#
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

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**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