Recycle changes the feed.
Cleaner tails return to the rougher. Changing cleaner selectivity changes the circulating load, upstream grades and cleaner capacity requirement.
+ 03 / CIRCUIT OPTIMISATION LAB
Balance the circuit.
Improve the whole.
Follow solids and copper through roughing, scavenging, cleaning and recycle. See how one operating change affects every connected stream.
ILLUSTRATIVE FLOTATION CIRCUIT Steady-state balance · Synthetic response model · Dry solids basis
AUTOMATED WALKTHROUGH 1 / 6
Observe the initial circuit.
Follow the feed, recycle and product balance before optimising.
A repeating sequence of balanced steady-state scenarios. Animated transitions illustrate setting changes, not physical process dynamics. Adjust any slider to take manual control.
CONNECTED PROCESS / CURRENT SETTINGS
Every stream counts.
Circuit Cu recovery
Product grade
Recycle / fresh feed
Tail grade
CIRCUIT-WIDE OBJECTIVE
Maximise recovered copper.
Potential change in recovered CuAt the same fresh-feed conditions
| Performance / setting | Current | Optimised |
|---|
CIRCUIT MASS BALANCE
Trace the material.
Internal streams include recycle. Only fresh feed, final concentrate and final tails define the external balance.
| Stream | Solids (t/h) | Cu grade (%) | Copper (t/h) |
|---|
The circuit is the objective.
Local gains have a cost.
Higher collection can recover more copper while carrying more gangue. Optimisation must respect product grade and capacity across the connected circuit.
Balance before optimisation.
Each candidate is solved for copper and gangue through every stage. Only candidates meeting both circuit constraints are considered feasible.
Model equations and assumptions +
For each component j (copper or gangue), combined rougher–scavenger recovery is rⱼ = rR,ⱼ + (1 − rR,ⱼ)rS,ⱼ. With cleaner recovery cⱼ and fresh component feed Fⱼ, rougher input is Iⱼ = Fⱼ / [1 − (1 − cⱼ)rⱼ]. Final concentrate is cⱼrⱼIⱼ, final tails are (1 − rⱼ)Iⱼ and cleaner recycle is (1 − cⱼ)rⱼIⱼ.
Normalised intensity a and selectivity s range from 0 to 1. Copper splits: rR = 0.76 + 0.17a; rS = 0.45 + 0.22a; c = 0.94 − 0.08s. Gangue splits: rR = 0.07 + 0.12a²; rS = 0.035 + 0.065a²; c = 0.42 − 0.26s. All coefficients are synthetic. The optimiser searches a 101 × 101 grid and maximises product copper flow subject to minimum concentrate grade and maximum combined cleaner-feed solids.
This demo is a steady-state, two-component dry-solids balance. It excludes water, time delays and changing inventories. The flotation application’s dynamic mass balance additionally accounts for accumulation over time; a plant implementation requires calibrated kinetics, measurement reconciliation and site-specific constraints.