# Calculations of Novel AFS Performance Modeling with Elliptical and Spherical Geometries

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## Calculations of Novel AFS Performance Modeling with Elliptical and Spherical Geometries

Surface mine production scheduling and sequencing are used to maximize the expected profit and investment returns from mining operations. They are also used to determine future mining investments, evaluate alternative investment options, and conserve and develop the pit resources. These processes are complicated by the fact that open pit operations are conducted on multiple benches and involve concurrent excavation of both ore and waste. The pit geometries and expansion rates, and the periodic volume of materials from different benches in a multi-bench, multi-face open pit mine determine the equipment requirements, which impact the maximized pit value. Under such regimes, fast, accurate and repeatable estimation of pit volumes are required for just-in-time (JIT) production decisions. The analytical geometric volume calculations require time lags that prevent rapid information for JIT decisions. The introduction of the novel at-face-slurry (AFS) oil sands method require fast, accurate and repeatable pit volume estimation using continuous flow process. In this study, a continuous flow process via partial differential equations (PDEs) has been used to model material volume, as well as pit layout changes from circular and elliptical geometries of an oil sands mine and compared with analytical geometric methods. The models were solved within Matlab. The results show very close agreement between geometric values and those obtained from PDEs for the pit configurations. This work represents the first successful attempt at using PDE in geometric calculations for open pit mines. The economic analysis shows that the NPV of the current mining system (CMS) is \$3.2 x 1010 while that for the cyclic excavator conveyor belt control system (CycEx CBCS) is \$4.06 x 1010. The PI for the CMS and CycEx CBCS options are 19.37 and 43.37 respectively. The IRR of the CMS option is 29.02% while that of the CycEx CBCS option is 33.37%. The DPBP for the CMS and CycEx CBCS options are 3.24 months and 1.92 months, respectively. The CMS option has an operating cost of \$1.386/tonne (\$2.774/barrel) while that of the CycEx CBCS option is \$0.779/tonne (\$1.558/barrel). The economic parameters show that the CycEx CBCS option is more economically viable, and the requirement for a fast, accurate and repeatable process for generating pit volumes is met by using PDEs.

Author(s) Details

Raymond S. Suglo
Botswana International University of Science & Technology, Palapye, Botswana

Samuel Frimpong
Missouri S&T, Rolla, USA