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Real FuelCells in KSA
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There is a lot writing about FC (Fuel Cells) in the internet, but often it is not quite clear what the electric power output is in dependence of mass flow rates.
Often there is volume flow used, and this is not unique since it depends on the hydrogen (or other fuel) state (liquid/gaseous at some often unknown pressure/temperature).
So that is why I really like the mass base for consumption calculation and especially that you consistently use the SI unit system in KSA .
------------------------
Basic chemical reactions
------------------------
Hydrolox:
2 H2 + O2 <-> 2H2O @142 MJ/kg H2
Molar masses : 4g + 32g <-> 36g
You need 8kg Oxygen to burn 1kg Hydrogen.
Methalox:
CH4 + 2O2 <-> CO2 + 2H2O @50 MJ/kg CH4
Molar masses : 16g + 64g <-> 80g
You need 4kg Oxygen to burn 1kg Methane.
Kerolox :
2 C12H26(l) + 37 O2(g) <-> 24 CO2(g) + 26 H2O(g) @44MJ/kg C12H26
Molar masses : 340g + 1184g <-> 1524g
You need 3.48kg Oxygen to burn 1kg Kerosine.
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Storage volume and needed system mass
-------------------------------------
212 g Fuel cell mass per 1kW electric power generated
233 ml storage volume needed per 1kW
--------------------------------------------
Summary ( given a 50% Fuel cell efficiency )
--------------------------------------------
Hydrolox : 7.889 kW @ 1 g/s Hydrolox massflow [ 0.111 g/s H2 , 0.889 g/s O2 ]
Methalox : 5.000 kW @ 1 g/s Methalox massflow [ 0.200 g/s CH4 , 0.800 g/s O2 ]
Kerolox : 4.908 kW @ 1 g/s Kerolox massflow [ 0.223 g/s C12H26 , 0.777 g/s O2 ]
----------
Discussion
----------
The (lower) heating value of hydrogen is : 1 kg of H = 33.393kWh (or 1kg of H2 if you prefer) .
A typical fuel cell has an efficiency of 50% (many are better, but let's take 50% here, for a serious estimation).
That means: 0.5 * 33.393 = 16.7 Wh/g fuel mass energy density for such kind of FC (fuel cell).
This leads to an energy output at a give fuel mass flow :
H_consumption = 1 g/h => 16.7 Wh electric energy generated in 1h => 16.7 W electric power ,
or :
H_consumption = 1 g/s => 16.7 Wh electric energy generated in 1s
=> (16.7*3600) Wh electric energy generated in 1h => 60.12 kW power.
(annotation: it is easier to always use the SI system for calculations, so heating value of 1kg H2 = 120.21 MJ , leads directly to 120.21 * 0.5 = 60.12 MW power at a massflow rate of 1kg/s with 50% efficiency. So I always use SI units during calculations, switching to common units when representing the results. You can completely (!) forget about any(!) units when consistently calculating in SI units, that is an unbeatable benefit!).
So if you take an efficiency of 50% you roughly get 60kW @ 1g/s H2 consumption rate, that is 60MW @ 1kg/s .
This is pure H2 mass (like for PEM FC used in cars), so you have to add the oxygen mass if you use the FC in space.
The mass ratio of liquid oxygen to liquid hydrogen (not supercooled) is 7.979 (let's say 8),
so you need 8kg O2 for 1kg H2 used, so the power output of a PEM Hyrolox FC in space becomes to:
60MW @ (8+1)kg Hydrolox/s => 667 kW @ 1kg Hydrolox/s .
I used the formula:
PowerOutput@x%Eff [MW/(kg/s)] = x/100 * HeatValFuel [MJ/kg] / (1+m_oxydizer/m_fuel)
yielding to :
Hydrolox PowerOutput@50%Eff = 0.5 * 142/(1+8) = 7.889 MW / (kg/s)
Methalox PowerOutput@50%Eff = 0.5 * 50/(1+4) = 5 MW / (kg/s)
Kerolox SPowerOutput@50%Eff = 0.5 * 44/(1+3.4824) = 4.908MW / (kg/s)
-------------
Sources :
en.wikipedia.org
en.wikipedia.org
https://en.wikipedia.org/wiki/Kerosene (chapter: engine)
Real FuelCells in KSA
---------------------
There is a lot writing about FC (Fuel Cells) in the internet, but often it is not quite clear what the electric power output is in dependence of mass flow rates.
Often there is volume flow used, and this is not unique since it depends on the hydrogen (or other fuel) state (liquid/gaseous at some often unknown pressure/temperature).
So that is why I really like the mass base for consumption calculation and especially that you consistently use the SI unit system in KSA .
------------------------
Basic chemical reactions
------------------------
Hydrolox:
2 H2 + O2 <-> 2H2O @142 MJ/kg H2
Molar masses : 4g + 32g <-> 36g
You need 8kg Oxygen to burn 1kg Hydrogen.
Methalox:
CH4 + 2O2 <-> CO2 + 2H2O @50 MJ/kg CH4
Molar masses : 16g + 64g <-> 80g
You need 4kg Oxygen to burn 1kg Methane.
Kerolox :
2 C12H26(l) + 37 O2(g) <-> 24 CO2(g) + 26 H2O(g) @44MJ/kg C12H26
Molar masses : 340g + 1184g <-> 1524g
You need 3.48kg Oxygen to burn 1kg Kerosine.
-------------------------------------
Storage volume and needed system mass
-------------------------------------
212 g Fuel cell mass per 1kW electric power generated
233 ml storage volume needed per 1kW
--------------------------------------------
Summary ( given a 50% Fuel cell efficiency )
--------------------------------------------
Hydrolox : 7.889 kW @ 1 g/s Hydrolox massflow [ 0.111 g/s H2 , 0.889 g/s O2 ]
Methalox : 5.000 kW @ 1 g/s Methalox massflow [ 0.200 g/s CH4 , 0.800 g/s O2 ]
Kerolox : 4.908 kW @ 1 g/s Kerolox massflow [ 0.223 g/s C12H26 , 0.777 g/s O2 ]
----------
Discussion
----------
The (lower) heating value of hydrogen is : 1 kg of H = 33.393kWh (or 1kg of H2 if you prefer) .
A typical fuel cell has an efficiency of 50% (many are better, but let's take 50% here, for a serious estimation).
That means: 0.5 * 33.393 = 16.7 Wh/g fuel mass energy density for such kind of FC (fuel cell).
This leads to an energy output at a give fuel mass flow :
H_consumption = 1 g/h => 16.7 Wh electric energy generated in 1h => 16.7 W electric power ,
or :
H_consumption = 1 g/s => 16.7 Wh electric energy generated in 1s
=> (16.7*3600) Wh electric energy generated in 1h => 60.12 kW power.
(annotation: it is easier to always use the SI system for calculations, so heating value of 1kg H2 = 120.21 MJ , leads directly to 120.21 * 0.5 = 60.12 MW power at a massflow rate of 1kg/s with 50% efficiency. So I always use SI units during calculations, switching to common units when representing the results. You can completely (!) forget about any(!) units when consistently calculating in SI units, that is an unbeatable benefit!).
So if you take an efficiency of 50% you roughly get 60kW @ 1g/s H2 consumption rate, that is 60MW @ 1kg/s .
This is pure H2 mass (like for PEM FC used in cars), so you have to add the oxygen mass if you use the FC in space.
The mass ratio of liquid oxygen to liquid hydrogen (not supercooled) is 7.979 (let's say 8),
so you need 8kg O2 for 1kg H2 used, so the power output of a PEM Hyrolox FC in space becomes to:
60MW @ (8+1)kg Hydrolox/s => 667 kW @ 1kg Hydrolox/s .
I used the formula:
PowerOutput@x%Eff [MW/(kg/s)] = x/100 * HeatValFuel [MJ/kg] / (1+m_oxydizer/m_fuel)
yielding to :
Hydrolox PowerOutput@50%Eff = 0.5 * 142/(1+8) = 7.889 MW / (kg/s)
Methalox PowerOutput@50%Eff = 0.5 * 50/(1+4) = 5 MW / (kg/s)
Kerolox SPowerOutput@50%Eff = 0.5 * 44/(1+3.4824) = 4.908MW / (kg/s)
-------------
Sources :
Proton-exchange membrane fuel cell - Wikipedia
Stoichiometry - Wikipedia
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