Metallurgical Response Curve Calibration Guide
The Metallurgical Response Curve (MRC) Calibration Guide is a standardized methodology for quantifying and modeling the relationship between feed ore characteristics (e.g., grade, mineralogy, hardness) and downstream metallurgical performance (e.g., recovery, concentrate grade, energy consumption). It enables predictive process optimization by empirically calibrating dynamic response curves using plant data, laboratory testwork, and statistical regression. The guide provides protocols for data validation, curve fitting, uncertainty quantification, and integration into digital twin and real-time optimization frameworks.
📖 Overview
📑 Key Components
🎯 Applications
- ✓ Block-model-based recovery forecasting
- ✓ Real-time flotation circuit optimization
- ✓ Mine-to-mill reconciliation and bottleneck diagnosis
📐 Key Formulas
Multivariate Recovery Response Function
R_i = f(\text{Cu}_{\text{lib}}, \text{S}_{\text{tot}}, D_{80}, \text{HGI}, \text{pH}, \text{[collector]}) + \varepsilon_i
Predicts metal recovery (R_i) for ore sample i as a function of liberation-corrected grade, total sulfur, grind size (D80), Hardgrove Grindability Index (HGI), pH, and collector concentration; ε_i is the residual error term
Calibrated Specific Energy Model
E_{sp} = \alpha \cdot \left(\frac{\text{Wi}}{10}\right) \cdot \left(\frac{1}{\sqrt{P_{80}}} - \frac{1}{\sqrt{F_{80}}}\right) \cdot \left[1 + \beta \cdot \left(\frac{\text{SiO}_2}{\text{Fe}_3\text{O}_4}\right)\right]
Modified Bond equation incorporating mineralogical ratio correction factor to predict specific grinding energy (E_sp) in kWh/t
Bayesian Prediction Interval
R_i^{\text{pred}} \in \left[\hat{R}_i - t_{\nu,1-\alpha/2} \cdot \sigma_{\text{pred}},\; \hat{R}_i + t_{\nu,1-\alpha/2} \cdot \sigma_{\text{pred}}\right]
95% prediction interval for recovery estimate, where σ_pred combines model parameter uncertainty and residual variance