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.