Difference between revisions of "Cheap synthetic fuel"

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'''<big>Chemistry; and Math-heavy Draft</big>'''
  
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Hydrocarbon fuels are just too useful as portable energy sources not to mention being the basis for plastics and lubricants.  All serious energy proposals (such as StratoSolar or power satellites) include making some synthetic hydrocarbons.  Even without considering climate problems, natural oil will eventually run out.  The problem is to make synthetic fuel for close to the current price of oil.
 
  
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Making synthetic fuel via the Fischer–Tropsch reaction is simple enough.  Sasol has a plant in Qatar (Oryx GTL) that makes 34,000 bbl/day from reformed natural gas. It has been running since 2007.  World consumption of oil is around 100 million bbl/day so it would take around 3000 of these plants to replace natural oil.  That's a large number, but not impossible.
 
  
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'''Carbon, Hydrogen and Energy'''
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Hydrocarbon fuels are just too useful as portable energy sources not to mention being the basis for plastics and lubricants.  All serious energy proposals (such as StratoSolar or power satellites) include making some synthetic hydrocarbons.  Even without considering climate problems, natural oil will eventually run out.  The problem is making synthetic fuel for a cost close to the current price of oil.  (Design-to-cost target of $100/bbl.)
  
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The Sasol plant uses reformed natural gas as a feedstock, made into carbon monoxide and hydrogen.  Synthetic fuel is roughly CH2.  If you incorporate the step of reducing CO2 to CO, the overall reaction is:
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Making synthetic fuel via the Fischer–Tropsch (F/T) reaction is well developed.  Sasol has a plant in Qatar (Oryx GTL) that makes 34,000 bbl/day from reformed natural gas. It has been running since 2007 and cost a billion dollars to build.  World consumption of oil is around 100 million bbl/day so it would take around 3000 of these plants to replace the current use of natural oil.  That's a large number, but not impossible.
  
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CO2 + 3H2 yields CH2 + 2H2O
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'''<big>Chemistry</big>'''
  
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44 + 6  ->     14 + 36
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The Sasol plant uses reformed natural gas as a feedstock, made into carbon monoxide and hydrogen. Synthetic fuel is roughly CH<sub>2</sub>. If you incorporate the step of reducing CO<sub>2</sub> to CO, the overall reaction is:
  
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It's not obvious this is the best way to go.  It's possible to electrolyze CO2 into oxygen and carbon monoxide.  If this is less costly (energy and capital) than making the extra hydrogen, that's the way to go.
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CO<sub>2</sub> + 3H<sub>2</sub> yields CH<sub>2</sub> + 2H<sub>2</sub>O
  
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34,000 bbl/day is 1417 bbl/hr. At 7.33 bbl/ton, 193 tons of hydrocarbons per hour of which 12/14 or 166 tons per hour is carbon   The CO2 input for an Oryx-sized plant would be 44/14 times this figure or 521 tons per hour. The hydrogen would be 6/14 of 193 tons or 82.8 tons per hour At 50 MWh/ton, this requires about 4.14 GW to make the hydrogen. The hydrogen energy is about 40 MW/ton (for 80% electrolysis efficiency).  At 1.7 MWh/bbl (12.46 MWh/ton) for the fuel, the F/T efficiency is 193*12.46/(82.8*40) `72.6% and the waste heat is about 907 MW) 
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44 + 6   ->    14  + 36 (mols, kg, tons, etc.)
  
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Air is about 1.2 kg/m^3 at 20 deg C and about 418 ppm CO2.  A cubic meter contains close to half a gram of CO2, 1000 cubic meters about half a kg, a million half a ton, a billion 500 tons.  Depending on the separation efficiency, upwards of a cubic km of air will have to be processed per hour to feed an Oryx-sized plant.
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It's possible to electrolyze CO<sub>2</sub> into oxygen and carbon monoxide.  Unfortunately, this is more costly in energy than making the extra hydrogen.  (161 kWh to 100 kWh)  Still, if the CO2 electrolyzers are less expensive than the hydrogen electrolyzers, they may be worth investigating.
  
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This is incidentally about 4.5 million tons of CO2 per year.  It would presumable displace oil that put 4.5 million tons per year of CO2 in the atmosphere.  If the X-prise people could be talked into crediting this, it would qualify because oil left in the ground would certainly stay there for more than 100 years.
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'''<big>Csrbon</big>'''
  
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Combining CO and H2 is exothermic.  As above, 27 percent of the energy in the feedstock has to be removed from the reaction vessel as waste heat.  Some of this can be recovered with steam turbines, though the temperature is not high enough for good efficiency.  However, the waste heat can be used to drive a chimney which sucks this huge volume of air through the CO2 separators and exhaust it far above the separator intake.
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34,000 bbl/day is 1417 bbl/hr.  At 7.33 bbl/ton, 193 tons of hydrocarbons per hour of which 12/14 or 166 tons per hour is carbon  The CO<sub>2</sub> input for an Oryx-sized plant would be 44/12 times this figure or 607 tons per hour.  
  
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Verdox, the company developing https://news.mit.edu/2019/mit-engineers-develop-new-way-remove-carbon-dioxide-air-1025 says to assume 5 m/s gas velocity and 200 Pa pressure drop through the CO2 separators.  A square meter of intake at 5 m/s will admit 5*3600 m^3/hr.  The input area for one cubic km/hr at 5 m/s would be about 60,000 square meters.  At 30 m high, this would be a wall 2000 meters long.  Bent in a circle around the chimney, this would be about 640 meters in diameter.  The CO2 separation at a GJ/ton would take about 145 MW, about 3.5% of the power needed for hydrogen production.
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Air is about 1.2 kg/m^3 at 20 deg C and about 418 ppm CO<sub>2</sub>.  A cubic meter contains close to half a gram of CO<sub>2</sub>, 1000 cubic meters about half a kg, a million cubic meters half a ton, a billion (a cubic km) 500 tons.  Depending on the separation efficiency, upwards of 1,2 cubic km of air will have to be processed per hour to feed an Oryx-sized plant.   
  
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During the day, the waste heat from the electrolysis can be added to the F/T waste heat.  The hydrogen production of 82.8 tons per hour has a waste heat of 10 MW per ton.  To provide enough hydrogen for the F/T to run full time, the hydrogen production, while the sun is up, will have to run at 4 times this rate or 82.8 * 4 * 50 MW or 16.6 GW.  That's a lot of power, but the Saudis are planning a 300 GW PV project that is more than 18 times this large.
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This is incidentally about 5.3 million tons of CO<sub>2</sub> per year.  It would presumably displace oil that put 5.3 million tons per year of CO<sub>2</sub> in the atmosphere.  If the X-prise people could be talked into crediting this, it would qualify because oil left in the ground would certainly stay there for more than 100 years.  
  
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3.312 GW. The total waste heat would be 4.22 GW.
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'''<big>Hydrogen and Energy</big>'''
  
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How much will 4.22 GW heat the air going up the stack?  At 300 K (27 C), the specific heat of air is 1.005 kJ/kg⋅K.  I.e., a kW-s (kJ) will heat a kg of air close to a deg K.  A GWh is 3.6 billion kW-s, a cubic km of air has a mass of 1.2 billion kg.  Thus, a GW will heat a cubic km of air per hour by 3 deg K and 4.22 GW will heat a cubic km of air per hour by about 12.66 deg K.  Nighttime heating will be much lower at around 2.7 deg.
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The hydrogen would be 6/14 of 193 tons or 82.8 tons per hour.  2/3rd of the hydrogen combines with oxygen from the CO<sub>2</sub> making water.  At 50 MWh/ton, this requires about 4.14 GW to make the hydrogen.   
  
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From https://en.wikipedia.org/wiki/Flue-gas_stack the stack will need to be about 180 m in diameter and a km tall to get a flow of a cubic km per hour. The velocity up the stack will be 11.5 m/s and the delta pressure 171 Pa. Wall friction for this size turns out to be about 0.2 Pa for a 1000 meter stack.  The air going up the stack has been stripped of CO2, making it slightly lighter.  The stripped CO2 at half a gr/cubic meter or half a kg in 1000 m would lower the pressure by 5 newtons per square meter or 5 Pa.
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The energy in hydrogen is about 40 MWh/ton (at 80% electrolysis efficiency).  At 1.7 MWh/bbl (12.46 MWh/ton) for the fuel, the F/T efficiency is 193t*12.46 MWh/ton/(82.8t*40 MWh/ton) = 72.6%.  The waste heat from the reaction is about 907 MW) The electricity to fuel efficiency would be 1.7MWh/bbl of fuel /2.92MWh per bbl input or about 58%.  But you are turning inexpensive electrical energy that can't be stored into valuable fuel which can be stored and shipped, so it might make a profit, especially in places trying to reach carbon neutrality (like California).
  
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The flow up the stack would be restricted by the pressure drop of 200 Pa in the CO2 separators.  An extra 1000 meters of the stack would about compensate.  The lower stack draw at night might require fans to provide the pressure.
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'''<big>Waste Heat and a Possible Use</big>'''
  
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'''Cost'''
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Combining CO and H<sub>2</sub> is exothermic.  As above, 27 percent of the energy in the feedstock has to be removed from the reaction vessel as waste heat.  Some of this can be recovered with steam turbines, though the temperature is not high enough for good efficiency.  However, the waste heat can be used to drive a chimney which sucks this huge volume of air through the CO<sub>2</sub> separators and exhaust it far above the separator intake.
  
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PV power in the Mideast has fallen to as low as 1.35 cents per kWh at the 900 MW scale.  Making 14 tons of fuel takes 6 tons of hydrogen.  At $13.50 per MW and 50 MWh/ton, the hydrogen energy cost for 14 tons of fuel would be $4050.  This is a bit less than $40/bbl.
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Verdox, the company developing https://news.mit.edu/2019/mit-engineers-develop-new-way-remove-carbon-dioxide-air-1025 says to assume 5 m/s gas velocity and 200 Pa pressure drop through the CO<sub>2</sub> separators. A square meter of intake at 5 m/s will admit 5*3600 m^3/hr.  The input area for one cubic km/hr at 5 m/s would be about 60,000 square meters.  At 30 m high, this would be a wall 2000 meters long. Bent in a circle around the chimney, this would be about 640 meters in diameter tapering into a 180 m diameter chimney.  The CO<sub>2</sub> separation at a GJ/ton would take about 169 MW, about 4% of the power needed for hydrogen production.
  
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A PV farm producing hydrogen for an Oryx-sized plant would be big.  At a GW/km^2, 4 GW would take 4 square km.  This has to be degraded by about 5 for the PV efficiency and another factor of 4-5 for the peak to average.  This means the PV farm would cover around 90 square km of land.  The CO2 separator can run all the time, but there must be storage for hydrogen while the sun is not shining.  3/4 of a day at 83 tons per hour is almost 1500 tons of hydrogen.
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During the day, the waste heat from the electrolysis can be added to the F/T waste heat.  The hydrogen production of 82.8 tons per hour has a waste heat of 10 MW per ton.  To provide enough hydrogen for the F/T to run full time, the hydrogen production, while the sun is up (an average of 9 hours a day for Qatar), will have to run at 24/9 times this rate or 82.8 * 24/9 * 50 MW or 11 GW.  11 GW is a large block of power, but the Saudis have signed a deal for 300 GW of solar by 2030.  That's enough for 27 Oryx-sized plants.  That may be what they have in mind.
  
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At 50 bar hydrogen is about 5 kg/m^3 or 200 cubic meters per ton. 1500 tons of hydrogen at this pressure would take 300,000 cubic meters. As a sphere that's 83 m in diameter.  The bisected area would be 5410 m^2 and the force would be area * 100,000 Ps * 50 or ~27 billion newtons.  That's spread along the circumference of ~260 m.  Per meter, it would be 104 million newtons.  For steel stressed at 200 million Pa, the shell would be half a meter thick and with an area of 21642 square meters would mass around 86,000 tons, close to the mass of an aircraft carrier.
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https://www.utilities-me.com/article-5367-japans-softbank-to-build-worlds-largest-solar-power-plant-in-saudi-arabia
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The waste heat from electrolysis would be 2.2 GW. The total waste heat during the day would be 3.1 GW.
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How much will 3.1 GW heat the air going up the stack?  At 300 K (27 C), the specific heat of air is 1.005 kJ/kg⋅K.  I.e., a kW-s (kJ) will heat a kg of air close to a deg K.  A GWh is 3.6 billion kW-s, a cubic km of air has a mass of 1.2 billion kg.  Thus, a GW will heat 1.2 cubic km of air per hour by 2.5 deg K and 3.1 GW will heat a 1.2 cubic km of air per hour by about 7.75 deg K.  Nighttime heating will be much lower at around 2.3 deg or the flow could be reduced and most CO<sub>2</sub> extracted during the day.
  
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This is not impossible.  Some steels can be stressed 5 times as much, but another solution such as an empty gas field would be more economical.
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From https://en.wikipedia.org/wiki/Flue-gas_stack the stack will need to be about 180 m in diameter and a km tall to get a flow of a cubic km per hour.  The velocity up the stack will be 11.5 m/s and the delta pressure 171 Pa.  Wall friction for this size turns out to be about 0.2 Pa for a 1000-meter stack.  The air going up the stack has been stripped of CO<sub>2</sub>, making it slightly lighter.  The stripped CO<sub>2</sub> at half a gr/cubic meter or half a kg in 1000 m would lower the pressure by 5 newtons per square meter or 5 Pa.
  
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https://www.utilities-me.com/article-5367-japans-softbank-to-build-worlds-largest-solar-power-plant-in-saudi-arabia
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The flow up the stack would be restricted by the pressure drop of 200 Pa in the CO<sub>2</sub> separators. An extra 1000 meters of the stack would about compensate. The lower stack flow at night might require fans to provide the pressure.
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'''<big>Cost</big>'''
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PV power in the Mideast has fallen to as low as 1.35 cents per kWh at the 900 MW scale.  It may fall to less than a cent.  Making 14 tons of fuel takes 6 tons of hydrogen (2/3rd of it combining with the oxygen from the CO<sub>2_</sub>.  At $13.50 per MWh and 50 MWh/ton, the hydrogen energy cost for 14 tons of fuel would be $4050.  This is a bit less than $40/bbl. 
  
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The first article says the capture method will work in the air. It
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If you write the billion-dollar Oryx plant down in ten years, the capital cost is about $8/bbl.
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takes about one GJ to capture a ton of CO2. A GJ is 278 kWh. At 1.69
 
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cents per kWh, it will cost about $4.70 per ton of CO2. Or $17.23 per
 
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ton of carbon. 14 tons of oil has 12 tons of carbon at a cost of
 
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$206. Per bbl, the carbon would cost about $2.00
 
  
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Oil is approximately CH2. Making hydrocarbons is scaled off the
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The current electrolyzer cost can be found here https://www.hydrogen.energy.gov/pdfs/19009_h2_production_cost_pem_electrolysis_2019.pdf. At the cited, $1000/kW, that is a billion dollars per GW.  It would be 4 billion if the power was on all the time, but (since it is intermittent PV) it is more like 11 billion dollars when you are making hydrogen only in the daytime.
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34,000 bbl/day plant Sasol built 12 years ago in Qatar, it would take
 
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about 3,000 plants. 1,000 if the plant size was moved up to 100,000
 
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bbl/day, but that may take too large a PV farm.
 
  
  
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need to fix here.  cost per bbl is ok, need better number on capital
  
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It may take reverse water gas shift to make the CO2 into CO. It is
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At 82.8 tons per hour, the production of hydrogen would be about 725,000 tons per year, 7.25 million tons over 10 years.  If the capital cost is $11 B over ten years the cost is about 88 dollars per bbl. This is over twice the cost of energy consumption.  The cost of electrolyzers will have to drop by a factor of ten for the per bbl capital cost of the hydrogen plant to reach the same as the per bbl capital for the F/T plant.  At this scale, such a cost reduction seems possible.
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also possible that the CO2 might be electrolyzed to CO and O2 at a
 
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lower energy cost than making the extra hydrogen.
 
  
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https://dioxidematerials.com/technology/co2-electrolysis/
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The capital cost for the chimney is unknown at this time. 6/22/21
  
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https://en.wikipedia.org/wiki/Water-gas_shift_reaction#Reverse_water-gas_shift
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Verdox expects the cost of the CO2 separators to be no more than $800 per ton per hour. That's less than half a million dollars, which in this context is negligible.  
  
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https://en.wikipedia.org/wiki/Sabatier_reaction
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The CO<sub>2</sub> separator can run all the time, but there must be storage for hydrogen while the sun is not shining.  3/4 of a day at 83 tons per hour is almost 1500 tons of hydrogen.
  
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https://en.wikipedia.org/wiki/Hydrogen_production
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An above-ground tank for the hydrogen would mass as much as an aircraft carrier.
  
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At 50 MWh/ton, 6 tons of hydrogen would take 300 MWh. That makes 14
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Another solution such as an empty gas field would be much more economical. If there is excess CO<sub>2</sub>, it could be mixed with the hydrogen and the feed to the F/T reactor modulated to get the correct ratio.
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tons of oil or 21 MWh/ton of oil. At 7.33 bbl/ton the energy required
 
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for a bbl of oil is about 3 MWh. For an energy cost of $13.50/MWh,
 
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the hydrogen energy cost is very close to $40/bbl.
 
  
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[Oil runs about 1.7 MWh/bbl so the energy efficiency of making oil
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A PV farm producing hydrogen for an Oryx-sized plant would be big. At a GW/km^2, 4 GW would take 4 square km.  This has to be increased by about 5 for the PV efficiency and another factor of 4-5 for the peak to average.  This means the PV farm would cover around 90 square km of land.
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this way is about 1.7/3 or about 57%.  It might be possible to
 
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increase the efficiency by electrolyzing CO2 to CO.  Some of the
 
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energy released by the combination of hydrogen and CO can be captured
 
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in the steam used to cool the exothermic reaction.]
 
  
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Add $2/bbl for carbon, and ~$10/bbl for the capital cost of the F/T
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It may be worth considering having the PV farm deliver ~1000 V DC. This would take some huge conductors, at 1000 V, a GW is a million amps.  Aluminum smelters use 250,000 A.  The conductors (from memory) were about 3 inches by 10 inches.
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plant. Carbon-neutral synthetic oil (fuel actually) would cost
 
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~$62/bbl, possibly less with more process optimization.   
 
  
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The take-home is that in some places PV has gotten so inexpensive that
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Other useful links
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it would be possible to make carbon-neutral synthetic hydrocarbons to
 
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replace natural oil for about the same price.
 
  
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The area needed for the PV is huge, 12% of Saudia Arabia or about 2.8%
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https://dioxidematerials.com/technology/co2-electrolysis/
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of the Sahara Desert. (check these numbers, 100 million
 
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bbls/day/34,000 bbl.day, ~3,000 plants at ~90 square km/plant.)
 
  
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[There is an factor of ten error here, it would only take 12% of SA or
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https://en.wikipedia.org/wiki/Water-gas_shift_reaction#Reverse_water-gas_shift
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3 percent of the Sahara]
 
  
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34,000 bbl per day is a rate of around 1466 bbl/hr. At 3 MWh/bbl for
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https://en.wikipedia.org/wiki/Sabatier_reaction
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the hydrogen, the average input to the hydrogen cells would be 4.25 GW
 
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and the peak about 4 times higher.
 
  
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Sunlight comes down at a ~GW/km^2. Between the peak to average and
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https://en.wikipedia.org/wiki/Hydrogen_production
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the PV efficiency, a factor of about ~20 needs to need to be applied.
 
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This takes the PV area per plant up to 85-90 square km.
 
  
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It could be done over many years, but the cost is going to be a
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The take-home is that in some places PV has gotten so inexpensive that it would be possible to make carbon-neutral synthetic hydrocarbons to replace natural oil for about the same price.
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problem. If we built the F/T plants at 300 a year, that alone would be
 
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$3 T. I am not sure what the capital cost for the PV would be,
 
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probably 4-5 times the billion-dollar plant cost.
 
  
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I don't believe this option has been considered in the context of the
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Footnote
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global effects of CO2.
 
  
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After checking the math and finding I had the area off by a factor of
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The U.S. Internal Revenue Service defines a BOE is equal to 5.8 million BTU.[1] (5.8×106 BTU59°F equals 6.1178632×109 J, about 6.1 GJ [HHV], or about 1.7 MWh
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ten, I am not so sure it is something that could be considered. The
 
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Sasol plant cost a billion dollars. 30,000 would be $3 T a year for
 
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ten years. Also, the area needed is so large that much black PV might
 
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cause serious weather problems.
 

Revision as of 05:44, 13 May 2022

Chemistry; and Math-heavy Draft


Hydrocarbon fuels are just too useful as portable energy sources not to mention being the basis for plastics and lubricants. All serious energy proposals (such as StratoSolar or power satellites) include making some synthetic hydrocarbons. Even without considering climate problems, natural oil will eventually run out. The problem is making synthetic fuel for a cost close to the current price of oil. (Design-to-cost target of $100/bbl.)

Making synthetic fuel via the Fischer–Tropsch (F/T) reaction is well developed. Sasol has a plant in Qatar (Oryx GTL) that makes 34,000 bbl/day from reformed natural gas. It has been running since 2007 and cost a billion dollars to build. World consumption of oil is around 100 million bbl/day so it would take around 3000 of these plants to replace the current use of natural oil. That's a large number, but not impossible.

Chemistry

The Sasol plant uses reformed natural gas as a feedstock, made into carbon monoxide and hydrogen. Synthetic fuel is roughly CH2. If you incorporate the step of reducing CO2 to CO, the overall reaction is:

CO2 + 3H2 yields CH2 + 2H2O

44 + 6 -> 14 + 36 (mols, kg, tons, etc.)

It's possible to electrolyze CO2 into oxygen and carbon monoxide. Unfortunately, this is more costly in energy than making the extra hydrogen. (161 kWh to 100 kWh) Still, if the CO2 electrolyzers are less expensive than the hydrogen electrolyzers, they may be worth investigating.

Csrbon

34,000 bbl/day is 1417 bbl/hr. At 7.33 bbl/ton, 193 tons of hydrocarbons per hour of which 12/14 or 166 tons per hour is carbon The CO2 input for an Oryx-sized plant would be 44/12 times this figure or 607 tons per hour.

Air is about 1.2 kg/m^3 at 20 deg C and about 418 ppm CO2. A cubic meter contains close to half a gram of CO2, 1000 cubic meters about half a kg, a million cubic meters half a ton, a billion (a cubic km) 500 tons. Depending on the separation efficiency, upwards of 1,2 cubic km of air will have to be processed per hour to feed an Oryx-sized plant.

This is incidentally about 5.3 million tons of CO2 per year. It would presumably displace oil that put 5.3 million tons per year of CO2 in the atmosphere. If the X-prise people could be talked into crediting this, it would qualify because oil left in the ground would certainly stay there for more than 100 years.

Hydrogen and Energy

The hydrogen would be 6/14 of 193 tons or 82.8 tons per hour. 2/3rd of the hydrogen combines with oxygen from the CO2 making water. At 50 MWh/ton, this requires about 4.14 GW to make the hydrogen.

The energy in hydrogen is about 40 MWh/ton (at 80% electrolysis efficiency). At 1.7 MWh/bbl (12.46 MWh/ton) for the fuel, the F/T efficiency is 193t*12.46 MWh/ton/(82.8t*40 MWh/ton) = 72.6%. The waste heat from the reaction is about 907 MW) The electricity to fuel efficiency would be 1.7MWh/bbl of fuel /2.92MWh per bbl input or about 58%. But you are turning inexpensive electrical energy that can't be stored into valuable fuel which can be stored and shipped, so it might make a profit, especially in places trying to reach carbon neutrality (like California).

Waste Heat and a Possible Use

Combining CO and H2 is exothermic. As above, 27 percent of the energy in the feedstock has to be removed from the reaction vessel as waste heat. Some of this can be recovered with steam turbines, though the temperature is not high enough for good efficiency. However, the waste heat can be used to drive a chimney which sucks this huge volume of air through the CO2 separators and exhaust it far above the separator intake.

Verdox, the company developing https://news.mit.edu/2019/mit-engineers-develop-new-way-remove-carbon-dioxide-air-1025 says to assume 5 m/s gas velocity and 200 Pa pressure drop through the CO2 separators. A square meter of intake at 5 m/s will admit 5*3600 m^3/hr. The input area for one cubic km/hr at 5 m/s would be about 60,000 square meters. At 30 m high, this would be a wall 2000 meters long. Bent in a circle around the chimney, this would be about 640 meters in diameter tapering into a 180 m diameter chimney. The CO2 separation at a GJ/ton would take about 169 MW, about 4% of the power needed for hydrogen production.

During the day, the waste heat from the electrolysis can be added to the F/T waste heat. The hydrogen production of 82.8 tons per hour has a waste heat of 10 MW per ton. To provide enough hydrogen for the F/T to run full time, the hydrogen production, while the sun is up (an average of 9 hours a day for Qatar), will have to run at 24/9 times this rate or 82.8 * 24/9 * 50 MW or 11 GW. 11 GW is a large block of power, but the Saudis have signed a deal for 300 GW of solar by 2030. That's enough for 27 Oryx-sized plants. That may be what they have in mind.

https://www.utilities-me.com/article-5367-japans-softbank-to-build-worlds-largest-solar-power-plant-in-saudi-arabia

The waste heat from electrolysis would be 2.2 GW. The total waste heat during the day would be 3.1 GW.

How much will 3.1 GW heat the air going up the stack? At 300 K (27 C), the specific heat of air is 1.005 kJ/kg⋅K. I.e., a kW-s (kJ) will heat a kg of air close to a deg K. A GWh is 3.6 billion kW-s, a cubic km of air has a mass of 1.2 billion kg. Thus, a GW will heat 1.2 cubic km of air per hour by 2.5 deg K and 3.1 GW will heat a 1.2 cubic km of air per hour by about 7.75 deg K. Nighttime heating will be much lower at around 2.3 deg or the flow could be reduced and most CO2 extracted during the day.

From https://en.wikipedia.org/wiki/Flue-gas_stack the stack will need to be about 180 m in diameter and a km tall to get a flow of a cubic km per hour. The velocity up the stack will be 11.5 m/s and the delta pressure 171 Pa. Wall friction for this size turns out to be about 0.2 Pa for a 1000-meter stack. The air going up the stack has been stripped of CO2, making it slightly lighter. The stripped CO2 at half a gr/cubic meter or half a kg in 1000 m would lower the pressure by 5 newtons per square meter or 5 Pa.

The flow up the stack would be restricted by the pressure drop of 200 Pa in the CO2 separators. An extra 1000 meters of the stack would about compensate. The lower stack flow at night might require fans to provide the pressure.

Cost

PV power in the Mideast has fallen to as low as 1.35 cents per kWh at the 900 MW scale. It may fall to less than a cent. Making 14 tons of fuel takes 6 tons of hydrogen (2/3rd of it combining with the oxygen from the CO2_. At $13.50 per MWh and 50 MWh/ton, the hydrogen energy cost for 14 tons of fuel would be $4050. This is a bit less than $40/bbl.

If you write the billion-dollar Oryx plant down in ten years, the capital cost is about $8/bbl.

The current electrolyzer cost can be found here https://www.hydrogen.energy.gov/pdfs/19009_h2_production_cost_pem_electrolysis_2019.pdf. At the cited, $1000/kW, that is a billion dollars per GW. It would be 4 billion if the power was on all the time, but (since it is intermittent PV) it is more like 11 billion dollars when you are making hydrogen only in the daytime.


need to fix here. cost per bbl is ok, need better number on capital

At 82.8 tons per hour, the production of hydrogen would be about 725,000 tons per year, 7.25 million tons over 10 years. If the capital cost is $11 B over ten years the cost is about 88 dollars per bbl. This is over twice the cost of energy consumption. The cost of electrolyzers will have to drop by a factor of ten for the per bbl capital cost of the hydrogen plant to reach the same as the per bbl capital for the F/T plant. At this scale, such a cost reduction seems possible.

The capital cost for the chimney is unknown at this time. 6/22/21

Verdox expects the cost of the CO2 separators to be no more than $800 per ton per hour. That's less than half a million dollars, which in this context is negligible.

The CO2 separator can run all the time, but there must be storage for hydrogen while the sun is not shining. 3/4 of a day at 83 tons per hour is almost 1500 tons of hydrogen.

An above-ground tank for the hydrogen would mass as much as an aircraft carrier.

Another solution such as an empty gas field would be much more economical. If there is excess CO2, it could be mixed with the hydrogen and the feed to the F/T reactor modulated to get the correct ratio.

A PV farm producing hydrogen for an Oryx-sized plant would be big. At a GW/km^2, 4 GW would take 4 square km. This has to be increased by about 5 for the PV efficiency and another factor of 4-5 for the peak to average. This means the PV farm would cover around 90 square km of land.

It may be worth considering having the PV farm deliver ~1000 V DC. This would take some huge conductors, at 1000 V, a GW is a million amps. Aluminum smelters use 250,000 A. The conductors (from memory) were about 3 inches by 10 inches.

Other useful links

https://dioxidematerials.com/technology/co2-electrolysis/

https://en.wikipedia.org/wiki/Water-gas_shift_reaction#Reverse_water-gas_shift

https://en.wikipedia.org/wiki/Sabatier_reaction

https://en.wikipedia.org/wiki/Hydrogen_production

The take-home is that in some places PV has gotten so inexpensive that it would be possible to make carbon-neutral synthetic hydrocarbons to replace natural oil for about the same price.

Footnote

The U.S. Internal Revenue Service defines a BOE is equal to 5.8 million BTU.[1] (5.8×106 BTU59°F equals 6.1178632×109 J, about 6.1 GJ [HHV], or about 1.7 MWh

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