Delimitation of the final pit of open-pit mines using the maximum flow Pseudoflow method

Document Type : Research Paper

Authors

1 Department of Mining Engineering, Faculty of Engineering, National University of Trujillo, Trujillo, Peru.

2 Faculty of Chemical Engineering, National University of the Altiplano, Puno, Perú

10.22059/ijmge.2024.360603.595076

Abstract

The primary aim of this study was to define the final pit boundaries utilizing the maximum flow Pseudoflow method in an open-pit mining context. Our methodology encompassed exploratory data analysis (EDA), establishing geomechanical and economic factors, and assessing the final pit. The study was conducted using Python 3.11 and SGeMS 3.0. We discovered that our block model comprised 480,000 blocks of 10x10x10 m dimensions. We generated 20 pits with revenue factors between 0.1 to 2, increasing by increments of 0.1. The Study indicated that pit 20 was optimal, with an estimated NPV of 17855 MUSD, extracting 212 million tons of ore and 58 million tons of waste rock, achieving a stripping ratio based on block model and market conditions, and is subject to change with further block sequencing analysis. Nevertheless, pit 20 emerged as the most advantageous when considering economic feasibility, given its high estimated NPV and favorable stripping ratio.

Keywords

Main Subjects


[1] Khalokakie, R., Dowd, P., Fowell, R. (2000). A windows program for optimal open pit design with variable slope angles. International Journal of Surface Mining, Reclamation and Environment, 14. 14, 261-275.
[2] Elahi, E., Kakaie, R., Yousefi, A. (2011). A new algorithm for optimum open pit design: Floating cone method III. Journal of Mining & Environment, 2(2), 118-125.
[3] Kolapo, G., Oniyide, K., Said, A., Lawal, M. (2022). An Overview of Slope Failure in Mining Operations. Mining, 2(2), 350-384.
[4] Mariko, I., Mireku-Gyimah, D. (2018). Open Pit Optimisation and Design of Tabakoto Pit at AngloGold Ashanti Sadiola Mine Using Surpac and Whittle Software. Ghana Mining Journal, 18(2), 37-47.
[5] Frempong-Boakye, V. (2004). Application of Surpac and Whittle Software in Open Pit Design: A Case Study. Unpublished MSc Thesis, University of Mines and Technology, 99-100.
[6] Amankwah, H. (2011). Mathematical Optimization Models and Methods for Open-Pit Mining," Linköping. LinköpingStudiesinScienceandTechnology.Dissertations, 1396.
[7] Boachie, S. (2013). Optimised Open Pit Design Using Minesight Software - A case study at Bisha Mining Share Company, Eritrea, East Africa. Ghana.
[8] Dongboi, M. (2013). Optimisation and Design of Open Pit of the Camplebell Town Ridge Deposit at London Mining Company Limited, Sierra Leone. Ghana.
[9] Elias, I. (2013). Optimisation and Design of an Open Mine: A Case Study. Tarkwa.
[10]            Akisa, D., Mikeru-Gyimah. (2015). Application of Surpac and Whittle Software in Open Pit Optimisation and Design. Ghana Mining Journal, 15(1), 35-43.
[11] Asad, M., Topal, E. (2011). Net Present Value maximization model for optimum cut-off grade policy of open pit mining operations. Journal of the Southern African Institute of Mining and Metallurgy, 111(11).
[12] Pana, M. (1965). The simulation approach to open pit design. Proceedings of the 5th symposium on the application of the computers and operations research in the mineral industries (APCOM), 127-135.
[13] Wright, E. (1999). Moving cone II – a simple algorithm for optimum pit limits design. Proceedings of the 28th symposium on the application of the computers and operation research in the mineral industries (APCOM). 367-374.
[14] David, M., Dowd, P., Korobov, S. (1974). Forecasting departure from planning in open pit design and d grade control. Proceedings of the 12th symposium on the application of computers and operations research in the mineral industries (APCOM), 2, 131-142.
[15] Akisa, D., Zhang, J., Huang, G., Richard, M., Matidza, M. (2020).  Ultimate Pit Limit Optimization using Boykov-Kolmogorov Maximum Flow Algorithm. Journal of Mining and Environment (JME).
[16] Musenge, P., Chanda, E., Bunda, B., Kaunde, J., Bokwala, B., Fyama, B., Kanke, S., Sebastian, A. (2022). Ultimate Pit Limits using Maximum Flow Algorithm Ford and Fulkerson: The Case of Study of North Mutoshi Project, DRC. International Journal of Engineering Research & Technology (IJERT), 11(2).
[17] Lerchs, H., Grossman, I. (1965). Optimum design of open pit mines. CIM Bulletin, 58, 47-54.
[18] Gherson, M. (1987).  Heuristic approaches for mine planning and production scheduling. International Journal of Mining and Geological Engineering, 5(1), 1-13.
[19] Meisam, S., Reza, K., Mohammad, A. (2019). Mathematical relationship between ultimate pit limits generated by discounted and undiscounted block value maximization in open pit mining. Journal of Sustainable Mining, 18, 94-99.
[20] Hochbaum, D. (2008). The Pseudoflow Algorithm: A New Algorithm for the Maximum-Flow Problem. Operations Research, 56(4), 992-1009.
[21] Boldyreff, A. (1955). Determination of the maximal steady state flow of traffic through a railroad network. J. Oper. Res. Soc. Amer, 3(4), 443-465.
[22] Golberg, A., Tarjan, E. (1988). A new approach to the maximum flow problem. J.ACM, 35, 921-940.
[23] Talaei, M., Mousavi, A., Sayadi, A. (2021). Highest-Level Implementation of Push–Relabel Algorithm to Solve Ultimate Pit Limit Problem. Journal of Mining and Environment JME, 12(2), 443-455.
[24] Radzik, T. (1993). Parametric flows, weighted means of cuts, and fractional combinatorial optimization. Complexity in Numerical Optimization, 351-386.
[25] Javad, G., Elham, L., Mehdi, N., Mohammad, S. (2022). Designing the most probable final pit limit of open pit mines considering price uncertainty. Journal of Analytical and Numerical Methods in Mining Engineering, 12(32), 77-86.
[26] Xiao, X., Qing, Y., Zong, W. (2021). Open pit limit optimization considering economic profit, ecological costs and social benefits. Transactions of Nonferrous Metal Society of China, 31(12), 3847-3861.
[27] Avalos, S., Ortiz, J. (2020). A guide for pit optimization with Pseudoflow in Python. Predictive Geometallurgy and Geostatistics Lab, Queen's University, Annual Report 2020, 11, 186-194.
[28] Thy, T. (2022). The application of Geostatistical software (SGeMS), llwis software and Kriging interpolation to simulate 3D stratigraphic structure model urban Rach Gia town, Kien Giang, Viet Nam. ICCEE, 347.
[29] Deutsch, C. (1998). Cleaning categorical variable (lithofacies) realizations with maximum a-posteriori selection. Canadá.
[30] Ares, G., Castañon, C., Álvarez, I., Arias, D., Buelga, A. (2022). Open Pit Optimization Using the Floating Cone Method: A New Algorithm. Minerals, 12(4), 495.
[31] Bai, X., Turczynski, G., Baxter, N., Place, D., Sinclair-Ross, H., Ready, S.  (2017). Pseudoflow Method for Pit Optimization. Dassault Systemes.
[32]Deutsch, M., Dagdelen, K., Johnson, T. (2022). An Open-Source Program for Efficiently Computing Ultimate Pit Limits: MineFlow. Nat Resour Res, 31, 1175-1187.
[33] Picard, J., Smith, B. (2004). Parametric Maximum Flows and the calculation of optimal intermediate contours in Open Pit Mine Design. INFOR: Information Systems and Operational Research, 42(2), 143-153.
[34] Hochbaum, D., Chen, A. (2000). Performance Analysis and Best Implementations of old and New Algorithms for the Open-Pit Mining Problem. Operations Research, 48(6), 849-914.
[35] Picard, J. Maximal Closure of a Graph and Applications to Combinatorial Problems. Management Science, 22(11), 1268-1272.
[36] Jelvez, E., Ortiz, J., Morales, N., Askari, H., Nelis, G. (2023). A Multi-Satage Methodology for Long-Term Open-Pit Mine Production Planning under Ore Grade Uncertainty. Mathematics, 11(18).
[37] Thomas, G. (1996). Pit optimization and mine production scheduling-the way ahead. APCOM 26 SME Inc, 221-228.Abdollahi, H., Saneie, R., Shafaei, S. Z., Mirmohammadi, M., Mohammadzadeh, A., & Tuovinen, O. H. (2021). Bioleaching of cobalt from magnetite-rich cobaltite-bearing ore. Hydrometallurgy, 204, 105727.