Long-distance phosphate concentrate slurry pipeline (gravity line)

A phosphate concentrate slurry carried 187 km downhill from a mine plateau to a coastal fertilizer complex, the shape of OCP's Khouribga to Jorf Lasfar line, rated segment by segment as a Bingham plastic. The publicly stated figures used are: the 187 km length (Rusconi, Lakhouaja & Kopuz, 'The Design and Engineering of the 187 km Khouribga to Jorf Lasfar Phosphate Slurry Pipeline', Procedia Engineering 138 (2016) 142-150), that the line is gravity powered (Wikipedia, 'OCP Group'), Khouribga at 786 m above sea level (Wikipedia, 'Khouribga'; the same article's text says 820 m) and Jorf Lasfar on the Atlantic coast, taken here at sea level. Everything else is REPRESENTATIVE, not OCP data: the 0.75 m bore, the 1.6 m/s velocity (about 2,580 t/h of solids), 60 wt% solids, the five-segment profile with a 30 m ridge, the 5 bar head station pressure, and the rheology. Solid density 3150 kg/m3 is fluorapatite's specific gravity of 3.1-3.2 (Wikipedia, 'Fluorapatite'); its molar mass 0.5043 kg/mol is Ca5(PO4)3F from IUPAC 2021 atomic weights. The Bingham yield stress (5 Pa) and plastic viscosity (15 mPa s) are illustrative values chosen by us: no published rheology for this concentrate was reachable, and a real design uses the measured flow curve of the slurry it will carry.

What the line shows, solved: the slurry is 1,690 kg/m3 and 32 vol% solids; it runs turbulent (Bingham Reynolds 1.35e5 against Hanks' transition at 4.4e4, Hedstrom 2.1e7, Darby-Mun-Boger friction), 85% above its laminar-turbulent transition velocity of 0.86 m/s, which is the operating limit a non-settling slurry is held to. Friction costs 52 kPa per km, 9.8 MPa over the line, against 13.0 MPa of static head gained on the mixture density, so the line needs no pumps, consistent with the gravity-powered description; the 37.6 bar left at the terminal is the excess head a real gravity line throttles in choke stations. The pressure dips to 10 bar at the top of the ridge, the point that would fall first if the flow rose. Each segment's Hedstrom and Reynolds numbers, regime, friction factor, static head and margin are in the pipe's Results tab.

Honest scope: steady state only (no slack flow in the descending legs, no startup or shutdown transient, no water-hammer); the rheology is a constant Bingham fit at one temperature; no heat transfer; the profile is five straight segments, not a survey; and this example is not validated against OCP operating data.