Determination of Optimal Block Dimensions Using Geostatistical and Simulation Methods in Surk Iron Ore and Esfordi Phosphate Mines

Summary
In this study, the method of selecting the optimal dimensions for block modeling in reserve estimation is discussed. Data gathered from Surk iron ore and Esfordi phosphate mines were used. A total of 256 block models were created for the mines, and kriging efficiencies were calculated for a wide range of block dimensions. In Gaussian conditional simulation method, 20 realizations were created and the variance between the realizations was calculated. With this method, the dimensions of 7.5×7.5×7.5 m³ were calculated for Surk mine and 10×7.5×10 m³ for Esfordi mine. The reserves with optimal block dimension were estimated for Surk mine about 9.84 million tons and for Esfordi mine about 11.93 million tons.
 
Introduction
An important part of mineral deposit modeling is block modeling. In this paper, various geostatistical methods such as estimation variance, kriging efficiency and Gaussian conditional simulation have been used to select the optimal block dimensions for Surk iron ore and Esfordi phosphate mines.
 
Methodology and Approaches
Statistical analysis of Surk and Esfordi iron ore data shows that the data follow an abnormal distribution. Normal Score Transform (NST) is applied for transferring data to Gaussian distribution. Variography of iron and phosphorus composite data was performed in different directions. At first, the optimal block size was determined using kriging efficiency values. In this method, the criterion for selecting the optimal dimensions was to maximize the kriging efficiency. Because the optimal dimensions obtained by kriging efficiency method are not compatible with the operating conditions and anisotropy of the deposit, in the next step, geostatistical simulation method was used. In the simulation process, 20 realizations were considered. The criterion for selecting the optimal block dimensions was to minimize the variance between the realizations in each block.
 
Results and Conclusions
In the Gaussian conditional simulation method, with the idea that the smaller the variance between the realizations, the greater the similarity of the realizations,  the optimal dimensions were calculated for the Surk mine as 7.5×7.5×7.5 m³ and for the Esfordi mine as 10×10×7.5 m³. The dimensions obtained from Gaussian conditional simulation method are in good agreement with the anisotropic ratios of each mine.
According to the optimal dimensions obtained from the Gaussian simulation method, the reserve estimation was made. Based on 20% iron cut off grade, the tonnage of Surk mine is 9.84 million tons with an average grade of 46.07%, and based on the cut off grade of 5% phosphorus, the tonnage of Esfordi mine is 11.93 million tons with an average grade of 13.85%.