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By Donald E. Scheck

Blasting practices based on sound engineering principles are well established but the successful application of these practices requires accurate information about the overburden geology and close supervision of the drilling and blasting operations. Good design alone is not sufficient to insure good results, but the process may be difficult to control unless steps are taken to measure the variables and to provide management and the operators with the information they need to establish and maintain control. Satisfactory blasting can be defined as loosening and fragmenting the rock so that it can be handled by the excavating equipment, while at the same time, governmental regulations on air blast and ground vibrations are not violated. Optimum practices achieve these objectives at the lowest combined cost of the drilling and loading operations and the blasting materials. Total system optimization, that is, taking into consideration the effect of fragmentation on the cost of operating and maintaining excavating equipment as well as drilling and blasting costs, probably is not a reasonable goal at the present time.

Jan 1, 1984

By Osvaldo A. Bascur, J. Pat Kennedy

Large metallurgical complexes have more data than a small city and much of it is "real time," changing rapidly as internal and external conditions evolve. As corporations buy and sell assets and reengineer their staff, the structures and tools that were used to understand these data are lost. The lack of an integrated approach makes the profitability of metallurgical plants lag behind that of other industries despite technical advances that have occurred in recent years. This results in significant deterioration in the ability to maintain a "smart” operation. The solution is to use the sophisticated new tools built for the Internet so as to leverage information in a familiar browser format that people can use and understand. Combining real-time infrastructure with portal technology is becoming an accepted methodology. This paper introduces real-time portals and team sites to support decision making by work- groups which require both real-time and documentary information from manufacturing assets, vendors, head office and the Internet. Workers get insight from the overall process effectiveness index based on key variables such as losses due to plant availability, performance efficiency and rate of quality. Real-time portals and smart clients are part of any real-time performance management (RtPM) solution. Three case studies in large metallurgical complexes are presented. PLANTS ARE YOUR STRATEGIC HANDICAP Information technology is arguably one of the fastest moving technologies used by the mining/metallurgical industry. However, the business model for managing that

Jan 1, 2004

By Bruce R. Sutherland, Jim B. Ramsden, Gerry L. Bolton

Conductive metal powders are important building blocks for today's micro-electronic circuitry. Formulated into inks, they provide the interconnects needed to complete a complex integrated circuit and the means to enter the world of miniaturization. Traditionally, the inks have been based upon expensive metals such as silver, palladium, platinum and gold because of their excellent electrical conductivity and resistance to corrosion and oxidation. The use of a copper based ink, as an alternative to precious metal inks, recently has received considerable attention. Instability in the prices and limited supply of certain precious metal systems have driven up production costs, making the development of a lower cost copper system more attractive to manufacturers. However, lower production costs are on1 y real ized if performance and reliability can be maintained. While the development has been driven by cost, copper does offer some significant performance advantages over noble metal systems: conductivity as good as silver and 4W better than gold; leach resistance better than silver and equal to gold; stability at high frequencies better than gold or silver; strong film bonding characteristics; and compatibility with most solders. These benefits, however, do not come without cost. The inherently reactive nature of pure copper, while providing unique performance properties, makes it difficult to process. Unl i ke precious metals which can be fired in air, copper would oxidize and so requires special furnaces and atmospheres. Despite these difficulties, the transition from precious metal thick film systems to copper is gaining momentum. Manufacturers of high density, high performance circuitry are exploring the performance advantages of copper over gold and silver and the manufacturers of consumer products are considering the potential cost savings of copper over silver-palladium. Sherritt has developed a fine copper powder for this industry. Through association with the ink manufacturers, it has been found that performance properties of the ink vary with the physical and chemical characteristics of the powder. Production Process The production of very fine copper powders at Sherritt is based upon the disproportionation of cuprous ions as outlined in Equation [1] (1).

Jan 1, 1990

By D. R. Babich, E. R. Bauer

Noise-Induced Hearing Loss (NIHL) continues to be a concern of the mining industry. A new noise standard (30 CFR, Part 62) is aimed at reducing NIHL in mining through engineering and administrative noise controls. However, the difficulty and expense of implementing engineering controls can make administrative controls an attractive alternative for reducing worker noise exposure. Over the last three years, the National Institute for Occupational Safety and Health (NIOSH) has conducted worker noise exposure surveys in underground and surface coal mines and coal preparation plants. The surveys revealed numerous possible administrative controls and an approach to implementation and analysis. The surveys have shown that worker dosimetry, time-motion studies, and equipment noise profiling are important aspects of effectively utilizing administrative controls. A description of the approach for selecting, implementing, and evaluating administrative controls, and a list of administrative controls, are reported.

Jan 1, 2004

By Ramon B. Santos

The Atlas Concentrator, reputedly the largest in the Far East today, is located on the island of Cebu in the Republic of the Philippines. It started operation on a 4000 TPD capacity in 1955. An expansion program, coupled with significant improvements both in the Crushing Plant and the Mil, made the Atlas Concentrator what it is today, treating about 14,000 tons of ore per day at a comparatively low cost of about $0.50 per ton treated. The Atlas Copper Mine is at present mainly an open pit operation, with ore supplied from two pits (Lutopan and Biga) north of the Concen¬trator. Development of an Underground Mine, situated on the main ore body at Lutopan, which will be a block caving operation, has been underway since 1963, and this underground mining operation is expected to b e in full production by the latter part of 1966.

Jan 1, 1966

By Kevin DeSomber, Scott Bird

Larger grinding mills continue to utilize large gear-driven drives or electrical wraparound drives. The panel will include presenters from operations with large mechanical and electrical drives. JIM HANDLEY: Before we get to the third and final session, I want to introduce my co-conspirator for this session, John Mansanti. John is manager of milling with Newrnont Gold Company, Carlin, Nevada, and was very active in securing participation in this innovative symposium. I'm Jim Handley and I'm with Cyprus-Amax Minerals at the Sierrita copper and molybdenum mine. Our third presentation is titled "Geared Up or Wrapped Up?" I hear this topic discussed, but never at great length. I think that's because the opinions are fairly strong and diverse, and people generally aren't reinforced properly in their arguments. The first person to enlighten us on this topic is Scott Bird. He has more than 20 years with Kennecott, is a graduate in metallurgical engineering from the University of Utah, and is currently operations superintendent and deals with this phenomenon every day.

Jan 1, 1998

By Lawrence K. Nordell

Historical methods of designing steel cord belt splices are compared with modern finite element modeling (FEM) methods. Dependence of the belt strength rating on the splice dynamic fatigue strengths is reviewed. A number of splice schematics are examined, using simple spring theory and FEM methods. Steel cord wire rope design is discussed. The importance of the insulation gum rubber properties and their splice dimensional factors and tolerances are analyzed. Splice fatigue lie analysis procedure is reviewed. This may be used to predict splice life or time of failure, depending on how the conveyor belt is operated.

Jan 1, 1993

By Miguel N. Herrera, Abbas H. Mirza, Fiona M. Doyle

The standard test methods used to determine the pyrite content of coal and mineral wastes, and their propensity to release acidic drainage, are critically reviewed. In addition to analysis of total sulfur by combustion, test methods using selective oxidation of pyrite by HNO3 and H2O2 are available. The oxidation kinetics of pyrite vary appreciably from sample to sample, and it is difficult to ascertain whether complete dissolution has occurred in heterogeneous materials. The reliability, reproducibility and suitability of different standard test methods were studied, using well characterized ore and coal pyrite samples. The kinetics of pyrite dissolution were also investigated. The results are discussed in terms of the fundamental chemical and physical characteristics of each sample, and the implications for waste characterization are considered.

Jan 1, 1992

By P. Hambach

Murer Company, Andermatt, Switzerland, can claim to have done pioneer work in the construction of inclined shafts. This happened in 1968/69, when we decided to bore with a Wirth tunnel borer an inclined shaft, 1100 m in length, 3.0 m in diameter, and with a grade of 65%, in the 2400 kilo pascall per sq. cm granite of the Montblanc Massive. The whole excavation was accomplished in ten months which, at least for European conditions, can be claimed as a record. It was, at least to our knowledge, the first inclined shaft to be bored full-face (Fig. 1). Encouraged by the experiences and performances attained at Châtelard, we approached other projects of the same kind. We were awarded, together with Hochtief Ltd., Essen, a contract from Schluchseewerke, Freiburg, Germany, in December 1969, for the construction of a penstock for the Hornbergstufe at Wehr, Germany, with a diameter of 6.3 m. This inclined shaft with a grade of 55% is located in Schwarzwalder granite with a compressive strength of up to 2000 kilo pascall per sq. cm, about 31,000 psi. As no exact geological data were available about the rock to be worked, and a fault zone from 80 to 150 m long had to be faced, as well as a few individual fissures of varying thickness, it was decided to use the multi-stage method. The 3-m diam tunnelling machine which had driven the oblique shaft at Châtelard had now finished work, and an immediate beginning was made with driving the pilot staft. This was very welcome to the contractor, since exact information about the type of rock present and the inflows of water was required immediately and before the final borehole diameter was fixed, for the purpose of dimensioning the supports to be subsequently installed.

Jan 1, 1974

By G. T. Adel, P. E. Richardson, R. Pazhianur

Cathodic protection using impressed current was employed to reduce mill wall wear during ball milling. Wear rates were determined from weight-loss measurements made on four 1-in.-diam mild steel coupons that were installed flush with the interior surface of the mill wall. Grinding tests were conducted on quartz, pyrite and quartz-pyrite mixtures at pH levels of 4.6, 7.1 and 9.2. Cathodic protection was shown to reduce mill wear by 30% to 60%. An examination of the coupon surfaces using scanning electron microscopy showed that cathodic protection greatly reduced pitting corrosion. The presence of a sulfide mineral, such as pyrite, was found to increase the wear rate significantly, possibly due to galvanic interactions. It was also found that the wear rate is significantly higher than the sum of abrasive wear and the corrosive wear, due to a synergistic effect.

Jan 1, 1998

By P. Soupios

Seismic geophysical methods have long been used by geologists and geophysicists to delineate subsurface features. These techniques work because different types and strengths of soil and rock transmit energy at different velocities. The Crosshole-Downhole tests (CH-DH) and seismic refraction survey (RS) are among the most used methods in engineering applications to obtain the elastic properties of subsurface layers. As a result, seismic methods have evolved into a cost-effective tool for rapidly determining depth to bedrock in engineering and construction projects. The seismic methods are best suited to sediment thickness analysis, bedrock quality determination and detection of the presence of weaknesses in the bedrock before the erection of any civil engineering structures such as bridges, tunnels, dams and portals. Seismic methods are also useful in estimating the rippability of bedrock ahead of construction. These methods are particularly useful for large-scale projects that require a significant number of drill holes, resulting in a substantial investment of time and costs for drilling. The CH-DH and RS methods are typically comparable in total cost to drilling, but provide significantly more information in 2-D and 3-D and therefore reduce the likelihood of conceptually oversimplifying the subsurface conditions. The above mentioned methodologies were considered to be the most appropriate geophysical methods for investigating the shallow structure and the dynamic soil properties of the area where the Ilarionas Dam is scheduled to be constructed. The main target of this work was to prove the potential of geophysical methods in providing accurate information to the civil engineer and to obtain information on the dynamic soil and rock properties for earthquake design analyses for the dam construction. Specifically, nine refraction seismic profiles and three cross-hole-downhole seismic tests were implemented to determine the subsurface conditions of the study area. The tests determined the shear and compression wave velocity profiles versus depth and other crucial parameters such as Young and Rigidity modules. Furthermore, they allowed the detailed 2-D mapping (along several profiles of the study area) of the subsurface variation of the soil and rock dynamic moduli.

Jan 1, 2006

By Jeff Salai

The CP-3A contract is the final segment of the MWWST’s 28.3 km (17.6 mile)pressurized water supply tunnel for the metropolitan Boston area. The 1,288 m (4,226 feet) of U-shaped tunnel alignment passed through five rock zones employing four different primary support systems. The short tunnel began in Weston, Massachusetts, at Shaft 5A in soft, completely weathered argillite, passed through a fault zone, and ended in Dedham granite. An 18-foot diameter horseshoe starter tunnel was built to accommodate a 4.94 m (16-foot 2 1 / 2 inch) diameter Robbins TBM. Heavy water inflows were anticipated and subsequently encountered during probe drilling. Pre-excavation grouting was implemented at high pressures to displace high water inflows in the starter tunnel and consolidate the fault zone. This paper will provide an overview of the tunnel construction with an emphasis on ground control, grouting and survey control.

Jan 1, 2001

By Jack G. Quade

During the summer and fall of 1973 a series of Skylab and high-altitude aircraft overflights provided excellent hard-copy photographs of the Great Basin. These photographs, with a wide range of ground resolution were used by the NASA Project of the University of Nevada, Reno, to conduct specific geologic studies. The principal objectives of these studies were to: select individual areas covered by Skylab photography for detailed studies, develop mapping techniques using varied film-filter products with a wide range of ground resolution, compare the results of the mapping techniques to existing geologic maps at comparable scales, verify the results wherever possible by direct field observations. These studies were conducted by Jack Quade and Dennis Trexler and by graduates and undergraduates of the Reno campus under a contract with the Manned Spacecraft Center Houston, Texas.

Jan 1, 1976

By Mingfei He, Jianhua Chen, Yingchao Liu, Yuqiong Li

Pyrite is one of the most common sulfide minerals on earth, which is usually grown with chalcopyrite and other sulfide minerals. In flotation practice, pyrite from different mines or different sections in a same mine may have different flotation behaviors. This is because the pyrite crystal contains lattice defect, including ionic vacancy and lattice impurity. The present work investigates the effects of three typical 3d transition metal (Co, Ni, and Fe) on the adsorption of CH3OCS2 −, OH−, and CN− on pyrite surface by density functional theory (DFT) calculations. Calculated results show that Co impurity reduces the adsorption energies of CH3OCS2 − and CN− on the surface of pyrite, while Ni and Cu impurities significantly increase the adsorption energies of CH3OCS2 − and CN− on the surface of pyrite. Co impurity has small influence on the adsorption of OH−, but Ni and Cu impurities significantly increase the adsorption energies. Calculations on Mulliken charge population of Co2+, Ni2+, and Cu2+ indicate that the Mulliken charges of Co2+, Ni2+, and Cu2+ after OH− adsorption are more than those after CN− adsorption. This suggests that the ionic property of the M-OH- coordination bond is greater than that of M-CN- coordination bond, while covalent bonding of M-CN- coordination bond is greater than that of M-OH- coordination bond. The adsorption results are discussed based on coordination field theory (CFT).

Oct 6, 2020

By B. W. Cavender

Capital investments are made for a variety of reasons, ranging from providing incremental capacity at existing operations to developing and implementing new technologies intended to radically improve a company's capabilities. These projects generate very different business opportunities and create value in distinctive ways. For incremental improvements, the capital budgeting process assures at least a loose fit between short-term goals and readily available resources. However, the criteria used to evaluate capital projects often prevent a company from committing to more aggressive goals, which lie beyond the firm's current abilities or resources. Such projects may not have clearly identifiable future cash flows, and the degree of interaction with other projects and the nature of the risk incurred may be difficult to estimate. Additionally, by focusing only on quantifiable benefits, the budgeting process often fails to recognize "soft" improvements such as increased operating flexibility or new knowledge generated by such projects. By rejecting these projects, the capital budgeting process may actually harm the company's future competitive position.

Jan 1, 1999

The estimation of local recoveries, such as the local recovered tonnage of ore and its corresponding grade at a given cutoff grade, is an important problem in a selective mining operation. Multigaussian kriging provides a simple solution to this specific problem. The solution is also complete in the sense that local recoveries are estimated together with their estimation variances. It is thus possible to assess confidence limit intervals on the estimated recoveries. Multigaussian kriging has been applied to the Jerritt Canyon deposit in a most realistic situation. The various steps of the estimation procedure are presented in detail and the potential of the method is demonstrated in view of the results. The obtained results show that the estimated recoveries are in good agreement with the actual recoveries and the actual estimation errors are correctly predicted by the estimation variances. Multigaussian kriging thus appears as a useful and fully operationable tool for the mining industry.

Jan 1, 1986

By E. S. Erickson, R. L. Stone

Introduction Evidence from blast furnace operations has indicated that using pellets with a higher ISO low temperature reducibility, a lower SiO2 content, and better resistance to low temperature degradation results in considerable coke savings and improved furnace operation. Although these benefits could not be directly related to reducibility differences alone, we believed there was sufficient evidence of the advantages in improved pellet reducibility to warrant laboratory investigation of ways and means to effect such improvements. It is well known that pellet reducibility can be significantly altered by changes in the basicity and the amount of non-iron oxide constituents. Past work (Friel and Erickson, 1980, 1982; Saeki et al., 1977; Thanning, 1974) has shown that with increased MgO contents, and at optimum CaO/S1O2 ratios, significant improvement in low temperature reducibility can be attained. The improved properties of such fluxed pellets have reportedly led to increased blast furnace efficiency and productivity (Saeki et al., 1977; Ilmoni, 1975). Less well known, however, is exactly what factors control reducibility in acid pellets. Because of this gap in knowledge, studies were undertaken of the factors affecting reducibility in acid pellets and to estimate their relative significances in modifying reduction behavior. This paper describes that part of our work done to determine the effect of bentonite on reduction behavior. Our approach was to first examine the effect of bentonite's presence on as pure an iron oxide as possible (i.e., a magnetite "superconcentrate" containing about 0.2% SiO2) so as to eliminate any gangue-binder interaction. The next step was to look at bentonite effects on concentrates with only limited amounts of gangue (containing about 1% SiO2), but of two different types, simple and complex silicates. Last, we

Jan 1, 1988

By Jim Dunn

For decades many of us who are associated with the mineral industry have tried to show the public its economic and strategic importance. Some of the mineral industry's proponents have been politically powerful figures and have been widely quoted. Yet, as measured by public opinion, legislative support, or almost any other standard, our efforts have been inadequate. It is apparent that a set of environmental beliefs that discredit industry, firmly held by a number of idealistic persons, has had wider coverage in the media and in schools than has the mineral industry's message. Although the fervor of our idealistic friends is often unfounded and, their stands unscientific, they must be considered seriously. Unless we address the issues in terms the idealists will understand, the mineral industry will have little influence on them or on the general public. A. striking thing is that, quite often, translation of idealists' views into action has been counterproductive. The reason is obvious. Excessive amounts of money and energy have been spent on relatively minor problems. The common result is that larger problems have been created. It may be possible to help anti-industry idealists understand their own dependence on minerals, and thus render their views more realistic, if they are shown more effective ways to reach their stated goals. If those goals can be shown to be held in common by all sensitive human beings -- including those in business and industry - the dialogue becomes one of how to achieve common ends. Individual mining companies acting by themselves have little possibility of success, and companies working in unison through trade associations have not been successful. Further, it is unlikely that industry in general can be successful in changing minds unless it seeks outside help. But friends among those who influence public opinion have been hard to find. Historically, help from media has proven difficult to get. Nor has enough help from educators been forthcoming. Yet, a war is going on in the technological, philosophical, and political trenches, even though much of the public is not aware of it. For the first time in years, there is row a significant and growing number of eloquent and brilliant thinkers on the side of free enterprise and industry, many of them environmentalists, but without the anti-industry mind-set. They have had remarkably little help from the private sector or even from the present administration. Industry may do far more for itself in the long run by encouraging these brave but bruised individuals and their organizations than by trying to work alone. These friends of free enterprise are working against a seemingly stacked deck relative to much of the media, the bureaucracy, and the educational system. However, despite their problems, their success to date has been remarkable. With more cooperation from industry they should do even better.

Jan 1, 1987

By Duk-Wom Park

INTRODUCTION he most important information required for the engineering design of structures in rock is its inherent rock properties. Without providing adequate parameters on the rock property, high quality of the engineering design cannot be expected. Many laboratory rock testing methods have been developed, but they are mostly for testing intact homogeneous rock without appreciable discontinuities. In reality, the intact rock properties do not represent the behavior of rock masses because rock masses include irregularities such as joints, cracks, interlayers, variations in mineral compositjon, etc. In general the type and intensity of the rock defects may be much more important than the type of rock which will be encountered (Terzaghi, 1977; Bieniawski, 1984). In-situ rock testing can provide better information on rock parameters, but it takes a tremendous amount of effort, time and cost. In recent years, numerical modeling techniques are gaining popularity as a design tool for structures in rock bodies due to the enormous progress in computer technology (Wang, 1985; Kripakov and Melvin, 1983; Park and Ash, 1985), but it is quite dangerous to use numerical techniques without having proper input data. Bieniawski (1984) states as follows: Some design methods such as numerical techniques have outpaced our ability to provide the input data necessary for the application of these methods. In order to provide an adequate amount of input data, an extensive testing program may be required, thus major efforts in time and expenses are commonly spent, In this paper, a new rock testing method, which utilizes the principles of laser holographic interferometry, is introduced. This method requires only a few minutes to measure the modulus of elasticity and quality of a rock core sample, which does not have to be cut or ground. The Poisson's ratio can also be measured in a few minutes from a sliced rock specimen. HOLOGRAPHIC INTERFEROMETRY Principles of Holographic Interferometry In 1948, Gabor invented holography, which is the technique of reviving three dimensional images using a monochromatic light source. A full demonstration was not made then because a clean monochromatic light source was not available. Later, in the early 19601s, the laser was adopted as a monochromatic and coherent light source (Leith and Upatnieks, 1963). Since then, applications have been made in many different fields ranging from crime prevention to three dimensional television. In this technique, an image is usually recorded by means of constructing a hologram which is a record of the interference pattern formed on a high resolution photographic system as shown in Figure I. A beam splitter divides the laser beam into two beams: (1) an object beam which is expanded while passing through a beam expander and illuminates the object, and (2) a reference beam which is expanded and illuminates the holographic plate. Subsequent to an exposure, the holographic plate is developed and illuminated by the expanded reference beam. The original scene of the object is revived in a three-dimensional image. The entire instrument should be placed on a vibration free environment. The wave fields reflected by the object in two slightly different configurations can be superimposed to form an interference fringe pattern. Thus, it is possible to measure the displacement that took place between the two configurations. This method is called holographic interferometrv. There are two methods of achieving this phenomena. The first is the double exposure method, wherein two exposures of the object are made prior to developing the film. The first exposure represents the original condition and the second, the disturbed condition. The second method is the real time holographic method. In

Jan 1, 1986

By B. J. Arnold

Froth removal rate is perhaps the most important parameter in scaling up from laboratory tests to plant froth flotation circuits. The WEMCO froth factor, the percentage of the froth height over the lip of the cell, accounts for the difference between laboratory and plant froth removal rates. As laboratory tests are generally run with a high pulp level, laboratory results are directly comparable to plant results only when a high froth factor (high pulp level) is run in the plant. When a plant does not have a high pulp level, laboratory results must be modified by using a ratio between laboratory and plant kinetics to predict plant results. This ratio, which accounts for the froth factor is important in testing any new reagents or reagent dosage levels. CQ Inc. researchers have used predictive scale-up equations using this froth factor coupled with equations for kinetics and the residence time distribution in the froth flotation cells. These equations show that modifying the froth factor in the plant can have a large impact on flotation cell yield and reagent use. EQUATIONS DESCRIBING FROTH FLOTATION Scaling up from laboratory- to plant-scale coal froth flotation has been the subject of much research and debate over the years. Determining the proper rate equation to describe flotation kinetics and an equation to describe the residence time distribution in a bank of flotation cells have been particular areas of study. As shown in Tables 1 and 2, various rate equations and residence time distribution equations have been proposed in the literature. These equations consist of one or two parameters giving the rate constant(s) in units of time-1 and a parameter for recovery at infinite time, [Roo]. Dowling, Klimpel, and Aplan (1985) evaluated the rate equations in Table 1 for their ability to fit froth flotation kinetic data and found that all of the equations give reasonably low standard errors. Several of these equations, however, proved to have superior confidence limits for the parameters. Other equations have also been proposed to describe the recovery versus time profile. Most recently, Diao et al. (1992) proposed a first-order form with a sine wave distribution. As indicated in Table 2, investigators have suggested many equations to describe the residence time distribution in continuous froth flotation. To measure the water residence time distribution in a bank of cells, a soluble tracer is often used, with the level of tracer being measured over time at the tailings discharge. This response is then put on a dimensionless basis as described by Austin et al. (1984) in order to compare mixing behavior between cells or under different conditions. Coal flotation cells are generally of the flow-through or hog-trough variety allowing for some degree of backmixing and short-circuiting. While the water residence time distribution (see Figure 1) at the end of one cell in a bank of 1.4 cu ft WEMCO froth flotation cells may approximate perfect mixing conditions (Arnold, 1989), the water residence time distribution at the end of a bank of cells does not. Figure 2 shows the RTD for various flotation cell types compared to that for perfect mixers in series. To better describe the water residence time distribution in coal froth flotation cells, Van Orden (1986) used an equation similar to the perfect-mixers-in-aeries equation. This

Jan 1, 1993