PROCESS MODELLING AND TECHNO-ECONOMIC ANALYSIS OF SOLID OXIDE ELECTROLYSER SYSTEM
Lappeenranta–Lahti University of Technology LUT
School of Energy Systems, Energy Technology, Master’s Thesis 2021
Eerik Lähdemäki
Examiners: Associate Professor, D.Sc. (Tech.) Tero Tynjälä Associate Professor, D.Sc. (Tech.) Antti Kosonen Supervisor: M.Sc. (Tech.) Henri Karimäki
Wärtsilä Finland Oy
ABSTRACT
Lappeenranta-Lahti University of Technology LUT School of Energy Systems
Energy Technology Eerik Lähdemäki
Process modelling and techno-economic analysis of solid oxide electrolyser system Master’s Thesis 2021
Examiners: Associate Professor, D.Sc. (Tech.) Tero Tynjälä Associate Professor, D.Sc. (Tech.) Antti Kosonen Supervisor: M.Sc. (Tech.) Henri Karimäki
74 pages, 26 figures, 13 tables, and 2 annex
Keywords: Electrolyser, Process Modelling, Hydrogen, PtX, Techno-economic analysis The national governments' climate groups and associations related to global climate change solving have called for technologies and methods to stop or mitigate global climate changes.
Green hydrogen production has been seen as one potential option to reduce climate changes by covering current fossil-based hydrogen usage with green hydrogen and utilizing it also for completely novel industrial applications.
The aim of this thesis was to examine the commercial feasibility of solid oxide electrolyser as an alternative low- or zero-emission hydrogen production system from a techno-economic perspective. The system was designed and modelled with Aspen Plus software, and the process model results were combined with economic data collected from the literature. The system's profitability was examined as a case study, where two main scenarios with different process steam prices and properties were defined. The scenarios were evaluated by economic metrics of net present value, internal rate of return, and levelized cost of hydrogen.
The main outcome of the study was that the system might reach a profitable status if the selling price of hydrogen stays above 2 €/kg and electricity price would not rise above 30
€/MWh. The system may be profitable even with higher electricity prices, but then higher hydrogen selling prices are needed as well. The process steam price itself seems to be quite negligible in examined scenarios. The most considerable sensitivities of the techno- economic model lie in success in the estimation of stack lifetime, operation hours, oxygen selling price, and capital expenditures.
By increasing the knowledge about techno-economics, benefits, and downsides of solid oxide electrolyser may boost the changes from fossil-based hydrogen to green hydrogen, especially if there can be shown commercially feasible scenarios.
TIIVISTELMÄ
Lappeenrannan-Lahden teknillinen yliopisto LUT School of Energy Systems
Energiatekniikka Eerik Lähdemäki
Kiinteäoksidielektrolyyserijärjestelmän prosessimallinnus ja teknoekonominen analysointi
Diplomityö 2021
Tarkastajat: Apulaisprofessori, TkT Tero Tynjälä Apulaisprofessori, TkT Antti Kosonen Ohjaaja: DI, Henri Karimäki
74 sivua, 26 kuvaajaa, 13 taulukkoa, ja 2 liitettä
Hakusanat: Elektrolyyseri, Prosessimallinnus, PtX, Vety, Teknoekonominen analyysi.
Kansalliset hallitukset, ilmastoryhmät ja yhteisöt, jotka liittyvät globaalin ilmastonmuutoksen ongelmien ratkaisemiseen ovat peräänkuuluttaneet teknologioita ja menetelmiä pysäyttääkseen tai hidastaakseen ilmastonmuutosta. Vihreän vedyn tuottaminen on nähty yhtenä potentiaalisena vaihtoehtona hidastaa ilmastonmuutosta. Tämä voitaisiin toteuttaa korvaamalla nykyinen fossiilisen vedyn käyttö vihreällä vedyllä ja hyödyntämällä sitä myös täysin uusissa teollisuuden sovelluksissa.
Työn tarkoituksena oli tutkia kiinteäoksidielektrolyserin kaupallista soveltuvuutta vaihtoehtoisena matala- tai nollapäästöisen vedyn tuotantojärjestelmänä teknoekonomisesta perspektiivistä katsoen. Järjestelmä mallinnettiin Aspen Plus-ohjelmistolla. Saadut tulokset yhdistettiin kirjallisuudesta kerättyihin kustannustietoihin. Järjestelmän kannattavuutta tarkasteltiin case study -periaatteella, jossa määritettiin kaksi erilaista pääskenaariota.
Skenaariot erosivat toisistaan prosessihöyryn hinnan ja ominaisuuksien suhteen. Skenaariot arvioitiin seuraavia taloudellisia mittareita käyttäen: nettonykyarvo, suhteellinen sisäinen korko ja vertailukelpoinen vedyn tuotantokustannus.
Tärkein tulos mikä tutkimuksesta saatiin oli, että järjestelmä voi olla kannattava, mikäli vedyn myyntihinta pysyy 2 €/kg yläpuolella ja sähkön hinta ei nouse yli 30 €/MWh.
Järjestelmä voi olla kannattava myös korkeammilla sähkön hinnoilla, mutta silloin myös vedyn myyntihinnan on oltava korkeampi. Prosessihöyryn hinta itsessään ei näyttäisi olevan kovinkaan merkittävä tarkastelluissa skenaariossa. Teknoekonominen malli on herkin kennoston eliniän, käyttötuntien, hapen myyntihinnan ja pääomakustannusten arvioinnin onnistumisen suhteen.
Lisäämällä tietämystä kiinteäoksidielektrolyyserin teknoekonomiasta, sen hyödyistä ja haitoista, voidaan mahdollisesti vauhdittaa siirtymistä fossiilisesta vedystä vihreään.
Etenkin, jos voidaan esittää kaupallisesti kannattavaksi osoittautavia skenaarioita.
ACKNOWLEDGEMENTS
I would like to thank the examiners of this thesis, Associate Professors Tero Tynjälä and Antti Kosonen from the Lappeenranta-Lahti University of technology LUT. Their comments and critics helped me to bring the thesis to a better academic conclusion than it would have been without it. Furthermore, the advice provided by the supervisor Henri Karimäki was greatly appreciated and helped me to understand what most relevant subjects are to express in the thesis.
I am particularly grateful for Wärtsilä Finland Oy and Tommi Rintamäki to enable this thesis work and provide that exciting topic to study.
Assistance provided by my brothers was greatly appreciated. Without their help, the grammar of the thesis would have been much worse. Finally, I would like to express my very great appreciation to my most valuable friend Ilari Karimäki who donated his old screen and keyboard. That enabled more efficient and ergonomic remote working in Turku, which in turn enabled the intermittent support of my other friends, whom I would like to thank as well.
Turku, 25.11.2021
Eerik Lähdemäki
Abstract Tiivistelmä
Acknowledgments Contents
Nomenclature & Acronyms
1 INTRODUCTION ... 10
1.1 Objectives and frame of the study ... 10
1.2 Structure of the study... 11
2 HYDROGEN PRODUCTION BY ELECTROLYSIS ... 12
2.1 Hydrogen as a product ... 12
2.1.1 Market value ... 13
2.1.2 Potential in Power-To-X ... 16
2.2 Basics of water electrolysis ... 18
2.2.1 Thermodynamics ... 20
2.2.2 Electrochemistry ... 22
2.3 Water electrolysis technologies... 24
2.3.1 Alkaline ... 24
2.3.2 Proton-Exchange Membrane ... 26
2.3.3 Solid oxide ... 28
2.3.4 Comparison of technologies ... 30
3 MODELLING OF PHYSICAL SYSTEM... 35
3.1.1 Basic concepts of modelling ... 35
4 MODEL OF SOLID OXIDE ELECTROLYSIS SYSTEM ... 38
4.1.1 State of the art SOEC-modelling ... 38
4.2 Modeling software ... 43
4.3 SOE model ... 44
4.3.1 Flowsheet ... 45
4.3.2 Components and blocks ... 46
4.3.3 Cell performance implementation to model ... 49
4.3.4 Case study ... 51
5 ECONOMIC EVALUATION ... 54
5.1 Analysis method ... 54
5.1.1 Operational expenditures (OPEX) ... 56
5.1.2 Capital expenditures (CAPEX) ... 56
5.2 Parameters for economic evaluation ... 58
5.2.1 Net Present Value (NPV) ... 58
5.2.2 Internal Rate of Return ... 60
5.2.3 Levelized Cost of Hydrogen ... 61
6 COMMERCIAL FEASIBILITY ... 62
6.1 Results of scenarios ... 62
6.1.1 Profitability of scenarios ... 62
6.1.2 Comparison of scenarios ... 64
6.2 Sensitivity analysis ... 66
6.2.1 Sensitivity of stack electrical efficiency ... 67
6.2.2 Sensitivity of fixed parameters ... 68
7 CONCLUSION ... 72
7.1 Further research suggestion ... 73
REFERENCES... 75
APPENDICES
Annex I i. Economic parameters result of scenario 1 Annex I ii. Economic parameters result of scenario 2 Annex II i. SCENARIO 1. Flow diagram and parameters Annex II ii. SCENARIO 2. Flow diagram and parameters
Nomenclature
Roman letters
A Heat flow area m2
B Temperature factor K−1
C Cost €
C Pressure factor bar −1
CF Cash flow €
D ASR factor Ωcm2
F Faraday constant C/mol
F LMTD correction factor
G Gibbs free energy kJ/mol
H Enthalpy kJ/mol, kJ/kg
I Current density of cell A/m2
M Annual production kg/a
P Power W
Q Thermal energy J
R Ideal gas constant J/mol K
S Entropy kJ/mol K
T Temperature ºC, K
U Voltage V
h Enthalpy kJ/mol, kJ/kg
i Discount rate %
𝑚̇ Mass flow kg/s
p Pressure bar
t Number of time periods
u Overall heat transfer coefficient W/m2K z Number of transferred electrons in moles
Subscripts
FOpex Fixed OPEX VOpex Variable OPEX act Activation aq Water
con Conversion el. Electricity
g Gas
inv Investment l Liquid
n Index
ohm Ohmic p Partial rev Reversible s Stack
tn Thermoneutral 0 Standard condition
Acronyms
AE Alkaline Electrolyser AEC Alkaline Electrolyser Cell ASR Area Specific Resistance BoP Balance of Plant
CAPEX Capital Expenditures
CCUS Carbon Capture, Utilisation and Storage GHG Greenhouse Gas
IEA International Energy Agency IRR Internal Rate of Return KOH Potassium hydroxide
LCOH Levelized Cost of Hydrogen
LMTD Logarithmic Mean Temperature Difference NaOH Sodium hydroxide
NPV Net Present Value
OPEX Operational Expenditures PEM Proton Exchange Membrane
PEMEC Proton Exchange Membrane Electrolyser Cell
PtX Power-to-X
rSOC Reversible Solid Oxide Cell SNG Synthetic Natural Gas
SOE Solid Oxide Electrolysis SOEC Solid Oxide Electrolysis Cell SOFC Solid Oxide Fuel Cell
TRL Technology Readiness Level WACC Weighted Average Cost of Capita
1 INTRODUCTION
While the ongoing discussion about global climate change and different kinds of mitigation methods has been under consideration by many different associations and groups related to it, there has been relatively recently rosed in broad awareness the subject called hydrogen economy. This subject is generally related to an opportunity to mitigate global climate emissions. In the first place, by covering the currently used fossil-based hydrogen with non- polluting or less polluting hydrogen, or/and by finding new solutions to utilize this “greener”
hydrogen to run recently used carbon-intensive technologies. Secondly, looking a bit further, by creating or implementing a wholly new economic network. However, to reach this ambitious goal, it is crucial to find a greenhouse gas (GHG) emission-free, commercially feasible method to produce hydrogen.
The political drivers are under consideration, and politicians in national governments are defining those mechanisms to support and accelerate the hydrogen economy. Their focus is presently on: Incentive competition to drive down costs, support rapid scaling, allow access to low-cost financing, facilitate a level playing field (not technology-specific) and not impose an unreasonable cost burden on consumers. (Timer energy, 2021)
The electrochemical water splitting is seen as a promising method to produce GHG-free hydrogen, so the water electrolyser technologies are coming under examination.
Nevertheless, the electrolysers call for renewable electricity to be GHG-free. Each electrolyser technology has its benefits and downsides. The solid oxide electrolyser has very high electrical efficiency compared to other electrolyser technologies, especially when it is possible to integrate with an external source of steam. The cost of hydrogen is the most important driver when projects utilizing green hydrogen are considered. The more hydrogen the system can produce with fed electricity, the lower the hydrogen production cost will be.
Therefore, the high electrical efficiency of the solid oxide electrolyser technology makes it so interesting to examine.
1.1 Objectives and frame of the study
The objective of this thesis is to accomplish a techno-economic analysis of a solid oxide electrolyser system in hydrogen production. The purpose of the analysis is to evaluate the commercial feasibility of the system as an alternative less polluting hydrogen production
method. To carry out the above objective, it is needed to design and perform a process model of the electrolyser system. The process model and its simulation were done in the Aspen Plus software.
This study is focused on the electrochemical water splitting with solid oxide electrolysis cells and the system boundaries restricted on electrolyser and heat exchangers. The system lacks pumps and fans, and the cooling energy is not considered, which is needed in the real case to separate water and hydrogen. The study utilizes the case study method, consisting of two main scenarios, including four sub scenarios. The considered case is that the electrolyser is integrated into the existing combined heat and power plant, which can provide the external steam for the electrolyser. The main scenarios differ from each other with the process steam properties and the price of it.
1.2 Structure of the study
The literature part of this thesis encompasses discussion about the background of hydrogen production and hydrogen as a product, including its further potential. Moreover, it discusses and compares the relevantly available electrochemical water splitting technologies, leading benefits, flaws, and summarises the function principle. Finally, at the end of the literature part, the fundamental modelling principles are presented at an elementary level.
The implementation part deals with the detailed design information about process modelling of electrolyser system. It discusses what type of blocks and software computing methods are utilized. Also, detailed assumptions and selections of the case study are presented. The end side of the implementation part discusses the used economic parameters and those principles.
At last, the results are presented, and the thesis is concluded with a further recommendation of study subjects.
2 HYDROGEN PRODUCTION BY ELECTROLYSIS
Water electrolysis has been known as a method to produce hydrogen since the turn of the 19th century. The first electrolysers were based mostly on experiments of scientists until Michel Faraday discovered the main laws of electrolysis in 1833–1834. However, electrolysis electrochemistry and thermodynamics development began in the late 19th century. In that era, the interest in electrochemical technology of hydrogen production evolves from its application for ammonium synthesis. Thus, the first industrial-scale water electrolyser was implemented in 1927 with the purpose of producing hydrogen for ammonium production by Norsk Hydro Electrolyzer. In further, two additional plants were installed more, which led the plant hydrogen productivity up to 60t Nm3/h. (Grigoriev &
Fateev 2017, 231–232) The 1920s starts an era where water electrolysis plays a major role as an industrial hydrogen production method close to the 1960s until natural gas reforming methods displaces it (IEA 2019).
At present, there are various options available to produce hydrogen, which are partial oxidation, steam reforming, autothermal reforming, gasification (coal, biomass), and water electrolysis. Currently, the vastly most common way to produce hydrogen is to reform a natural gas. (IEA 2019) However, due to the CO2 intensity of fossil source reforming, the water electrolysis has been rosed again as a considerable option to produce hydrogen in a carbon-neutral way.
2.1 Hydrogen as a product
Hydrogen demand can be divided into pure hydrogen demand and demand of hydrogen mixed with other gases. The pure hydrogen demand is typically satisfied with dedicated hydrogen production and the mixed hydrogen by by-product hydrogen. (IEA 2019) In this section, only pure demand is considered. The total pure hydrogen demand in 2018 was 73 Mt, with fractions of refinery 38 Mt, ammonia 31 Mt, and others 4 Mt (IEA 2019).
For decades hydrogen has been treated as a feedstock or an industrial gas. The feedstock covers the primary demand, and industrial gas is a small fraction of it. Hydrogen is applicated for example: as a feedstock to produce ammonia and for refineries to improve their products, and as an industrial gas cooling a large-scale power generator, glass and semi-contactor manufacturing, heat treatments, and analytical chemistry (Grigoriev & Fateev 2017, 266).
Lately discussions about how to solve the persistently growing volatility of electricity on power grids, caused by increased implementation of renewable energy sources, have been focused thoughts to consider hydrogen as an energy carrier as well. The Power-to-X (PtX) technologies will probably play a crucial role in hydrogen energy carrier projects in the future. Hydrogen has a great initial energy content of 142 MJ/kg, which supports those thoughts. However, the density of hydrogen is 0.089 kg/m3 (0 °C, 1 bar) in gaseous form and in liquid 70.79 kg/m3 (−253 °C, 1 bar). Thus, its smallest and lightest element and so have a much lower energy density per unit of volume compared to fossil-based carriers.
(Boudellal 2018; IEA 2019) 2.1.1 Market value
The predictions show that the demand for hydrogen is not supposed to decline in the future.
Conversely, the predictions show that there is an expected increase in demand. Actually, there are plenty of announcements of international and regional mandates and policy incentives, which aim to support the increment of hydrogen technology implementations.
The sector-specific announcements cover six main areas, with transport being by far the largest. (IEA 2019) The incentives and subsidies may affect the future demand for hydrogen, as well it may affect how the hydrogen is valuated in different sectors of hydrogen usage.
For instance, if subsidies or incentives are targeted to the transport sector to increase the attraction of hydrogen vehicles, there might become a situation that hydrogen producers have a better price from hydrogen by selling it to distributors as a fuel than by selling it to refineries or chemical industry as a feedstock. Moreover, the Emission Trading System (ETS) of the EU regulates carbon dioxide prices in the EU region. The t CO2 -price is almost doubled during 2021, now around 70 €/t CO2 (Ember 2021). If the recent trend continues, the ETS will affect the price of fossil-based hydrogen in favour of green hydrogen.
In the future, the steel industry may also appear as a large hydrogen demand sector. In 2018 the hydrogen demand in the steel industry was 4 Mt H2/a. However, there have been announced many projects which are aiming to implement pilot or even commercial steel production facilities which use mostly hydrogen to reduce iron ore instead of coke or comparative fossil-based substances. For instance, “HYBRIT” where SSAB, LKAB, and Vattenfall co-operate to define the feasibility of steelmaking with modified direct reduced iron – electrical arc furnace process design. “SALCOS” where Salzgitter AG and Fraunhofer
Institute co-operates to implement partially hydrogen-based reduced iron ore. (IEA 2019) The size of HYBRIT electrolyser is 4.5 MW and for SALCOS 2.5 MW (IEA 2021). Power Engineering International (2021) mentioned in their article that the production capacity of SALCOS electrolysers will be 450 Nm3/h, which can correspond to 320 t/a of hydrogen with 8000 operation hours. IEA has studied the development of further hydrogen demand by different sectors. In their net-zero emission scenario, the hydrogen demand of the iron and steel industry in 2030 might be around 12 Mt H2/a. (IEA 2021) For a more comprehensive picture of how they have been seen, the further hydrogen demand development is shown in Figure 1. That figure underlines well that even the hydrogen economy change may start with projects where fossil-based hydrogen is covered with green hydrogen; There most likely will be substantial new markets for green hydrogen in coming decades.
Figure 1. Hydrogen demand by sector in the Announced Pledges and Net-zero Emissions scenarios, 2020–
2050 (IEA 2021).
When evaluation of the hydrogen market value is considered, it is essential to understand that influential factors are not totally the same in every extraction source or technology. For example, in a fossil source reforming, the cost of feedstock (natural gas, coal) can be noted as the most significant single factor, even regardless of the region. For comparison in water electrolysis the water (as it could be considered as a feedstock) have a pretty negligible effect
on hydrogen production cost. Instead, the electricity and full load hours become a significant role in valuating hydrogen. (IEA 2019)
At present, hydrogen production is CO2 intense. However, global agreements like the Paris agreement of climate change push the industry towards low-carbon production, which may be reflected in the future as higher t CO2 -prices. The rise in the price of t CO2 is likely to affect the competitiveness of water electrolysis. On the other hand, there is also a possibility to utilize Carbon Capture Utilisation and Storage (CCUS) technologies to reach low-carbon production. Provided that storage takes place so that the carbon is stored for an extended period of time. In IEA’s report (2019) has been estimated in Figure 2. that it is still more likely to stay in the lowest end of hydrogen production costs by implementing CCUS system to natural gas or coal reforming plant (known as blue hydrogen) than produce hydrogen with electrolysis. Albeit the estimations refer to Europe in 2030 and are made for a CO2 -price interval 40 to 100 USD/t CO2, renewable electricity price 40 USD/MWh, the weighted average cost of capita for 8% (WACC), 4000 full load hours of electrolyser, sensitivity analysis based on ±30% variation in capital and operational expenditures (CAPEX, OPEX), and fuel cost change with variation of ±3%.
Figure 2. Hydrogen production costs for different technology at 2030 (IEA 2019).
However, even it seems to be more profitable from an economic point of view to add CCUS system to the natural gas reforming plant, the issue may not be as simple. Howarth and Jacobson (2021) have presented in their recent study that in GHG -emission point of view,
the CCUS method is not necessarily that effective as what has been assumed. They state that carbon dioxide equivalent emissions of natural gas reforming with CCUS are only 9–12%
smaller than without CCUS; this is caused mainly by fugitive methane emissions. Moreover, the study discovered that even direct natural gas burning for heat has lower carbon dioxide equivalent emissions than natural gas reforming with CCUS. There is also mentioned that there are no experimental data available for carbon dioxide storing on a commercial scale.
2.1.2 Potential in Power-To-X
Power-to-X is basically considered as a concept for converting renewable electric energy (power) into goods (X), which are possible to utilize, transport or store. However, most often, the concept for converting renewable electricity into a chemical energy source or carrier is mentioned. Firstly, conversion of electricity to hydrogen, and toward to the methane, methanol, liquid fuels (diesel, kerosine etc.), and formic acid (product X). Hydrogenation of carbon sources to hydrocarbons enables the production of some chemicals as well as other industrial products. In conclusion, PtX represents a concept to harness renewable electricity to produce zero, or at least, close-to-zero carbon emission products, like hydrogen, synfuel, chemicals. (Arnold et al. 2020; Hermesmann et al. 2020) A general layout of the PtX facility can be illustrated as in Figure 3., but the balance boundary location can vary depending on the considered case.
Figure 3. The general layout of the power-to-X facility
Renewable way produced hydrogen opens many potential options to mitigate greenhouse gases. For instance, it is possible to cover fossil-based hydrogen production, which is responsible for 830 Mt CO2/a, according to IEA 2019. In turn, Hermesmann et al. (2020) has been studied that if PtX facility utilizes water electrolysis and CO2 -capture technology to produce feedstock for hydrogenation of CO2, it might be possible to mitigate the GHG by covering the fossil-based products by PtX products. The GHG mitigation potentials are shown in Table 1. Noteworthy is that the electricity or heat used to run processes must be produced by the renewable way, like solar or wind power.
Table 1. GHG mitigation potential of product X’s according to Hermesmann et al. 2020
Methane Diesel Methanol Formic acid
114.8 Mt CO2-eq./a 1.496 Mt CO2-eq./a Product X Specific climate change
mitigation potential
Annual production
volumes Mitigation potential 2.90 kg CO2-eq./kg
3.51 kg CO2-eq./kg
7494 Mt CO2-eq./a 4920 Mt CO2-eq./a 1.98 kg CO2-eq./kg
2.41 kg CO2-eq./kg
2583 Mt/a, in 2018 1400 Mt/a, in 2017 58 Mt/a, in 2012 0.621 Mt/a, in 2012
Rackley (2010) states that there are available three main approaches to capture CO2, which general schematics are shown in Figure 4. In the process modification approach, a process is modified so that the CO2 stream comes as pure or near-pure to make the capture process easier. Sometimes the existing process can be just modified; sometimes, the whole process needs to be reengineered. For instance, the existing power generation plant might be modified to oxyfueling power plant. Typically, the post-process capture has utilized additional technology to concentrate CO2 lean stream (for instance, power or cement plant flue gases) to nearly or wholly pure CO2 stream. And for last, the direct air capture where the CO2 is separated from the air.
Figure 4. Main approaches to CO2 capture (Rackley 2010. p. 19)
The PtX technologies are already quite well known, and the readiness of related
technologies is at least in some applications at a mature level. Nevertheless, there is still space for the development of PtX technologies. However, in this regard, the obstacles to widespread PtX plant implementation are economic nature rather than technological. From an economic perspective, it is essential that the PtX plant is located near to place where affordable renewable energy generation is available. (Arnold et al. 2020)
2.2 Basics of water electrolysis
Water electrolysis is a water splitting process that consists of three main elements: anode, cathode (electrodes), and electrolyte. Good resistance of corrosion, electric conductivity, and
catalytic properties are required from electrode materials, as well as suitable structural integrity. When an electrical current is applied through the anode and the cathode, and ion exchange is allowed due to the electrolyte, the process induces that hydrogen forms on the cathode by a reduction reaction, and oxygen forms on the anode by oxidation reaction.
Hydrogen and oxygen streams must be separated with a diaphragm, separator, or similar, to avoid products recombination. (Ursúa et al. 2012) Basically, the electrolysis cell forms from those previously mentioned main elements anode, cathode, electrolyte. To pile one cell, also sealants and bipolar plate are needed. The electrolyser stack is made by adding several electrolyse cell assemblies in series. By connecting the cells in series, it allowed reaching practical voltage levels and capacities. The general schematics of the PEM electrolyser are presented in the Figure 5. Nevertheless, the main idea of structure is very similar no matter which technology is viewed. Electrolyser plant usually includes several stacks and a balance of plant equipment to run the process. The schematic of electrolyse system is presented later in this study.
Figure 5. General schematics of PEM electrolyser (Lin 2009, 383).
The basics between different types of water electrolysis methods are pretty similar, and the basic formula for water vapour splitting reaction at standard conditions (298 K, 1 bar) can be written as follow (Millet, Grigoriev 2013):
H2O(g)+ 228.6kJel.
mol+ 13.2kJHeat
mol → H2(g)+1
2O2(g), ∆𝐻0= 241.8 kJ
mol (2.1)
The difference between processes forms mostly electrolyte performance, a material used in three main elements of electrolyser, and an operation condition. (Millet, Grigoriev 2013) 2.2.1 Thermodynamics
The function of water electrolysis is based on electrochemical features, and the process can be described as the conversion of electric and thermal energy into chemical energy. By the fundamentals of thermodynamics, it is possible to explain the functions, which lead to the energy conversion in the level of electrolyser cell. The electrolyser can be described at reversible and constant operation conditions of pressure and temperature as follow (Millet, Grigoriev 2013):
∆𝐺 = ∆𝐻 − 𝑄 = ∆𝐻 − 𝑇∆𝑆 (2.2)
Where the ∆H represents the need for total energy to water electrolysis reaction (process enthalpy change) [kJ/mol], ∆S is the entropy change [kJ/molK]. T is the absolute temperature [K], and ∆G is Gibbs free energy [kJ/mol], the amount of electric energy needed in addition to the Q amount of heat in electrolyser cell to decompose water [kJ]. The water splitting reaction is endothermic (∆H > 0) and non-spontaneous (∆G > 0) up to ≈ 2500 °C; over this temperature, the enthalpy term is predominant over the entropy change. (Millet, Grigoriev 2013; Ursúa et al. 2012)
The enthalpy of water decomposition stays quite stable during operation temperature increases. In contrast, entropy increase leads to a significant decrease of Gibbs free energy and affects electrolysis voltage, as shown in Figure 6. (Grigoriev & Fateev 2017)
Figure 6. "Temperature dependence of main thermodynamic parameters for water” (Grigoriev & Fateev 2017, 234).
The reversible cell voltage Urev is a variable that represents the lowest theoretical voltage enough for the electrolysis to take place, and it can be expressed as a function of ∆G as follow (Ursúa et al. 2012):
𝑈rev =∆𝐺
𝑧F (2.3)
Where F is the Faraday constant represents the magnitude of electric charge per mole of electrons [96 485 C/mol], and z is the number of transferred moles of electrons per mole of hydrogen (z = 2). In most commercial cases, the thermal energy T∆S is provided with electricity [J], and the thermoneutral voltage Utn is the minimum known voltage to occur in water electrolysis [V]. It is possible to obtain thermoneutral voltage as equal to enthalpy voltage U∆H if the process is ideal. Thus, the total energy required equals enthalpy change
∆H, [kJ/mol]. In that case, an equation can be expressed as follow (Ursúa et al. 2012):
𝑈∆𝐻 = ∆𝐻
𝑧F
𝑖𝑑𝑒𝑎𝑙 𝑝𝑟𝑜𝑐𝑒𝑠𝑠
→ 𝑈tn = 𝑈∆𝐻 (2.4)
Nevertheless, the process is not ideal, caused by the thermodynamic irreversibility of additional electric and thermal energies. The thermodynamic irreversibility is the leading cause that hydrogen and oxygen flows contain water vapour, the lower temperature and pressure of the supply water with respect to the operation set-points. In reality, the process has convection and radiation losses of thermal energy. In the end, the energy demand of electrolysis process depends on operation temperature and pressure, and the magnitudes of those are influenced by characteristics of voltages. (Ursúa et al. 2012)
Ursúa et al. (2012) state in their review paper that by increasing the electrolysis process temperature from 25 °C to 1000 °C, the electric energy demand is reduced by 25.1%. On the other hand, the thermal energy demand increases by 132.3%. However, this phenomenon sets steam electrolysis as a potential option for water decomposing method and increases its interest, especially when excess steam and heat are available.
2.2.2 Electrochemistry
The cell's electrical potential can be used to define the electrical energy consumption of electrolyser. It is related to the cell component, temperature, gas species concentration, and average current density. The cell voltage consists of a reversible potential and all irreversible losses caused in the cell while the electrical current passes through it. In Figure 7. it is expressed how the shears of irreversible losses and reversible voltage acts as a function of the current density. (Udagawa et al. 2007)
Figure 7. Reversible potential and irreversible losses as a function of current density at 1023 K. Cathode supported cell. (Udagawa et al. 2007).
According to the Ursúa et al. (2012), the electrolysis cell voltage Ucell [V] can be expressed as follow:
𝑈cell = 𝑈rev+ 𝑈ohm+ 𝑈act+ 𝑈con (2.5)
Where Uohm represents the resistive overvoltage [V], the term Uact is known as charge transfer overvoltage [V], and Ucon is mass transport overvoltage [V].
The ohmic overvoltage is a voltage loss due to the electrical resistance of the electrodes and the resistance of the flow of the ions in the electrolyte. Thus, according to Ohm’s law, the Uohm is proportional to the electron flow over the circuit. (Slobodan 2021)
The charge transfer is an activation component of overvoltage, and it represents voltage loss caused by the slowness of the reaction at electrodes (anode and cathode). This voltage drop permits the reaction to happen. The factors that define charge transfer overvoltage are mainly the reaction speed and the amount of electric current. However, the voltage loss can be
reduced by raising the cell temperature, increasing the surface area of electrodes, adapting higher concentrations or pressure, and developing more efficient catalysts. (Slobodan 2021) The mass transfer overvoltage represents the voltage losses caused by the reactant concentration between electrolyte and electrodes (convection and diffusion). If the rate of reaction and the current are increased, the cell eventually reaches the point where the concentration on the electrode surface is reduced as much that the Nernst diffusion layer cannot increase. Thus, it can not support the reaction anymore, and the limiting current has been reached. Hence, the voltage loss is so high that the operation of the cell ceases.
Basically, this phenomenon is caused by gas bubble formation on the electrocatalyst surface.
The gas bubbles block the porous electrode pores. The phenomenon is known as a screening effect. Increasing the operating pressure, temperature, and flow rate of water makes it possible to decline the screening effect on electrodes. (Slobodan 2021; Ursúa et al. 2012;
Grigoriev et al. 2020)
2.3 Water electrolysis technologies
There are basically noted three leading technologies for the water electrolysis process:
Alkaline (AE), Proton-Exchange Membrane (PEM), and Solid Oxide Electrolyser (SOE).
The forthcoming sections discuss the basics of each electrolysis process, typical structure, function principle, materials used in cathode, anode, electrolyte, some background, and development status. At the end of sections are compared and reviewed weaknesses and advantages of different processes.
2.3.1 Alkaline
Alkaline water electrolyser is a well-known technology and is primarily used in electrochemical water splitting. It has a long history in the chemical industry, and the state of development is highly advanced. Hence, the technology readiness level (TRL) of AE has reached level 9, according to Roxanne et al. (2020). High popularity and development state are largely due to the simplicity of AE technology. Progress in further development of newer water splitting technologies shows how long the success of AE eventually is. (Ito et al. 2016) In Figure 8. is presented the general scheme of alkaline electrolyser cell (AEC). There are two electrodes submerged in an electrolyte solution, typically potassium hydroxide (KOHaq) and water. The concentration of solution commonly varies between 25 to 30 wt%. Also,
sodium hydroxide (NaOH) is used in some cases. The KOH has a higher ionic conductivity and a lower solubility of carbon dioxide than the NaOH. If carbon dioxides have access to dissolve from air to electrolyte solution, it results in the formation of carbonates into the solution, which causes a decrease in ionic conductivity. (Ito et al. 2016a)
Figure 8. The general scheme of AEC
The half-cell reactions (oxygen evolution reaction and hydrogen evolution reaction) of AEC can be expressed as follow (Ito et al. 2016a):
𝐴𝑛𝑜𝑑𝑒: 2OH− → H2O +1
2O2(g)+ 2𝑒− (2.6)
𝐶𝑎𝑡ℎ𝑜𝑑𝑒: 2H2O(l)+ 2𝑒− → H2(g)+ 2OH− (2.7)
The AEC operates in an alkaline environment; thus, the materials do not necessarily need to be made from more expensive acid-resistant materials. Electrodes are commonly made from materials that consist of nickel. In order to maximize the surface area of electrodes, porous or mesh-like structures are normally used. (Ito et al. 2016a) Since asbestos was banned in
the mid-1970s due to health hazards, starts the development of various alternative materials for the diaphragm. For instance, Cummins (before known as Hydrogenics Corporation) are used their inorganic ion-exchange type membrane. Furthermore, some anion exchange membranes have good thermal stability and the potential to be used in the electrolysis temperatures above water vaporization. For the last, there were polymer membranes appeared with hydroxyl ion conductivity. The focus of research activity in this field is mainly on optimizing catalyst/electrode materials. (Grigoriev et al. 2020) After all, in the big picture, the AEs development is toward higher temperatures and pressures, which might enable the higher efficiencies (Keçebaş et al. 2019, 309).
2.3.2 Proton-Exchange Membrane
The Proton-exchange membranes have seen very potential water electrolyser technology.
One of the main advantages is that the technology allowed a high dynamic operation. Its roots are in fuel cell applications and more emphasizing “chlorine electrolysis.” However, the PEM water electrolysers were come more popular in the 1960s, after the chemically stable proton-conducting polymer membrane became available in a commercial form.
(Grigoriev & Fateev 2017) The basic structure of the proton-exchange membrane electrolyser cell (PEMEC) is shown in Figure 9. The feedwater supply is on the anode side of the cell, where the water decomposition takes place. When sufficient electrical potential is applied, the oxygen gas is evolved on the anode, while the membrane allows protons (H+) to travel through it. Protons and electrons are combined at the cathode, and hydrogen evolving occurs. (Koponen 2020)
Figure 9. Schematic of PEMEC
The half-cell reactions (oxygen evolution reaction and hydrogen evolution reaction) of PEMEC can be expressed as follow (Ito et al. 2016b):
𝐴𝑛𝑜𝑑𝑒: H2O(l)→ 2H++1
2O2(g)+ 2𝑒− (2.8)
𝐶𝑎𝑡ℎ𝑜𝑑𝑒: 2𝐻++ 2𝑒− → H2(g) (2.9)
The core of PEMEC is a membrane electrode assembly (MEA). The membrane is often known as Nafion, which is DuPont’s commercial name for their sulfonated fluoropolymer product. The thickness of the membrane varies according to designed operation conditions (25–300 µm); values vary depending on the reference. Catalyst layers can be coated straight to the surface of the membrane or onto each of the transport layers. While the PEM electrolyser process is highly acidic, the material selected for catalysts is restricted to the rare transition metals due to their stability in acidic conditions. At present, the anode is typically iridium oxide, and the cathode is platinum. The purpose of transport layers (known as well as gas diffusion layer) is to improve electric connection through the cell and ensure effective mass transport of the product gas and the reactant water. The cathodic transport
layer side is often made from carbon paper. Due to the highly oxidative conditions of the anode side, the carbon paper is not suitable for that side. Thus, the anode side transport layer is often titanium or comparable inert metal mesh. (Chisholm & Cronin 2016; Grigoriev et al. 2020)
2.3.3 Solid oxide
The solid oxide electrolyser cell (SOEC) technology development started as late as the 1970s, and the first research paper considering such a concept was established in 1980. There are two different ways to put solid oxide electrolyser in action, an oxide ion-conductivity and a proton conductor electrolyte. However, at present, the oxide ion-conductive electrolyte is the most popular and developed, mainly because materials under research for proton conductivity electrolyte have not, at least yet, reached desirable stability in elevated temperatures. (Grigoriev et al. 2020; Matsumoto & Leonard 2016; Grigoriev & Fateev 2017) SOEC can be seen as a reverse technology for solid oxide fuel cell (SOFC) technology.
Hence, the most achievements in SOFC development apply to SOEC as well. SOFC technology has a more extended history, and its maturity has reached even commercial level, at least in some applications (Singhal 2013). Thus, the development of SOEC relies highly on the progress of R&D in the SOFC field. Research activities focus on searching for the new electrolyte to oxygen ion and proton conductors (even mixed ion/electron conductivity is considered) and electrode materials. Moreover, new technologies are examined to produce thin electrolyte films, electrode layers, or the method to electrolyte layers on electrolyte/electrode surfaces. Despite several attempts to operate SOEC/-FC successfully at lower temperatures (400–700 °C), satisfying results have not been obtained. Thus, the most used material in SOEC electrolytes is still zirconium dioxide stabilized by yttrium oxide or comparable oxides. (Grigoriev et al. 2020)
A schematic of plate type SOEC with oxide ion conductivity is shown in Figure 10. The cathode and anode are placed beside solid oxide electrolyte (ceramic membrane). In the case of oxide ion-conductivity SOEC, the water vapour supply is located on the cathode side, where hydrogen evolving occurs. Thus, it is possible to produce pure oxygen on the anode side with oxide ion-conductor electrolyte, whereas collecting pure hydrogen on the cathode side requires the hydrogen/water vapor separator. The difference in the proton conductor electrolyte is that in the proton conductor method, the water vapor is fed to the anode side,
and hence the hydrogen stream is pure from water vapor. (Grigoriev et al. 2020; Matsumoto
& Leonard 2016)
Figure 10. Schematic of plate type SOEC with oxide ion conductivity
The half-cell reactions (oxygen evolution reaction and hydrogen evolution reaction) of an oxide ion-exchange electrolyte SOEC can be expressed as follow (Matsumoto & Leonard 2016):
𝐴𝑛𝑜𝑑𝑒: O2− → O2(g)+ 2𝑒− (2.10) 𝐶𝑎𝑡ℎ𝑜𝑑𝑒: H2O(g)+ 2𝑒− → H2(g)+ O2− (2.11)
Cathode electrodes are often made from nickel composites (cermet). The nickel is typically stabilized with zirconia (Ni-yttria stabilized zirconia), whereas the anode utilizes a combination of a perovskite-type oxide and transition metal, like (La0.8Sr0.2)0.95MnO3. (Matsumoto & Leonard 2016; Grigoriev & Fateev 2017)
SOEC has two additional features that raise the interest in future development. Both half- cell reactions are fully reversible in SOEC operation temperature. As mentioned earlier in this section, the SOEC and the SOFC are basically equal devices, at least from a structure perspective. Hence, one device can operate reversibly and be used as a regenerative SOEC/SOFC stack. The second interest of development is that it is also possible to electrolyse CO2 (CO2→CO+O2) by feeding it onto the cathode at such a high temperature.
Furthermore, it is possible to produce a syn-gas (CO +H2) by co-electrolysis (CO2+H2O → [cathode side CO +H2] + [anode side O2]), with supplying both water vapour and CO2 in cathode stream. Nevertheless, the additional reaction on the cathode (H2O + CO→H2 + CO2) makes the process pretty complicated. (Grigoriev et al. 2020) This co-electrolysis possibility could give some additional value for some e-fuel production systems where syngas is needed in any case. The integration of it may simplify the overall process and thus reduce expenditures.
2.3.4 Comparison of technologies
As presented in the above sections, each water electrolysis process has a slight difference in its structure. This obviously means that each has a different performance, so advantages and disadvantages vary between technology. By plotting the current-voltage curve of each water electrolysis technology, it is easy to compare their performances. In Figure 11. it is clearly seen that the AE’s kinetics are not so optimized, and the cell resistance is relatively high, resulting in the limitation of current density to a few hundreds of mA/cm2. The limitation is due to its materials and so-called screening effects (gas bubble formation on the electrodes decreases electric conductivity of cell (Grigoriev & Fateev 2017)). Thus, the AE has the only medium capability to manage load cycling.
In contrast, PEM has good flexibility in load cycling, which is shown much longer and lower slope in the current-voltage graph. Even SOEC seems suitable for load cycling according to the slope; the high operating temperature limits the load cycling performances in an actual situation. The electrocatalysts are made from platinum group metals, and a highly conductive protonic membrane makes the kinetics of the PEM electrolysis that efficient. The slope of SOEC in the current-voltage graph is dictated mainly by the conductivity of ceramic. The strict rise at the end of the SOEC slope is due to the kinetics of water vapour transport to the reaction sides, which is emphasized in the case of low pressure. The lower cell voltage of
SOEC comes from thermodynamical reasons, as discussed earlier in this study. (Grigoriev et al. 2020)
Figure 11. "Comparison of typical current-voltage curves measured on alkaline, PEM, and SOEC water electrolysis cells" Grigoriev et al. 2020, 26049.
Basically, the higher the operation temperature, the lower the amount of electrical energy required for the water splitting process. In that point of view, the SOEC technology has advantages over the other technologies. However, the overall efficiency might decrease depending on the heat source. AE and PEM electrolysers typically operate at the temperature range of 20–95 °C, whereas solid oxide electrolyser operates at 700–900 °C. Thus, the highest electrical efficiencies are presented for the SOEC 74–81%, while for the AE 63–
70% and for the PEM 56–60%, according to IEA 2019. However, high operation temperature places severe challenges for materials because those should be able to manage such harsh conditions (Grigoriev et al. 2020; Grigoriev & Fateev 2017), like the interlayer diffusion and the long-term cell stability (Chisholm & Cronin 2016). Furthermore, such a high operation temperature causes a delay to start-up and shutdown; hence it is not optimal in cases where constant running is not considered.
Increasing the operating pressure of the electrolysis process makes it possible to reduce the compression cost of hydrogen in cases where the hydrogen is stored in the pressurized form.
Due to the performance of used material, and lower operation temperature, than SOEC, the
PEM and AE are able to operate at elevated pressures. At least at present, the problem of operating SOEC at elevated pressures is the lack of suitable gaskets, which endure the operation temperature of SOEC. There is considered one backup type solution for SOEC to operate at elevated pressure, which is to place the SOEC-stack in a pressurized container.
However, it causes extra costs for the system, so it is not very reasonable, at least according to present knowledge. On the other hand, hydrogen production at an elevated pressure may cause some product purity and safety problems. (Grigoriev et al. 2020; Grigoriev & Fateev 2017)
From an economic perspective, the cheapness of AEC materials and manufacturing maturity afford an advantage to AE over the PEM and SOEC. Grigoriev et al. (2020) state estimation in their study that the current capital costs of the AE system lie between 900–1700 €/kW in a system scale of 300 kW to 5 MW. The PEM system is the second expensive by the estimated CAPEX of 1700–2500 €/kW in a system scale of 300 to 500 kW. However, most experts believe that PEM takes the incumbent status in electrolysis systems from the AE during the period from 2020 to 2030. Even though, Minke et al. (2021) predict in their recent research that it might be expected that the scarcity of iridium became a bottleneck for the PEM scale-up forecasts. They mentioned that at least a catalyst target loading of iridium should drop to 0.05 g/kW by 2035, and the recycling percent of iridium should be increased to 90%. The SOEC is considered the most expensive water electrolysis system, with a 2000–
4000 €/kW CAPEX estimation. Nevertheless, many experts have a vision that over the period until 2030, the costs of SOEC may drop to the scale of 500 to 1000 €/kW. However, it is notable that there is a considerable variation in estimated capital expenditures of water electrolysers between estimation actors. For instance, Christensen (2020) used the Monte Carlo- approach to analyse a group of collected cost estimations from different sources in his research and up come with results as shown in Table 2., which can be seen as a lower estimation, than Gregoriev et al. (2020) has been stated.
Table 2. Electrolyser CAPEX prise parameters (Christensen 2020).
The expected electrolyser stack lifetime is a crucial characteristic of electrolyser systems.
The voltage degradation is the key parameter to define the lifetime of the electrolyser.
Voltage degradation describes how much the cell voltage increase during a determined time period; the measurement unit of µV/h (operation hour) is often used. The increase of the cell voltage is caused by many types of degradation processes, but mostly in the electrolyte/electrode assembly elements, and hence affect the cell resistance negatively. This obviously has an effect on efficiency as well, and the relation of voltage and efficiency degradation can be seen directly relevant to the electrolyser lifetime. The lifetime is often determined in percentage drop of efficiency; however, the acceptable level of the drop be relative to operator acceptance levels, for instance, “when capital investment in replacement stack may be beneficial.” Nevertheless, often it seems that the manufacturer gives a lifetime roughly to 10% decrease of efficiency, or the average efficiency penalty 5% if assumed as linear degradation over time. (Bertuccioli et al. 2014, 10–12)
The degradation of materials due to the high operating temperature has been kept as one of the key challenges to developing the SOEC systems to the commercial stage (expected lifetime 10000–30000 h). However, it is not only the SOEC systems problem. According to the IEA’s “the future of hydrogen” report (2019), the PEM electrolysers (expected lifetime 30000–90000 h) use expensive and scarce materials and still has a relatively low lifetime compared to the AE (expected lifetime 60000–90000 h), which has the highest lifetime expectation of these three main electrolyser systems. Nevertheless, it is remarkable that there is quite a considerable variation in estimations between the stack lifetime depending on the
reference (especially with PEM and SOEC lifetimes), and IEA’s estimations appear to be the most optimistic end.
Table 3 summarizes each water electrolyse technology's typical operation ranges, properties, and characteristics. It is notable that some values are directional and may vary between research papers and articles.
Table 3. Comparison table of electrolyser technologies (Grigoriev et al. 2020; Roxanne 2020 (TRL); IEA 2019 (Stack lifetime, Electrical efficiency)).
Electrolyser type Operation T range (°C) Operation pressure range (bar) Electrical efficiency (% LHV) Conventional current density
(A/cm2)
Technology raediness level Anode catalyst
Cathode catalyst
Electrolyte
Charge carrier ion Separator
Sealant
Curren distibutor
Containment material
Load cycling Stop/go cycling T cycling
Stack lifetime (th) Capital costs (€/kW)
weak good weak
weak good waek
MgO-ZrO2, CaO-ZrO2
metallic
(La,Sr)MnO3, (La,Sr)(Co,Fe)O3
Platinum Ni-YSZ or Ni-GDC cermet
perfluorosulfonic acid Y2O3-ZrO2, Sc2O3-ZrO2,
steel Ni-Mo/ZrO2-TiO2
9
Ni2CoO4, La-Sr-CoO3, Co3O4
nickel foam/Ni- stainless
nickel plated steel
0.2-0.5 0-3 (up to 20) 0-2
glass and vitro-ceramics synthetic
rubber/fluoroeleastomer
5
Ni
H+ O2-
Polymer membrane ceramic
polysulfone-bonded
polyantimonic acid, ZrO2 on
polyphenylsulfone, NiO, polysulfone impregnated with
Sb2O5 polyoxide, asbesto (old)
titanium ferritic stainless steel
OH-
6-8
KOH(aq) (25-30wt%)
Ir/Ru oxide 63-70
50-80 650-1000
30-80 1
56-60 74-81
AE PEM SOE
60-80 1-30
stainless steel
(Crofer APU)
900-1700 1700-2500 2000-4000
60-90 30-90 10-30
medium good good
stainless steel
3 MODELLING OF PHYSICAL SYSTEM
In engineering and industrial activities, the status of mathematical modelling as a key role player has increased in the last two decades. The importance of the central function of the models has been rosed along the emerging complexity of the systems to be designed due to the designer's restricted capability in accounting variables concerned to the process. In this regard, the models may have appeared as algorithms that can replicate the system understudy's performance. There are also some advanced usages of modelling nowadays. In some cases, it is possible to embed models into the system to implement functions like diagnosis, control, monitoring, maintenance scheduling, safety tasks, or unsupervised operations. (Marra et al. 2016, 7)
3.1.1 Basic concepts of modelling
There are a few different ways to do physical process modelling depending on the aim of simulation, and those are shown in Figure 12. Typical distinctions are between phenomenological and empirical modelling. The development of empirical modelling has followed the development of computing capabilities. The empirical model does not necessarily need a complete understanding of the physical background of the process. That kind of system or physical process is even possible to model without having any knowledge of it. In that kind of case, the model is based on artificial intelligence, genetic programs, and so forth. That type of model is known as a “black box.” It can be considered literally like a box with several in- and outputs. It is necessary to have large amounts of experimental data to validate such a model. In contrast to the empirical model, the phenomenological models rely on physical laws. The phenomenological (sometimes physical or white box) model is a good tool for sorting out why the process acts as it does. Thus, in the phenomenological model, all parameters have a physical meaning, whereas empirical and semi-empirical.
(Stempien et al. 2013)
Figure 12. Schematic of model categories and phenomenon of physics
Semi-empirical (or grey box) models fall between the black and white boxes. Those model types are often developed to utilize experimental data availability and physical content. The gray box model affords a good compromise between experimental and computational burden being in a middle level of model type category. (Marra et al. 2016, 27)
The state aspects of modelling describe the time dependence of the model. In practice, steady-state is time-independent, and transient is time-dependent. The steady-state is commonly used when modelling aims to predict performance and optimize design and operation parameters. In contrast, transient models are useful when the interest of modelling is on understanding the actual operation. (Stempien et al. 2013)
Models can be differentiated by the scale as well. In this category, the aspects describe them self’s quite nicely. For instance, in the case of the SOEC, the micro-level scale means that the model aims to assess the cermet electrodes or other component level performances. The system scale model is considered when the energy level analysis is deliberated. The macro scale is somewhat a combination of both of the above.
The number of analysed dimensions is the last distinction between the models. These category aspects can be related to the above category (scale). The model dimension basically
describes the level of spatial variations or distribution of model performances (Marra et al.
2016). System scale models are often zero-dimensional, whereas macro scales are 1D, 2D, or 3D. In microscale models are typical to use a 1D or 2D.
Simply put, the lower the dimension involved, the faster the computation will be. Modelling the geometry of the cell, one of the dimensions may be easily recognized; the thickness of the cell is way smaller than all others. Hence, modelling the cell as one-dimensional should be more effective. In contrast, the three-dimensional model in the stack configuration design models is often adopted. (Stempien et al. 2013). For instance, it is very common that grey box models are zero-dimensional. One to few variables is considered state variables to describe steady-state and transient conditions in system behaviour level. (Marra et al. 2016, 27)
4 MODEL OF SOLID OXIDE ELECTROLYSIS SYSTEM
Under this chapter is described the process model, methods, and parameters, which are utilized in simulations of this study. At the very beginning, the state of the art of SOEC modelling is presented to increase the understanding of the need for this type of study. After that, is presented the selected modelling software and its utilization. This is followed by the description of the SOE model itself, process flow components, and parameters. The last is presented and described the case study with presumptions.
4.1.1 State of the art SOEC-modelling
The experimental validation and optimisation are assessed as the best way to prove the potential of SOEC assemblies factually. However, experimental studies of SOEC stacks are expensive. In the optimal case, plenty of identical stacks must be tested in exactly the same conditions to avoid faulty observation due to slight production variation or inconsistent testing conditions. Even the aftermath analyses, to solve the cause of failed stack may be tricky because such high operation temperature usually accelerates the effect of cracked cell or sealant. Hence, the initial cause of failure may not be directly detectable. Numerical modelling may use as a tool to predict the physical phenomena occurring on the operating SOEC stack and/or in microstructural level its cells. A large number of physical parameters are required for a good model; such a complex compound system as the SOEC parameters are rarely well-defined. Typically, ideal values are used for fundamental parameters, values, or factors which are taken from the literature with a lack of doubt of their adequacy. The capability to determine the actual value for these parameters assessed on SOEC architecture or material combination would allow the models to be more precise in their representativeness and increase confidence in their predictions of phenomena that are impossible to measure. Therefore, it is essential “that efforts to test, characterise and validate cells and stacks be accurately synchronised with the mathematical modelling of the phenomena and processes that make up the physical objects.” In that way, it is possible to understand well, control, design, the performance, and the behaviour of the SOEC, and keep up the market commissioning of this energy conversion technology. (Beale et al. 2021) The SOEC stack operation is guided by many complex interconnected phenomena occurring widely on different levels of cell structure. Microscale phenomena which occur in a porous
electrode structure inside the device are impossible to examine experimentally. Regarding the above, numerical modelling, including sub-models, is crucial for predicting physical phenomena in different cell sections. For example, some parameters are difficult to measure or obtain experimentally but readily predicted in a model study. (Beale et al. 2021)
There are several zero-dimensional modelling papers in the present research literature where the simulation performance of solid oxide cells is considered. However, the focus has been mainly on the fuel cell operation. There are published many experiments with high- temperature electrolyser in the last three decades. Nevertheless, there is a lack of publications concerning modelling the SOE operation. This is construed by the methodologies used to assess the mass and energy balances, including electrochemical mechanism, are correspond for both SOEC and SOFC. As a result, it is not necessarily very meaningful to reproduce the same numerical analysis for SOEC models that are already made for SOFC. Furthermore, there are some studies that introduce a combination of both operating states and the operation of reversible Solid Oxide Cell (rSOC). (Motylinski et al. 2021)
In one of the latest research papers concerning solid oxide electrolyser operation at the system level, Motylinski et al. (2021) present a modelling study that approaches the rSOC switching operation in two different ways. On the first step, they focused on evaluating the operation of a 1 MW rSOC-based system, specifically the switching moments of SOFC and SOEC modes. The model simulates transient operation and takes into account the BoP. The simulation design and implementation were made by Matlab/SIMULINK environment. For the second, they assess the temperature changes and distribution of rSOC-stack, which are caused by variation of load/applied current between fuel cell and electrolysis states. The model considers both endo- and exothermic operation in the electrolysis mode. Aspen HYSYS software was used to do the numerical activities of modelling. The outcome of their study was a dynamic model of an rSOC process system integrated into the grid balancing service with consistency with wind electricity production profile. In turn, Abdullah &
Ibrahim (2018) has studied a 1 MW scale SOE system for hydrogen production purpose. The study is made from thermodynamical and electrochemical modelling and optimization perspective. They consider the SOE system in two ways. The first was SOEC stack and BoP, and the second was as the first but in an additional hydrogen compression unit. They are considered in their study that heat and high-temperature steam are provided entirely or partially externally with respect to the electrolysis unit. Regarding that, the SOE system has
