Real flowsheets, already solved
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Grinding 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, and that is a limitation rather than a choice. A real grinding circuit recycles the screen oversize back to the mill, and it cannot be drawn here: a mixer flashes its outlet and drops the stream's solids payload, so the recycled ore arrives at the mill with no particle size and the mill rejects it. The same limitation stops a cyclone feeding a baghouse in series (see the dust-collector example). Stated here because an open circuit reports a lower circulating load and a coarser product than the closed circuit a plant actually runs.
5 unit ops • PENG-ROBINSON
9 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
9 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
78 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
106 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
121 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
168 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
170 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
173 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 • NRTL
165 1
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
79 0
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 • NRTL
167 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 • NRTL
146 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 • NRTL
167 1
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