multivariate regression

Due to the role of recovery in calculating the economic value of ore blocks and the impact of the block's economic value on the design calculations of the final pit and production planning, determination of the amount of metal recovery from the ore material sent to the processing plant is very important. The aim of this study is to investigate the capability of estimating the recovery rate of ore in qualitative manner with three methods based on data classification from data mining techniques and quantitatively using multivariate regression and artificial neural networks. Hence, the Miduk copper mine was studied using 58 analyzed samples of the feed of the plant, including Cu, CuO and CuS grades, and the recovery rate of Cu in the final product of the plant. The process of predicting the total recovery of the reserve was made qualitatively by decision tree method, classification based on Bayes rule and k-nearest neighbor (kNN) classification algorithm. For quantitative estimation of recovery, multivariate regression and artificial neural network models were established between the mentioned grade parameters and recovery rates (For 47 samples of 58 samples) and with the 11 additional analyzed samples, the obtained models were validated. The coefficient of (R2), Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) in the regression model were 0.77, 0.027722 and 0.029722, respectively, and in the artificial neural network model, 0.82, 0.015753 and 0.024040, respectively. Therefore, the artificial neural networks model acts as a more accurate tool for predicting recovery versus the multivariable regression model. The results of sensitivity analysis of artificial neural network model showed that Cu grade is the most important factor and grade of CuO and CuS, respectively, as well as other factors influencing the changes in recovery rate.

Due to the increasing demand for more production rates and output from oil reservoirs, the re-activation of oil wells in Iran is a vital task. Oil production reduces overtime because of a decrease in reservoir's pressure and also as a results of the closure of cracks and microscopic holes. Hydraulic fracture, as a method for stimulating oil reservoirs related to various factors, including characteristics of the environment in which the fracture grows. Mechanical properties of layers has been recognized as one of the most effective parameters on the progress of hydraulic fracture and its geometry. In this study, the primary rock was considered as non-cracked. In this research, numerical modeling was done by ABAQUS software in 21 different cases for which the effect of each input parameters on the hydraulic fracture pressure was investigated by performing sensitivity analysis. The input parameters were well's data and included Young's modulus, minimum and maximum horizontal stress, vertical stress, tensile strength, Poisson''s ratio and pore pressure. The required data is obtained from the excavated wells in carbonate rocks in Iran. The results showed minimum horizontal stress has the highest impact on the hydraulic fracture pressure. Finally, using SPSS software and by performing multivariate regression analysis, a formula was made using the numerical modeling data to estimate the hydraulic fracture pressure. The results of statistical analysis corroborate the precision of regression line and consequently the suggested formula. In this formula, the parameters such as minimum horizontal stress, the difference between minimum and maximum horizontal stresses, pore pressure and tensile strength, have the most effect on the hydraulic fracture pressure respectively. Using the presented formula in this study, the hydraulic fracture pressure in carbonate wells with different properties could be obtained. Gaining this pressure will help to determine the proper pump and case to reduce operating costs.