Real flowsheets, already solved
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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.
3 unit ops • NRTL
3 0
View & openPhosphate ore to marketable rock: attrition scrubbing, desliming, flotation
The front of the phosphate chain, ahead of the acid plant: 100 kg/s (360 t/h) of a sedimentary phosphate ore at 21.9% P₂O₅ (47.9% BPL) is scrubbed, deslimed at 105 microns and floated to a concentrate. The ore is fluorapatite with quartz, dolomite and kaolinite clay; it declares its size distribution and its composition by size, with the clay concentrated in the fines and bound into agglomerates in the coarse classes. Mineral densities are the published ones (fluorapatite 3.15 within the 3.1-3.2 range, quartz 2.65, dolomite 2.84, kaolinite 2.6 g/cm3). The attrition scrubber releases 80% of the coarse-bound clay below the cut and deslimes at 105 microns (150 mesh, the size Florida plants deslime at, Zhang et al., OSTI 1439932). 17.3% of the solids go to the slimes at 11.2% P₂O₅, so 8.9% of the P₂O₅ is lost with them; the deslimed sand is 24.1% P₂O₅. How much P₂O₅ a plant loses here is set by how much apatite is in the fines: Florida's matrix loses about a third of its P₂O₅ to the clays (the same report), this ore much less. The rougher floats fluorapatite at a rate set by each particle's grade: with 1 mm grains, 46% of the apatite in the deslimed feed sits in liberated particles. It recovers 95.3% of the deslimed apatite into a concentrate of 30.5% P₂O₅ (66.7% BPL), inside the 28.7-31.3% P₂O₅ of marketable phosphate rock (Smol et al., Materials 2023), at an overall recovery of 86.9% of the ore's P₂O₅. Bounded, and stated. Every ore parameter is illustrative and fitted to no deposit: the size distribution, the grade by size, the clay disaggregation, the grain size and the flotation rate constants are measured per ore and reagent scheme, and 1 kWh/t of scrubbing energy is a placeholder for the power figure. One rate constant serves all gangue, so dolomite floats no better than quartz here, which is the opposite of the real difficulty with carbonate phosphates (a reverse carbonate flotation or a dense-medium step is the usual answer). No froth, no entrainment beyond water recovery, no reagent consumption.
7 unit ops • NRTL
1 0
View & openGrinding to liberate, flotation to recover: a copper rougher
97 t/h of a 2 wt% chalcopyrite ore in quartz, crushed to a 2 mm median, is ground in a grate-discharge mill and floated in an 8-cell rougher bank. The feed declares its composition by size (psd_minerals) and its texture (150 micron grains), so every unit acts on mineral by size, not on one distribution. The mill is Whiten's perfectly mixed mill with a 0.6 mm grate: nothing coarser can leave, so the coarse fraction is held and ground until it passes. That is why the mean residence time comes out at 643 s against the 300 s the fines see, and the mill holds 17.9 t. The product P₈₀ is 240 microns for 615 kW. Chalcopyrite breaks 1.5 times faster than quartz here, so it ends up enriched in the fines. Liberation is computed, not assumed: at 150 micron grains only 17% of the chalcopyrite sits in fully liberated particles at this grind. The rougher floats every particle type at a rate set by its grade, so a composite floats slower than a liberated grain and drags quartz with it. It recovers 87.0% of the chalcopyrite into 15.4% of the mass, a concentrate grade of 11.3% against 2% in the feed, and leaves 0.31% in the tailings. The sensitivity is the grind-recovery trade. Grind longer and recovery and grade rise together (80% at 100 s, 93% at 900 s) while the mill's power rises with them, which is the decision a concentrator's grind size is set on. Bounded, and stated. Every ore parameter here is illustrative and fitted to no deposit: the selection rate, the grain size and the flotation rate constants are measured per ore (the breakage-fit tool measures the first from a batch test). A composite's flotation rate is taken as proportional to its grade (linear exposure); there is no froth recovery, no size dependence of the rate beyond liberation, and one valuable mineral.
6 unit ops • PENG-ROBINSON
56 0
View & openClosed-circuit crushing and grinding, with the size distribution carried
180 t/h of quartz ore at a 60 mm median goes through a cone crusher in closed circuit with a 16 mm screen, then a ball mill in closed circuit with a 150 micron screen. Every solid stream carries its full particle-size distribution, class by class, so each unit acts on the distribution rather than on a median and a spread. The crusher is Whiten's model: everything finer than its 12 mm closed-side setting passes, everything coarser than its 30 mm open-side setting is broken, and between them a classification function decides. It reduces the circuit feed from an F₈₀ of 90 mm to 13.4 mm for 165 kW, and the screen returns 19% of what it receives to it. The mill is a breakage/selection-function size-mass balance in three mixed stages, not a target size: its product is whatever the breakage of each class produces, fines tail included. The 150 micron screen sends 72% of the mill discharge back, a circulating load of 258% that nobody specified — it is where the recycle settles given the breakage rate and the screen's sharpness. The circuit product leaves at a P₈₀ of 158 microns, and the screen recovers 81% of the true undersize, because a screen with a sharpness of 3 is not a perfect cut. Bounded, and stated. The mill's power is Bond's law applied to the mill's own throughput and its own F₈₀ and P₈₀; Bond's work index is defined on the circuit's fresh feed, so read it as a screening number. The breakage function is Broadbent-Callcott and the selection exponent 1.0 — an ore's own breakage and selection parameters come from its laboratory tests and replace them. Dry circuit: water is not carried.
8 unit ops • PENG-ROBINSON
55 0
View & openGrinding circuit: what a size reduction costs
Ore at 1 mm is ground to a 100 micron P₈₀ and screened at 150 microns. The number the example exists for is the 172.3 kW the mill draws, and it is not a parameter — it is Bond's Law computed from the size reduction itself: W = 10 x Wi x (1/sqrt(P₈₀) - 1/sqrt(F₈₀)) with sizes in microns gives 9.57 kWh/t at a Bond work index of 14, and 18 t/h of ore turns that into 172.3 kW. Halve the product size again and the law's inverse-square-root shape is what tells you the power does not halve — comminution is where a mineral plant's electricity goes, and this is the relationship that decides it. The screen then splits the ground product 27.9% oversize / 72.1% undersize, and it genuinely sorts: the oversize leaves at a 247 micron mean against the undersize's 81 microns, from one 100 micron feed. The cut is applied to the real size distribution (GSD 2.0), not as a specified split fraction. Open circuit, for the Bond's-law arithmetic. A real grinding circuit recycles the screen oversize back to the mill; that closed circuit, with the particle-size distribution carried class by class through a crusher, screens and a breakage-function mill, is the closed-circuit-crushing-and-grinding example.
5 unit ops • PENG-ROBINSON
190 0
View & openDust collector selection: cyclone vs ESP vs baghouse
The same kiln offgas — 500 mol/s at 420 K carrying 8 mol/s of 20 micron dust (sphericity 0.7, GSD 2.2) — offered to the three gas-cleaning devices side by side, because choosing between them is a real design decision and the three models answer different questions. The cyclone catches 85.6%. That number is not specified anywhere: it is computed from the particle size distribution against the device's own cut size, and its d50 lands at 10 microns — half the dust's mean size, so everything finer escapes. It is the honest ceiling of a device with no consumables and no electricity, and it costs the most fan power of the three here at 1555 Pa. The ESP reaches 99.81% by Deutsch-Anderson on the migration velocity and plate area — also predicted, not specified — at essentially no pressure drop. The baghouse reports 99.8%, and this one you should read differently: its capture is the penetration you gave it, an INPUT. The baghouse model predicts pressure drop (37.7 Pa here, from the Cooper & Alley filter-drag law) and cloth area (1149 m2 at a 0.015 m/s air-to-cloth ratio) — not efficiency. Two of these three efficiencies are predictions and one is a specification, and a comparison that hides which is which is worse than no comparison. Why three parallel trains and not one series train. A cyclone roughing into a baghouse polishing is the standard industrial arrangement, and it cannot be drawn here: the cyclone folds its escaped dust back into the gas stream without a solids payload, so a second collector downstream sees no solids to catch. That is a modelling limitation, not a physical one, and it is stated rather than designed around. Bounded: the ESP's zero pressure drop is a model simplification (a real precipitator runs a few hundred Pa), and the pressure drops here are screening values from published correlations, not vendor guarantees.
15 unit ops • PENG-ROBINSON
188 0
View & openCopper recovery from a leach residue: CCD washing + hydroxide precipitation
A leach residue leaves a heap/tank-leach circuit as a slurry — insoluble gangue solids carrying entrained copper-sulfate pregnant liquor that would be lost to tailings if simply thickened. A counter-current-decantation (CCD) wash train recovers it: the residue is washed with clean water flowing counter-current to the solids across a chain of thickeners, so the dissolved copper is displaced into a pregnant-liquor overflow while the washed solids go to tailings. The new ccd_washer unit op models the whole train in one block via the classic counter-current washing equation f = (R-1)/(R^(N+1)-1) (Perry's §18; Coulson & Richardson Vol. 2): five stages at a wash ratio near 4 recover ~99.9% of the dissolved copper, leaving only ~0.08% with the tailings. The pregnant liquor is then dosed to pH 8, where the copper drops as Cu(OH)2 sludge (the precipitator op on the CRC-cited solubility-product chemistry), leaving a barren raffinate for recycle.
8 unit ops • BRINE
259 0
View & openProduced-water scale removal: precipitation + thickener dewatering
Oilfield produced water carries the classic mineral-scale ions — barium and strontium against sulfate (barite BaSO₄ / celestine SrSO₄, the notorious hard sulfate scales that plug tubing and need milling to remove) plus calcium against carbonate and sulfate (calcite / gypsum). A precipitation stage throws every over-saturated scale mineral at once — the precipitator unit op keyed on its CRC-cited solubility-product table, with each mineral removing BOTH its metal cation and its anion from the water — and a gravity thickener then dewaters the slurry into a dense underflow sludge and a clarified overflow. The barium (the worst offender) comes out essentially completely as barite.
5 unit ops • BRINE
286 0
View & openAcid-mine-drainage neutralization: staged lime precipitation
Acidic, metal-laden mine water (dissolved ferric iron, aluminium, nickel and zinc over a sulfate background) is cleaned in a two-stage lime-neutralization circuit — the classic hydrometallurgy / water-treatment precipitation train. Stage 1 doses to pH 4.5, where ferric iron (Fe(OH)3, pKsp 38.6) and aluminium (Al(OH)3, pKsp 33.0) drop out as a sludge while the base metals stay dissolved; stage 2 raises the liquor to pH 9.5, where nickel (Ni(OH)2) and zinc (Zn(OH)2) precipitate, leaving a clarified effluent. Both stages are the new precipitator unit op wrapping the codebase's CRC-cited metal-hydroxide solubility-product chemistry (thermo/electrolytes.hydroxide_precipitation) — dose to a pH setpoint, read off what drops out — the same selective-precipitation workflow a real neutralization plant runs.
6 unit ops • BRINE
298 0
View & openBattery cobalt recovery: leach, neutralize, D2EHPA Mn SX, Cyanex 272 Co SX, electrowinning
Spent NMC111 black mass is leached in sulfuric acid with the acid consumption tracked (lithium as Li₂SO₄, each transition metal as its sulfate), so the pregnant leach solution carries the residual free acid a real leach leaves. A neutralizer then titrates that liquor with 20 wt% caustic to pH 4.0 on the aqueous speciation: the caustic dose is solved, not assumed, and the heat of neutralization (55.8 kJ per mole of acid neutralized) warms the liquor; the caustic header is the supply, and what the titration does not take is returned. Two solvent-extraction circuits on the pH-isotherm chemistry follow, the common NMC arrangement: D2EHPA at pH 4.0 takes manganese into the organic while cobalt and nickel stay behind, and Cyanex 272 at pH 5.0 then takes cobalt and rejects nickel and lithium to the raffinate. The Cyanex 272 isotherms are one published measurement (Liu et al., Metals 11 (2021) 401: 0.4 M in ShellSol D70, 40 C, sulfate; pH50 cobalt 4.15, nickel 6.06), and the 1.9 pH-unit gap between them is why the cobalt organic carries about 0.6% of the nickel, against about 3% with D2EHPA at the same cobalt recovery. The loaded cobalt organic is stripped into a dilute sulfuric strip liquor, and that advance electrolyte goes to cobalt electrowinning: Faraday's law at a 90% current efficiency, 90% of the cobalt plated as cathode cobalt, the anode's oxygen and the 10% of the charge that evolves hydrogen reported as cell gas, and one mole of sulfuric acid regenerated per mole of cobalt plated.
20 unit ops • BRINE
18 0
View & openBattery black-mass recycling: leach -> SX -> BPED -> LiOH crystallization
Spent-battery black mass (an NMC111-like LiNi1/3Mn1/3Co1/3O2 lump, sulfuric acid-leached at a screening-level yield/stoichiometry — see the stated scope) dissolves into a pregnant leach solution carrying Li/Co/Ni/Mn. A 15-stage D2EHPA solvent-extraction circuit (the same real pH-isotherm chemistry the co-ni-solvent-extraction example uses, operated at pH 7.5 — above every curated Co/Ni/Mn pH50 — so all three transition metals extract into the kerosene organic phase while Li, which has no curated D2EHPA isotherm, stays in the aqueous raffinate untouched) purifies the liquor before it ever reaches the lithium-recovery chemistry. A Faraday's-law bipolar-membrane electrodialysis (BPED) cell (the same real electrochemistry as the direct-lithium-extraction example, sized up for this liquor's larger Li flow) converts Li+ to LiOH, which an MSMPR crystallizer takes to battery-grade LiOH solid. Every step reuses an already-real, independently-tested unit op (,,,) chained into the one train none of them had been assembled into before.
11 unit ops • BRINE
348 0
View & openDirect lithium extraction + LiOH crystallization
A Salar-brine DLE train: an Al-based sorbent column selectively loads Li+ (rejecting the brine's much larger Mg2+ background — real DLE sorbents cut a ~290:1 Mg/Li mass ratio down to under 1:1), the loaded sorbent is eluted with fresh water into an aqueous strip liquor (bridging the sorption column's own documented single-pass-loading scope), RO concentrates it, a real bipolar-membrane electrodialysis (BPED) cell converts LiCl to LiOH — Faraday's law links the applied current/membrane area/current efficiency to the actual Li+ transport rate (replacing an earlier placeholder fixed-conversion reactor), reporting real cell voltage and electrical power draw — and a forward-feed two-effect evaporator train (vapor from effect 1 heats effect 2) concentrates it to battery-grade LiOH·H₂O crystals. Real boiling-point elevation throughout via the Pitzer-electrolyte brine thermo package. Isotherm parameters per the sorption column's own citation (2024 Desalination study, Al-based DLE sorbent).
17 unit ops • BRINE
348 0
View & openCobalt/nickel solvent extraction (D2EHPA)
A laterite leach liquor (Co/Ni/Mg in dilute sulfate solution) meets a D2EHPA-in-kerosene organic phase across a 20-stage countercurrent extraction circuit run at pH 5.2 — the real industrial operating window (e.g. Bulong, Murrin Murrin, Western Australia) that exploits the ~1 pH-unit gap between Co and Ni's D2EHPA extraction isotherms: Co extracts into the organic while Ni (and Mg gangue) are rejected to the raffinate. The loaded organic then meets fresh dilute-acid strip liquor across a 10-stage strip circuit at pH 1.0 (well below Co's isotherm), reversing the equilibrium to recover a concentrated cobalt strip liquor and regenerate barren organic. Real pH-isotherm chemistry throughout, not a fitted shortcut K_D.
8 unit ops • BRINE
357 0
View & openCrystallize → thicken (dewatering)
An MSMPR crystallizer precipitates the salt, then a gravity thickener dewaters the crystal slurry into a dense underflow while a clarified overflow leaves the top — the solid-liquid separation a hydrometallurgy plant runs before filtration.
5 unit ops • BRINE
346 2
View & openGrinding-circuit hydrocyclone classifier
A hydrocyclone classifies a mineral slurry by particle size — the unit that closes every closed-circuit grinding loop (mill → cyclone, coarse underflow recycled to the mill). A quartz slurry (200 µm mean, spread by a log-normal PSD) is split about a 100 µm corrected cut size (Plitt 1976): the coarse solids report to the thick underflow and the fines to the dilute overflow, split by the short-circuit recovery. The underflow comes out much coarser (~300 µm mean) than the overflow (~80 µm), and the solids mass balance closes exactly. Honest scope: the d50c is the real Plitt correlation, but the partition sharpness and water recovery are screening params.
5 unit ops • COOLPROP
258 1
View & openCrystallization + granulation finishing
A continuous MSMPR crystallizer, cake filter, and dryer feed a granulator that grows the dried crystals into free-flowing granules — the finished-product train after the mother liquor and dryer vapor leave.
8 unit ops • PENG-ROBINSON
346 2
View & openCrystallization with agglomeration (distributed CSD)
An MSMPR crystallizer solved with the rigorous distributed population balance (not just moments): the full crystal-size distribution is computed on a size grid, and an agglomeration (aggregation) kernel combines fine crystals into larger ones — coarsening the mass-weighted mean size (d43) and broadening the distribution (CV rises above the growth-only MSMPR value of ~1.0) while conserving mass exactly. The distribution, its coefficient of variation, and d43 propagate on the solid stream into the filter and dryer — the gPROMS/gCRYSTAL capability the moment model structurally cannot provide.
7 unit ops • PENG-ROBINSON
324 0
View & openSolids train (crystallize → filter → dry)
An MSMPR crystallizer feeds a cake filter and dryer — the crystal size and cake moisture propagate on the stream's solids payload (pharma / minerals workflow).
7 unit ops • PENG-ROBINSON
346 2
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