Gold Processing5 min read
Twelve bottle-roll points scattered across dose and pH will still leave an argument about “the best condition.” A designed experiment answers a different question: which factors…
Author: Wayne Ncube
Twelve bottle-roll points scattered across dose and pH will still leave an argument about “the best condition.” A designed experiment answers a different question: which factors actually move recovery, how large the effect is, and where the model stops being trustworthy. Central-composite designs provide a useful way to test those questions; this article uses a teaching case to make the method practical.
Illustrative design points
Each marker is an illustrative bottle-roll run from a central-composite teaching design — not a drawn curve.
Hold constant and document:
Vary only the factors the design assigns. If pH drifts because lime addition is inconsistent, the design is already broken.
| Design | Factors | Coded region | Centre | Illustrative max recovery |
|---|---|---|---|---|
| Cyanide (NaCN) | A: 147.6–232.4 ppm · B: pH 9.90–10.60 | 13 runs, central composite | ~190 ppm · pH 10.25 | 92.10% at 220 ppm / pH 10.5 |
| YX500 | A: 0.14–4.66 kg/t · B: pH 9.90–10.60 | 13 runs, central composite | ~2.4 kg/t · pH 10.25 | 96.23% at 4.66 kg/t |
Both fit first-order models of the form Recovery = b₀ + b₁·A + b₂·B. Interactive cursor:
Illustrative first-order fits:
| Quantity | NaCN model | YX500 model |
|---|---|---|
| Equation | R = 55.8326 + 0.0996·A + 1.3626·B | R = −72.6799 + 3.429·A + 14.6514·B |
| Model F | 43.50 | 12.07 |
| Model p | <0.0001 | 0.0022 |
| Dose term | highly significant | significant |
| pH term | not significant (p ≈ 0.32) | significant (p ≈ 0.02) |
| Lack of fit p | 0.5652 (not significant) | 0.1201 (not significant) |
| R² | 0.897 | 0.707 |
| Adjusted R² | 0.876 | 0.649 |
| Mean response | 88.73% | 85.73% |
Interpretation discipline:
An illustrative tailings study varies particle size (75–212 µm) and cyanide concentration (600–1200 ppm) with bottle rolls on thickener-underflow composites. The teaching method sketch uses ~500 g solids, ~1:1 L/S, quicklime to pH 11, a 24 h leach with hourly solution samples, residue dried at 105 °C, cone-and-quartering, and XRF for elements of interest.
Use the same skeleton for any new ore:
| Step | Decision |
|---|---|
| Composite sampling | One representative basis for feed and residue |
| Factor ranges | Wide enough to show curvature or clear slopes |
| Centre repeats | ≥3–5 to estimate pure error |
| Controls | Plant pH, time, density as defaults |
| Response | Residue Au, solution Au, free CN remaining, consumption |
Illustrative economic comparison (using the example assumptions): at maximum recovery, YX500 net ~4.31 B Tzs vs cyanide ~4.76 B Tzs; near 90% recovery the gap narrows (~4.61 vs ~4.66 B). The example basis includes ~47,000 t/month, head grade ~0.87 g/t, gold price ~4 M Tzs/oz, reagent prices ~8 M Tzs/t (cyanide) and ~4 M Tzs/t (YX500).
net value = recovered gold value − reagent cost − operating cost − waste treatment − incremental capital
A 96% recovery that requires kg/t-scale reagent and different waste handling can lose to a stable 90–92% cyanide circuit.
1defrecovery_cyanidecyanide_ppmph2return55.83260.0996cyanide_ppm1.3626ph34defrecovery_yx500kg_per_tph5return72.67993.429kg_per_t14.6514ph67printf"NaCN 220 ppm, pH 10.5 -> {recovery_cyanide(220, 10.5):.2f}%"8printf"YX500 4 kg/t, pH 10.5 -> {recovery_yx500(4.0, 10.5):.2f}%"
13 runs
central-composite design size in both illustrative trials
R² 0.897
NaCN first-order fit (teaching case)
4.13 pp
illustrative max recovery gap: YX500 vs NaCN
| Design mistake | What it looks like later |
|---|---|
| No centre replicates | Cannot separate noise from curvature |
| Factors coupled (pH fixed by reagent) | Confounded coefficients |
| Unequal ore splits | Entire surface is ore variability |
| Optimising on residual-free extrapolation | Pilot fails outside tested dose |
| Recovery-only decision gate | Economics and waste surprise the board |
Bottle-roll and DOE work still involve cyanide and alternate lixiviants under laboratory controls. Follow the site chemical hygiene plan; this article does not replace method statements.
Further reading in this series: