1. Introduction

Figure 1. Power-to-Gas and Gas-to-Power scheme [3].

Figure 1. Power-to-Gas and Gas-to-Power scheme [3].

Figure 1. Scheme of Don Quichote installation [8].

Figure 1. Scheme of Don Quichote installation [8].

2. Electrolysis

2.1. Introduction to Water Electrolysis

Electrolysis is an electrochemical process that produces hydrogen and oxygen from water using an electric current. Several types of electrolyzers have been developed, including proton exchange membrane (PEM) electrolyzers, alkaline electrolyzers, and high-temperature solid oxide electrolyzers (SOE). The overall electrolysis reaction can be represented as follows:

$$2H_{2}O\to 2H_2+O_2$$

(1)

In 1833-1834, Michael Faraday formulated the laws of electrolysis, which provide a quantitative description of the process occurring during electrochemical reactions, fundamentally based on the law of mass conservation:

$$m=\frac{MQ}{nF}$$

(1)

where: m, kg is the mass of the substance released, M, kg/mol is the molar mass of the substance produced, Q, C is the total electric charge passed, n, is the number of electrons involved in the reaction, F, C/mol is Faraday’s constant.

Electrolysis requires an input of energy. For low-temperature processes, this energy is solely electrical. In high-temperature electrolysis, both electrical energy and heat are required. The energy needed to decompose one mole of water is its enthalpy of formation $\mathsf{\Delta }H$:

$$\mathsf{\Delta }H=\mathsf{\Delta }G+T\mathsf{\Delta }S$$

(1)

where: $\mathsf{\Delta }G$ represents the electrical energy, $T\mathsf{\Delta }S$ represents the thermal energy.

Under standard conditions, the electrical work required to split one mole of water is:

$$\mathsf{\Delta }{G}^0=nF{E}^0$$

(1)

where: $E^0$, V is the standard thermodynamic voltage (for water at 25°C, $E^0=1.229$ V).

According to the second law of thermodynamics, the enthalpy of formation can be provided as both thermal and electrical energy. Figure 1 illustrates the energy requirements for electrolysis as a function of temperature. The abrupt changes around 100°C are associated with the evaporation of water. As the operational temperature increases, the total energy demand slightly rises, but the ratio of electrical to thermal energy decreases more rapidly. Thus, at higher temperatures, electrolysis requires less electrical energy and more thermal energy.

There exists a thermo-neutral potential in the electrolysis process, which is the voltage level for a given operational temperature where the electric power supplied generates sufficient heat through the Joule effect, making additional heat unnecessary. At this point, all the heat demand is met solely by the electrical energy stream, rendering the process adiabatic with a constant temperature. The thermo-neutral potential is defined as:

$$V_{\mathrm{neutral}}=\frac{\mathsf{\Delta }G}{nF}$$

(1)

To calculate the open circuit voltage for SOE, the Nernst equation is used. For a hydrogen cell, it is expressed as:

$$E=E^0+\frac{RT}{nF}\ln \left(\frac{p_{H_2}{p}_{O_2}^{1/2}}{p_{H_{2}O}}\right)$$

(1)

where $p_{H_2},p_{O_2},and{p}_{H_{2}O}$ are the partial pressures of hydrogen, oxygen, and water, respectively.

For voltages between the open circuit voltage (EOCV) and $V_{\mathrm{neutral}}$ , additional heat energy must be supplied. For voltages higher than the thermo-neutral potential, the reaction becomes exothermic due to the Joule heating effect, resulting in heat release.

Figure 1. Energy required for electrolysis [11].

Figure 1. Energy required for electrolysis [11].

The efficiency of a device is a critical factor in any energy application. The electrical efficiency of electrolysis can be defined as the ratio of the useful energy output from the system to the electrical energy input. The useful energy is the heating value of the produced hydrogen multiplied by its flow rate, while the electrical energy input is the product of the current and voltage of the system.

$$\mathsf{\eta }=\frac{{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{\mathrm{P}}_{\mathrm{e}\mathrm{l}}}=\frac{\mathrm{L}\mathrm{H}{\mathrm{V}}_{{\mathrm{H}}_2}}{\mathrm{I}\cdot \mathrm{E}}$$

(1)

where: LHV– lower heating value of hydrogen, $m_{H_2}$– output mass flow rate of hydrogen, I – electric current of the electrolysis, E – electrolysis voltage.

2.2. Solid Oxide Electrolysis and Electrolysers

Solid oxide electrolysis (SOE) typically occurs at temperatures between 800 and 1000°C. Theoretically, electrical efficiencies close to 100% are possible. A typical solid oxide electrolysis cell consists of three basic layers: two electrodes (anode and cathode) and an electrolyte that separates them. The electrolyte functions as an electrical insulator and an excellent ion conductor. The reaction at the cathode involves steam reduction:

𝐻₂𝑂₍𝑔) + 2𝑒⁻ → 𝐻₂(𝑔) + 𝑂²⁻

(1)

The oxygen ions are transferred through the solid electrolyte to the anode, where molecular oxygen is produced:

𝑂²⁻ − 2𝑒⁻ → 0.5 𝑂₂

(1)

Scheme of SOE is presented in the Figure 8.

Figure 1. Scheme of SOE cell [12].

Figure 1. Scheme of SOE cell [12].

The operation of a solid oxide electrolysis (SOE) cell is also associated with the occurrence of losses, which can be categorized into three types: ohmic losses, activation losses, and reactant transport losses. These losses are illustrated on the voltage-current characteristic curve in Figure 1.

Figure 1. SOC losses [13].

Figure 1. SOC losses [13].

Electrochemical reaction activation losses arise because some energy must be supplied to the reactants to overcome the potential barrier for the reaction to commence. These losses are most significant near the open circuit voltage and decrease at higher operating temperatures, as the reactants already possess more thermal energy.

Ohmic losses are due to the ionic and electronic resistances of the cell components. These losses depend on the temperature, the materials of the cell components, and the current, varying linearly with current.

Transport losses result from the limited ability of the electrode materials to transport species to the electrolyte contact zone. These losses depend on the current density and the porosity of the electrode material.

A solid oxide electrolyzer can be considered as one mode of operation of a solid oxide cell (SOC). The second mode is the solid oxide fuel cell (SOFC), which performs the opposite process, generating electricity and heat from hydrogen and oxygen. The voltage-current characteristics of these two modes are presented in Figure 1.

Figure 1. E-i curve for SOE and SOFC [14].

Figure 1. E-i curve for SOE and SOFC [14].

The blue line represents the voltage at a given current, either drawn from or supplied to the cell. The green line indicates the open circuit voltage (E_OC), which is the voltage at zero current flow. E_OC can be considered the minimum voltage in SOE mode and the maximum voltage in SOFC operation. The red line represents the level of the thermo-neutral potential for the SOC.

In the given scenario, the current at the thermo-neutral potential is around -30 A. Between this value and zero, the electrical power delivered to the cell is P_e,u, However, for the reaction to occur, additional energy (P_ext) must be supplied, making the total energy delivered equal to the red line, which represents the thermo-neutral potential. When the cell's voltage equals the thermo-neutral potential, the electric energy delivered and the heat generated by the Joule effect balance the energy requirements of the process.

Above the thermo-neutral potential, the Joule effect generates more heat than is needed, and this excess heat can be either utilized for other purposes or simply wasted. In SOFC mode, the voltage decreases, and the heat generated by the Joule effect steadily increases with rising current.

2.4. Reported Power-to-X Installation Based on SOE

In 2015, a project aimed at creating the first fully operational and grid-tied solid oxide electrolysis cell (SOEC) and solid oxide fuel cell (SOFC) installation for energy storage began as a collaboration between Boeing and Sunfire, located in Huntington Beach, California, USA. The project was tested while connected to the Southern California Edison grid. The scheme of the installation is presented in Figure 1.

In this setup, electrical energy from renewable energy sources (solar or wind) and from the grid is used to produce hydrogen in the SOE mode of Sunfire’s reversible SOC stack (RSOC). After compression, the hydrogen is stored in a tank. When there is a need for energy, the mode of operation switches to SOFC (energy generation), and hydrogen from the tank is supplied to the RSOC stack to produce electricity. Sunfire’s RSOC produces 50 kW of electrical power in SOFC mode and requires 120 kW in SOE mode. The storage tanks and compression systems were developed by Boeing. The hydrogen production rate is 3.5 kg/h. The efficiency of the SOEC mode, relative to the lower heating value (LHV), was found to be 60.5%, while the SOFC mode achieved an efficiency of 49.2%. However, further improvements in efficiency levels are possible [2].

Figure 1. Boeing and Sunfire's RSOC project's scheme [15].

Figure 1. Boeing and Sunfire's RSOC project's scheme [15].

Sunfire's next step is its participation in the project named Green Industrial Hydrogen, funded by the Fuel Cells and Hydrogen Joint Undertaking (FCH JU). The project has several key objectives:

-

Achieving an overall LHV efficiency above 80%

-

Scaling SOEC to 150 kWAC of power input

-

Reaching a lifetime of at least 10,000 hours with a degradation rate below 1% per 1,000 hours

The project is located at an iron-and-steel factory owned by Salzgitter Flachstahl GmbH in Germany. The scheme of the installation is presented in Figure 1.

Figure 1. RSOC installation in Salzgitter's iron-and-steel factory [16].

Figure 1. RSOC installation in Salzgitter's iron-and-steel factory [16].

In SOEC mode, the system produces hydrogen using hot steam heated by waste heat from the factory. Electricity is supplied from renewable energy sources and the grid. In SOFC mode, hydrogen, process gas, and natural gas are used as fuels. The hydrogen must be sufficiently clean and compressed to 8 bar, tasks managed by the Hydrogen Processing Unit (HPU) visible in the scheme.

When cheap renewable energy is available, the system operates in SOEC mode. When electricity prices are high, the system switches to SOFC mode, using hydrogen to produce electric power. The presented RSOC system contains a total of 1,440 cells (48 stacks, 30 cells each). The system's maximum hydrogen production rate is 40 Nm³/h, and its maximum power output in SOFC mode is 30 kWAC. This power output is achieved using hydrogen, while fueling the cells with natural gas produces only 25 kWAC. However, the efficiency of fuel cells using natural gas is slightly higher (50%) compared to hydrogen (48%).

Before reaching the cells, gases are heated to the required temperature in two Gas Processing Units (GPUs). For fuels other than hydrogen, reforming occurs in the GPUs. During testing, the highest electrolysis power intake was found to be 200 kWAC, making it the world's largest SOEC unit [2].

3. Methodology

The Description of the System

The SOE system consists of a stack of cells connected in series and various ancillary devices necessary for the system's proper operation, such as heaters, blowers, pumps, and heat exchangers. These components are essential for generating steam and heating it to the required operating temperature, as well as for recovering heat from gases exiting the stack and transferring it to incoming reactants.

The SOE stack in this system is modeled with 750 cells, each having an active area of 16 cm². The system scheme, which is a modified version of the system proposed in [17], is presented in Figure 1.

Figure 1. Scheme of the system. Based on [17].

Figure 1. Scheme of the system. Based on [17].

The "SOEC" element represents the electrolyzer stack model, which is connected to streams of a steam/hydrogen mixture and the oxidant, air. Electric heaters raise the temperature of the incoming streams to the required level. The stream leaving the oxidant electrode is enriched air at a significantly higher temperature than ambient air, enabling it to be used to preheat both the incoming steam and air streams in heat recovery exchangers. The stream leaving the fuel electrode is also utilized in thermal recuperation, transferring its heat to a water stream, which eventually evaporates.

The gases from the fuel electrode, a mixture of steam and hydrogen, need to be separated. The first step involves cooling the stream so the steam condenses, allowing easy separation from the hydrogen. Cooling is achieved using an external water stream with an initial temperature of 8°C. The hydrogen is then divided into two streams: one being the final product of the SOE system, and the other recirculated. Recirculating hydrogen in the incoming stream helps limit chemical degradation of the electrode’s surface material.

The mathematical model of the analyzed electrolyzer system (Figure 13) comprises two parts. The model of the electrolyzer stack itself was created using an analytical approach and mathematical formulation, implemented in Aspen HYSYS 8.8 as a spreadsheet element. The other components of the entire electrolyzer system, such as heat exchangers, pumps, and blowers, are standard HYSYS models. The "SOE" element, which contains all the mathematical formulas modeling the behavior of the solid oxide electrolyzer cell, is integrated with the other system components. This setup enables automated simulations that provide all the necessary data for performance maps.

The Aspen HYSYS model of the installation is presented in Figure 1. The "SOEC" element is a spreadsheet where all electrochemical calculations are conducted. The "System" spreadsheet is used to obtain the results of the simulations. Other elements in the model mimic the behavior of real physical devices, such as pumps and blowers.

Figure 1. Scheme of the installation in Aspen HYSYS.

Figure 1. Scheme of the installation in Aspen HYSYS.

4. Results of Simulations

Figure 1. Voltage-Current curve for operating temperature 700^°C.

Figure 1. Voltage-Current curve for operating temperature 700^°C.

Figure 1. Efficiency of the system at 700^°C.

Figure 1. Efficiency of the system at 700^°C.

Figure 1. Efficiency of a system working at 700^°C.

Figure 1. Efficiency of a system working at 700^°C.

Figure 1. Ratio of BoP to total power input at 700^°C.

Figure 1. Ratio of BoP to total power input at 700^°C.

Figure 1. Working point of air blower for -0.1 A/cm^2.

Figure 1. Working point of air blower for -0.1 A/cm^2.

Figure 1. Voltage-Current curve for operating temperature 750^°C.

Figure 1. Voltage-Current curve for operating temperature 750^°C.

Figure 1. Total power input of the installation at 750^°C.

Figure 1. Total power input of the installation at 750^°C.

Figure 1. Efficiency of the system at 750^°C.

Figure 1. Efficiency of the system at 750^°C.

Figure 1. Ratio of BoP to total power input at 800^°C.

Figure 1. Ratio of BoP to total power input at 800^°C.

Figure 1. Voltage-Current curve for operating temperature 800^°C.

Figure 1. Voltage-Current curve for operating temperature 800^°C.

Figure 1. Total power input of the installation at 800^°C.

Figure 1. Total power input of the installation at 800^°C.

Figure 1. Efficiency of the system at 800^°C.

Figure 1. Efficiency of the system at 800^°C.

Figure 1. Ratio of BoP to total power input at 800^°C.

Figure 1. Ratio of BoP to total power input at 800^°C.

5. Discussion

6. Summary

References

1. Kupecki, J.; Milewski, J.; Edenhofer, O.; Pichs-Madruga, R.; Sokona, Y.; Farahani, E.; et al. Climate Change 2014: Mitigation of Climate Change. Contribution of Working Group III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Int J Hydrogen Energy 2018, 83, 171–178. [Google Scholar] [CrossRef]
2. Posdziech, O.; et al. Efficient hydrogen production for industry and electricity storage via high-temperature electrolysis. Int J Hydrogen Energy 2018. [Google Scholar] [CrossRef]
3. Introduction to Power-to-Gas n.d.
4. 4. Fuel Cells and Hydrogen Joint Undertaking n.d.
5. Japan car giants team up on hydrogen stations n.d.
6. Santos, D.M.F.; Sequeira, C.A.C.; Figueiredo, J.L.; Bi, L.; Boulfrada, S.; Traversa, E.; et al. Toyota Mirai Technical Specifications. Int J Hydrogen Energy 2014, 4, 9457–9466. [Google Scholar] [CrossRef]
7. Japanese group unveils SOFC ENE-Farm residential cogen unit. Fuel Cells Bull 2012, 4, 4.
8. Don Quichote Project n.d.
9. BioCat Project n.d.
10. Aneke, M.; Wang, M. Energy storage technologies and real life applications – A state of the art review. Applied Energy 2016, 179, 350–377. [Google Scholar] [CrossRef]
11. Bi, L.; Boulfrada, S.; Traversa, E. Steam electrolysis by solid oxide electrolysis cells (SOECs) with proton-conducting oxides. Chem Soc Rev 2014, 43, 8255–8270. [Google Scholar] [CrossRef] [PubMed]
12. H2e Power Technology n.d.
13. Larminie, J.; Dicks, A. Fuel Cell Systems Explained; John Wiley: New York, 2000. [Google Scholar]
14. Penchini, D.; Cinti, G.; Discepoli, G.; Desideri, U. Theoretical study and performance evaluation of hydrogen production by 200 W solid oxide electrolyzer stack. Int J Hydrogen Energy 2014, 39, 9457–9466. [Google Scholar] [CrossRef]
15. Mermelstein, J.; Posdziech, O. Development and demonstration of a novel reversible SOFC system, for utility and micro grid Energy storage. Fuel Cell 2017, 17, 562. [Google Scholar] [CrossRef]
16. Green Industrial Hydrogen Project n.d.
17. Kupecki, J.; Motyliński, K.; Skrzypkiewicz, M.; Naumovich, E.; Brouwer, J. Energy analysis of 10kW-class power-to-gas system based on solid oxide electrolysis (SOE) stack. 5th Int. Conf. Contemp. Probl. Therm. Eng. (CPOTE Poland, 2018.