Cut-off Grade Research Articles

Creation of Histograms for Data in Various Mineral Resource and Engineering Problems: A Review of Existing Methods and a Proposed New Method to Define Bin Number

Histograms are widely used in geosciences for data analysis and visualization. In cases where a distribution is not fitted to data, histograms are often used to address various sampling- and interpolation-related aspects. However, the results of these applications are substantially affected by the histogram’s number of bins as determined by several binning methods. This paper proposes a new binning approach and compares it with various standard approaches to demonstrate the relative performance of the new approach. Cut-off grade optimization for polymetallic deposits, Monte-Carlo modeling, and derivation of conditional distribution, all of which use histograms, are used as case studies. The proposed technique is based on calculating the squared error for each bin in a histogram, and combining the error values to evaluate the total error for each histogram. The new technique then selects the bin number which minimizes the total error. The results showed that the new binning approach is well suited for binning small datasets and can be used in geoscience applications if needed.

Optimal mill cut-off grade modeling in the mineral deposits via MIP: Haftcheshmeh copper deposit

Cut-off grade play a critical role in defining tonnages mined and processed, average grade of mill feed, cash flows, mine life time, and all major characteristics of a mineral deposit. Simply, the cut-off grade is the lowest grade at which material is considered ore and is processed to create a concentrated commodity product. Essentially, it asserts that the mill cut-off grade is a function of the ore availability and the needs of the mill. The focus of this paper is upon one of these long time-scale decisions: whether to process the extracted material, or to waste it. Consequently, an effort is made for the development of a model for optimization of mill cut-off grade which considers grade blending of mineral deposit. A new mixed integer programming (MIP) model is proposed to deal with this objective and with this model determined the mill cut-off grade of Haftcheshmeh Copper deposit. The results show the obtained mill cutoff grade from proposed model generates the optimum average grade. Therefore, generated net value (NV) from this model is nearer to reality.

Stochastic strategic planning of open-pit mines with ore selectivity recourse

Stochastic mine planning algorithms have been extended to better represent ore selection decisions. Under geological uncertainty, existing algorithms generate plans that may violate the mineral processing capacity; under such geological scenarios, the excess ore undergoes a recourse action which is not as profitable as regular processing, hence decreasing the net present value. This decrease has previously been represented as a penalty on excess ore, which may not accurately represent actual operations. The new framework considers the most typical recourse: increasing the cut-off grade into the mineral process. This approach is demonstrated by adapting the VND algorithm of Lamghari et al.

Ore selection to maximise value

Ore selection is generally aimed at producing product with a consistent target grade matching a perceived market requirement. A composite selection criterion ‘Comp’ (a linear function of the grade vector) can be used to maximise ore tonnage at a specified target grade (in Fe and contaminants) extractable from a block model. The blocks correspond to the selective mining units, with grades interpolated from diamond drill-hole data. An iterative procedure has been developed to identify the coefficients and cut-off value for the composite function ‘Comp’, maximising potential ore tonnage at target grade. Commonly, target grade is pre-determined by marketing. However, there is no guarantee that maximising ore tonnage at a specified target grade maximises the potential value of the mine. If the value of ore could be expressed as a linear function of the grade components, then these coefficients would be appropriate for the selection criterion ‘Comp’; the cut-off value for ‘Comp’ would correspond to the marginal cost of production; all blocks with a ‘Comp’ score above the cut-off would be classified as ore, and the cumulative grade of these ore blocks would be the average product grade over the life of the mine. Unfortunately, no such value function for iron ore is generally available. Methods for estimating the value function are discussed, using the spot price and sensitivities based either upon operational tolerances for Fe and the contaminants or upon published price differentials. This approach has been applied to an anonymous Pilbara deposit with about one million blocks averaging 1.1 kt. It is shown how the optimal target grade, cut-off grade and maximum tonnage can all be explored as a function of marginal cost and iron ore price. Alternatively, given marginal cost and an iron ore price, the effects of changing the tolerances (and therefore the relative costs of the contaminants) can also be explored. The procedure can enable informed decision-making for an iron ore mine. Rather than setting final policy for the entire life-of-mine, it enables target grades and tonnage estimates to be revised by re-computation as the mine life proceeds, to recognise changes in market conditions and knowledge about the resource. It should be emphasised that this paper is concerned with ore selection rather than ore sequencing. Appropriate ore selection is a necessary but not sufficient condition for maximising value. Having identified the set of blocks that potentially maximise value, the sequence in which they are mined will present a trade-off between producing at constant grade and extracting high-value ore early. The sequencing issue is not considered here. It is shown that optimum ore selection for an open-pit mine is independent of any consideration of discount rates, although ore sequencing will depend upon the time value of money if the product grade is to vary across time. Although the study considers an iron ore deposit, the method can be extended to any open-pit mining where ore value can be expressed as a linear composite of multiple grade components.

A review of cut-off grade policy models for open pit mining operations

In an open pit mining operation, the heterogeneity of the grade-tonnage distribution of the deposit dictates that all available material within the boundaries of an open pit may not be processed. Given this heterogeneity, it is imperative that the valuable (ore) and waste materials are clearly identified. In this context, the cut-off grade defines the quantity of ore and waste, ensuring smooth supply of ore to the processing streams. While, the earliest significant effort towards the development of models for cut-off grade policy dates back to 1960s, a number of contributions on this vital aspect of a mining operation have been made since then. This paper presents a comprehensive overview of the available literature on cut-off grade policy models and suggests possible areas of future research.

Analyzing operational real options in metal mining investments with a system dynamic model

ABSTRACTThis article presents a detailed system dynamic (SD) model of a metal mining investment that is usable in ex-ante profitability and operations management analysis. We show how the SD model can be used to analyze the profitability effect of three operational real options: the option to temporarily close production, the option to abandon production, and the option to increase production through cutoff grade change. The SD model allows for intuitive modeling of the multiple interactive real options and arriving at results that are difficult, or impossible, to reach with commonly used spreadsheet software. We also analyze the effect of mining project debt ratio to the project value and show that correctly choosing the debt ratio affects project profitability. The effect on the project value of using three different future metal price scenarios with two different stochastic processes is illustrated to highlight the importance of correct process selection in modeling future metal price paths. A realistic case of a high-cost nickel (Ni) metal mine is used as a basis for the presented numerical illustration of the model.

Effect of copper slag recovery on hydrometallurgical cut-off grades considering environmental aspects

Determining the hydrometallurgical cut-off grades specifies the destination of low grade materials and this is subjected to more benefits in mining. Copper production rate is considered as one of the fundamental issues in hydrometallurgical cut-off grades determination. Slags are remarked as one of the main sources of copper. It is not only regarded as a waste but also identified as another resource extracting base metals. Slags are characterized by copper high grade. Thus, slag copper recovery can be led to different cut-off grades and net present value (NPV). The current research scrutinizes the effect of slag recovery by both flotation and hydrometallurgical methods on the hydrometallurgical cut-off grades. For this purpose, the optimum cut-off grade algorithms of hydrometallurgical methods are developed by considering associated environmental parameters, incomes and also the costs. Then, their optimum amounts are calculated with NPV maximization as an objective function. The results indicate that considering slag copper recovery in the hydrometallurgical cut-off grade algorithms reduces the environmental costs caused by slag dumping and leads to more NPV by 9%.

Underground long-term mine production scheduling with integrated geological risk management

A stochastic integer programming (SIP) model is presented to optimise long-term scheduling of underground mine operations while considering geological uncertainty. To integrate this uncertainty, a set of stochastic simulations is generated, corresponding to representations of the deposit, and is used as primary inputs to optimisation. The two-stage SIP model developed considers a variable cut-off grade and accounts for maximum development, material handling flow conservation, mill and mine capacity, and activity precedencies for an underground nickel mine. The results show that the schedule generated has a higher expected value when considering and managing grade risk. They also demonstrate the benefits of risk control, which this approach allows.

Functional Outcome of the Facial Nerve After Surgery for Vestibular Schwannoma: Prediction of Acceptable Long-Term Facial Nerve Function Based on Immediate Postoperative Facial Palsy

To examine the relationship between immediate postoperative facial palsy and long-term facial palsy and identify a treatment strategy for vestibular schwannoma considering long-term outcomes of facial nerve function and tumor control. Patients (N= 385) who underwent surgery in a single institution were reviewed retrospectively; 12 patients with neurofibromatosis, 6 with preoperative radiosurgery, and 14 with multiple surgeries were excluded. The generalized estimating equation method was used to show the correlation between immediate and later postoperative facial palsy and to identify the cutoff grade of immediate postoperative facial palsy. The tumor control rates for 1 year, 3 years, and 5 years were 88.7%, 83.9%, and 80.0%. Preservation of facial function above House-Brackmann (H-B) grades 1 and 2 was achieved in 47.9% of patients immediately postoperatively, in 50.1% after 1 month, and in 74.5% after >2 years. The immediate postoperative facial palsy grade showed a statistically significant relationship with the facial palsy grade on long-term follow-up (P < 0.001). H-B grade 3 immediate postoperative facial palsy was identified as the cutoff grade that showed the most significant relationship between the grade of immediate postoperative facial palsy and the grades above the cutoff (H-B grade 1-3) on long-term follow-up (P < 0.001). H-B grade of immediate postoperative facial palsy can predict facial palsy at long-term follow-up. H-B grade 3 immediate postoperative facial palsy is the lowest tolerable grade that guarantees functional improvement on long-term follow-up. Planned facial nerve preservation surgery followed by radiosurgery is thought to be optimal treatment in patients with vestibular schwannoma for both tumor control and facial nerve function.

Mining rate optimization considering the stockpiling: A theoretical economics and real option model

In the extraction of metal from a mine, the intermediate ore between the economic and the breakeven cutoff grade is usually stockpiled for future processing once the mine is depleted. This research establishes a theoretical two-stage economic model to derive the value of this stockpile and how it affects optimal mining rate. By deriving the optimal condition for objective profit function and parameterized analysis, this research finds the stockpiling option can significantly boost a mine's profit. Processing the stockpiled material affects the optimal mining rate and cutoff grade strategy significantly compared to the case that it is not processed. The research also investigates the optimal mining rate's sensitivity to input variables such as commodity price, discounting rate, capital cost, and processing capacity, etc. In addition, the intrinsic advantages of this approach compared to the broadly used Lane's model (1988) are discussed.

University Admission Grades and Academic Performance of Students in University Course Examinations: A Study of Delta State University, Abraka, Nigeria

This study investigated the relationship between the admission cut-off grades and university course examination grades obtained between two sets of students at the Delta State University, Abraka. The two groups sampled were students reading Counselling Psychology in the Faculty of Education and those reading Pure Psychology in the Faculty of the Social Sciences. The intention was to find out whether the set of students admitted with higher admission grades also performed better in university courses than those admitted with lower admission grade. The purpose was for the research to have basis for making suggestions and recommendations about the relevance of using different admission grade to place students in different faculties and departments. It was a descriptive study that used a survey design. Data was collected from the scores of the two sets of students in five courses taken in three years. The result indicated that the higher admission cut-off grades did not influence positively the performance of students in university course examinations. The researcher recommended among others that admission score into the different faculties and departments may not be different but be based also on the interest of students to read particular courses, and comparable conditions of service for workers. DOI: 10.5901/jesr.2016.v6n1p59

Cut-off grade optimisation to maximise the net present value using whittle 4X

Cut-off grade optimisation is necessary for operational decision making in the many different circumstances affecting mine operations. The cut-off grades are supposed to reflect particular circumstances of specific mines in order to achieve the maximum economic return over the life of the mine. The relationship between cut-off grade and NPV provides a means by which cut-off grades are optimised. Using Lane's approach, the economics involved in each stage are identified independently and integrated to provide an optimum cut-off grade. A block model from a hypothetical gold mine is used to illustrate how Whittle 4X applies Lane's approach to generate an optimal cut-off grade policy for the mine. The cut-off grade in this project slightly changes along the mine life. Higher grade ore is mined in the early years (years 2 and 4) while the lower grade ore is mined later.

Impact of discount rates on cut-off grades for narrow tabular gold deposits

The purpose of this study was to establish the impact of discount rates on cut-off grades for narrow tabular gold deposits as characterized by the goldfields of the Witwatersrand Basin in South Africa. There are various methods available for determining the cut-off grade, from simple breakeven calculations to sophisticated software packages that consider a variety of inputs to optimize the cut-off grade. For this study a simple financial model was created in Microsoft Excel ® that links the ore flow, block listing, and the cash flow. This allows the cut-off grade to be optimized considering how the cost of capital and chosen discount rate affect the cash flow. The discounted cash flow (DCF) and resultant net present value (NPV) are a widely used valuation method for production properties according to the South African Code for the Reporting of Mineral Asset Valuation (SAMVAL Code). The financial model in this study utilizes the Solver function, as well as simple Microsoft Excel spreadsheet formulae to optimize the NPV. Solver was chosen as it is a standard feature in Excel and thus no additional software costs are incurred beyond the basic Microsoft Office suite. For the purpose of this study, just narrow tabular gold deposits of the Witwatersrand Basin were considered. An example of a typical ore block listing, as well as the costing figures, was obtained from an operating gold mine. The results obtained from the study financial model were compared to the current cut-off grades obtained from the mine using their proprietary optimizer program, and were found to be comparable. The methodology utilized for this study thus appears valid. The cut-off grade was optimized considering the cash flow, which includes the variable mineral resource royalty tax, the variable gold income tax, as well as the discount rate. By comparing the resultant NPVs using discount rates of zero, 9%, and 12%, the impact of the discount rate on cut-off grades, resultant life of mine, and average mining grades (AMG) could be compared for the example ore block listing.

Cut-off grade optimisation to maximise the net present value using whittle 4X

Cut-off grade optimisation is necessary for operational decision making in the many different circumstances affecting mine operations. The cut-off grades are supposed to reflect particular circumstances of specific mines in order to achieve the maximum economic return over the life of the mine. The relationship between cut-off grade and NPV provides a means by which cut-off grades are optimised. Using Lane's approach, the economics involved in each stage are identified independently and integrated to provide an optimum cut-off grade. A block model from a hypothetical gold mine is used to illustrate how Whittle 4X applies Lane's approach to generate an optimal cut-off grade policy for the mine. The cut-off grade in this project slightly changes along the mine life. Higher grade ore is mined in the early years (years 2 and 4) while the lower grade ore is mined later.

Effects of the volatility of input parameters on cut-off grade optimisation, a case study of Sungun copper mine

Cut-off grade is the lowest grade above which the mined material is considered as ore. Volatility of the parameters involved in its calculation affects the mine operation and economics. For example, the sold products under a highly volatile commodity prices leads to sub-optimal cut-off grade strategies. The paper describes a modified cut-off grade optimisation procedure based on the Lane's optimisation algorithm at Sungun copper mine under volatility of the metal price by generation of the future commodity price schemes using geometric Brownian motion (GBM). Moreover, the effects of the difference in haul distances and consequently the different mining costs, have been investigated by dividing of the pit into various fields and separately optimisation of the cut-off grade in each site. Study revealed that in upper benches of the mine, where the distance to waste dump is much shorter than the route to ore crusher, the calculated cut-off grades are much higher.

Increasing the value and feasibility of open pit plans by integrating the mining system into the planning process

�&72,353 We present a model that allows us to consider mine production scheduling coupled with the mining system at different levels of detail: from the standard origin-destination approach to a network considering different processing paths. Each of these is characterized by variable costs, capacities, and geometallurgical constraints. We then apply this model to a real mine, comparing the results with those obtained by traditional methodology: the destination of materials defined a priori, before computing the schedules, using standard criteria like cut-off grades. As expected, using optimization to schedule and define dynamically the best processing alternatives shows a big opportunity for potential value improvement. However, the main result is that using only origindestination and fixed cut-off grades may produce schedules that are not feasible when the actual constraints of the mining system are taken into account. Therefore, it is essential to include the considerations proposed in the planning process.

Using the proportion of barren samples as a proxy for minimum grade in a diamondiferous linear beach deposit - an application of the Nachman model

�7.,!*-* Over the past 80 years, the Namibian diamondiferous marine placer has been studied extensively to develop solutions for mining and sampling challenges. The types of studies include the statistical modelling of the distributions of the stone counts per sample; investigating the relationship between geology and the grade distribution; assessing the quality potential of the entrapment of the available diamond pulse; using predetermined acceptability of barren samples (zero proportion (Z p) samples) to model distributions; optimal sample sizes; and more. During early-stage project evaluation it is more important to find out if a particular area is likely to be above a specific cut-off grade than to focus on sampling for the purpose of accurate resource estimation. Previous work using mixed Poisson and Sichel distributions to model the abundant onshore diamond data has been very successful in modelling the long- tailed nature of these linear beach deposits. The means of these distrib- utions are, however, sensitive to extreme values. Technical and cost constraints prevent a similar scale of sample collection in an adjacent, geologically equivalent, submerged beach environment. A method not sensitive to extreme values is thus required to make early-stage assessments of the likelihood that the grade of a particular target is above a minimum cut-off grade. The Nachman model describes the functional relationship between the mean population density and proportion of barren patches (Z

Impact of the South African mineral resource royalty on cut-off grades for narrow, tabular Witwatersrand gold deposits

Impact of the South African mineral resource royalty on cut-off grades for narrow, tabular Witwatersrand gold deposits

Multiple cut-off grade optimization by genetic algorithms and comparison with grid search method and dynamic programming

Multiple cut-off grade optimization by genetic algorithms and comparison with grid search method and dynamic programming

Development of a computer-aided application using Lane's algorithm to optimize cut-off grade

The work reported in this paper is part of a PhD research study at the University of the Witwatersrand.