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.