Jet fuel

I has a request for an abstract so here it is:

It is noted that the costs of home heating with oil and with (ohmic) electricity are approaching parity. Methods to use renewably generated electricity for other needs while also heating the home are considered. It is suggested that indoor winter time food production can pay for the needed equipment and reduce carbon emissions related to transport of produce. With the anticipated reduced cost of renewably generated electricity and appropriate lighting technology a sharecropping-like business model might eventually be viable. It is found that renewable production of jet fuel using atmospheric water vapor and carbon dioxide as feed stocks could stabilize both heating and jet fuel costs while using both less land area than biomass based methods and less space in the home than winter vegetable co-heat production. Reuse of existing oil delivery infrastructure makes the conversion easier in terms of building a viable business model. It is also noted that reuse of natural gas delivery infrastructure could allow total US jet fuel use to be renewably sourced through co-production of volatile hydrocarbons with home heating, delivery to warmer regions and subsequent final conversion. A novel approach to the Fischer-Tropsch process for producing hydrocarbon fuel which relies on direct energy transfer to the catalyst using microwaves is proposed which has potential to reduce bulk heating requirements and improve loading of the reactants on the catalyst. This method should use carbon dioxide rather than carbon monoxide as an input. A possibly pedagogically useful analogy for understanding the PdV path integral is given in an explanatory note.


The average retail price of heating oil hit $3.29 a gallon this week while the average retail price of electricity is around $0.11/kWh. So, with a 75% efficient oil furnace the cost of heating a home with oil is about 3.2 cents per thousand British thermal units (BTUs), the same as for electricity using ohmic heating at 100% efficiency. And, since it is easier to selectively heat parts of a home with electricity, it is now cheaper to pull out those space heaters than to buy oil. People in Maine though, who are selectively heating just their beds with hair dryers because they are on fixed incomes need immediate relief because the cost of replacing your plumbing every year (if you don't drain it and create a public health hazard), is still pretty high. Our ambitions to set record oil company profits by violating the ninth commandment to sow violence in the Middle East have many follow-on costs.

Ohmic heating such as you get with an electric space heater has a Heating Seasonal Performance Factor of about 3.4 which is just the BTUs per watt-hour. In more moderate climates you can do about a factor of three better using an air heat pump so for people with these systems, their cost of heating is 3 times less than for oil heat.

Since I am moving over to less expensive renewable energy for electricity I've been planning on switching off of oil in any case to reduce carbon emissions but I have not settled on a heating system though I've been favoring a geothermal heat pump. For these, the constant ground temperature is used so that you don't have any ohmic heating at all since you aren't exposed to very cold outside temperatures when air heat pumps don't work and thus resort to heating coils. My resistance to ohmic heating is showing here. It is a rule of thumb that says don't waste electricity on heat since it is a much better energy source than that. As we've seen, the idea of wasting real energy does not make a lot of sense, but old habits die hard. George Monbiot, who wants to retain the use of natural gas for heating in England, wants to generate electricity in the home with a gas generator and use the waste heat from that to heat the home. My problem is the opposite, I want to use the electricity for something more useful first and then get the heat as a bonus. But, I can't really turn on enough appliances to heat the house so what to do?

One way to reduce carbon emissions is to eat locally, especially fresh greens which require a lot of fossil energy to get here from across the country. Looking at the improvements in lighting efficiency and the spectral requirements of plants it looks as though I could grow quite a lot of my winter greens with a basement greenhouse that uses blue and red light emitting diodes. Because plants are not all that efficient at using light, even when you spoon feed them their favorite colors, most of the light will turn to heat and heat the house. From my investigation so far though, it would be hard to turn this into a business because I can only anticipate a couple hundred dollars worth of vegetables which just covers the cost of equipment using the less expensive compact fluorescent lights. Also, I've run into trouble finding seeds locally. When I explained my idea to the salesperson at the hardware store where I did find some half price wax bean, green bean and pea seeds from Baltimore, I heard the same idea from him that electricity is more expensive than oil for heat, though as we've seen that is no longer really the case. I think that the potential for growing plants using renewable power is going to get better as the cost of power comes down and the cost of lighting reduces. One way to make this work would be to contract for wind power with demand management so that the lights are on when the wind blows. Then the cost of electricity should be about 6 cents per kWh and people who let their basements be used to grow plants in the winter could get a reduced price for heat. But, this is probably a few years off and individual efforts that document successes and failures would be the best way to proceed right now.

Not everyone is going to want to have a cellar sharecropper coming in and out delivering milk, eggs and vegetables every week while tending to the harvest and not everyone has an 8 foot by 10 foot space to devote to this. But, thinking more about George Monbiot's favorite subject heat, there is a valuable commodity that could be made at home using electricity and which could answer his last dilemma, air travel.

There is a fairly important paper by Agrawal et al. published this year in the Proceedings of the National Academy of Sciences that grapples with the problem of biofuels just not having much of a place in a renewable energy economy owing to the low efficiency of plants at converting sunlight to energy. The paper goes about half way to converting our transportation fuels to renewable sources by supplementing plants with hydrogen generated from electrolysis. But, they still rely on plants to provide the carbon. We can see that we need the other shoe to drop if we consider the ill-fated Biosphere II experiment compared with the International Space Station. Biosphere II needed a little more than three sunlit acres, in theory, to support the respiration of a crew of ten. The space station devotes the volume of two fairly small canisters of zeolite and a small portion of the solar power they collect to do the same task for a crew of six. We are simply much better at collecting carbon from the atmosphere than plants are. A slight modification of the scheme proposed in the Proceedings of the National Academy of Sciences paper reduces the land area needed to produce liquid fuels that cover all our current transportation as we do it now from their admirable million square kilometers to just 100 thousand. Now, we don't really need to use liquid fuels for most of our transportation. We can do much better using electricity directly. So, really, the place to look at liquid fuel needs is aviation where its use seems irreducible without cutting service. This was Monbiot's sad conclusion, that he could retain most of our activities while cutting carbon emissions but aviation would have to be cut. He morns the loss of love miles.

So, lets make renewable jet fuel without encroaching on food production or wilderness. There are a lot of ways of doing this so what is outlined here may not be the cheapest but lets just put together a system that gets both carbon and hydrogen from the air and turns it into jet fuel while heating a home all while using renewably generated electricity. First we need our hydrogen and carbon sources. These are water vapor and carbon dioxide. We'll plan on producing about 150 gallons a month of jet fuel as our maximum production rate so we need to condense about 0.4 kg/hour of water and 1.9 kg/hour of carbon dioxide. We could go higher if we concentrate on the efficiency of our production method, but remember we want to heat a house so we'll put half the energy use into the chemical bonds in the jet fuel and half into heat (50% efficient) so we want to make about as much jet fuel as we would normally burn as heating oil. The water is easily had using a standard dehumidifier running at about 220 watts. We'll prefer this source of water to avoid impurities and in a basement application a dehumidifier is often welcome. To get the carbon dioxide we'll use the same system used aboard the space station, There are other methods such as that being developed by Klaus Lackner's collaborators in Arizona which may be more energy efficient but since we are heating a home, we'll just pick one since we want the waste heat.

The zelotite used on the space station has been characterized by NASA so it is fairly easy to estimate our material and power requirements for obtaining our carbon. The amount of air we need to process to get our hydrogen at 20 C and 25% relative humidity is 100 kilograms per hour. To get our carbon we need to process more air than this, about 4000 kilograms per hour. Entraining 20 C air with the output of our dehumidifier at -10 C we get the proper air flow at 19 C. The zeolite will carry about 10 grams of carbon dioxide per kilogram of absorber at this temperature and the partial pressure of carbon dioxide in the atmosphere so assuming 20 minutes each to equilibrate in both the loading and unloading phases, and taking the the space station model of constant operation using two separate zeolite components, we need 63 kilograms of zeolite in each component. Since zeolite has about the density of water, the space needed would be about the size of two relatively small adults. So far we are keeping our apparatus to a space smaller than a regular oil furnace so that the space issue that winter time basement farming might run into is not arising here. If we want to be more parsimonious in our use of zeolite, we can use the cold outside air to load the carbon dioxide, reducing our use of zeolite by a factor of about two for 0 C air. NASA didn't characterize zeolite below this temperature, but extrapolating suggests that we might limit our zeolite use substantially more if we were willing to throw energy at the problem, chilling the outside air. But, by then we'd have heated the house because this would be a standard air heat pump. Again, other technology might be used so we won't speculate further.

Now we just need to calculate the energy needed to pump the carbon dioxide from the unloading pressure of 0.01 torr (to get better than 90% unloading) up to a pressure that will be useful for Fischer-Tropsch synthesis, about 17 bar at 19 C if our working temperature is to be near 230 C. To do this we need a 410 watt pump. So far we've used 630 watts of power collecting our hydrogen and our carbon. The rest is chemical energy, and, as Agrawal et al. point out we only really need to separate the hydrogen out of the water since we could use the carbon dioxide in out Fischer-Tropsch process though we'll look at an interesting means of producing the traditional carbon monoxide in a bit. But let us look at the land area needed to gather a kilogram of carbon. Our 410 watt pump will run for 4 months a year gathering about 0.52 kilograms of carbon an hour. So all together it gathers 1500 kilograms of carbon. To do that it would need one third of the annual output of a three by three meter square solar array. You might power air conditioning in the summer with the same array. Here we are assuming 15% efficiency for the solar array for comparison with the calculations in Agrawal et al. So, to gather 1 kilogram of carbon we need a land area patch about 7 centimeters on a side and no tractor. Now we can see our advantage over plants at collecting carbon. They need about a square meter to do the same thing over a growing season. Even though the plants provide the carbon striped of oxygen, the awkwardness of compacting soil to collect the carbon and gather it all in for processing makes it seem silly to burden our ecosystem to provide jet fuel when we can do so much more compactly in a system where the infrastructure is already in place. In Maine, small oil companies are having a great deal of difficulty because their customers are only placing small orders so that they are running all over the place delivering very little oil at each stop. Would it not be better to go pick up 300 gallons of jet fuel every two months and take it to the airport in Portland or Bangor? Would it not be better to cap the price of heating and jet fuel now by contracting with Mars Hill Wind Farm to provide the power. At a flow through rate of $0.07/kWh it may be possible to beat the current price of $2.62/gal for jet fuel. At the least, Maine's fuel assistance program should be looking at this as a means to help in meeting the State's obligations under the northeastern regional agreement on climate change.

Well, as we've seen, the energy involved in gathering the hydrogen and the carbon is not so large. The main energy involved is in converting water and carbon dioxide into jet fuel. And, this is also where the relative inefficiency of thermal processes makes the production of sufficient heat for a home a natural result. The Fischer-Tropsch process revolves around the carbon monoxide bond which is one of the strongest, higher than the ionization potential of many elements. It is the strength of this bond, 11.2 electron volts, that determines what kind of dust, silicate or hydrocarbon, that stars form at the end of their lives. Oxygen and carbon are paired up one to one in the expanding atmosphere of the star until one or the other is used up. If there is extra oxygen left then silicate dust is formed, if there is extra carbon left, carbonaceous dust is formed including large molecules called polycyclic aromatic hydrocarbons. Carbon monoxide is a tough molecule and so quite a lot of energy is needed to separate it. This is the reason for the fairly high temperature used in the Fischer-Tropsch process. High pressure is used to ensure that hydrogen and carbon monoxide get well enough layered onto the catalyst that helps to move oxygen off of the carbon monoxide molecule so that there is always another molecule to carry the oxygen away. To do standard Fischer-Tropsch we would first produce carbon monoxide from the carbon dioxide. This can be done rather elegantly using silicon as an assisted photcatalyst. If we were to use this method we would use artificial light for photons. Once we have the carbon monoxide we would mix it with hydrogen from electrolysis of the water we've collected and pass it through a kiln (ohmic heating) at high pressure within a pipe that contained our catalyst. Once brought up to temperature the process is exothermic and releases a large portion of the energy we have stored through making hydrogen and carbon monoxide. Water produced in the process would be recycled into hydrogen. This, together with the desired hydrocarbons, would be cooled by heating the home.

Perhaps alternatively we might dispense with the carbon monoxide production and use light in a similarly innovative way. Metal powders are easily heated with microwaves and microwave generators are more robust than kiln elements so we might arrange our catalyst as a powder suspended in fiberglass. Loading onto the catalyst works better at low temperatures so we might get a faster reaction if we pulsed microwaves to allow a load/react cycle. Since microwaves will tend to drive off water preferentially to carbon dioxide, carbon monoxide, hydrogen or the hydrocarbon product, we should expect the oxygen to transfer from the carbon dioxide and carbon monoxide to hydrogen to form water. If the catalyst is shaped to include sharp points, it may be that corona discharge or simply strong electric fields owing to the induced currents in the catalyst will assist in transferring the oxygen without the need to reach bulk temperatures as high as usually used. The main thing though would be the better loading of hydrogen which should eliminate coking (we've already eliminated ammonia poisoning) and thus allow the catalyst to be used for a heating season or more. The use of silicon dioxide as a supporting material could be problematic but another non-conducting material might be found to be used as a alternative. In this case, the reactions is less exothermic than when carbon monoxide is used so that we would get a greater fraction of our home heating from the inefficiency factor of the electrolyzer.

Chemistry is fun so that little bit of speculation should be taken as just that, it is untested. But, running a standard Fischer-Tropsch process to make jet fuel is proven and even certified by the Air Force. Doing it in a way that produces only fuel, oxygen and heat is somewhat novel but relies, ignoring speculation about using microwaves, on demonstrated technology. Heating is used through the day and night, so using wind power seems like a good match. One could store a bit of hydrogen and oxygen as a backup in case the wind died down for a while and use this for process heat or for just straight home heat until the wind got blowing again. Right now, carbon dioxide is an industrial waste gas produced in pure form in the manfacture of quicklime for cement for example, so it may be best to begin using that supply first rather than condensing it out of the air. External tanks of liquid carbon dioxide could be sized so that deliveries could be no more frequent than pickups of of jet fuel. Adequate filtering of town or well water could also substitute for our dehumidifier. As the cost of renewable electricity continues to fall, it is almost certain that we will make fuel for aviation in this manner, but right now, people whose incomes are low and indexed to an inflation rate that excludes both energy and food need help. Making a start at a way to make home heating pay seems like something to pursue. Here is a sketch of how the whole system flows:


Schematic renewable jet fuel production method. Energy inputs assume 100% efficiency so heat output is a lower limit. 70% efficiency in electrolysis implies and additional 3000 W of heat.

The Northeast and Mid-Atlantic originate quite a lot of air travel and are also where heating fuel is most used. It is likely that conversion of homes that use oil to jet fuel production can supply the regional demand. But, to supply flights originating where home heating does not use so much energy would require using another kind of existing infrastructure. Forming hydrocarbons up to butane and sending them from homes through existing natural gas pipelines to the South and Southwest might allow minor further conversion to be done in those regions to produce their jet fuel.

Now, if I can just find some lettuce seed....

Calculation:

I get razzed sometimes for "not doing my homework" when in fact I am just leaving out details that people who might make that sort of comment could fill in themselves. I'm trying for a discursive engaging style here where the language is evocative. I was trained to the idea, attributed to Martin Rees, that you lose 10% of your readers with each equation. Ten equations, zero readers. So, I allow the blog to be a little less easy to use in the interest of making it more generally useful. Scan that again: You might need to pull down a calculator sometimes and fill in the blanks but you should be able to read all the way through an article and enjoy it before going back to check the math. Comments are open in case I've been too opaque on the maths.

In any case, I thought of a nice analogy for calculating the work done in pumping a gas up to a higher pressure that I thought might be pedagogical so if you have read this far and are a high school physics teacher, this is all yours.

When you calculate what is called PV work where PV stands for pressure times volume rather than photovoltaic, it makes a difference how you manage things. I learned statistical mechanics before I learned standard thermodynamics so I didn't get this drilled into me as much as some of you might have. But, I understand that it can be confusing.

A lazy man's load is trying to carry too much. If you are moving a wood pile into a wood shed, a very good idea because the wood shed works harder than you do (why?), you might think that you'll get the job done in fewer trips if you really load up on each trip. The lazy man wants to make fewer trips. But, what happens is that you end up dropping several sticks along the way so that you have to go back and bend over three times to pick these up so you end up doing more work than you would have if you had just taken loads you could handle. How much work you do to move the wood pile depends on the manner in which you do it. The great bugaboo of thermodynamics is just this kind of thing. If you go dropping sticks all over the place, creating more randomness than you need to, you end up doing more work. In statistical machanics, you are increasing the number of states avaiable to the system. In thermodynamics, you are raising the temperature.

We're going to use the ideal gas law, PV=nRT, to calculate how much power we need to condense carbon dioxide from 0.01 torr up to 17 bar. A torr is about 1/760th of 15 lbs/square inch, about atmospheric pressure, and a bar is about 15 lbs/square inch. In our equation, P is pressure, V is volume, n in the number of moles, R is the universal gas constant and T is the temperature. We can adjust R to whatever units we are using, but we need to be careful about T. To see why this might be, consider making both sides of the equation zero. To get zero pressure with finite volume and material we need a very special kind of temperature called absolute temperature. There is obviously atmospheric pressure on Earth when the temperature is zero in F or C so this is not what we mean by zero temperature. We use a scale called Kelvin which happens to have the same spacing as the C scale but has a value of about 273 K when water freezes (0 C). There will be about 385 parts per million of carbon dioxide in the atmosphere by the end of the year so its partial pressure is about 0.28 torr so that is why we want to pump to 0.01 torr for unloading.

Now, we have two ways to increase P which is what we want to do. We can increase T or we can decrease V. Decreasing V is the way we'd like to increase P, but when we decrease V, both T and P go up. Try it. Get a bicycle pump and start pumping. You'll find that the base gets pretty warm. But, increasing T is a probem because the gas will eventually cool, but in the meantime you are working away against pressure that is going to come down with the cooling. This is the lazy man's load problem. If you get to 17 hot bars, you'll need to pump some more latter once the gas has cooled to get up to 17 cool bars. So, we're going to assume that the gas at high pressure can cool efficeintly as we are pumping so that we are not doing that extra work. So, we hold T constant at 19 C or 292 K. So we want to add up all the little bits of work we do to go from a large volume and low pressure to a low volume and high pressure so we want to keep track of P as we make small steps in volume and add up the products of the pressure and volume changes. When we do this kind of adding up, we notice that P changes like 1/V so the answer will look like the logorithm of the ratio of the beginning an ending volumes because that is what happens when you add up little bits of that form. This will be multiplied by the other terms, nRT, that we got when we wrote pressure in terms of volume. We know what that ratio is from the ideal gas law, it is just the ratio of the beginning and ending pressures. We are collecting 1.9 kilograms of carbon dioxide per hour so that is about 43 moles per hour. The logarithm of the ratio of the pressures is about 14, R is about 8.314 and T is 292 so we get 1.47 MJ of energy expended each hour or about 410 watts.