Slide 1: Production Reconciliation for Mineral Resource Modelling in a Porphyry Copper Gold Deposit
PRODUCTION RECONCILIATION FOR MINERAL RESOURCE MODELLING IN A PORPHYRY COPPER GOLD DEPOSIT W ASSIBEY-BONSU, J DERAISME, E GARCIA, P GOMEZ AND H ROIS August 2015
Slide 2: The Great Man: Professor Daniel Gerhardus Krige
The Great man Professor Daniel Gerhardus Krige 26 August 1919 – 2 March 2013 2
Slide 3: Production reconciliation of a multivariate uniform conditioning technique
Production reconciliation of a multivariate uniform conditioning technique for mineral resource modelling in a porphyry copper gold deposit 3
Slide 4: Outline
Outline • Introduction. • Methodology – Recap of Uniform Conditioning – Localized Multivariate Uniform Conditioning • Case study. • Production reconciliation case study, based on a porphyry copper gold deposit in Peru. • Conclusions. 4
Slide 5: Introduction
Introduction • The extension of Uniform Conditioning (UC) techniques to the multivariate case is available by using the Discrete Gaussian Model (DGM). • It is based on the use of correlations between different variables and one “main” variable used for selecting the selective mining unit’s (smu’s).
Slide 6: UC Methodology
UC Methodology • We estimate for a selection block v: - Ore: T ( z ) 1Z1 (v ) z1 - Main Metal: Q1 ( z1 ) Z1 (v)1Z1 ( v ) z1 (to be multiplied by block tonnage = volume x density) • For a second element we want also: - Secondary Metal: 6
Slide 7: UC Methodology
UC Methodology In the univariate case, the change of support is based on the three assumptions (DGM): – E[Z(v)] = E[Z(x)] = m – Krige’s relationship: D2(v|D)=D2(0|D)-g(v,v) – Cartier relationship: E[Z(x)|Z(v)] = Z(v) 7
Slide 8: DGM for change of support
DGM for change of support • The block distribution is modelled by the block anamorphosis Z(v) = r [ Y v] • The point and block anamorphosis are related through the integral relation: r ( y ) (ry 1 r 2 u ) g (u ) du • The change of support coefficient r is calculated by means of the Krige
Slide 9: Multivariate UC
Multivariate UC Additional assumptions are: • Z1(v) conditional to Z1(V)* is independent of the other element grades of the panel. The UC estimates for the main variable are the same as in the univariate case. • Z1(v) and Zi(v) conditional to (Z1(V)*, Zi(V)*) are independent of the other element gra
Slide 10: UC in the multivariate case
UC in the multivariate case • Distribution of Zi(v) for a generic block v in panel V is conditioned by Zi(V)*. • We want at zero cutoff: E[Zi(v) | Zi(V)*] = Zi(V)* so Zi(V)* is implicitly assumed to be conditionally unbiased: E[Zi(V) | Zi(V)*] = Zi(V)*. • UC estimates: Ore TV ( z )* E 1Z (v )
Slide 11: Localized Uniform Conditioning
Localized Uniform Conditioning • UC consists of estimating the grade distribution on smu support within a panel, conditioned to the estimated panel grade, usually based on Ordinary Kriging (OK). • In this case study, Simple Co-Kriging (SK) with local mean has been used to condition the panel grades,
Slide 12: Multivariate Uniform Conditioning
Multivariate Uniform Conditioning Extension to multivariate case: The metal quantity of the secondary variables are obtained from multivariate UC, i.e. the tonnages and the related cut-offs are dependent only upon the main variable. Thus, the mean grades of secondary variables can be interpolated wi
Slide 13: Case Study: Geology and database
Case Study: Geology and database • The mineralization is found in intrusive rocks within a sedimentary host environment. • Oxidation, weathering, leaching and subsequent secondary enrichment has led to the formation of four mineral domains with different metallurgical characteristics. • Sulphide min
Slide 14: Geology Modelling (Porphyry Cu & Au Ore body)
Geology Modelling (Porphyry Cu & Au Ore body) A view of the deposit showing geological domains – Cerro Corona, South America Oxide Supergene Mixed Hypogene Barren Diorite Cretaceous Sediments 14
Slide 15: Case Study: Geology and database
Case Study: Geology and database • The resource drilling data grid spacing were on average up to 50m x 100m. • These were composited on a 2m basis, and were used to derive the LMUC estimates. • The initial MUC’s were based on simple co-kriging of 40m x 40m x 10m panels, assuming 10m x 10m x 10m smu’
Slide 16: Case Study: porphyry copper gold deposit in Peru
Case Study: porphyry copper gold deposit in Peru. Drill-hole layout of the Annulus domain 16
Slide 17: Case Study: porphyry copper gold deposit in Peru
Case Study: porphyry copper gold deposit in Peru • Two economic elements are considered: total gold and total copper (AUTOT, CUTOT). • Using economic parameters, both elements are combined into the Net Smelter Return (NSR). CUTOT AUTOT NSR CUTOT 0.69 0.88 AUTOT 0.69 0.95 NSR 0.88 0.95 Matrix of coef
Slide 18: Case Study
Case Study • In addition to the Resource drilling data, a comprehensive 6m x 5m blast hole data grid was available from mining. The blast hole data were not used for the MUC/LMUC Resource. • These were used as the follow-up “actual” block values for judging the Follow-up Database comparative efficie
Slide 19: Case Study
Case Study • The efficiency of the reconciliations is measured on the basis of the spreads of percentage errors, defined as follows: Percentage Error = (Actual/Estimate -1)x100% Basis for the Production reconciliations • Actual represents Plant production, or in-situ grade control block estimates, b
Slide 20: Case Study: Results
Case Study : Results Support correction is achieved with sill normalization NSR CUTOT AUTOT Punctual Variance (Anamorphosis) 276.117 0.08 0.528 Variogram Sill 270.45 0.076 0.536 Gamma (v,v) 128.191 0.045 0.212 Real Block Variance 147.926 0.035 0.316 Real Block Support Correction (r) 0.7754 0.69 0.82
Slide 21: Case Study: porphyry copper gold deposit in Peru
Case Study: porphyry copper gold deposit in Peru • In providing the co-kriging panel conditioning estimates required for the MUC/LMUC, significant conditional biases were observed with Ordinary co- kriging (OK), as demonstrated by the large negative kriging efficiencies (KE) and poor slopes of regre
Slide 22: Case Study: porphyry copper gold deposit in Peru
Case Study: porphyry copper gold deposit in Peru • The LMUC approach provides smu grades with a variability closer to the actual variability. Variable Estimated LMUC "Actual" Dispersion Dispersion Variance Variance Gold 0.33 0.38 Copper 0.08 0.05 Table II: SMU Dispersion variance of “Actual” versus
Slide 23: Monthly Production Reconciliation
Monthly Production Reconciliation • Provides the production reconciliation of the monthly LMUC Resource estimates with the corresponding Plant results. • The reconciliation results are provided on the basis of the spreads of the percentage errors. • The lower and upper 10% confidence intervals have
Slide 24: Distributions of Percentage Errors
Distributions of Percentage Errors Tonnes, Au and Cu grades for monthly reconciliation (Resource model vs Plant) 24
Slide 25: Reconciliation with Production for different Periods
Reconciliation with Production for different Periods • Distribution of percentage errors between Resource model and Plant production over various production periods. • The results further show percentage errors of +6%/+2%/-7% on a quarterly (i.e. 3 monthly) basis for tonnes, gold and copper grades r
Slide 26: Reconciliation: MUC/LMUC vs Grade Control
Reconciliation : MUC/LMUC vs Grade Control • Reconciliation between Resource models and the Grade control model • The table below shows that the Resource models compare well with the Grade control model (also when compared to the internationally accepted 15% errors: e.g. for annual production period
Slide 27: Reconciliation: LMUC vs Grade Control
Reconciliation : LMUC vs Grade Control • However, the individual LMUC selective mining block estimates, based on Simple co-kriging conditioning (SK), show some conditional biases as reflected by the slope of regressions of 0.7/0.52 for Au and Cu respectively. • The conditional biases are as a result
Slide 28: Regression of LMUC vs Grade Control
Regression of LMUC vs Grade Control 28
Slide 29: Conclusions
Conclusions • Gaussian models (in this case MUC) used for calculating recoverable resources provide consistent results in modelling the change of support and the information effect in the multivariate case. • The production reconciliation results show the overall advantage gained by using MUC/LMUC e
Slide 30: You Made the World a Better Place
You Made the World a Better Place Professor Daniel Gerhardus Krige 26 August 1919 – 2 March 2013 30