# How green is your electric car?

You often see "zero emissions" plastered over the backs of electric cars, as if the energy to run them is magically pulled from the ether. I'm curious about some of the practical considerations for a large scale adoption of electricity as a form of energy for road transportation, and what sort of overall impact this may have on environmental issues.

Let's try to calculate (on the back of an envelope!) the impact of an imaginary, immediate and total conversion from petrol and diesel to electric cars.

## Scale of emissions

Based on statistics released by the UK Climate Change Commission, in 2012 the UK released about 600 mega tonnes of CO2 (MtCO2) into the atmosphere. Approximately 110Mt was related to surface transport of all kinds [Note 1], including rail, passenger cars, vans, and freight in trucks/lorries/HGVs. Private passenger transport accounts for around 60% of transport related emissions [Note 2] or around 11% of total CO2 emissions [Note 3]. By comparison, electricity generation emitted around 160MT of CO2 in the same year, or in other words about two and a half times as much as passenger transport [Note 1].

## Electric supply

The scale of emissions above suggests that if we were to suddenly replace all the petrol and diesel cars in the UK with electric vehicles then we could cut total UK emissions by about 65MtCO2 or 11%. However, in reality this is not the case as most energy for electric cars comes from the grid...

In England in 2011, almost 80% of that energy is generated by burning fossil fuels (the figure is less in other countries within the UK) [Note 4]. Does moving emissions from an internal combustion engine to a fossil fuel power plant reduce total emissions at all? Let's do the rough numbers...

### Calculating the emissions

#### Energy in fuels

Not all fuels are created equal. The reason why petrol and diesel have become so ubiquitous is that it gives you very good bang for buck - it lets you carry around a lot of energy in a small tank. For each kg of petrol you burn, you can theoretically "liberate" 44MJ of energy. For coal and natural gas this value is around 35MJ [Note 5]. Therefore to produce 44MJ of energy, you could burn 1kg of "gasoline", or $$\frac{44}{35}=1.25kg$$ of natural gas or coal.

#### Efficiency of power sources

To make this a back of the envelope calculation, we'll have to ignore distribution and transmission efficiency and just concentrate on generation efficiency. A typical internal combustion engine is between 25 and 45% efficient. This means that to generate 44MJ of energy at the fly wheel (i.e. before the mechanical losses from the transmission) then we don't need to burn 1kg of fuel, but actually between $$\frac{1}{0.45}=2.2kg$$ and $$\frac{1}{0.25}=4.0kg$$ of fuel.

A power plant may have higher efficiency in the range of 40-60%, meaning we have to burn between $$\frac{1.25}{0.4}=2.1kg$$ and $$\frac{1.25}{0.6}=3.1kg$$ of fuel [Note 6]. To be fair to petrol engines we should factor in the electric car motor efficiency, which is less than 100%, but luckily much higher than for petrol engines. We will assume a generous 90% efficiency, meaning that to get 44MJ of energy at the electric motor "flywheel", we have to burn between 2.3 and 3.4kg of fuel at the power plant.

#### CO2 emitted by fuel

Finally, we need to work out how much CO2 is emitted by burning each of these fuel types. A simplified chemical reaction for petrol combustion is

$$C_8H_{18} + 12.5(O_2 + 3.76N_2) \rightarrow 8CO_2 + 9H_2O + 47N_2$$

These units are in mole, but using the atomic weight of the molecules we can determine from this reaction that for every kg of petrol we burn, we produce around 3kg of C02. [Note 7]

This reaction assumes complete combustion and ignores CO or NOx emissions

Similar values can be worked out for coal and natural gas, but for simplicity lets use a table which gives kg of CO2 per kg of fuel of 3.3kg/kg for petrol, 2.8 for natural gas and 2.3 for coal [Note 8].

Therefore to produce 44MJ of energy from petrol, we would have to release between $$2.2kg \times 3.3kg/kg = 7.3kg$$ and $$4kg\times3.3kg/kg = 13.2kg$$ of CO2, depending on the fuel type. (Diesel is typically more efficient at the cost of higher nitrous oxides, but we'll assume everything is petrol for now).

Using England's split of 20.8% of power supplied by low emission sources, 29.2% by coal and 50% by natural gas [Note 4], we can calculate the equivalent emissions for power plant generation at between

$$0.29 \times 2.3kg \times 2.3kg/kg + 0.5 \times 2.3kg \times 2.8kg/kg = 4.8kg$$

and

$$0.29 \times 3.4kg \times 2.3kg/kg + 0.5 \times 3.4kg \times 2.8kg/kg = 7.0kg$$

Comparing the two reveals that burning fossil fuels as opposed to fuel can result in emissions being reduced to 53-66% of their petrol counterparts.

## Now what?

In short, this pretty basic analysis tells us that if we took the 65 MTCO2e from passenger transport and converted it all to 2011 England electric power, we would reduce CO2 emissions to between 35 and 44 MTCO2e for passenger transport under current power generation technology. The reduction would equate to around 5% of total emissions.

In reality, the impact of even total adoption of electric vehicles on CO2 emissions would be small to negligible under current power generation technologies. Whilst electric vehicles are cool, a far more pressing need is to develop and commercialise new, cleaner ways of generating electrical energy.

## Notes and assumptions

### What is missing?

Energy analysis is by definition complex, and calculation CO2 emissions and fuel economy is even more difficult given the very wide range of factors at play [Note 9].

This analysis is based on operating emissions only - that is the emissions required to supply the energy to move a vehicle from point A to point B. Factors like hybrids, regenerative braking, the higher mass of electric vehicles and potential changes to driver habits are ignored, as are the total lifetime emissions of vehicles from digging ore out of the ground to end of life vehicles.

For instance, this analysis completely ignores the exotic metals electric motors require or the problem of disposing of vast quantities of end of life electric vehicle batteries.

### References

[NOTE 1] CO2 emissions by sector http://www.theccc.org.uk/charts-data/ukemissions-by-sector/

[Note 3] $$\frac{60\% \times 110MTCO_2e}{600 MTCO_2e} = 11\%$$

[Note 7] As 1kmol of $$C8H18$$ weighs $$8\times 12 + 18 \times 1 = 114kg$$ and produces 8kmol of $$CO_2$$ weighing $$8\times(12 + 2\times 16) = 352kg$$