dollar a gallon gasoline
Demand for petroleum products is growing while existing oil fields are declining. If it is not already here, peak oil is not far off. What to do?
One way of engineering, especially for very large markets, is "design to cost."
What would it take to make dollar a gallon, possibly carbon neutral, synthetic gasoline?
Size of the energy problem
If the majority of energy were coming from space based solar power (SBSP) satellites as electrical power, and the US still burned the same amount of synthetic oil that it now burns in natural oil (20 million bbl/day), making synthetic oil will require enormous amount of electrical energy. That will be somewhat compensated by the relatively higher efficiency of making synthetic oil vs. the average efficiency of thermal cycles power plants being used to make electricity from coal. For example, replacing coal plants in the US at current consumption will require about 300 GW of SBSP electricity. That will cut coal and gas primary consumption ~1 TW.
Making 20 million bbl of oil per day (at 1 M bbl/day per 100 GW of power feed) will take ~2000 GW. This is conceptually simple since all the elements of technology are available to make carbon neutral synthetic fuel from electric power, water, and carbon dioxide from the air. Worldwide, about 12 TW of SBSP electricity would replace 15 TW now consumed.
Given growth of 3% per year, energy consumption will double in 25 years. So a planning target over the next 25 years is 25 TW, or an average installation rate of ~1 TW per year. Building up from zero to 2 TW per year over 25 years starting in 2016 would compensate for the expected fall off in fossil energy and provide enough additional energy to bring the population of the world up to western energy consumption standards.
For SBSP to displace fossil fuels "naturally" it has to under price them. Because it is an untested source of energy, it needs to severely undercut the next least expensive source of energy. Coal is probably the least expensive source in competition with SBSP at 3-4 cents per kWh. Thus SBSP should target 1-2 cents per kWh.
If off peak SPSP is available for 1 cent per kWh, synthetic fuels should cost about $1 per gallon.
Hydrogen and gasoline are energy storage media, like batteries but much higher performance. In the case of current gasoline the energy was stored in the hydrocarbons a long time ago. Unlike batteries, one of the reacting chemicals (oxygen) comes from the air. Gasoline is 25 times as energy dense as lithium ion batteries.
Hydrogen is widely considered a future fuel. It has serious drawback in that it either has to be stored as a very cold liquid, under high pressure, or absorbed as in hydrides. All of these are low density. "Liquid hydrogen has worse energy density by volume than hydrocarbon fuels such as gasoline by approximately a factor of four." 
The hydrocarbons that make up gasoline, diesel, jet fuel, etc. are energy dense liquids at normal temperatures and pressures. There is over 100 years of technology base and infrastructure behind using them.
As we run out of fossil hydrocarbons, some other very large primary energy source will have to replace oil. However, if we have such an energy source, we can make hydrocarbons. All it takes is very large amounts of low cost energy.
Making synthetic hydrocarbons
Sasol's Fischer-Tropsch processes  provide two ways to do this. The reaction converts syngas to synthetic oil. Syngas is carbon monoxide and hydrogen made by burning coal with limited oxygen and water or reforming natural gas into a mixture of hydrogen and carbon monoxide.
Mining old landfills and feeding them into plasma gasifiers can also make syngas.  More carbon would come from coal, biomass or even separating CO2 from air and reducing it to carbon monoxide with hydrogen. The water gas reaction, H2O + C--> H2 + CO makes syngas. It's endothermic at 131 kj/mol, about 11 kJ/g or 11 MJ/kg. A kWh is 3.6 MJ so the reaction uses three kWh/kg of carbon or three MWh/t. The best way may be to heat coal in steam with an electric arc to the point the ash forms a melt.
Coal fired power plants will be idled as they are displaces with less expensive (and carbon free) space-based solar power. They are valuable rebuilt as coal to syngas plants or as coal to synthetic oil. They would pump the resultant synthetic oil into the nearest crude oil pipeline or the syngas into a re purposed gas pipeline. The hydrogen content makes this a bit questionable, but until the much safer natural gas displaced it in the 1950s, syngas with its poisonous carbon monoxide was distributed in iron pipes and used in homes.
The Fischer-Tropsch process needs twice that much H2, 2H2 + C0 --> (CH2)x + H2O. Making electrolytic hydrogen takes about 48 kWh/kg or 48 MWh/t. One sixth of a ton of hydrogen would take eight MWh, for 11 MWh/t of input carbon. This would result in 14/12th of a ton of oil or about 9.4 MWh/t or 1.3 MWh per barrel of oil. Processing 100 tons of carbon an hour, such a plant would draw 1100 MW and produce 730 bbl/hour or 17,500 bbl/day. This may sound like a lot of synthetic oil, but it would take 20 converted power plants of this size to feed ExxonMobil's 350,000-bbl/day refinery at Beaumont, TX. It would take over a thousand of them to make the 20 million barrels per day of oil the US now uses. There are already power lines from these plants that could be used to send power to them from rectennas.
An alternative reaction is C + H2 --> (CH2)x where a ton of carbon and 1/6th ton of H2 are reacted with heat and pressure. This takes eight MWh/t of carbon, 6.9 MWh/ton of oil, or .95 MWh per bbl.
These are worst-case numbers since all coal has some hydrogen.
Recent work out of MIT has claimed to improved the efficiency of electrolysis. At 48 kWh/kg of hydrogen, the process is about 70% efficient. Improving it to 100% would reduce the power input to 33 kWh/kg and the energy per bbl down to 0.75 MWh/bbl as the lower limit.
For rough analysis this page will use 1 MWh/bbl as the energy cost to make synthetic oil from coal. At a penny per kWh, a MWh is $10, for two cents $20 per bbl.
Coal ranges from $15/ton to $150/ton. Figured at $70/ton of carbon, synthetic oil would cost about $10/bbl for the carbon, $10 for energy (at 1 cent per kWh) plus the capital charge for the synthetic oil plants.
Sasol's most recent plant at Qatar cost $30,000 per bbl/day1 for an oil synthesis unit fed with natural gas and the refinery to sort out the products. A modified power plant heating coal in steam with electricity should be less complicated and while it could turn out local diesel, it would probably just put the whole output into a crude oil pipeline to take advantage of existing refining infrastructure. If the power plant conversion cost $30,000/bbl/day, the capital cost would under $10/bbl (ten year write off at $3000/year, 300+ days/year.) Making a profit on the oil, a power plant converted into a coal to oil plant would make synthetic oil for perhaps $35 a barrel. Fed to existing refineries, gasoline from $35/bbl oil would be about a dollar a gallon.
Fischer-Tropsch process converts cleaned syngas to a mix of hydrocarbons. This process has to clean out all the sulfur out before the syngas goes into the reactor or the sulfur poisons the catalyst. The reactions don't produce any carbon dioxide at the plant; the trains, aircraft, ships, trucks, farming tractors and personal transport release the CO2. Sooner or later (depending on greenhouse gas considerations) the plants will have to make do with biomass (turning all the carbon into liquid fuels), or even pull C02 from the air. The initial coal to oil process reduces carbon dioxide emissions by about half because the power plants no longer produce any.
If all 1.3 billion tons of coal per year the US burns in power plants became synthetic oil, the rate would about 120,000 t/hr of carbon or about 21 million barrels of synthetic oil per day, equal to current consumption. The conversion plants would draw 1300 GW. That is 2.6 years of power sat production at 500 GW/year.
Per the above, the formula for costing synthetic fuel is ~$20 for capital and carbon plus $10 x cost of power in cents per kWh. The cost of power is important, 10 cents per kWh electric power could be used to make $120/bbl oil. $120/bbl oil refined into gasoline gives a cost of about $4 at the pump--which is about what gasoline cost in the summer of 2008 when oil was at $120/bbl.
If a plant can buy penny kWh electricity, then on an industrial scale it should make dollar a gallon synthetic gasoline out of coal.
It takes about 100kWh/t to remove carbon dioxide from the air. See http://www.eurekalert.org/pub_releases/2008-09/uoc-cd092908.php (This is equal to 360 kWh/t of carbon.)
Experimentally these researchers have removed CO2 from air at a rate of 20 tons per year with a square meter of scrubber
Liquid fuels can be made out of carbon dioxide by n(CO2) + n(3H2) --> (CH2)n + 2n H2O.
Electrolytic hydrogen requires 48 MWh/t currently. Recent results from MIT make it possible the energy might get down to 33MWh/t. The chemical equation above requires six t of H2 to 12t of carbon.
Taking (CH2)n as roughly diesel fuel, and using high efficiency electrolysis cells, the reaction requires 200 MWh for the hydrogen plus 4.3 MWh for the CO2 to make 14 tons of fuel. If a MWh is priced at $10, (1 cent/kWh) the energy cost would be $2000 for 14 t of fuel. At 7.33 bbl/t, 14 tons is 103 bbls of fuel. This makes the energy cost per bbl starting with CO2 about $20, twice as much as starting with coal, but you don't have buy the coal so it washes out.
For 14 tons of fuel/day the the power draw for hydrogen, CO2 and compressors would be around 10 MW. The scrubber area would be 880 square meters. For 140 tons of fuel per day, the the energy requirement for hydrogen, CO2 extraction and compression for the F/T process would be about 100MW. The CO2 scrubber would require 8800 square meters of area. Built across the prevailing wind, and ten meters high, it would be nearly a km in length.
Capital equipment has no exact current counterpart, but even including the CO2 capture might run about ten dollars a barrel per day capacity. That would produce $30/bbl synthetic oil and make possible dollar a gallon, carbon neutral fuel.
Electricity, even in industrial quantities, is at least five times too expensive for this and we want *renewable* which makes solar the energy source of choice. Can we get solar power into this price range?
Next: Penny a kWh
1. "Sasol's first international joint venture, a plant in Qatar that turns natural gas into liquid fuel, cost $1 billion, or about $30,000 per barrel of capacity. According to Sasol CEO Pat Davies, that's twice as much as a more conventional oil refinery costs."