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Study Calculates Theoretical Maximum Oil Yield of Algae

Theoretical maximum yield as a function of latitude for different cell oil contents. Weyer et al. (2009) Click to enlarge.

At team of researchers from Solix Biofuels (earlier post), Colorado State University and the National Renewable Energy Laboratory have calculated both an absolute upper limit to solar-based algal oil production as well as a feasible target range for production based on realistic efficiencies (calculated for six global sites). Algal oil can be used as a biofuel feedstock.

Based on physical laws and assumptions of perfect efficiencies, the team calculated the theoretical limit to be 38,000 gal·ac-1·yr-1 (354,000 L·ha-1·yr-1) of unrefined oil with an uncertainty of roughly 10% and with 50% cell oil content. Limits for the practical cases examined in their report ranged from 4,900 to 6,500 gal·ac-1·yr-1 (46,300-60,500 L·ha-1·yr-1) of unrefined oil.

Practical maximum yield by site, with different cell oil content. Weyer et al. (2009) Click to enlarge.

The calculated theoretical limit is lower than the 53,000 gal·ac-1·yr-1 figure presented by Solix’s Dr. Kristina Weyer, co-author of the paper, at the 2008 Algae Biomass Summit in Seattle, Washington. (Earlier post.)That figure, however, assumed 70% oil content in the algae, among other factors. The practical range remained the same.

The equations, calculations, and discussions in this paper have shown that, because physical laws dictate the theoretical maximum, it represents a true upper limit to production that cannot be attained regardless of new technology advances. However, if algal biofuel production systems approach even a fraction of the calculated theoretical maximum, they will be extremely productive compared to current production capability of agriculture-based biofuels.

—Weyer et al. (2009)

A number of studies have assessed the maximum theoretical efficiency of photosynthesis, but they have not specifically examined algal biofuel production or calculated maximum instantaneous efficiency and maximum annual production yield, the authors note.

The limits calculated in the paper apply to any large-scale algal production system that relies only on solar energy input to drive growth and oil production; the authors did not consider systems that use artificial lighting or other additional energy inputs, such as sugars for heterotrophic growth (e.g., earlier post.)

The calculation for theoretical maximum yield is based on physical laws; an established value for quantum yield; solar irradiance assuming perfectly clear weather and atmospheric conditions; and assumes 100% for unknown efficiencies.

Thus, the theoretical maximum yield is a true upper limit: a value that cannot be surpassed without breaking fundamental physical laws. Due to the numerous assumptions of perfect efficiency employed in the theoretical calculation, it is an unattainable goal. A practical case is also calculated, in order to provide designers with a realistic goal, which employs solar irradiance data for several sites and reasonable but conservatively high values for some efficiencies that were assumed to be 100% in the theoretical case. The practical case therefore represents what may be possible with system optimization.

—Weyer et al. (2008)

The primary physical law that limits the production capabilities of algae is the first law of thermodynamics, which states conservation of energy for any system. For a system of photosynthesizing algae, it is the rate of incident solar irradiance on the production area and the rate of chemical energy storage by the algae as oil and other biomass. The amount of stored chemical energy is directly limited by the amount of solar irradiance available.

For the theoretical case, total solar irradiance was calculated assuming year-round clear skies and minimal atmospheric absorption. For the practical case, total solar irradiance was calculated using weather data for six global climates, because the actual amount of irradiance is greatly reduced from the theoretical by clouds and other absorptive atmospheric conditions.

Only a portion of the solar spectrum is utilizable for photosynthesis; PAR (photosynthetically active radiation) is commonly defined as 400-700 nm.

Cell oil content is the portion of the cell that can be refined into a usable biofuel. A theoretical maximum value is not yet known, and oil content is highly specific to species and growth conditions. Studies have cited algal lipid contents ranging from 15 to 85% (dry cell weight), although the highest values can correspond with reduced biomass productivity.

The authors selected 50% oil content was chosen for both the theoretical and practical maximum cases, “though it is acknowledged this may be an overestimate of what will be achievable for production systems.”

While the practical case includes the estimates for efficiencies that may be improved with optimization of the growth system and chosen algal strain, the theoretical case includes no estimates and thus continues to represent an unattainable limit despite system optimization and even genetic improvements to algal strains. Any possible genetic improvements would be aimed at improvements in the efficiencies included in the practical case. These might include decreasing photoreceptor antennae to reduce photoinhibitive effects, increasing temperature tolerance, or improving resistance to predatory species. These effects are already assumed to be nonexistent in the theoretical case.

Despite any discrepancies among approaches, all estimates affirm the productive potential of algae as a biofuel feedstock. The lowest projection in this paper, is 4,900 gal·ac-1·yr-1, for Kuala Lumpur, is drastically higher than reported yields for corn (18 gal·ac-1·yr-1), canola (127 gal·ac-1·yr-1) or even oil palm (637 gal·ac-1·yr-1). Thus, the bounds on algal production presented in this paper should not be viewed as unpleasant news about physical realities, but as a realistic check that confirms its potential and will serve the industry in its pursuit of maximum algal biofuel production.

—Weyer et al. (2009)




I'll guess a lower heating value of 30 MJ/L for algae oil, in which case 60,500 L/ha/yr is 504 MWh/ha/yr. After combustion in a 35% efficient diesel engine, you get 176 MWh/ha/yr. Compare to Stirling SunCatcher CSP farm, which has a rating of 989 MWh/ha/yr, which means 773 MWh/ha/yr delivered to the motor (after grid, charge/discharge efficiency). That's 4.4 times better than the algae route.

Of course the SunCatcher value is a lower bound (being built today), and the algae number is a "practical upper bound". The SunCatcher value might increase, while the algae number might never be practical.


640 acres per square mile at 5,000 gallons per year means one square acre could yield ~3 million gallons per year.

Devote a 10x10 square mile patch of land and now you have 300 millions gallons per year.

put together 40-50 of these algae farms in the sunny southern states and you have ~14 billion gallons of oil a year.

I believe the US uses ~140 billion gallons per year.
Wow. We use a lot of oil. Those 50 10milex10mile patches nevertheless would provide 10% of our current oil needs.

No miracle cure for our addiction anytime soon. Electric cars with a back up generation like the volt might fit in nicely with a reduced oil appetite.

Henry Gibson

China could order its third CANDU 600 nuclear reactor and it could be operating within 5 years or less like the first two. It could make hydrogen with known methods of electrolysis and combine that hydrogen with CO2 to make Methanol for a price per joule that is less than oil at $120. It could combine that hydrogen with coal for liquid fuel at an even lower price. The heavy water needed for such reactors is not substantially used up and can retain most of its full value for hundreds of years, so its cost must be evaluated differently. If this is done, such units seem much more competative with pressurized water reactors. Now calculate how this would compete with algae with much lower land area costs. Reactors can be deeply buried so that they take up almost no surface area.

Oil, gas, coal, nuclear, wind, sunlight and geothermal energy are all provided free by the earth or sun, but there is a cost to collect it and the CO2 cost of using some of them. It is the collecting cost that must be considered, and not the fact that they are all freely provided by the universe. Nuclear electricity can be used directly in battery powered cars with at least five times the efficiency so can solar electricity. If put into mass production, parabolic small stirling or turbine generators will be far more efficient cheaper collectors of energy than algae.

Because of the existence of nuclear submarines, it is obvious that nuclear power plants can be sunk into and operated on coastal plains with cables that bring power to land, so no land is required for nuclear power nor is any fresh water.

Hyperion Power Generation and others are proposing very low maintenance buried reactors, and such could be put off shore and submerged with turbines. I have seen more than three refrigerators that have operated for over 30 years, and so small turbo-generators can be built with very long life. ..HG..


Henry Gibson, if the world got all of its energy from nuclear, we would still have global warming, because of the blackbody effect. See the analysis in Long-Term Global Heating from Energy Usage, Eos, Vol. 89, No. 28, 8 July 2008 page 253-254. Here is an excerpt: "More realistically, if world population plateaus at 9 billion inhabitants by 2100, developed (Organisation for Economic Cooperation and Development, or OECD) countries increase nonrenewable energy use at 1% annually, and developing (non-OECD) countries do so at roughly 5% annually until east-west energy equity is achieved in the mid-22nd century, after which they too will continue generating more energy at 1% annually, then a 3ºC rise will occur in about 320 years (or 10ºC in ~450 years), even if carbon dioxide emissions end."

If you want a long-term solution, solar is the way to go. At 3,850,000 EJ/year of insolation, a single year of sunshine has far more energy than all the reserves of U235, U238, and Th232 combined. Remember that these are a kind of fossil fuel too (coming from the supernova that seeded our solar system).


eak, all those black body calculations and what not are just fancy ways of saying that in any finite system you can't have infinite growth forever.
It would be trivially easy to simply extrapolate energy use to show that your preferred solution, solar, couldn't cope with indefinite geometric expansion either.
Back in the real world though, solutions like liquid fluoride thorium reactors can provide 9-10 billion people or so all the power they would need to support a good lifestyle for billions of year.
It wouldn't in reality need to do it on it's own, as solar and so on can certainly contribute.
It is much easier to engineer energy solutions when you use solar at times and places where it is sunny, not when you try to use it to supply Hamburg in midwinter.
Nuclear is good at that.
Dense energy sources are needed to complement diffuse renewable resources, and nuclear is around 1 million times as dense as fossil fuels.


It could be that algae farms become our next source of food when the topsoil runs out or the weather becomes uncooperative.


HG et al:
Nukes may make sense, and I am not opposed to them, but they will not get built -- unless the Government guarantees them 100%. Better to guarantee wind, solar, and capstone generators. Less risk, less cost up front, and probably less cost in the long run.
The financial markets will not support building nuclear plants on the financial return alone. If they won't, why should the taxpayers. If I am wrong, fine. I just don't think we will ever see it.

Paul W

We need algae biodiesel in a big way. We are wasting time on everything that is not, Wind, Nuclear and algea.
All the other technologies my come in time but these thing will work now.
We will experience another and another world recession until we fix the energy problem we are now in. We have maxed out and if we can increase oil production with Algae or offset the loss of production, we stand a chance at growth that will provide more funds for these other technologies.


Great news about upper limits of algae production, does that count using mirrors to increase exposure to sunlight? Anyway, the competing angles and agendas of various suppliers of energy may result in an agreement to diversify energy sources in general until the best options rise above the others.

Stephen Bowers

These figures are hopelessly erroneous. Try this which actually gives the data

Overall 2H2O + CO2 CH2O + O2 + H2O
Benson- Calvin cycle Z scheme 8 photons of light for each CH2O + O2 produced
I mole CH2O has an energy content of 468kJ
I mole of red light photons = 176kJ
Therefore theoretical efficiency = 468/( 8 x 176) = 33% efficiency
But typically nearly 10 photons of light energy is required =26.5% efficiency
However only about 43% of PAR radiation is actually adsorbed. This reduces the maximum efficiency to around 11%.
Respiration occurs 24hrs per day. Plants consume between 0.3- 0.7 of the
-(CH2O)- during respiration which brings the overall efficiency to 5-6%
In US south west Mean PAR is 100 W/m² ( Germany 65 W/m²)
Max Theoretical Yield is (100 x 0.06 x 8760 x 3600) = 189 MJ carbohydrate/ m²/yr
If 50% of the net carbohydrate produced was converted to oil ( approx 28%) at no losses this would equate to around 2.5 kg oil per m² or 25mt per hectare/yr.

Thus the absolute best, which is hopelessly unatainable would be 10.4 mt/ acre or 3000 us galls /acre.

Source date. Dimitrov, Walker, Benemann, Steiner.

However you calulcate the yield the energy cannot exceed 189 MJ/ m2/ yr.

1 acre = 4000 m2 approx. = 756 GJ/ acre which includes the energy of ALL products - oil + residues. It's called the First Law of Thermodynamcics.

In reality you would acheive only a fraction of the theoretical.

Sorry to disappoint you all.

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