Both Low EROEI and Low Power Density is a Serious Problem - Wind Addition

In my last post I talked about how having both low EROEI and low power density is a serious problem.  I used solar as an example.  In the comment section someone mentioned something about 80% of our power coming from wind, but wind isn't much better. It has a higher EROEI, but it's power density is terrible.  I'll explain below. 

If you haven't read the last article you might want to do so now.

First I'll start with the sources.

Source One - Catch 22 of energy storage.

EROEI for wind with storage is 3.9. 

Source Two - Sustainable Energy — without the hot air

The red stack (i.e. energy consumption) in figure 18.1 adds up to 195 kWh per day per person (page 103).

4,000 m^2 land per person in UK.  

Source Three - Rethinking wind power

Keith’s research has shown that the generating capacity of very large wind power installations (larger than 100 square kilometers) may peak at between 0.5 and 1 watts per square meter.

Now lets think about it a little.

Lets start by talking a bit about EROEI.   The comment that inspired this post gave me a link that says EROEI is meaningless.  I disagree.  EROEI is very important when it gets close to one.  I'll explain but first let start with this definition from Wikipedia for anyone unfamiliar with the term.

In physics, energy economics and ecological energetics, energy returned on energy invested (EROEI or ERoEI); or energy return on investment (EROI), is the ratio of the amount of usable energy acquired from a particular energy resource to the amount of energy expended to obtain that energy resource.

EROEI is important because it creates a multiplier effect for other quantities.  Other quantities include things like space, different material and man power.   The closer EROEI gets to one the closer the need for those other quantities get's to infinity.

For example:

Imagine that you had a some solar panels that had a EROEI of 2. One meter square of them produces let say 5 watts average. For simplicity's sake lets stick with only this one kind of power source for now.

If you wanted to get 5 watts from these panels you would need both the one meter squared, plus another half a meter squared to maintain the one meter squared, plus another quarter meter square to maintain the half meter square and so forth.  This goes on endlessly, and when you sum up the results you get the multiplier.

∑n=0∞12n=1+121+122+...+12n+...=2

Thanks to Mark44 on physics forums for this!

Now lets talk about the multiplier

The multiplier works for all quantities not just area.

For example:

if it take 5 people to maintain some generation that produces 5 watts and the multiplier is 3 then that 5 watts really needs 15 people (5 X 3 =15).

Here is the formula you need to figgure out the multiplier for any given EROEIs.

Where X = EROEI

This doesn't only apply to a one power source systems.  Any power source that with EROEI close to one would require outrageous amounts of different resources in order to contribute significantly to our total energy supply.  

Now for Wind

The multiplier for wind isn't that bad, but the power density is crap.  At between 0.5 and 1 watts per square meter even if you covered the whole of the UK with wind turbines the yield would still kind of suck.

Here's the math

4,000 m^2 is space in uk for each person.

1.34 is the multiplier for wind

So...

4000 / 1.34 ≃ 3,000

Around 3,000 is how much possible space for wind for each person when you minus the space for wind turbines needed to maintain the system.

So between...

           (3,000 * .5 * 24)/1,000   ≃ 36  kWh per day per person

           (3,000 * 1 *  24)/1,000   ≃ 72  kWh per day per person


So maybe you can get close to 80% if you cover the whole of the UK with wind farms (assuming the EROEI doesn't drop because of diminishing returns).  Do you think people can really cover so much of the UK with renewable energy?  What about space they need for other things like energy storage.  It's really hard for me to believe, and even if you could I think it would be pretty horrible.  

Both Low EROEI and Low Power Density is a Serious Problem - Solar PV Addition

Taking information from two sources I'm going to show that a combination of low EROEI, and low power density is a huge problem.   Here is the first source which talks about EROEI with energy storage.  It's called catch 22 of energy storage.  Here is the second that talk about power density among other thing.  It's called Sustainable Energy — without the hot air.  Both of them are a good reads if you haven't read them already. 

From the First Source

The EROEI for solar pv with energy storage is listed at 1.6.

From the Second Source

If we covered 5% of the UK with 10%-efficient panels, we’d have
≃
10% × 100 W/m2 × 200 m2 per person = 50 kWh/day/person. (page 41)

The red stack (i.e. energy consumption) in figure 18.1 adds up to 195 kWh per day per person (page 103).

Now lets think about this a little

EROEI describes the energy that is needed to be invested (i.e. used) in order to get more energy. If the EROEI is 2 then one unit (of some unit of energy) invested will get you 2 (of that unit). If solar is to become a permanent thing then maintaining any given area of it will take energy. The amount of energy is determined by it's EROEI. Lets say that the EROEI is 2. Then maintaining 1m² of it would take 1/2m². That 1/2m² would need 1/4m² and so on. The sum of all these works out to some finite number.   In order to work it out you need something called the Geometric series.

Here's the equation where X = EROEI

Using the formula I get 2.67(1/(1-(1/x))) using solar PV's EROEI. The number 2.67 is a multiplier we can use to figure out the total area needed.  That means instead of 5% of the uk's land providing 50 kWh/day/person it would take 13.3 % (5 X 2.67 = 13.3) when taking EROEI into account.   In order to get 195 kWh/day/person it would take 51.87 % (13.3 X (195/50)) or 207,480 m² per person.

That doesn't even count the area of land used by the energy storage.  Pump hydro for the source given.   Here's a good source that talks about that.  Guess what it take a lot of space, and don't forget that there are other land uses as well. 

Source Two Page 41

And don't think you can do without most of the storage because of demand response, management, whatever you want to call it.   Solar power manufacturing facilities cost a lot.  In order to keep the prices down they need to be run 24/7, so at most you can only ration 37.5 % (1 / 2.67 = 37.5) percent of that power. 

This is simply madness, or more like a fantasy.  It's time people came to terms that they have two choices.  Fossil fuel, or nuclear power.   Fossil fuel's give us a few short years in exchange for our climate and our children's future while nuclear power gives us hope and a better life for countless millions.   I know which one I'm rooting for. 


Update:  I changed a lot.  Credit to my brother Jeremy for helping me with the math.  I also added another post that talks about the same thing for wind.