Renewable energy sources, etc.: What are the challenges in getting to a new energy economy that is

· Low-carbon

· Based on domestic sources

· Efficient and equitable in allocating costs

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The first two criteria focus on security - security of the climate, and of the energy supplies themselves. A fourth criterion is also weighted highly in various discussions, the criterion of low pollution, construed as low production of nitrogen and sulfur oxides, reactive organic compounds, polycyclic aromatic hydrocarbons, airborne mercury and other heavy metals, and fine particulate matter (PM10 and PM2.5). Progress on the fourth criterion is well ahead of progress on the first two, which is the reason that this discussion focuses on these two. I also touch on some aspects of the third criterion of cost.

Commonly, this is economy is taken to be based on renewable energy sources (hydropower, solar photovoltaics, solar thermal power, biomass, wind), although this is not the full story (nuclear power and coal-fired electric power with carbon capture and sequestration meet the criteria). While renewable energy sources are being actively developed, there is a long way to go, as will become apparent.

Another contributor to a lower-carbon, domestically based energy economy is energy efficiency, both in production and use of energy. Energy efficiency has increased over the decades, markedly in some cases (fourfold for home refrigerators). It has a mixed record of improving our energy economy, however. Most increases in energy efficiency in consumer use have not led to decreased total energy use. With greater efficiency, consumers have typically added more energy-using appliances, so that the per-capita energy use has not improved. California is a rare success story, discussed later.

The presentation here is a selection of major issues to be addressed on the way to the new energy economy. I have largely excluded the purely economic aspects such as where the investment comes from, who pays, etc.

The issues are presented in an outline form, without references or much elaboration. This presentation is intended as a basis for discussion and not as a set of answers, most of which are either poorly known or else subject to deep value judgments. What I offer is a set of facts and constraints that focus the discussion. Such discussion should be profitable among people representing energy utilities, extractive industries, consumers, policymakers, and regulators, in various combinations.

The geographic scope herein is the US as a nation because the US is the largest energy user (though now second to China in CO₂ emissions) and because the topics seem to have the most heated debate in the US. Many of the considerations presented here apply to other political entities as also the whole globe.

The conclusions are at the end, if you wish to jump there.

I begin the discussion with an issue that has come up repeatedly in energy conferences and in conversations with electrical utility personnel and consumers:

How can electric utilities support the base load when using renewables?

Consumer appliances, and, even more so, industrial and commercial processes, need stable electric power (voltage and frequency). This is challenging for utilities to provide as demand fluctuates. Utilities provide the bulk of power as base load, which is the minimum power output that a utility must provide to its customers at a given time of day and season. It is provided by high-capacity generators that cannot be turned up or down quickly to meet fluctuating demands. The latter are met with peaking units such as gas turbines that can be changed quickly but which are expensive to build and to run.

Thus, with conventional means of electric power production, utilities can match supply to demand within acceptable limits. Changes in supply are under their control. This is not the case with most renewable energy supplies:

Solar photovoltaics (PV) and wind - are primary candidates as renewables…but both are rapidly interruptible, solar PV by cloud passage and wind by shifting weather patterns

To match supply to demand when using these renewables, the electric utility needs either:

* fast spin-up of peaking units using fossil fuels (and more of them for every solar or wind source put online,

* OR it needs storage with ability to tap rapidly.

Without such backup, voltage fluctuations at end-use points will be unacceptable and even dangerous to industrial process equipment

Peaking units are expensive to operate, and their operation cuts the value of the renewables for reducing CO₂ emissions

Only a few storage technologies are cost effective and large-scale (e.g., batteries are out)

Storage of some types (pumped water reservoirs) is limited by geographic area or unproven (high-capacity thermal storage for solar thermal power)

Tying together many wind turbines over a large geographic area has been shown to reduce the fluctuations in power delivery, but the fluctuations are still large

Bottom line: Few renewable energy sources can supply the critical base load (other than using biomass as a combustible in standard power plants, and this is rather energy-inefficient. Solar- and wind-based renewables will only be supplements to more conventional technologies and it will add extra costs to accommodate them.

Low-carbon alternatives exist other than renewables - what are their constraints and trade-offs?

A major reason to use renewable energy sources is to cut the emission of greenhouse gases, esp. CO₂. This goal can be met with other, non-renewable energy sources that are long-lasting and low in CO₂ emissions (coal with carbon capture, nuclear power). They can also meet another goal for using renewables, which is basing our energy economy on domestic supplies, offering greater energy security against embargoes, wars, etc.

Nuclear power

Current technology is overly expensive à Generation IV reactors are being developed…but this may take over 20 years (10 for development, >10 for large-scale deployment)

Current technology generates waste for which we haven't a disposal mechanism (that is technologically and politically sound)

Current technology generates weapons material that cannot be fully consumed in other reactors (even the French gave up on Superphenix)

Building nuclear reactors requires manufacture of steel and concrete, which both generate significant amounts of CO₂; they are not CO₂-neutral, despite the industry claims.

Bottom line: The high capital cost of current nuclear plants, and the lead time for new nuclear technologies, will keep them as modest players in the low-carbon energy economy for probably 40 years or more. A few technologies might be fast-tracked, such as liquid fluoride thorium reactors, proven in the past at intermediate scales (60 MW output) and possibly cheaper, or "mini-nukes" of small capacity (several MW or tens of MW), fast to build and rather safe.

Fossil fuels with carbon capture and sequestration (CCS)

This will cost at least a 20% premium in electric power rates

Compared to climate change, this may be very acceptable

Rise of rates in California actually led to lower total power bills for the average consumer

The technology is only in the demonstration stage now

There are concerns of local inhabitants about the safety of high-pressure CO₂ storage in rock strata. No big tests have been done yet. Also, Greenpeace is concerned that a 1% leak rate will just put all the CO₂ back in the air in a century, to generate the full global warming when it's at its worst. There are, however, proposals to use irreversible reactions of CO₂ with the rock peridotite to keep the CO₂ captured.

Bottom line: CCS is projected to add supportable cost increases in electric power and will likely be the first low-carbon technology to make appreciable contributions to the national energy budget.

Overall bottom line on renewables and the low-carbon energy economy:

Low-carbon energy technologies will come to dominate only on a time scale of many decades; the rise in atmospheric CO₂ by that point will be dramatic; one hopes that some of its effects will be reversible.

Transmission of power - how does it constrain the use of renewable (and all) energy?

Grid capacity is inadequate even now - Localized and even regional overloads of the electrical transmission grid have occurred at intervals. Utilities (who are not always the owners of the transmission lines) have had little economic incentive to invest in adequate grid capacity. There are also 'roadblocks' to siting new lines, as landowners, municipalities, and counties often block passage of a line, and higher governmental levels are commonly reluctant to invoke eminent domain to force siting.

On top of that, new lines to add in renewable energy sources must run to outlying areas, where most renewable power is generated. Wind power addition to the grid is stalling in Texas, and waiting time in California for most recent request (last in line) to hook up renewable supply is 47 years.

The situation is partly solvable with necessary upgrade of grid for standard power sources

The grid is largely insecure against outages caused by geomagnetic storms and hostile actions (this vulnerability is not related to renewable use)

Cost of installing protection against geomagnetic storms is estimated at 5-10% of standard capital costs

Utilities are not doing this yet

To be energy-efficient, at both utility and consumer ends, and to be reliable, the grid must be a smart grid (computer controlled at many levels, with sensors feeding back detailed information from users).

While substantial features of this grid are incorporated in Europe, the US does not have a smart grid. It is under active design, such as by the Electric Power Research Institute and its partners

Trade-off: a smart grid is susceptible to malicious intrusion, just like the Internet is now. Extreme security measures must be developed.

Grid ageing and improper use (trading that generates loop currents) are serious problems now

Most of the US grid was built in the '50's and '60's. The average age of major transformers is 40 years. Expect a 1.5% failure rate per year. Outage of one large transformer might cut a major city's supply, and it can take 2 years to build a custom transformer (these are not in stock!)

Spare capacity in the system to cover such outages is minimal. Originally, grid redundancy was designed to allow for alternative supplies in case of failure of a distribution leg. Now the redundancy is exploited for short-term trading, rerouting power on the basis of fluctuations in demand and price. Regulations are not in place.

Bottom line: the US needs to invest an estimated 1 to 3 trillion dollars in the next decade or two to upgrade, extend, and modernize our power grid. The expense will be borne ultimately by ratepayers, but it is necessary - they are the primary beneficiaries and they have been granted a deferral of these expenses to date.

What is the incentive provided to utilities to promote the use of renewable energy sources?

Utilities must recover their investment, esp. for distributed power on home and other buildings

Not unrelated: what is the incentive provided to utilities to promote energy efficiency, such that consumers use less energy and utilities sell less energy? The major success story is that of California utilities. Rates are reset to allow acceptable profit levels, in a practice called utility decoupling. Consumer rates per unit energy use have risen, but consumer bills, as rates * use have gone down significantly, because consumers in California use much less power now.

One specific problem, rather new, arises from the encouragement of installing solar PV panels on individual homes, with the panels tied to the grid. The utilities are obligated to buy the power provided by the home installation, and they regulate (maintain) the voltage and frequency of power into the home. This setup avoids major problems of solar energy storage and is both energetically and economically efficient. (The alternative, using batteries and inverters for home system, makes the system very expensive, as well as less reliable and also contributory to environmental impacts from the manufacture of batteries). However, it reduces utility sales of power, even as utilities are mandated to maintain lines and other infrastructure to customers using these panels.

New rate structures can help, allowing utilities to charge for maintaining service, separately from charging for energy delivery.

Bottom line: changes in the rate structure are required to proceed with improvements in timely fashion. Mandates and regulations are one mode of implementing the use of renewables and any rate changes, but they are problematic for utility planners and others. A coherent energy policy is needed, at both federal and state levels. The US has never had such a comprehensive policy, more than 40 years after the idea was first promoted. A crisis bigger than the Arab oil embargo of 1973 appears to be necessary. It will come.

How can the rate structure for using electricity support of good development?

Should big users be given lower rates to encourage energy-intensive businesses to move in, or should big users be given higher rates to encourage conservation? Note also that big users probably require less infrastructure per unit energy use (the 'final mile' is cheaper per unit energy transferred if it is in high-capacity lines).

Opinion: it is the energy use per end-user that should count. A big business that serves many people efficiently may use a large amount of power, but it may use less per person served that some alternatives. We need a tool to assess the energy use per end-user and then a regulatory policy that accounts for this in setting rates.

How can we ensure equity in consumer credits for renewable energy?

Consider the implementation of solar tax districts, in which a city or county floats bonds so that they can pick up a major part (even all) of the capital cost of installing solar PV systems on homes. The homeowner does not face the high hurdle of the initial cost and pays back the cost in his/her utility bill over many years.

This promotes the use of solar energy in the large. The increased scale drives manufacturing of more panels, which reduces costs.\

Problem: the city or county can only afford to sell bonds to buy a limited number of PV systems, covering a tiny percentage (1%? 2%?) of homes. However, all the residents have to pay for the bonds with a tax levy. Do the non-PV customers pay to support the (richer) PV customers?

In the short term, yes

In the long term, all customers could benefit from improved energy security and climate security

The same considerations apply to another practice that prods the use of solar PV systems, that of paying a premium to homeowners whose panels supply power. Again, it is the other ratepayers who support the homeowners who could afford to install the systems.

Bottom line: We need a fair way to redress the short-term/long-term trade-off, while still encouraging the expansion of the solar PV economy.

What is a sustainable monetary system to support a sustainable system of energy and resource use?

In the long term, growth is the only thing that pays back investment, but growth has both limits and unintended consequences(pollution, social stress of crowding, …).

All money is debt, says Paul Grignon (moneyasdebt.net). The current monetary system relies on exponential growth of consumption, as population growth multiplied consumption per capital. Population growth is not sustainable; the peak in world population is predicted for about the year 2050. Neither is the increase (or perhaps even maintenance) of per capita consumption. It is not sustainable for fossil energy or other material resources. What will be the financial incentives for energy provision and innovation of technologies in an ultimate zero-growth economy (or, regrettably, in an economy of the current structure with periodic collapses)?

What is the long-term future of the economic system? Long term may be 2050, when population might peak (and also consumption per capita - given its unintended consequences)

In the end, what is the scope of renewable energy sources in reducing CO₂ emissions?

Many renewable energy technologies are aimed at providing electric power - consider solar PV, solar thermal energy, wind power - and the same is true of some other low-carbon energy technologies such as nuclear power. The final impact remains complicated to compute, nonetheless:

The new low-C technologies could be used in the transportation sector, replacing oil-based fuel use in vehicles with electric power generated with low-C sources and distributed to vehicles. (This is distinct from the recapture of energy in hybrid vehicles that was originally generated from fuel use but stored electrically.)

The change in CO₂ emissions depends on:

* The fuel source used by the electric utility to provide electrical energy to the vehicles - at one extreme, CO₂-intensive coal is used. It generates about twice the CO₂ per unit of energy that gasoline does, though the power plant is about 1.5x more efficient at energy conversion than the gasoline engine.

* The difference in efficiency of using energy supplied to the drive train by the engine or the electric motor. Energy losses in braking and other places in a gasoline or diesel vehicle consume more than 40% of the energy supplied by the engine. In an electric vehicle, regenerative braking converts the kinetic energy of the car to electrical energy that is stored. The losses in braking are much reduced. However, an electric motor operates at low efficiency in some conditions such as hard acceleration. Overall, the gain in average energy efficiency on going to electric vehicle propulsion is modest.

* Any changes in patterns of vehicle use - would plug-in electric vehicles be smaller, or would they reduce average trip length?

The practicality of using electrical energy for vehicles has challenges:

The electrical grid is limited in capacity, in placement, and, increasingly, in reliability. This can be fixed, with a large national investment.

The infrastructure to distribute electrical energy to vehicles is almost nonexistent currently. There is a chicken-and-egg problem - the recharging stations won't become common until electric vehicles become common, and vice versa. Of course, the same problem has faced other technologies - gasoline engines themselves, electric lighting, and so on. The result is that a new technology typically takes more than 20 years to make major market penetration.

Heavy vehicles (highway trucks) are unlikely to be served adequately by electric power trains. They will continue to use liquid fuels. They consume only about 5% of liquid fuels, so this is not a major problem.

The supply of battery materials (lithium) has to ramp up. Reserves of lithium worldwide appear to be adequate for several billion cars. The geographic distribution of lithium ores might generate a lithium cartel.

The practicality of using renewable energy for vehicles adds some considerations. As we have seen, putting renewables into the electrical power supply faces a number of challenges, so these carry over into using renewable-based electric power into vehicles. On the other hand, renewables may be used to generate liquid fuels or hydrogen gas to run vehicles. This usage could solve part of the problem of energy storage that plagues the use of renewables in providing electric power. For example, wind-generated electrical power could be used on-site or near-site to electrolyze water to hydrogen and oxygen, with the hydrogen then being compressed to use in special vehicles. This system is being developed. Solar thermal power might generate liquid fuels directly.

Renewable energy sources could also be used in the building sector, which consumes about 40% of US primary energy (energy in fuels, before any conversion such as to electricity). Energy is used for heating, ventilation, and air conditioning (HVAC) and for lighting. For heating, liquid or gaseous fuels are practical, so that fuels of this type generated from renewables are usable, which again ameliorates the problem of having to store energy captured intermittently with many renewable sources. The main use of energy in buildings is electrical, and the challenges remain that were listed earlier, of putting renewables into the electrical power system. It should also be noted that electrical power is ultimately preferred for all HVAC - it can be used to power heat pumps, which move 2 to 5 times the energy as heat that they consume as electrical power.

Bottom line: Renewable energy sources are more or less difficult to enter into the energy supply, depending on the usage sector (transportation, buildings, …). Overall, they are a better fit in the total energy system than they are in the pure electrical energy sector.

What is a supportable use of land area?

All renewables use large land areas, because solar power is a diffuse driver or source

Have we frittered away energy sources, the fossil fuels, that, even as they are high in carbon impact and pollutant potential, seem to have used relatively little land area per unit of energy output? The answer is surprising and reassuring.

In an Appendix, I give a rough calculation of power provided per unit land area from the 'worst' fossil energy source, coal, vs. that provided by solar PV central plants, as one of the best renewable sources. Coal comes out as about 6+ times better at power density, or only using about 1/6 as much land for the same energy production. Strip mines of coal seams 20 meters deep that take land out of use for 40 years have an average yield of final electric power of about 140 watts per square meter (about 14% of peak sunlight or about 60% of average sunlight at the surface). Solar PV farms yield about 22 watts per square meter. Oil and gas extraction have extremely variable 'footprints,' yielding very low to very large power densities per unit of land committed.

Also on the renewables side, wind power can also have a fairly small footprint, so that a turbine rated at 500 kW peak (150 kW average) situated on 1540 square meters (0.38 acres) produces an average of 97 watts per square meter. Note that there are adverse impacts (bird and bat kills; aesthetic impacts) and additional potential impacts when wind power is used on a large scale (extraction of wind energy decreases regional windspeeds and changes weather patterns)

Biomass energy production is, however, very land-intensive. It is based on capturing solar energy in photosynthesis, a sustainable but very inefficient process. Globally, natural and cropped vegetation only converts about 0.3% of solar energy to embodied (i.e., combustible or metabolizable) energy. The best whole-season efficiency in open-field conditions for a land crop was 6.6% with sugarcane. A reasonable expectation for optimized biomass production with field crops is perhaps 1.5% and perhaps 3% for algae. This implies high land use, certainly compared with solar PV, for example, which has a conversion efficiency near 15%. (Both systems have further energy inefficiencies, not detailed here yet.) Consider an algal farm at 3% gross efficiency and 2% final efficiency to biomass after using energy for water circulation, drying, etc. If this biomass is combusted in a power plant (at lower temperature and lower efficiency of 30% vs. 45% for coal), the final efficiency from sunlight to electric power is about 0.6%. At an average usable sunlight delivery of 200 watts per square meter, this is a tiny1.2 watts per square meter out. A similarly low yield occurs if the biomass is made into liquid fuel and used at 28% efficiency in an internal combustion engine.

Solar thermal power has the promise of greater thermodynamic efficiency and lower land use than some other renewable energy sources and a number of non-renewable fossil energy technologies. If 80% of land area is used and process temperatures are reached 60% of the time, the thermal energy captured is about ½ the solar energy density of 234 watts per square meter, or 117 watts per square meter. Converting this to electricity at 30% efficiency gives 35 watts per square meter as average yield. The thermal energy might also be used to make liquid fuels from CO₂ and water at a similar efficiency to fuel energy or about 10 watts per square meter at a vehicle's engine. The technology for fuel synthesis is only under development currently.

All solar and wind energy sources used to make electric power need energy storage for providing base load, including during nighttime, cloudy times, or low-sunlight seasons (winter). See the discussion on base load at the beginning. There are energy losses in pumping storage and then retrieving the energy, and, of course, there are added costs.

Bottom line: we have to accept the fact that we will be using large amounts of land for renewable energy sources, with concomitant loss of habitat for plants, animals, and other life forms, plus absolute and aesthetic restrictions on land use for human activities. The activities lost include farming of food crops, with attendant rises in food prices. Land use per unit of energy (really, power, as energy per unit time) may be only modestly changed (increased, likely) by the switch to renewable energy sources. Total land area used will increase further from population increase, which deserves great attention.

Some renewables use large amounts of water - how much?

Most energy technologies use water, even if only for cooling. Biomass energy technologies necessarily use vast amounts of water per unit of energy produced, from the basic principles of photosynthesis. In land plants (vs. algae), water is lost through leaf pores (stomata) than need to be open to allow entry of CO₂ as a starting point for making sugars and final biomass. Water vapor is much more abundant in air than is CO₂, with the consequence that, over a season, an average of perhaps 1000 masses of water are lost per mass of plant matter grown. This is the reason that agriculture for food will always be the major use of human water supplies. There is no escaping this trade-off. For biomass energy, the impacts are obviously large. On an economic basis alone, this is an adverse trade-off. Energy crops might be valued at US $20 per dry ton at the farm gate. Food crops represent about ¼ of the final biomass, so they are grown with about 4 times the amount of water, but they are worth more than $110 per moist ton or $130 per dry ton (about $4 per bushel of corn with a mass of 32 kg (70 pounds) per bushel). That's 6.5 times as much for only 4 times the water use. The value per unit water used is far higher for horticultural crops such as tomatoes.

Algal biofuel production loses somewhat more water per land area than does field crop production, because the ponds are uncovered. (Covering ponds with transparent materials is very costly, in monetary terms as well as in energy invested to make the cover material.). Biomass energy yields per land area might be higher, perhaps twofold, than field crops. Algal production may use brackish water that has lower value than fresh water needed for crop irrigation, and the brackish water might be in higher supply in some localities.

Bottom line: biomass energy production is a niche market (by geographic area) and a bridge technology to energy sources that use less land and water (US Dept. of Energy). It is a large niche in absolute terms, though a modest niche (no more than 5-10% at most) in our total energy supply. We will also be accepting significant impacts on food prices.

How climate-neutral are renewable energy sources? That is, do they, too, cause some global warming?

First, energy is used in harvesting energy, and much of it is fossil energy (e.g., coke used in making steel for all power plant structures; coal, oil, and natural gas used in power plants that feed plants manufacturing solar PV cells; coal and natural gas used in plants that manufacture nitrogenous fertilizers for biomass crops; horrific cases of using coal combustion to distill ethanol produced from corn; etc.) Some renewable technologies have a favorable return on this input of fossil energy. For example, current solar PV cells require only about 10% as much energy to make as they provide over their lifetimes.

Second, harvesting energy means absorbing solar energy, and more than the land did before the solar technology was deployed. This turns out to be negligible in most cases. Consider solar PV cells. In a notional calculation (Appendix II), their extra absorption of solar energy in a desert area is 70 watts per square meter. At the same time, they produced about 35 watts per square meter of electric power. Over 25 years of operation, their use averted the emission of about 2.4 metric tonnes of carbon in CO2. This CO₂ has a warming potential about 350 times higher than the albedo change from using the solar cells. They are a clear winner.

Bottom line: not even renewable energy sources are really carbon neutral. To make up for this and for the cumulative CO₂ emissions from fossil fuels, we will have to actively scrub CO₂ from the air to restore CO₂ levels to levels that avoid adverse effects on climate as well as on ocean life (coral reefs start dissolving at about 450 ppm CO₂ in air, which we're on target to reach in about 20 years) and on other biogeochemical functions that we need.

Avoiding warming alone might be possible with so-called geoengineering - putting reflective elements between the sun and us, such as sulfate aerosols injected into the air. Geoengineering is not a full solution. It does not avoid ocean acidification and some forms actually increase it. It is predicted not to help (or even to worsen) polar warming, with its effects on ice cap melting (à sea level rise), polar life, etc. Finally, it is not even certain to work as planned; current climate models cannot account for a good part of the extra energy being captured by the earth from human activities.

What's the comprehensive bottom line on energy sources, investments, environmental impacts, and consumer impacts that enter into our new energy economy?

Foremost, it is clear that every new energy-supply technology:

· Every new energy-supply technology brings in significant trade-offs in environmental impacts (land use, water use)

· Each is an incomplete solution that cannot be simply plugged in to replace current high-carbon energy technologies; renewables' application is limited variously by their intermittency, ability to tie into our current energy infrastructure, perhaps also by materials availability (not discussed much above), and other constraints.

· Adoption of multiple new technologies is required, and each one will take time to achieve high market penetration (high contribution to our energy economy).

· Incentives to utilities and other energy providers must be changed to drive the required high levels of investment in new technologies.

· At the same time, equity among consumers in bearing the costs requires careful design of new incentives and regulations.

· No combination of new technologies of energy production and energy use will halt the rise of atmospheric CO_2­ and thus halt global climate change. Active carbon extraction from the air and/or geoengineering will be required, as will socioeconomic adaptations to high CO₂ and climate change. Impacts on biological species and biogeochemical functions that support all life will be adverse, to an extent that depends on the speed of our implementing effective solutions.

Appendix I. Calculation of land use for comparable amounts of energy derived from fossil fuels vs. renewable sources.

This is not a familiar calculation but it is very worthwhile to do.

Fossil fuel use: consider coal as most land intensive

System: strip mining a 20-meter-deep seam of coal over 20 years, but putting land out of use for 40 years

Raw energy content in the coal, per unit land area: this is the energy content per mass of coal, multiplied by the mass of coal per unit area.

Assume that the seam is 80% recoverable coal, for an effective depth of 16 m (meters).

The density of coal is about 1.5 times higher than water, or about 1500 kg per cubic meter.

Thus, the amount of recoverable coal under a square meter of land is about 24,000 kg

The energy content of coal (enthalpy of combustion) is about 20 kJ per gram. So, in 24 million grams of coal, we could derive 480 billion = 4.8 x 10¹¹ Joules (J)

Let's reduce this to 80% as much, to account for energy used up in mining, processing, and transporting coal, to 3.84 x 10¹¹ J

This energy was provided over a span of 40 years, or 1.26 billion = 1.26 x 10⁹ seconds, so the power delivered, as energy per unit time, is 3.84 x 10¹¹ J/1.26 x 10⁹ s = 304 watts (per square meter of mine)

This is converted to electrical energy in a modern coal-fired power plant at 45% efficiency, so that the mine is providing, over the time it disturbs the land, a power of 137 watts per square meter.

Compare this to the power provided by a quite efficient renewable energy technology, solar PV cells

Solar energy intercepted by the cells, over days and nights, cloudy and sunny times and all seasons of the year, may average 234 watts per square meter (this is the global average). It may be exceeded in sunny climates, perhaps up to 280 watts per square meter. We can use the latter, optimistic figure.

Not all the land area is covered with solar cells in a practical plant - assume it is 80% covered, so that over the whole plant area, solar energy is intercepted at 0.8 * 280 = 224 watts per square meter.

The cells convert solar energy to electrical energy at 15% efficiency, giving 34 watts per square meter. This is one-fourth the yield from coal strip mining.

Solar PV cells can be made more efficient with multiple energy-absorbing modes and concentration of sunlight, perhaps to 44%, about triple the figure I just used. These cells are more expensive to make, in both dollars and process energy, so we might debit their energy delivery (by one-fourth? I have no clear figures on this), which partly re-inflates their land use. With these rough estimates, the new solar cells might deliver about 74 watts per square meter. This is pushing near the value for coal, though well below the value for oil wells.

The land-use figures for oil production are problematic to obtain. The US Dept. of energy report about 525,000 oil wells in the US, producing about 5 million barrels of oil per day or 58 barrels per second. One barrel of oil weighs about 127 kg and the energy content of oil is about 40 megajoules per kg, so a barrel contains about 5.1 billion J of energy (enthalpy of combustion). The US production rate is then 296 billion Joules per second (watts). We may discount this to 80% (or less) of this figure for the energy consumed in drilling and processing the oil, to arrive at an estimate of 237 x 10⁹ watts.

We may then assume a conversion to electric power at 40% efficiency, in order to make a comparison with solar PV power. This gives us a potential for electric power production of 95 x 10⁹ watts. (Other uses, such as in an internal combustion engine, are at even lower efficiencies, of course. This would downgrade the estimate of total usable power.)

The area of land occupied and disturbed by an oil well (its footprint) is highly variable, as is the production rate of a single well. The average well is producing only 10 barrels per day or less, while the best wells produce 100,000 barrels per day. The footprint of new wells is small, claimed as 2 acres (8100 square meters), vs. figures 8 to 10 times larger for old wells (which surely dominate the landscape). It is hard to fathom the small wells actually occupying 16 to 20 acres, if one has viewed old wells such as in Bakersfield, California. I propose, in the absence of additional estimates, to use 2 acres for all wells in production. This gives a total land area of about 4.25 billion square meters.

The power density is then 95 billion watts from 4.25 billion square meters, or 22 watts per square meter. Surprisingly, this is worse than solar PV cells using sunlight as a diffuse source.

Appendix II. Global warming potential of using solar PV cells, compared with the warming potential they avert by replacing fossil fuel use

Solar PV cells are darker than the land that they cover, so per area more sunlight is converted to heat.

Assume that they are deployed over desert sand, which had an albedo (fractional reflection) of 0.4. The cells have a much lower albedo, perhaps 0.15. That is, an extra ¼ (25%) of solar energy is now absorbed.

The long-term average solar energy flux density over the earth is 234 watts per square meter. In desert areas where the solar cells might be deployed, it is higher, perhaps 280 watts per square meter.

The extra solar energy absorbed is then 70 watts per square meter. (It does not matter if some of the energy is exported for use off-site - the warming from that use still occurs, at the remote site.)

The use of solar PV energy averts the use of fossil fuels for the same amount of energy, and thus it averts the emission of CO₂ and the warming effect of that CO₂

How much energy do the solar cells provide?

Per square meter, operating at 15% efficiency, they provide 42 watts per square meter.

We can compute the energy provided for any given time period. Let's take it over their 25-year lifespan, of about 790 million seconds (7.9 x 10⁸ s).

Over this time, 1 square meter of PV panels produces 42 W * 7.9 x 10⁸ s = 3.3 x 10¹⁰ Joules of electrical energy

How much coal would it take to produce this much electrical energy?

Let's take coal as the energy source, and assume it's used in a modern power plant at 45% efficiency. We would have to combust enough coal to produce 1/0.45 = 2.2 times that much thermal energy, or 7.3 x 10¹⁰ Joules

Coal has an energy content near 20 kJ = 2 x 10⁴ Joules per gram, so we would have to combust about 7.3 x 10¹⁰ J / (2 x 10⁴ J per g) = 3.7 million grams (3.7 metric tonnes).

Of course, not all electrical energy comes from coal. Other sources are less carbon-intensive. Let's reduce the carbon impact to 2/3 of this, or 2.44 x 10⁶ grams. Each 12 g creates one mole of CO₂, so this would create about 204,000 moles of CO₂.

Now we need to estimate the warming potential of this much CO₂ as it spreads over the earth. The area of the earth is 5.15 x 10¹⁴ square meters, and it is covered by air that has a mass of about 10,000 kg per square meter, making the mass of the atmosphere about 5.15 x 10¹⁸ kg. A mole of air is about 29 grams = 0.029 kg, so the atmosphere contains about 1.78 x 10²⁰ moles. Of these moles, 385 out of a million are CO₂ (that is, CO₂ is at 385 parts per million in air, by volume or by moles), so there are 6.84 x 10¹⁶ moles of CO₂ in the air. The 204,000 moles added by the coal-burning we just estimated would increase the amount of CO₂ in the air by a fraction 204,000/6.84 x 10¹⁶ or 2.98 x 10^-12 (about 3 parts per trillion).

Doubling the CO₂ in the air (adding an equal amount of CO₂, that is) would add 4 watts per square meter of radiative loading, so that adding a fraction of 2.98 x 10^-12 would increase warming over the whole earth by 4 x 2.98 x 10^-12 watts per square meter. Over the whole globe, this increases the radiative load by the area of the earth multiplied by this load per area, of 5.15 x 10¹⁴ m² x 4 x 2.98 x 10^-12 watts, or about 6150 W.

The solar panel added 70 W per square meter but cancelled out 88 times as much warming potential.

The warming from CO₂ persists for the average lifetime of CO₂ in the air, about 100 years or 4 times longer than the solar panel operates. Thus, it adds 4x more heat to the earth than the 88-fold rate increase would indicate. Thus solar PV panel averts about 350 times the warming that it produces itself.