Energy Engineering - Electrochemical Energy Conversion and Storage

Full exam

EECS – Prof. A. Casalegno – 1 3 th Ju ly 202 2 1 Standard EECS exam [duration 1 h 4 0 min ] Students who passed TiP reduced number of questions marked with ( TiP ) [duration 1 h 1 0 min] To upload (maximum 5 single - side A4 pages – PDF file name MUST BEGIN with person code) Basic Part ( 4.5 points per question, minimum score 12) ( TiP : 7.5 points ) 1. Write the Butler - Volmer kinetics equation for hydrogen oxidation reaction ( HOR ) 2. Write Faraday’s law for electrolyte and reactants of an alkaline electrolyzer 3. ( TiP ) Write an example of electrochemical reactions occurring in a Lithium - ion battery and the typical battery voltage range Exercise ( TiP ) A Li - ion battery with nominal capacity of 50 Ah operates at ambient pressure and temperature , requiring 3. 8 V for discharging at SoC=80% and C - rate= 2 h - 1 . Assuming that : 1. Tafel kinetics is valid for both electrodes 2. ion and mass transport effects in electrodes are negligible 3. activities of reactants in charge are close to the value of (1 - SoC) 4. electrolyte resistance is equal to 1.8 mΩ 5. transfer coefficients of both electrodes during discharge are equal to 0.5 During charge at C - rate=1 h - 1 , the voltage reaches the valu e of 3.8 V, estimate the achieved SoC. Interm e diate Part ( 3 points for each question ) ( TiP : 5 points ) 1. Show how current density equation , derived from Nernst - Plank equation , simplifies in the case of a solid electrolyte with fixed charge 2. ( TiP ) Depict in the chart D V=f(SoC) a typical discharge curve of a Lithium - ion battery and the curves of D V loss attributed to positive electrode , negative one and ele c trolyte EECS – Prof. A. Casalegno – 1 3 th Ju ly 202 2 2 Exercise ( TiP ) A PEM fuel cell operates at 8 0°C with pure H 2 and air at 0.25 MPa pressure and supplies at 0. 65 V a current density equal to 1.7 A/cm 2 and related impedance is reported in the figure . Assuming that: 1. anode behaves as an ideal H 2 electrode [ ! ! + # ! =0] 2. ion and mass transport effects in catalyst layers are negligible 3. the average O 2 molar fraction in the cathode channel is equal to 0. 07 4. diff usion la yer diffusivity D ref is equal to 0.05 cm 2 /s (at 0.1 MPa ) and its thickness is 15 0 μ m . Demonstrate that, reducing the pressure down to 0.1 MPa, the current density at 0.7 V is higher than 1 A/cm 2 . Difficult Part ( 1 .5 point s ) ( TiP : 2 .5 points ) Exercise ( TiP ) A Li - ion battery with nominal capacity of 20 Ah operates at ambient pressure and temperature, during discharge at C - rate 1/20 h - 1 and SoC=80% the voltage is equal to 4 V . Assuming that: 1. BV kinetics is valid for the positive electrode 2. Tafel kinetics is val id for the negative electrode 3. transfer coefficients of both electrodes during discharge are equal to 0.5 4. ion and mass transport effects in electrodes are negligible 5. $ ! ( &' 80% ,-. ) = 5 2 6. & #$ = 3 #$ % = [ 0 . 85 ,-. + 0 . 05 ] % 7. 7 8 & = 550 2 During discharge at Crate= 2 and SoC=80% the voltage assumes the value 3.78 V, calculate the electrolyte resistance and the relative voltage loss . Laboratory Part (1.5 points) ( TiP : 2 .5 points ) 1. ( TiP ) Draw the voltage transient of a lithium - ion battery obtained opening the circuit after a discharge period ( i.e. relaxation): what is the reason of such transient period ? What is the order of magnitude of its duration ? Is the duration affected by the discha rge current ? !"($) −'(($) 0.1 - .(2 −0.017 - .(2 0.14 - .(2