Nonsense about Solar: (Long and lots of numbers.)

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.

you reached. It never fails to amaze me that here in Arizona we aren't growing solar panels like cactus :think:

... on the Green Party ticket in 2002, said, in response to a mining company's request to expand its mining operations by fifteen square miles, that a study the NM Greens had commissioned said that fifteen square miles of solar cells would just about supply the electrical needs of the state.

Obviously, those figures are optimistic, and probably based on investment driving higher efficiencies (along with the higher availability of sun in NM), but 84 sq. miles of solar cells to replace a gas station is clearly a number meant to convince the non-mathematical folks that solar is without merit.

Of course, when ExxonMobil runs out of reserves, they'll invest in renewables, and then come running to the government for handouts because their business is necessary for the national good... that is, as soon as they can figure out how to get legislation for renewables which is the equivalent of the oil depletion allowance....

At least if you're looking at photovolaic. (PV) The panels are now often warranteed for 20 years, but some other components (such as batteries for overnight and bad weather backup) are much shorter lived. So the costs aren't quite that good.

Regarding how much space these take up, I'm always amused when people bemoan all the farmland or forests that will need to be covered with panels to obtain this level of generation. To them I just say this:

Ever been up in a plane over a city or it's suburbs? What do you see? Miles and miles of rooftops. And in the summer, all those roofs are hot. That heat is wasted energy. Even worse, not only is it being wasted, purging that heat from buildings takes EXTRA energy. (Air conditioning.)

Now imagine all those roofs being shaded by PV solar panels. Imagine the lower cooling bills. Imagine the power being generated everyday. Imagine excess daytime power being used to pump water up hillsides, so that it can flow back down at night, driving turbines to meet nightime power needs.

We don't need solar farms. We need solar roofs.

They could never cope with the idea of distributed energy gerneration. There's no opportunity to gouge the consumer if the consumer owns the means of production. There's always the maintenance side of it for long term sustainable business model, though.

While we're at it, we have plenty of opportunity for greater efficiencies in our house and building designs. Stick frames on concrete slabs are remarkable energy innefficient. We drive horribly innefficient cars for our daily commutes. And we're driving them longer each day. A little reorganization will go a long way to reducing our energy requirements, which will in turn go a long way to allowing us to supply our energy from renewable resources...

which is huge, both in economic and environmental terms.

I've been hearing about economies of scale and solar voltaics for thirty years. What I haven't seen is a single place in the world where photovoltaics have replaced even electrical generation on a grand scale, never mind replaced motor fuels. If it were as practical as advocates claim, the mutterings of the Exxon chairman would be no impediment to their development.

Photovoltaics are potentially useful peak load devices, but they are in no way anywhere near being useful strategies for constant load electrical devices, and may never be such devices. They are even worse devices for transportation purposes. Even though in a purely thermodynamic sense a joule is a joule, that is hardly the case in a practical sense. In the practical world, the form of the energy, it's location and timing are all critical values that have a huge effect on both internal (out of pocket) and external (environmental) costs. Ignoring such factors has the effect of undermining the credibility of an energy strategy by overpromising and under delivering. If we want to advance the use of solar energy, this hardly the thing we should do.

The best use of photovoltaic cells is for locations where delivery is impractical or the cost of delivery is prohibitive. In northern Ontario, many people opted for combined solar/wind installations because it's cheaper than getting hooked up to the grid, but the biggest expense is the storage batteries. Maintenance and periodic replacement of the batteries makes the ongoing cost similar to the cost of hydro.

it works best at our peak usage hours. If I were king for a day, I would allow 100% of the cost of installation for a rooftop system to be deductable from taxable income.

But instead, we live in a country where I can deduct 100% of the cost of my new H2, thus encouraging me to waste even more fossil fuels

If we're going to subsidize something, photovoltaics in places like the Southwest would be an excellent investment.