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.
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).
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.
On the global scale, we can say that 70% of the sunlight incident on the ?R² 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.
Case Study: Replacing U.S. Oil with Corn Ethanol
Most people have already caught on to the fact that corn ethanol is a poor substitute for petroleum in the U.S. Leaving aside corrosive challenges to storage, distribution, and politics, we’ll just look at energetics.
The U.S. uses about 7 billion barrels of oil each year, amounting to an equivalent power demand of 1.3 TW. Corn ethanol requires significant energy inputs to plant, fertilize, harvest, and process the corn mash into ethanol. Some estimates conclude a net energy loss. The more optimistic estimates put the energy returned on energy invested (EROEI) at around 1.4:1, meaning a net energy of 0.4 units for every 1.4 units harvested. Under the assumption that we use the energy derived from corn ethanol to run the whole operation, we get an efficiency of 0.4/1.4, or about 30%. Combining this with 1.5% photosynthetic efficiency for incident sunlight and 50% for a half-year growing season leaves us with 0.2% efficiency over the year.
During the growing season, and given the 3-d advantage plants have over flat panels, we’ll again use an optimistic 350 W/m² rate of insolation. Multiplied by our overall efficiency, this turns into 0.7 W/m² delivered to the ethanol product. To hit our 1.3 TW goal requires an area 1400 km on a side! The figure below illustrates just how serious this is.
Square area needed to replace U.S. oil demand with corn ethanol.
Square area needed to replace U.S. oil demand with corn ethanol.
Ethanol from sugar cane can have a substantially better EROEI, somewhere in the neighborhood of 5–10:1. Brazil has pursued sugar cane ethanol in a big way, at the expense of rain forest. The resulting changes in micro-climate (desertification) and in soil quality/erosion may present significant barriers to sustaining this practice at a large scale.
Feeding the Beast
Another way to highlight how daunting a full-scale embrace of biofuels would be, consider that global oil consumption amounts to 6 TW of power (30 billion barrels per year, or 1000 barrels per second, at 6 GJ per barrel). This is about 12 times the human metabolic dietary intake—largely derived from agricultural lands. We’re not about to give up eating, so in the simplest analysis, we would have to find an additional cropland approximately ten times the area of our current cropland.
For scale, Earth’s land totals about 140 million square kilometers. About 50 million are classified as agricultural (includes permanent grazing land), and 13 million as arable. On what planet would we find enough land for sufficient biofuel crops?
Farmers work hard. Land issues aside, if we wanted to take the biofuel plunge, we would have to scale up farming efforts (and the number of farmers) by a substantial factor. Unlike solar panels, wind turbines, nuclear plants, etc., biofuels require a never-ending yearly push to plant, tend, and harvest the goods. The EROEI is poor, irrigation may not be available at scale, and bad growing seasons would seriously impact our economy.
This is why I call it the Biofuel Grind. We’ve become accustomed to living off of a fossil fuel inheritance, and we have been living like kings as a result. Transitioning to biofuels is like having to get a real job and work for the annual yield, year after year. No more freebees from nature, sitting around for millions of years waiting to be scooped up.
Cellulosic Plant Waste and Algae.
I have been treating biofuels as coming from food-crop-like sources. Some may think this to be unfair, given the potential for using agricultural byproduct, algae, etc. We’ll get to that. But first I’ll point out that virtually all the present biofuels are indeed from food crops: ethanol from sugar-cane and corn; and biodiesel from soy and vegetable oil crops. (I looked at why waste cooking oil for biodiesel is not scalable in a previous post.)
In principle, the energy stored in plant stalks and leaves could be converted to liquid fuel. Rather than sugars that can be fermented into alcohol, the cellulosic material must be broken down by other means. Termites do this in their guts, assisted by microbes. If termites (or these microbes) pooped alcohol or oil, we’d be in business—however icky their “business” might be. Many talk of genetically engineered microbes that could be coerced into making alcohol.
With genetic engineering, we can do anything. Witness the fact that we have eliminated most genetically-triggered diseases, eliminated the genes that cause cells (and people) to age, and can make a three-headed goat on demand. Or wait—that was a dream I had last night: then the goat turned into my mother-in-law. I’m eager to see us start racking up successes on the genetic engineering front, but it’s a hard, hard business, and talk is cheap. Let’s keep working on the magic microbe, but let’s also have a plan B in the works in case genetic engineering does not live up to its promise in the next several decades.
As for algae, these little buggers have some serious advantages over traditional food crops: no direct competition with food; higher photosynthetic efficiency; able to work in otherwise unproductive desert-land in bags/tubes; easier to harvest liquid systems (plumbing replaces clumsy harvesters combing untold acres).
An attractive idea is to erect towers of algal tubes/bags that would seem to make splendid use of land by building up into the third dimension. Let me caution against being overly swayed by this notion. There is only so much sunlight per square meter of land. Tilting a flat array of algal bags to face the sun is one way to make better use of a given land area, but depth in the direction perpendicular to the sun does little good: self-shielding keeps the deeper levels from being productive.
If we start with 6% efficient algae, and imagine that we could convert 50% of the stored energy into a useful form (including the energy cost of processing), then a desert location receiving an annual average insolation of 250 W/m² would produce the equivalent of 7.5 W/m² of useful energy. We would require a square about 425 km on a side, which is about the same land area as North Dakota.
The numbers for algae are certainly more favorable than for traditional (proven) biofuel sources. But keep in mind that we don’t see a clear path yet to squeeze useful juice from algae at appropriate scales/efficiencies. Much of the talk is around genetic engineering to make the algae excrete something useful in quantity. I need not repeat my case for non-complacency regarding this prospect. Also, anyone who has failed at aquarium maintenance (everyone who has tried?) knows how pernicious algae can be at clogging the plumbing and sticking to tube walls, etc. So they should also be working on genetically engineered teflon-coated algae. By that time I’ll also be able to enjoy that three-headed goat!
A Synthetic Approach
The one approach in all this mess I find I’m able to get excited about is synthetic photosynthesis. In particular, a large effort ($115M over 5 years) led by Prof. Nate Lewis of Caltech seeks to develop a solar-to-liquid process via artificial photosynthesis. I had already read about Prof. Lewis’ research, and was intrigued, when I saw a talk he gave at a recent conference. The talk was filmed and can be accessed here. Search for the word “Leaf.” (Incidentally, I also gave a talk summarizing some previous Do the Math posts: search “Expiration” if interested.)
Prof. Lewis summarizes the daunting scale of the energy challenge we face, and points out that because no other renewables come close to solar in terms of total energy availability, together with the fact that liquid fuels are by far the most energy-dense means of storage (short of nuclear), some day we will have a way to convert sunlight to liquid fuels directly. I hope he’s right, because this would indeed be a game-changer. Will we get there in time?
The bottleneck is that we do not know of a catalyst that can mediate the reaction in a way that is simultaneously efficient, robust, and cheap (pick two, Prof. Lewis says, and we can do it today). Their approach is to try every combination of up to three elements out of a total of twenty “interesting” occupants of the periodic table. Tried in a wide variety of fractional combinations and annealing processes, the combinatorics are ridiculous. But they are developing a method to screen a few million combinations at once (cleverly using LCD monitor indexing technology to measure currents in the samples deposited in a pixelized matrix). The expectation is that in 5 years, all sensible combinations will have been exhausted and tested.
There are 1350 ways that three elements out of 20 can be combined in X, XY, and XYZ arrangements. But now allow multiplicity in each element (up to 100 instances per element in the compound) and we get about 10,000 possible XmYn pairs where m and n are numbers from 1 to 100. I’m being lazy about knocking out duplicates—like X3Y6 and X11Y22 essentially being the same thing—just to get an upper bound, but I am also not considering the combinatorics of structural arrangements. In addition, there are one million combinations for any XmYnZo XYZ trio. This comes out to about a billion combinations altogether. Testing several million at a time, one set per day, allows this ensemble to be probed in a year. Allow for different annealing/preparation techniques and you have a few years on your hands.
I don’t mean this in a disparaging way, but it’s a lot like picking up the periodic table by its ankles, shaking vigorously (for a few years), and seeing if anything interesting falls out. I absolutely think this is what we should be doing: if we can, what possible reason would we have not to try? How will we know if it’s possible otherwise? But at the same time, it speaks to a bit of desperation. We honestly don’t know if it will work. Not everybody can be a catalyst, and one wonders why a catalyst better than any we have discovered by ordinary scientific processes has escaped our attention for this long. It could happen, and I sure hope it does. But let’s have a plan C.
Not an All-or-Nothing World
I have acted like we need biofuels to be able to completely replace our current oil consumption in the foregoing analysis. No one who is serious about the matter is proposing we do so, exactly. But I think it’s useful to appreciate limitations to ideas on our horizon so that no one is misinformed or simply assumes that any of the myriad solutions we discuss can plug the hole and make us whole. Don’t trust anyone who says that biofuels are the answer. Fine if they want to say “part of the solution,” but I’m not breathing easy at the claim that they’ll fix our wagon.
In any case, I can understand why biofuels were not considered to be a likely large-scale contributor to a crash mitigation strategy in the Hirsch Report. While the fossil fuel solutions (e.g.,natural gas to liquids, coal to liquids) have their own scale challenges, they do not face the same sorts of bottlenecks or lack of demonstrated technologies that biofuels suffer. Even so, the fossil fuel mitigation strategies will be hard-pressed to catch up to the decline in conventional oil, if full-scale initiation waits until the decline has started. And in the end, the fossil fuel mitigation strategies will all face the same finite resource problems as conventional oil, and therefore can only represent a temporary solution.
So biofuels—as difficult as they are—may ultimately play a key role in applications where other options do not work. Airplanes really do need liquid fuels to keep doing what they’re doing. Trans-oceanic ships and cross-country trucks may also need whatever help biofuels can offer. Personal light-duty transport can more easily transition to electric drive—perhaps with biofuel hybrid reserve for the occasional trip. Indeed, the U.S. military is experimenting with biofuel airplanes. All I’ve got to say is that we’ll be disappointed with that choice if we continue to fight wars in desert regions! Now if we could get our jets to fly high on opium…
For further reading (similar numbers, similar conclusions), see Helmut Burkhardt’s analysis.
By. Tom Murphy
This is a guest post by Tom Murphy. Tom is an associate professor of physics at the University of California, San Diego. This post originally appeared on Tom's blog Do the Math