[Nat333]

Hi,

I was attempting some kinetics/fuel cell problems and thought about the expertise of chemical engineers in an online forum.

I'm a market researcher trying to understand fuel cells on a part-time course. The problem is I'm totally lost reading the course material. I get the concept of electricity generation from a fuel cell, but I just seem unable to understand or connect the underlying chemical engineering concepts.

Would it be possible if you could explain to me how I might go about the questions below, please? Or maybe if you worked them out I'd be able to understand and then take it from there? I've been able to solve 2 other related questions on equilibrium constant.

I recognise you might be busy, hence your assistance will be very much appreciated. In fact, I'm more than happy to compensate you for your time.

I look forward to your reply.

Thank you.



1.
a)   Hydrogen is to be produced by the electrolysis of steam at temperatures of 500  to  800 °C,. 

i). Explain how this may be achieved in a practical system.


ii) Show, how the cell voltage of the electrolyser varies with temperature in the range of temperature, 500  of  800 °C, at a  current density of 1000 mA cm^-2 and  pressures of 5 and 20 bar.

Data:

Anode and cathode kinetics are given by a Tafel equation with the following data for exchange current density and transfer coefficient (or Tafel slope):

 Cathode
Exchange current density;       jo = {RT/2F}kelectrode exp[-Eelectrode/RT]

                     kelectrode = 6.54 x 10¹¹    S m^-2,  Eelectrode= 1.4 x 10⁵     J mol^-1.

   Tafel slope 30 mV/decade

Anode
Exchange current density;       jo = {RT/2F}kelectrode exp[-Eelectrode/RT]


                     kelectrode = 2.35 x 10¹¹    S m^-2,  Eelectrode= 1.37 x 10⁵     J mol^-1.

   Tafel slope 60 mV/decade

Electrolyte specific conductivity (Siemens per metre) = 33.4 x 10³ exp[-10.3 x 10³ /T]   S m^-1

Cathode electrical conductivity = 80 x 10³ S m^-1

Anode electrical conductivity = 8.0 x 10³ S m^-1

Electrolyte thickness = 40 µm

Cathode thickness     = 400 µm
 Anode thickness       = 40 µm


b) The electrolyser above is to be used as a fuel cell operating at the same temperature and pressure, using hydrogen and oxygen.

Estimate the cell voltage at a current density of 1000 mA cm^-2.



2.

When petrol is burnt in an engine the combustion proceeds according to the following reaction:

   C₈H₈  +  12.5 0₂     8 CO₂  +  9 H₂0             (1)

For every mole of petrol that is burnt 7074.2 kJ of energy are released. In an internal combustion engine approximately 35% of this energy will be converted into power to drive the car. In a fuel cell hydrogen reacts according to the following equation:

   H₂  +  0.5 O₂     H₂0               (2)

For every mole of hydrogen that is burnt 241.8 kJ of energy are released. Petrol can be represented chemically as octane. This can be steam reformed to produce hydrogen according to the following reactions:

   C₈H₁₈  +  8H₂0     8 CO  +  17 H₂   (3)

This reaction consumes 1232 kJ of energy for every mole of octane that reacts. The energy required for this reaction is provided by combustion resulting in the emission of a further 1.54 moles of carbon dioxide, for every mole of octane that is fed to the reactor. The carbon monoxide produced by reforming is combined with steam to produce hydrogen and CO2 according to the water gas shift reaction:

   CO  +  H₂0     CO₂  +  H₂   (4)

This reaction produces 41.2 kJ of energy for every mole of carbon monoxide that reacts. In equations 3 and 4 water vapour (steam) is used.

This has to be generated by the evaporation of water, resulting in the emission of a further 0.05 moles of carbon dioxide per mole of steam.

For any reaction the conversion of reactant A is defined as follows:


%conversion of A = 100 [ 1 - (moles of A at the end of the reaction / moles of A at the start of the reaction) ]


It is proposed that a steam reformer is used to generate hydrogen from petrol. The conversion of petrol in the reformer is 81% and the conversion of the carbon monoxide in the water gas shift reaction is 95%.


Question

How efficient must the fuel cell system used to ‘burn’ the hydrogen and power the car be, in order that less CO₂ is emitted via the steam reforming route in comparison to burning the petrol in an engine?


Notes:

1.The comparison should be made based on the amount of CO₂ produced by octane combustion/reforming not on the basis of energy.

2.The energy for the reforming process and steam generation is provided by octane combustion. The amounts of CO₂ produced as a result of these processes are given in the question and do not require calculation.

[Arkcon]

The first part requires some really specialized information.  It would be a lot of hard work to type it out in a forum posting, maybe you can try to figure that problem out with the text portion of the book you got the problem from.

The second part is, at least, possible for a novice to figure out.  It gives the energy  needed to make components, and the energy you get out after you react your components.  Then tries to make you do some simple math -- how efficient must production be for the final product to be cost effective, in energy terms, not money terms.  See if you can work that part out for yourself.  The skill will come in hand for the next problem of this sort ... and the next ... and the next ...

[Nat333]

I've been able to solve everything by understanding my course notes better and by further research.  Consequently I now know a lot about fuel cells! Thanks for your suggestion, however a novice certainly would not figure out any of these questions!