I have some issues with the paper Depletion of phosphate rock reserves and world food crisis: Reality or hoax? as among other things, IMO phosphate resources do not get 'depleted', they get diluted.

However, let it serve as a starting point for this topic

CONCLUSION

The major source of phosphorus for world food production is phosphate rocks. The demand for more food to feed the ever increasing human population has necessitated the use of more P fertilizers mainly the inorganic sources over the years. This has exerted increased pressure on the mining of PR deposits which are unfortunately finite. To facilitate proper planning of the utilization of PR sources, many attempts have been made to predict the quantities of existing PR deposits. However, these estimates are fraught with uncertainty as more deposits continue to be discovered. As a consequence, two diametrically opposed viewpoints on whether there is a looming crisis due to imminent PR depletion have emerged. The pessimists predict that the PR deposits will be depleted in the next few decades and that unless serious efforts are invested in the efficient utilization of the current deposits, the world could be faced with serious food and political crisis. There are others however who view such predictions as scaremongering with an aim of arm-twisting the donors to invest more in phosphorus research. They argue that the existing PR deposits can last for several hundreds of years. However, what is not in doubt among these view point is the finiteness of PR reserves. An approach that encourages society to adopt a sustainable utilization of phosphate resources should therefore be advocated.

Apparently not.

So I''ll have a little monologue on the thermodynamics of phosphorus recovery.

Recovering anything from diluted form invokes an unavoidable entropic cost of TdS = RT ln(source concentration/product concentration)

Therefore a ten-fold concentration with waste heat exhaust to 300K costs an absolute minimum of 5.7 kJ/mol or 180 kJ/kg (phosphorus) ~ 0.050 kWh/kg ~ $0.01 /kg

Doesn't sound much, does it?

Commercial phosphorus in some arbitrary form is ballpark $1 /kg based on currently worked reserves.

Each of us produces ~ 1 g of phosphorus in about 1 kg of urine per day, a thousand-fold dilution. Hence due to logarithmic dependency, a three-fold cost wrt ten-fold dilution ~$0.03 /kg)

Spread over 8 billion people that's a surcharge of ~$90 million per annum to meet ~ 20% of current world phosphate fertiliser demand (currently a ~$75 billion pa industry)

Compare with extraction from deep seawater @ ~ 100 ppb (10⁷-fold dilution) where that minimum waste heat cost rockets up to $0.07 /kg

Now all we need is the technology to perform the processes efficiently, the CAPEX financing, and the will-power to face up to future unavoidable challenges. No biggie.

How does that compare to livestock?

3 hours ago, CharonY said:

How does that compare to livestock?

Pig slurry recycling is a pretty well-established farming practice.

Actually, I've just had a rather memorable Kekulé/Ouroboros Dream moment

I went to bed wondering if I was absolutely sure about the guff I'd posted above. I sort of knew the dilution entropy equation was right (I did check just in case), but I wasn't 100% sure I understood why.

Three hours later, my subconscious (?) shook me wide awake and showed me an TS diagram of a standard Carnot Engine. Immediately, I became aware that dilution is analogous to a heat engine, concentration to a heat pump. Also that the same form of equation must apply to diminution (eg grinding), packaging, product distribution, bag filters, electrostatic precipitators, chemical precipitation, rainfall and much, much more. Expansion of the universe perhaps (or am I getting ahead of myself). Also explained why the logarithmic term can be a ratio of concentration, mass fraction, density, temperature, partial pressure, activity etc., according to context.

Beats having to actually think about it. But I better still work through it in the morning (which will probably now be sometime in the afternoon).

And now I've got to find out what the hell homospatial and janusian processes are.

Photosynthesis, respiration, and transpiration. It's a bag of worms! Unbagged dispersing worms!

All eating their tails.

I'm paying attention (some may recall me posting on peecycling a while back, and a brief and draining conversation) to phosphogeddon but not seriously worried. Will try to get back to this and follow entropic cost analyses. I can confidently assert my subconscious has never shown me a Carnot engine.