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By T. M. Yegulalp

This article summarizes some of the results of the continuing research activity at the Henry Krumb Schools of Mines, Columbia University, directed towards a better understanding of the stochastic behavior of slurry flows in underground coal-slurry pipeline systems. Fundamental ideas supported by field observations are presented and a Semi-Markov model of the slurry flows is developed. As a result of this formulation, behavior of combined slurry flows from N independent coal faces can be expressed in analytical form. The contents of a slurry surge tank receiving slurry flows with certain stochastic characteristics is investigated in a function of discharge pump characteristics and time.

Jan 1, 1983

By Tuncel M. Yegulalp

This article summarizes some of the results of the continuing research activity at the Henry Krumb School of Mines, Columbia University, directed towards a better understanding of the stochastic behavior of slurry flows in underground coal-slurry pipeline systems. The slurry system under consideration here replaces all conventional haulage systems between the coal face and the coal preparation plant on the surface. At the beginning of the pipeline system, flow rate and frequency of coal slurry is very closely related to the activities of production equipment at the coal face. Due to several scheduled and unscheduled interruptions in continuous miner's coal mining activity, resulting slurry flows possess stochastic characteristics. Proper understanding of these characteristics is believed to lead to a more realissic and economic design of slurry handling equipment. Fundamental ideas supported by field observations are presented and a Semi-Markov model of the slurry flows is developed. As a result of this formulation, behavior of combined slurry flows from N independent coal faces can be expressed in analytical form. The contents of a slurry surge tank receiving slurry flows with certain stochastic characteristics is investigated as a function of discharge pump characteristics and time.

Jan 1, 1981

By Juan J. Monsalve, Mario Karfakis, AMAN SONI, Nino Ripepi, Jim Hazzard

Pillar collapses are events that due to their severe consequences can be classified as high risk. The design of pillars in underground room-and-pillar operations should migrate to risk-based design approaches. The authors of this work proposed a risk-based pillar design methodology that integrates stochastic discrete element modeling for pillar strength estimation, and stochastic finite volume modeling (FVM) for stress estimation. This paper focuses on the stochastic FVM component for stress estimation. The mining and geomechanical aspects of a case study mine (CSM) are described and pillar stresses are estimated by using three approaches: (1) analytical solutions, (2) 2D finite element modeling, and (3) 3D finite volume modeling. This operation extracts a 30° dipping deposit, which makes current underground stone mine design guidelines inapplicable for this CSM. This work compares results from each stress estimation approach and discusses uses the point estimate method as a simplified stochastic approach to evaluate the effect of rock mass elastic properties variability on pillar stress distribution. Results from this work show that the three estimation approaches lead to different estimations, possibly, due to the wide range of assumptions each estimation approach considers. It was also determined that the horizontal to vertical stress ratio has a significant impact on pillar stress magnitude. Therefore, it is recommended to perform in situ stress measurements, or assume worst-case-scenario values to account and reduce uncertainty due to this parameter. The stochastic stress estimation approach used in this paper provides results that can integrate a risk-based pillar design framework.

Sep 24, 2022

By C. Ketata, M. C. Rockwell

During the operation of a mineral processing plant, the unit processes are investigated by analyzing the data extracted by means of stream sampling. The data structure is identical to the time series form. Data analysis is a crucial step in understanding the plant performance. To control the plant performance efficiently, it is very important to avoid sampling errors, which is impossible. However, it is possible to minimize these errors. The factors influencing these errors are divided into two categories: material properties illustrating its heterogeneity, and sampler features. The purpose of this paper is to study the influence of the material composition variation on sampling errors, and to compare our evaluation method with that of Gy. Note that the stream mass flowrate is assumed to be constant during the sampling process.

Jan 1, 2001

By Roussos Dimitrakopoulos

Conventional approaches to estimating reserves and optimizing mine planning and production forecasting result in single, often biased forecasts. This is largely due to the non-linear propagation of errors in understanding orebody attributes from a limited finite number of drilling data, throughout the chain of mine planning and mining. A new mine planning paradign is considered herein to include two interacting and potentially fusing elements: stochastic simulation and stochastic optimization. These two elements provide an expanded mathematical framework that allows the modelling of orebody uncertainty and its direct integration to mine design, production planning and valuation of mining projects and operations. This stochastic framework has shown to increase the value of production schedules in the order of 25%. In addition, case studies show that stochastic optimal pit limits are about 15% larger in terms of total tonnage, compared to the conventional (deterministic) optimal pit limits. This difference extends life of mine and adds approximately 10% of net present value (NPV) to the NPV reported above from stochastic production scheduling within the conventionally optimal pit limits. Furthermore, results suggest a potential new contribution to the sustainable utilization of natural resources.

Oct 1, 2009

By Nasser Madani, SULTAN ABULKHAIR

The geological and geostatistical modeling of mineral deposits requires densely sampled drillholes that provide accurate and reliable hard data. Furthermore, quantifying orebody uncertainty through geostatistical simulation can allow mining engineers to assess long-term risk in mine planning. Nevertheless, ore deposits can sometimes lack dense drillhole information, reliable hard data with proper quality assurance/quality control (QA/QC), or sometimes both. This study is based on a coal mine located in the Republic of Kazakhstan, where an iron dataset is based on data from three newly drilled drillholes, and geological information comes from a massive collection of legacy drillhole data with no evidence of proper QA/QC. For this reason, a workflow was introduced to construct a representative training image from legacy data and stochastically model geological domains within these three drillholes using a multiple-point geostatistics technique. Once the geological model was obtained, a two-point geostatistics algorithm was applied to model the iron inside each geological domain. The direct sampling algorithm was chosen for modeling geological domains, and sequential Gaussian simulation for iron grade calculation. Both methods were extensively evaluated using different statistical tools and analyses.

Aug 1, 2022

By Nasser Madani, SULTAN ABULKHAIR

The abstract of the paper discusses the challenge of quantifying iron content in a coal deposit in Kazakhstan. The iron dataset is limited, coming from only three drill holes and some stope samples, while a large amount of geological information is available from legacy drill hole data. The paper proposes a workflow using multiple-point geostatistics to model geological domains and two-point geostatistics to model iron content within these domains. The results show that the direct sampling (DeeSse) algorithm effectively reproduces the complex seam layers, and sequential Gaussian simulation models the iron within each domain.

Mar 30, 2022

By R. W. Chappell, M. W. Hills, R. L. Olsen

A stochastic approach was developed and applied to the Butte, Montana Hillside abandoned mining site for modeling stormwater runoff and subsequent receiving stream loadings. This approach enabled capture and quantification of the uncertainty associated with stormwater quality data and allowed the prediction of copper and zinc concentrations in the receiving stream caused by runoff from the Butte Hillside during storm events. Runoff flows and stormwater concentrations were input to the model as probability distribution functions. Monte Carlo simulation allowed prediction of expected instream concentrations in the form of cumulative distributions functions. The modeling results allowed evaluation of current best management practices (BMPs), targeting of future BMPs, and identification of key data gaps to fill during future sampling activities. This modeling approach is considered extendable to other active and inactive mining sites. Output from a model of this type is easily understood and can be used to communicate effective stormwater management to site regulators. Furthermore, application of this modeling approach will facilitate the development and implementation of a site-specific stormwater management plan and will optimize efforts to achieve standards for compliance with stormwater discharge permits.

Jan 1, 2002

By R Dimitrakopoulos, R Goodfellow

One of the primary objectives when optimising a mining complex is to maximise its value for the primary stakeholders. In order to achieve this objective, it is necessary to holistically optimise all aspects of the mining complex, including decisions of when to extract materials from the available sources, how to blend or stockpile these materials and how to best use the available processing streams to satisfy customer demand. Existing methods for global, or holistic, optimisation ignore the compounded effects that risk has on the performance of a mining complex. Over the past decade, several stochastic optimisation approaches have been proposed to integrate various forms of uncertainty into the open pit mine design and production scheduling. These methods, however, are limited in their ability to simultaneously optimise the production schedules for the portfolio of mines, material destination policies, the use of the available processing streams and the various products that are produced at each location of the mining complex.This paper aims to discuss a new method for the global optimisation of open pit mining complexes with geological uncertainty. The proposed generalised methodology is capable of modelling and holistically optimising mining complexes, including aspects related to production scheduling, blending, stockpiling and non-linear interactions that often occur in practice, but are over-simplified in existing models. Two case studies are discussed to highlight the need for these complex, stochastic optimisers. First, a case study for a nickel laterite blending operation highlights the need to integrate geological uncertainty into the optimisation in order to ensure product quality constraints are respected. Second, a case study for a copper-gold mining complex highlights the added value when simultaneously optimising the production schedule and the stockpiling and treatment of extracted materials.CITATION:Goodfellow, R and Dimitrakopoulos, R, 2014. Stochastic optimisation of mineral value chains – developments and applications for the global optimisation of mining complexes with uncertainty, in Proceedings Orebody Modelling and Strategic Mine Planning Symposium 2014 , pp 13–22 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Nov 24, 2014

By Liam Findlay

Optimizing a production schedule with semi-mobile in-pit crushing & conveyance (IPCC) requires integrating extraction sequence, destination policy, crusher relocation, conveyor layout, and truck fleet investment decisions. An integrated stochastic optimization framework is proposed to produce long-term schedules for mining complexes using multiple semi-mobile IPCC systems. The optimizer selects the crusher locations and designs the conveyor routes from anywhere in the mines. The stochastic framework considers simulated multi-element orebody realizations and manages associated risk. A hybrid metaheuristic based on simulated annealing and evolutionary algorithm is implemented for the optimization. The method is demonstrated using an iron ore mining complex.

Jun 25, 2023

By Roussos Dimitrakopoulos, Liam Findlay

Semimobile in-pit crushing and conveying (IPCC) systems can help reduce truck haulage in openpit mines by bringing the crusher closer to the excavation areas. Optimizing a production schedule with semimobile IPCC requires integrating extraction sequence, destination policy, crusher relocation, conveyor layout and truck fleet investment decisions. A mining complex with multiple mines and IPCC systems should be optimized simultaneously to find an optimal schedule for the entire value chain. An integrated stochastic optimization framework is proposed to produce long-term production schedules for mining complexes using multiple semimobile IPCC systems. The optimization model has flexibility to select the crusher locations and conveyor routes from anywhere inside the pits. The framework uses simulated orebody realizations to consider multielement grade uncertainty and manage associated risk. A hybrid metaheuristic solution approach based on simulated annealing and evolutionary algorithms is implemented. The method is demonstrated using an iron ore mining complex

Nov 1, 2024

By Roussos Dimitrakopoulos

Overview ?Uncertainty matters: The economic side ?Models of geological uncertainly ?Shifting the paradigm: Stochastic mine planning ?Using uncertainty to improve project performance ?Conclusions: Quantified uncertainty based models are great!

Oct 1, 2010

By S Chatterjee

The production scheduling of an open pit mine determines the optimal extraction sequencing that significantly impacts a mine’s life as well as net present value. The optimisation of production scheduling of large open pit mines with geological uncertainty is a computationally very intensive process. In this paper, an approximation algorithm is proposed to schedule an open pit mine, where instead of solving the whole problem at once, the production schedule is generated by sequentially solving subproblems. The subgradient method is used to generate the upper bound solution of the Lagrangian relaxed subproblem. If the upper bound relaxed algorithm is not a feasible solution, a mixed integer programming is solved on the generated upper-bound solution. An application at a copper mine with an orebody represented by 16 532 mining blocks is presented using the proposed algorithm. Results show that all constraints are satisfied. The net present values are also calculated and results reveal an 11 per cent higher net present value (NPV) is generated when compared to the NPV generated when the same approach is applied to the deterministic model of the deposit where uncertainty is not accounted for.CITATION:Chatterjee, S, 2014. Stochastic production scheduling – solution through Langrangian relaxation with the branch-and-cut algorithm, in Proceedings Orebody Modelling and Strategic Mine Planning Symposium 2014 , pp 323–328 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Nov 24, 2014

By V. S. S. Yadavalli, J. Hager, R. Webber-Youngman

"This article investigates the complex problem of a budgeting process for a large mining operation. Strict adherence to budget infers that financial results align with goals. In reality, the budget is not a predetermined entity but emerges as the sum of the enterprise’s operational plans. These are highly interdependent, being influenced by unforeseeable events and operational decision-making.Limitations of stochastic simulations, normally applied in the project environment but not in budgeting, are examined and a model enabling their application is proposed. A better understanding of budget failure in large mines emerges, showing that the budget should be viewed as a probability distribution rather than a single deterministic value.The strength of the model application lies with the combining of stochastic simulation, probability theory, financial budgeting, and practical scheduling to predict budget achievement, reflected as a probability distribution. The principal finding is the interpretation of the risk associated with, and constraints pertaining to, the budget.The model utilizes a four-dimensional (space and time) schedule, linking key drivers through activity-based costing to the budget. It offers a highly expressive account of deduction regarding fund application for budget achievement, emphasizing that ’it is better to be approximately right than precisely wrong’."

Jan 1, 2015

By J. Kang

Large-scale land reclamation has been undertaken in Singapore since the 1960s. In the early years, the fill materials excavated from the hills. In recent years, sea sand is the main source of the fill materials. The contractors used to import the sea sand from the neighbouring countries such as Indonesia. However, in early 2000, the sea sand import from Indonesia and Malaysia was banned. Cambodia, Myanmar, and Philippine therefore became the alternative sources for sea sand. Distance between the jobsite and these countries is over 1,200 km, and transporting sea sand from these areas became a critical issue that could affect the contractor?s performance. Figuring out the right combination of transportation means for a longdistance sand transportation would be challenging because of uncertain situations. We developed a stochastic simulation model, using ARENA, to figure out the right quantity of small-size barges, bulk carriers, and loading/unloading equipment, which could help project managers yield the most production for sand transportation. This paper presents how we developed the simulation model, how it was applied to figure out the optimum combination among various size barges, different bulk carriers, and various types of loading/unloading equipment, for the sand transportation project in Singapore.

Aug 1, 2013

By V. Osterholt

Sustainable development of mineral resources is based on a spatial model of the orebody that is only partly known from exploration drilling and associated geological interpretations. As a result, orebody models generated from the available information are uncertain and require the use of stochastic conditional simulation technique. This paper considers three methods for simulating orebody geology: (1) pluri-Gaussian simulation that limits the allowable contacts between the various units; (2) sequential indicator simulation using indicator kriging; and (3) an experimental multiple-point approach that captures some higher-order spatial statistics. The data requirements of the methods, how to meet them in mining applications, and performance characteristics are discussed. The application of these methods in a hypothetical deposit consisting of three geological units provides a comparison and illustrates the advantages of the different simulation approaches.

Jan 1, 2005

Material scheduling, sequencing planning and execution are the core tactical mine plan for achieving production targets that maximize the objective function of any mine production entity. This objective function is constrained by several exogenous and endogenous constraints including geological, operating, technological, marketing, financial, political, social and local field constraints. Linear and dynamic programming techniques have been used to formulate algorithms to solve the problems associated with scheduling and sequencing operations. These algorithms possess the mathematical rigor for dealing with the fundamental problems but they fail to provide adequate answers to random and dynamic process problems. Materials scheduling and sequencing are carried out within the bounds of random and dynamic fields. The functional relations between the output and dependent variables are random, and thus, current algorithms are limited in their abilities to address the problems arising from these random field processes. In this study a production simulator is developed to capture the random field process associated with materials scheduling and sequencing in an open pit environment. The algorithm incorporates a geometric pit evolution model, using solid geometry of an ellipsoidal frustum to capture material displacement dynamics. Taylor series expansion about the dimensions of the initial frustum is used to provide numerical solutions to the resulting partial differential equations governing the pushback dynamics. A production simulator, derived from the stochastic and dynamic models, is developed, validated and used to simulate the changes in the pit volume resulting from periodic incremental pushbacks and the random field process. The hybrid stochastic-optimization algorithm provides a powerful tool for addressing the random field and dynamic process problems. Combined with a hybrid stochastic-optimization dispatch system, tactical production planning and execution will be efficient and economic for achieving desired.

May 1, 2004

By L. Robles-Stefoni

"Multiple-point simulation (MPS) methods have been developed over the last decade as a means of reproducing complex geological patterns while generating stochastic simulations. Some geological spatial configurations are complex, such as the spatial geometries and patterns of diamondbearing kimberlite pipes and their internal facies controlling diamond quality and distribution.Two MPS methods were tested for modelling the geology of a diamond pipe located at the Ekati mine, NT, Canada. These are the single normal equation simulation algorithm SNESIM, which captures different patterns from a training image (TI), and the filter simulation algorithm FILTERSIM, which classifies the patterns founded on the TI. Both methods were tested in the stochastic simulation of a four-category geology model: crater, diatreme, xenoliths, and host rock. Soft information about the location of host rock was also used. The validation of the simulation results shows a reasonable reproduction of the geometry and data proportions for all geological units considered; the validation of spatial statistics, however, shows that although simulated realizations from both methods reasonably reproduce the fourth-order spatial statistics of the TI, they do not reproduce well the same spatial statistics of the available data (when this differs from the TI). An interesting observation is that SNESIM better imitated the shape of the pipe, while FILTERSIM yielded a better reproduction of the xenolith bodies. IntroductionThe simulation of geological units poses several technical problems that challenge the capabilities of available geostatistical simulation approaches and their ability to deal with spatial complexity of categorical variables. The spatial geometry of diamondbearing pipes and their internal facies controlling diamond distributions are a specific and well-known difficult modelling problem. The geometry of a kimberlite pipe is typically like an inverted cone (Figure 1); the wider part is known as the crater and is located near the surface, and the narrower, deeper part is known as the diatreme. Xenolith bodies can also be found inside the pipe. A very important contribution to the geological modelling of the contours of the pipe is the measure of uncertainty about the location of the contact between the kimberlite pipe and the host rock."

Jan 1, 2016

By W. Abdellah

Underground mine developments, such as haulage drifts and cross cuts, play a vital role in providing access to ore extraction areas for mine production. The stability of mine developments is thus of crucial importance during the life of a mine plan. Many Canadian mines use longhole mining methods or one of its variants. These methods require access to the orebody through mine developments such as haulage drifts and cross cuts on multiple levels. This paper examines the stability of mine development access intersections with respect to the planned mining sequence. A case study, the #1 Shear East orebody at Vale?s Garson Mine in Sudbury, Ontario, is presented. A three-dimensional, elastoplastic, finite difference model (FLAC 3D) was created for a development intersection situated 1.5 km below ground surface. The stability, or performance of the intersection, is evaluated in terms of the strength-to-stress ratio. The ratio threshold is set at 1.4 for temporary openings. Unsatisfactory performance is defined as a strength-to-stress ratio less than this threshold value. The performance of the intersection stability is evaluated at various modelled mining stages and the probabilistic method of analysis is then invoked to study the probability of unsatisfactory performance of the intersection. The results are presented and categorized with respect to probability, instability, and mining stage.

Aug 1, 2013

By Richard J. Lund

Stock piling-and by that I mean well-organized stock piling on a substantial scale-is almost as old as the hills themselves. It was back in early Biblical times, as recounted in the Book of Genesis, that Joseph was charged by Pharaoh with the responsibility of stock piling food during the seven years of plenty to guard against the seven subsequent years of famine that were revealed by the Pharaoh's dream. And this same policy of storing up food or materials to provide for future anticipated emergencies can be traced repeatedly down through the ages. So our own efforts are anything but new. Our modern concept of stock piling-the purchase and storage of strategic materials to assure supplies needed in time of some future war- stems from our experience in World War I. In 1920, the War Department was charged by Congress with the responsibility of procuring all War Department supplies and mobilizing industry in the event of another war. During the two decades that followed there were many authoritative studies made of our deficient mineral problem, all of which pointed out the urgent necessity of stock piling certain strategic materials as a reserve against future war. One such study, made in 1925 through the combined efforts of the Mining and Metallurgical Society and the AIME, was done at the ex- press request of the War Department. Eight years later another more de-

Jan 1, 1949