How to simulate 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.
- 1Open the ready-made model
Open the "Grinding circuit: what a size reduction costs" model in the MaximaLabs workspace — no install, no license. It loads live on the canvas, ready to edit and run.
- 2Confirm the thermodynamics
This process is modeled with the PENG-ROBINSON property package over co2 — already selected, so the phase equilibrium and enthalpy are physically consistent from the first run.
- 3Review the flowsheet
The flowsheet chains MILL, Screen. Every block is a real, solvable unit op you can reconfigure on the canvas.
- 4Run the simulation
Click Run. The deterministic solver converges the material and energy balances (recycles included) and fills the live stream table — the AI never invents a number.
- 5Read the results and iterate
Inspect the converged streams, tweak a spec, and re-run — or ask the AI copilot to explain a result or diagnose a failed solve in plain English.
- Thermodynamics
- PENG-ROBINSON
- Components
- co2
- Unit operations
- MILLScreen
Opens live on the canvas — free, no install.
Explore the model & flowsheetFrequently asked questions
- What does the Grinding circuit: what a size reduction costs model simulate?
- 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.
- Which thermodynamic method does it use?
- The PENG-ROBINSON property package, over co2 — already selected. You can switch the method on the canvas before running.
- Which unit operations are in the flowsheet?
- It chains MILL, Screen. Every block is a real, solvable unit operation you can reconfigure, add to, or remove.
- Do I need to install software or buy a license?
- No. Grinding circuit: what a size reduction costs runs entirely in your browser on MaximaLabs — free, no install, no license. Open the model to load it live and run the deterministic solver.
More guides like this
Grinding-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.
Superheated-steam drying loop with MVR heat recovery
A wet cake is dried in a superheated-steam dryer (steam as the drying medium instead of hot air), and the evaporated moisture — pure steam — is recovered by mechanical vapor recompression (MVR) plus a trim superheater into high-grade superheated steam that reheats the recirculating drying medium. Superheated-steam drying is the energy-efficient route for biofuel and food solids (distillers' grains, beet pulp, lignite): because the drying atmosphere is steam, the evaporated water leaves as more steam whose latent heat is recompressed and reused, instead of being lost in a humid exhaust.
Dust 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.
Solids 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).
Crystallization 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.
Crystallization + 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.