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By Edward Holloway

The basis for the selection of the ultimate pit for an open pit mining operation is generally opaque. Some form of value-based analysis will generally guide the final decision; however, the value will often gradually plateau whilst the ultimate pit size continues to increase. There is no established framework to guide specialists in the selection of the ultimate pit, with such decisions regularly made on a somewhat arbitrary basis. The key component that is missing from the analyses typically used to select the size of the ultimate pit is risk. Once risk is quantified within the analysis framework, the decision-making range is significantly reduced, and the process for selecting the ultimate pit becomes more consistent, replicable, and defensible. This paper provides an approach to including risk in the process used to select the ultimate pit.

Feb 21, 2024

By L. Bergkvist

"History can provide many answers with regard to what today’s mining industry looks like and how we got to where we are today. It has always been self-evident that safety has to be given the highest priority and, throughout history, many mine workers have been injured, become ill and have even sacrificed their lives due to the way in which attempts have been made to extract the ore, often due to ignorance of the dangers being faced. In more recent stages of history we have seen certain dangers being compensated by means of higher wages and bonus systems in order to have the work carried out: one example of this is when the rock heating method was employed and the men who first went underground to put out the fires that were burning, were paid extra. The working conditions, to which these people were exposed, with smoke-filled closed spaces, shortened their life expectancy considerably and today we can ask ourselves whether it is really possible to value these efforts just by higher wages. In all mines worldwide the working environment has been improved and many mining companies have a zero vision where work-related injuries and accidents are concerned. Despite this, incidents of varying severity still occur and a continuous improvement process and ongoing training is necessary in order to constantly minimise risks and improve the working environment. Atlas Copco takes this into account in all its development and we not only review our own production units but also the needs of our customers, with regard to the machinery that is produced in order to cater for customers’ safety and production objectives. Underground mining probably started at the beginning of the 11th century when people with modest tools tried to extract ores that were present in the bedrock. Methodology has developed enormously over the years with a strong focus on increased efficiency and higher production. In different parts of the world the development is driven forwards at different rates depending on which controlling factors are regarded as necessary. Political decisions, profit goals and productivity have partly controlled the development, but the greatest factor where improvement is concerned still remains with increased understanding of the totality. During more than 1000 years since underground mining has been conducted, all individuals at all levels have constantly improved their expertise and the human element has been of great importance with regard to the development that has been made, even though technology often occupies a leading role when we describe the improvements made."

Jan 1, 2011

By B. N. Thompson

The main industrial minerals produced are non-metallic - clay, dolomite, limestone, pumice, salt, serpentine, and silica sand. The other minerals, some with minor production, include diatomite, feldspar, magnesite, sulphur, asbestos, and perlite. Energy and metallic minerals and aggregate are excluded from this account. These industrial minerals occur in a wide range of rock types and geological ages. For example clays are known from the weathering products of Cretaceous rhyolite and leaching of Eocene coal measures; from Quaternary weathering of contemporary loess and shallow marine sediments, and of greywacke of Triassic-Jurassic age; and from the hydrothermal alteration of Late Cenozoic acidic volcanic rocks.

Jan 1, 1982

"With millions of dollars and thousands of lives at stake, the Iron Ore Company of Canada (IOC) turned to a private wireless network for help.IOC needed a network that possessed the ability to adapt to changes in a nanosecond and to function seamlessly in the most rugged of environments.Canada’s largest iron ore producer required a private wireless network powerful enough to support all mine applications and deliver all data to one central point — without any existing cellular/3G/Wi-Fi coverage.Operations at IOC, a leading global supplier of iron pellets, involved dispatch, drill management and equipment monitoring, pump control and remote video that must service three distinct pits. Due to its setup, the facility does not offer a great deal of flexibility for transmitting signals.IOC serves a robust customer base made up of North American, European and Asian steel producers. It also employs nearly 1,900 people. Catastrophic death and destruction are two very real potential consequences of system communication failure.Technology for tough terrainKinetic mesh technology was born in the wake of the 9/11 terrorist attacks on the United States, one of the most high-stakes emergency situations in U.S. history. The failure of the communications infrastructure on a massive scale that day underscored the need for networking technologies that could provide service even in the most chaotic of conditions.Kinetic mesh networks allow organizations to deploy networks at sites where communications infrastructure has been compromised, as well as quickly establish networks in places where they did not previously exist. Kinetic mesh networks have also demonstrated a better ability to adapt to network changes on-the-fly versus other types of networking technologies."

Jan 1, 2015

By S. Fernández, L. Klinger, T. Vallejo

In the municipality of Rio Quito, department of Chocó, Colombia, alluvial gold has been illegally exploited by suction dredging. The project consists of using geospatial techniques to identify degraded areas and analyze the viability of remediation dredging to mitigate environmental liabilities. The area has sediments contaminated by mercury and cyanide, so it is necessary to reconform the riverbed with the remediated material. The work is part of the Mine Closure Plan that seeks to jointly articulate the communities, academia, the company, and the state

Mar 2, 2022

By R. J. Pugh

The coagulation of dispersions of weakly magnetic oxide mineral ultrafines (such as natural hematite or chromite) in an external magnetic field can be described from inter-particle forces. Essentially, coagulation occurs when the short range London-van der Waals interactions and the long range magnetic forces outweigh the stabilizing electrical double layer repulsion. From the classical colloid chemistry theory, we have calculated the various components of the potential energy for different sized particles at a series of ionic strengths and magnetic field intensities. We have related this theoretical analysis to experimental studies where the magnetic field-induced coagulation of ultrafines of natural hematite and chromite in aqueous suspensions was investigated using a laboratory scale electromagnetic solenoid. The experimental results relate the coagulation process (as determined by magneto-sedimentation analysis) to the particle size, the slurry pH and the external magnetic field. In the magnetic fields, maximum coagulation occurred near the pH of zero point of charge (pHzpc) of the minerals (where the electrostatic double layer repulsion was reduced to a minimum) enabling the particles to enter the "primary minimum" energy sink. On the other hand, in cases where the electrostatic repulsion was not suppressed, then the long range magnetic forces enabled coagulation to occur in the "secondary minimum". This caused the formation of chains which appeared to be relatively stable during sedimentation.

Jan 1, 1993

By F. Stanley, A. Noble, G. Luttrell

"The supply chain for coal-fired power stations involve a multi-stage network of mining units, preparation plants, blending facilities and transportation systems. Attempts to optimize the supply chain have historically been difficult due to the lack of communication/coordination between the various groups involved in coal production, transportation and utilization. In light of this issue, a new approach for globally optimizing the coal supply chain called Micro-Price Optimization has been developed to simplify the optimization problem and to provide coal producers with fundamental insight needed to improve the profitability of their operations. This fundamental concept assigns unit values to each particles (or groups of particles) passing through production units. Optimization occurs whenever the maximum tonnage of positive value particles are recovered and passed to market, while the minimum tonnage of negative value particles are recovered. Elements considered by the concept include factors such as target boiler cost/efficiency, waste disposal costs, coal quality parameters, emission penalties, transportation charges, or other quantifiable impact factors. This article reviews the basis for the micro-price concept and provides a detailed industrial case study involving the determination of optimum coal qualities that need to be supplied by mine operators to feed a coal-fired power station. INTRODUCTION The performance of coal preparation plants have long been known to play an important role in determining the overall profitability of mining operations. This significance is due to the fact that the misplacement of just 1 ton/hr of clean coal to reject resulting from poor plant performance can represent nearly $300,000 per year in lost revenues for a mine producing a steam market coal (i.e., 1 ton/hr x $50/ton x 6,000 hr/yr = $300,000/yr). This loss can be even more pronounced, occasionally approaching $1 million per year for each 1 ton/hr of misplaced clean coal, for operations producing high-quality coking coal products sold into the premium metallurgical market (i.e., 1 ton/hr x $150/ton x 6,000 hr/yr = $900,000/yr). Detailed economic studies indicate that improvements in plant yield resulting from increases in organic efficiency have one of the largest overall impacts on mine revenue when compared to other cost centers within the mining operation. One of the first studies to show this important financial impact was reported by Norton-Hambleton Consultants (Norton, 1979). Their study indicated that an unfavorable change in plant efficiency was second only to coal transportation in terms of its impact on profitability, while an unfavorable change in the cost of underground mining was a distance third. This longstanding realization has continued to provide a strong financial incentive for coal producers to optimize the separation efficiency of their coal processing and blending operations."

Jan 1, 2015

By A. Bruynesteyn

Results are presented from a series of tests designed to determine the beneficial effects of the microorganism Thiobacillus ferrooxidans upon the leaching of uranium from a pyritic uranium ore. Minus 1-inch (-25mm) 0.0711 percent uranium containing, pyritic ore from the Rio Algom Mine at Elliott Lake, Canada was leached with lixiviants of various Eh and pH as well as being subjected to a biologically-assisted ferric iron leach. In all cases, the biological leach gave superior extraction. At pH 1.6, the biological leach gave 100.6 percent extraction and the ferric iron leach 69.8 percent. This improvement in extraction is associated with a relatively rapid biological breakdown of the pyritic material, thus liberating uranium mineralization associated with these pyritic materials and regenerating the ferric sulphate lixiviant in situ.

Jan 1, 1981

By Emily Rose

The concept of risk management is applied to multiple aspects of the mining lifecycle including safety, mine design, business plan—anything that affects getting the ore to the mill for production. However, risk management is not a topic that can readily be taught in universities. Many situations require knowledge gained from experience to know how this impacts current and future operations. Recent graduates, who must develop and apply decisions based on geotechnical monitoring, likely have not developed “operational experience” and may not be aware of options and typical applications. Thorough resources that explain different monitoring systems, and when and how to implement them, are available for geotechnical professionals. Accessibility to this information can often cause information overload, leaving one unsure of where to start, without knowing where to start. This paper is intended to serve as a high-level overview of development practices, levels of risk, and risk tolerance for entry-level geotechnical and mining professionals who do not come from a geotechnical background. Summarized detail on typical monitoring practices, types of instrumentation, and how to communicate what the data indicates to key stakeholders are provided.

Feb 22, 2026

By T. Bauerle, G. Poplin, Z. Dugdale

"The issue of mine worker fatigue is as complex as it is understudied. Generally, worker fatigue lies somewhere on a continuum between psychology and physiology, which makes the measurement and management of it difficult with no easy solutions for operators or workers. Answers to even basic questions remain elusive—such as what is fatigue, how is it measured, and how can organizational resources reduce fatigue—and answers seem to present no single, clear path to action for the health and safety of the worker. This manuscript supplements the growing body of interest in the problems of fatigue in the mining industry by reviewing some of what is known about worker fatigue in general and in the mining industry in particular. The material covered here includes basic topics of the hows and whys of worker fatigue; an overview of fatigue models, findings, and evidence-based solutions with a focus on mining; and potential future directions aimed at mitigating miner fatigue. INTRODUCTION “It is recommended that the whole fatigue test problem be stated in a form the nature of which may be indicated by the following suggestions: that the term fatigue be absolutely banished from precise scientific discussion, and consequently that attempts to obtain a fatigue test be abandoned [emphasis added].” – Bernard Muscio, Pioneer Australian Philosopher and Industrial Psychologist, in a 1921 Report to the Cambridge Industrial Fatigue Research Board Fatigue presents several challenges for the mining industry. Depending on the specific occupation, daily work, or operational setup on any given mine site, mining jobs can have a fair amount of labor-intensive tasks mixed with monotonous and repetative duties. Combined with the long working hours and shift-work schedules of mining work, the prevalence of fatigue in mine workers may seem rather unsurprising. On the one hand, mining is certainly not alone in facing the challenge of addressing worker fatigue. Indeed, many of the characteristics above mirror the similarities of fatigue in other industries, such as health care, aviation, and security. To the extent that fatigue in mining acts like fatigue in any other industry, then any fatigue management applications, trainings, or interventions in existence can be borrowed from other industries and applied to mining in a “cookie-cutter” approach. On the other hand, some have argued that mining in particular is especially susceptible to increases in the prevalence of fatigue beyond the characteristics listed above due to the multifaceted combination of factors in mining environments associated with fatigue: dim lighting; limited visual acuity; hot temperatures; loud noise; highly repetitive, sustained, and monotonous tasks; shiftwork; long work hours; early morning awakenings; and generally poor sleep habits (Canadian Centre for Occupational Health and Safety, 2012; Legault, 2011). Legault (2011) in particular argues that it is the combination of these factors simultaneously that can make mineworkers particularly susceptible to sleep deprivation and fatigue in comparison to other industries where these factors are often not present alltogether. If fatigue looks and acts different in mining, as others have argued, more research is needed to determine if, how, and why worker fatigue might need to be managed differently in mining."

Jan 1, 2018

By M. H. Col

Within the last few years, there have been numerous techno-logical advancements within material handling due, in part, to the introduction of conveying systems and mobile material handling systems to the industry. Although the traditional material handling methods are still commonly used, the introduction of conveyors to the industry has provided companies with some very efficient and economical options. These "new" systems change with the industry to accommodate rigorous demands, ease of operation, and low operating cost requirements. The number of mobile material handling systems utilized in mining operations is increasing, especially in heap leaching applications. Ten years ago, mobile material handling systems like Mobile Stacking Conveyors (MSC) were considered a novelty. There were two (2) MSC's in actual operation and only one of those in a heap leaching application. Today there are numerous proven systems operating at mine sites around the world-La Coipa, Zaldivar, Florida Canyon, Cananea, El Abra, Chuquicamata, and Radomiro Tomic. The popularity of mobile systems is due to the benefits realized by individual projects. As technology advances, so do the concepts behind mobile material handling systems. Implementing self leveling mechanisms, Programmable Logic Controllers, and Global Positioning Systems to control the equipment are just a few of the recent advances that will be discussed in this paper. We will also discuss current proven systems, and touch on what we see as some of the future advances.

Jan 1, 1998

By W. J. Martin

At the termination of mining, the quality of ground water in the ore-zone aquifer must be returned to a condition predetermined by the permitting agency. To immobilize the redox-sensitive elements (e.g., uranium, arsenic, selenium, molybdenum), it has been suggested that a reducing agent be circulated through the leached ore zone. We have conducted laboratory experiments to test the ability of sodium sulfide as such a reducing agent. Sodium sulfide lowered the redox potential of the effluent such that insoluble minerals containing the redox-sensitive elements should be stable. The uranium concentration of the solution decreased by more than three orders of magnitude. In column experiments, by the time ten pore volumes of the sulfide solution had flowed through, sulfide minerals were forming. The experimental results indicate that the addition of sodium sulfide should cause the chemical reduction of the leached sediments, thereby producing long-term stability of the ground-water/sediment system.

Jan 1, 1986

By P. Gelfi, J. Vanderbeek, J. Enriquez

"The Cerro Verde copper-molybdenum mining complex is located near Arequipa, Peru. A 108,000 t/d copper concentrator (C1 concentrator) commenced operation in late 2006 and was debottlenecked to a 120,000 t/d capacity in 2011. A feasibility study, initiated in May 2010, assessed the potential for expanding the processing rate of the large Cerro Verde sulfide reserve via the installation of a second, stand-alone, concentrator (C2 concentrator) capable of processing a nominal 240,000 t/d ore. The feasibility study was successful and the project advanced through engineering, permitting and construction. Ramp up to nameplate capacity was ahead of schedule. The overall project was completed on schedule and within budget. The details of the project and supporting components are described. The design philosophy and design basis of the concentrator facilities are discussed as are factors that influenced the concentrator layout. Risk mitigation features included in the design are reviewed. The factors that drove the successful and rapid ramp up to nameplate capacity are discussed. Operational experiences in the first year of plant operation and project lessons learned are described. INTRODUCTION/BACKGROUND Sociedad Minera Cerro Verde S.A.A. (SMCV) operates a copper mine near Arequipa in southern Peru. Small scale operations operated intermittently until 1970 when the deposit reverted to the ownership of Minero Perú S.A (Peruvian government). Minero Perú S.A. commenced mining and processing of oxide reserves in 1972 and placed an SX-EW plant into production in 1976. The ownership of the property has changed hands several times over the years. Minero Perú sold Cerro Verde to Cyprus Climax Metals in 1994. Cyprus was acquired by Phelps Dodge in 1999. Freeport-McMoRan (FCX) acquired Phelps Dodge in 2007. Several studies were undertaken during the 1990’s that tried to establish the economic justification to process the large primary sulfide resource that underlies the surface oxide deposit. None of these studies produced an economic conclusion until a feasibility study was completed by Phelps Dodge and SMCV in 2004. This study provided the economic justification for the construction of a 108,000 t/d concentrator during 2005 and 2006. The key to the success of this study was identifying a water source that was sufficient to support processing economies of scale. Concentrator operations commenced in late 2006. The original design production rate of 108,000 t/d was achieved on a 30 day moving average basis on the 266th day after ore was first introduced. During 2009, studies and evaluations were performed that had the objective of addressing observed concentrator bottlenecks to allow a production rate of 120,000 t/d to be achieved. The 120,000 t/d figure represents the sustainable production limits associated with the installed primary crusher and tailing thickeners which would have been prohibitively expensive to upgrade. Debottlenecking activities were implemented during 2010 allowing sustained production rates of 120,000 t/d to be achieved."

Jan 1, 2017

By Peter Schmäh, Tobias Engel

The E-Power Pipe technology was originally developed for the trenchless installation of protective pipes and pipelines of 10" to 28" diameter, over long distances of more than 4,000 ft. The twostage process combines elements from Horizontal Directional Drilling (HDD) and microtunnelling technology. A microtunnelling boring machine (MTBM) excavates the borehole using a specially designed, temporary jacking pipe. A Rack & Pinion jacking frame pushes the equipment during the pilot bore and pulls in the prefabricated pipe string in a second step. The slurry microtunnelling machine is equipped with a jet pump, creating the so-called AVNS machine type. A new generation of small hard rock cutting wheels complements this considerable achievement for the tunnelling industry

Dec 1, 2022

By C. Okrusch, C. Roos, M. Akers, S. Rosenthal

Modern mining consistently faces controversy. Public sentiment impacts the permitting and development of mines, so a quality public relations (PR) program for mining companies may improve society’s impression of the mining industry. Developing mines face more permitting challenges than operating mines, which stems from a lack of societal trust given the history of mining and its impact on the environment. Two case studies were selected based on the type of public controversy they face to demonstrate how pervasive permitting issues are in industry. Both Pebble Mine, owned by Northern Dynasty Minerals (NDM), and Black Butte, owned by Sandfire Resources America Inc (SRA), experienced difficulties with their water permitting due to potential risks their mine developments posed to local fish populations. Pebble has, to date, failed in all of their attempts to become permitted due to concern for the water and the fish. Black Butte dealt with the same problems, on a smaller scale, but was able to become permitted. These two mines will be discussed in detail including local history, mine setting, mining history in America, prevalent culture groups, technology development, and intercultural communication competence (ICC). The mining industry needs to evaluate its ICC skills since ICC directly determines the effectiveness of PR. Based on Barna’s Stumbling Blocks for intercultural communication, methods for improving the mining industry’s PR will be suggested in the hope of easing the permitting process for future mines by developing ICC.

Mar 2, 2022

By M. Mustafa Kahraman, Sean Dessureault, W. Pratt Rogers

Most contemporary mines have considerable amounts of data. Structured and unstructured large data sets are colloquially named big data. Much of the data in mining operations come from a variety of systems, each with different databases and reporting environments. Standard technology deployments create a Bsilo-ification^ of data leading to poor system benefit. Through modern server monitoring and systematic approach, data utilization and value can quantifiably be measured. The Data Utilization and Value Index (DUVI) can quantify business intelligence best practices and user interaction. This study seeks to provide a data management tool to measure data utilization across the process of converting data into action.

By T. N. Andersen

The history of gold and silver analyses shows an interesting duality. On one hand, classical chemical and instrumental methods have evolved to meet changing needs, but on the other hand, the age-old and somewhat empirical fire assay has remained a popular tool. Inasmuch as gold and silver generally have been present in ores at low concentra¬tions, methods have been challenged by a need for sensitivity and selectivity coupled with reasonable assay time. A progressive increase in the importance of low grade materials as ore sources has led to the need for improved methods. Assays of these materials are required for process control and accounting in operating plants as well as for guiding research and development activities. The analytical response to these needs is evidenced by numerous reviews published through 1977-¬e.g., cf Kolthoff and Elving (1966), Beamish and Van Loon (1966, 1972, and 1977), Young (1971) , Mallett (1970), and Sen Gupta (1973). In this paper we present a brief sketch of the history and status of various gold and silver methods. A more detailed summary of atomic absorption spectroscopy (AAS) is Given, as this method has gained in popularity more than other assay methods. AAS methods currently in use are summarized and discussed briefly. This paper is not meant to be a detailed review, as are the above mentioned publications. Rather, we borrow from those works and more recent papers to report trends in gold and silver analyses (particularly in AAS). Also, we discuss some selected poten¬tial problems, and problems that have been experienced by this laboratory.

Jan 1, 1981

By F. N. Siddiquie, Mohd Shaif, Rajiullah Khan, Juned Alam

Manganese ore bodies of Banswara Mn belt were classified into stratiform and stratabound types, based on their mode of occurrence, distribution, and their chemical characters. These ore bodies generally composed of braunite, pyrolusite, cryptomelane/ psilomelane, wad, etc. The stratiform-type Mn ore bodies are conformable with the associated host rocks (Mn phyllite, etc.) and occurred in the form of layers, bands, etc., which are variable in their shape and size. These ore bodies are also strongly folded with the enclosing host rocks. The others, which are stratabound-type Mn ore bodies, also showed an intimate association with the associated host rocks. These types of ore bodies occurred in thin layers, pockets, lenses, stringers, etc. The classified ore bodies are confined with Kalinjara formation of Aravalli Supergroup of Paleoproterozoic age. The ore bodies are structurally controlled and well associated with phyllite, schist, limestone, quartzite, etc. The stratiform-type ore bodies constitute a marginal to low Mn grade and are also characterized by lower Mn content (26.19–39.24%) along with the Mn/Fe ratio of 7.16–12.23, while the stratabound-type Mn ore bodies are rich in Mn (35.92–49.64%) along with the higher Mn/Fe ratio of 14.15–23.97. However, the poor Mn grade along with high siliceous impurities of Banswara Mn deposits is subjected to them for intermittent mining activities in the past and, consequently, did not attract the scientific and industrial community for the evaluation of these resources. Therefore, the authors attempted this study in a scientific and systematic manner (mode of occurrence/distribution and possible methods for evaluation/exploration) to evaluate the potential of existed and newer Mn deposit resources in the Banswara Mn belt. The whole findings would be very much helpful for exploration/ mining geologist along with other concerned, to completely evaluate these Mn deposits in the future.

Aug 16, 2021

By Thomas E. Browne

The Electric Power Research Institute Energy Supply Program is developing coal supply forecasts. By coal supply forecasts I mean the future relationships between coal price and production levels. A representative supply curve is shown in Figure l. It will make the rest of my presentation clearer if at this point I give you some background about EPRI and the Energy Supply Program. EPRI is funded by the nation's electric utility industry to develop new technologies for the production and conservation of electricity. Most of the research is conducted by outside contractors. We participate in joint projects with the Department of Energy and other organizations. The Energy Supply Program is one of three "economic" programs. The other two are Energy Demand and Conservation, and Systems. The Systems Program's main function is to provide the means to integrate the output of the other two Programs. The primary function of the "economic" programs is to provide information pertaining to future energy prices, availability, requirements, etc. to the EPRI personnel planning R&D programs. A secondary role that is becoming more and more important is providing information of direct use to the electric utility industry. I should note that the results of all EPRI's contract work are available to the general public. A "Coal Supply Analysis System" is being developed for EPRI by Charles River Associates. To the extent possible it will draw upon existing work, but much additional work needs to be done in the area of coal supply economics.

Jan 1, 1977

By Nelson M. Solow

Raise boring of mine ventilation shafts in many cases offers a lower cost and higher speed method of construction in comparison to conventional shaft sinking. Where underground access is available for raise boring the potential savings indicate that raise boring should be considered as an alternative to other methods. Raise boring machines are currently in use which have the capability for reaming shafts up to twenty feet in diameter, depending on the strata and depth. These large capacity machines make it possible to consider raise bored shafts for moving large volumes of air. Although we will consider here only ventilation shafts, raise boring should also be considered for men and material shafts. When the mine planner has determined the volume of air required through a shaft at a particular location he is faced with the problem of selecting the shaft size. The principal factors in optimizing the shaft size are the construction costs for the shaft 'and the power cost to move the air through the shaft. The larger diameter the' shaft is the more it costs to construct, but for a given volume of air the power required (cost) becomes lower as the diameter increases. The construction cost is paid only once, when the shaft is constructed. The power costs, however, are paid throughout the life of the shaft. Methods of optimizing air shaft size found in the literature (References 1 and 2) amortize the construction cost and include it in the average annual cost of operating the airshaft. These methods derive a formula for the average annual cost vs. shaft size and de-rive the formula to compute the optimum size for a given air flow rate. It is, however, desirable to take into account tax considera-

Jan 1, 1977