This week I was very excited to learn that a Canadian company has developed technology that can remove carbon dioxide from the air. Obviously the hope is that removal of this greenhouse gas will help to prevent climate change. Moreover, the company, Carbon Engineering, plans to fund the operation by converting the extracted carbon dioxide back into a fuel, which can then be sold. It should be noted that their announcement concerns a prototype but if they are successful, they will really have achieved something remarkable – turning a profit by saving the world.
Some people might consider that to be quite a big if. When I shared the story about the prototype, a friend responded as follows: “Surely the technology uses a lot of energy. This sounds like a perpetual motion machine.” My initial reaction was that Carbon Engineering would not have published the news if this were the case, but that is not a very satisfactory response. The electrochemists Martin Fleischmann and Stanley Pons embarrassed themselves in 1989 when they prematurely claimed to have developed cold fusion. That would have solved various crises but unfortunately it turned out they were mistaken. As such, in the interests of producing a more satisfactory response, I thought I would do some basic sums to investigate the feasibility.
First of all, we need to consider how the machine works. Air is forced through a solvent, in which carbon dioxide dissolves in the form of carbonate ions (CO32-). This is achieved with a fan, which drags the air through the solvent. A specially designed container ensures that contact between the air and the solvent is maximised. Afterwards, the carbon dioxide can be extracted from the solution. It can then be reacted with hydrogen to produce a hydrocarbon fuel. One option is methane, the gas we use to cook with and the one on which I will base this investigation.
First of all, I looked up the typical power consumption of fans. It varies depending on the pressure they generate and of course the volume of air they draw through. Truthfully, I am not at all sure what the pressure requirements would be, so I selected a value from the middle of a list of power consumption values for typical fans. That value was 500 Pascals (Pa). If such a fan is used to draw through 1,000 cubic metres (m3) of a gas per hour, the typical power consumption would be 0.1 kilowatts (kW). The consumption is as follows:
One fan at 0.1kW for one hour:
Total power: 0.1kW
This is equivalent to 100 joules (J) per second
One hour is the same as 3600 seconds
So the total energy required to run the fan for one hour is 360,000J
Assuming that the efficiency of the fan is 80%, the actual energy consumption will be: 450,000J
The fan draws 1,000m3 of air through the solvent
One mole* of any gas has a volume of 24dm3 (at room temperature and atmospheric pressure) which is equal to 0.024m3
Therefore, the number of moles of air that will be drawn through the solvent is 1000 / 0.024 = 41,666 moles
The current proportion of CO2 in air is 0.04%
This means that the number of moles of CO2 drawn through the solution would be 0.04/100 x 41,666 = 16.7 moles of CO2
Carbon Engineering reports that the prototype machine is able to extract 80% of all the CO2 that passes through the solvent, meaning that 13.36 moles of CO2 would be extracted
*A mole is like a chemist’s dozen. It’s a way of indicating the amount of a substance by the number of atoms or molecules it contains rather than its mass. A mole of anything contains 6.02×1023 of the thing you are counting, so if you had a mole of donuts, you would have 6.02 x 1023 donuts.
Next, the equation for the reaction between carbon dioxide and hydrogen is:
CO2 + 4H2 –> CH4 + 2H2O ΔH = −165.0 kJ mol-1
This tells us two things. First of all, one mole of carbon dioxide produces one mole of methane. Secondly, the reaction is exothermic, meaning that it gives off energy rather than absorbing energy. Unfortunately, the reaction still requires high pressure and a temperature of between 300 and 400 oC.
So in theory, 13.36 moles of carbon dioxide should produce 13.36 moles of methane. That would mean a reaction yield of 100%, in other words, every last molecule of reactant was successfully converted to product, which basically never happens. If we assume a reaction yield of 80%, 13.36 moles of carbon dioxide will produce 10.69 moles of methane.
How much energy is released when methane is combusted? Its enthalpy of combustion is:
ΔHc = −882 kJ mol-1
So the energy transferred when the methane is combusted will be:
10.69 x 882
Remember that the energy consumption of the fan was 450,000J. This means that the output energy is significantly more than the input energy. Having said that, the calculation is far from complete. Things that I have left out are:
*the energy used to remove the dissolved carbon dioxide from the solvent
*the energy cost of producing the hydrogen gas to react with the carbon dioxide
*the energy cost of generating the necessary temperature and pressure to run the reaction between carbon dioxide and hydrogen
Also, I made numerous assumptions, including
*The efficiency rating of the fan
*The pressure the fan would be required to exert
*The yield of the reactions
*That 100% of the energy transferred by the combustion of methane would be useful energy
Even putting aside these notable omissions, there is still a problem about the actual impact the technology would have on the atmospheric concentration of carbon dioxide. If all the extracted carbon dioxide is turned into fuel, the technology will not actually reduce the current concentration of carbon dioxide in the atmosphere. That presents two possibilities. The first is to expand the operation rapidly enough to meet a considerable proportion of the world’s energy needs. If sufficient fuel could be provided to leave all remaining fossil fuels underground, the concentration of carbon dioxide could be held at current levels. This does not seem very likely. The second possibility is that the operating firm holds back some of the extracted carbon dioxide, rather than returning it all to the atmosphere in the form of combusted fuel.
The climate change crisis has not been solved just yet but I am still excited by the news of this invention. Climate change scientists have increasingly been branded alarmists, which is really nothing but the old story of shooting the messenger. We absolutely should be alarmed, by the enormity of the risk and the urgency with which action has for so long been required. Sadly, alarm has instead so often taken the form of incredulity at claims dismissed as preposterous. If this technology is successful, it will provide a far more carbon neutral means of providing energy, in such a way as to minimise the need to change our current energy infrastructure. Nothing succeeds like success and the stakes in this case include the survival of our species. I hope the sums check out.
Feel free to improve on this calculation in the comments box below. Teachers: why not get your students to improve on the calculations? =)