Nonsense about Solar: (Long and lots of numbers.) [View All]

The CEO of Exxon made strange statements last night on the Charlie Rose program about the amount of space required for solar panels to replace oil as a source of energy.

Let's work the math. (I will use scientific notation --- mostly.)

Oil Use in US:
360,000,000 gals/day (3.6 x 10**8 gals/day)
(3.65 x 10**2 days/year) x (3.6 x 10**8 gals/day)=
1.314 x 10**11 gallons/year (131 billion gallons year)

Solar Equivalent per Square Foot/Year:
120,000 (1.2 x 10**5) BTU's for a gallon of gasoline and diesel (a number in between the two)
Kwhr = 3,400 (3.4 x 10**3) BTU's
whr = 3.4 BTU's
10 (1 x 10**1) w/sqft = Solar cell production
2000 (2 x 10**3) hr/yr = average production at 10w/sqft (roughly 46% of daylight hours --- not a high number).
(2 x 10**3 hr/yr) (1 x 10**1 w/sqft) = 2 x 10**4 whr/sqftyr
(2 x 10**4 whr/yr) x 3.4 BTU's/whr
6.8 x 10**4 BTU's/yr
(6.8 x 10**4 BTU's/sqftyr) / (1.2 x 10**5 BTU's/gal) = 5.67 x 10**-1 gal/sqftyr (or .567 gallons per square foot over a year)

Space Needed for Solar:
(1.314 x 10**11 gallons/yr) /( 5.67 x 10**-1 gal/sqftyr)
2.32 x 10**11 sqft of solar panels. Sounds like a lot.
But a square mile is 2.788 x 10**7 (27,878,400) sqft
(2.32 x 10**11 sqft) / 2.788 x 10**7 sqft/sqm =
8231 sqm

Now this is a very large area to be sure. But lets us look at the supposed 84sqm (I have no link, but I heard him repeat it numerous times --- but perhaps I was mistaken) needed to replace a single Exxon gas station according to their CEO.

How many Square Miles of Solar to replace the average gas station: (since the numbers are small I will use decimal notation here)
160,000 gas stations in the US
8321sqm /160,000 gas stations =
.051 sqm/gas station equivalent.

Allowing for the use of slightly different figures for number of gas stations or other factors we can fudge this number to .042 (I am going somewhere).

Notice something interesting. This number is 1/2000 of the figure mentioned by the Exxon CEO when comparing the energy "output" of a gas station with its solar equivalent. 2000 is the number of hours of production that we used for a year in our calculations --- therefore using 84 sqm as the solar equivalent of a gas station compares a YEAR of gas station sales with an HOUR of solar production.

Where I come from, this would not be considered nice! At the very least, 2,000x or 200,000% is a pretty bad rounding error.

Moreover, solar efficiency has been improving. 20% efficiency is certainly practical and there is promising new technology that might allow for 50%. So we could take that 8321 sqm and cut it in half or perhaps even a fifth.

These guys have reason to be worried.

So What's the ROI on All This
Well it depends. I will run calculations based on current solar values and ones that might reasonably be obtained by a concerted development/manufacturing development process.

Current values:

10% efficiency
$100 sqft for solar
20 year life
2.32 x 10**11 sqft for solar panels (from above)

Using these figures
(2.32 x 10**11 sqft) x (1 x 10**2$/sqft) =
$2.32 x 10**13 (23.2 TRILLION Dollars --- ouch)

Realistic target values.
20% efficiency
$25 /sqft
40 year life.
(to say nothing of upping the 2000 hours per year of production at rated values, which active positioning can do.)
(1.16 x 10**11 sqft) x (2.5 x 10**1 $/sqft) =
$2.9 x 10**12 (2.9 TRILLION Dollars)

"Raw" (no taxes) cost of gas to consumer over lifetime of solar units.
$1.25/gal (no taxes --- a low figure when future demand and the likely, related price rises are considered)
(1.314 x 10**11 gallons/year) x (2 x 10**1 yr) x (1.25$/gal)
= $3.285 x 10**12 ($3.285 TRILLION Dollars)
(1.314 x 10**11 gallons/year) x (4 x 10**1 yr) x (1.25$/gal)
= $6.57 x 10**12 ($6.57 TRILLION Dollars)

In the "realistic" scenario, the payback is two to one, with a large margin left over. Even using 40 year life, 20% efficiency and $50/sqft it is roughly break even, with allowances for maintenance and research --- not bad -- not great -- but not bad.

Bottom line, at current cost, efficiency and expected life, solar does not stack up well. However with reasonable assumptions for performance/cost gains it looks pretty good.

And this says nothing about the savings in the form of reduced emissions, etc. Or the potential of significantly higher solar efficiencies or even lower production/installation costs. Economies of scale alone should result in considerable cost savings.

Now at its best this analysis doesn't answer questions as to whether solar can actually replace gas, but it does provide some estimates of solar equivalent requirements and costs.

And it puts the lie to claims by Exxon's chairman. But perhaps instead of 84 square miles he meant 42/1000ths of a square mile --- they sound so much alike.

No wonder these guys are worried.