The Biofuel Grind

Editor’s Note: EarthTechling is proud to repost this article courtesy of Do The Math. Author credit goes to Tom Murphy, a UCSD physics professor.

When we enter the decline phase of conventional oil—likely before 2020—we will scramble to fill the gap with alternative liquid fuels. The Hirsch Report of 2005, commissioned by the U.S. Department of Energy, took a hard look at alternatives that could respond to the scale of the problem in time to have an impact. Not one of the approaches deemed to be currently viable in the report departs from fossil fuels. But what about biofuels? To what extent can they solve our problem? We’ll dip our toes into the math and see where a first-cut analysis leaves us.

Photosynthetic Scale

If you add up all the photosynthetic activity on the planet—accounting for virtually all life except for oddball extremophiles—you get a number like 80 TW (80 trillion watts; I see credible estimates ranging from 40–140 TW). About half is from all the plankton in the ocean (and its derivative food chain), and the other half happens on land, capturing every microbe, plant, and dependents. Compare this to human power consumption around 13 TW, and to human metabolic activity of about 500 GW (7 billion people operating on a little less than 100 W, or 2000 kcal/day).

image via Shutterstock

First, note that the human industrial power scale is comparable to the photosynthetic scale. If you react by saying that 13 does not look much like 80, fair enough. But I’m impressed by the similarity in the exponent: both are within a factor of three of 3×1013 W! Of all the places the comparison could have ended up, it’s about the same order-of-magnitude.

Next, observe that humans comprise about 0.6% of the total biological activity on the planet. I oscillate between thinking that this makes us a massively dominant species (of the millions of species, for any one to account for nearly 1% is impressive) to thinking that this is a small number compared to what I sense in my human-dominated daily life. But I don’t see the vast oceans or rain forests every day.

Finally, reflect on the fact that our industrial enterprise has amplified human power by a factor of 25 or more (13 TW compared to 0.5 TW). We carry a lot of muscle, thanks to fossil fuels. Let me see those biceps!

So our first stop along the way is to notice that converting our fossil fuel enterprises to biofuels would mean commandeering (enslaving?) a substantial fraction of the Earth’s bio-activity for our purposes. Factoring in the massive energy it would take to harvest the Earth’s bounty year after year, we would have to—for all intents and purposes—take over the Earth’s ecosphere to serve our ends.

Note that the dream of continuing growth to five times the current scale, as discussed in the post on what “sustainable” means is not possible via the bio-route alone.

Photosynthetic Efficiency

On the global scale, we can say that 70% of the sunlight incident on the πR² projected face of the Earth is collected by the Earth (the rest is reflected by clouds, atmosphere and land), and 50% of the total is absorbed at ground level. At 1370 W/m² of incident power flux, this means that the Earth’s surface is absorbing about 100,000 TW of solar energy. Thus global photosynthetic efficiency is about 0.1%. Pretty weak.

Okay, in fairness to photosynthesis, the limitation on the scale of bio-activity tends to be availability of water and mineral nutrients—not incident sunlight. Plankton blooms are associated with discharges or upwellings of (often nitrogen-rich) nutrients. Our agricultural fields achieve “corn blooms” year after year thanks to the use of fossil-fuel-derived fertilizers to provide such nutrient services.

How does an individual plant fare, given adequate care and feeding? One way to estimate our way into an answer is to guess at the mass put on by a plant in its growing season or lifetime, assign a caloric value of 4 kcal/g for the carbohydrates (and cellulosic) material, and compare this to the solar flux presented to its leafy area in the same time period.

Let’s pick the carb-o-licious potato plant for an example of an energy storage machine. Let’s say that our plant produces a half-dozen half-pound potatoes (about 1.5 kg) in a growing season—plus an equivalent mass in leaves, stems, and roots for good measure. 3 kg at 4 kcal/g yields 12,000 kcal of energy storage, or about 50 MJ (see page on energy relations for conversions). Meanwhile, perhaps a 0.5 m² footprint at an average summer insolation of 350 W/m² delivers about 2 GJ of solar energy in four months (the insolation estimate factors in day, night, weather, and the fact that plants are not flat—so better at collecting light than a flat panel would be). The result is 2.5% efficiency.

This is not too far from reported photosynthetic efficiencies: many plants in the world realize 0.01–0.1% efficiency, while well-tended crop plants tend to be around 1–2% efficient, and algae can reach numbers like 4–6%. I have to say that I gain much more trust in such reported numbers when common-sense estimation puts me in the same ballpark.