A key part of Rhodes' analysis:
(...)however, for algae to grow, vital nutrients are also required, as a simple elemental analysis of dried algae will confirm. Phosphorus, though present in under 1% of that total mass, is one such vital ingredient, without which algal growth is negligible. I have used two different methods of calculation to estimate how much phosphate would be needed to grow enough algae, first to fuel the UK and then to fuel the world:
(1) I have taken as illustrative the analysis of dried Chlorella , which contains 895 mg of elemental phosphorus per 100 g of algae.
UK Case: To make 40 million tonnes of diesel would require 80 million tonnes of algae (assuming that 50% of it is oil and this can be converted 100% to diesel).
The amount of "phosphate" in the algae is 0.895 x (95/31) = 2.74 %. (MW PO4(3-) is 95, that of P = 31).
Hence that much algae would contain: 80 million x 0.0274 = 2.19 million tonnes of phosphate. Taking the chemical composition of the mineral as fluorapatite, Ca5(PO4)3F, MW 504, we can say that this amount of "phosphate" is contained in 3.87 million tonnes of rock phosphate.
From the internet, for the cyanobacterium Microcystis aeruginosa :
The P quota of these cells was high (mean concentration 132 mmol per kg dry weight)
One converts 132 mmol P X (31 mg/mmol) = 4092 mg = 4.092 g P. This gives 4092 mg P per 1000 g of dry cyanobacteria, or 409.2 mg per 100 gram of dry cyanobacteria. The number 409 is less than half of Rhodes' 895, but who wants to quibble?
The "amount of phosphorous" matter is not the biggest problem with the analysis of Chris Rhodes. Rhodes assumes that the phosphorous is lost. In many algal/cyanobacterial biofuel production schemes (e.g., US 6,306,639; US 6,699,696; US published application 20090155871 ), carbon dioxide and water lead to secretion of biofuel in the absence of consumption of any biomass. The phosphorous argument presented by Chris Rhodes is inappropriate against those schemes.
As Ramachandra said, “We do not harvest milk from cows by grinding them up and extracting the milk. Instead, we let them secrete the milk at their own pace, and selectively breed cattle and alter their environment to maximize the rate of milk secretion” [ Ramachandra TV, Mahapatra DM, Karthick B (2009) Milking diatoms for sustainable energy: Biochemical engineering versus gasoline-secreting diatom solar panels. Ind Eng Chem Res 48:8769–8788. ]