Friday, September 5, 2014

Where's My Algae-Powered Jet-Pack?

There is a math formula called the "logistics curve/equation" which pretty accurately models population growth including technological innovations growth. It starts slowly but rises exponentially to about the 50% saturation level before leveling off at the point where everyone has a cell phone, or all steam engines are replaced with diesel or (whatever). 
(Click to enlarge)

Applied to renewable technology, it could be the point where everyone has an electric car, all houses are covered with solar panels with battery backup, and all central power stations rely on wind, tides, currents and sun, while algae-based oils power airplanes.

You can see this for phones here (Click to enlarge):
For 2008 they made this projection for world-wide cell phone use (Click to enlarge):
By the end of 2013 we can see the 2008 projection was dead accurate (Click to enlarge):
I would guess we are near the bottom of the logistics curve for PV, EV, and Wind - around 2%-3% penetration - where it is just about to take off.  Roughly the equivalent of 1990 on the above cell phone charts when cell phones were symbols of wealth and privilege.  See Gordon Gekko from the movie "Wall Street"
So rich and pwoerful he has a private helicopter, yacht and "Gasp!" a cell phone!
It took less than 25 years for cell phones to go from that level to a dollar-three-ninety-eight at 7-11 world-wide!  So the future looks good!

But not as good as we would like.  I estimate solar generation alone, even at growth rates greater than those seen to date, will replace only 50% of electricity generation by 2032, more reasonably by 2040.  Countries need to agree to an 80% reduction in Green House Gas (GHG) emissions with large developed countries (the G8) reducing 2.5%/year starting in 2012 and developing countries coming in 10 years later.  See:

Annual global growth in Photo-voltaic solar cell capacity is between 41% and 48% but capacity is *not* the total electricity generated since PV capacity depends on the sun.  Currently 10%-20% is a rough number for capactity utilization for PV solar.  See:

and for solar capacity utilization:

To estimate the growth rate of cumulative installed solar panel generated electricity, consider that installed PV capacity grew from P0 = 3.7 GWh (Gigawatt-hrs) in 2000 (“t” = 0) to P = 128 GWh in 2012 (t = 12).

Using the formula for exponential growth P(t) = P0er(t)  for the population (P(t) as a function of time with
growth rate of “r” and an initial population of P0. This gives  128 = 3.7er(12).  Where r = the rate of growth and t = time = 12.  Taking the natural log of both sides gives:

 (1/12) ln(128/3.7) = r = (1/12)ln(34.6) = 0.295 = 29.5% CAGR

Let K (max possible solar electricity production) be the current 2013 global energy consumption of 840TWh (Terawatt-hours) = 840,000 GWh.  See:

This doesn’t allow for the possibility of electric vehicles replacing transportation energy consumption but has the advantage of simplicity.

The PV generated numbers are too small to be usable in the logistic function but we can estimate the time to hit 50% of that 840,000 GWh using pure exponential growth at a rate of 29.5%.  To find the time "t" when  P(t) = 1/2 (840 TWh) we get:
420,000 = 3.7e0.295(t).  

Solving for "t" by taking natural log "ln()" of both sides gives t = 39.5 years = 2040.

Taking a more optimistic rate of 41% growth rate (doubling every two years) starting from 2013 gives:

420,000 = 128e0.41(t)

Solving for t by taking “ln()” of both sides again gives t = 19.7 years from 2013 or 50% carbon free energy by 2033.

We need to do better, and I cross my fingers that battery-backed solar will cross a magic threshold to become cheaper than coal and gas soon.

The most hopeful thing I've seen is a "climate swerve". See NY Times article  Basically, it seems that things are getting so obviously very weird in terms of weather that global warming is no longer an abstract concept.  People and animals are dying around the world from floods, drought, and heat waves to the point that a lot of people have started to get off the fence and demand action from their politicians.