Editor’s note: The following column was co-authored by Alex Johnson, a post-doctoral fellow at Harvard University.

Editor’s note: The following column was co-authored by Alex Johnson, a post-doctoral fellow at Harvard University.

For the past several years–until the credit crisis–investors have flocked toward renewable energy. Their hope is that solar radiation can be harnessed directly and through intermediaries such as the wind and biosphere to power the global economy into perpetuity. This hope is understandable since renewable energy has benefits that range from the environment to geopolitics. Nevertheless, care and scientific rigor should be used to quantify the challenge of converting society to renewable energy.

The maximum theoretical potential of advanced lithium-ion batteries that haven’t yet been demonstrated to work is still only about 6 percent of crude oil.”

The most significant challenge to renewable energy is competition from fossil carbon–the world’s predominant source of primary energy for the past 150 years. Fossil carbon has dominated the energy market for many reasons–not the least of which is its intrinsic mass and volume energy densities. Indeed, 1 kilogram of crude oil contains nearly 50 mega-joules of chemical potential energy, which is enough to lift 1 metric ton to a height of around 5,000 meters. Furthermore, crude oil happens to be liquid at Earth’s surface conditions, making it easy to store, transport, and convert.

The energy densities of natural gas and coal, around 55 mega-joules per kilogram and 20-35 mega-joules per kilogram respectively, are similar to those of crude oil. Fossil carbon is packed with chemical energy because carbon and the hydrogen it stabilizes in a condensed form react strongly with oxygen to form carbon dioxide and water. In addition, geologic processes have concentrated large quantities of fossil carbon into relatively small geographic areas such as coal mines and oil fields. Biofuels such as ethanol and biosynthetic diesel can have volume and mass energy densities equal to that of fossil carbon, but since they’re regularly harvested, their areal energy densities are substantially lower.

Renewable energy–unlike fossil carbon–is harnessed dynamically from the environment. Therefore, it won’t be as useful as fossil carbon until it can be stored and transported with similar ease.

Many companies and scientists are diligently trying to improve energy storage technologies, and we’re confident that substantial progress will be made. We can, however, use thermodynamics to calculate the upper limits of what’s possible for a variety of technologies. And when we do this, we find that many technologies will never compete with fossil carbon on energy density.

Let’s start with batteries. Today’s lead acid batteries can store about 0.1 mega-joules per kilogram, or about 500 times less than crude oil. Those batteries, of course, could be improved, but any battery based on the standard lead-oxide/sulfuric acid chemistry is limited by foundational thermodynamics to less than 0.7 mega-joules per kilogram.

Due to the theoretical limits of lead-acid batteries, there has been serious work on other approaches such as lithium-ion batteries, which usually involve the oxidation and reduction of carbon and a transition metal such as cobalt. These batteries have already improved upon the energy density of lead-acid batteries by a factor of about 6 to around 0.5 mega-joules per kilogram–a great improvement. But as currently designed, they have a theoretical energy density limit of about 2 mega-joules per kilogram. And if research regarding the substitution of silicon for carbon in the anodes is realized in a practical way, then the theoretical limit on lithium-ion batteries might break 3 mega-joules per kilogram. Therefore, the maximum theoretical potential of advanced lithium-ion batteries that haven’t been demonstrated to work yet is still only about 6 percent of crude oil!

But what about some ultra-advanced lithium battery that uses lighter elements than cobalt and carbon? Without considering the practicality of building such a battery, we can look at the periodic table and pick out the lightest elements with multiple oxidations states that do form compounds. This thought experiment turns up compounds of hydrogen-scandium. Assuming that we could actually make such a battery, its theoretical limit would be around 5 mega-joules per kilogram.

So the best batteries are currently getting 10 percent of a physical upper bound and 25 percent of a demonstrated bound. And given other required materials such as electrolytes, separators, current collectors, and packaging, we’re unlikely to improve the energy density by more than about a factor of 2 within about 20 years. This means hydrocarbons–including both fossil carbon and biofuels–are still a factor of 10 better than the physical upper bound, and they’re likely to be 25 times better than lithium batteries will ever be.

What about storing energy in electric fields (i.e., capacitors) or magnetic fields (i.e., superconductors)? While the best capacitors today store 20 times less energy than an equal mass of lithium-ion batteries, one company, EEstor, claims a new capacitor capable of 1 mega-joule per kilogram. Whether or not this claim proves valid, it’s within about a factor of 2 of the physical limit based on the bandgap of the dielectric material. Electromagnets of high-temperature superconductors could in theory reach about 4 mega-joules per liter similar to our theoretical batteries given a reasonable density; existing magnetic energy storage systems top out around 0.01 mega-joules per kilogram, about equal to existing capacitors. Here again, both the realized technology and its ultimate physical potential are far behind the energy density of common hydrocarbon fuels.

That brings us to the option of storing chemical potential energy as fuel that can be oxidized by atmospheric oxygen. We do it today, but with two differences: We generate this fuel renewably and convert it to work more efficiently than in combustion engines, either by fuel cells or air batteries. Zinc air batteries, which involve the oxidation of zinc metal to zinc hydroxide, could reach about 1.3 mega-joules per kilogram. But if we take elemental zinc all the way to zinc oxide, then we can theoretically beat the best imagined batteries at about 5.3 mega-joules per kilogram. Zinc has proved interesting enough that several writers (not us) have imagined a “zinc economy.”

To get really ambitious, we imagine storing energy as elemental aluminum or elemental lithium. Those two highly electro-positive elements yield a theoretical energy density–when oxidized in air–of 32 and 43 mega-joules per kilogram. At least now the theoretical limit is between 60 percent and 80 percent to that of hydrocarbons; we just have to figure out how to extract a large fraction of the energy from that oxidation.

A more promising approach is to use fuel cells with liquid and gaseous fuels. The two obvious choices for such fuels are hydrogen and hydrocarbons; in terms of energy per unit mass, hydrogen beats crude oil and natural gas by a factor of almost 3. Alas, hydrogen is a gas at surface conditions, so its volume density is horrible unless it’s compressed to several hundred atmospheres of pressure. At 700 bars, for example, hydrogen has an energy-volume density of around 6 mega-joules per liter, while gasoline at 1 bar has about 34 mega-joules per liter. Both hydrogen and hydro-carbons can be produced from renewable energy sources, though doing so economically and at a global scale remains a challenge.

There is one more energy-storage approach that theoretically beats hydrocarbons. Energy density comparable to lithium-ion batteries has been demonstrated with flywheels, and a theoretical device composed solely of toroidal carbon nanotubes could reach 100 mega-joules per kilogram. But the fabrication and safety challenges inherent in such a device render it unlikely that even a small fraction of this potential will ever be realized.

The bottom line is that nature has given us hydrocarbons in the form of fossil carbon and biomass, and their energy-mass and energy-volume densities are superior to the thermodynamic limits of nearly all conceivable alternatives. Thus, it’s quite likely that hydrocarbons of one form or another will be humanity’s primary energy storage medium for quite a long time.