In preparing my previous post on Net Energy Trends I wanted to include a back of the envelope calculation on the ERoEI of hydro electric power using the Three Gorges Dam as an example. But I got my decimals pretty muddled leading to an answer that was implausible. But I’ve now had a few days off to clear my head and I put a new battery in my calculator and so hopefully the calculation is now on the money.
Looking at just the labour and embedded energy of the concrete and steel and assuming a 45% capacity factor and 70 year life yields a partial ERoEI of 147. And so, despite substantial environmental harm and social disruption I must give dispatchable hydro electric power a big thumbs up. See the calculation below the fold.
The Three Gorges Dam on the Yangtze River in China is the largest hydroelectric scheme in The World. Operational since 2008 it has 22.5 GW installed capacity. The Itaipu Dam on the Parana River between Paraguay and Brazil produces a similar amount of electricity from 14 GW capacity and achieves this through a higher capacity factor.
Recent posts on ERoEI indicated that hydroelectric power had ERoEI >> 50 and I just wanted to check these claims. But before proceeding lets get the metric prefixes sorted since we have to manipulate some fairly large numbers:
mega = 10^6 = million
giga = 10^9 = billion
tera = 10^12 = trillion
peta = 10^15 = one thousand trillion
exa = 10^18 = one million trillion
Three Gorges Vital Statistics
Installed generating capacity = 22.5 GW 
Capacity factor = 45% (0.45) 
Concrete = 27.2 million m^3 
Concrete = 65.2 million tonnes*
Steel = 463,000 tonnes 
*1 m^3 concrete = 2.4 tonnes
1 TWh = 3600 TJ 
1 toe = 42 GJ 
The Energy Return
This is always the easier part of the ERoEI calculation but even here assumptions need to be made about capacity factor and lifespan. Wikipedia report 45% capacity factor which I presume is based on design criteria and performance to date. And I have assumed a 70 year lifespan. Lifespan could easily be much longer and this will simply add to the ERoEI.
0.45 * 22.5 GW * 24 hrs * 365.25 days * 70 years = 6213 TWh = 22.37 EJ
The Energy Invested
I am not going to attempt a detailed and complete analysis here but will try and make ball park estimates of energy consumed by labour and the main materials – concrete and steel.
60,000 workers laboured on the project that began in 1994  and was completed in 2003. Taking 1998 as the mid point China had a population of 1.242 billion and consumed 905 million tonnes oil equivalent (Mtoe) in energy that year . This yields a per capita consumption of 0.75 toe. The sum for the energy cost of labour therefore is:
60,000 workers * 0.75 toe per annum * 10 years = 450,000 toe = 18.9 PJ
There is a range of numbers for the energy content of materials. I am going to use:
Concrete = 1.9 GJ / tonne 
Steel = 20 GJ / tonne 
65.2 million tonnes concrete * 1.9 GJ / tonne = 123.9 PJ
463,000 tonnes steel * 20 GJ / tonne = 9.3 PJ
Total Energy Invested
labour 18.9 PJ + concrete 123.9 PJ + steel 9.3 PJ = 152.1 PJ
The partial ERoEI
Energy return = 22.37 EJ / energy invested 152.1 PJ = 147
Energy pay back time works out at an incredible 6 months.
(Energy produced in 1 year = 22.37 EJ / 70 = 319 PJ. Energy invested = 152.1 PJ. Hence energy pay back time = 152/319 = 0.48 years.)
I am quite satisfied with this answer. Some of the input numbers used may be wide of the mark and the energy inputs are far from complete. For example the diesel used on the construction site is not included along with many other energy inputs. But the answer is in the same ball park as calculated by other workers. Hydroelectric power is a tremendous source of dispatchable renewable energy. It does however come with high environmental and social costs. There’s no such thing as a free lunch in the energy world.
 Wikipedia: Three Gorges Dam
 Facts and Details: THREE GORGES DAM PROJECT
 Australian Government: Embodied Energy
 Wikipedia: Embodied Energy