{-2}$ | 30$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}18$ A m${}^{-2}$ |

Evaporation | 42$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}9$ A m${}^{-2}$ | 70$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}34$ A m${}^{-2}$ |

Precipitation | |
---|---|

Inlet conc. concentration | 6.2 mol kg${}^{-1}$ |

Inlet dilute. concentration | 2.1 mol kg${}^{-1}$ |

Outlet conc. concentration | 6.1 mol kg${}^{-1}$ |

Outlet dilute concentration | 2.2 mol kg${}^{-1}$ |

Evaporation | |

Inlet conc. concentration | 6.2 mol kg${}^{-1}$ |

Inlet dilute. concentration | 0.1 mol kg${}^{-1}$ |

Outlet conc. concentration | 5.3 mol kg${}^{-1}$ |

Outlet dilute concentration | 1.0 mol kg${}^{-1}$ |

Specific Mass Flux | Mass Flux/kg h${}^{-1}$ m${}^{-2}$ |
---|---|

Precipitation | |

Flux of water, ${\mathsf{\Phi}}_{\mathrm{w}}$ | 8.36 |

Flux intlet conc. solution (from RED) | 13.6 |

Flux intlet dilute solution (from RED) | 10.1 |

Flux outlet conc. solution (from RED) | 13.5 |

Flux outlet dilute solution (from RED) | 10.3 |

Flux of salt from dilute to conc. solution | 0.295 |

Flux of water from dilute to conc. solution | 0.295 |

Flux of solution from conc. to dilute solution | 0.476 |

Evaporation | |

Flux of water, ${\mathsf{\Phi}}_{\mathrm{w}}$ | 2.92 |

Flux inlet conc. solution (from RED) | 4.75 |

Flux inlet dilute solution (from RED) | 2.95 |

Flux outlet conc. solution (from RED) | 4.49 |

Flux outlet dilute solution (from RED) | 3.21 |

Flux of water from conc. to dilute solution (eva.) | 2.62 |

Flux of solution from dilute to conc. solution | 2.88 |

**Table 11.**Energy needed per volume hydrogen produced from RED using evaporation and precipitation at 40 ${}^{\circ}$C. * Due to the restriction on the ohmic and lumped electrode losses (see Section 3.1), there is no uncertainty.

Process | V | j | P | W | W |
---|---|---|---|---|---|

V | A m${}_{\mathbf{cross}}^{-2}$ | W m${}_{\mathbf{cross}}^{-2}$ | kWh m${}^{-3}$ | kWh kg${}^{-1}$ | |

Evaporation | |||||

Reversible work | 1.23 | 70$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}34$ | 86$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}42$ | 2.57 | 32.7 |

Electrode comp. loss | 0.10 * | 70$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}34$ | 7$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}3$ | 0.21 | 2.7 |

Ohmic loss RED-stack | 1.33 * | 70$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}34$ | 93$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}45$ | 2.78 | 35.3 |

Regen. heat (eva.) | 24$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}10$ | 70$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}34$ | 1600 ± 1000 | $49\pm 22$ | 600 ± 300 |

Total | 26 ± 10 | 70 ± 34 | 1800 ± 1000 | 55 ± 22 | 700 ± 300 |

Precipitation | |||||

Reversible work | 1.23 | 30$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}18$ | 86$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}42$ | 2.57 | 32.7 |

Electrode comp. loss | 0.10 * | 30$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}18$ | 3.0$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}1.8$ | 0.21 | 2.7 |

Ohmic loss RED-stack | 1.33 * | 30$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}18$ | 40$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}24$ | 2.78 | 35.4 |

Regen. heat needed | $0.341\pm 0.008$ | 30$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}18$ | 10$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}6$ | $0.71\pm 0.02$ | $9.1\pm 0.2$ |

Regen. heat (dissolve) | $0.94\pm 0.02$ | 30$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}18$ | 28$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}17$ | 1.96$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.04$ | 25.0$\phantom{\rule{0.166667em}{0ex}}\pm \phantom{\rule{0.166667em}{0ex}}0.6$ |

Total | 3.94 ± 0.02 | 30 ± 18 | 167 ± 52 | 8.23 ± 0.05 | 104.8 ± 0.6 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Krakhella, K.W.; Bock, R.; Burheim, O.S.; Seland, F.; Einarsrud, K.E. Heat to H_{2}: Using Waste Heat for Hydrogen Production through Reverse Electrodialysis. *Energies* **2019**, *12*, 3428.
https://doi.org/10.3390/en12183428

**AMA Style**

Krakhella KW, Bock R, Burheim OS, Seland F, Einarsrud KE. Heat to H_{2}: Using Waste Heat for Hydrogen Production through Reverse Electrodialysis. *Energies*. 2019; 12(18):3428.
https://doi.org/10.3390/en12183428

**Chicago/Turabian Style**

Krakhella, Kjersti Wergeland, Robert Bock, Odne Stokke Burheim, Frode Seland, and Kristian Etienne Einarsrud. 2019. "Heat to H_{2}: Using Waste Heat for Hydrogen Production through Reverse Electrodialysis" *Energies* 12, no. 18: 3428.
https://doi.org/10.3390/en12183428