Nonimaging PVT collector and some thoughts on nuclear power

 

To convert solar energy into electricity that will be later used to produce ammonia (electrolyzing water and Haber–Bosch process) I propose that photovoltaic thermal hybrid solar collectors (PVT) with compound parabolic concentrators (CPC) mounted on dual axis trackers should be used. cpc_c.ods is my attempt to describe basic parameters of CPC with high-school math (to achieve best results ray-tracing and realistic models of irradiance at various conditions should actually be used).

Solar tracker that can be seen in tracker_dr_7.pdf file is  a concept of robust device that has 4 bearings mounted below collector array (each bearing ideally supports ¼ of the array weight). Axis of the top-back bearings lies on a another bearing that is centered on azimuth axis. This fifth bearing lies on top of fixed hyperboloid structure. Other two bearings that directly support array are put on top of linear actuators. Below those actuators, another two bearings are installed, allowing actuators to move freely when they raise and lower front part of the the array, changing its altitude angle (elevation). Actuators are put on top of of a “carriage” that has wheels/rollers located underneath. “Carriage” can move along fixed ring/track/rail left and right (force that moves the “carriage” can be applied to the wheels/rollers, but a variation of rack railway or winch may be preferential). While on my drawing carriage is much shorter than the ring/track/rail, it may be a good idea to attach a “roof” to the carriage, that would prevent any snow, ice or leaf buildup. Also, automated mechanism that cleans glass surface of the collectors could prove quite beneficial.

As for the electricity production, perovskite–silicon tandem solar cells seem promising, but perovskite films are sensitive to high temperatures, so in PVT collectors only Si solar cells probably can be used for now. Advanced low cost tandem PV cells could be be used in pure electricity producing variation of my proposal (demand for ammonia/electricity could be quite substantial after all). Different solar cells in the single collector unfortunately could receive different levels of irradiance, so it may be best to use many power optimizers or solar micro-inverters in the single collector. PVT variant of this collector should be insulated from from the environment as much as possible (lots of polymer foam on the back and sides and low pressure inside), while pure electricity producing version should have lots of radiators and possibly even fans (PV cells have higher efficiency at lower temperatures). PVT collector should have “rectangular“ pipe (actually it could be rounded inside to better resist pressures, what is important is that it has to have one flat face) behind solar cells that is filled with flowing heat-transfer fluid. Water is a good choice for this fluid, as it has high specific heat capacity, but it must be mixed with antifreeze. Most popular choice for home collectors is non-toxic propylene glycol but it degrades quickly, so I propose that methanol can be used instead (but it has much lower boiling point, so installation will have to survive higher pressures). 

Average Polish household (2.86 persons) uses 81 GJ/y (except for hot water, source [Table 3.1]). According to this webpage, 65% of household energy consumption was space heating (resulting in 63.4 GJ/y), hot water used 16% (15.6 GJ/y), lighting and electrical devices used 10% (9.8 GJ/y) and food preparation used 8% (7.8 GJ/y). Polish households with passenger cars (58.9% of all households) additionally used 43 GJ/y of motor fuels. Hot water and space heating use 79.0 GJ/y of low temperature thermal energy, motor fuels and and half of food preparation energy could be replaced by 46.9 GJ/y of H2 chemical energy, and on top of that, 13.7 GJ/y of electricity are required. Assuming that seasonal thermal storage in large water tank is used, with temperature range of 40-70°C, where the tank has to store 60% of total yearly demand (Drake Landing Solar Community satisfies about half of its heat demand with the energy recovered from BTES), it can be deduced that this tank has to hold 504 m^3 of water. Note the if we assume that this 4.94m radius spherical tank is insulated with 1m thick rock and slag wool loose-fill insulation (R-value of 20 m^2*K/W) it will loose additional 22.2 GJ/y of heat to the surroundings (calculated after 3 iterations, 46K average temperature difference between water and air is assumed [mean air temperature is 9°C, water 55°C]). So actually 101.2 GJ/y of  low temperature thermal energy have to be gathered to meet the demand of the average Polish household.

This article (you can use this website to access full version freely) estimates than electricity can be converted into H2, then into storable NH3, and later cracked into H2 at 44.6% efficiency. Alkaline fuel cells can achieve 55% efficiency, giving 24.5% round-trip efficiency. Some electricity could be produced from short-term H2 storage tank with a round-trip efficiency of 36.6%. This tool claims that an location located in Warsaw (52.232,21.006) receives 1716 kWh/y (6.18 GJ/y) of in-plane global irradiation per square meter (PVGIS-SARAH2 database, two axis tracking).  I assume that only about 90% of the theoretical in-plane irradiation could be used due to to shading of collectors by other objects and other negative factors, making only 5.56 GJ/y available per square meter of collector aperture. We can assume 34% efficiency of heat collection (typical value at Drake Landing Solar Community), and 14% efficiency of PV cells (monocrystalline solar cells with higher efficiencies are available commercially, but they degrade over time and efficiency decrees at higher temperatures and at low irradiance).

Given those numbers, we can calculate how many square meters of collectors are required to meet requirements of the typical household. Collecting low temperature thermal energy will require 53.5 m^2 of collectors. Replacing motor fuels and half of food preparation energy with highly storable ammonia that is later cracked into H2 will require 135.1 m^2 of concentrator photovoltaics. As for the electricity consumption I estimate that 10% of it could be used directly, 20% could use short-term H2 route and missing 70% could be supplied from NH3 storage. This adds to 61.7 m^2 of  concentrator photovoltaics for stationary electricity production. So, in total, 53.5 m^2 of PVT collectors and 143.2 m^2 of pure concentrator photovoltaics are needed to fully meet energy demands of an average motorized Polish household. Household without a car would require only 53.5 m^2 of PVT collectors and 8.1 m^2 of pure concentrator photovoltaics.

Now, let’s calculate how much solar equipment for the whole Poland. According to this document, Poland uses around 630 PJ/y of electricity, 950 PJ/y of gasoline and diesel. Other niche fuels such as coke are also used, I will group them with motor fuels so that equivalent of let’s say 1.10 EJ/y in H2 cracked from NH3 is need to power transportation and some parts of industry. To calculate requirements for low temperature heating of spaces and water I will just double the requirements of all (hypothetically solar powered) households, which will result in consumption of 2.73 EJ/y of heat. If we crunch the numbers we will see that completely solar powered Poland would require 2 837 square kilometers of photovoltaics for electricity production, 3 169 square kilometers of photovoltaics for transportation and other applications requiring fuels that can achieve high temperatures. Heating would only require 1 444 square kilometers of collectors, which can be shared with photovoltaics. Areas given here are total sum of sun facing sides of equipment that harvests light rays, so actual area of all PV cells can be smaller if concentrating optics are used. I would say that the total amount of land that would be occupied by solar farms needs to be at least 4 times higher than that of actual collectors. Additionally, seasonal thermal energy storage would require 13.6 Gt of water inside tanks. Those tanks would take at least 3 051 square kilometers, and additional equipment that would convert electricity to NH3, store it and crack it would take just as much land. I estimate that at least 30 126 square kilometers would be needed for this ambitious project, 9.8% of Poland’s land area. 

So total green transition seems to be quite problematic. Solar cells with higher efficiencies would help a lot. More conventional solar farms with long rows of solar panels, that do not track sun’s daily movements would occupy less space. Producing enormous amounts of solar equipment would require powerful economy. I estimate that per every m^2 of solar collector/panel 10 kg of glass and 30 kg of steel (this includes supports and tracker’s structure) are needed. Producing those light-capturing devices would require 180 Mt of steel, while producing spherical tanks for seasonal heat storage would require additional 191 Mt of steel (to calculate that I used this equation with assumption of 300 kPa pressure difference, 7800 kg/m^3 density of material, and its maximum working stress was 250 MPa). To complete transition in 10 years Polish economy would have to produce 37 Mt of steel per year. Production of steel in Poland in 1975 achieved 15 Mt, while in 2019 only 9 Mt of steel were produced.

My PVT collector and seasonal heat storage system based on well insulated water tank was designed with the purpose of providing energy to single-family houses in sparsely populated rural areas. If many houses/apartments are nearby BTES could be used. As I said, fully solar powered economy can be problematic to achieve. I propose that solar power should be used mostly in rural areas, where large areas of unused land are present. Cities should rely on nuclear fission. Poland has quite limited uranium reserves and I am fascinated by the idea of energy autarky, so in my opinion Poland should be building gas-cooled fast reactors (liquid metals can also be used as coolants) that convert U-238 into Pu-239. In those designs argon could potentially be used as heat-transfer medium. I only found one mention of a paper that contemplates this possibility, but using abundant Ar instead of He has some advantages. Neutrons won’t transfer as much energy to the coolant atoms when they strike them (Ar-40 has 10 times higher mass than He-4), but capture cross-section is quite high (but still similar to Na-23 used in Soviet/Russian breeders). Usage of heavy monoatomic gas will require more energy to pump it through the reactor, but monoatomic gas with high heat capacity ratio increases efficiency of Baryton cycle. High-temperature heat coming out of reactor could be used for water splitting (hydrogen production). Copper–chlorine or sulfur–iodine cycle can achieve this goal. It would be nice if power plants using those reactors would be able to send heat rejected be electricity (or hydrogen) generating equipment to customers seeking to heat their homes (seasonal thermal energy storage of heat coming from nuclear fission is a fun idea to contemplate).

PUREX method is used to produce new fuel for the reactors. There is some concern about nuclear weapons proliferation, but if Путин is allowed to place weapons of mass destruction wherever he pleases, others should enjoy the same right. Also, nuclear explosions can be used for peaceful purposes. I am actually quite fond of mutually assured destruction doctrine. While nuclear weapons can only actually be used to deter potential invaders, tanks and infantry can be used to subjugate peaceful protesters or to grab new land for the imperialist wishing to control more means of production.

Files:

nonimaging_pvt_collector_pre_v1.zip, mirror, SHA256: b0b5a660fcef92a78855938968dd6e5eac34eba88f79991d49c56ffb3e3b6b9d)