Answer:
(c) [tex]F_{H_2O}^{desired}=33.8\frac{kgH_2O}{h}[/tex]
(d) [tex]F_{air}^{desired}=51.6\frac{kgAir}{h}[/tex]
Explanation:
Hello,
In this case, the problem is:
Assume that you are designing a reformer reactor that is part of a fuel cell fuel processor system that will use natural gas (primarily methane, CH₄) as the primary fuel for a 100 kWe fuel cell.
Thus, the undergoing chemical reactions are:
[tex]CH_4+1/2O_2\rightarrow CO+2H_2\\CH_4+H_2O\rightarrow CO+3H_2\\CO+H_2O\rightarrow CO_2+H_2[/tex]
Hence, assuming a 60% overall efficiency for the fuel cell and considering that methane's heat of combustion is 50000 kJ/kg, the flow rate methane turns out:
[tex]F_{CH_4}=100\frac{kJ}{s}*\frac{1}{60\%}*\frac{1kg}{50000kJ}*\frac{3600s}{1h} =12kg/h[/tex]
Now, one could compute the desired steam flow-rate by assuming a steam to carbon ratio of 2.5 to avoid coking:
[tex]F_{H_2O}^{desired}=12\frac{kgCH_4}{h}* \frac{1kmolCH_4}{16kgCH_4}*\frac{2.5kmolH_2O}{1kmolCH_4}*\frac{18kgH_2O}{1kmolH_2O} =33.8\frac{kgH_2O}{h}[/tex]
Finally, to compute the desired air flow-rate, it is necessary to specify a O₂ to CH₄ ratio of 0.5 (based on the first reaction):
[tex]F_{air}^{desired}=12\frac{kgCH_4}{h}* \frac{1kmolCH_4}{16kgCH_4}*\frac{0.5kmolO_2}{1kmolCH_4}*\frac{1kmolAir}{0.21kmolO_2}*\frac{28.9kgAir}{1kmolAir} =51.6\frac{kgAir}{h}[/tex]
Best regards.
