Dec 10th 2008

Renewable Energy: The Cold Facts

by David Eichler

The author is a professor of physics at Ben Gurion University in Israel. He received his Ph.D. in 1976 from the Massachusetts Institute of Technology. Further biographical information can be obtained at http://www.bgu.ac.il/~eichler/.

Renewable energy sources, such as wind, direct solar power, hydroelectric power, and biomass and the biofuels derived from it may be the basis for future civilization. The primary source of energy that generates each of these forms, however, is the sun, so the available power in each is limited by the power in sunlight that reaches the Earth. The wind is driven by heating of the Earth's surface, and is thus driven by the sun. Hydroelectric power is due to the sun, which evaporates water from the surface of the Earth. Is there enough sunlight, and land to collect it, to support the world in the modern American lifestyle? The oft stated argument that renewable energy can compete with sufficiently high priced fossil fuel breaks down when global limits are approached. No matter how much fossil fuel costs, and no matter how cheaply solar collectors and windmills can be built if mass-produced, there will always be a limit on how much energy per year is available in renewable energy. Proper analysis of this issue should be done not in terms of present incremental costs or projected extrapolations, but rather in terms of attainable power per unit area.

Basic numbers

Mankind's present energy expenditure is about 15,000 billion watts, just over two kilowatts (2000 watts) per person, assuming there are about seven billion people. There are nearly 150,000 billion square meters of land (just over 20,000 square meters of land per person), so about 0.1 watts per square meter are consumed.

If all of the sunlight hitting the top of the Earth's atmosphere could be converted to useable energy, it would be about 10,000 times as much as our present demand. (Here and below, very round numbers are used whenever possible.) While this factor of 10,000 may seem a comfortable margin between demand and supply, further inspection shows otherwise. First, oceans, night, winter, clouds and dust in the atmosphere need to be taken into account in a self-consistent way, and it is convenient to consider the time-averaged amount of sunlight that reaches any given point on dry land where it is most readily collected. The average power in sunlight that strikes a square meter of the Earth's surface - about 150 watts - provides, during the course of one year, about as much heat as the burning of just over a million food Calories,[1] or about 120 kilograms of carbon. This is about the amount of carbon per annum that the normal person eats. (This coincidence is not entirely accidental, as a person has about one square meter of surface area, and radiates a flux of body heat that is comparable to the average solar flux). Photosynthesis, wind, and hydroelectric power each capture only a small fraction of the solar energy reaching the Earth, so far more than one meter per person would be needed to feed the world, still far more than that to supply its overall energy consumption (which exceeds the energy equivalent of its food consumption by a factor of 10), and still far more than that to support the modern American lifestyle (as Americans, per capita, burn energy at nearly 6 times the current world average).

Photosynthesis

The efficiency of photosynthesis is typically about 1 percent of the sunlight that hits the plant. (The exact value of course depends on the type of plant and a host of other factors. The most efficient crops have a photosynthetic efficiency of about 3 percent.) When the facts are factored in that most of the Earth's surface is ocean, that clouds reflect back into space much of the sunlight that hits the Earth, and that much of the Earth's land surface is barren desert or arctic, at the end of the proverbial day, only about 0.1 percent (one part in a thousand) of the Earth's sunlight budget is captured by photosynthesis. So, while it receives more than ten thousand times the human energy budget, the Earth stores only about ten times that budget in biomass. In order to fuel human energy consumption with biomass, we would have to collect about 10 percent of all the biomass that grows in the wild each year. While this is possible, as demonstrated by crop harvesting, the fact remains that car engines cannot presently be run on grass clippings and dead leaves, not even on corn kernels. Even if we eventually learn how to convert most forms of biomass, such as cellulose, to biofuel, it is not clear what the efficiency of that process would be. It has been claimed, for example,[2] that converting even the edible component of corn to ethanol is a losing proposition and that the industry that does this is kept afloat by subsidies. (Evidence for this, goes one argument, is the fact that ethanol producers power their industry with fossil fuel, not ethanol. The exact numbers seem to still be a matter of some controversy.) One could imagine burning the biomass, using the heat to generate electricity, using the electricity to charge batteries and then running cars on the batteries. Each step represents a sacrifice in efficiency, and an increase in the fraction of the world's biomass that would be needed.

The plot thickens when we consider the U.S., with its per capita energy consumption of nearly six times the world average, while its available land per capita is only about one and a half times the world average. The U.S., then, needs about four times as much land per capita as the rest of the world to sustain its present energy consumption with renewable energy of solar origin.

Could the U.S., with a one percent sunlight to biochemical energy conversion efficiency, supply its energy needs with biomass? With its per capita energy consumption weighing in at 8.5 tons of carbon per person per year - just over 100 times the minimal food requirement of 2000 Calories per day[3] - the U.S. would need to devote about 6,000 square meters (slightly more than the area of one football field) worth of vegetation-based sunlight collection per person to power its overall energy consumption. This is about a fifth of all the land area in the U.S., and about a quarter of the area in the contiguous 48 states, which get most of the sunshine. (Assuming the more liberal value of 3 percent efficiency for photosynthesis, which would entail cultivating very high yield crops such as corn and sugarcane - including fertilizing, spraying and irrigating, - would lower the estimated land requirement. However, 3 percent efficiency risks soil erosion - long term productivity requires plowing under the stalks and rotating the high yield crop with less efficient crops - and 1 percent is a more realistic long term average.)

The above estimate makes the wildly optimistic assumption that all the biomass could be burned for fuel. In fact, the efficiency with which the carbon in biomass, such as corn, can be converted to biofuels, such as ethanol, is only about 50 percent[4], and energy expenditure in harvest, processing and transportation still have to be factored in. All these factors raise the estimate of required land.

It is doubtful that so much land would be made available without the costs of land, and of the food that is grown on it, skyrocketing. However, the land is there, and ultimately the market should determine what it is used for. Nearly 15 percent[5] of all the land in the U.S. is used to grow high yield crops such as corn for feeding livestock, and some additional cropland lies fallow. Should America choose to trade most of its meat and dairy for biofuel, it might well have enough cropland to supply most of its energy by growing the latter, assuming it could burn biomass without much further energy investment for processing it.

Wind

Wind gets a somewhat higher fraction of the solar power hitting the Earth than photosynthesis, but it is much harder to harvest than crops. It must be caught at the exact time and place that it blows, otherwise it is lost, and, wherever one may build a windmill, the wind doesn't always blow there. So the question remains how much of the world's surface would have to be devoted to windmills in order to fuel the world's energy consumption, which would be equivalent to gathering, at the very least, a percent or so of all the wind that blows and converting it to electricity. This is literally a tall order. Much of the wind is at high altitudes - several kilometers - and it is hard to collect wind above a hundred meters or so from the Earth's surface. It is hard to see how mankind could ever collect even one percent of the Earth's wind budget. To state the problem in different terms, the energy flux in wind blowing 24/7 at 20 miles per hour would be about 0.5 kilowatt per square meter, and about half of that can be realistically recovered by a wind mill. Even if this generous number represented typical wind conditions, supplying the world's current energy expenditure with wind would require a wind collecting area of about 8 square meters per person, or over 50 billion square meters. This is about the area of a curtain over a kilometer high wrapping around the entire circumference of the Earth.

Hydroelectric power

Hydroelectric power is limited by the rate at which water is evaporated off the Earth's surface - about a ton per square meter per year. This evaporation is balanced by the precipitation, rain and snow. About 2/3 of the rain and snowfall over land is evaporated back from the land, and about 1/3 flows back to the ocean via rivers and streams, groundwater seepage and so forth. Were all the backflow, about 1/3 of a ton per square meter of land, to return to the ocean only after passing over a 300 meter-high waterfall or dam, the potential hydroelectric power so released would be about 1/30 of a watt per square meter of Earth's surface, which is significant but not enough to supply the world's current energy demand. While not every drop of rainwater can be expected to make its way to a large dam, much of the world's rain does in fact eventually make its way to a river, and the convenient concentration of the water flow into river beds makes hydroelectricity worthy of much consideration, in this author's opinion. The Hoover Dam, for example, produces enough in electricity every six months to match its entire cost. A payback time of months is a dream for renewable energy. Yet, the net production of hydroelectric power in the U.S. has not risen much over the last six or seven decades, so it may be that it too is close to its global output limit. But one should not rule out the potential of significant increase in small hydroelectric plants in all sorts of small streams that have until now been too obscure to attract careful study. Their potential clearly depends on the market price of electricity.

Geothermal energy

Geothermal energy depends not on the sun but rather on the nuclear energy released by radioactive elements within the Earth. As the Earth's interior is molten iron at a temperature of several thousand degrees, there is the same order of magnitude of energy in heat as would be obtainable if the entire Earth's interior were made up of fossil fuel.[6] This is clearly a much larger reservoir of energy than fossil fuel by any reasonable estimate. The trouble is that it leaks to the surface of the Earth very slowly, taking many billions of years to do so. Had it reached the surface any faster, it would have been gone by now. The power per unit area of geothermal energy that arrives at the Earth's surface from below is only about 1/16 of a watt per square meter. (Compare this with the roughly 150 watts per square meter that arrive as sunlight.) This is less than 20 percent of the US usage, which is about 0.3 watts per square meter, and about 60 percent of the world average. Considering that the efficiency of tapping this energy is inevitably much less than 100 percent - as one could hardly cover the Earth's surface with geothermal energy systems - geothermal energy, though significant, is insufficient by itself to maintain the world in a Western lifestyle. The advantage of the depths of the Earth is that they are less prone to seasonal variation. Thermal connection to layers well below the foundations of ones house,[7] for example, can help cool the house in the summer as well as heat it in the winter, thereby reducing the demand for energy. But geothermal heat does not arrive from below in sufficient quantity to run the world in the style to which it is becoming accustomed.

Direct sunlight

Another promising mode of renewable energy, in the specific context of space heating, is direct sunlight. The sunlight streaming in through a window pane is 30 or more times as efficient, in terms of energy per unit area, as the photosynthesis of the most efficient energy crop. A well designed house in a sunny climate can get by with little need for fossil fuel heating.

Heat, however, is distinct from transportable or transmittable forms of energy such as electricity or fuel for vehicles. The conversion efficiency to the latter with current technology is about an order of magnitude times that of photosynthesis, but costly. As with all things, the cost is partly in labor, partly in materials, and partly in energy itself. Solar energy farming can be promising if the price is right, and efficient conversion of solar energy to a transportable or transmittable form could satisfy much of the world's energy heating needs given enough land area. But again, the current cost estimates for solar energy systems, which are area-intensive, typically assume only the small incremental costs. When production is massive enough that it strains the supply of land, or the supply of metals and other materials for the reflecting surface and structure, a proper cost analysis should figure in the sharp rise in costs that such high demand would create.

Even at current incremental costs, supplying overall energy needs with solar energy would, to say the least, require a revolution in the world's economy. The planned Topaz solar energy facility in California, for example, is slated to cost over one billion dollars, will generate an annual average of about 1100 billion watt-hours, and is said to occupy 25 square kilometers[8] of real estate (though it is not clear from their website exactly how much of this is covered with solar panels, how much is infrastructure, etc). This amounts to 125 megawatts, about 8 parts in a million of the world's human power consumption, while those 25 square kilometers represent 0.17 part per million of its land area. Supplying the world's energy consumption would, at this efficiency, require over two percent of the world's land area, and would cost, at current incremental costs, over 125 trillion dollars. Supplying California's overall energy consumption, which is about 8 times the world average in power consumption per unit area, would require about 17 percent of California's area. Each acre of land would generate 20 kilowatts, which, at a market price for energy of 10 cents per kilowatt hour, would be $17,600 worth per acre annually. Well outside big cities, California land, at current market levels, does not add appreciably to the price tag of the solar energy collectors - over $160,000 per acre. One wonders, however, what the prospect of solar energy will do to the price of rural land, which until now has been generating food at typical annual yields of the order of $1000 dollars per acre. Hint: California, one of the world's richest agricultural regions, produces about 30 billion dollars worth of agricultural output per year, and lately spends between 75 and 150 billion dollars per year on energy.

Tides

Tides are powered mainly by the Earth's rotation, in which there is plenty of energy. Even at the best locations, however, where the tide may raise the water level twice a day by, say, ten meters, the amount of energy released per unit area must be less than the energy released when dropping 10 cubic meters of water 10 meters. This amounts to only about 25 watts per square meter, which, while being an order of magnitude higher than the most efficient photosynthesis, is less than direct sunlight and highly restricted in location.

Cooperative Economics

None of this it to deny that solar, wind, geothermal, and hydroelectric power, in limited amounts, would be marketable if energy were to cost what it is truly worth to us. The point is that the true cost of large amounts of renewable energy must include the cost of the land that supports it, and the cost of land can increase sharply as demand rises. The recent sharp rise in food prices following a very modest increase in ethanol farming illustrates this point.

The existence of global limits, in fact, changes the way we need to think about economic issues. Our mentality is one that equates a healthy economy with growth. We are accustomed to thinking of mass production as introducing economy of scale. For example, large factories can produce manufactured items at less expense per unit output than small, garage scale companies, and one naturally assumes that mass production works in favor of affordability. Solar energy panels may be expensive, the argument goes, but, if a company were to receive a large number of orders, the price would surely come down. That is the way things have worked up until now. The lowering of price with growth in volume means that the cheapest method of production tends to dominate the market. The method that is cheapest among a set of competing methods sells for less, attracts more customers and more demand, and the subsequent growth in volume of production makes it even more affordable than its competition, leading to further relative demand and so forth. The emergence of fossil fuel as the world's main energy source illustrates this point. While the very first oil well may have produced energy that was more expensive than the first solar collector, mass produced oil is nevertheless cheaper than solar energy.

As global limits are approached, however, the cost per unit energy of any given form increases with volume. It thus becomes less competitive relative to other forms of energy as it becomes more popular. By the same token, it enhances the attractiveness of other forms of energy by relieving the demand on them and thereby reducing their cost per unit energy. The different ways of producing usable energy then enter into a relationship that is more cooperative than competitive. While each is limited by the same basic problem, the finite supply of area, they may share that area is complementary fashion. The best cropland is not in general the best place for a hydroelectric dam. The best place for solar energy may be people's roofs and windows. The best place for geothermal connection may be under people's basements. While none of them alone can supply all of our energy needs, maybe they can team up. By relieving demand on the others, each source lowers their cost per unit volume when the latter would rise with increasing demand. In microeconomic terms, the different mechanisms for producing usable energy equilibrate to the point where the incremental cost of each is the same. This encourages the market to make use of all of them because no one of them is far cheaper than any other. The fact that so many forms of alternative energy are being considered and whose costs are within the same ball park of each other suggests that this equilibration mechanism is already at work in various subtle ways. It makes little sense for intellectuals and politicians to argue over which form of energy production to "invest" in (i.e. subsidize), since the various forms of alternative energy production can best develop by developing together.

The ultimate support for renewable energy, of course, is the curbing of demand for energy, as it makes renewable sources more likely to provide a significant fraction of the demand. The problem is that government policy until now has, despite all its ostensibly good intentions, made it difficult for renewable energy to survive its infancy. Popular desire for cheap oil has caused wild fluctuations in the price of fossil fuel, so that, even if renewable energy is competitive when oil is 140 dollars per barrel, companies that supply it can go bankrupt once fossil fuel returns to the cheap phase of its cycle, when it undersells renewable energy. This would have been the case even if demand were low, and it would be bad enough. But it gets worse. As demand for energy grows insatiably, driven in part by the US role model for developing nations, renewable energy is becoming less relevant. The limited supply of renewable energy will soon be too small to meet the growing demand.

A price floor on fossil fuel, enforced in the form of an energy tax, would not only guarantee alternative energy sources a stable chance in the marketplace, it would lower consumption, and keep the world from driving up the price of renewable energy by excessive demands on land area.

Not mentioned in the above is nuclear energy. It may be dangerous or incur expensive security costs to keep it safe. It seems the only non-fossil fuel alternative to renewable energy. As the limits on the latter are approached, and people witness the consequences first hand, it is not unlikely that nuclear energy will be regarded as the lesser of dangers. However, the supply of uranium is also limited.

Summary and Implications

The finiteness of the planet and the size of its population will soon force people to make choices that they would have preferred to avoid. For starters, we will probably be forced to choose between meat, whose production is extremely area intensive, and energy, or build many nuclear power plants very quickly, with all of the constraints imposed by environmental and safety issues. The mechanisms by which these choices will be made may be (a) the free market, where people individually decide what they can and cannot afford, (b) democratic legislation, where, ostensibly, people collectively decide what they may and may not have, or (c) force, whereby people are told what they may and may not have - or worse.

Acknowledgements

The author's research is presently funded by the Israel-U.S Bi-national Science Foundation, the Israel Science Foundation and the Joan and Robert Arnow Chair of Theoretical Astrophysics. The views of the author are not necessarily endorsed by the sources of funding. Past support has come from the U.S. National Science Foundation, N.A.S.A., and via fellowships from the National Science Foundation and the Alfred P. Sloan Foundation.



[1] A food Calorie is one thousand calories, and a calorie is the amount of heat needed to raise one gram of water one degree Centigrade in temperature.

[3] The U.S., of course, devotes far more than the bare minimum to grow food

[4] http://www.greencarcongress.com/2006/07/syntec\_gearing\_.html

[5] Watersheds Messenger, Summer 2002, Vol. IX, No. 2, The Truth About Land Use in the United States, George Wuerthner

[6] Fossil fuel releases enough heat, when burned, to heat its own weight in iron to over ten thousand degrees

[7] e.g. by circulating water through pipes that carry water to great depths and back up to one's home

[8] http://en.wikipedia.org/wiki/Topaz_Solar_Farm


Copyright: David Eichler

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