Common use of Data (Post) Processing Clause in Contracts

Data (Post) Processing. Here, the post processing of the test results (TIPs and TOPs) shall be described. When reporting, the significant figures of a test variable should be consistent with its measurement uncertainty. For a calculated test variable, the lesser number of significant figures of all of the involved test variables should determine the significant figure. The standard deviation (stdev), relative standard deviation (RSD) and standard error (stderr) should be expressed with at least one additional figure. The RSD should be reported with two significant figures. i zi Electrochemical reaction H2 2 H2 + O2-πŸ‘ͺ H2O + 2e- CO 2 CO + O2-πŸ‘ͺ CO2 + 2e- CH4 8 CH4 + 4O2-πŸ‘ͺ CO2 + 2H2O + 8e- CpHqOr 4p+q-2r CpHqOr + (2p+q/2-r)O2-πŸ‘ͺ pCO2 + q/2H2O + (4p+q-2r)e- O2 4 O2 + 4e-πŸ‘ͺ 2O2- H2O 2 H2O + 2e-πŸ‘ͺ H2 + O2- Faraday constant F = 96485.3 C mol-1 = 96485.3 A s mol-1 Oxygen fraction in air xO2 = 0.2095 Lower heating[7] value (LHV) of H2 LHVH2 = 119.93 kJ g-1 = 241.77 kJ mol-1 Higher heating[7] value (HHV) of H2 HHVH2 = 141.86 kJ g-1 = 285.98 kJ mol-1 Voltage equivalent to LHV of H2 LHVH2 / (2F) = 1.253 V Voltage equivalent to HHV of H2 HHVH2 / (2F) = 1.482 V Molar gas constant R = 8.31446 J K-1 mol-1 Normal temperature Tn = 273.15 K Normal pressure Pn= 101325 N m-2 = 101325 Pa Molar volume of an ideal gas at normal temperature and pressure 3 -1 -1 Vm = RTn/Pn = 8.31446 x 273.15 / 101325 mn mol = 22.414 ln mol Number of electrons transferred when one molecule of reactant component i is electrochemically reacted (zi) Gas utilization (Ugas) Number of repeating units in the stack: N Flow rate of reactant component i (i = 1 … n) in the negative/positive electrode of the stack: fi,in(nlpm) Theoretical current (Itheory) assuming 100% gas utilization (all reactant gas is consumed through electrochemical reactions): 𝐹 βˆ‘π‘› 1 𝑧𝑖 Γ— 𝑓𝑖,𝑖𝑛 96485.3 βˆ‘π‘› 1 𝑧𝑖 Γ— 𝑓𝑖,𝑖𝑛 πΌπ‘‘β„Žπ‘’π‘œπ‘Ÿπ‘¦ = βˆ™ 𝑖= = Γ— 𝑖= π‘‰π‘š Γ— 60 𝑁 22.414 Γ— 60 𝑁 βˆ‘π‘› 1 𝑧𝑖 Γ— 𝑓𝑖,𝑖𝑛 = 71.74 Γ— 𝑖=𝑁 gas utilization at current I: π‘ˆ = 𝐼 Γ— 100%= 𝐼×𝑁 Γ— 100% π‘”π‘Žπ‘  πΌπ‘‘β„Žπ‘’π‘œπ‘Ÿπ‘¦ 71.74Γ—βˆ‘π‘› 𝑧𝑖×𝑓𝑖,𝑖𝑛𝑖=1 Nernst voltage / reversible (thermodynamic) voltage / theoretical open circuit voltage (VN) 𝑅𝑇 𝑝𝑂2,π‘π‘œπ‘  𝑉𝑁 = 4𝐹 𝑙𝑛 𝑝 (considering SOC as an oxygen concentration cell) 𝑂2,𝑛𝑒𝑔 π‘Ÿ 𝑉 = | βˆ† 𝐺(𝑇,𝑝) | (for any reaction) 𝑁 𝑧𝐹 βˆ†π‘ŸπΊ(𝑇, 𝑝): β–‡β–‡β–‡β–‡β–‡ free enthalpy of reaction as a function of temperature and pressure. For the reaction: H2 + 0.5 O2 = H2O1 𝑝2 𝑝𝐻2,𝑛𝑒𝑔 βˆ†π‘ŸπΊ(𝑇, 𝑝) = βˆ†π‘ŸπΊ0(𝑇) βˆ’ 𝑅𝑇𝑙𝑛 𝑂2,π‘π‘œπ‘  𝑝𝐻2𝑂,𝑛𝑒𝑔 1 βˆ†π‘ŸπΊ(𝑇, 𝑝) βˆ†π‘ŸπΊ0(𝑇) 𝑅𝑇 𝑝2 𝑝𝐻2,𝑛𝑒𝑔 𝑉 = βˆ’ = βˆ’ + 𝑙𝑛 𝑂2,π‘π‘œπ‘  𝑁 2𝐹 2𝐹 2𝐹 𝑝𝐻2𝑂,𝑛𝑒𝑔1 𝑅𝑇 𝑝2 𝑝𝐻2,𝑛𝑒𝑔 = 𝑉0(𝑇) + 𝑙𝑛 𝑂2,π‘π‘œπ‘  𝑁 2𝐹 𝑝𝐻2𝑂,𝑛𝑒𝑔 βˆ†π‘ŸπΊ0(𝑇): β–‡β–‡β–‡β–‡β–‡ free enthalpy of reaction at standard pressure 𝑉0(𝑇): reversible voltage at standard pressure 𝑁 Thermoneutral voltage (Vtn) βˆ†π‘Ÿπ»(𝑇) 𝑉𝑑𝑛 = 𝑧𝐹 βˆ†π‘Ÿπ»(𝑇): Enthalpy of reaction as a function of temperature. (Note: the enthalpy is independent of the pressure under the assumption of ideal gases). z: number of exchanged electrons in the electrochemical reaction. For water electrolysis reaction: H2O πŸ‘ͺ H2 + 0.5 O2 Vtn = 1.482 V at 20 Β°C, 1.283 V at 700 Β°C, 1.285 V at 750 Β°C and 1.286 V at 800 Β°C Average RU voltage (VRU,av) βˆ‘π‘ 1 π‘‰π‘…π‘ˆ,𝑖 𝑖= π‘‰π‘…π‘ˆ,π‘Žπ‘£ = 𝑁 Electrical power of the cell / stack (Pel) 𝑃𝑒𝑙 = 𝑉𝑐𝑒𝑙𝑙/π‘ π‘‘π‘Žπ‘π‘˜ Γ— 𝐼 (Area specific) 𝑃𝑒𝑙 𝑃𝑑,𝑒𝑙 = 𝐴 Γ— 𝑁 Electrical efficiency of the stack (SOFC mode) The electrical efficiency of an SOFC stack can be defined as the ratio of electric power output to the total enthalpy flow input (based on either LHV of HHV of feed fuel gases). 𝑃𝑒𝑙 πœ‚π‘’π‘™,𝐿𝐻𝑉 = 22.414 Γ— 60 Γ— βˆ‘π‘› 𝐿𝐻𝑉 Γ— 𝑓 𝑖=1 𝑖 𝑖,𝑛𝑒𝑔,𝑖𝑛 𝑃𝑒𝑙 πœ‚π‘’π‘™,𝐻𝐻𝑉 = 22.414 Γ— 60 Γ— βˆ‘π‘› 𝐻𝐻𝑉 Γ— 𝑓 𝑖=1 𝑖 𝑖,𝑛𝑒𝑔,𝑖𝑛 𝐿𝐻𝑉𝑖: LHV of fuel component i (J mol-1) 𝐻𝐻𝑉𝑖: HHV of fuel component i (J mol-1) 𝑓𝑖,𝑛𝑒𝑔,𝑖𝑛: flow rate of fuel component i (i = 1 … n)(nlpm) When using H2 as fuel: π‘ˆπ‘”π‘Žπ‘ ,𝑛𝑒𝑔 Γ— π‘‰π‘ π‘‘π‘Žπ‘π‘˜ πœ‚π‘’π‘™,𝐿𝐻𝑉 = 1.253 Γ— 𝑁 π‘ˆπ‘”π‘Žπ‘ ,𝑛𝑒𝑔 Γ— π‘‰π‘ π‘‘π‘Žπ‘π‘˜ πœ‚π‘’π‘™,𝐻𝐻𝑉 = 1.482 Γ— 𝑁 Electrical efficiency of the stack (SOEC mode: H2O electrolysis) The electrical efficiency of an SOEC stack can be defined as the ratio of enthalpy flow of fuel gases produced by the electrolyzer (based on either LHV of HHV of produced fuel gases) to the electrical power consumed by the stack for the electrochemical reaction. Here electrical power consumed by the water evaporator, gas preheaters and the furnace in the test station is not considered. It should be noted that for the calculation of system efficiency, these consumptions have to be taken into account. For H2O electrolysis and assume 100% current efficiency: 1.253 Γ— 𝑁 πœ‚π‘’π‘™,𝐿𝐻𝑉,𝐻2βˆ’π‘π‘Ÿπ‘œπ‘‘π‘’π‘π‘‘π‘–π‘œπ‘› = π‘‰π‘ π‘‘π‘Žπ‘π‘˜ 1.482 Γ— 𝑁 πœ‚π‘’π‘™,𝐻𝐻𝑉,𝐻2βˆ’π‘π‘Ÿπ‘œπ‘‘π‘’π‘π‘‘π‘–π‘œπ‘› = π‘‰π‘ π‘‘π‘Žπ‘π‘˜ Degradation The absolute degradation βˆ†π‘‹ of a quantity 𝑋 within the time from 𝑑0 to 𝑑1 is calculated as the difference between the final value 𝑋(𝑑1) and the initial value 𝑋(𝑑0): βˆ†π‘‹ = 𝑋(𝑑1) βˆ’ 𝑋(𝑑0) The relative degradation βˆ†π‘‹π‘Ÿπ‘’π‘™ is calculated by dividing βˆ†π‘‹ by the initial value 𝑋(𝑑0): 𝑋(𝑑1) βˆ’ 𝑋(𝑑0) βˆ†π‘‹π‘Ÿπ‘’π‘™ = 𝑋(𝑑 ) Γ— 100% 0 The degradation rate (rate of change) of quantity 𝑋 during the time interval (t1-t0) is then calculated by: βˆ†π‘‹ = βˆ†π‘‹ (with the unit [unit of X/time unit]) βˆ†π‘‘ 𝑑1βˆ’π‘‘0 βˆ†π‘‹π‘Ÿπ‘’π‘™ = βˆ†π‘‹π‘Ÿπ‘’π‘™ (with the unit [%/time unit]) βˆ†π‘‘ 𝑑1βˆ’π‘‘0 Degradation rates are typically expressed by the absolute or relative change per 1000 hours. It is thus advisable to normalize the results to 1000 h time interval. This can be simply done by converting the unit of time interval to kh. Example: An SOFC stack with 5 RUs shows a stack voltage of 4.500 V at t0 = 500 h. At t1=1300 h, the stack voltage dropped to 4.482 V. The absolute and relative degradation rates of the stack voltage during time interval 500-1300 h are: βˆ†π‘‰π‘ π‘‘π‘Žπ‘π‘˜ = π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (𝑑1) βˆ’ π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (𝑑0) = π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (1300 β„Ž) βˆ’ π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (500 β„Ž) βˆ†π‘‘ 𝑑1 βˆ’ 𝑑0 (1300 βˆ’ 500)β„Ž(4.482 βˆ’ 4.500) 𝑉 βˆ’0.018 𝑉 βˆ’0.018 𝑉 = = = = βˆ’0.0225 𝑉 π‘˜β„Žβˆ’1(1300 βˆ’ 500) β„Ž 800 β„Ž 0.8 π‘˜β„Ž βˆ†π‘‰π‘ π‘‘π‘Žπ‘π‘˜,π‘Ÿπ‘’π‘™ = π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (𝑑1) βˆ’ π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (𝑑0) Γ— 100% βˆ†π‘‘ π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (𝑑0) Γ— (𝑑1 βˆ’ 𝑑0) π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (1300 β„Ž) βˆ’ π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (500 β„Ž) = 𝑉 (500 β„Ž) Γ— (1300 βˆ’ 500)β„Ž Γ— 100% π‘ π‘‘π‘Žπ‘π‘˜ 4.482 βˆ’ 4.500 βˆ’0.4% βˆ’0.4% = 4.500 Γ— (1300 βˆ’ 500) β„Ž Γ— 100% = 800 β„Ž = 0.8 π‘˜β„Ž = βˆ’0.5% π‘˜β„Žβˆ’1 Additionally, when long-term cycling is performed (thermal or load cycles for instance), it is common and relevant to express the degradation rate in relation to the number of cycles m as follows for absolute and relative degradation: 𝑋(𝑑1) βˆ’ 𝑋(𝑑0) βˆ†π‘‹π‘š = π‘š 𝑋(𝑑1) βˆ’ 𝑋(𝑑0) βˆ†π‘‹π‘š,π‘Ÿπ‘’π‘™ = 𝑋(𝑑 ) βˆ™ π‘š βˆ™ 100% 0 Area specific resistance (ASR) The area specific resistance can be determined from the j-V characteristic. Therefore, a small voltage interval where the current voltage curve is nearly linear is needed. The difference in voltage (βˆ†π‘‰(𝑗)) divided by the difference of the corresponding current density (βˆ†π‘—) is used to calculate the ASR. βˆ†π‘‰(𝑗) 𝐴𝑆𝑅(𝑗) = | | βˆ†π‘— Note that the ASR is dependent on the current/current density. In the non-linear region of the j-V curve, it is recommended to choose small voltage and current intervals. Temperatures Some stack designs do not allow direct measurement of the internal temperature of the stack. In this case an average temperature of the stack Tav should be calculated as a substitute for the internal temperature. The calculation can include the temperature of gases as well as the temperature of the end plates. Depending on which temperatures can be measured an average temperature can be calculated exemplarily as follows: 𝑇𝑇𝑃+𝑇𝐡𝑃+𝑇𝑛𝑒𝑔,𝑖𝑛+𝑇𝑛𝑒𝑔,π‘œπ‘’π‘‘+π‘‡π‘π‘œπ‘ ,𝑖𝑛+π‘‡π‘π‘œπ‘ ,π‘œπ‘’π‘‘ π‘‡π‘Žπ‘£ = 6 A stack can be damaged during the start-up/shut-down if the temperature gradient between the gas inlets and the stack itself is too high. A value for the maximum temperature difference during start-up/shut-down can be calculated with the following formula if the internal temperature cannot be measured directly: (𝑇𝑛𝑒𝑔,𝑖𝑛+π‘‡π‘π‘œπ‘ ,𝑖𝑛) (𝑇𝑇𝑃+𝑇𝐡𝑃) π›₯π‘‡π‘šπ‘Žπ‘₯ = | 2 βˆ’ 2 | Electrochemical Impedance Spectroscopy Alternating current signal (galvanostatic mode) in the time domain: 𝐼(πœ”, 𝑑) = 𝐼̅sin( πœ”π‘‘) Angular perturbation frequency: Ο‰ = 2πυ Alternating voltage response in the time domain: 𝑉(πœ”, 𝑑) = 𝑉̅ sin( πœ”π‘‘ + πœ‘) Impedance Z(Ο‰) of an electrochemical component in the time domain: 𝑉(πœ”, 𝑑) 𝑉̅ sin( πœ”π‘‘ + πœ‘) sin( πœ”π‘‘ + πœ‘) 𝛧(πœ”) = = = |𝑍| βˆ™ 𝐼(πœ”, 𝑑) 𝐼̅ sin( πœ”π‘‘) sin( πœ”π‘‘) Impedance in the frequency domain (Fourier transform, FT space): 𝛧(πœ”) = 𝐹𝐹𝑇{𝑉(πœ”,𝑑)} = |𝑍| 𝑒π‘₯𝑝(π‘–πœ‘) = |𝑍| cos(πœ‘) + |𝑍|𝑖 sin(πœ‘) = 𝑍 + 𝑖 βˆ™ 𝑍′′, 𝐹𝐹𝑇{𝐼(πœ”,𝑑)} Magnitude or modulus of the impedance: |𝑍(πœ”)| = βˆšπ‘β€²(πœ”)2 + 𝑍′′(πœ”)2 𝑍′′(πœ”) π‘‘π‘Žπ‘›πœ‘(πœ”) = 𝑍′(πœ”) Imaginary unit property: i2=-1 1. IEC TS 62282-7-2:2014, Fuel cell technologies - Part 7-2: Single cell and stack test methods – Single cell and stack performance tests for solid oxide fuel cells (SOFC) 2. IEC TS 62282-1:2013, Fuel cell technologies - Part 1: Terminology 3. JCGM 100:2008. Evaluation of measurement data - Guide to the expression of uncertainty in measurement (GUM). Joint Committee for Guides in Metrology. 4. Documents of EU-Project FCTESTNET 5. EU-Project FCTESQA: Test Module PEFC ST 5-3, β–‡β–‡β–‡β–‡://β–‡β–‡β–‡.β–‡β–‡β–‡.β–‡β–‡.β–‡β–‡β–‡β–‡β–‡β–‡.β–‡β–‡/fuel-cells/downloads-0 6. EU-Project Stacktest: Stack-Test Master Document – TM2.00,β–‡β–‡β–‡β–‡://β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡.β–‡β–‡β–‡- β–‡β–‡.β–‡β–‡/β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡/β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡/β–‡β–‡β–‡β–‡/β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡_β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡/β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡/β–‡β–‡β–‡/β–‡β–‡_β–‡-β–‡β–‡_β–‡β–‡β–‡β–‡β–‡- Test_Master-Document.pdf 7. Selected Properties of Hydrogen (Engineering Design Data), β–‡.β–‡. β–‡β–‡β–‡β–‡β–‡β–‡β–‡, β–‡. β–‡β–‡β–‡β–‡ and β–‡.β–‡. β–‡β–‡β–‡β–‡β–‡, National Bureau of Standards Monograph 168, Washington, 1981, p.6-289

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Data (Post) Processing. Here, the post processing of the test results (TIPs and TOPs) shall be described. When reporting, the significant figures of a test variable should be consistent with its measurement uncertainty. For a calculated test variable, the lesser number of significant figures of all of the involved test variables should determine the significant figure. The standard deviation (stdev), relative standard deviation (RSD) and standard error (stderr) should be expressed with at least one additional figure. The RSD should be reported with two significant figures. i zi Electrochemical reaction H2 2 H2 + O2-πŸ‘ͺO2-οƒ  H2O + 2e- CO 2 CO + O2-οΏ½O2-οƒ  οΏ½ CO2 + 2e- CH4 8 CH4 + 4O2-4O2-οƒ  πŸ‘ͺ CO2 + 2H2O + 8e- CpHqOr 4p+q-2r CpHqOr + (2p+q/2-r)O2r)O2-οƒ  -πŸ‘ͺ pCO2 + q/2H2O + (4p+q-2r)e- O2 4 O2 + 44e-οƒ  e-πŸ‘ͺ 2O2- H2O 2 H2O + 2e-οƒ  2e-πŸ‘ͺ H2 + O2- Faraday constant F = 96485.3 C mol-1 = 96485.3 A s mol-1 Oxygen fraction in air xO2 = 0.2095 Lower heating[7] value (LHV) of H2 LHVH2 = 119.93 kJ g-1 = 241.77 kJ mol-1 Higher heating[7] value (HHV) of H2 HHVH2 = 141.86 kJ g-1 = 285.98 kJ mol-1 Voltage equivalent to LHV of H2 LHVH2 / (2F) = 1.253 V Voltage equivalent to HHV of H2 HHVH2 / (2F) = 1.482 V Molar gas constant R = 8.31446 J K-1 mol-1 Normal temperature Tn = 273.15 K Normal pressure Pn= 101325 N m-2 = 101325 Pa Molar volume of an ideal gas at normal temperature and pressure 3 -1 -1 Vm = RTn/Pn = 8.31446 x 273.15 / 101325 mn mol = 22.414 ln mol Number of electrons transferred when one molecule of reactant component i is electrochemically reacted (zi) Gas utilization (Ugas) Number of repeating units in the stack: N Flow rate of reactant component i (i = 1 … n) in the negative/positive electrode of the stack: fi,in(nlpm) Theoretical current (Itheory) assuming 100% gas utilization (all reactant gas is consumed through electrochemical reactions):βˆ‘ οΏ½οΏ½ βˆ‘π‘› 1 𝑧�, οΏ½ Γ— 𝑓𝑖,π‘–βˆ‘ 𝑛 96485.3 βˆ‘π‘› 1 𝑧𝑖, β„Ž Γ— ��𝑖= ,𝑖�� 𝐼𝑑= β„Žπ‘’π‘œπ‘Ÿπ‘¦ = βˆ™ 𝑖= = Γ— π‘–βˆ‘ = 𝑉�� Γ— 60 οΏ½, οΏ½ 22.414 Γ— 60 = 𝑁 βˆ‘π‘› 1 𝑧𝑖 Γ— 𝑓𝑖,𝑖𝑛 = 71.74 Γ— 𝑖=𝑁 gas utΓ— ilization at current I: π‘ˆ = 𝐼 Γ— 100%= β„Ž 71.74Γ—βˆ‘ Γ—, =1 𝐼×𝑁 Γ— 100% π‘”π‘Žπ‘  πΌπ‘‘β„Žπ‘’π‘œπ‘Ÿπ‘¦ 71.74Γ—βˆ‘π‘› 𝑧𝑖×𝑓𝑖,𝑖𝑛𝑖=1 Nernst voltage / reversible (thermodynamic)2, voltage /4 theoretical open circuit voltage (VN) 𝑅𝑇 𝑝𝑂2,π‘π‘œπ‘  𝑉𝑁2, = 4𝐹 𝑙𝑛(, 𝑝 (considering SOC as an oxygenβˆ†( concentration cell) 𝑂2,𝑛𝑒𝑔 π‘Ÿ 𝑉 = | βˆ† 𝐺(𝑇,𝑝) | (for any reaction) 𝑁 𝑧𝐹 βˆ†π‘ŸπΊ(𝑇, 𝑝): β–‡β–‡β–‡β–‡β–‡ free enthalpy of reaction as a2 2 fuβˆ†(, nction of βˆ†0(temperature and pressure.2, 2, For thβˆ†(e reaction:βˆ†0( H2 + 0.5 O2 = H2O2 2, 1 𝑝2 𝑝𝐻2,𝑛𝑒𝑔 βˆ†π‘ŸπΊ(𝑇, 𝑝) = βˆ†π‘ŸπΊ0(𝑇) βˆ’ 𝑅𝑇𝑙�2, 2 2 2 2,1 2 2, οΏ½ 𝑂2,0(π‘π‘œπ‘  𝑝𝐻2𝑂,𝑛𝑒𝑔 1 βˆ†π‘ŸπΊ(𝑇, 2, 2 2, βˆ†0(𝑝) βˆ†π‘ŸπΊ0(𝑇) 𝑅𝑇 𝑝2 𝑝𝐻2,𝑛𝑒𝑔 𝑉 = βˆ’ = βˆ’ + 𝑙𝑛 οΏ½οΏ½2,οΏ½0(οΏ½π‘œπ‘  𝑁 2𝐹 2𝐹 2𝐹 𝑝𝐻2𝑂,𝑛𝑒𝑔1 𝑅𝑇 οΏ½οΏ½2 𝑝𝐻2,𝑛𝑒𝑔 = 𝑉0(𝑇) + 𝑙𝑛 π‘‚βˆ†(2,π‘π‘œπ‘  𝑁 2𝐹 βˆ†(𝑝𝐻2𝑂,𝑛𝑒𝑔 βˆ†π‘ŸπΊ0(𝑇): β–‡β–‡β–‡β–‡β–‡ free enthalpy of reaction at standard pressure 𝑉0(𝑇): reversible voltage at standard pressure 𝑁 Thermoneutral voltage (Vtn) βˆ†π‘Ÿπ»(𝑇) 𝑉𝑑𝑛 = 𝑧𝐹 βˆ†π‘Ÿπ»(𝑇): Enthalpy of reaction as a function of temperature. (Nοƒ  ote: the enthalpy is independent of the pressure under the assumption of ideal gases). z: number of exchanged electrons in theβˆ‘ electrochemical r, eact, = ion. For water electrolysis reaction: H2O οΏ½οΏ½ H2 + 0.5 O2 Vtn / = 1.482 V at 20 Β°C, 1.283 V at, 700 Β°C, 1.285 V at 750 Β°C and 1.286 V at 800 Β°C Average RU voltage (VRU,av) βˆ‘π‘ 1 π‘‰π‘…π‘ˆ,𝑖 𝑖= π‘‰π‘…π‘ˆ,π‘Žπ‘£ = 𝑁 Electrical power of the cell / stack (Pel) 𝑃𝑒𝑙 = 𝑉𝑐𝑒𝑙𝑙/π‘ π‘‘π‘Žπ‘π‘˜ Γ— 𝐼 (Area specific) 𝑃𝑒𝑙 𝑃𝑑,𝑒𝑙 = 𝐴 Γ— 𝑁 Electrica, l efficiency of the staβˆ‘ ck (SOFC mode) The electrical e=1 ,, , fficiency of an SOFC stβˆ‘ ack can be defined as t=1 ,, he ratio of electric power output to the total enthalpy flow input (based on either L,,HV of HHV of feed fuel gases). 𝑃𝑒𝑙 πœ‚π‘’π‘™,𝐿𝐻𝑉 = 22.414 Γ— 60 Γ— βˆ‘π‘› ��𝐻𝑉 Γ— οΏ½, οΏ½ 𝑖=1 𝑖 𝑖,𝑛𝑒, 𝑔,𝑖𝑛 𝑃𝑒𝑙 πœ‚π‘’π‘™, ,��𝐻𝑉 = 22.414 , Γ— 60 Γ— βˆ‘π‘› ��𝐻𝑉 Γ— 𝑓 𝑖=1 𝑖 𝑖,𝑛𝑒𝑔,𝑖𝑛 𝐿𝐻𝑉𝑖: LHV of fuel component i (J mol-1) 𝐻𝐻𝑉𝑖: HHV of fuel component i (J mol-1) 𝑓𝑖,𝑛𝑒𝑔,𝑖𝑛: flow rate of fuel component i (i = 1 … n)(nlpm) When using H2 as fuel: π‘ˆπ‘”π‘Žπ‘ ,𝑛𝑒𝑔 Γ— π‘‰π‘ π‘‘π‘Žπ‘π‘˜ πœ‚π‘’π‘™,𝐿𝐻𝑉 = 1.253 Γ— 𝑁 π‘ˆπ‘”π‘Žπ‘ ,𝑛𝑒𝑔 Γ— π‘‰π‘ π‘‘π‘Žπ‘π‘˜ πœ‚π‘’π‘™,𝐻𝐻𝑉 = 1.482 Γ— 𝑁 Electrical efficiency of the stack (SOEC mode: H2O electrolysis) The electrical efficiency of an SOEC stack can be defined as the ratio of enthalpy flow of fuel gases produced by the electrolyzer (based on either LHV of HHV of produced fuel gases) to the electrical power consumed by the stack for the electrochemical reaction. Here,,2βˆ’ electrical power consumed by the water e,,2βˆ’ vaporator, gas preheaters and the furnace in the βˆ† test station is not considered. It shoul0 d be n1 oted that for the calculation of system efficiency, these co(1nsumptions have to be taken (0into aβˆ† ccount(1. For H2(0O electrolysis and assume 100% cuβˆ† rrent efficiency: 1.253 Γ— 𝑁 βˆ† πœ‚π‘’π‘™,𝐿𝐻𝑉,𝐻2βˆ’π‘οΏ½οΏ½π‘œοΏ½(0�𝑒𝑐𝑑(1π‘–π‘œπ‘› =(0 οΏ½οΏ½π‘ π‘‘οΏ½βˆ† οΏ½οΏ½οΏ½π‘˜ ( 1.482 Γ— 𝑁 πœ‚π‘’π‘™,𝐻𝐻𝑉,𝐻2βˆ’π‘π‘Ÿπ‘œπ‘‘π‘’π‘π‘‘π‘–π‘œπ‘› = π‘‰π‘ π‘‘π‘ŽοΏ½οΏ½οΏ½οΏ½ Degradation The absolute degradation βˆ†π‘‹ of a quantity π‘‹βˆ† withβˆ† in the time from 𝑑0 to 𝑑1 is calculated as the diffβˆ† 1βˆ’0 βˆ† erence bβˆ† etween the final value 𝑋(𝑑1) and the βˆ† 1βˆ’0 initial value 𝑋(𝑑0): βˆ†π‘‹ = 𝑋(𝑑1) βˆ’ 𝑋(𝑑0) The relative degradation βˆ†π‘‹π‘Ÿπ‘’π‘™ is calculated by dividing βˆ†π‘‹ by the initial value 𝑋(𝑑0): 𝑋(𝑑1) βˆ’ 𝑋(𝑑0) βˆ†π‘‹π‘Ÿπ‘’π‘™ = 𝑋(𝑑 ) Γ— 100% 0 The degradation rate (rate of change) of quantity 𝑋 during the time interval (t1-t0) is then calculated by: βˆ†π‘‹ = βˆ†π‘‹ (with the unit [unit of X/time unit]) βˆ†π‘‘ 𝑑1βˆ’π‘‘0 βˆ†π‘‹π‘Ÿπ‘’π‘™ = βˆ†π‘‹π‘Ÿπ‘’π‘™ (with the unit [%/time unit]) βˆ†π‘‘ 𝑑1βˆ’π‘‘0 Degradation rates are typically expressed by the absoluteβˆ† or relative1 change per 10000 hours. It is thus advisable to normalizeβˆ† 1 the 0 results to 1000 h ti500)β„Ž (4.482 me interval. This can be simply done by converting the unβ„Žβˆ’1 (1300 it of time interval to kh. Exampleβ„Ž βˆ†, : An SOFC st1ack with 5 RUs0 shows a stack voltβˆ† age0 of 4.501 0 V 0at t0 = 500 h. At t1=1300 h, the stack voltage dropped to 4.482 V. The absolute and relative degradation rates of the stack voltage during time intervaβ„Ž l 500-1300 h β„Žβˆ’1 are: βˆ†π‘‰π‘ π‘‘π‘Žπ‘π‘˜ = π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (𝑑1) βˆ’ π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (𝑑0) = π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (1300 β„Ž) βˆ’ π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (500 β„Ž) βˆ†π‘‘ 𝑑1 βˆ’ 𝑑0 (1300 βˆ’ 500)β„Ž(4.482 βˆ’ 4.500) 𝑉 βˆ’0.018 𝑉 βˆ’0.018 𝑉 = = = = βˆ’0.0225 𝑉 π‘˜β„Žβˆ’1(1300 βˆ’ 500) β„Ž 800 β„Ž 0.8 π‘˜β„Ž βˆ†π‘‰π‘ π‘‘οΏ½οΏ½π‘οΏ½(1οΏ½,π‘Ÿπ‘’π‘™(0 = π‘‰οΏ½βˆ† οΏ½οΏ½οΏ½π‘Žπ‘οΏ½(1οΏ½ (οΏ½οΏ½1) (0βˆ’ π‘‰π‘ π‘‘π‘Žβˆ†, π‘π‘˜ (( 𝑑0) Γ— 100% βˆ†π‘‘ π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (𝑑0) Γ— (𝑑1 βˆ’ 𝑑0) π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (1300 β„Ž) βˆ’ π‘‰π‘ π‘‘π‘Žπ‘π‘˜ (500 β„Ž) = 𝑉 (500 β„Ž) Γ— (1300 βˆ’ 500)β„Ž Γ— 100% π‘ π‘‘π‘Žπ‘π‘˜ 4.482 βˆ’ 4.500 βˆ’0.4% βˆ’0.4% = 4.500 Γ— (1300 βˆ’ 500) β„Ž Γ— 100% = 800 β„Ž = 0.8 π‘˜β„Ž = βˆ’0.5% π‘˜β„Žβˆ’1 Additionally, whenβˆ†( long-term cycling is performed (thermal or load cycles for instance)βˆ†, it is common and relevant to expreβˆ†(ss the (degradationβˆ† rate in relation to the number of cycles m as follows for absolute and relative degradation: 𝑋(𝑑1) βˆ’ 𝑋(𝑑0) βˆ†π‘‹π‘š = π‘š 𝑋(𝑑1) βˆ’ 𝑋(𝑑0) βˆ†π‘‹π‘š,π‘Ÿπ‘’π‘™ = 𝑋(𝑑 ) βˆ™ π‘š βˆ™ 100% 0 Area specific resistance (ASR) The area specific resistance can be determined from the j-V characteristic. Therefore, a small voltage interval where the current voltage curve is nearly linear is needed. The difference in voltage (βˆ†π‘‰(𝑗)) divided by the difference of the corresponding current density (βˆ†π‘—) is used to calculate the ASR. βˆ†π‘‰(𝑗) 𝐴𝑆𝑅(𝑗) = | | βˆ†π‘— Note that the ASR is dependent on the current/current density. In the non-linear region of the j-V curve, it i++,+,+,+, s recommended to choose small voltage and current intervals. Temperatures Some stack designs do not allow direct measurement of the internal temperature of the stack. In this case an average temperature of the stack Tav should be calculated as a substitute for the internal temperature. The calculation can include the temperature of,+, gases as +well as the temperature of the end plates. Depending on which temperatures can be measured an average temperature can be calculate(d exemplarilΜ…siny as follows: 𝑇𝑇𝑃+𝑇𝐡𝑃+𝑇𝑛𝑒𝑔,𝑖𝑛+𝑇𝑛𝑒𝑔,π‘œπ‘’π‘‘+π‘‡π‘π‘œπ‘ ,𝑖𝑛+π‘‡π‘π‘œπ‘ ,π‘œπ‘’π‘‘ π‘‡π‘Žπ‘£ = 6( A stack cΜ… an be damaged during the sZ(tart-up/shut-down if the temperature gradient between the( gas inlΜ… ets and the stack itself is t(oo high. A v|| alue (for the Μ… maximum temperature difference during start-up/shut-down can be calculated with the fo): (llowing formu{(,la if the inter|| (nal temperatu|| cos(re cannot be m|| sin(easured directlβ€²β€²y: (𝑇𝑛𝑒�{(,οΏ½,𝑖𝑛+π‘‡π‘π‘œπ‘ ,𝑖𝑛) (𝑇𝑇𝑃+𝑇𝐡𝑃) π›₯π‘‡π‘šπ‘Žπ‘₯ |()| = | 2 βˆ’ 2 βˆšβ€²()2 | Electrochemicβ€²β€²()2 β€²β€²(al Imped(ance Speβ€²(ctroscopy Alternating current signal (galvanostatic mode) in the time domain: 𝐼(πœ”, 𝑑) = 𝐼̅sin( πœ”π‘‘) Angular perturbation frequency: Ο‰ = 2πυ Alternating voltage response in the time domain: 𝑉(πœ”, 𝑑) = 𝑉̅ sin( πœ”π‘‘ + πœ‘) Impedance Z(Ο‰) of an electrochemical component in the time domain: 𝑉(πœ”, 𝑑) 𝑉̅ sin( πœ”π‘‘ + πœ‘) sin( πœ”π‘‘ + πœ‘) 𝛧(πœ”) = = = |𝑍| βˆ™ 𝐼(πœ”, 𝑑) 𝐼̅ sin( πœ”π‘‘) sin( πœ”π‘‘) Impedance in the frequency domain (Fourier transform, FT space): 𝛧(πœ”) = 𝐹𝐹𝑇{𝑉(πœ”,𝑑)} = |𝑍| 𝑒π‘₯𝑝(π‘–πœ‘) = |𝑍| cos(πœ‘) + |𝑍|𝑖 sin(πœ‘) = 𝑍 + 𝑖 βˆ™ 𝑍′′, 𝐹𝐹𝑇{𝐼(πœ”,𝑑)} Magnitude or modulus of the impedance: |𝑍(πœ”)| = βˆšπ‘β€²(πœ”)2 + 𝑍′′(πœ”)2 𝑍′′(πœ”) π‘‘π‘Žπ‘›πœ‘(πœ”) = 𝑍′(πœ”) Imaginary unit property: i2=-1 1. IEC TS 62282-7-2:2014, Fuel cell technologies - Part 7-2: Single cell and stack test methods – Single cell and stack performance tests for solid oxide fuel cells (SOFC) 2. IEC TS 62282-1:2013, Fuel cell technologies - Part 1: Terminology 3. JCGM 100:2008. Evaluation of measurement data - Guide to the expression of uncertainty in measurement (GUM). Joint Committee for Guides in Metrology. 4. Documents of EU-Project FCTESTNET 5. EU-Project FCTESQA: Test Module PEFC ST 5-3, β–‡β–‡β–‡β–‡://β–‡β–‡β–‡.β–‡β–‡β–‡.β–‡β–‡.β–‡β–‡β–‡β–‡β–‡β–‡.β–‡β–‡/fuel-cells/downloads-0 6. EU-Project Stacktest: Stack-Test Master Document – TM2.00,β–‡β–‡β–‡β–‡://β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡.β–‡β–‡β–‡- β–‡β–‡.β–‡β–‡/β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡/β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡/β–‡β–‡β–‡β–‡/β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡_β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡/β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡β–‡/β–‡β–‡β–‡/β–‡β–‡_β–‡-β–‡β–‡_β–‡β–‡β–‡β–‡β–‡- Test_Master-Document.pdf 7. Selected Properties of Hydrogen (Engineering Design Data), β–‡.β–‡. β–‡β–‡β–‡β–‡β–‡β–‡β–‡, β–‡. β–‡β–‡β–‡β–‡ and β–‡.β–‡. β–‡β–‡β–‡β–‡β–‡, National Bureau of Standards Monograph 168, Washington, 1981, p.6-289

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