My phosphogypsum research notes. Part 2

I learnt about phosphogypsum in some 2011. After that I thought and read about it occasionally. How it can be reused? In January 2024 I realized that thinking without doing makes no progress and decided to do something.

What changed since 2011?

REE prices decreased some 10 times. 
Solar energy increased its share in the energy pie. Solar electricity is intermittent energy source. Dealing with intermittency is a challenge, and reusing phosphogypsum could be a good opportunity to use solar energy.

How pure gypsum can be extracted from phosphogypsum?

Gypsum has solubility of 2 grams per liter of water – not too much. Dissolving gypsum and evaporating water will need 2,26 MJ of energy per 2 grams of gypsum, or 314 MWh per ton. This amount can be reduced some 50 times by distilation using mechanical vapor recompression, it means 6,28 MWh of energy per ton of gypsum. 1 MWh costs some $100, so this way is not economically viable.

What if change the temperature of the solution? Heating a liter of water by 100 degrees needs 420 kJ of energy. It means 58,3 MWh per ton of gypsum. And counter-flow heat exchangers can reduce this amount by some 50 times, so it could be 1,2 MWh per ton. It is better but still high.

Energy required per ton is not only energy cost but also equipment cost (CAPEX). And another problem with low solubility is huge amounts of the solution to pump, filter, store, etc. I needed to find another way to dissolve and precipitate gypsum.

My phosphogypsum research notes. Part 1

First time I heard about phosphogypsum was in some 2011. I read an article, and it said phosphogypsum is unused industrial waste and also it contains rare-earth elements. I thought that REE sounds interesting and I would like to extract REE from phosphogypsum. I was thinking for several days about such extraction and was reading about phosphogypsum. Phosphogypsum mostly contains gypsum, and I realized that the optimal way is extracting pure gypsum. Pure gypsum can be sold easily, and after extracting it from phosphogypsum REE extraction becomes more simple.

So, the goal is to extract pure gypsum from phosphogypsum.

But how to extract gypsum? I assumed that dissolution and precipitation can do it. While gypsum is dissolved it can be purified.

So, the goal is to dissolve gypsum and then precipitate it.

An idea for compressed-air energy storage

Compressed-air energy storage is used to store energy, more details in Wikipedia. It contains pressurized air. 

The idea is to use the compressed air to help extracting gases from air, e. g. water wapor, carbon dioxide and others. So, Direct air capture combined with Compressed-air energy storage will be more efficient compared to standalone Direct air capture.

Will photovoltaics and LEDs compete with usual greenhouses?

What if replace transparent coverings of a greenhouse with non-transparent thermally insulated walls, attach photovoltaics and add LEDs in order to save money on heating. 

Long-range high-speed electric airplane

Imagine solar-powered ion-propelled aircraft. Ion propulsion allows flight at high altitudes like 40-50 km. The air is rarefied at high altitudes, that means the aircraft should have high velocity like 1-2 km/s to maintain the altitude. Solar energy allows unlimited range. So, such an aircraft can be long-range and high-speed. 

For high velocity such an aircraft should have enough power like 0.2-0.4 watts per gramm of mass.
If it has some 5 watts per gramm, it might be able to reach the space.

Non-rocket spacelaunch using solar powered ion engine. It might be possible for small payloads

Imagine a fixed-wing airplane with ion engine and solar panels. Currently it cannot take off from Earth surface due to very low thrust. It is caused mostly due to insufficient power of energy input.

But what if the size of the apparatus decreases. According to Square–cube law, decreasing dimensions n times will lead the surface area decreases n*n times while the volume and mass decreases n*n*n times. This means power-to-mass ratio increases n times. Small enough apparatus might have enough power to take off from the surface, fly in the atmosphere and become a satellite.

Travelling in lower and upper atmosphere seems to be possible. See Ion-propelled aircraft and Atmosphere-breathing electric propulsion.

Photovoltaic is good as an energy source:
1. Virtually unlimited amount of on-board energy.
2. High electric power density - thin-film solar cells might generate some 10 Watts per gram. For comparison Plutonium-238 generates 0.57 Watts of power per gram, that power yet needs to be converted to electricity.
3. Photovoltaic can produce high voltage output just by connecting solar cells in series. High voltage is necessary to power ion engines.
4. Lasers can provide additional power. The lasers can be designed to be safe for eyes.

So, there is a chance, Non-rocket spacelaunch will appear in the near future for small-sized payloads, e.g. several grams.

Page Merge Sort

Stable, O(nlog(n)) time, O(sqrt(n)) additional memory.

It is a sorting algorithm based on the approach of merging algorithm described here: https://max-arbuzov.blogspot.com/2021/10/merge-sort-with-osqrtn-auxiliary-memory_22.html